Lifetime predictions of miniature fuses and semiconductor

Lifetime predictions of miniature fuses and semiconductor
Lifetime predictions of miniature fuses and
semiconductor protection fuses
Meng, X.Z.
DOI:
10.6100/IR449473
Published: 01/01/1995
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Citation for published version (APA):
Meng, X. Z. (1995). Lifetime predictions of miniature fuses and semiconductor protection fuses Eindhoven:
Technische Universiteit Eindhoven DOI: 10.6100/IR449473
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Lifetime Predictions of Miniature Fuses and
Semiconductor Protection Fuses
PROEFSCHRlFT
tel' verkrijging van de graad van doctor aan de
Technische Universik:it Eindhoven, op gezag van
de Rector Magnificus, prof.dr. J.H. van Lint, vOOr
een oommissie aangcwczen door hct College van
Dekanen in het openbaar te verdedigen op
vrijdag 8 december 1995 om 14.00 uur
door
Xian Zhong Meng
geboren te Ningxia, China
Dit proc!\;ehI'iH
i~
goedgekclJr'd doni' de prnmOlOl'Cn:
]Wof.dr.-ing. II. Rij(ln(o
en
pr(1Cir.
(i.e. Darnslnl
Copn)mntor:
ir' . .f.( i.J. Sinot
CIP·l)ATA KON1NKLlJKE B1BLlOTIl EEK, J)EN HAAG
Mcng, Xian 7.hong
Liklimc rm:dict i()l1~ of miniature fuses and semiconductor
pl'Otc.ction fLLSC~ / Xian Zhong Meng. - Eindhoven:
Eindhovl,;l1 iJniversi(y nfTechnnlngy
Thcsi~ Tcchni~che Universi!cit Eindhoven.
[SI3N 90-386-047 6- l )
Subject headings: Elcetrit:
thermal buckling
fu~es
I
cle~;Ir'ic
transients I
Lifetime Predictions of Miniature Fuses and
Semiconductor Protection Fuses
To Ying
and
our parents
Table of Contents
Nomenclature
Part I
VI
Introduction
~
Chapt.er I Overvkw
1.1 Electric fllses .................................... """"".".,,"",,."""" .. """"",,. " .. " ................
2
1.2 Literature review ........................................................................................................... :)
1..1 Topics rel,l1cd with 1his 1hesis""".""".,, ....................................................................... 4
1.4 Content of this thesis ................................................................................. ,. " .. ,., ..... 10
d
Part II
•• ' . "
Experiments
Chapter 2 I..itetimc Experiments with Short Current Pulses
14
2.1 Studies oflltime lag fuse ............................................................................................ 14
2.2 St<l1is1i~nl di~triblltiolJ ""." .. """""""""".""""""".".".".,,,.,, ",." ........................ I X
2.3 Results and discussion .................................................................................................... I g
2.4 Influence ol"intcrnal constructions on lifetimes ........................................................... 24
2.5 CnJlcillsi()l1S ............................................................................................. .
............ 27
Chapt.er J I.ifetime I·:xpedment.s with I.()ng C·urrent Pulses
3.1 I·:xperiments .................................................................................................................... ~X
3.2 Results" ...................... "" ...... "." ...... """""".,,." ......... " .. " ......... " .................................. 29
3.3 Resistance changes .......................................................................................................... 32
J.4 LildilIl(; relationships "" "., "., "" "" "" "" "'" "" "'" "., " ... ,,' "., "., "., ". "" ... ," "" ''', .. ,." '''' ,,,.32
3.5 Conclusions ...................................................................................................................... %
37
Chapter 4 Experimenb for Notched Strip Fuses
4.1
4.2
4.3
4.4
4.5
I.'.xpet·imen(;ll sct-up .......................................................................................................... \7
Lifetime experiments with short current pulses .......................................................... , /11
Motion of notched elements " ......... " ............................................................................. 44
Minimum melting i't value ...................................................................................... , . 17
Microseopic study ol"dcf<mnation ...................... " .......... """." ... ,,. ".,.,.,..
" ........ AX
4.6 COl1dusions ... "."""""" ........ ,, ... ,................................................................................... ~ I
Part III
Thermal Modelling
Chapter:; Nonlinear Thermal Modelling for Miniature
hlSl~S
5.1 Thermal mo(it,\h " ............................................................................................................ ))
5.2 Analogies and circuits .............................. "" .... "'''''"."'''"."''".,,'',,.,, .. ,, .. ,...... ,..........~:;
5.J App!il;il1ions ................................................................................................................ )7
IV
5.4 Condusions ........................................ ""."". "" ........................................ " ... " "" ............. ().;J
Chapter 6 Th(;rmal Modelling ihr Semiconductor Fuses
65
6.1 Considerations lor lhermal modelling ................. """""".,,,, ........................................... (1:)
0.2 Netw()I'k representation ........... " "." "."",, ... " ......................................... " ....... " .... " .......... 6R
6.3 Dala input and oUlput jiles ................................... ".""."" .. " ............................................
n
(i.4 Rewlts Mld dis<;ussion ."""".""."" .. ".".,, ................................................ """ ... " ....... ".,,.72
6.5 ConciusiollS ........................................................... "."""."".,,",, ...................................... 7.:1
Part IV
Thermal Buckling and Lifetime Predictions
Chapter 7 'rhel'mai B\Jckling of Win:
Ek:m(;nt~
7.1 Buckling concept .............................................. " .. "",, ... ""." ... """",, .............................. 76
7.2 Analyti<;aI study ."."""".""." ... "".,, ............................................................ "." .. " ............ 77
7.3 Finite clement formulation .................. ""."""."."".""."."".,, .......................................... 79
7.4l)i~plac(;ment measurements .................................................... """."".""".,,,, ................. 82
7.5 Re.~\l1ts and discllssion .. ".""."."""".".""".,,",,.,, ............................................................ 10
7.6 Conclu~ions and future work ................................................. ,,""""""".""",, ................. 90
Chapter g Lifetime Predictions
<)]
g.l
8.2
8.3
8.4
Introduction ................................... " ....... """".""."".""."."".,,",, .................................... 91
Lifetime prediction for ~h()l't current pulses ............... """"""""""""."""".,,,, ............... n
Lifetime prediction of miniature fuse~ for long current. pulses .. "" .. """"""""""""""".96
Lifdim\: prediction for a continuous loading """""."." ................................................ 100
fi.S Change of current - time characteristics ........................... "" ... ". """"""" "" "" "" ."",, .. I 0 I
8.6 Lifetime prediction for notched strip fuses ..... " ............................................................. 102
iU Application of the method to results from literature ......... ,,"""" """"""" """" "" "" "". 105
H.H Recommendations .......................................................................................................... 106
1:\.9 Conclusions. "" " ..... "" ....... " ... " .... ,," "" .... ,,"" "." "." "." "." "". "".,," .. "" ........................ 107
Part Y General Conclusions
ChapH;r 9 Conclusions
109
<).1 Main rcsuits ... " .... "." .... "" ..... """"""""" ... "".,,""""",,.,,"""""""".""""" .. "" .. " .. ,,",,. I()<)
9.2 Suggestions for future work ........................................................................................... 110
Appendix Photos of Fuses Hnd Experiment SetllP
112
ILl
Summary
120
Samenva(ting
122
Acknowledgements
124
Curriculum Vitae
125
v
Nomenclature
A
C
('Iii
DIII'I~'
F
Gr
' II
1/1
'W"A
1"1
2
'.,'1>111.\·"
trlll{li
'I!
"KI/
M
MI)
N
N
Nt!
No
NH'~
Nu
P
PI'
()
R
Ra
R"I
Rill
50'
T
7'.,
(/,
V
W"
W,j
er()~s sectional area (n/).
capm;itam;~ (Fl,
thermal capacitor (F or J/K),
maxim urn displacement (m).
modulus of elasticity (Pa)
Grasho r numbcr.
.;urrent (A).
4
area moment of inertia about neutral axis (m ).
rukJ (;urr~nt (A).
peak current (A).
integration or current s,\me ov~r tim!;; (A 2S),
12( of a current pube (A "s).
minull1ull1 melting
value of luses (A\).
prospective Curn:l1t (Al·
injected current t{lr coupled network (i\ or A'. ohm).
constant.
moment (N,m),
initial woment (N.m).
in-plane force (N).
number of wrrent pulses to blowing.
initial in-plane f(xce (N),
numher of current pulses for the reference paramckr,
number or segmenl.
r'r
Nussdt number.
input energy to a segment (W),
Prandtl number,
,lcriv,l1ion energy (l).
resistance (0).
Raykigh number.
electrical resistance (ohm).
thermal resistance (ohm or K/W),
radial smfllec (m\
tcmpcrature rise (I(, "C).
temperature of the wire (K).
temperature inside the glass tube (K).
air temperature outside the glass tu bl;: (I().
t:ritil;'lllemperatUt'c l'ise (K, dc).
total potential en(~rgy (.1).
voltage (V).
energy f()]" real elongation (J),
defi)rma,1ion energy (J).
VI
NomenclQfure
W,I,
bending energy for buckling shape (J),
(.
speedle heal (J, kg,] K' ').
actual elongation related with spring (m).
axial strain.
strain,
strain.
gravity constant (g '0 9,81 m, s'\
heat transition coefficient for the convection (W. m-2 K- I ).
current (A),
current density (Am-\
curvature (m- I ).
spring constant (N ,mol),
length ofa segment (m).
length 01" the fuse clement (m),
number of segments,
heat dissipation in a segment (W).
heat conduction in a segment(W).
heat convection from a segment(W),
heat radiation from a ~egment(W).
outer nldius of the end cap (m),
radius of the wire (m).
inner radius of the glass tube (m),
outer radius of the glass tube (m).
time (5).
melting time (s),
on time (5).
ofTtiml: (s),
displacement in z direction (m).
displacement derivative.
displacement iny direction (m),
initial displacement (m).
derivative of vertical displacement.
second order derivative of vertical displacement (m'').
relevant dimension (for a cylinder, x, is the diameter) (m).
co-ordinates,
d,.
e
em
g
II
J
k
k.r
I
[n
n
q,
qk
q"
q..
w••
x,
X, y,
Z
VB
a
~
thermal diffusion cocn1cient (1112. s).
tem[i¢I",l(ute <;oeOi!.:icnt orr(;;~i~tivity (K-').
thcrmal expansion coefficient (i'<)r a gas 1\= If!"... F..-\
deflection factor.
ma% density (kg. ])l'\
length increase (m).
length of a ~lIbvolllITlC along the x axis (m).
length of a subvolume along the y axis (m).
length of a subvolumc along the z axis (m).
volurno:.: ol"a scgmo:.:nt (6.V = I A, m\
apparent strain range.
m(;t:hanical strain range.
therm;l] strain tilllge.
virtual work done by internal forces.
vjrtmil work done by external forces.
them);\] diffusion depth (m).
emissivity.
!;
strain.
0..
(I
y
y
6L
;\;c
lI.y
ill
AV
2.1;"
i\l,:1l1
Ar: th
oW;",
OW"XI
o
~"
<
Ie
p.
v
p
(J
1./1
creep strain.
steady state (.:reep rate (s' ').
thermal conductivity (W. m-I K-'),
dynan1il,; visl.)osity (kg. m"l 5. 1).
kinematic viscosity (m 2 . s-').
resistivity (ohm.m).
Steflln Boltzmann constant (5.67 *
electric potential (V).
viii
JO.3
W. m- 2 (c\
Part I
Introduction
Chapter 1 Overview
1.1 Electric fuses
Fuses an: designeLl for the protection of electric circuits and equipment. Fuses WCIT invenil.:d
nr()llnd I t-:64 II I. Nowadays, they are produced in a wide variety or phy~iu~1 dirm~T\~ioll~, slt,lpes
and internal constructions and mainly us(;d iii conjunction with 1\ISC clips, motll\!!ng.s and
holders, Among lI1any el¢ct~icill devices, tlEes arc well known for their p()j1ularity in hOllsl~
apparatus and installations.
In the instrument tei,;!mt1l,)gy, rtlst~ wilh '2 mA r'(ller;:! cmrcnt C3n he f()und. Ikcallsc of
lilt; expln.sive development of computer industries, an i,;normolls arnowll oi' )Irir\li~I\lrl;C 1"11.~CS
is required, On the otlier hand, the r'arid incl'eased demand for large seml"ondll(;tor
devices leads t.o th~ nced of vcry high ratings of scmicondudllr prott;.;tio1\ I\rs.;s (r,ltings
higher than 2 kA and 1000 V). h)~ high voltage applications. products with ratings of ! 00
A ,Hid 72.) kV are nrrHed.
hlscs T\"\ily be gr'oupcd under four headings: miniature fuses, high vulUlge fuses. low
voltage power fuses and scmieomhl(;tor protection j'us¢=s. The heart" of a fusc always
consists or a eonducti ve strip or wire element, which carries an electric current. This piece
of lMteri,ll is made of metals or their alloys and it is defined as a f"USJ; ckment. FigUl'c
1.1 shows a typical fuse for st:miconductor protection. The construe! ion consists of a fuse
dcmr.:nt, r.:;ermnir.:; body, contacts and sand.
-.': ..i
(
.........
:
Fuse element
Figure 1.1 Typical semiconductor protection fuse
Fuses must be <lbll;; to open circuits at currents which I;;xcc~d a givcll value within u
certain time. Application normally requires thaI the fuse operating time should be shorter'
fot, higher current valu(;s. This behaviour of the fuse is dcscrib(;d by il~ cllr'rJ;1\1 - time (It) characteristic,
The 1 - { characterist.ie is defined as a curve where the valuc of the mclt ing ti nll~ i ~
expressed as a function of th(; prospective symmetric current. under stu((;d (;ollditinllS of
2
Overview
.1
operation. In the short time ~at)ge, the Joule int~gnll /, i~ defined as the integral of the
sqlwre or the (;urrent over a given time intervaL if the lime interval is short enough. A
typical f - I characteristic of semiconductor ruses i~ shown in Fig. 1.2, where the melting
time t is expressed as a function of the effective current / (r.m.s.). For short melting times,
/t values are provided together with melting times.
Melting Time Data
660 V 160 A fuses
till [ms]
"tt
[A?sJ
< 1
5
4200
7600
10200
11300
10
15870
1
4
Silver
element dimension
18 ml11* 0.13 111m
10.2 '---~~~~~--'-'---'--~-~~~'--'-'-'
1d
1if
1~
[AJ
Figure 1.2 Typical current - time characteristic of
a semiconductor protection fuses
I n general, because of ageing effects. 1 - ( characteristics of ruses tend to shi (1 As a
result fuses can blow after a number of current pulses at values faster than expected from
the originall - t curve. It is obvious that the deterioration of 1 - t characteristics can lead to
unrel iable functioning of electrical systems, In order to improve the reliability or electrical
systems, lifetime estimation of fuses are required by users and manufacturers.
1.2 Literatu re review
Basic knowledge of fuses has been provided by Wright [I], Johann [2] and Wang [31 in
their textbooks. Two Iitcratun:: ~tudies [4, 5 J are available for further studies in fu~e
designs and their applications. In this section, only a hrief review will be given and
particular attention will be paid to the stale or art in the fuse developments.
1.2.1 Pre-arcing characteristics
Extensive contributions have been made since 70 's to simulate prcarcing chara'teristics
and applications of various types of fuses. Among them. the finite difference method [6.
7J, finite element method [8, 9, 10] electl'ical analogue method [II] and TLM [111
4
( 'lioprer
(Transmission Iin!:: matr~x method) (Jre widely used to condlLct the p~!' 1{)I'mancc si 1ll1L lat ion.
A good guidance. fOl' clement designs may bc provided !'romthe simulation.
Fuses should operate at short circuit ur oVI,;r!oad I,;urrenl. llow~:v~~r, they sll()llld not
operate at nominal load conditiom which are rdated with continUO\lS Of plll~cd (cyelle)
currmts, In pradice. thl.: und(;sired change of fuse hehaviour, for inSl<\I1CC uncxpedcd
blowing, C(J.n occur nfter some time in usc as a result of ddcrioration pw,:l,;ss,:s. This i.~
usually called ageing. To describe a!;cinl;;, liJdime for V<"IdOIIS aprl kali()ns can b~ Jd'ined
as thl; time for reaching the ilcc.eptable change of current" time charaetcristi"s of fllSI,;~,
the time for fuse blowing or the time for a certain pl,;l"()ent of r~:Slstall~:1,; irH;I"t';ilse. h)I'
ageing studies. literature review will b~~ presented in Section 1.:).
Many gcnCl'al purpose fi.1sC links arc provided with low rn~:lting poil1! Ill<lkriah Ivhich
arc allar,;h~d tu fllsr,; ~klrl~rlts. t\.~ (J result of diffusion, a reduction of the mclting point (If
fuse clements is rcalised. 'rhe phenomena related with this r,;lTr,;t,;t is )"I,;rt,;rr(~d In ils the M t;rfl;;d namt,;t! II ftt,;r Mdl;al r. To achiev!: desired eurrcnt - time characteristics () f fuses, Meffect W(lS ot't.en used. I fowcver, ror certain current shapes, the M-dTec\ can briJig ahout
undesired diffusion and result in ageing. Daaldcr 1131 and Ilo!"!nilrln 114 I conducted
studies of M·eJlects, they conelud~d that if the fuse element is pt'operly de~igllcd,
interdiJ'J\lsion ha~ no dl!trirnental effeet on fuse performance. Recently, Ikaujean 1151
pr()p()~ed a ~imlllatl()n method for current· time eharaderistics whert' intcradil)n~ bctwl,!l,!n
silver strip and low melting point materials were considered.
1,2,2 An,':iog phenomena
A It.hough many studies have heen eunducted experimentallY mId tileoret iCillly t () predIct
arcing behaviour, thl,; use ofVllriOU$ model~ is limited to specific types and load conditions
[16, 17, I g, 19]. Thc arcing process is still not fully understood, therefnre, the t1!:~;cript ion
of the arcing process is largely dependent. on empirical parametcrs.
1.2.3 Fuse designs
Among many developments, the following new types of fuses can be nWJltioned: surface
mount fuses \20. 21], suhstrate fuses [22], vacuum fuses 123. 24 I. SF(, Ihsc~ 1251,
electronic fu~es [261 and smart fuses 127 I. These new development.s are focllsed on high
rcliability 121, 23, 24. 26, 27 I, I;;xtreme compactness [20, 21. 22] and easy avai lahi lity 126.
271·
1.3 Topics related with this thesis
As it ha~ been mentioned in S\:(;tion 1,2, two main unsolved problems remain in th~
description of fuse b<::haviour, vi7. arcing and agcing. The slIhjf!ct or llris 1hesis will be
for.:ttsed on ageing mechanisms, as fill' as these lire caused hy thermal mechanical reasons,
The ~tlIdied fuse configurations are limited to those normally dlll~C[l I'm ll1ir\i<rtur'~ and
semiconductor protection fiJses. Section 1,3. I rresen1S stat I': of art of lil"ctime stuJics in
general. Section 1.3.2 gives a hri~r descriptions of basic mechanisms nj' metal
deformation, Se(;tiorl J .J.} addresses reliability items in exiS1ing ~tandat'ds for mmiature
Overview
fuses, low voltage fuses and high voltage fuses. Scction 1.3.4 introduces the minimuOl
value and describes the phenomena of thermal buckling related wit.h fus~ dements.
/1
1.3.1 Lifetime studies in literature
Ageing can take place at continuous loads and cyclic loads. The latter may be
distinguished in pulsed current with
high amplitude and short conducting time
low amplitude and long conducting time
Such ageing can happen in circuits with power electronics. Also, motor starting.
transformer Hnd capacitor inrush al'e related with such pulsed currcnts.
Various attempts have been made to provide solutions for the problem oj" fuse ageing.
For cyclic duties, compressive slre~ses arc induced due to temperature rise during current
How. During the pcriod without current, the compression is released due to cooling. This
thermal effect becomes cyclic in nature. More than continuous heating, this cyclic heating
results in ageing of the fuse element. In the former investigations, resistance changes.
mOvement and cracks of fuse elements have been noticed. Some specific properties arc
stated bdow.
Because of Current surges, fuses may be subjected to fatigue problem~. Several
methods for I ifetime estimation for specified currents have been presented in the past.
POSSibly the first paper {28 Jcorrelating cycles to failures with eurrcnt parameters appeared
to be in 1969. In resi~tance welding applications. fuses should be derated to protect
thyristors. Cycles to fai lure for fuses were presented in a graph as a linear function of the
ratin of rated melting 1't to the actual f I passed through the fuse during the cUrrent
conducting time. Tak ing the fuse elemenl temperature excursion as a p<lrametcr was al~o
addressed as an alternative.
In 1974, W.J.lluber experimentally investigated effects of the minimum j]/ change for
fuses to have proper inrush capabi! ity for the protection of power transformers {29J. Two
successive half cycle Current pulscs spaced four seconds apart were suggested to (es( the
fuse's rated minimum melt /{ value of fuses. It was indicated that the minimum melt {2,
value of fuses can he taken as a criteria for fuse to withstand the transformer inrush and
lightning protcction.
1;01' fuses, exposed to a cyclic currcnt, the number of pulses which fuses can withstand,
was considered as a linear function of the percentage of the rated current [30J. The on timc
and ofT time from five seconds to 10 minutes were used during tests, For fuse selection in
the protection of semiconductors, it was recommended that thc equivalent r.m.s. value of
an occasional overload current should not exceed 85~;') of the current value fro111 { • ,
characteristics for the same duration. For frequent overload currents, the limit was !'edllc~d
to 70%. For cyclic duties, the current for the on time was suggested not (0 cXi,;ccd 50% of
the value of Current corresponding to { " , i,;haracteristics. For this duty and in case of
overload duration ahove I hour, the r. m. S. current was limited to the rated CUrrent. It was
suggested 1h!ll the lifetime of fuses is consumed by electric currents. N~) mOll vatioll
these recommenciations was presented by experimental or thcon::tical analysis.
ur
The microstructun; <.:hallges oj" suomini<HUI'e fuses have heen l'xamint'd [.\ I [ hy \Ising
and energy dispersivl.; X-ray Tlli\;r()~l"OpC I FOX). The
1"\IS~ demen1"s werc made of sil vcr copper alloy wires. A flcI the wi IC l,xplTicllccd t iiI:
pulsed current of all on timc lip to 225 microseconds, partial melting ,lIld IT<.:ryst<11I i!:<lt i nn
wnc found in localist:d areas within the grain structun:. Sq:rqHtioJ) was found al the
~lIrrace of a wire. Taking the energy dissipation during the p\ll~~ t:tJt'I'cnl as erituia 1321.
lifetime limits were detcrmined ror fuses or copper silver alloy wires. Thc lhrcsholds 01"
Ii I"t;(irne.~ HI dilTt:l'cnl lemperature rises were expcc(l:d to bc: maxi m\lm Ii 1"<.:1 i 1Ile: cnndillon
at 100 'Y;; more than 200{){) cycks at 300 OC; more (han 1000 cycles at :)IJO "('; potl.;nti<11
singk pube al SOO c·T.
~<':'llIl1illg !;;ki;(WIl nlicl'o~'()pe (SF.M)
Klepp ["331 conductcd compamtivt; ~t\ldie~ of nickel or lin plated conlacts witli ~ilve]"
plnled 'Onl<1ct~, (:OI1(;lcl re~istanec of nickel or tin plated cOlltal,;ts i,~ li)lIlHI 10 incrcase in
high tempcratUl'e and aggressivc atmospher(;, Ku(.;d [14.1 ill1alysed failmes ()f fuses uscd ill
thc circuits or nu<.:il;;llI' gl;;[)~rating stati()n~, suggestions werc made ror improv i I) ~ ft:1 iahi Iity
of control t;.ircui( t\lses.
F()f' high voltage fuses, Anti ["35[ (;ondu(;kd expel'iment.al mol ion studies or l,km(;nts
for mouel fuselinks in cyclic lifetime tests, The notched fuse ekment was malle
~ilv~r.
For a straight fuse demcnt, movement of the elemcnt was obs(;rv~~d during plllscd current
hy X-rilY photography. When fuses expcrienced cyclic (Iments, originally benl I"tIS~'
clements were changed into ripples; cracks were found in the element notrh/;;s. i\gt;;ing in
fuse clements was explained by lhermal fati gue, Ii fe1imes wer(:~ prl;;scnt(.;d ilS il function of
Current I'el at.ed with CUI'I'ent • time charaeteristics,
or
High voltage expulsion fuses arc widely used in the power ~y~lem [)J'otection. As 11
circuit fhult occurs, the arc in these !\lses is extinguished by the expulsion dIet1 (1 I' ga~es
rr()(illCed hy the arc. After 15 kV high voltage expulsion fuse~ were exposed to l,ydil:
currents, deterioration or I - I ch~racteristics and resistan(;e dlang:~~s hav~~ h~~~~n nhserved
1361, Fuse wires m<1de of copper, tin silver copper alloy, and (in le;ld alloy were used in
(hl~ exrerin1ents. l'he amplitude of' pulsed current was 120%, the amp! itude of the fusl;;
1',lIed current. The on time was I hour. A long off ti me was adopled 10 cool du\vn 1he
tested fllse.
For eydic duti!';s, Ii fdime was ~uggested
rdated with /1 values during the on time,
to
he presen((;d [:;7 [ liS
~
filllCl Ion
0
J' current
As the thermal efTed was directly taken into aecount [381, thl;: Ii reI imc ohservations
were lilted and presented as a funetion or a combined variahle of" ternpcralll)"(.; ri.~e ~Ind
mean temperature. i\ coefficient which ret1eets dcfle!,;tions lws heen i ntr\)dueL'd to rdatl.;
the mechanical strain wil h 11 fetimc. Its valm, was determined from the Ii fcl iml~ rq;fc~si()n
ilTiidysis.
Nuisan(';l:: opel';)1 ion of high voltagc ru~es during storms has becn rer()l"tl~d []'), 40, 41,
421 in (I SA, Canada and Austral i<1, As t.he fuse operation was ~onsidet'cd to he caused by
lightning, the estimated opcl'ating rate [40J can he op to f).4;% from I.hc ficld ohsnvatioi\,
Ai,;cording to We.~t.l'()m's wot:k, alh:r tin fusc links were uscd in the sy~t~~m I'M years of
Overview
- - - - - - - - - - - - - - - - - - - - _.." ...
_-"-7
sel'vice, 2% ofthe fuses showed a tim() reduction above lO% with the melting i,;urrent 1381.
They recommended large ratings or ruses for th() protection to avoid nuisance npl!r<1tion,
Limitation of fuse lifetime, caused by oxidation of silver coated eoppcI' wires, h,l,~
been investigated [43] for cont.inuous currents, Cracks induced in the fuse wires were
reported, Because of chemical reactions in the t:h:ment to occur at Hn devatcd
temperature. resistance of a fuse goes up. A~ regards the resistance changes. measurements
have been performed on different element materials. The on time of pulsed current was I
hour during the cyclic tests, Fuse clemenB of silver. copper. silver coated copper, nickel
coated copper, tin silver copper alloy wCre studied. For a given current. energy dissipation
increases. this results in the final interruption of fuses in serviec~.
Thesc preliminary studies provided qualitative indication of fuse agcin¥ mechanisms.
However. because motion of the fuse clem()nts was not defined or even was not taken in10
account, various parameters in the proposed models have to be determined by using the
ClIrve fitting method. Use of thi~ method is limited for certain types, and normally a large
number of tests are required.
1.3.2 Basic mechanism of metal deformation
Metal deformation [44] can be distinguished in: clastic. plastic and creep types, Elastic
and plastic deformations are considered as instantancou~ deformation caused by applied
stresses. while creep deformation is modelled as time dependent.
Elast~c
de formation is reversible. plastic deformation is non-iineOlr and irn;versible,
arc considered as the instantaneou~ deformation response to the application of a
load. Plastic deformation may have two forms; slip and twinning. Slip is the most COmmon
form. it is considen:d as the shearing of crystal blocks over one another e.g, in multiples of
the unit displacement. The displacement of crystul blocks occurs consecutively In the
small region or slip plane and spread outwards. The boundary between the region~ where
slip has taken place and where slip has not occurred is called a dislocat.ion, The dislocation
is commonly represented as a line in the slip plane, By contrast, twinning is used to
describe the fractional displacement of crystal blocks, Plastic deformation causes
permanent changes in the material.
Th~y
Creep 1451 s!lInds for the time dependent deformation and rupture. it is also
irrcvcrsi ble. Because the failures due to creep are similar to those induced hy pias1 ic
deformation, the creep deformation is normally treated as a plastic deformation. CI'CCP
deformation is divided into intragranular and intel'granular deformation. A.s 1he name
implies, intragranular creep stands for the creep inside a grain and intergranular creep for
the creep among grains. lntragranular creep deformation includes crystallographic slip and
subgrain formation. The plastic deformation takes place due to Slip of dislocations by
gliding on certain prd"erred slip planes, As regards with subgrain formation, because of
the inhomogeneity of creep deformation, many opportunities of local bending are provided
within a single crystal or individual grains of polycrystals. Local bending further causes
dislocatioTls of one sign line up, The dislocations arrange themselves by eros~-slip into
low angle subgrain boundaries due to interaction between dislocalion~, Subgrain
boundaries are formed in the primary stage of creep. Intcrgranular creep deformation
( '/wp/el"
_._------_.", .
indudes grain boundary sliding,
boundary migration,
I,;rc~p
!.:avily IlUch;!il(ion, tdd fnrmillinn and grain
Bi1scd (In the diffusion concept, scveral models have been deve1opt'd (0 rrcdi,:1 tlie
creep hehaviour. From an atomic or molecular pcrspcdiv,~. diffusion in solids i~ the
migration of atoms or mole()uil:s from one latti,e site to another iauke sile. The atoms
mu~1 have ~unil,;ilJnl ent;rgy 10 hreak bonds and then rci"orm them al anolh~r 1,!lli<;1; site.
This enel'gy is known as the activation energy, Whl;[1 Iwo h\!Ik iIlalcriah afC In cnntaet,
interdiffll~ion takes pia.,;!;;, At. Ihe surface nl()iecuie5 from one material ran migrale in(o
another hy ctiffiISion and vice-versa with different diffusion I'ales.
In addition (0 lh~ .~tI'~ss, clevated temperature and tempemlme dIHllg,:.S <;illl lead to
faiimes, namely thermal fatigue. Ac(;ording to (he I';)nge for stress c; and temperature T .
difkrent llIodds rd<"lted with the shear modulus (; and the melting (l:rnp,:riltUrC I;!! were
1
pl'npmed in the past r44, 45, 461. If Ci <:' 10. (J and T '" 0.5 Till' latl icc diffusIOn creep
(Nabarro-Herring creep) model is lIs\:d, lhl:: w~ep proces~ is controlled by diffusion or
atoms and vacancies under low <lppllcd stress, temperature is above ().5 Te". Ml1tcriab
deforrn in (he lenSlle (1itect.ion. Creep also exists under low stress and low tt;1T1pl;r'ltIII'C. If
(i .-.: I ((I U and. T ~:~ 0:5 .T"" the .pr<:eess can bc ~,(;S(;r~bed b! groin. bOllndary di ffusion
(Coble creep). II i 0 C <: Ci <". 10 (j and T> 0,5 fl/l' d!slocatlon motion controlled (;reep
deformation O<;';urs by both dis location gl iding and dislocation dimbing, l f (J" '. I ()"I (i and
1':;. O.S Till' grain boundary sliding and superplasticity rrwy oCC\1I'. (,I'ilill boundary slidinf!.
m,1 in Iy cOlltrihut~~s 10 (hI.: creer ill t.he primary stage. Because the agn~ement 0 r (1<;1 i v,lt ion
energy of creep and lattice sdf diffusion, the sliding is cDnsidered as a diffusion
wntrolled PTO(;CSS, If several mechanisms arc mUlually independ~~I!L I))~~ fastest
mechanism governs the creep behaviour. while if Ihe mechanisms arc dcpendcnl, the
slowcst mc!.:hallisTll governs the cI'eep hehaviour.
l'he creep curve IS a strain time relationship where strain is detlned as a function 01"
ti me undel' a constant load or stre~s, The slope of lhe curve is defined as the creep rak,
The creep is distinguished into three stages: primary creep, secondary creep and tertiary
creqJ, Thc (;rt;ep rMe in the secondary creep stage is termed as the steady >:tate creep rate.
Bt;c,1\Ise wost defOl'mation involves this stage. it is 0 r primMY importance.
Considering the dTeds of qclic thermal stresses 011 metals, the numhcr
faillll"l': "an hc directly related with clastic strain and plastic stnlin,
01" t~ydes
tn
Application of metal ddorrnation mechanisms can be found for bOlh Il!rgc rnc(.;liHni<;,Li
(;ompol1l.:nts and small electronic devices, such as pOWf,;r phlr)t QHnpOl1L'l1ts and prinled
cil'cl!1t hoard.~. Overall component dimensions may vary from meWrs 10 m inoHl!;;tl;;rs.
Whm fuse dements made from metals experience elt:cll'ic cllt'rcnt.~, therma I and
electromagnetic efICus can lead to dcformal ions ()f fu~e elemcnls. For (UlTC1L( rubes,
cyclic thermal stress in thl,: rU~t; clement is involved.
1.3.3 LifeHme cousi(lcrations in standards
[n the modern world. there is no d()uhl (hat. commercial industrial products h"vo: In meet
their standards, lEe Publication 127: miniature fuse~ 1471 i~ the 1l'lnst. important standard
for miniature fuses. This standard spccili(;s two types of tesls rclaLed wllh lifeli)l)~
Overview
9
expectancy. The first one is the endurance test stated in [Ee Publication 127-1 Sub-dau~c
9.4 and the ~econd is thepulS2 test specitled in [Ee Publication 127·1 Sub·clause 9.6.
Endurance tests require fuscs to withstand 100 cycles. Each cyck consists of an on
timc of [ hour with a current and an off time of 15 minutes without current, The Currcnt
magnitude is normally 1.2 times the rated eummt of tested fuses. Direct current is used in
the test. The voltage drop after tests is measured by applying the rated cUI'rent to thl:: testo.:d
fuse. The incrl::ase of th(: voltage drop is required to he not rnOre than [0% of the- value
measured before test.s.
[n contrast to endurance te~ts, pLlI~e tests are performed to gain information of ability
to withstand I.:urrent surges normally experienced in service. These tests req 1I ire [000
timcs specified current pulses. The vOltage drop arter tests is measured hy exerting the
ra1l:(] current on the tested fuse. The increase of the voltage drop is required to hc not more
than 10'Vo of the value measurcd hefore tests. The main feature of the test is that current
pulse has a larger magnitude and a shortcr on time compared with that in endUriHH.;(; tests.
In lEe Publication 269-4 (1986) [48], concernin!,; fuse-links for the protection of
semi(;onuuetor devices, overload curves are requit'ed (see lEe 26c)-4, SlIh-Clause 5.6.4
and R.4. 3.4). f;uses are subjected to 100 load 9cle~. each cycle has a total durat ion of 0.1
tim(;s the conventional time which is defined by fuse ratings. The "or)" period with a
current value and a duration corresponding to the co-ordinates of the overload capability
to be v{;;rified. the "orr' period forms the rcst of the cycle. The time co-ordi nates Me
sugge~ted to he within the range ofO.OJ to 60 seconds.
[n [Ee Puhlication M4 (1979) [49], concerning high voltage fuses for motor circuit
applications, two test sequences are recommended for fuses to withstand repetitive starting
(;onditions. Thl": first test e()n~ists of 100 cycles and the second consists 01'2000 cycle.~ (sec
Clause 8).
6
For most appl ications, however fuses have to withstand more than 10 CUrrem pulses,
2000 (;U1Tent pulses arc often far too less to mect uscrs requirements. Lacking of guidancc
from existing standards, manufacturers have to accumula.t.e experience to deal with lhe~e
practical problems, a good service is normally realised by a trial and error met.hod.
Therefore to understand ageing mcchanism~ of fuse~ and to perform reliahility slLLdie~ arc
of a practical value for industries.
1.3.4 Minimum
/1(
valuc and thcrmal buckling
Refore main contents of this thesis arc outlined, the minimum r't valuc of fuses and thc
con(;cpt of thermal buckling related with lifetime predictions will be exrlained i1nd
described first.
(1) Minimum 12 t value
Current • time characteristics of fuses show a spread for the melting time at a given
current. The minimum
value is the current square times the minimum melting time for,a
given current. Below this value, fuses do not operate. [n many cases, the minimum tr
It
10
vidue at 10 illS ~,ln be directly related to the sdcdion
eledrical components.
( "Iii/pier
., . ....•. _"._-,._--_ .. - - -
01" I"u~!,;~ 1(1)" (ill.:
pm1L'cti(\n
01
hlr miniu(urt; rll~US. as stntcd by manufacturers. lhis valu!,; is urrro~I1))atdy a cnn~tant
IKcausc the adiabatic heating may he ,lssumed for mo~t wire clements (with 2() mill OVl,;nll!
It:ng(h). \;or (r<Hlsformcr protections, 25 times the transl"orm~r rakd (';lll'rCIl\ for' I () ms is
sometimes required in ordn to hav!: fuses withstand transf(m11cr inrush currcnts. Data
shedS fnr semil::ond\lcl"ol' devices, for example thyristors, qUO\(; a ligurc CDr the l"ll<L'(i01\Il1\
surge current that devices can survivl;;, A hal f sine rulse witll a w idtll 0 r I () ms (:)() lIz) is
usually taken to indic,)(e tilt: ,21 rOt, fusing. This I't valuc represents the enlTl,:y tl1<1t (;,lil ht;
p(lssed hy serniconductot' deviccs without damaging them, Th(~rcl"O!T in this thcsk tht:
minimum melting /,'1 value is chosen as one of tht; pl1rameters. In some applications. I"uses
'lre rt~qllired to blow bdow a cert<"lin /2/ V<1I\le. Therefore, in principle, the maxirnuill
melting /1 valu!,; and the average melting /t value can also be used
(2) Thermal bw;kling
Thermal huekl ing i~ a concept 10 uts{.;ribe the movement of components due to thermal
ot'igin.~. In 19119, Moulin 150] conducted a n:vicw of tht:mwl buckling allalysis methods.
]""01' declri(; I"lIS!.::S under discussion, their elements can be considered cilh~~r U~ (;01 umns
with two !"ixed ends or plates with two Jixed edges. FI)r' a column with !.W1' fixed ends or 1I
plate with t wo lix(~d t:dg~s, beciluse of the boundary constrains thl~ eompr!'::~S)VI; force
increases as (h~ temper,llme of the column or the plate rises, A1 the heginning, the column
Or' th~ plale reserves its original shape. This slale is called as pre /)"ckllrlg. As the
temperatmc increases further, the column Or the riMe may start to move. The process is
called as thermal buckling because of its thermal origin. The temperature rise Iimit for
thermal buckling to take place is defined as the critical tt;rnperature rise. Afie!' motion of
the clement is initiated. the di~plaeement of the column or the plate increascs signi Ciean11y
with tr;::rnperatllr~, This is called <1S thenml post huckling.
1.4 Content of this thesis
I'rcvious studies and current standards do not provide geneml valid methods to dl~serihe
fuse reliability. This study attempts to de~crihc methods to prcdid the I"us..: li1Clime
expectnncy in t he case where thermal mechanical prot:I:~St;$ Me domi nan!. rhe first task 01"
this work is t{) answer questions t'elated with the ageing me(.;hani~rn of ))"liniatllr'e fuses
during short time pulse currents.
When fuses experience long tim~ {.;ydic cmt'ents, ageing or I"u~es may di ITt:r fr'lllll that
in short time cycli(; (.:urrcnts. Accordingly in lEe Publi{.;(\tion 127: rniniaturc I"uses,
endurance tests are spec-ificd. To predict fuse lifetimes for long: time currents. Iht: s~t;on(!
goal is to investigate relevanl bdHlvioHf during long time currents,
Because of the VMi())l~ dimensions and shu pes of fuse clemcnts, t1 may be askr.;d
whether' it is possible to find a modd for liktime estimation compatible with all situillions.
Consequently, to rl;;solvl: this diff1culty heeomcs the third obje(;tiw Ill' lhis wode
Overview
for semicomludor protcction fuses, notch~d fuse delll/.:nts may have dlffetent shapes.
they can be surrounded by sand Or bound sand. Thel'e are many paraml~tcrs which
i ntluence lildimt: of commercial products, and hence to study these CiHlses and prdiCl
Ii fetime becomes OUr fOllrth objecti ve.
As it has heen st(.lted, tlw prim~: objective of this thesIs is to provide (J general
theoretical method for lifetime predictions {lftd to evaluate the change of Ulrrf'nt - lime
characteristics ((Iier jl(ses are submitted to current pll!ses, Because lifetime is depefllkl1l
on the stress - strain relationship, displacements of the fllslf dement have to be
determined. However, displacem.ents are developed due to electric he(]tin~ which depends
On heat tranJ/er processes. Therefore, in accomplishing these tasks. first e.tperim({nt(li
relationships of lifetime (md important parameters are investigated. Secondly. thermal
rlfsponse of JuS!! elements is analysed Jor different currents. Thirdly, metal d<!fimna/ion
due to the.rrnul ef(eds is swdied together with the resu.lting stre.ss. Finally on the hasis of
Ihe. r mal./(1Iigu(! due to cyclic stress/slrain, 'hI";! li/etime can be predicted th({or<{Ii<:oUy,
Following this ~cheme, the work is dividl:d into five pal·ts: introduction (Chapter I),
experiments (Chapters 2, 3 and 4), heat transfer modelling (Chapters 5 and 6). thermal
buckling (Chapter 7) and lifetimc predictions (Chapter 8). and general conclmion~
(Chapter 9).
Chapter 1. presents experimental results oC pulse tests. It describes experimmtlll
equipment and tcst procedures. Fuses are submitted to short current pulses in the order' of
10 milliseconds to obtain lifetimes. This chapter also discusses possibilities to present
lifetimes as function of several parameters related with current.
Chapter 3 covers lifetime studies related with endurance tcsts and long time ageing
behaviour. Tests arc relevant to endurance tests specified in lEe Publication 127:
miniature fuses. The chapter discusses the possible relationship between lifetimes and
currcnt parameters: magnitude and on time.
Chapter 4 describes experiment~ for studying the ageing mechani~m of semicolldu(;tv[
protc:ction fuses r51], Experimental observation~ of lifetimes and ddormation arc
prescntcd.
Chapter 5 presents thermal modelling methops [521 for miniatUre fuses. Here, heat
radiation and convection of fuse clements arc considered to be non-linear functions of the
element temperature. lhe purpose is to calculate the tcmperature response and diqribution
for fuse elements excited by any currents. Application 0]" this model may also rc~ult in
current - timc charactcristics (l - t) of miniature fuses which are of importancl: to
manufacturers.
Chapter 6 presents three dimensional thermal transient simulations 153:1 due to electric
current for semiconductor fuscs by using EMTP (Electro-Magnetic Transient I'rogram
[54]). In the simulation, the current density distribution in the fuse eiemenl is considercd
in two dimensions.
Chaptel' 7 pre~ent~ analy~i~ of element motlon~ for thermally stn:ssc:d fusl:s due to
electric CurrentS. The present study d~scribe~ two buckling models. Thc first one i~ based
on the work [55] where the maximum displacement of a straight fuse win: is obtained to
( 'flap!er
12
ht: a function of tht: eit:ml:nt temperature, Tht: second huckHng model USeS tile finitlo:
element. method, it de.~cribes displacements in the axial dircction and the perp<:ndiuilar
direction of the wirc. Both models attempt to analyse the slrl;:~s Mid strain of f\ls~ wires
Jut: 10 thermal llrigiJl, The purpose is to predict the breaking location and to gain an
insight of mechanicill "csponscs due to clectric current~.
Chapt.er g presen1.s models for Iifetimc predictions for miniature fusl~s 15(1. )7. 5XI ,11\([
for semiconductor protection fuses for cyclic eurn::nts, II dis(.usses ,Igei!lg orll,!IIl~ of bnth
types of fuses and possibiliti(:s 1i.)r improving J\lSC lifetimes. (jeneral applicatiolls oj" the
methods to various types of fuses arc addressed.
Chapter 9 summarises main eondusiol1S from the previous chapters.
Part II
Experiments
Chapter 2 Lifetime Experiments with Short Current Pulses
Thi~
chapter presents (lild analyses experimental resulls of litdime reducti()!} of cnmmcreial
miniature fuses by the short current pube, For curl'ent pulses, t'" 'I""" /"" and /"1/ may h~:
ddined I;)~ J()llow~;
/,
',II"'"
I,,,,
'dfi
is th ..~ ":UIT~~rlt ~q\l(Jr(': integrat over a period, fbI' a single "~UlT(::nt pul~{,! (u11it ill ;\ 1S
is t.he peak current of it (;LUTent pubt: (unit in A )
is the current pube time (unit in ms)
is tht; ti1!u;~ pt)r1od het.ween two successive (;urrent p\lb,;~ (unit in s!:t:ond).
)
As fill' as the currcnt pulse time is (;oncerned in this t.hesis, current pulses rnay hI;; d'issitled
into two categories: short current pulses and long current pulses. A short clIrrt:nt rube means
that the current pube time js in order ohevcral milliseconds,
As stated in the. f1rst ehaptcr, miniature fuses twve diffe.rent clement shapcs as regard~ \0
their applieations. On the basis of current - time characteristics, miniatur(; JiIS"~S arc di~tlJlgilishcd
as: very tast acting ["uses (Fl',), fast. acting fi..1scs (F), mediuITI time Ing t\ISt!S (M), lime lag ruses
(T) and very time lag fus:es (TT). Essential di1ference among them exist~ in their prearcing r',
values. For example, prearcing /1 values show hig differences at 10 tim(;s the ra(t.;d (;Urrent. hlSt
ut;ting ruses nren earlier than timc lag fuses fur a ~hort circuit CUtTent. So in practice. w
withstand inrush curre;;nts during the switching of equipment, tiITIe lag fuses Me .sllgge~ted in
Lwour. Materials of fuse clcmcnts otlcn diner for various current ratings. As a conscqumcl:. the
questiun of lildinll: vnrialions rise.s due to properties of ckmt:nt mat.eri,t[s. Bet'iH'e any large scale
studies on lifetimes arc started, II case study is carried out. So to get an impression of e;;ftccts of
current pul~es on fi.lse lifetimes. experill1ents start with a typil'al time lag fllse,
Bccllusl: of construction diffel'ences of fuses, it is reasonable to ask wheth~l' cnnciusiollS drawn
from the case study represent generalities or not. In other words, (l general method should k
purs\1ed h)1' all practical fuses. To lind the solution for the~e problems, several typical
configurations are studied. Because experimental procedures fi)r all hl~"~~ <Irt: mOre ()l' less the
same, experimental descriptions will t.ake the time lag ti.lse as an ~~xmnple hll' the illustration.
This chapter mainly covers two parts, The first part. describes the ei1()I"\S to study Ii Ii:timcs ()f
a typical time lag fuse amI the se.;;ond p,1I1 describes thl: intluenl,;e of othcl' parameters of fuses on
litdiml:s, M,lin ohjeetives arc:
to determine cxpl.:rirn~ntally the lifetime of minia(urt: Flses exposed (0 cyclic
rectangular and sinusoidal pulse shapes tor long off times.
to study the intlllencl:: o1"the internal eOllStl"llction of fllse~ on their lifetimes.
"~U1Tl~11(
with
2.1 Studies of a time lag fuse
2,1,1 Test Qb.iect
Figure 2.1 shows a typical (:onstruction of the chosen !est obje<:t (l,iltem,se type 21 8.1\()O) , l'ill!
!'\lse elemenl or these time lag fuses is a straight wire element and is positioned ill~ldt; il glass
14
Lifetime Experiments with Short Current Pulses
15
tube, Two ends of the wire element are soldered onto end caps. The element of te~ted fuses is
made from a clad wire of 50% silver and 50% tin-7,inc alloy by weight. The wire diameter is
1
0.103 mm, Fuses an: rated at 800 mA and the minimum mcHing it value is 1.3 A s. as indicated
by the fuse manufacturer (see Appendix),
2.1.2 Measurements of voltage drops
To study fuse ageing, technical infonnation of new fuses should be collected, As resistance change
was considered as OnC of the main points related with fatigue, measurements of voltage drops were
performed.
Glass tube
End cap
Fuse element
Figure 2.1 Typical time lag miniature fuse
According to lEe Publication 127 ; miniature fuses [47J, the rated current should be used for
determining the voltage drop and then the power loss. fn normal practice, the heat produced by
10% of the rated Clll"ttnt is considered to be negligible. For these reasons, to measure the cold
resistance of fuses 10% of rated Current can be chosen. To guarantee the measuring accuracy, the
four tcm1inal method [59, 60J was adopted. Figure 2.2 shows the principle scheme, where I is thl;
applied current, U is the measured voltage between two teoninals.
+
U
Figure 2.2 Four terminal method for measuring the fuse resistance
For 800 rnA time lag fuses, voltage drops across 74 fuse samples were obtained by using the
fuse rated Current (800 rnA). Accordingly, 80 rnA was taken in the measurement to detennine the
cold resistance.
16
---------------------.~--,-.,
.. "
2.1.3 Test circuits for current pulses with hlilf sinusoidill wave forms
To study the influence of curren 1 wave forms on ii.tse lilbimes. two tyrit,al t:lIrr,'rH \\';!Ve j(lrIn.~
were used: pulsed currents with IUlIJ" sinusoidnl and r~l,lng\lli1l' wave tlH'tllS. Thc IKi.lk currenl
ranged lip 10 20 ampel'L:~. The relative J"t value varied from 0.16 to (L85 whit:h \Va.~ ddillcd ,'IS llit!
ratio oCthe Jlt value 01' the pulslXi nlrren( (0 (h'.: minimum l"nel1lng /, vahlt! nf I\m:s a.~ staled by lhe
manuhJ.durer.
In the following. experiments l()l" eurren( pub'.:s with a twlf sinlJsoi(i<l1 Wilve l{)l'(\\ will be
discussed. Pulse (cs(s in this work are aimed at collecting lifetime data of fuses. when li.lst~s art~
subjected ((1 current pulses. To continue the pulse tesl, lesl li.leililiJ.:s an: rJ.:yuircd 10 he rnfpt:rly coordinated so that a series of current pulses ar'.: exposed 10 rJ.Js~~s. S~cnJ\(1ly. the liin': interval
between two pubJ.:s arc adjustable. Resistance or voltage dmps in this penod should also be
measured. To accoJTlplish these duties, iln experimental set-up was eonslruc!cd as shown in hg.
2J.
Curren1
---··-·----··-·l
,."1..___.__
.__._~~::~~.t:r_. <·r
f'M 2130
~'M 2121
lE;E;E488
1==",b""LlS=d
PM 2101
~
_.
[
'".",
eM 2535 multimeter
..... ,..
. ....,_.. _----"
Figure 2.3 Experimental setup for petforming pulse tests [61]
The Sel-Up mninly consisted ofa computer, a digital input/output unit (PM 2130), J digital low
level switch (PM 2121), an IEEE intcrhlCc (IEEE 488 PM 210]), a digital multimeter (PM 2535)
and a current pulse generator. The digital 110 unit and the low level switch were used (0 produce
switching signals <1nd control operation for tests. With (he digital multirntler. vnlta.ge drops across
tested fi.ISCS can he Im:asurl,;d by uSing a current source ofRO mA (or gOO rnA). The gencra(or was
aClually all LC circuit with a thyristor which can he controlled by (hI:: <,:olT\pnll!l" iTller'hc~ to ohtain
current pulses with an approximatdy hall" sinusoidal wave form. Several I.lrses were tesled in one
series <11 the S(lme t.ime. Figme 2.4 shows the test circuit of one unit in thl! ClltT('nt pulse generator
which was designed by P. van Ridscholcn (see Appendix).
To evaluate the Ii Idimc distribution. in the first. st.age this process was repealed un(il all 1~lsl;~
operated, afterwards until (hree of five fuses interrupted. Resistan(;c VllIUI;S ,!nu lh\! numhcr of
pubes whid\ fuses wJlhstood were stored in disk files. Addilion,dly, the tI.lSC voltage. the eum:n(
~lnd the /t value of pulsed eUITen(s were saved.
2.1.4 Test
cin~uits
for current Jlulses with rectan1!;ular wave forms
To ~tudy 1\.t~e ageing due to applying <I rectangular current pulsc. similar
Section 2.1.3 were CMried out to gather liictirn(;s.
dJ.Jli~s
nlcn(lnr1cd in
The experimental SCHlP r621 d(:signed by P. V(ln Rietsehotcn is shown in hI,:. 2.5. The systom
mainly consiskd oj" a d.c. supply, n digital control unit, counters. an t:k:(:(['()nic switch. a current
Lifelime Experiments with ShOl·' Current Pulses
17
detl:(;( switch, a digital potential meter (DPM) and a shunt. The d.e. supply can deliver a I,;urrent
between 800 rnA. [0 20 A. Within 100 "",,s, the Current rcaches its top value and hcps constant. In
one scries 12 fuses can be tested, during the test the resistance of fuscs was measured. Aller fuse
breaking thl: numbers of cycles to failure were recorded by counters and put into (hc computer fix
further analysis.
L
R
Sl
~~~~~~--~C~
Dill". amp.
.<J{~
s
S
DC
c
Shunt
u
Yrlac
-f
Trigger
Ground
Figure 2.4 Test circuit diagram for sinusoidal pulsed currents
S, S1 : Relays (V23100 - V71); Triac.' Tic - 263 M
L "" 2.2 mH, C = 1.3 mF, R '" 220 ohm
Counters
Currcnt detector
Current
Source
Shunt
Digital control
Master counter
Figure 2.5 Test circuit diagram for current pulses with rectangular waVe forms [62J
---_ .._.. _.__ .
__ - - - - - - - - - -
( '110171('1"
...
.)
2.2 Statistical distribution
Two types of distrihutions, namely the normal distribuliol7 and the Welhull dislrihllllOn. arc USI;:<!
in this thesis to estimak the distribution of ohserved parameters. ~u.;h ,IS vllitilge drops_
resistance and the number of current pulses to fi:\ilures, 'rhe model of the nornwl dislrih/llion is <I
summation of independent identically distributed random variabl~s. It i~ widely used to evaluak
pM;)meters of products to deserihe their new situation, For example, dimensi()n~, w(~iJ,:ht and etc.
The Weihull dislrihution has been widely used in reliability studies as ,I 111(ldd j\)i' the
Ii/dime 0]" products including the description of a wide rang!.: of htigul: rhcllomena. I-'or this
reason, this distribution is chosen as a startin~ point in this I'c.~carch. The most popular IlI!.:th(ld of
lithime analysis is to lit the distribution to lifetime data by the maxilll1l111 lik~lilh)()d method
(ML), As ,Ill 'lHemat.ive, the distribution is often titt~d to lifetime data by using (I gr(lphi~
procedure_ one advantagt: or this method is to visually d1el.;k wh~th<;!r lh0 I)b~l!t'ved lili:.'limes
b<:long (0 this distrihution.
For the W(;ibull
di~trib(ll.ion,
its curmdalive density/i.mction is
1'(1) ~ J - C)(p( - (All)
.Ii)/" I;::
(2.1 )
I)
where t is the random variable, A. ::- 0 and 0 ~, 0 arc the scale and shape pM;lmetcrs, respectively.
In this situatiolll is the (ime related with the number 0]" Current pulses which rUSl~S can withstand,
lIlt: d(;!nsily/imcti()!-'l for the Weibull distribution is
1(1) -" 11,11 j~t~-I exp(-(Aljr)
/>()
The mean value orthe Weibull distribution is
6"
111 =
/.,.1
r (/
+
Wi )
RcnrganisMion of Eq. 2.1 leads to
Jog", [ - /oj!". ( 1 - F(I))
1=
0 IOKIlI A.
+ fl
[oKIlI I
To obtain a linear rdalionship hetween lifetime log) II I and the corresponding valu(: of til!.:
cumulative (lensity function, log III I must be plotted again~t log III r.log.,( I.FO)) I. Til!;; I.;(HTH11On
pradice [631 is to plot log)/) Ik against PH = (k-O.5)ln, where 1),12, ... , Ij, "', I" lire th(~ OI'dered
obSl;:"rv(ltioJ)S ft'om thc population. n is the number of total samples (I :. k ,,:. II). If the
expel'imental results can be fitted 10 a straight line in this graph. lhc validity of the W(~ihull
distribution is assumed. The slope of thc line is a measure of parameter 0.
2.3 Results and discussion
During ruhe tests, both sinusoidal and rectangular wave 16rms of current pulses wen.~ uscd. th~
purpose is to examine the influence of wave forms on the fuse lifetime. Thl.; CUrTent th1'Ough the
tested fuse and the corresponding voltage across the fuse were mcasur~d hy a digital oseilloswpt:.
rigure 2.6 shows typical traces for a current pulse with the sinu~ojdal wave lilm!. 1\ (iIlH~ bg i(ll"
the vultage trace exists as comparl;:"d with its corresponding curn:nl. This physically means thllt
during the period or a current rulse, the fuse wire clement is heated up (resistllnc~' im;r(:(lsc~).
Bdore the lest with current publ.; starkd, conditions of new prodUi.;1s \V",'" evaluated tirst. the
initial cold resistance was measured I(,)r 74 samrles. Voltage drops oJ" fuses were measured al a d,l;.
current of800 m;\ (rated current).
19
Lifetime Experiments with Short Cl./rrent Pulses
I [AJ, U [V]
R [mol
w,
12
r
10
R
120
100
8
80
_72mn
6
60
4
40
2
·20
0
2
0
5
4
3
Time
0
6
8
7
[ms]
Figure 2.6 Measured pulsed current and corresponding voltage
I : measured current; U ; measured voltage;
R ; resistance; Rcold: initial resistance
Figure 2.7 presents the histogram of voltage drops. If the voltage drop is assumed to follow the
normal distribution, then the mean value f.t = 68.3 mV and the standard deviation cr = 1.9 can be
obtained. The 90% confidence interval of this voltage distribution is [65, 71.4J mY, which is
corresponding to resistance values from 81.3 to 89.3 mO.
Histogram of voltage drops
20
1a
16
14
12
10
8
6
-4
2
0
~----L.l..Jnl
62
66
Voltage drops at
sa
aoo
70
72
mA (mV)
Figure 2.7 Histogram of the voltage drops before current pulses
if the nonnal distribution for voltage drops is assumed,
then mean value j..l. ::;; 68.3 mV and standard deviation cr 0:: 1.9
20
( 'hopler
I'-or both (ype~ of [lulses. ri1r<lme1.ers of current pulses 1"1,
'J
'/w",
lind I"" an,; 111,~a~un'd hy Ilsing a
W(;n; Il\<::\'~IIt'cd Ilntil (he end of
lifC.. For tlm::e time lag thses, Fig. 2.8 displays (ypi,-al meaS\ll'I1lg results Ill' \ohagc drops (IS <I
limdion or lime, Mcasurcn)(;=n($ wer'e pertormed between current pubes. i\ppro:-;illl,lkly sI1\lIsnidal
CllI'!'ent p\llse~ were applied (sec Fig. 2.6) with it = (),61 A2~, 'I"ilk
14.6 A (,,/' (,,2 illS. 1.,11 '" 3 s.
digital oscilloscope. I\lso during the lifetime test, (he voi(ag(; drops
Voltage drop
[m\!]
80
.... .. .
75
70
•
....... . •
;~ ':~': y ,;-: :.,' .~ :..: )( )'.
:
65 :-
60
....
x :.-( ',( x
...
o
2
. ..
"oJ'~'
I-:
•
3
5
4
Number of current pulses
7
6
8
[Thousands]
Figure 2.8 Measured voltage drops at 800 mA against
number of sinusoidal cr;rrent pulses
2
Pt'" 0.61 A s, I~a~ = 14.6 A, ton :::: 6.2 ms, toff'" 3 s for 3 fus()$
hgure V) shows mea~\.Ired voltage drops fOr three l'llses expo~ed to rectangular current pulses
with the same
The parameters of current pulses are ft 0.61 A2s, 11""" ~ X A f",,' I () Ins. 1"(1 ,.
:l s.
rt.
'0
Voltage drop
1m\!]
85 [
80 I
"
75
"
"
70
0
o.
o·
65
60
I
•........• 1. .• _._._ .•• 1..
0
2
4
I
l.............. _L. __ .. _ ... :
6
8
Number of current pulses
10
12
[Thousands
i
14
16
1
Figure 2.9 Measured voltage drops against number of rectangular current pulses
PI = 0.61 A"s, Ipeek'" 8 A ton = 10 ms, foil'" 3 s for 3 fuses
Lifetime Expel"iments with Short Current Pldses
21
The common point of Figs. 2.8 and 2.9 is that in general the resistance increases as [he number
of current pulses increases. Initially. the resistance increases rapidly until the number or <"lpplied
pulses reaches a value of about 1000 pulses. Afterwards. t'esistance increus(;s slowly and
sometimes it also decreases. At the final stage, near the end of fusc lite, resistance increases
sharply again. From a number of experiments, it is noticed that fuses show the final resistance
increases later when submitted with rectangurar cun:ent pulses as compared with half sinusoidal
current pulses. Examples are shown in Figs. 2.8 and 2.9. This is possibly due [0 the fact that the
input energy rat(; during the rectangular current pulse (low(;r i"t(,k, longer t,,~) is lower than thm
during sinusoidal current pulses.
Observations of the fuse behaviour just before breaking provide a possible approach to study
lifetime criteria. From a large amount of tests, lifetime median and corresponding median of the
percentage resistance increases before fuse breaking are obtained. Statistic medians (50% value) of
fuse lifetimes and percentages of resistance increases are calculated from five tested samples. The
average increase of resistance is found to be 9.8 0/0.
10 estimate fuse lifetimes according to a statistical model, the first goal is to examine
whethcr lifetimes follow a specific pattern of distribution. Figure 2.10 shows the accl101l1lat(;d
frequency as a function of lifetime on probability paper of the Weibull distribution. In Fig. 2.10,
ClIrv(; "a" shows the results for It = 0.61 A\ ip<ok = 14.6 A, t~~ = 6.2 ms. t"fT= 3 s: curve "b" tor
It '" 0.61 A 2S. lp<ok = 10.4 A, tv n = 5.6 ms, tQ!r= 5 s and curve "c" for = 0.61 A2s, lJ.H!"~ = 8 A, (,,'
= 10 ms, t"n·=; 3 s.
it
99
90
(f)
80
0
70
60
w
z
UJ
~o
8w
40
30
20
c::
LL
c
~
:J
b
10
a
:t
~
(j
~
10
100
1000
10000
100000
NUMBER OF PULSED CURRI;Nr$
Figure 2.10 Probability paper for the Weibull distribution of fuse lifetime
for current pulses with different parameters
2
ft '" 0.61 A s, IPQ~k '" 14.6 A t/)l1 '" 6.2 ms, toff '" 3 s, sinusoidal
2
b,' /it'" 0.61 A s, lpeek'" 10.4 A ton = 5.6 ms, tOff = 5 s, rectangular
c: Pt'" 0.61 A~s, IptJ~k '" 8 A ton '" 10 ms, toff = 3 s, rectangular
a:
22
In Fig. 2.1 0, k!';lIUS~ ob~erv<ll.ion~ are tltted into a line, the Weibull di~lrih\l1 inn ean be used to
estimat.e lifetimes. [n addition, this graph shows thai lor Ihe snlnc /1 value of current pulses, r\l~'-'
lilCtimc will be short ,IS Ihe currcnt pulse timc for current deereasl;;s. In (llh~r wllrds, the peak
current incmase leads to a decrease of lil(;tin1(':.
or
From a large amount
pulse lests, mean lifetimes can be estimated hased (ll) 11)(: Wei hull
distribut.io1\. Lifetimes expressed in number of (;urrenl pubes al'e presented in labk 2.1 as fuses
were exposed to halfsinusoidnJ c\lrrent pulses and rectangular currenl pulses,
Table 2.1 Experimental results from the pulse tests
2
11,1lJ1.\'j
Wav~
1011
I,,;;
rtlrlln
form
[ms]
Is]
$
s
s
s
s
Cl.2
6,2
6.2
6.2
6.2
7
7
s
(,.2
s
s
r
6.2
6.2
0.89
0.65
0.55
0.52
r---... '······," ..
OA7 ........
r----.,--."
0.47
0.42
OJ7
f--------7-.... -•.
n.57
0.57
0.52
-,._
0.47
... ""' ...........
r
r
0.47
o.:n
r
7
7
7
3
7
7
__ "..... 101.-,,"'····
Mean liklirm:
2.2
18
372
2Mi(j
f--.
r...
--
5<;lTl
_._-_._-_.-
2656
13099
555fd
._.- .... "..... . .... , " .. ,,-- _.... ,~.,
12
12
5.6
4
2
10
5
5
3
):;
3
5,6
1605
"'-
_ _... '--
1272
.,-" ..
2261
5259
8973
265400
In Table 2. L "s" and hI''' represent the sinu~oidul arId I'ectang,ular wave forms r(;spe(.:livdy.
Corresponding parameters are detlned as follows: /t l ",/". is th(': r l vahle of each current puIs(;~
1\",,, is Ihe minimum 12, value corresponding (0 the I ~ ! characteristic of filses fi)r Ih!;; ~iIT'ne time
a~ I"" . To simplify the !;;slimotion, in this case, the minimum (IdirIh()li~'12J value is used however.
During pulse (CSIS, the gradually changing voltage dl'ops or resistances were n}!.:a~lIrt)d and
r(':sulis are shown in Fig. 2.R and Fig. 2.9. On the basis of these ohservations. three hilSic pattcrns
C,Ul he recognised. Resistance incr(':nses during pulse tests in general. AI tht) heginning rcsiSHtnCl~
increases very fast; ailer about 1000 current pulses. n;sistances become more or less stahle. AI Ih~
final stag~, resistance increases sharply again.
Figure 2.11 shows normalised resistance change patterns (or diHerent /t values Juring puls~
tests. Each type ofmnrks represents a tracc ofvoItage drop corresponding to lifetime mcdian for a
series of pulse lest. This graph indicaks thnt during the fuse lifetime, thl: resisl;lnce nf fuses will
increase with similar normali~l.xj pau.erns for a hroad rangc of pulse Shapes. l;l'Om this graph. il (;UI'I
be concluded thut a~ Ihe ,1veragc voltage drops im:r~ase Uj'l to about 75 mY. the Ijjdim~: (If fllsc~ is
wnsumt;:d. This otTers indeed 11 useful guideline in practice, to ehed whdht::r ;1 1\lse is Ilcarly al
the cnd ofIifC.
Lifetime £"x:periments with Short Current Pulses
Voltage drop
23
1m\!]
90r-----~----~------~----~----~
85
x
x++
80
x++
75
x
x++ +
70
o
0
o
x
+
0
++
0
0
0
65
60~----~~
o
20
__~~____~____~____~
40
60
Lifetime percentage
80
100
%
Voltage drop at 800 mA as a function of
percentage lifetime for current pulses
2
+: ft = 0.48 A s, f~8k = 8 A tQl1 '" 8 ms, toff:;:: 3 s, rectangular wave shape
2
x: ft = 0.74 A s, f~Bk:;;: 8 A too = 12 ms, toff "" 4 S, rectangular wave shape
Pt;;;; 0.61 A 2s, lpeak'" 14.6 A too = 6.2 ms, toft '" 3 s, haff sinusoidaf Wdve shape
Figure 2.11
0:
One should remind that parameters of Current pulses in Figs. 2.8-2.11 are measured values, a
certain accuracy may be assumed. For instance (see Fig. 2.9), lp<~k = 8 A and tOil '"' 10 mS lead to
f t = 0.64 instead of 0.61.
Using Table 2.1, Fig, 2,12 presents fuse lifetimes against the relative I"t value of currenl
pulses, where 1\'''ls~ is the it value of a single current pulse; I"tmin is the minimum it value of
the melting (
1.3 A 2S ). By using the curve fitting method [641, lifetimes are found to be a
simple function of the relative
value of the pulsed current, It is expressed to be
it.,i. '"'
it
f2 IplIl.••
log\o N = C,log\o-1-+Cu
/
)
(2,] .
tllli:n
where C 1 and Co are constants determined from experimental observations. In this case C 1 = •
12.6 and Co = " 0.38. Co indicates whether ageing offuses is faster (Co < 0) than that expected
from current - time characteristics. C 1 is a measure for ageing sensitivity to current pulses.
In Fig. 2.12, mark ~ indicates lifetimes of fuse where current pulses with a half sinusoidal
wave form was applied; mark. indicates lifetimes of fuse where current pulses with a rectangular
valuc reaches 1, the number of current pulses is
wave form. It call been seen that as the relative
also near I; as the
value increases, lifetimes decrease. From this graph, it can also he seen that
Iifctimes for current pulses with a half sinusoidal wave forms slightly differ from those tor Current
pulses with a rectangular wave fOlms. This encourage us further to investigate the lifetime
rt
rt
24
----------------"-"._.--,--------
('hI//Jll'f-
2
hchaviollr of other typcs of fuses, on the basis (ll,,( (be I~f VilillC nf current pulses i, tlte dctcnll)lIing
t-hctor j()r the hldime n:du(;(ion, Becil1lse the test circuits j()r sinusoidal (';urrClll Wil\~ J\m\lS arc
mudl ca~i~r (0 huil(! than the test circuits lor the cum:nt pubes with fcetanglliar wave rorms, thus
test circuits fill- producing current p\llses with sinusoidal wave forms w~~r~~ ~:(1nstl'lIckd tn lest other
types of fusl,;s,
Number of current pulses
Figure 2_12 Fuse lifetime as a function of the relative
ft value of
current pulses
a half sinusoidal wave form
• ; cumJmf pulse with a rectangular wave form
t, : cummt pulse with
2.4 Influence of internal constructions on lifetimes
10 Section 2.3, lifetime determinations have been presented for a time lal; illse. where tht:
number of cyeles to failure showed to be a function ofthe relative r' I value of n!rrenl pulses_
The question here is whether it is possible to generalise this dcpcndmo.;y I~)r other f\lse types_
In this section, with the same circuits in Fig. 2.4 effc)[ts will be m<lde therefore to determine th~~
Ii fdimes
other lypes of fuses_ RecaLise test (;ir(;uits have the same principle 0(;h(;I11(;, the
descriptions of test procedures will nol be addressed again.
or
2.4.1 Element materials
For low voltage rust;S and high voltage fuses. silver and copper arc thl;; besl krunNn ~Icmcnt
rnaterbls_ 1'01' miniature ru~e~. alloys are also widc:ly u~(;d be<:()lIse of practical rcquirl;;mt;;ots in
manun~eturing and applications. To get a general impression, dif'f(;r(;nl dernCrlt mataials wen;
chosen_ T'hey may be used 10 make fast acting fuses and time lag fuses_
2.4.2 Element shapes
As the element shapes arc (;oncerned, there arc a llumb(;r or choices. The most commonly I!sed
types arc shown in Fig, 2, J 3: straight wire dements. corrugated elements_ wound wirv clements
25
Lifetime E.'(.periments with Short Current Pu.lses
and S - shaped plates. However, in this thesis, results of straight wire clements and corrugated
clements are presented only.
/
'\ i. . 1.'1,.',".
/ \J \j \1 \\/ \) \; \::' ', . \". \.
i\ fl
Straight wire ( -
r
Wound wire
I'.
S shape
;,\111\,
)
__ •...
i.
r.
~
1\ :\ .:".
<~~'--- Corrugated wire ( '- )
~\!)
Figure 2" 13 Typical elerru:mt shapes
2.4.3 Results and discussion
According (0 the analysis for fuses (Littelfuse type 218.800) in Section 2.3, the fuse lifetime in
number of Current pulses can he presented as a linear function of the It value of the pulsed
current, on a double logarithmic scale. To check the general validity of the relationship
concerning different element materials and shapes, following types of fuses were used as
~xamplcs: Nickel wire elements, silver alloy wire elements (Ag,Cu.Zn.Cd: 50%Ag, 15.5%Cu,
16.5%Zn and 18%Cd), silvcr plated (3%) copper wire elements; silver plated (20%) copper
wires, and silver clad wire elements (AglSnZn: 50% Ag and 50% tin-zinc alloy 85% Sn and 15%
Zn). Experiments wcrc conducted in UtteJfuse. Figure 2.14 shows lifetimes or miniature fuses
(Littelfuse type 217001,2]7002) for current pulses with sinusoidal wave forms, where lines are
obtained according to Eq. 2. I with different coetlicicnts.
10
6
(j
1,1)
Q)
!!l
10
-I
:::J
10
1:
~
:::J
10
'0
10
0.
(j
til)
3
b
J
2
1
.0
E
:::J
10
Z
0
10
10
12tpuIS8
I~tmin
Figure 2.14 Lifetimes for fuse made from silver plated (3%) copper wires
for sinusoidal current pulses (Eq. 2. 1)
a: Littelfuse type 217002; b : Litte/fuse type 217001
26
('fwplu
2
l;or various different types of fuses, t.he eurve slope ibm the regressioll allalysis Eq, 2,1 is
in Table 2,2, where corrugated and straight dements are indica(t;tl by ""--- and '"-"
respectively.
outline~j
Table 2.2 Slope of lifetime relationship
Element material
Element shapl;
Fuse tyre dl-1 111
C1
Cli
0.99
217J15
50
Ni
20.1
._ ..
.17.1
217.500 68 -- ._--, AgCuZnCd
IJ ..
.._---_
._.
217001
Cu, Ag plated 3%
1.26
60
" 15.2
.
_
..
,,_.,.
",II'''''
217002 1---_.- 15.\
0.04b
Cu, Ag platcd 3%
.- -_._-- . ..
...
- 3.M .....
19.2
235001
52
Cu, A!i.p"l~"lted 20~;',
-_._--_
'-.'
I
R_1l
2Yil.25
62
Cu, Ag plated 20%
J.n
..__._ .. ,.
.._--- .._- ----_.
.."_
--...
lY_)
- J, I _.
23501.6 73
Cu, Ag plated 20%
-~1'_'
911
Cu, Ag plated 20%
- 1.54
_. - In_9 ..... -,--_.,--_.,-... --235002
.....-.............. .. F~···-·,-·.
-(UX
12.6
218800
103
Ag/Sn.7l~ ..
.- B.b
21ROOI
117
AglSn.Zn
..... _..
,._- .__ .. ".__ .,-_... _-_. - "-6.64
--- 1.14
Ag/Sn.Zn
- 9.0
134_._-_ .•.
2181.25
- 0.90
21801.6
AgfSn.Zn
·9.4
156
- ~.X
235.500
0.27
AgCuZnCd
.-..
.... _._---- ~--235.700 63
0.17
AgCuZnCd
_.......... ,."'",,'u.... ·· ----.-----=X:t.I':I-- . - 0.33
237001
96
Ag/Sn.Zn
-
~.-.
•• _,,_, ............... ~~
-
,
-
"'III'~
-
,
,,_
~,.,
-
IM~~,""·.-
~
-,'
- - - , , - , . - , - , . ",j
--~
horn Tabk 2,2, it i~ clear that the regression lines from (hI;; \;urV~ Jit.tjllg ilre nut always
through the unit relative t't value. For the most cases, th~ points are loeawd to Ihe left \)rthe lIlli(
relative J"t value. To examine lhl; inlluence of matet'i<ll~ 011 the relationship_ the c(lenicienl~ C 1
arc prescntcd in Fig. 2.15_
25
20
'15
- C 1 10
5
o
-t--jf·-,-v."7 i / ,j Ii'/ . i/"'j/-Iii1- ...... ~ Ii
AgfSnZn Ni AgCuZllCd CuAg20% CuAg3%
Figure 2.15 Influence of element materials on slope C 1 in Eq 2 1
Lifetime Experiments with Short Current Pulses
27
For thl: same series, as indicated by manufacturers. current· time characteristics are usually
presented as a curve with the spread in one graph, where the ratio of prospective current to the
rated current is taken::ls a variable. However, as indicated in Table 2.2 and Fig. 2.15, because of
different clement materials (see 235 series), the slope for lifetime relationships may diner
largely. Consequently, the lifetime relations can no long be prcsented as one simple Curve l'or all
type~ of fuses in one series.
A higher slope means that as the ft value decreases. the lifetime inercases faster. Figure 2.15
shows that the element made ofnickd gives rise to the highest slope for the lifetime rclationship,
while the clement made of alloys produces a low slope. Silver plated copper elements ofTer also
a relativelY high slope (217.001, 217002; 235001. 2351.25, 23501.6, 235002), while silver Clild
wire elements provide a low slope. H is then clear that silver plated copper wire elements give
the hest lifetime results for corrugated clements. Fuse elements made from nickel and silver
plated copper have high melting points and a relatively high slope. In practice, las! acting fuses
arC normally made from the materials with high mdting points, it is therefore suggested (hat lilSl
acting fuses arc bettcr than time lag fuses, as the number of current pulses for fuses to withstand
is concerned.
2.5 Conclusions
In this chapter, lifetime experiments of miniature fuses for short current pulses were performed.
According to statistical analysis for the time lag fuses (Uttelfuse type 218.800), lifdimes of fuscs
can he described by the Weibull distribution, USing It as a characteristic. During the lifetime of
fuses, resistance increases as fuses are subjected to short current pulses with the pulse time in order
of 10 ms. The value of resistance increase before breaking is about 10% for the time lag fuses
studied (Littelfuse type 218.800).
Lifetime is mainly detennined by the It value of Current pulses, the wave shape of current
pulses has a secondary influence on the lifetime of fuses, From the regression analysis, the lifetime
of fuses is found to decrease exponentially with the ft. The slope of the line (the fuse lifetime as 11
function of the It of the pulsed current) is from 7 to 20 for most miniature fuses. To improve the
lifetime offuses, the high steepness or slope is desired,
From comparisons oflifetime relationships for different fuses in Table 2.2, silver plated copper
is considered to be a good material for fuse elements. Withstand abilities for time lag fuses are
generally not so good as fast acting fi.lses on the basis of the relative ft value, which is
contradictory to common prOlctice.
Chapter 3 Lifetime Experiments with Long Current Pulses
Jr1 Chapter 2, lifetime studil;:s have been performed on (he bMis of experimental (lhSlTVil(inllS
when miniature ro.~e.~ nre suhjeeted (0 shor( current pulses. In norrmil ~~rvic~. fuses may abo
l;i1rry low currents with 11 long conducting timc either I,;ydic or conl'inuous. Fuses an: expected
not to operate also under (hese circumstances.
In si(ua(ions offrequent switching, fuses experience eyelic loading. In JI;C publication: 127
minia(ure fuse.~, endurance tests are specified to evaluate (hc quality of fu~es tn withsllInd IOllg
time cyclic currents. The pulse time is required to bl;; one hour, followed by a period (If 15
minutes withoul Current. This duty should be repeated 100 times.
Th~ question here is whether luses still fulfil their (asks ancr these I.~sts.rhcrcrore. (hI;
objective of this chapter is to evaluate fuse Ii/dimes for more extended 1,;1Irr(;n\ ~:yel~s and
amplitmks. This ch!lpter covers enduralKe studies for miniatun: h.lses during IOllg pulse lillie
current pulses and eontinuoll~ loading. On the basis or experimental observations, tht: TJlIrnher of
current pub:~ is relatcd with the pulse current and the on time, using shlti~(ical analytic mClhod~
bnscd on the Weibull distribution.
3.1 Experiments
3,1.1 Test objects
Commercial minia(ure tbses (l ,ittelfuse Series 21B.800) were ehosl;;n as test O\)jeels. '["he teehni~aJ
data have bt~en diSClIssed already ill Chapter 2.
3,1.2 Test method
To investigate th<.: deformation of ihse5 and monitor the long term /il(igu<;: proccss, experimcnts
wl:.n: perlCmned tor current pubes with different magnitll(ks and plllse times. Resistancl.: increase
has been noticl'Li as ,lJ\ indicator of flttigul;: [65 J for electrical interconnections. Therelhre, during
(he experiments, resistan ..~c was measured betwem current pulses by lIsing H)~ fl)\lr tenninal
method. Numbers of current pulses whioh l\lses withstood wel'l;: collected. The experimental sd-up
for this study is the same a~ shown in Fig. 2.5.
To get l~()mparabJe r'eslllts with endllnlflCe tests specified in lEe 127 minialllre fllses. the first
experimenl was performed for difkn:nl currents with the same on and off t.imes as staled in IU.:
127 (one houfot) and 15 minute~ oft}
Before the test ~larkd. initial voltages aeross the 111se-link werl.: m<;:asIlNd. ;\ testing current I
specified from 1.2*ln up to l.R*JIl flowed through the fuse-link tor a period I,,,, or l)[1e hOllr, wkre
I" was (he [(Ited Cllrfent of the rus~. One minute bcJ<m;: the end of the on time 1,,,,. \he voltage across
(he I\.lse-link was mcaslIn:d and stored in the comput.er. The ellrn:n( W,l$ then ~witchcd oif I~)r n
period t'!11 of 15 minutes.
To investigate thc inllul,;lIce of the current pub!; tim~ Il!m the second ~;r.:p~rimcnt was carried
out with a I,;hangcable pulse times I,,,, in range f!'Om 10 scconos (0 10 minl1tes.
28
29
Lifetime Experiments with Long Current Pulses
The third experiment was performed to examine whether the resistance would change due to
continuom d.c. current ( 1= 1.5 * I" ). The test lasted about 250 hours.
II
3.2 Results
3.2.1 Endurance
From the first experiment, resistance changes were obtained and found to increase with the
number of current pulses. Figure 3.1 shows typical results of resistance increase percentages for
eight fuses until all fuses interntpted, where ~ is the cold resistance. The test current was 1.5
time the rated current with t.~ = 1 hour and toff"" 15 minutes. This graph indicates that resistances
may increase up to 50% before fuse blowing.
For current pulses with 1.4 to 1.7 times the rated currtnt, the final resistance increase before
illse blowing is presented in Fig. 3.2, where ~ is the cold resistance. Above 1.5 times the rated
current, the resistance change decreases. Extrapolation of the results indicates that above 1.9
times the rated current, resistance increases do not occur before final fuse operation. This value
is in agreement with thc minimum fusing current according to characteristics irom the fuse
manufacturer. For currents smaller than 1.5 times the rated current, it seems that the resistance
increases slowly and tends to approach a constant value.
(R-Ro)/Ro
60 r·_·_···_-_·-
%
50 1.
401
30 1
20!
....1
200
400
600
800
Time [hour]
Figure 3.1 Resistance increase as a funotion of time
during current pulses for 8 fuses
with I ::0 1.5 In, ton ;;;; 1 hour, tDrr = 15 minutes
Chapter
30
'i
(R-Ro)/Ro %
70
601
8
i
50!
"
(\
,'\
\~
40:
I
I
301
'\
I
\
\~
201
10
°1
1.2
1.4
1.6
2
1.8
Illn
Figure 3.2 Final resistance increase in endurance tests
From the endurance experiments, for (;urrent·s with one hour on time and 15 minutes ofT time_
results arc summarised in Table }, I,
Table 3.1 Results from extended endurance tests
(In =
lIJ"
ROO rnA)
the minimum number
of CUlTcnt pul~es
from 20 fuses (5% value)
-
..-~------'-
1..')
91
Hi
19
L7
2
-
., ....... ,... ...... ,".I\
f.------...-.
~
_'M
1.8
I
3.2.2 Influence of the on time on lifetimes
From the second experiment, numbers of current pulses which fllses with.s.tood were obtained in
Table 3,2, The testing current I varied from 1.4 A to 1,7 A with the on lime Irlll from 1/6 to 10
minutes, 1,'(f from I to 5 minutes.
Aner fuses were subjected to long current pulses, resistance was found to increase, For
practical applications, it is also of importance to know whether this is (we fnr continuous
loading, Figure J ,J gives an impression of the gradual resist<lnce increase for a typical currenl of
1,5 times the rated current.
31
Lifetime Experiments with Long Current Pulses
Table 3.2 Number of current pulses fuses withstood
1
[A]
1.41
1.52
1.58
1.62
J.47
1.52
1.58
1.50
1.47
1.42
1.52
1.37
1.52
1.53
1.58
1.6J
1.72
1.47
to.
IOff
[min] [minJ
I
I
1
I
1
I
1
I
5
5
5
5
Number of Current Pulses
416
148
435
113
3
4
1
18
5
2
38
8
I
I
II
4
13
816
20
7
3
49
8
2
5
5
5
5
(
10
I
I
69
88
95
1
10
II
334
116
1
1
1
1
683
41
13
152
2
156
91
1/6
I
98
1
9
650
10
10
10
10
1/6
116
116
I
1
I
868
75
102
26
to
13
5
4
54
15
3
7
22
112
2
393
7
20
170
295
9
663
115
62
117
36
6
10
5
313
272
155
632
35 • .__ ._. __ .__ .. ,
63
16
4
ID
26
107
74
14
5
66
20
4
11
29
119
120
8
385
10
342
161
56
7
190
9
427
8
131
163
37
2
325
....~-;---
llO
94
15
6
80
20
6
15
34
137
9
368
12
114
117
19
6
109
26
7
18
34
155
2
410
8
739
910
174
45
8
221
181
23
328
/-.
-
J
4
1298 1455
24
lID
30
59
8
9
109
127
30
49
9
1
25
33
67
36
183 232
15
9
174 261
14
8
2013 1002
230 241
61
3
24
4
1769 6107
,:::.,
/
1-/····
/f;/· .~/ . - -. .
/
10
/.
/
/
f:J:;··i
.II ,._:::/E-./
" . { ' j : ? _.. j"
.
/ ....
j/ . .I:! 'Y' ___./'" . . . -
:~@~-~~- --- ----o
50
1DO
150
200
Time [hour 1
.,
250
Figure 3.3 Resistance increase at a continuous current 1.5 In for eight fuses
('hapla
32
3
3.3 Resistance changes
From t;xpl;;rirm:nts it C,H] he concluded that tor COr)tilWOllS loading as wt.:ll liS ~\Irl"l:!ll pulses.
incrcascs. For II typical Cur~ent of 1.5 times the ralt;d !;\Im:nl, cyclic l()aJin~s rC~\lll in
a highl::f value of the final reSiSHlI1Cl~ ini,;r~a~e about soo!., in avcragl;;. 1'"01" I;O!lllnuotls iO[ldings
with the ~amc current, tht~ llnal reshtancc increase is about 25'%. ()n the other hand. f\lsc~ may
allow a shorter scrvic~~ lime (about 200 hours) for contiuuom loading~. in C()Jllw~l In lhe time hr
cyclic loading~ (about 500 hours).
!'e~istance
[n lht; lEe rcconHnendations, it was suggested that. endurance wsls providd ,\ qualifleation
for fbses in the normal service. where both continuous loading lind eyel it loading arc involwd.
Howevcr. comparisons of bot.h situations show a discrepancy in resistancl.: incrl.:asl~ b~tween our
~xperimentol results and IRe recommendations. Al thh moment. no phy~i~~,tl explanation has
been found and further studies arc needed. It is theretore suggested lhal n)l)r~ cnnccrns should be
added in the TEe reeommmdatiollS for these aspects.
3.4 Lifetime relationships
Figure 3.4 and Fig. 3.5 show lifetime distribuliom on the Weihull paper for din~~l:nl
expl;;riml;;ntld I;ondit.iotls from Tabk 3.2.
99
<IJ
w
U
z
w
§
tE
C!
uJ
~
90
80
70
60
50
40
30
20
a
----:7'-----=''-''---...... ---.----
10
:::)
:;;;
:::J
b
<.J
~
100
10
NUMBER OF
CU~RENT
1000
PULSES
Figure 3.4 Distribution of number of current pulses fuses withstood
a : / = 1. 52, ton '" 1 minute. torr '" 1 minute
b . / = 1 52, ton'" 5 minutes, tolf "' 5 minutes
c: I .. 1.52, (,,' = 10 minutes, inff '" 1 minute
33
L{!etime ExperimenlS with Long Current Pulses
99
ill
C3
zw
=>
C'
w
f£
@
~~
90
BO
70
50
60
40
30
20
10
~
:::l
~
10
100
1000
10000
NUMBER OF CURREN, PULSES
Figure 3.5 Distribution of number of current pulses fuses withstood
tOr'l = 10 seconds, toff = 1 minute
a: 1= 1.72, b.' 1.61, C.' 1.58, d; 1.53, e: 1.47 A
It may be seen that in general the data agree reasonably well with a straight line 01) Weibull
paper. It is therefore concluded that the lifetime distribution obeys Weibull distribution. Another
feature is that for different current parameters the slopes of regression lines W) are
approximately the same.
In Chapter 2, it hus been demonstrated that for short current pulses the It value ofa current
pulse can be used as a parameter in the prediction of fuse lifetimes. However, for a long puls(:
time current, because much energy is transferred to end caps and surroundings, induced
deformation can not be expected to be simple expressions of the It value. Therefore alternatives
should be found.
Attempts in this chapter are to resolve the problem based on statistical approaches. To
comply this task, experimental data for lifetimes (numbers of current pulses which fuses
withstood) will be used to estimate the 5%, 95% values and the mean of fuse lifdimes for a
specific current pulse. Once these estimations are available, the effort is to define an expression
in general.
The visual examination (see Figs. 3.4 and 3.5) has shown that lifetimes obey the Weibull
distribution. Using lifetime data in Table 3.2, the maximum likelihood method is adopted to lind
the scale and shape parameters of the distribution. Results of the scale and shape parameters (A.
~) from estimations are summarised in Table 3.3.
Table 3.3 shows a number of experimentallitdimes and derived parameters for the Weibull
distribution. To enable a comparison of the different results, it is suggested to use regression
analysis on the basis of statistical results.
34
(JlllpIC!'
3
-_ ..., - - - - - -
Table 3_3 Parameter estimations according /0 TaNe 3.2
I
[AJ
torl
toft
[min]
[min]
mean
yv"
N
460
963
1.52
20
flO
Ug
1.7
17.4
1.62
1.7
22.4
5
!.4 !
1.47
1.52
1.'i1l
1.50
1.47
1.42
!
5
5
5
5
10
10
...
10
1.52
1---._-..._.
1.37 __ ... 10
....
",,_.,.
l.S2
10
.- ......
5
--- _...
5
5
'~r-··'
--
3.fI
71
19.7
0.6
3_8
1.5
13
29
131
7.9
54.7
2.8
177
1.53
116
108
1.58
1.61
1.72
If6
60
116
11
1.47
116
116
1466
JL~)QQL J 5
151\ - -" (),Oll _~J~
45_R
0.0(5) _._.I:L ___
g,l)
o. 17
~ .·1_.
2..1
129
O.OI~_ _.-.,-----... __ ., ... _-,.
""'"
42.4
8,9
,.... _-, .. ,.- ....32
O.O4.~
1.7
0.2]
1.5
--,." ..
0.071
IJ
2.1
S6
211
O.()O()R
3.0
g,g
15.7
0.1
.~·L
319
455
15 -" .....,
1688
24[;
135
O,()On
.".,.
726
151
60
4.8
3244
1.2
914
II
"A
o.()]
7.9
_",.1,]
95'%
___._
.......4.)
,---
0, II
2.1
_._-
1.:'\
0,0012
..... ,. __.
_ _ - , ..... 1,.
0.0059
0_015
-.
2,~____
1.6
-'-.,_.,
9.4
0_18
2.0
6174
O.(J()()2
2.1
","
-,.
For different current parameters, a comparable cOnstont slope W) has hl~l,;n li)\lll(! in the
Weihull distribution riM (~ee Figs. 3.4 ami 3,5), Thet'efore, the slope B m;.ly hc assumed to be
i[)dependent of the on time 1111 , and the off timc {<>If at a rderence current or vin~ \ll:!r~a. ()n the
other hand. the sc,lle pat'ameter A. im:rt;,lses a~ the /1 valuc 0[" puhed cut'rent inneasl;s Ii}!' the.
S,IIllC nn time I,,,,. This suggests that the scale parameter' A depends on lht;! Cllrrcnt I and Ihc on
time {,,,,, Bceausl;; ["or 1"/ . . () there i~ no damage (() the ruse ckTlll;:n(., a t.rivial expressioll I(lr A is
n;(;ornmendcd as
where x > O. y ::. 0, k > () and ao >0, The physical meaning ("If this exprl~ssi(ln is that for any
cuneot pulses, fuses hav/; intltliw lifetimes a~ long a~ either the ~:urn:nl I or the on tim~~ ',,11 is
zero_
First, a reference mean valut: is taken as E[1:o(J, 1,,,,).1 fOl' A(I_ According 10 the defInition of
meiln value or the distribution, the ratio
the expected mean val\le (N ,. Li t{ 1",,)\) (()r a
specifk eurrmt pulse tn the rcference mean value E[1:o(/.I,,,,)[ i~ givcn hy
lh~
or
~1.:_(.~~2]
Flt"({,/,,,,}[
r
Lifttime E"'(periments with Long Current Pulses
It follows that the number of Current pulses N
35
COIn
be approximated by
(3.1 )
Introducing regression analysis into this expression, coei1'icicnts in Rq. 3.1 are itlLmd to be
k~ 2A5,A~
x = II,y= 0.5,
=9
The values of k and A" corresponding to the 90% confidence level are estimated to be
k"'in =
2.4, k",,,.,." 2.58, A".
n,in =
R.8, All. ",nx
=
9.19
Comparisons of experimental observations and results of Eg. 3.1 are presented in Fig. 3.6.
10
4
-~
..
i
I
I
CJ
01)
~ 10
3
<)
~
0.
C
I)
ill
t::
2
~10
0
0
0
~
t
..c
0
u
§ 10
0
1
(9
z
0
10°
2
10
0
0
"--'
..
0
I I
10
3
11\'n 0.5
Figure 3.6 Number of current pulses as a function of a combined parameter [11 ton 0. 5
Because this relationship is derived irom the experiments for long time current pulses,
therefore predictions from the graph should provide a guidance for practical situations for the on
times above 10 seconds. Using Eq. 3.1. the number of current pulses fuses withstood telr
different current pulses with the on time tV" = 1 hour is predicted. Figure 3.7 shows comparisons
of predictions with observations irom Table 3.1. Mark "x" indicates observations corresponding
to 5% value (Table 3.t), Mark "0" indicates observations for 1.4 I" and 1.5 1" . 'fhree Curves
indicate results for 5% values, 95% values and the mean respectively.
However it $hould be kept in mind that predictions obtained are based on two conditions; lhl.:
constant slope Or shape parameter ~ and the scale parameter J". can be expressed as a power
function of rto/' The first condition is supported by experimental results which are shown in
Figs. 3.4 and 3.5. The second condition is further derived from Figs. 3.4 and 3.5. Because a
comparable Constant slope ~ in Table 3.3 (in accordance with Wei bull plots) has been
demonstrated for high currents above 1.5 In' For the current less than 1.5 I" , the slope tends I()
increase (see Table 3.3). This result provides the support for the resistance increase percentages.
where the increase tendency has been found to saturate. Nevertheless, it may be clearly seen in
- - - - _........." .. _- - - - - - - - - this graph that regression analysis on the hasis of litCtime observal iOIlS rill' (1)(.: Oil lillle 1m. frolll
10 seconds In 10 minutes may be used 10 prcdi.,;1 lif~lin1~S I()t' mLlch I()llg plll:;l~ limes (;lhOIII I
hour).
r--··if]
Q}
fi)
10
5
4
'3
10
D;=: 3
.-----, "'-:z-_____.
--------'"i.
------'"
"'---.-
~,--..-
........
2
(J
'0 10
<i.i
:z
10
10
'---.'*-.:. .--..::::::>.-.._-. ................. ."..
'1
E
10
::,:
-...-'-':'.~".-....-
-......
... -....
0.9
-----.
----.---..
.-... ~~--....
0
-1
._,
~"
~ 10
::J
r" -- -'---T--'-'---"
n
"--..
.-.-...... /
-~-.-.--.
.J.
1
1.1
_ _-,-I_ _ _'--,-1___ .__ .... _ .1
1.2
Current
1.3
1.4
1.5
[AJ
Figure 3_7 Comparisons of predictions with obsetvations relevant to endumnce
Mark "x". obsetved 5% values from Table 3.1
Mark "0" : observations for 1.4 In and 1. 51/1
3.5 Conclusions
Frol11 experimental studies. resistance i~ (i.)lmd to increase after lbses are subjected 10 long lime
current PU]sI;;S Or continuolls loading. Observation shows that continuous loadll1gs kat! t(l slnall
resistance increase compared with eyclic loading hefore fuse blowing. The r~~sjstmH;~ change
bctore fuse breaking decreases as the magnitude Df currents increases ilild knds to approach a
constant value bdow 1.4 limes the rated current for cyclic ]ooding.
This work has pmposcd a method for combining statistical methods and rcgr\;~~i()n analysis
on the basis of ohscrvations. Using liletime ohservations of diJT~[I:rll <Hi ,lilt! ,liT times frolll 10
seconds to 10 lTlinHlt!~. estimations of lifetimes have heen carried out. Bas~~d on lh~~c I·c.sults
~omparison of predictions and observations for the on time I hnl1r and off time 15 minuks i\r'~
made and found (0 he in rcasonabk good a.greement. This means thaI lh~ I inl~ required to
eV!.lluatc annoying cndllmn~~ lest.~ can be greatly reduced hased on s~'vcnll .~horl lime
cxrt.:rim~r1ls.
Chapter 4 Experiments for Notched Strip Fuses
This chapter describes attempts to observe thermal buckling and deformation of notched fuse
elements. Using high speed photography, motion orthe element was observed and displacemems
wcre mcasured during current pulses. After fuses were su~iected to Current pulses. the surface of
the filse elements was examined by using electron st;anning and optic microscopes.
Conccrning previous investigations, ageing related with notched 1i.lse dements may be
roughly divided into four types: unreliable contacts [33] due to contact resistance increase;
diffusion of metal interactions [13, ]4]; thermal fatigue induced by temperature variations [35]
(strain cycling) and electromagnetic reaction.
The prime objective of this chapter is to provide quantitative experimental observations for
understanding physical phenomena rdated with lifetime reduction of fuses for silver notched
strip elements. Thermal fatigue induced by short current pulses is assumed to be the only ageing
mechanism. Three series experiments are intended to be performed: withstand ability of short
current pulses, displacement measurements by using high speed photography and ddonnation
studies by applying a scanning electron microscope and an optical microscope.
4.1 Ex.perimental set-up
4.1.1 Circuit scheme
To produce a pulsed current, a RLC circuit with ten parallel capacitor branches was realised
[66]. Figure 4.1 shows the principle of the lest circuit. Basically a capacitor and a thyristor
formed a branch. and an inductance was used in series with a lest objec!. Firs! capacitors were
charged by connecting them to a d.c. supply. After isolating the d.c. source, capacitors wert then
discharged by triggering thyristors, Consequently a Current pulse was produced.
k •
D1
L
.
Fuse
u
R
Uc
C2
C1D
Shunt
RI,I
Figure 4.1 Electrical circuit for producing the pulsed current
L.- 78. 7 ~lH, C.- 114 +30/-10% mF, Shunt.- 60mVl100A, T.- T 24 N
37
Triggering sig[wb or 120 mA WC[C individually exerted on 10 thyristors 10 prO\id~ rdi,lhk
(riggering and to prevent damage of thyristors. The separate triggering l;irt.:lIil 151 I is shown in
Fig.. 4.2.
-~120
a10
Figure 4.2 Triggering circuit
The test current irom the circuit was of a half sinusoidal wave form, which can be
(;hamc.terised hy parameters as /1, I" ' I,," (on lime) and {<'Ii (orr lime). The on time run is the
,;ondu,;hng lime lor (he pulscd Current if is (he integral or lil~ Curr~n( squ<ltC o\'~~r (tIC 011 tim\;. II'
is the peak value of the pulsed curt'en!. The off time l"lf is the time between two successive
pulsed currents.
4.1.2 Peak current and J2 t valm~~
With the circlIit shown in I'ig. 4.1, a curt'ent peak value up to 2.11 k/\ can be produced, dependent
on the charging voltagt~ or capacitors, The shortest durillion between IWi") pulsed cllrrt!nh wa~
chosen tn he abnut 2 minutes, the on time for each currcnt pulse can be chosen to be 5 ms or 9
InS,
Figure 4.3 shows measured peak currents and if values as f\lnctions of Ilw dwrging vol(ilgC
or i,;uplli,;iIDrS, Two curves indicul~ (he peak CUrrent and J2 1 v,llu~ t'espectivcly 1\)1' pllises with a
duration 01'9 ms.
E:x:periments.!or Notched Strip FuSe.l·
39
12t
Peak current Ip [AJ
2500
[A 2s]
.----~--~---r----_.__~-__,
25000
2000
20000
1500
15000
1000
10000
500
5000
M
Charging voltage of capacitors
Figure 4.3 Relationships betvveen peak current, lit and
charging voltage of capacitors
4.1.3 Tcst objects
Commercial fuses (160 A and 660 V) for the semiconductor protection were chosen as test
objects, Figure 4.4 shows a typical clement geometry, whe,e dimensions are given in
millimetres. The thickness was 130 !-lm, Elements of three typical shapes ("type A", "type C' and
"type D") shown in Figs. 4.5, 4.6 and 4.7 were used in the Jifetime tests,
8
.,., ''\ I' •• _-, ••..•.•• \,
n
u
()
(')
Ii
()
(')
\)
U
()
0
n
0
0
I)
()
(")
..•... "._. __ -'
~
..•••
..".~
.r" ......._ .. ,\
o
o
n
n
o
u
0
U
.,/ \
I"~
()
()
o
o
(.1
I" - •
()
(l
0
()
()
()
U
n
C)
U
.. , .__ ,. ___ . .! .. ~_., _. __ ., __ I \
_.o"() .. 'i--"'r"
I
(\.
ii'
()
I
()
;' I
(.\
:
I
I
g... ··1··· t·· J.~.
o
u
(I
1.66
1.5
I
I
' 18
.. ~ .... L
21.5
Figura 4.4 Element geometry for type A, C, D and E
40
( NIPI(!1"
~Ls-­
~' L· .....--
4
43
Figure 4.5 Type A
32=----_..:;.!
43
Figure 4.6 Type C
~
!T(--
~
.:: _._. __ .......4;.1 ..
Figure 4.7 Type 0
Because the ckmcnt in commercial fuses for ratings of 160 ;\ and MO V has nvc rows of
notches (see hg. 4.4). it h dift1cult and time consuming to determine the displacemcnt for ea~h
row at d!Jfercnt currents. For this reason. straight rust.: elt:ments with five r'OWS (/Y[JI' F) and one
row (type F) oj" notches were proposed. Figure 4.8 shows the dimensions of fuse clement "(we
P' composed of only One row of notches in the middlc of the clement. The overall Sl,-C waS the
same as the dements llsed in commercial products.
,•
1.66
1.5
18
27.5
Figure 4.8 Notched element "type F" for displacement measurements
Experimel1lsfor Notched /:;trip Fuses
41
--~----------------------------------------
4.2 Lifetime experiments with short current pulses
Experimems for lifetimes were perf{)rn1Cd in Siba GmhH Germany for three types of commen:ial
fuses: T.)Jpe A, C and D (see Figs, 4,5,4,6 and 4.7). The test (;irl~uit was given in Figs. 4.1 and
4.2. Roth sand and bound sand were used as arc extinction materials in the ceramic body of
fuses. The on time t"" was chosen to be 5 ms ar 10 ms.
4.2.1 Results of lifetimes
In experiments, Current pulses wert applied to tcst objects until fuses blown. The number of
current pulses which fuses withstand were obtained and summarised in Tables 4.1. 4.2 and 4.3.
Table 4.1 Testing results of lifetime for type A fuse elements (t¢n'" 10 ms)
Filler type
It
2
As
T atal samples
Sand
Sand
15800
14200
8
19
26,29,54,86,
72, 158, 182, 195, 273, 276, 323, 345,
103, 187, 190, 372,383,508,621,741,939,969, 1161,
326
1232
Table 4.2 Testing results of lifetime for type C fuse elements
Filler
Sand
Boun
d
Sand
Sand
Sand
80und
Bound
It Als
10735
10961
14280
15082
15400
15082
15400
tQnms
5
5
10
10
10
10
10
Samples
4
4
5
14
14
4
6
76
299
1027
1173
1328
1525
1755
1811
1754
1865
2732
2863
3213
305,545, 93,190,
685,741, 223,457,
753, 795, 482,503,
951,1060, 624,625,
1197,
737,860,
861,876,
1284,
1374,
1131,
1399,
1799
1530,
1901
2249
>5000
>5000
>5000
2794
4288
>5000
>5000
>5000
>5000
Table 4.3 Testing results of lifetime for type 0 fuse elements
... __..... , ... ,...
"
Filler
/, A2~
....... ,..............
Sand
Sand
Bound
Ion:)
- ... .... .... _--
---_.. "
15082
10961
"
Sand
BOllnd
5
Samples
15400
I:')mu
."'. - - .. .. .
,
:;
----_._-
4
4
4liO
200
22')
701
23
1161
21M
Bound
..,.~'.'--.-'--
,
rem rn.s
- - - - . - - '--'r'
I')
6
...... _"....,,,
24311,
2722,
~
441O,
>5000
:;. :')000
,""
10
10
10
.1.1','·'·'---'
1934,
>5000
._._-_ ...., .
10
1.~4()0
,
- ._-
1169,
1502,
1501l,
1839,
22()(),
321\ 1.
4
124l\,
1649,
2261.
101\2
1231'!
2.lI
4Fl
1843
1927
7h7
~~6
4.\60
3424,
3281,
:Ibn.
4213, >5000,
>5000,>5000
4.2.2 Lifetime distribution lmd prediction
B~',w.s<;! so Ill,lny parameters influence the lildilTI/;;s of fuses (see '["ahles 4.1-4.3), tirs(, slalisli~:al
approaches are llsed lU lind the JiJl:tilne (listrihution. Figure 4.9 ~hows lifc1ilm: (iistrihllli()!ls on
tile Weihull paper [63:! [()r a typit:al fuse t:kmenl ('yp~~ C) for different /, values, exp~Tinml!,d
results in Table 4.2 wl.:re used. It may be seen that in gcn(;rallht; data ar!.: well Jilled with straight
Jines 1.11\ the Weibull prohability plot. It is lht:rtfore concluded thill the lifetime distribution obeys
t.he Wcibul! distribution.
Accumulated Frequencies
99
90
i~
/2t::o 15400
sand
12 , '" 1421\()
sand
30
20
10
1 ..l...--,...-.,......,.L,-,..,..,.,..---~f--,.......,---,-,...,..rl.-----,----,r--""T< "T~r'r"
10
100
1000
10000
Number Of Pulsed Currents
Figure 4.9 Lifetime distributions on the Weibull probability plo/
2
for type C element at different 1 t values
Experimenls/or Nolchf!J Sirip
FZlse.~
43
For di ffercnt typcs of fuse dements. the slope parameter of the Wt:ibull distribution an: on~n
found to vary with the if value of current pulses. However, it also has been noticed that tor
certain experiments, this slope keeps the same, for example, results in Table 4.1. In attempting to
present a simple relationship between lifetime and J t value. the slope is assumed to be a
constant. From this point, the ratio of mean lifetimes E['t(lt)1 is given by
El,t (( t)]
_
E[t (/"' til)] -
fell
( 4.1 )
').(1-' t)
where ftl) is the reference it value and 1.0 is the scale parameter of the Weibull di~tt'ihllti()n at
ilo . Further the relationship is expre~~ed as
( 4.2 )
where
No:
N;
the mcan value of lifetime at the reference il value
the mean value of Hfetime (N '" E[t(f't)] )
Because of no damage to the fuse element tor
be
Ie ....
all
it = O. a trivial expression tor A is suggested to
(I) t )<
(
4.} )
This implies that for il '" 0, fuses should have infinite lifetimes. It follows that the lifetime N
can be approximated by
( 4.4 )
Eq. 4.4 provides a linear extrapolation for the lifetime determinations on the douhle
logarithmic scale. However, it should be kept in mind that the ,esult here is obtained based on
the assumption that the constant slope or shape parameter and the scale parameter can be
expressed as a power function of f t value.
4-2.3 Comparisons with literature contributions
Using different expressions of the scale parameter A leads to the different lifetime relationships:
( I)
assuming A is dependent on the temperature rise 8 ofthe fuse element
( 4.5 )
(2) assuming A is dependent on the temperature rise 8 and the average temperature e~" at
the hottest spot of the fuse element
)..=(10(88,:,)'
( 4.6 )
where aI), x and k arc cOnstants.
From Eq. 4.5 the lifetime expression similar to that proposed by Arai [35] can be achieved,
while from Eq. 4.6 the lifetime expression similar to that suggested by Wilkins 1671 can be
obtained.
44
('Iwplel"
-I
4.3 Motion of notched elements
To under~tand physical phenomena or lifetimc consumption related with mot inn or clcments,
quantitalive observations of motion are to he provided from experirn~Jlt~,
4.3, I S~r- .. p for measuring displacements
Figure 4.10 shows an illu~tration of the experimental set-up j()r rIll:a~uring the displaccment
dllring a current pub/,;, Fuse elements arc normally surrounded by sand and nnt visible to the
oLLtside. To eonfil'm whether the fuse element moves Or not when a current is exerted. a dummy
rust: was used for observations. In the dummy fusc, one cdge of the fuse elem<.:l\t !;Iced a glass
plate, the disti1nce between the plate and the ekrnent was small~r than lhl~ grain silT or sand so
that the element can be easily monitored, In stich H way, the inJlucTI/,;c oUhe plale on the possible
clement mot.ion can be neglected, Sand p<lcking density l~)r ru,~l,;s is ~')Wll1illed to h;;
approximately the same as fhr commcrcial products. 1\ high ;.;peed camera was I()cated in lhmt of
Ih~ l\lse, A nash light was positioned al a angle of" about 45 0 bdwcen the plale. "ro Jl:lenninl: the
exact expo,mre time, a light. detector was installed to pick up the light signal. A four charmd
Jigital oscilloscope was used to rccord fuse current, voltage, an opening .~ignal from t.he camera
shutler and a signal related with the exposure period due (0 ~~ nash light,
Light
detector
jI
Glass plate
Lens
~.
!
Ceramic body
J
Element
Flash
,
Sand
tube
Film
Figure 4.10 Experimental set-up for measuring displacements
4.3.2 Results
Typical traces recorded by a four ch,lnnel digital oscilloscope are dhplnyed 11\ Fig. 4.1 L the
current was pl'Oduced by charging capacitors to about 70 volts. During a current pulsc. the
corresponding voltage across the fuse was mt~asured, Tht; closing conl<ld of the high spt;ed
cHrnenl indicated th~ shutter release, produced an action signal abo\lt 3 ms bef'l)1'l! cur'tent p\ll~~s
were triggel'cd and this shutter releasing signal was sent to the oscilloscope. An optil:al sensor
was installed 10 pick up thl,; light signal which indicated 111m exposure period. TIi<.: /,;XT)(l.sUtt; took
place about 900 )lS he fore electric current flowed.
Experiments plr No[,·hl/.J Strip Fuses
45
I (kA]. iJ [V]
5~--~~--~----~
____
~
____
~
Shutter, FI~SM
____
___
~
~~
4
0\ ",,--2
F la s h
: \
i 'y' ..... \" .. -
.,.
I/·,··<·~I"
_ ~,-L
o
'
u J \ \ __ .. __."._ ..~.. _._--'-_--L-
'10~--~5~---710~--~15~--~4~O~--~2~5~--~3~O----~35
Time
fl'n$]
Figure 4.11 Typical oscilloscope traces for measuring displacements
J .' current; U .' voltage
Displacements at the element notch were measured for different It values of pulsed currents.
The element thickness 135 I-illl was taken as the measuring reference, measuring accuracy was
within ±S J,tm. Figure 4.12 shows typical displacements of the element at two locations (point I
at the notch edge and pOint 2 at a distance of I mm along the strip) together with the pulsed
current against time.
2000
Current [AJ
I
/
2
1
-----!
1
Displacement [).Iml
100
1500
75
1000
50
sao
25
0
0
0
~
-500
0
5
10
0
20
15
Time [ms)
25
30
-25
Figure 4.12 Measured dynamical displacement induced by pulsed current
.--. : displacement at location 1,' 0--0: displacement at location 2
46
As shown in Fig. 4.12, the clement starled to move in about 2 111,. (IlkI' tll,' UI1Tl'll1 w"s
cxort(;d. Slightly alh:r the (.;urrent pt:<lk, 11le clemenl illTlvcd al lhe maximuill dispJa~'CIllCllt ill
about 7 ms aitcr currcnt conducting. As the current deereascd. thl,; dement Ill()\',~d !!r,ld\J"lly
Ie,,:;t l'i In:; ill this
bal,;kwarJs, hiler the curr(.;nt reacl)(.;d /,cw, (he elenH;:nl sllll nct:ds time
casc) tn move hack to its original position.
«It
In addition to thes(.; displlli.;r!l1c!lt nwa~urements. (wo s(ands(ill poinls wen: 1(II!Ild tn hc
spa(;l,;d about 5 mm across thl.: nu(~11 Cor corrent pulses wit.h di ffel'ent. 1", valuc::. For lhl' ~traight
lhsc eh;!III/:rl(S with live rows of notches (.~ee Fig. 4.4), high order huckling shapes ]wve bel'lI
observed. Significant displac.cl11ents w(.;re tktcctc.d at one or more I)o(ch 1(1~::JiiollS h,,'
quantitativI.: analysis. mOl"(; c)(pcrirm~nts an~ ilt:.eded,
4.3.3 Discllssion
]"]H;;rrrwi cxpansiuIJ i.s propor(ion~Jl to lhe temrerature t'ise, tllus the eomprc.ssl\,(: forcl' dm, ((l
expansion in the clement increases with tl.:mpcraturc, I j" this c(lmp1"l;ssiv~: 1(1I"I;l.: t'xl;l.:eds " cCl'laln
limit motion
the ekment. St.ill'h. This i~ ~imilar to the proee~;s in miniature ruses to he
described in Chapter 7.
or
The total thermal strain induced is also prnportioflill to (emperal\!re rise, so In prllKiplc, the
nHlxinlllnl displacement as i1 function of time ~hould have 11 relation with the temperature Imu;,
Supposing that th~ maXim\lfn dlspl(lcement i~ corresponding to the maximum tctnpl~rature ri~e
lh~ element notch, then tile maximum temperature of the notch may bt, t~)(pJ.;(;t(~d at .lh,l\ll 7 Ills
aftcr c.urrent conducting according to Fig. 4,12. Btcausf.: tilt: displ,wement at 11I~ nlicldk ilf the
notch can not be measured dirc<.;(ly. thc dispJa.;ement al the locat.ion 1 indicated in Fig.. 4.12 t,an
providc il rough ilf\pwxirnation of the maximum displacement.
or
For l,ompact sand, elasticity may be assUlm:d. DII~ing (.he lIIolinn (11' Ihe denncnt. Silild is
cOInprt:ssl.!d,
pMI nr the energy is stored in sand. The compressive rore~' in the eklll(;I)(
detTeast's with the temperaturJ.;, In sm:h H ~ituation, sand acts as a compl'cssed spring due to the
movemcnt of the rllsc element. When the temperature 01" th~~ delll(:lIl is hl,!low tht; valilc
cOITl.:sponding to th(; ·cornprJ.;ssiv(.; ror.;e of Sand (as a spring), sand pushes the ckmcnt
hackwards. This prohahly explains why after current zero the clement slightly ost:illlllc~ t sl;\~ Fig.
4.12). only a l"ter a rather lonp. time, thc dement goes hack to ih original pojt ion
,I
BecausJ.: oj" saml g.rains. ont might also expect the eienlCtll. to move among grains, however.
sud! a motion requircs very high force in t.he axial direction. For the eommonl) llsed ,and sizJ.:~
(s~weri11 hundred micl'Ometers in diameter), this condition can not he Il!liilkd, This is c(Jniitllld
hy observations where the displacement prolilc has bt:en found r<\ther Sllw()th all'ng tile clement.
On the basi~ of obaervatio!lS in Section 4.3.1, the integral 0(" current square uwl the
corresponding timo;: bJ.:i(lre the motion started can be dciinJ.:d as special paralTlctt'r~ ~i,nil;lr III Ihe
dei1nit.ions of prearcing time and 1\ which are nott:d ;Is 1\, ,ljHI '" rc~peetivdy. From
ml.:aSllrl;lTIl.:nt~ iix dii"1i!rent /1 values of current pulses, th(;sc r)(lra!l)l;t~:rs ;!I li1l' 1I1oli(}l1 st:II'ting
moment can also be determined as ruodioTlS oj' I.he 1", valuc of puis cd currents
Result.s related with these parameters arc given in Figs, 4, 13 ~lI)d 4.14: as Ihe r', value or
current pulsJ.:s inerl.:asl.:s. the time I()r motion to begin decreases. This leads to a reduction 01" (il~~
It value for the motion sl.arting. For the /1 value below 3 kA 2s (th~: pt:i!k L;um:l1( ahOllt XOO A),
tho movement will not start fi.)!" the ob.ied undcr discussion. Because the maximum 1'1 value III
47
/:'xperimentsfor Notched Strip Fuses
rt
Fig. 4.14 is near the melting
for thi~ element type, the maximum displacement lor the tt5lr.:d
element is limited within about I 00 ~lm (sec Fig. 4.14). This value is in the order of the element
thickness (130 ).1m).
tb [ms]. I<t [kA~sl
7 r-------~----~-------.-'-~'-'
6
5
4
3
2
°0~----~5~----~1~0------~1~5------~20
H
[kA 2 sj
Figure 4.13 Motion starting time tb and starling Iltb against /2t of current pulses
100
90
Displacement [~ml
r-~--~--~~--~--~~--~-.
80
70
60
50
40
30
20
10
a0
2
8
I~t
10 12
(kNs]
14
16
18
Figure 4.14 Measured maximum displacements as a function of
the It value of current pulses at the location 1 indicated in Fig. 4.12
4.4 Minimum melting
It value
it
As it has been introduced in Chapter t that the usc of the minimum melting
value can avoid
unexpected interruptions in service. In addition, this criteria will be used in the lifetime
4fl
('IIU/I/("/"
. _-------------------------
-I
estimation in Chapter 9_ This section describes Cm)r!.s lor (kt~rl11ining the minimum nK'lting (/
vJlues and prl:sents eXlxTimcntal results,
I.~xperirnental set-up tkscribed in Section 4_1 was used to dckrminc the minimuill / I \alm:~
the tWO types ("(vpe r sce hg" 4,2 and "type £") of <::!cnlellts, hgun,; 4,1) ~lio\V~ Im:i~~lll'!Cd
results of the melting /1 values tor two types of clements_
f()I'
12[
[kA 2s]
18
- ----------------.,--- -.----.-- -.-
17
16
15
14
o
o
13
12
11
(1
10
1,5
2_5
2
Peak current
[kAJ
Figure 4.15 Determination of the minimum melling
• _ Melting 12t values type C
ff vaiwi
2
0 _ Melting 1 t values type F
!n this gr'aph, mark "~,, iHid mark "0" depict the mciting 1"1 values corn:spondillg to dil"krcllt
peak currents (or melting times)_ As the peak current increases above 2_1 kA, wrnmerrwl I"uses
wil! blow_ The melting time decrcases with the p<::ak (;urrCnt.. hl)" ckm(..:r\ls with one row of
not dies, similar results wcn: obtaiJlt;d, H is ti)erel(xe eonl1rmcd the minimul11l11clting /1 valuc is
,Ihnut !7 kA 2S (8':1;' I'ig, 4_ 15)_
4.5 Microscopic study of deformation
AileI' fuses wel'e suhmitted to current pulses, notches wcre exarnincd hy (J ~,:mlllil1!; ~kell'oll
rnino~l:op(; and an opti(;ul rnicms(,:OrH~- This section presents dcf<:mnation studie:; for eieml.:lIls ill
commercial fuses C"()ifJi:" 1:":' and ""tFpe C' ) with ratings of 160 A ,111(11)60 V_
4_5.1 Microscope vicw
tt
1
Aller 100 pulscd currents with
value 01" 14,7 kA s, 1hc fuse elemcnt was taken ()Ill from the
ceramic hody and put undcr the s(;(Jrlning electron mkroseopc_ Typical vicw~ of till' llC\-V fuse
eiel1ll.:nt and thl.: clement allcr tcst iln;! given in Fig~_ 4_16 and 4_17. wherc 150 Ilm[lliiica(J()n \'IUS
uSl:d,
Experiments/or .Yotched Strip Fuses
49
Figure 4.16 SEM photo of a new element notch (type E)
Figure 4.17 SEM photo of an element notch after tests (type E)
From Fig. 4.16 it can be seen that scratches exist even for new fuse elements. After fuses are
subjected to current pulses, plastic deformation is situated in the notch region and the surface
becomes rough (see Fig. 4.17). The damage can be characterised by a length parameter d shown
in Fig. 4. 17 (about 0.16 mm).
50
4.5.2 Damage length distribution
h)t 22 ~alllpies "Iyp(! C", the damage length of the middle row notches wa~ illc,lsllred by an
optical microscope. The damage length d is described with thc Weibull diatrihutioll. its tkllsily
rll!\~t illJl./(d) ( d> () ) is (,';xpr~ssed as
( 4,7 )
I;igllt'e 4.1 ~ presents experimental results of the damage lengt.h with calculated vailles Il)r the
density fi..1I1etioll of the Wcibutl distribution (the scale parameter Ie ,= 1.38. the shapl' parmnctlT I~
.\.7). The Illt:an damage length is e~timated to be (U mm with tht; I;(mf)(lence 11l1L:rv,1i WI, 1·0.1
at I ()<% eont1dence level.
f(d)
4.5 ...-......-------.~---~·--. - .. ·····~ .. ~-- .. ·-·. ·--· ..
3.5'
3
2.5 .
2
1.5
0.5
0.5
Damage length d
1
1.5
[mm]
Figure 4.18 The density function of the damage length (type C)
Bar . observations;
Gwve : estimation
On the hasis of Figa, 4,17 and 4,18, it is clear that the damage length increases a Ikr ruses arc
subjl.:c(l.:d to l:urrent pulses, lhis suggests resistance change or fi.lses during their I i Ii: I ](I\\'n','t,
prior to eus<: breaking vet'y small increase of resistancc has bel,;H tkl<:d<:d (I) h,: witllin the
t'e~ist01nce spread of' ncw products. It is therd'orc (;onduded (il,lt 1'I.~si~tancc mca,uremcl1ts during
thl,; service 01" sl,;l11icondu(;lOr prote(;tion fuses CJll n()t indicatc thc lifctime cOllsulllptioll hl.:!()rt~
I"use br<:aking,
Experimellt.l"/iJr
N()tch~d
Strip Fuses
51
4.6 Conclusions
From the presl:nt studil:s, following main points arc concluded:
( I)
The number of current pulses which fuses withstand is described with the Wei bull
distribution; it is also approximated as a lin~ar function of 1"t value on the douhle
logarithmic scale.
( 2)
As fuses with sand fillers arc subjected to current pulses, displacements of the fuse
dements may take place during the fuse clement heating up.
( 3)
The maximum displacement of tested elements has been found to increase with thc Jll
value of current pulses. However, experiments show that the maximum value is limited
within IOOj.tm (in the order of the element thickness and notch width).
( 4)
The minimum melting it value of the tested objects has been found to be 17 kA 1S,
( 5)
Afkr flow of pulsed currents, plastic deformation is accumulated in the notch region.
Scanning electron microscope pictures show that surface of the fuse element becomes
rough as compared with new fuse clements, The damage length increases with the number
of current pulses,
(6)
Existing methods for resistance measurements can not provide replacement information
for semiconductor protection fuses in service.
Part III
Thermal Modelling
Chapter 5 Nonlinear Thermal Modelling for Miniature Fuses
This chapter presents an electrical thermal analogue method for the heat transfer probltm~ in
miniature fuses, As in the foregoing, it has bem stated that /( is a dominant hctm fix fuse
ageing, therefore the related temperature change i~. Numerical solutions oj" temperature
distributions of the fuse element are found by solving the equivalcnt electrical network rclation~,
Heat conduction, convection and radiation are considered for the ruse element. Non·linear
behaviour related with material propertie~ and heat convection are introduced, Thl:: thermal
analysis is considered as the basis to enahle eycl ie Wess determinations which on their tUl'll are
related directly to fuse ageing,
Because temperature values of thin fuse wire elements during the normal load afe cxtr~illdy
difficult to meaSUfI:. kmperature changes should he calculated, During the la~t 20 years, several
calculating methods have been proposed [6. 1,8,9, 10, 11, 12]. It has been demonstrated that the
thermal problem can be modelled by its electrical equivalent [,11]. Among many advantages,
components in the networks have clear physical meaning. The convergence of numerical
solutions is guaranteed [12] because of the existence of real components and their physical
behaviour, Linear or constant material properties are normally used. effects of end caps arc otten
omitted. For miniature fuses, a special request should be fulfilled tor sOlving non-lin car
problems due to element materials and heat convcction [25, 52].
To fulfil the task of simulating the temperature variations due to electric currents, in this
chapter a thermal model will be developed on the basis of a thermal and electrical analogue
~cheme. It starts from the description of physical models according tD the thelTl1al process.
Afterwards corresponding networks arc described. A software package used for the electronic
circuit analysis, is chosen to simulate netwOfks hecause of its possibility to model components
with lookup tables. In the simulation, heat conduction and storage within the end cap are
considered. In addition, non-linear behaviour related with material properties and heat
convection arc used.
5.1 Thermal models
To bl~ general, commercial mll1lature fuses with straight fuse wires were chosen as studying
objects, The wire was positioned along the middle axis of a glass tuhe. To describe the thermal
process of fuse wires due to electric currents, the fuse wire was divided into several axial segments
between end caps. The diameters of the wire elements are 50 ).1m (nickel wire element) and 103 pm
(silver clad wire clement). The number of segments n can he arbitrary. In the thermal modelling,
the following temperature can be distinguished: Til' (wire temperature). T",g (temperature inside the
glass tube) and T. .. (air temperature outside the glass tube). The temperature at the same axial
position z inside the wire element was assumed to be the same because tht: heat translCr in (hI.:
clement i~ much better than in air. Figure 5.1 shows geometry notations.
53
54
X i
j
\
._.
( 'h(Jp!,,/"
.5
. . _......... _ " ......_.,_J\ ..... " "'"".,,,._-
Gl~ss
tube
1.5 mm
2.25 mm
I'~ I'll ".
_. End (;ap
.
( r" ,= 2.6 mill
i',
1~_S_.O_ld_er____________________________
o
---
~Ekm."
L___ ._ . __ ..
L = (7.5 mm
F;gure 5.1 Geometry notations of a miniature fuse
Basic thenmtl analysis used in the following can be jound ~n litemtl1re loX. 69, 70]. hlr heat
transfer due to the forced coovection in the tube, the natural convection was assumed.
Energy input
The Joule heating due to electric current i(t) within each segment obqs
P=i1(r\pLl(nrr.r,;)
Heat dissipation
The heal dissipation is cont.ributed to the temperature rise of the wire, whidl is
rate. of temperature change. mass density, spcciii(; heat and the volume to he
dl;;k~rITIim:d
by (he
aT
q, = y cf\V -_.
al
Heat conduction
The heat conduction along the wire is determined by the product of the temperature gradien!
along the wire, thermal conductivity and (;rOSS sectional area of the wire. It Illay be expressed by
fiT
q,=-AA ...
OZ
Heat convection
Heat loss caused by eonvcdion is determined by
q, =hS'(
r.. - r;1I~)
The etTecl of heal convection [7 (, 72, 73, 741 can be represented by a resistance
R
Hl//\"
=_L.
~'h
The cooling elTel;:l ofc()r\ve.ctioll is usually expressed by the Nu.~.~elt Ilumber Nu
N
"
hx
=---.!
A
Nvn/lnear Thermal Modellil1g./bl· Miniature Fuses
55
for a cylinder x, is the diamet.er. Other rth:vant dimensionless numbers lor the convection are the
Prandtl number PI'
(.' ~(
l', '" f....-
and the
Gra~hornumber
Or
1
_
1'l(1',-/' )X,
(j'" r -~
1-'
~I
ro,'
'-r
l)
The Rayleigh number Ra is defined as
Ra = Pr*Gr
The Nusselt number is expressed as
N"
= 0.36 + O.048(G, p,.)" I~I + 0.52 ((II' l~ )(I,j
4nder the following conditions:
o
o
o
o
hOl'izontal cylinder in geometry
natural convection
wire in air and with small diameter ( in order of 50
10- 7 -<.' Or PI' -:: 10 8
~m)
Heat radiation
The heat
los~
due to radiation may he approximated by [68, 69]
q,
= cr e S(r.:- T.~)
5.2 Analogies and circuits
On the oasis of the descriptions in tht: above section for heat transfer, the thermal model can he
rewritten in terms of electrical components by USing the following analogues:
heat now
temperature
thermal resistance
thermal capacity
electric Current
voltage
electrical resistance
elec1rical capacity
Table 5.1 shows cquivalent expressions which represent electrical components u(;wrding to
the analogue [52. 75 [. All parameters an: tt:mperature (voltage) dependent. In Tahle 5. LT .
300 K.
To establish a simulating scheme, the fuse was divided into similar axit(l scgment5 bctwecn
the end caps. Because of symmetry, only half of the element was necessary to be simulated. Figure
5.2 shows subcircuits of one segment and one half segment. The subcircuit of the half segment
wa~ connected to the subcil'cuit of the end cap. Component parameters were determined by
reorganising the thermal expressions. equivalent resistance and capacitance.
The end cap is as~umed to be of a rOom temperature (typically 20 DC) during short current
pulses (in order of 10 ms), because the end caps have a massive volume as compared with the wire
element. It was represented hy a fixed voltage source, in this situation the source was the (;ircuit
earth. For d.c. current or long time current periods, heat storage and conduction within the end
56
--------------.---.----~-.-
5
..... ".".-.. ---..----.. --.-._.._ (.'lIu,'I<'I'
_----
caps should be considered_ This suggested that tht:rmal behaviour or (li~~ e1ld ~:'IJIS ,:(\11 h,~ Siinulatcd
by capacitors and resistors. Capacitors rcprcsm!cd twa( dissiplltioll in lilt: end caps. and resistors
represented the conduction and eOllVf.:diOn loss in the end caps. Thc l:ompklc cirl'tlit I(lr lk
s!I\lul(l(joJl W(lS n.)f'Jncd by connecting all the sub circuits. The rekreIln~ poinl ill Ih~: electrical
network I"or the () vol! was chosen (0 be corresponding to .100 K.
Table 5.1 Thermal and electrical analogues
,..-----_._--_._._".,...._-_ .... _----,..,,---:----------,
p
C'
p(V) I.
.
{-(I)
I
nrc
~I
L
2.,,; r.:n'A,(Ji)
----4---I-.,-'I'-,..-:-2-rr-I.-I-n-·[~;_-~-)----'-""------_._... _--_._- .... ,.•.. ,
n
2.,,; ~I r.
('W + .( / + l~' ) ((I + 2 *
I; C/
'I: )
rl
21l r.ILh(V)
:---------_.,........ -._--_._-----+-------:---------j
",-."
I,rr!";!-. C.' (I-! .\
y, ......
n
_ J~T) ---.. -. -.-.Y'/II _:____ .L_... _:.'.._c"". (II)
1 rr (r ~
fJ
! - - - - - - - - - - - - - - ! - - - . -..'... m_r----.;---.-----1."11; (Ii, .. r;)
y ,../~I" •..... -----,--.--- C}!{IIU (V )
n
-----c:::::::J--- --.. -..
1'( t)
~
1c
-- _... __...- ...-
c:::::J ... --...
[]
1\"",
---'-
-,R'lld
R,II. gl""
.-
f----·l
1"-1
~:I ( '",r
--1
.[. . ._:L . . ._
C~I;~~:.
Figure 5_2 Black box model for a segment and a half segment
57
Nonlinear Thermal Modellin.g/or Miniature Fuses
To simulate the transient behaviour, an extra suhcircult for the time dependent current SOurce
is often necessary. In practice, electric current exerted to fuses does not always follow a well
defincd wave shape. For this reason, the digital values of CUlTent should he taken to form the
subcircuit. Electric current is expressed as a function of time in a lookup table (time and current
pairs). To introduce this table into the network, a piccc wise linear function is used to convcrt
time into voltage. Therei(xt numerically speaking, current as 11 function of time is equal to tbe
voltage control eurrcnt source in this subcircuit.
5.3 Applications
In Sections 5.1 and 5.2, descriptions for solving heat transfer problems related with Il1ll11aturc
fuses have been provided. In the following, applications will be illustrated for two typical
commercial miniature fuses. The first olle is a fast acting fuse for a rated current or 315 rnA. its
element was made of pure nickel (length = 17.5 lUlU, radius rd = 25 ""m ). The second is a typical
time delay fuse of which the element was made of silver clad wire (length = 17.5 mm, radius r~ =
51.5 f-l-rn ), the rated current was 800 mAo Simulated results of ClIn"ent • time chlltllcteristics.
voltagc response and resistance increase due to current pulses will be compared with \:xpcrimental
determinations.
5.3. t Fast acting fuses (Nickel element)
The technical data of fuses are as follows: Linelfuse type 217.315; rated voltage: a.c. 250 V~ ratl:d
current; 315 mA.; the melting it value: 0.13 A 2S.
Temperature dependency of electrical resistivity p of nickel was used 152, 76J. For the heat
storage within the nickel wire and the air inside the tube, temperature dependent values 168, 761
were used for the specific heat. for the thennal conduction in the axial direction along the wire and
in the radial dircction across the air, temperature dependent values of conductivity [oS, 76] were
used. For the glass tube, constant values [77] were used for the thennal conductivity (/..~I~~' = 1.95
W.m·'.K ' ) and the specific heat. The emissivity fi.lr nickel was taken to be 0.23. Component
parameters for n = 7 in the simulation circuit were detennined by introducing the material
properties. Figures 5,3 to 5.8 show their numerical results of components as functions of the
st:gment temperature.
R
1.0
[Ohm]
•• ,••.• " 'r
0.8 I
0.6
0.4
0.2
I
o
I
I
o
5'0'0
.-( 066
Tw
1500
2000
[Kl
Figure 5.3 Electrical resistance of nickel wire as a function oftemperature (n"'7)
._______
( ·hap~
58
R [kohm]
30
25
20
i
0
15
150
100
Tw
200
[K]
Figure 5.4 Thermal resistance of nickel wire as a function of temperature (w= 7)
14
R [kohm]
12
10
8
6
40
I
500
1000
Tw
1500
2000
[K]
Figure 5.5 Convection resistance of nickel wire as a function of temperat(J{e (n;;;;; 7)
R [kohm]
2000
1500
1000
500
o
o
500
1000
1500
Tw [K]
2000
Figure 5.6 Radiation of nickel wire as a function of temperature (n"'7)
Nunlinear Thermal ModellingJor Miniawre Fuses
59
C [uF]
35
30
25
20
15
o
500
'fobo·
T VI
1500
2000
[K]
Figure 5.7 Heat capacity Df nickel wire as <'3 function of temperature (n;;; 7)
C [uFl
25
20
,.
\
15
10
5
oo'
50'0 ...... 10"60
TI"~
Figure 5.8 Air capacity as
1500
",i
2000
[K]
a function of air temperature(n;;;; 7)
The whole model in (he above is strongly dependent on a number of assumptions for (he heal
flow behaviour and material properties. As a check of (he validity, the I-t characteristic of nickel
fuses which is well documented experimentally and also determined with our thermal models.
Figure 5.9 shows a comparison of simulated results and the manufacturer limits. Apparently, a
rather good agreement has been achieved with respect to the temperature of the wire ekmcnts.
which encourage uS (0 use the thermal mOdelling fbr temperature determinations during p\llse load.
60
('hapler
[s
6
10
5
l
4
10
10
:1
..
10
·2
~-':..'
I
I
~""""
.......... .
"
--- ... -
--.
-
-I...
'1._'"
-4
10
,
[I
10
10
Illn
Figure 5-9 Comparison of I-t characteristics of nickel fuse wires
Dashed line: manufacturer limits; solid line: simulation
Furth(;[ the measured voltage response for a givm cummt pulse wilh i'l peak value of 4 A wa~
compared with simulation results. Figu[~ 5. to shows the measured voltage and the simuhltions tor
the cun-cnt pube togdhcr. The gfi'lph indicates that theoretical valuc~ llrt: slIghtly hciow the
rnt;'I~\1r~rr'¢nt.S.
Current [A] and Voltage [V
6
1
~-~---'---r-'--""-
5
r
4
Voltage
--_. : Simulation
: Measurement
3
2
-.- ..... --.,.
a
8
10
12
16
18
14
Time [ms 1
20
22
Figure 5.10 Voltage response of a current pulse with a peak value of 4 A
- : Simulation; " _ : Measurement
Nonlinear Thermal Model/lng/or Miniature
FIISlOs
61
From the current and voltage measurements, the rcsistance wa~ obtained as a function of time.
For the same Currcnt pulsc, the calculated resistance was also obtained, the results are compared in
Fig. 5.11. For both resistance determinations the initial resistance was reasonable in accordance
with the cold fuse resistance (about 800 mQ). During the cUI'rent peak, both simulations and
derived rt:sistanec from measurements were similar. After the Current peak, simulated values are
below those del ermined from voltage and current mcasurements. One of the po~sibh; reasons is
that as current decreases, the accuracy in the ratio of vOltage 10 Currt:nt becomes low.
Current [A
1 and
r
4
Resistance [Ohm
1
Current
:'::
3
Resistance
: Voltage/Current
- : Simulation
2
a
8
10
12
14
16
Time
[ms
18
1
20
22
Figure 5.11 Comparisons of nickel wire element resistance for a given current pulse
... .- Determination from voltagB and current ratio; - .- Simulation
5,3,2 Time delay fuses (Silver clad wire)
Element composition of this fuse wire was 50% silver and 50% tin - zinc alloy by weight. Tin -zinc
alloy was composed of 85% tin and 15% zinc. Technical data arc; Littclfuse type 2tS.ROO; rated
voltage: a.c. 250 V; rated current: 800 rnA and the minimum melting min : 1.3 A ~s.
Il
Th(; electrical resistivity p and temperature coefficient of resistivity 0'. were determined [rom
measurements by using the four terminal method. Because of the obvious difficulty in
dt:!ermining material properties, mass density y, specific heat c and thermal conductivity "J.. were
estimaled according to their composition and wire construction. In the simulation, the followilltl
values were med: p ,= 3.7 + lO's ohm.m, (t. '" 4.5~ (0,3 K.'l, " .-= 254 J.kg-lX· l , Y = 8.6* 10' kg.m-',
l
f... .., 220 W.m- K"l, Resistivity and its temperature cocrtieient [551 arc in accordance with
manufacture data. Specific heat c and thermal conductivity f... are evaluated nccording to win:
compositions, which might contribute the deviations to simulations. Specific heat c is also in
<lccordance with the value suggested by manufacturer.
por a given pulsed current, the voltage across the fuse and the temperature distribution (n~ 7)
were calculated. Figure 5.12 illustrates tht: simulated fllSt: voltage from the model and the
2
measured voltage corresponding to a pulsed currenl with If '" 0.6 A s. On the other hand. !I'om
voltage and cun'ent measurements, resistance values were found. Because the initial resistance
bdore current flowing wa~ known, tht: avcrag(; temperature rise can be determined by using thc
62
( 'h(l!I/er
5
relationship betweenlemper<lture and resistance. Figure 5.13 di~plays a typical trace of the average
temperature rise from the simulation, where the temperature rise derived jl-OI11 (hc l1u;asurcd
voltage. CUITcnt values is also prc~cn(cd. In (hi~ graph, (hI: dday or tcmpcr;)tun: ptnllie l.s dearly
identiHed referring 10 thl! current pllise. The maximum temperature risc is rcaehed after th~~ (~lIn-cnl
pulse started anout 5 ms.
15
Current [ A
.......
1
Voltage [V
-> r
,.' ~~
,,--,-< ..
"
\
Voltage
.
1
---,-.... --'\1 5
----,.--.--~,-~-~-~-
. Measurement
---. Simulation
I
11
10
I
I
.
0
i
i
5
10 .5
I
. "---.-..
o0
"'\', I
---.~.-~--~-~--~-~
2345678
Time [ms
a
1
Figure 5.12 Comparison of the simulated and experimental fuse voltage
2
2
for a current pulse 1 t = 0.6 A s (silver clad wire)
Temperature rise [ Celsius
1
180
Current [A
. -, ----....
1
~----....
160
18
16
140
14
120
'\. Temperature rise:.
12
100
.-.- ; Simulation
.. : Measurement
10
80
8
60
6
eu rrent --'
40
20
o
,',/'.1
"""
L-_.L...C.'"",.~. __ ..... __
o
2
3
4
5
Time [ms J
4
..
~ ~..
""
I
7
8
""""':::::'1
6
2
0
Figure 5.13 Comparison of the average temperature rise of
2
2
the fusf: (Silver clad wire) for a current pulse 1 t = 0.6 A s
Nonlinear Thermal Modellingjor Miniatw'e Fuses
63
From a previ()us study [55J, the maximum displacement in the middle oflhe wire cl!.:mcn( was
lound (0 be 300 ).lm for a constant current of 1.3 A. By using l\ well defined relationship [;'i5]
bet\'.leen displacement and the average temperature rise, the corresponding temperature rise was
found to be 70 Celsius. To study the influence of end caps and further to examine the analogue
method, the temperature distribution for a eun'ent of \.3 A is calculated and shown in Fig, 5.14.
The average temperature rise is about 60 Celsius.
Temperature rise (Celsius j
90
,--,
...
-'~
... _, .. __....
-------............
60
70
60
50
40
30
20
10
0
J..........,.,..,"', .......
0
10
Position [ mm
5
15
20
1
Figure 5.14 Temperature distribution for a current of 1.3 A
Whlle Fig. 5.14 is related with a constant current of 1.3 A, Table 5.2 also presents temperature
values for current pulses with a duration of about 7 ms (see Fig. 5.13).
Table 5.2 Average temperature rise corresponding to
different lit values of pulsed currents
It
2
A s
0.22
0.37
0.60
0.78
0.98
0.17
0.28
0.46
0.60
0.75
W1
164
205
284
60
111
207
301
431
50
93
[69
218
328
it
ft min
52
T•.,p [0C]
"
T"" [¢Cl
1-.-----
~----
T"m [0C]
In Tab[e 5.2, T"" is the temperature rise under the adiabatic assumption. T'IIII is (h~ valll~
from network simulations, and T"'F is the temperature rise determined ("rom voltage and current
Chaple)'
64
5
measurements. pit",;" indicates the minimum melting /1, Compi~ti~on hetween the calculated
temperature rise$ is made in Fig. 5.15 with the temperature values obtaim~d by ml.~asuring voltag.e
(~nd current.. This gri1ph indicates that as f't values increase, th~ simulation results move up and
above the results determined from voltage and (;UITent measurements, l;igures 5.1 () tn .").1 'i show a
deviation or aboul I() % between simulat.ions and experimental results.
Temperature rise
[Celsius 1
450,---~--~--~--~__~
Figure 5.15 Comparisons of temperature rises
x : Values from voltage· current measurements
b : CalCl.llated results under adiabatic assumption
c : Simulation results
To examine the simulation, the average temperature rise for wire clements has been
determined frol1l the resistance mea5urem~nts, namely, from the vOltage and current
me,lsureOlents, l i or t.he llniform distrihution of the temperature along the fusl.~ elemenl. Ihi~ rlll;thod
is always valid. For the circumstances where the electric resistivity or the j'lIse element. is a linear
fi.1l1l~lion of the temperature rise, the vandity can also be proved to he ind~pend~nt of th~
temper<ltllre distribution. The resistivity of silver clad wire has been cxpo:=rimenli1lly dt;.1ct'lllincd,
results indicate that the resistivity can he approximated by a linear thncti(1) (0:. ' 4j"I((1 K"). For
the nickel wire, as the temperature is above 600 K, because of nonlinearity of resistivity the
accuracy of this method relies on Hs temperature distrihution. The temperature ri~e I.leterrnincd
from the resistance is slightly higher than the real aVl::rage tempera1ure rbc, and tile deviation can
be evaluated to be within 13%,
5.4
Conclusions
Hei,;ause both melting characteristics and voltage. current rclation~ prc(li(:(ed by the thermal
analysis arc reasonabh: in accordance with experimental results, the thermal analogue method
can he cOllsidered as a tool for stress analysis which is essen(.ially ha~ed on thel'mal hehaviour.
Chapter 6 Thermal Modelling for Semiconductor Fuses
The primary objective of the fuse reliability project is to understand li.lsc ageing mectl<lni~m~ and
to provide application guidance for industries, This chapter deserihes a method to simulate tht,t:;c
dimensional transient thermal n::sponscs of semiconductor ti.ISCS ~timulated by electric current.
The results will he used for thermal $tre~s determinations related with fu~e lifetimes,
For miniature ["uscs, bccause of their simple construction, thermal mDddling could he
performed with electrical analogue technique5. However. for semiconductor protection fuscs.
because of nOllunif()rm current density distribution and complex of the construction. mort
sophisticated programming techniqucs are needed.
I'-or thermal simulations of fuses. the linitc different method 16, 71 and the finite element
method [8, Y. 10 I and thc network analogue method II L 12] may he applied, To find the solution
0(" thc three dimensional thermal problems of semiconductor protection fu.~es. EMTP r541
(Electro-Magnetic Transient Program) as 11 tool is chosen in this work, EMTP has been wiclely
used for simulating electrical transients in networks, EMTP, compared with other available
sotlware packages, such as PSPICE and MICROCAf', is capable of handling very largl;:
networks (more than (0000 components) for Apollo workstation with 4 MB memory, EMlP
allows various components which cover TACS (Transient Analysis of Control Systems), models.
switches, resistors, capacitors, controlled voltage Or Current sources, look up tables (point by
point function) and sub circuits (including files). Additionally. students in power engineering can
get the knowledge ofEMTP for huge electrical network simulations [78, 79, 801,
Two dimensional electric Current distribution within the notched fuse element is numerically
resolved by using resistive networks, Thermal behaviour of fuses has been simulated in FMTP
(Electro-Magnetic Transient Program) by using the thermal electrical analogue ml;;thod, Thc
probkm of three dimensional heat trnnsler within fuses is converted into electrical modelling
where relevant electrical components represent heat conduction, generation and dissipation, The
validity of the thermal model has been checked by comparison of tht; resulting melting
characteristil.; with the manufacture curve; however, thl:: final purpose is to use EMTP j()r
lifetime determinations,
6.1 Considerations for thermal modelling
6.1.1 Geometry of the fuse element
Commercial power fuses for semiconductor protection arc chosen as simulation objl;:cts. with
ratings of 160 1\, MO V and breaking capacity 120 kA. Figurl:: 6, I shows a typical element
geometry. when: dimensions arc given in millimetrcs.
65
( '!JOllier
0
8
4
,
\
(
:
I
:
)
I
:
,,
i )
( )
(
)
,:
!
)
I
I
!
,
,
1.66
i
"
.'
1.5
)
I !
\
18
,:
..
:
,
"
i
!
i
21.5
Figure 6_1 Element geometry
The fuse element made uf silver without M-spot.s consists of jive rows o/" no(ches and each
row has 10 holl.:". The hole has a diametel' of 1.5 mm. The overall delllt:rlt si;:e is
43mrn* 18mm*O, 135mm.
The fuse clement is surroumkd by sand with an average grain size diameter of OJ6 rnm. The;)
sand packing density is ahemt 1_79 glcm:l. The thiiJknc;:ss or t.he surrounding ceramic body IS
about 5 mm. The distance bctwi;;cn (he body and the element is about 9 mm.
6.1.2 Thennlll behaviour of fuses
In order to jind the temperature distribut.ion, two equations should be solved.
( 6.1 )
V'V'(I,d)
DT
01
Y (.' --_ .. =V A. V' T
f
P/
.,
( 6_2 )
The first. is t.he field equation, whieh describes the elect.ric potential distribution. Thc scwnd is
the energy halanee equation. It states that the input energy due to .iouk heating i~ balanced hy the
heat iJondUdion and tile energy to raise the tcmpcraturt of the object- The boundary conditions
ar~
speci fled
T
,IS
To:' 20
0('
~.~ 4)0 '" ()
~ =
¢tl
iJll is a known constant at one buundary.
Regarding fuse ~geing and thermal behaviour, sim\llations for both long time and short time
Current conduction arc required. To get an insight of heat transfer, it is easy to ~(art willi (he idea
of thermal diffusion depth (ur (he penetration depth). This cun~ep(~ Wlt~$ thi'lt tht: distance
71zermaf Modelfjngfor Semiconductor Fllses
67
depends On the heal conducting time and the thermal diffusion cllellicient. An approximation 01"
the diffusion depth [681 is given by
('(')~Ji2U'f
( 6.3 )
The diffmion coefficient is given by
A
( 6.4 )
0;=-
Yc
To understand the heat transfer process in the fuse, the middle row of the notch is considered
only, bec<luse it has the highest temperature as electric currcnt flows.
Using [hc fusc clement dimensions and the expression of diffusion depth, the 1011owing lime
limits are established. For times less than 0.3 ms, heat conduction is limited within the notch
zone (0.75mm), hence adiabatic heating is suggested, Diffusion depth is about 4 mm in the silver
element for 9 ms. Diffusion depth in sand is equal to the thickness of the element (0.13 mm) for
7 ms, These two time limits give an impression of the adiabatic heating. After about 150 ms,
diffusion depth reaches 4 rum in sand. From 150 mS to 300 ms both heat conduction in the
clement and sand have the influence. After about 300 ms, heat conduction from the central notch
reaches the end contacts. Heat transferred to contacts can not be neglected, After about 30
seconds, heat conduction reaches the ceramic body. Therefore in this range contacts and sand arc
heat transkr media. Heat convection and radiation of the ceramic body take place. As a
consequence, all possible heat transfer factors should be considered above this time limit.
Wilhin 300 ms, heat cncrgy conducts in the silver element and sand. There is nO heat
conduction in the ceramic body for this period. Figure 6.2 shows relcvant dimensions fOI' this
simulation. Because of geometric symmetry, only a small region of the total fuse element is
required to be simulated. Above 300 ms, to simplify tht: simulation, the contact temperature and
the outer surface temperature of the ceramic body are assumed to be the same as thc surrounding
temperature. Figure 6.3 shows the simulation region of the fuse element for longer time studies.
y
~
o IiO I .·
x
!
4
z
Figure 6.2 Simulation region for times shorter than 300 ms
68
('hopl~r
(j
9
o
z
21,5
Figure 6.3 Simulation region for times between 300 ms and 30 s
6.1.3 Electrical equivalents
To realise the electrical analogue method, the simulatiun r~gion is divided InlO ~mall sub
volumes. Electrical equivalents arc ndwork components transformed from the thermal ami
cledrical problems. like already discussed in Chapter 5. Quantities of cledricul components are
defined according to Eqs. 6.1 and 6.2.
6.2 Network representation
In the prtvious :;tClion, general forms of component representations hnw b.;:en
section, sub cit'cuits corresponding to subvulUfnCS will be represented.
dis.;u~sed.
1n this
6.2.1 Sub-volume generation
To achieve high resolutiun. small subvoluJrles are necessary. Figure 6.4 shows a typical
subvolumc and its dimensions.
z
y
~
,
'1
x
Ay
6x
Figure 6.4 Co-ordinates and sub volume dimensions
6,2.2 Sub circuits
C()rr~spondjng
to Fig. 6.2 and 6.3, the area ior the electric current now simulation in Ihe silvt;:!'
hlt' fl sllhvolunlc. cledrical behaviour is represented hy
Ciln he divided into small sub-vol limes,
69
Tht;:rmal Modelling/or S'emiconduc/or Fuses
tour resistances, [{of (j =1, 2, 3, 4 ). I\. two dimensional representation is adequate hcre because
of the small thickness of the metal strip. The corresponding subcircuit is represented in Fig. 6.5.
Four mea~uring. switches (type 91 device in TACS) are used to obtained the electl'ic current in
the nc(work.
u
Rel
L
.,.J'.
l
MI
1··--: ....
_.+
R
!
X0101
+
)
6
D
Figure 6.5 Subcircuit for efectfic current flow
The resistance values are determined by subvolume dimensions and its reSIstiVIty. The
length is from the centre point of the subvolume to the boundary surface. It is assumed that the
current direction is perpendicular upon the relevant cross section. The resistivity of silver is
dependent on the temperature of the subvolume which is represented by a type 98 device in
T ACS as a look up table.
For heat transfer, three dimensional modelling is necessary. Heat conduction is represented
by six equivalent resistances, i,l> ( j =1, ... , 6 ). Resistance values depend on the thermal
conduction coefficient. Energy due to electrical current flow is represented by injecting an
equivalent thermal current. Energy used to increase the ~ubvolumc temperature is represented by
charging an equivalent capacitor. figure 6.6 shows the equivalent subcin;uit lor thermal
simulation. Temperature coupled to a type 90 device in T ACS is also measured by using ;"j
measuring switch and introduced into a type 98 device. In this way, 11 injected cun'ent source
(type 60 device) is realised with the resistivity dependence of temperature in thermal network.
Component parameters for the sand and the ceramic body can be obtained in a similar way.
Of course, no branche~ exist in the suhcireuit for the electric current flow in sand. The complete
circuit consists
all sub circuits. From this circuit. temperature values at different nodes are
obtained.
or
70
('/Iople r
(\
L ",
F
A0101
Figure 6.6 Equivalent subcircuit of heat conduction
For decoupk:d solutions, ClH'l'cnt distrihution and temperature distribuLion are obtained
separately. I [owcver, fbr the coupled solutions, two networks havl: (0 be ~()lvt~d ~imul«lrleo\lsly.
In the: subl,)in;ui( Jor simulating current now, the tempet'atlH'e dependent I'e~istanee is represented
(IS ,1 ctment source ilild (I constant resistance together. Consequently. the subcircui( shown in Fig,
(i.7 is used t.o simulat.e the electric current flow. Output of" (;urrCn( is realised by " (YPt~ 31 device.
Figure 6.X presents the coupled subcircui( tor the heat transfer in t.he silver strip (see !;ig. 6.7).
u
I
,
R,,/
R,/.
l
R",
L
,I
R
ld
-I
"'
I
X0202
D
Figure 6.7 SubcirC(Jit for electric current flow inc/uding temperature dependence
thermal Modelling for SemiwnduCior Fuses
71
u
B
RI1,J
L 'I
R'h
~.
R ]
M :.'
II!
.L..l./.f:<.a' (., _I/.""':
b H
6
,. L1
.,/'\'
,.'
I
":' •... ·t·
TI 1()
4
., ..,/:",/ Rlh
,.,/
J
I':.
L
A0202
.. IA0202
I
C1h
··r....
D
Figure 6.8 Coupled equivalent subcircuit for the heat conduction
in the silver strip (s8e Fig, 6. 7)
In Fig. 6.8, two TACS controlled switches are used to couple the electric and thermal
networks. A sample and hold function is introduced to keep the capacitor voltage. Two type 23
devices art used as triggers which control two switches represented as type 23 devices. To solve
the complete network, an iteration procedure has to be applied. This is shown in Fig, 6,9, where
T is the period for the coupled network simulation, The process is realised hy exerting two
triggering signals to switches a and b (TACS controlled switches). First, two switches arc closed
hy trigger I, Temperature values at all nodes are calculated, The temperature of the silver strip is
measured hy the measuring switch b in One timc step. These two switches are opened by trigger
2. Consequenlly, temperatures at all nodes are hold, New electric current distribution is
calculated during two time steps because of nonlinearity. As the stable state is reached, two
switches are closed again and then temperatures at the next instant can be calculated,
T
.......-----_.,-_..,.- ......
a, b
~
Close
Open
,--;-----"... ....
'~-
Q
1M Ht
Trigger I
0
Triggcl' 2
I At
>
3~t
.126t..-_.
3 J.t
...._+-._-_._, .... _--4~t
5L1t 6L'1t 7t..t
a
I
4~t
St.t 6Llt 7 Ilt
a
1-,···-_· ...·_-_···,··,,· .... . .1,
0 I bot 2t.t 3t.t 4L1t
. . J..__.~
Silt
(,l1t
7At
Figure 6.9 lteration scheme for the coupled non-linear network
72
- - - - - - - - - - - - - - - - - - - - - - ---------"6.2.3 Boundary conditions
In the simuJiltion, the last sand layer and the network nou(;s ul thl.: t~nd contacl ;1r'C eOlljlectcd to
the thermal network ground. The temperaluH: of the layer is at a mom temperature. I·kat
condudion through the narrow edges of the silver strip into sand is assumed to lx~ negke1ctL
6.3 Data input and output files
I'·or the network, a pmgram (SEMIFllSE.PAS) is used to generuk data input Ilks fiH' 1:·MTI'. All
resistances, capacitors, switches, current sOurces and TACS (Transient Analysis of Control
Systems) are connect.;(i <lccording to the suhvolume representation.
Resistivity as a fbnctiol1 oftempcralure, thermal condul.Aivity, specifIc IH;::al and mass density
of silvcr wcre taken (rom the literature 1g I I, l"or sand and ceramic. t.he commonly used vulucs
were introdun:tL SO[rl1.: properties am given in Table (j.l.
Table 6_1 Material properties In ti1e simulation
y kg/fly1
1\ W/mK
J/kgK
L"
................ """-...............
silve.r
391
10492
276
sand
0.3
1670
gOO
ceramIc
L46
2200
670
6_4 Results and discussion
Figure 6, 10 shows a typical temper<lture distribution ncal' the notch (the maximum tcmpt:ratuf!;":
574 "C) at the tinle imtant of 7 ms for a sinusoidal cun-mt pube of 125() ;\. I"his gr,lpll indicates
the most heawd h)(~atiDn is around lh~~ notch within abOllt I 111111_
.,
600
::l
500
~
Q
400
'"'"c:
300
~
::J
.~
:lO[)
'"c.
E
100
~
0
------------------------.
0.5
~
------~
y[mm]
----
o
0
~
1
___ ---,--
-
4
3
2
"lmm]
Figure 6_10 Three dimensional temperature distribution
at tms for a 10 ms current poise of 1250 A
!!!.ermal Modelling jiJr Semi(:onduCfor Fuses
73
Figure 6,11 shows simulation results of the maximum temperature rise tor 11 current pulse of
700 A. The current indicated in the graph is 1144 vallie of the total current through the fuse
element, The graph indicates the simulated temperature profile as a function of time. After the
current flows, the temperature rises lip with 11 time delay. The maximum temperaturc of [he
element is reached after the current peak, the temperaturc delays ahout 2 ms, As the current
decreases, the tt!n1pcrlItun:: falls down.
[A]
25
"\ r
,
~O
"
70
Temperaturc
60
\
50
\
15
, 40
I
'yC"~t
10
5 '
I.
()
T [0C]
30
~O
10
..
0
. ,. ___ -.1 •.• - _____ ,_,_ ••.• ,,_,_._, .•
2
0
4
6
8
[0
12
14
16
)8
20
[m s]
Figure 6.11 Simulation for current pulses
To examine the current· time ( I-t ) characteristics in the long time range, measurements of
melting times for 300 A, 400 A and 600 A were perfonned. Experimental results from
measurements arc summarised in Table 6.2.
Table 6.2 Measurements for checking 1- t characteristics
1
[AJ
tm
[s]
1 rA]
tl1j
300
220
400
20
300
154
600
2.8
300
220
600
2
400
10
600
1.8
400
15
600
2
400
19
600
1.8
[s J
From manufacturer data of it values for the time range within 10 ms, the prospective current
Ip and the virtual current Iv [82 J was obtained for the corresponding melting times. The results
are presented in Table 6.3.
74
._ _~___ ~ _______ .______ ._._. _ ___ .~I!}le~_ ..
~
2
Table 6.3 Prospective current II" virtual current Iv and 1 t values
1I.2~
I"t
.• _.,
,_~
ms
7600
I
II' II.
IOg54
10200
4
1824
1m
11300
5
1503
15R70
10
1260
I,
s
----_ ..
".,
... ,.
2756
-
----,_._-,---_ .. ,.. _.
1579
._-,-,-_."
1503
12M
__ .____ .. __. _ L - .
"".-
_..-
Comparison of thc munuhdurcr J-t dHlracteristic. the mt;<lsuremenls ilrld ql!,:u!,lted results
from EMTP is m<lde In Fig. 6.12. The minimum fusing current from thc simulation was !(lund 10
be 205 A.
1000.
100
10
_... - - Minimum fusing current
L:::
\<:\ ~ Manufnelul'cr Clll've
t ~
'loheordlca
. l'j\' \.
OJ
.§
0.1 :
'''"'~
\
'~
0.01
\.
0.001 :
100
1000
Ip
10000
[AI
Figure 6.12 Comparison of theoretical results wilh
manufacturer curve and measurements"."
This graph shows th<lt measured values (It .") arc slightly below the n1<ltlufacturc curve as
welJ <IS the ~Imuialed results. In general, it can also bt; seen that calculatiotls arc in agl"(;I.~ITIent
with both results from the fuse manufacturer and the measurements.
6.5 Conclusions
II.s before, the proposed analogue method proved to be a powerli.1i tool I()r simulating thermal
transient responses, EMTP numerical results of curn:nt - time characteristics of fuses show
reasonable agreement with both manufacturer CUrve and measurements. Numt~rit;al !,:,lil;lliations
have heen conducted for currt;nt pulses. This study shows that the proposed I;MTP modelling
mcthod can be used to predict thermall'esponses of fuses. as it will he necessary for the lifetime
analy~is,
Part IV
Thermal Buckling and Lifetime Predictions
Chapter 7 Thermal Buckling of Wire Elements
As stated in Chuptl.;r l. to predict I\Jse !i fetimes. thermal response and displae..:ml~nt or the I"u~~~
dt.=ment should be known tlt'st. This chapter describes efforts to sDlw the th!';rlll,1I post hm~kl ing
pmblem of thin metal clliumns whidl curry dC!,;tri(; (;urr(':r\t. The snhJl.iOI\ or analyt kal studies is
bas!,;J on thl.; pril1(;iplc or the minimum potential energy. Besi,h.;s. th~~ d"1i.;(;( 01" (~~I1\]1~I"i\t\\t'C is
included in a theoretical finite clement rormulation, Both methods have taken veni(;;iI
displacements into uccount in contrast 10 existing methods. Mechanical material properti~~s Me
cunsidered (0 h~ 1.e1l1pcmture independent. Also edge ,~om!ition~ an; 'IS~ll!ned to he illllllnvabk.
Numerical results of displacements tlrC con1pMed v,ilh measuremcnts f)·om a microscope and
high speed photography, In the presen1 investigation, these two methods arc lls..:d to llnaly~e
[)"lotion ofwit'e elemenN suhje.cted to thermal loads.
7_1 Buckling concept
Thermal buckling due to electric ~:urrent may be of interest. in many areas such as printd l~in;uit
boards. c(1nnectinns of elecl.ronic components, overhead lines and !,;ables 1831, For rl1~<: wi,'c
clemcnts, hecause they arc fixed onto end I.;aps. thc therm~1 exp,lIIsioll cluJ: to J:lcctr1c kating is
suppressed, As ~l n:sul1. temper,HUi't:, change produces thermal strain that kads to therrrwi ~tress.
·rhis may hring about strain cycling and changes in m<llerial pl'opert1cs. ('on:;cqucntly, it can
resull in thl.:rmal l"atigul;; aod lil~1imt:! reduction of wire clements.
In I'>!\), Arai [:l:'i] condLleted both experimental and analytic ~(\ldies 10 (kl.t:rmine lifetime of
notchcd flIse clements_ Motion of the Iils!;; element was shown and suggested to be related wilh
liktime, however, without an)' ljU,Hltit,l1iv{) models. The objective 01" the present study is to
provide a t[uantitativc dcscriptioll.
Figure 7,1 gives a schematic view to illustrate the motion of wire clcments. ·I'hc motion is
simplifk.d to be one Jimmsionul in the y-z plane and thc magnitude is only dependent of one
sp,lhal vari,lbk ;:. When wire dements are subjected to c!edri(; (;llrren(' Il~rnrera1l!1'c dscs. As a
consequence. thermal stresses arc built up,
y
w
~--------------r~~,
-....::....".-t-~=-----
Pre -- '
.....-...-.
----
10
._._-----------+ -:.--
Figure 7.1 Buckling geometry and sign notation
z
:>
77
Thermal Buckling of Wire Elements
The thermal strain corresponding to the thcrmal stress induced in thc wire clement is
proportional to the thcm1al expansion coefficient and the temperature rise of fuse wire without end
constraint5;. It is expressed as
( 7.1 )
Bccause the wire is fixed at the ends, temperature rise results in stress. The wire keeps it~ original
position; this process is called pre buckling, As the thermal stress exceeds a certain valuc. the wire
clement starts to move. The start of the motion is called buckling. The complete movement is
called post buckling. During the post buckling, one part oftbe thermal strain is contributed 10 the
motion of the wire element, another part is converted into compressed deformation. Timoshenko
[84] proposed a fimction to describe the displacement (see Fig. 7.1) a~
y (z) = 0.5 D,." (J • cos ?:rz )
l~
( 7,2 )
For the determination of the maximum displacement D"",-" no valid theoretical method W<lS
available. Further literature [85, 86, 87, 88] shows that most methods are based primarily on
linear structural theory with empirical corrections to account for non-linear behaviour. Namely,
most investigations are limited to displacements comparable with the thickness of plates or the
diameter of columns. In our situation, however, the maximum displacement of wire elements can
be up to 10 times the diameter of the wire and even mOre. A suitable solution for thermal post
buckling of fuse wire elements has therefore not been found yet.
This chapter describes the mechanical response of a fuse wire element during thermal
buckling for miniature fuses su~iected to electric current. Two methods wi!! be addressed to find
the post buckling solution for thin columns. The first attcmpt is to present an analytic study
which describes the process in terms of energy [55]. The second describes efforts to develop a
finite element formulation by USing the virtual work principle [85]. Numerical results from these
methods will be compared with experimental observations.
7.2 Analytical study
This section introduces an analytic method [55] for solving thermal buckling problems,
Deformation causes are limited to thermal origins, oxidation and creep are neglected. In addition,
temperature rise along the column is assumed to be constant.
To describe buckling, Eq. 7.2 still can be used as one of the possibilities of curved forms in
equilibrium [55, 84 J in the neighbourhood of the bifurcation point. This point is referred to the
location of the maximum load without causing displacement perpendicular to the load in the
load - displacement curve. Using the y(z) function, the increase of fuse wire length after buckling
follows
78
- - - - - - - - - - - - - - - - - -...
( 'flaplC31'
7
,~.-~-
l'Or a linear spring with the actual elongation d,. the stored encrgy i~ expressed lo ht, 1+ ,Ii j k,
(1/. With the imillysed system. the lotal energy consists of the deformalion eJ1l'q(y, hl,;i\ding ~ncrgy
and energy due to the actual elongation in the po~t huck ling. The dd(mnalinr1 C:llergy due to tlu;
compression is
W,J
~
i
E A ('
1\ T - K"
D,~",>
)'
'II
( 7.3 )
The energy due to the actual elongation in motion is
( 7.4 )
rile hending energy
to
keep the bu/,;kling takes
W
'"
III
"
()
I.
.1
2n:
fo I / _ ..
16'
m () lJIII~L~
If!,
The total potential (clasti/,; energy)
potentiaL one may writ!;
COr1Si~t~
( 7.5 )
of W", WI, and W",.
[)t~n()ling l1y III
the tOlal
( 7.6 )
(/1
The total potential cncrgy has to he minimum f()r realising a p\l~~ihle huckling mode and
thereJi.m; th~~ d~riva(jw of (J.r to a position variabk 11 is Lero, )( foll()ws
dU I'
()
( 7.7 )
where '1 is e4uailO
2
D ,,,,,,,
The maximum displaccment ean be obtained from Eq. 7.7 to he
. ,\\,\\
J-T-'''-~~,''
f\ ! -
21"
,~
1) ..
2
TI
2n:! 1m
----.- .
j(i~
A
(7)\)
Substitution or Eqs, 7.g into 7.2 leads to an expression of the buckling shap~' for lhl,;
condition. According to Eg. 7.1\, let D",,,,, = 0, the critical temperature rise is j(Hllld to he
r
.'
~
4~ ,
!
_.....E.. ... !'.'
t
~A
~t'llic
( 7.9 )
The dellection f,ictot' y is deflned as
y
,~ .~_~ = I
6 cn
!l~~rb
( 7.10 )
I\CIIJ
It me(ltlS physically that the mcdHl[lical strain is a fraction of lht; the!'Jml slrain expressed in J ':q.
7.1 during the post buckling. Bd()rc thc bud ling OCCUl'S, thc wire is m()ti()Ilk~s . t11cnnal stl'CSS is
e(ju(ll to mechankal strcss (r~l), During the huckling. the tildor is calC1l1ated !I'OI11
'I.
y
+ " n:
:3
I,;
~
.!!.IL
A
/
.. _.".
rT
(7.11 )
Thermal Bud/ing 0/ Wire Elements
79
7.3 Finite element formulation
[n Section 7.2, the analytic approach has b~en presented to determine the displacement re~pome
due to temperature rise, where the temperature rise along the column is taken as a constant. In
practical situations, temperature decreases as the location is near the fixing ends. This motivates
a rnOr~ m;curate simulation methot! lor the mechanical response concerning arbitrary temperature
distribution along the column. In 1991, Locke [85] conducted studies or thermal buckling ror
beams, the de~cription is considered to be useful and relevant with this work. The f()llowing
pre~ent~ an extended description to enable analysis of large def1ection~ of thin columns.
7.3.1 PhY!lic91 models
The principle of virtual work [85, 89] states that for a column in equilibrium under the ac!ion of
internal and external forces, in undergoing an infinitesimal virtual displacement [901 the work
done by the external forces is equal to the work done by the internal forces. This can be written
as
oW;,"
=
0 W,."
( 7.12 )
To describe the formulation, Fig. 7.1 shows sign notations for a column (fuse wire), where
the undeformed co-ordinates are applied. Suppose that the damping and acceleration an::
m:gkctcd, because the external work is zero during the thermal post buckling, the left side
remains to be zcro. The virtual work of the internal forces is written as
( 7.13 )
The first and sccond terms describe the virtual work in the axial direction. The third term
represents the virtual work needed/or the vertical displacement. which is not present in Locke's
work [85]. Po~sibly because this term is small and thus it can be neglected. For fuse wir~
dements, the vertical displacement w can be many times the wire diameter during the post
buckling. Therefore (his (erm can nO longer be neglected.
The large deflection strain· displacement relation [85] for an initially deflected beam is
given by
(7.14 )
where
e;;;;e", +i\
e In = t.I~
e~
="21 W, + W, Wo,
1
( 7.15 )
k= - w"
10 an initially straight column, w() is zero. For an uniform column, subjected to a temperature
T(z), the in-plane force N and moment resultant M art given by
N = E A f. + No - E A BT( z)
M=Elk+MQ
(7.16)
In this work, the initial moment MI) and the initia! in"plane force No are assumed to be zero.
r;.~e
( "/111(1/('1'
7
80
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .._ - - - - - -
7.3.2 Formuilltion
To describe the
virtl.l~1
work, the column is divided into a number of
Sl~gLl\CIlIS
()j"
subvoluHlcs
Nseg. For each subvoluTIle (Iz.l ' zi.>II, j ,= 0, .. ., Ns(W) , the pril)!;ipk oj" virt\J,iI w())"k Ill"} be
applied. Summarising the virtual work in each .~uhvolllmc !cads to thc total vlrtual work in the
eolumll, l"igure 7,2 shows notations of the nodal displacements for a subvollimc.
y
u~:
node 2
node 1
Figure 7.2 Nodal displacements for a
At (wo nodes, displacement
t.he nodal values as follows
II'
SUbVO/(HrJfj
and its derivative, dispiaceml;;[l( 11 and t¢lnpeC,l1mc dsc T give
(tI" (I·_l WI ,(1 J ,
14]
,0 1 I
( 7.17 )
lei",l!"=! u u!1
1
'
{7: }T .. , 7; ,7; ,
( 7.111 )
Displacement functions wand u at any IOi,;ations are represented by nodl: values and expressed as
w=(x
,+(1); +(1 /;', ex 4 ( '
(7.19 )
u=rl+B1f.
where the co"ordinate C, is lransronn.:d
(\"Onl
I', _ 2 (z--",)
,
h
1
(=1 I
( 7.20 )
zll.
2
Accordingly, a l • (X·; _ Ct.;, a~. I~I no(l r2 al'e ((lund as rlll1l~tions 01" Iwd,11 v,\lucs. I~y using
Hermil's high order functiolls. displacement wand u Carl be rcwriucn as
w :~(x. 1-Hi
Ii
~
lS ·l-a.,/:, 1 +a 4~ \ =[N] {(II,)
P, + r~! <; = ( N.,] {(Jm \
( 7.21 )
Thermal Bucklin.g of Wire Elements
81
where Nand N" are Hermit's shape functions. Their eXpres5ions arc
N(l)= 1 (2-3C,
4
.
i.j:))
'0
N(2) =~ .!.(1-~ -~ ~ +e)
24
N(3)
=± (2 +31; _~.l)
( 7.22 )
N(4)=~..!.(-1-~+e +~l)
24
N Ir (l)=..!.(l-I')
2
~
I
N.(2)=2"(l+1;)
( 7.23 )
In a similar way, the temperature rise in a subvolume is defincd as
( 7.24 )
where N T "-' N•.
For the column, the nodal displacements {qh in a subvolume
displacements {Q} are respectively defined as
U=
0, ... , Nseg) and the nodal
( 7.25 )
Introducing Eqs. 7.17-7.24 into Eqs. 7.14-7.16, the virtual work (see Eqs. 7.12 and 7.13) reads in
general
N.rJ'-J
A{Q)oQ
= LG,(q,) oq,
( 7.26 )
I-I
Because this expression holds for arbitrary variations 6Q, according to the strain-strc5s
definitions, the dcment equations in matrix fom1 can be expressed further as aJ ( qJ ) '" 0, and the
corresponding system equations can be reorganised as
Aa Q
=
F
( 7.27 )
where Ao is a matrix, F is the right hand vector. The vector Q represents complete nodal
displacements. Both Ail and F are functions of nodal displacements.
7.3.3 Programming and numerical solution
A finite dement program was developed based on the previous formulation. The program was
coded with Maple:: [64] which i5 a symbolic mathematics package. One of the advantagc5 is that
variables involved can be easily changed, for example, the matrix calculations. At the time
beiog, initial deflection and moment were not considered in the calculation.
Thc rC5ulting equations of motion represented by Eq. 7.27 were solved by using Newton's
iteration technique [91]. For any Q, a vectOr function G is defined as
_. .... _._._._ . ________.__.~I!.!:::._/'_!.
82
(i(Ul ~ A(IW)(J
F(())
For the system equation Fq. 7.27. thl.: Ncwton'~ melhod dellr1c~ a ~cljue!llX' (/' (/', V-', ... , Ihl~n
(;,.,
(j
~
ci' + H'
(Q' ) + J(Q' ) If'
=n
where the Jacobcan matrix J((/.l cont<lins the partial derivatives or thc vCclOl' functioll G(U"j·
Tlw i-til equation orlhc system is given by
1'( N •.•,.I)
(j (u')+
,
-
f.J (j ({
>' )
L .:..... ~.:,:.
/.1
80;
Il~
()
for I 1..... :\ • (N.'"<I/ - I). The iteration COnlinuc~ until II (I ((.I' ) I ~:: ~" , where ~~II i;; n:laU:d with thl~
required iterati()n al,;l,;\lr<lc1'.
The iteration requires lhe initial valucs of nodal di~placements which were given III two
ways. The nt'~1 method is hased on Eq. 7.2 whil;h describes the column shape in lhl!
neighbourhood of the bifurcation poi!)! 192, 931. The maximum disphll,;~~rrlerll Vililite 1)"/,,\ Ii'om
Fq. 7.B (I()r the known aVI;r'age temperature rise) is used. As an allcr1)!lliv{;, arbitrary values
smaller than the wire diametel" f()r example I 0 perc~nt value of lhe wire diameter, can also bl,;
llsed without influencing the final solution J(J[ the buckling. The second method uses the idea
Ihal if the imperfection of thc l~oluITIn tends to zero and then the solution is l~()[]sidered
~pproximately as the real solution. The impertection in the iteration seh(;lm~ was represenled by
difkrent small nodal di~pl(lcements. Both methods for giving illiliill iktalior1 nodal
di~placement.s were tested, results show no significanl. difference.
7.4 Displacement measurements
A miniature fuse is (;ornposed of J fuse element or wire, end caps and ,1 glnss lilhe. Ihe straight
fuse dement can be positioned inside the tuhular visible glass body. The demcnt. i:; tixeu onto
two end caps. Therefore, the fuse wire can be assumed t.o he a column with two lix(;;(1 ends.
Column dimensions arc simplilied to be diameter and lenh>th.
exposed to electde currents, thermal expansion of the clement Ol~l,;urS. In
ohservc the buckling effecls Jnd verify the proposed numerical scheme.
experiments t()r both d.l,;. \,;urrenl Jnd current pulses were perfOl'med 1'01' two types ()I" ruse.~
(LittclJuse tYPI;; 217.315 and 21 g.8(0). Their clemenls were made from pure nil;kt,:1 wire and
silver clad wire (AgISn.Zn) respectively. The later consisled or 50'Y., silver, :'i0% tin·/inl,; alloy
(R5% tin and 15% zinc) in weight.
As ruses
<lIT
[lttt~rnpling 10
7.4.1 DC current
Flcthre measuring displ'lcement.s of fuse wires due to d.l;, currenl, to check whether (he glass
tuhe has inJ1ucnl,;c on the measuring accuw()y. the displacements were n'll'lIsur(;d with and
without I,;urrent Hawing for n.lses. Thcsl.: lwo meaS\lrements did not show di Ih~n.:ncc j()r the same
samph:. During experiments, the test current 01' to 1011. can lx~ supplied. which wa.~ measured by
tl Fluke 11000 digital multimder. The voltage acl'Oss the tested fuse Wils mcaslln:d hy a Keithky
179 digital TRMS multime!i;;r. The disrlacements in the two perpeTldielllil1' directions of tht; fusc,:
wire were measlIn:d hy \Lsing a Nl KON microscope 15:'i I·
Thermal Buckling of Wire Elements
- - - - - - - = - - - = - - - - - - - - - - - - - - - - - - - - - - - -.-.-..~"
7.4.2 Current pulses
For measuring the displacements of fuse wires, an LC circuit was constructed to generate Cllrr~nt
pulses. A thyristor was used to switch on and off the current through the (csli::d fuse. ;\ high
speed camera was used to measure the displacement. To get enough illumination for filming. a
flash tuhe was installed. Images were produced with the help ofaehromats and micro zOOm lens,
The wire diameter was taken as a reference tor determining the displacement During the
experiment, fuse Current and voltage werc recorded hy a digital 12 bit oscilloscope. An optical
sensor reacted to the flash tube and produced thl.": exposure signal. In the meantime, thl.": caml.":nl
shutter rl;;lcllse signal and thc exposure signal were also obtained and written down in the
oscilloscope, For determining the maximum displacement, a spatial resolution of 10 ~lm per mm
was achieved.
7.5 Results and discussion
Tabk 7.1 summarises material properties used in the displacement calculations fix Ag!Sn-ll! fuses
and Nickel ttlSes,
Table 7.1 Material properties and dimensions
Element type
Ni
AglSn.Zn
Length of fuse element
10=17.5 mm
11/""17.5 mm
Diameter of fuse element
d=50 ].lm
d=103 !J.Ol
Thermal e):pansion coefficient
~= 13.3* 10-6
p=22.1 '" 10- 6
Elasticity
E=199.5~ 109 Pa
E==61 * 10 Pa
Cross sectional area
A= 1.96* 10-9 m1
A=8J3* lO·q m~
Area moment of inertia
1.,=3.07* 10-18m~
1","'5,52* 1O-I~m4
9
III the table, diameter and elasticity wen: measured values. In theoretical calculations elasticity
docs not influence the displacement as long as the deformation can bl.": assumed to be elastic.
J,ength was evaluated according to the fuse manufacturer's requirements for the element, which
was also examined by the resistance measurements, Thermal expansion coefficient in the literature
[76] was used for nickel wire, while the data for AgISn.Zn wire was taken from the manufllcturer's
information.
During the experiment for d.c. current. voltage, current and displacements were measured. On
thl;; basis of temperature dependency of resistivity, the temperatUl'e rise of fuses was determined,
Theoretical values of displacements were found by substituting thl.":sc experimentally determined
temperature rises into Eq. 7.8. Figure 7.3 and Fig, 7A show comparisons of theory with
observations of the displacements for nickel fuses and AglSn.2n fuses. Because of the nonlinearity
of resistivity of nickel due to temperature rise, the average temperature rise determined from the
voltage and current measurements may not represent the real average temperature rise of the wire
clement For the existing element configuration, the inaecUl'acy is within 13% for d.c, Currents and
7% for short current pulses. In addition for the average temperature rise ahove the magnetic
..._____________ .~1I(':~ __ .:
R4
tran~ition point (about oJO K), the evaluat.ed value hom the rcsistance rncasun,;nKnl is higher lhan
the real ,IVel'ilge lemperature ri~c. This means (hat cxpcriml;:f)!<llly <;:vaillaled rcslills in Fig. 7.3 til
caleu lations (Eq. 7. X) better i nhis nonlinearity of resistivity is laken inlo aecounl.
Maximum displacement
[f1 m
1
1200
1000
.....•• J
".-
800
........
.-.;.-.--
.,.-.-"
·1,
600
+'
..
+'
400
200
~~~
o
o
-It.
fr·-··-~--·-~·..,.-----,~.-
200
400
600
Temperature rise
800
1000 1200
["C J
F;gure 7.3 Dependence of displacements on temperature rise (nickel wires)
"+" : microscope observation;" ": theory (Eq. 7. 8)
Displacement [um J
400 r··
...... - . - - . - - - - . -........ .
350
-I:'"'T-
.,
!.... ---
80
..
~.
100
Temperature rise [Celsius J
Figure 7.4 Dependence of displacements on tempera((J(e rise (AgISn.ln wires)
"+" ; microscope observation; '~-.-".' theory (Eq. 7. 8)
By introducing the mea~urcd (,:urrent into thermal modelling, (he average lel1lperalUr(' ri~(,: W,lS
tound tor dillcren( (I valuo~ ofcurrcnt pulses. Using the dhplaccment. lel1lrenl(III"": ri~l: 1'l.:lulion in
S~~cti(1n 7.2, theoretical displaecTm~lJh wete nhtaincd. Tabk 7.2 iisiS ~xtH~dml'l1tal resul!~ limll
high speed pho(ograrhy ,11\<1 temperature eakulatior\~ I"mlll thcrl1lall1lotlellin~.
Thermal Buckling of Wire Elements
85
Table 7.2 Results of measurements and calculations
for different ft values of pulsed currents
1",
0.22
0.17
0,60
0.7R
0.98
0.17
0,28
0.46
O.M
0.75
l~xr
52
101
164
205
284
Dm",
247
349
458
516
590
%
0.11
022
0.36
0.45
0.62
t.e. %
0.05
0.10
0.17
0.21
0.28
t.8",%
0.06
0.12
0.19
0.24
0.34
T,,,,
60
111
207
301
431
T'im
50
93
169
218
328
D3i ..
250
349
475
541
665
2
As
Tt
r'lI/iN
-
t.8 1h
-
Figure 7.5 shows that theoretical calculations and results determined by using high speed
photography for AglSn.2n fuses; in agreement with experimental observations.
[lAm 1
Maximum displa.cement
700 ..... -..--~--~--~-.-
600
500 ..
400
300
_•• .,1", ,•••••• __ •• ,---..J._, _ _ _ ---'----
0.4
0.6
12t
[A 2s
0.8
1
Figure 7.5 Displacement as a function of t't value for current pulses (AgISn.Zn wires)
.~",' theory (thermal modelling. Eq. 7.8)
"0"'- observation from high speed photography;
According [0 Table 7.2, [he dcllection factors were caleulated and shown III I'ig. 7.h. The
aHrage value wils ab()lIl 0.54 for AglSn.2n fuse clements during !':ui'l'cnt ptdscs. I;or d.e. l'UITcnh.
(IS (emp~rat\lrc rise incrca~cs, the ddketiDn bet Or d\)(;re,lSe~ dowll to a vailic small llHiIl 0.5.
Deflection factor
()
o
0.3
o
50
250
.. J
300
Tem perature rise
Figure 7.6 Relationship between deflection and tempflrature rise (AgISn.2n fuse w/(/3)s)
"0" _ d. c. current; "+" _ pulse curren I; ': . . -" _ theory (Eq. 7.8)
To c-xamine thc inJluenl,;c of (emperature distribution (m [he dispIJ.cClllent, Pl'ot1k: or vcniull
displacements is compared with measurements for a d.c. current or 960 mi\ First, the
krnpemlnre distrihution for thl: (~urrmt waS simulated, thc results arc shown in i'i g 7.7.
45
rem perature
rise
( "C
1
,'" ....... .....- ..
rh
40
35
30
r
25
il
20
15
10
5
°0
5
15
10
POSition z
20
Imm 1
Figure 7.7 Temperature distribution for a d.c. current of 960 mA
a _ average temperature rise 18°C from voltage current meas(Jf(tmenls
b . tilerma/ modelling
Thermal Bucklin!? nf Wire Elements
R7
In Fig. 7.7, curve "0" indicate~ the average temperatul'e l'ise from the voltage and CUI'rcnt
measurement. Curve '"1/' indicates the distribution obtained fi·om the thermal modelling.
Figur(; 7,8 ~h()w~ the displ<lcernent. w as funct.ions of posit.ion ~ obtained Il\)!l\ difkrcnt
simulation methods.
Displacement in the y direction w
[pm J
300
250
200
150
100
50
0
0
10
5
z
15
20
[mm)
Figure 7, 8 Displacement for AgiSn. Zn fuse wires
a: Locke's method; b: Eq. 7.8; c: FEM at 30 Celsius;
d: FEM with temperature distribution (see Fig. 7.7)
In Fig. 7Y, eurve "a" indicates the results obtained by using the literature method [R5J.
Curve "b" gives the results from Eq, 7,8, Curve "c" presents the results from the Jinite dement
method, where the average temperature rise was used. Curve "d" presents the results from the
finite element method, where the temperature distribution in Fig. 7.7 was used. Mark "0"
displays thl;; observed displacements due to the d.c. current. This graph shows that the higgcsl
deviation hetween curve "a" and the observations exists. Therefore, methods presented in this
work offer~ a better solution than that in literature [85J.
Figure 7.9 shows the displacement u as functions of position z, Curve "(1" indica(es the
rt;suHs ubtained by using the literature method [RS]. CUl've "e" present~ the results from the finite
elemeot method, where the average temperature rise was used. Curve "d" prt;scnts lh<:: r<.:sllIIS
from the finite clemen! method, where the temperature distribution in Fig. 7.7 wa~ used.
Concerning the temperature distribution during the d.e. current below the minimum melting
cUI'rcnt, the di~placement u takes the direction towards two end caps, As the temperature is n~a!'
the uniform distribution (constant temperature rise), the displacement acts as eurve "a" and ""(;",
Displacement
1.5
In
the z direction
u
r----~----~---
I r~m 1
...... ".-.. y------"---
0.5 .
o
-0.5
·1
.1 5
L _ _ _ _~_ _ - ' - _ .
o
5
....- .... -~---.
10
z
15
20
I mm 1
Figure 7.9 Axial displacement for AglSn.ln fuse wires
a : Locke's method: c .' FEM at a temperature rise 30 Celsius,
d .' FEM with temperature rise If) Fig. 7. 7
l;igllT\~ 7.10 shows the FEM nurnl:rir<ll solutions of the strains e",
cnt'!'esponding to 1\'1. 7.1:'i hased ()i1 difter~nt. temperature distrihll[iun~,
11.:
;111<1 ,,/,
(U*II',
. "r
0.06
0.04
#. 0.02···
<=
~
U3
0··
-0.02 -
-0.04
o
Figure 7.10 FEM solution of strains em and eli for AgISn,Zn fuse wires
a temperature rise 30 Celsius; b : em temperature rise in Fig. 7. 7,c : eb for both temperature distribution (see Eqs. 7. 14 and 7. 15)
8' em at
Thermal Buckling of Wire Elements
l\9
In Fig. 7.10, Curve ';a" gives the results by assllrnin~ the uniform temperature distribution.
while Curve "b" gives the results corresponding to the temperature diwibution in Fig, 7,7, Curve
.'{~" displays the strain Ch for both temperature distributions.
Figure 7, II shows the relative stress as a function of position axial z. The stress is equal 10
1he ratio of the in-plane force N (see Eq. 7.l5) and the average thermal force stress EArl T.
0,---------,--------,---------,-----0.2 _.
!Il
!Il
~ -0,4
u;
(j)
:>'
~ ---=-~~==- ~
l a
~b
~ -0.6
ID
cr:
-0.8
-1 '---______----''---______----'______._---'-1~~.,_ •.•~
5
10
15
20
o
z
[mm]
Figure 7.11 FEM solution of relative stress for AgISn,Zn fuse wires (Eq, 7, 15)
a : at a temperature rise 30 Celsius; b : temperature rise in Fig. 7. 7
Temperature rise T takes the average value of the whole wire element. Similar to Fig. 7.10.
curve "a" gives the results obtained by assuming the uniform temperature distribution, while
(;urve "b" gives the results corresponding to the temperature distribution in Fig. 7.7. This graph
indicates that the in-plane force is compressive (negative) along the wire clement. For the
uniform temperature distribution, the in-plane force is almost a constant. The breaking location
is expected to be at the middle point. orland at the soldering position (near end car~) a~ a result
of the bending s1ress, Curve "b" indicates three points (one at the middle point and other 1wo
ncar end caps) subjected to larger stresses. Between the point neal' the end cap and the middle
point, additional two pOints also hay\: relatively high local strl;;ss,
As the heat transfer increases along the wire element, the extemion in the middle of tile wh'c
dement increases and the extension nCar the end caps decreases. It is concluded tha11he particles
with high 1emperature at1empt to move towards the location wllere 11le temperature is low.
Because the stress due 10 the bending reaches the highest value in the middle and at the end caps,
the maximum ddi)rmation depends largely on strain e which includes the contribution Df e", and
eh' Again because of bending, the breaking possibility at the middle point is the largest. These
explain why the fuse element breaks in the middle region for current pulses and for short time
d.e. currents.
9()
__
7
----_._--. __ . ( 'hol?/(.'"
._ ......... _--
However. (()r long cyclic loading, creep takc~ place. aller motion the wi),e dement may haw
dirIieully to l'OTIle had~ to its original position. In lhis case, if the defi:)fIl1ation is assumed to he
l,tlHtrolkd hy th~ s(rnin ('I, (see Fig. 7.10). then breaking locations can he expel,1cd lit 1h<;! plaee
where el, is the maximum. This assumption is supported by the rcsulls or lik(irn~: experiments
thr long current pulses, where thl,; breaking location is verified.
Figure 7.11 also show~ that the relative stress is IIPP!'OXimillciy a eonstanl about 0.6 "long.
the wire ckmt;:I)1. If the maximum kmperatllr~: rist.: in Fig. 7.7 is used, lhe r"I(11iv~: sll'css will
(it.:CI'CilSC to about (l.4. Bccallsl,; the dellQdion flletor in Sectiun 7,2 i~ n:latcd lVith this rd,l1iv~,
stress. comparison o("the dcllection fllctor in Fig. 7,7 "lith the relative stress hCUII)]l~~ obviolls.
7.6 Conclusions and future work
AnalYlit: sollltiom ,Ind t.he IInite demcnt (i.mnu]atil)n ,H'e prescnted I()r the hllcklhlg ()f thamally
stressl,;l! ~virc clemcnts under assumption of the clastic dcl()l"!lHlt ion. Tll~ analytical approOidl
aSSlIlllCS the unit()rmly di~tributcd 1emperature. The in - pl(Ul~ str(:ss a!ong the middle plml!.: of the
demml is ab) eval\l,lled to be the same, hom the Hnit.c clement Ii.)rrnulation, (lisplaecments or
wil'e elcm~nts arc ealculalcd and presented f()I' both lhe unifllrIll 1empcmture distribution (Ind
arbitrary temperature dis(rinut.ions. The analytic appro,lell provides a simple solution t{X the
vertical disrlaecrTll~r\t, Th~~ I1nite delllt:nt ()lmulatioil ()fkl'~ hoth vcrlical and a.xwl di~pl,\Ccmcnts
with consumption or numerous computer time, Tht! nrei1king locations or Ille wir(:: clement is also
discu~s(,;d,
I:ot' the practical interest, thi~ work can be improved in two aspects in the li.lturc. Tk I!rst i:;
tn extend thc (illite t:!I,;IIICIl( {clI'Illulation of thermal post budding problcnl~ for
stl'ip fuse
clcmcnL The second task is to indude the initi~l deflectioll fi.)r desiglling tile optimal shHJx~ of
thl.: ruse ekmen1..
,I
Chapter 8 Lifetime Predictions
This chaptcr presents physical models of lifetime predictions for dtC!ric fuses, when fuses
experienct; current pulses. Commercial miniature fuses and semiconductor protection fi.lses have
been used to verify the proposed modds. For short current pulses, lifetimes are estimated based
on the elastic fracture mechanism, while for long currcnt pulses the eomhination of Munson Coffin law and (he creep process is used, After determination of material and design propcrtics,
lifetime predictions are finally obtained from theory, in agreement with exp~rin1ental
observations. Consequently, change of current" time characteristics is indicated by using results
of lifetime predictions. Recommendation" are also made to reduce the experiments needed for
detcrmination of fuse lifetimes in praetice.
8.1 Introduction
Engineering materials are normally su~jected to stresses in the temperature dependent
environment, consequently, components show a limited lifetime. Because of the importance of
enginecring reliability, extensivc studies of metal deformation and fatigue [94, 95, 96] have hecn
perfonned in this century.
Before the lifetime of fuse is determined, main contributions to the element damage should
be defined. When fuses are sU1:liected to current pulses, temperature rise brings about thermal
strain due to thermal expansion. The strain produces stress due to the constraints of il)Se
elements. A cyclic thermal stress is applied to the fuse. The thermal stress fatigue is only of
cyclic nature, as long as the time period for each current pulse is short enough. At thc time heing,
this time limit is assumed to bc in sevcnll milliscconds, later this limit will be discLlssed again.
For long current pubes, in addition to the cyclic strain, thermally activated creep may playa
role. For continuous loading, thermally activated creep is the main origin for the damage.
As it ha.<; been discussed in tht: first chapter, previously proposed methods in lifetime
determination [35, 79, 971 are based on curve fitting of experimental results; lifetime relations
are purely empirical either without statistical analysis or clear physical meaning. Existing
standards lOr fuses abo do not provide enough information for lifetime expectancy. This means
for the prediction of lifetime that many experiments arc required for each design again, above all,
methods arc not general, they can not give an overview for fuse ageing.
Chapters 2, 3 and 4 have extended the study to improve lifetime estimation by using statistical
methods. The objective of this chapter is to develop physical models for lifetime predictions ti)r
fuses in genentl. This work is concerned with cyclic !hennal fatigue for both short and long current
pube~. Resides, creep during long Cllrrent pulses and continuous loading is also discussed. In the
dt;scription
this chapter, a typical time lag fuse [47]ls used as an example. Afterwards, the
theory i~ applied to semiconductor protection fuses. Results of high voltage fuses and low voltage
power rllS~S from literature are also prc~ented by using the mcthods proposed in this thesis.
or
91
8.2 Lifetime prediction for short current pulses
During lhermal buckling, u parI 01' t.he thennal ~triliil contrihutes to me~hanical .,train to result in
~II'e%. This mechanical ~tri\in may be divided into clastic straill ,Ind plastic strain. Bas(;d Oil the
rciationship belw~eil .~lre.~" and strain, tile number oj" currenl pulses which Ii.N:S C,I1\ withslam!
will he predicted. f()!lowing physit;u! modelling.
8.2.1 Physic:;.1 models
Although less general modelling of fusc lifetime behaviour has beeil pUhlishcd up to now,
enormous work has he(:n cOllducted sincl: 50's on Ii fetime modelling of mcchmlieal C()IJ)rl(lncnts
!46, 57,98,99. 100. 1011. This section attempts to make conneclion hetween g,:ncral m<.:chanies
studies and speci Ik l\lse hehaviOlIr.
Lifctime for thc clastit stmin range
In terms oi' the llunlhcr N oj" cycles to i)lilllrc, the 111(ldulu~ or elasticity I;, «Tld Ihe Ilwllotoni(:
Ihlclurc strength r;'r. lhe c.lastic "tmin C<.ln he expressed 146. ()() I
( !i.11
where
!>.cj2
E
elustit.: .~train amplitude
modulus oi' ebsti(;ity
stress amplitude
fatigue stress cocfj1cient
numb(;r of C\ltTcnt pulses to blowing
fatigue strength expmlent from -0.07 to -0,15
Lildimc for the plastic range
In 1954, Manson ,lnd Coffin 1981lwvc made two important e()ntribution~ nn the subject of metal
thermal 111t iglJ(~ at the sarn~ lime indepmdeotly. These contributiL1t1s propos!.: u I'~~lationship
hetwccn the plastic ~tr,lill and the numb~r of cycles to litilurc which have rOnlll:d foundatioTls 1('1'
thermallt\tigu~ stlldies up to nOW. rhi~ relatioll~hip is named as Mnnson - Collin law 14/\ 9K. l)l)l
With this relationship, th~ plastic part 0(" the strain is related wjlllthc number 01' ~:yclcs to failure
D.~: /'
2
t,:;p/2
r.'r
N
c
*. N'
( K.2 )
plastic strain nmplitude
!iltigue duetility cuen1cient
number current pulses to hlowing
ltlligue ductility ~xponent from -O,S to -0.7
or
Thermal bU(:kling for wire c1emcnts
Thermal S(I'i\in indue(;J ill lhe fhse dement due to a ellrr~!ll pulse is giv(;;l1 hy
Lifetime Predictions
r
where
is temperature coefficient for the thermal expansion and T is temperature difference.
Thcrmal buckling occurs (see Chapter 7) for the temperature ri~!;; abov!;; the critical limit. Only a
part of this thermal strain contributes to the actual mechanical strain. In Clwpter 7. the ddkuioll
factor is derived as
I
2111
1
I
Y="2+T
;-;:;:-r
() )
r'
( 8.3 )
For intermediate and high l't values of eurrent pulses, the detlection factor y is
constant. the mechanical strain is
6€!II = Y D.~"I
ajmo~l 11
( 8.4 )
According to the discussion above. the mechanical strain amplitm!c ~t;mi2 is generally given by
6&., _ 6c"
D.~ I'
---+222
8.2.2 Results of lifetime predictions for miniature fuses
To demonslrate the validity of our models, comparisons will be presented by using both
predictions based on measurements of displacements and predictions purdy from simulations.
For the lifetime predictions, material properties listed in Table 8.1 are used. The values directly
measured or derived arc indicated in the source item as TUE. The values from fuse
manufacturer and from the literature are also indicated, In addition, diameter, resistivity.
temperature coefficient of resistivity, fracture stress and elasticity have also heen
measured.
Table 8.1 Material properties in the modellinJ.
Properties
Source
Values
Units
wire diameter d
Litlclfusc
O.103R-3
m
fatigue strength exponent h
Hertzberg l46 J
-O.Og
fatigue stress coefficient (I}
Llttelfllse
115E6
Pn
Littelfusc
22.1 E"6
m/mK
Littelfuse
6lE9
Pu
equivalent mass density y
TUE
8.6E3
kg/m3
equivalent specific heat C
TUE
254
JikgK
resistivity at 20°C Po
Litlelfuse
3.48F-8
W.rn
fatigue ductili(y expont:nt ()
Hertzbergl46]
-0,5
temperature coefficient of
TUE
4,5E-3
TUE
0.5
thermal expansion coefficient
modulus of elasticit.y
E
""'""-
~
resistivity u
deflection factor y
_.
--
11K
94
- - - - - - - - - _ .. _---_..._" ..-.-.( hUjl!t'/'
01) mC:'lsuremellt~
Predictions based
S
of displacements
Frorn clispIHl.:~ment In~~Jsur(;ment~, mechanical strains wen:; detcrnlin~d 1'1:\ )71 as pr~'sented ill
Table X.2. The mechanienl strain 6.E", was considered ns the difference hetween the thermal .~I[·,dl\
A~1I1 contrihuted hy the temperature rise and Ille Jpparent strain i.\E" determined li'ofll lhe I1)ilXiIllUm
displacement hy the high speed films. J{i;':s\llts related with di l'krcn( /"/ vall!~~s 01 t:\[ITcnt pulses arc
summariscd in Table ~.\.2 with the c,llclllatcd lifetime N Il)r thi.; d,[~li~: rebtionship (SC.l' t-:'1. K.I).
Table 8.2
'"I/!IIlri'
A
"s
Lifetime predictions based on elastic strain ranges
T 0('
t.E:lh
')2
0.22
1\\, %
IY()
n.ll
Li£,"
101
_...
_
..
0.60
_.. _164
..... ". ....... ,.,._.....
205
--_. ,..
O.9f1
284
0.12
!.tJ+ 1(('
0.l9
:).:::"10';
-.
""~
0.21
0.45
.-
.-..
n.62
0.28
._-_..-
... ,.- ..... -
0.17
0.36
.......
n.n
0.10
0.22
N
9.5* I (J'i
OJl6
0.05
....-
0.017
I;t(}
__ ...
_ __. -
..... ...
0.24
281
0,34
3.6
. __ ...
.-
hgure 8.1 WIllpan:s these calculated liJdirnes (see T,lh!!;) fUj with experimmtaJ results, when;
1\";,, is the minirrHl)ll /, value corresponding to Cllrrent - time characteristics "I (hi;! silille time as
the pulse time. 1(\1' a current pub;.
10
_
10
6
~ 10
:oJ
_<J
4
010
ki
~
~ 10
10
2
o
10
___ •. 1 ... _ _ _-'--_ _
(J
·1
10
2
1 tm,n
Figure 8.1 Comparisons of experimental results with life tim 0 precfictioflS "ffi"
based on displacement measurements for different current pulses
"x". sinusoidal (exp.): "0".' rectangular (exp.)
Lifetime Predicfions
95
~----------------------------------------------------
In thi~ graph, Mark "0" indicates the obsetvations for rectangular current pulses and mark ·'x"
depicts the results thr sinusoidal current pulses. The cUlve with mark ffi gives the predicted values
of liJetimt~s bascd on the elastic strain relationship.
Purely thcorctic9llifctimc predictions
In order to estimate lildimes without use of any empirical relation, later on the temperature rise
and the resulting mechanical strain have been simulated by using PSPICE. By introducing the
material properties listed in Table 8.1, lifetimes of fuses for pulsed currents WI,;n.: computed with
Eq. 8.1 and tabulated in Table 8.3. where r.'im is the calculated temperature rise from the thermal
modelling.
Table 8.3 Theoretical lifetime for pulsed currents
f tp./s<
0.38
0.50
0.63
0.78
0.95
1.04
0.29
0.38
0.48
0.60
0.73
0.80
Trim °C
83
114
(56
208
276
31g
N
4.7* 10
8.9* IO~
1.8* 10
487
14
2.4
A 1s
ft,,)JJf$r.'
_.. rl
min
7
4
Figure 8.2 compares observed lifetimes with predictions from Table 8.3. The solid line
presents the lifetime calculated by using the temperature rise obtained from the thermal modelling
[52J.
Number of current pulses
o
x
x
8
x
x
1 0° '-:-____~_,,_""'_ ___~~--~~~--~~~-x.........J
10. 1
10°
2
1 tpulS€
2
1 tm1n
Figure 8.2 Comparisons of lifetime predictions (Eq. 8.1) and experimental results
"0": rectangular; "x'': sinusoidal
8.2.3 DiscuSSion
Both Figs. g.l and fU show thaI the numbcr of CUlTcnt pubes which h.lses with:;tand imTI:<!$eS as
the IIi valul: dc!;reas~.~, predictions arc well tiHed with lifetime observati(Hl,c.;, supposing that clastil:
strain is dominant. Bel,;l]usl,; temperature rise T is appro.xinlalely pmportionai to (" so Ih~~ !lumher
oj" current poIses N is approximately u linear l\lllclion of ft on the doubl!; logarithmic scalc.
J'hc()1'ctieally, the clastic
~traiT\
is of the most signiJLcunce fhr the high eyek
11!lipll~,
while J()r
low cycle fatigue. the plaslic slrain will bc the dominant item. The takeover point is sil\latcd lit
lildimes about 1.000 t;:orrcsponding to the strain amplitude lUll \46.991, PHO 11001 !l1l(ll.ogsdoll
! I02! studi(;d the thermal fhtigue oj" solder joints. Pan suggested tilat the cln~tic i"radure is "Iso
dOnlin(li\t for low cycle bligue J/.Jf thin layers with thickness of 0.2:\4 mm. bccal!s\.~ there is
ji\S\Jft1cicnt thickness to ai,;commodate the plastic inJ(mlWt(On. This is in lICU}nhIIH,:~~ with our
experimental observations (set) Figs. R.I and 8,2). whet'c wires with diarnl:1r.;rs III nt'der oj" 0.1 I1ml
arc used.
Although agt'cCmetll has been I(Hlnd betwccn lildime predictions and actual valucs, it should
hI,; ,!W(lrC that for a fusc cll,;mt~r)(, the ddhrmation Carl be developed in the axial direction and in the
radial direction. The ~tr~ss in the rmiial dir(;clioJl depends on the thermal expansion coefli(;ierlrs or
silver. tin-f,inc alloy and thc temperature rises. In the prediction ahove, the radial slmill :md stress
arl~ not r.;onecrncd. l3l:sides. tile ductility coei1i(;icnt, oxidation in the derm~llt, t.hc c,onnectiol1
technology and the local tCmper;llure rise may also have in11ucnccs on lildimt:s. In Chapters 2 and
1, the resistam,e increase has been reported during the 1i..lse lik. h()w~:vcr, no usc of l"(;sistaoce
change has bl:cn made t()r the liktimc determinations.
8.3 Lifetime prediction of miniature fuses for long current pulses
;\ !"ter flLses are sui:lk~~t~d to a number of long time current pulses, the position oj" ~~I~mt;nts
changes. Additio[l,llly, after breaking longitudinal cracks can also be foulld OJ) the element
!>ut'lbce rot' long current p\llses, in contrast to the radial cracks for short cUI'I'ent pulses, This
suggests that the pi<lstie deformation is induced. l3ec1IUse nf cycltc naturl~. ti"H: Id'etime is
suggcstod to follow Manson - Co(11n law. [n this process, the steady ereql strillrl rate is taken For
(I1~ determination oj"plastic ~trains.
8.3.1 Temperature relationship
Temperature risc fot, long current pulses can hc dclermin~d hoth hy simulatio1!~ ,llHt cxperiment~,
Twn experimental methods have. been applied to determine the aver<"lge temperature ri~c or ftlSC
wire clements. The nt'st mclh{)d i~ ba~ed on the mea~llrement of the volt1Ig~~ and current. from
which resistance is ddcrmincd. As the [(;:~islivity dcpcndenr.:~~ nf' material \)11 templ:rill\[rC is
known, thc average tempcrature ri~e can he calculated,
The second procedure! 551 is derived from the buekling theory proposed 11\ Chapter 7. When
currents ar~~ applied to fllses, thermal buckling (",lkes place. Hoth curl'CL11s and
dispiaceml:J\r.s may be measurr::d, As it has been proved that the maxiwum displaccment IHls (I
well defined rciatlonship with the average tr;;mperatUL'e rise. thl.; r~lat iOllship hl'lwl~(;n the
temperature risl~ and the currcnt is found,
~Icctric
Uji!lime Predictions
97
Figure 8.3 shows results 01" average ((;mperature rise~ obtained from m(;Usurements 01"
displacements. The experimental relation between the average temperature riSG T and the d.l.:.
current I is tktermincd from curvc fitting to be
T= lOon I'
Thls suggests
fI
general expression for the temperature rise T whleh can be described by
T ex:
/,,1
where Of is a constant.
Temperature rise
140
[Celsiws]
-~""-"'-.-.-----~--~-~-~---,
120
100
80
60
40
20
o O~~~~~~~~--~~~~~~
0.2
0.4
0.6
O.S
1
1.2
1.4
1.6
Current
[A]
Figure 8.3 The average temperature rise determined from
displacement measurements as a function of d. c. current
8.3.2 Creep ra te
The creep rate is related to stress, temperature and time in general. Various relationships based
on experiments have been proposed in the past One of the common u~ed relationships is the
power law creep 145,461 for the steady state creep rate.
This states that at intermediate to high stresses and at temperature ahove 0.5 7;", where the
thermally activated cn:ep process is dominated by the activation energy for self - diflusion. the
creep rate is given by
.
~., (.C (J
~11
wherc 112 is 11 constant (112 = 4~5 ). This stress dependency has been demonstrated and hold3 hr
pure metals and their solid solutions (silver, copper, aluminium, nickel and etc.J.lf (J 0: 'l~ the
creep rate i3 rewritten tl3
For the determination of creep, the relationship with time is essential. Concerning time
influence. during each period, the creep rate may be assumed to be
---.---
" _ ....
_---------------" , - - - - - - - ( 8.5 )
wherc
In
is a material (.Cl1nstant.
!:U.3 Lifetime relationship
as~umcd
If the plastic strain is
ratc, it follows
!\~: I~
6.t: I~
tl\ he equallo
(;[ct;":p
stmin contribuled by tilt.: ,tcildy st(ile
tT~~Cp
I'; \ {
=
All
trl+~I' t
( X.1i )
lllli
COllihinlltion of hqs. R.2 and 8.6 leads 10 the relationship I(lr the 1l11l11hcr of current pubes fix
J\ISCS to blow
( 8,7 )
l:il1ally. the relationship fnr the I1ll1l1her oj" eum:nt pulses whieh fuses withstand is IItJlncd.
S.3.4 Determination of parameters
a,
For the time dCi<ly fuses ill discllssion, the value = 3 can bt.'= ohtained from Fig. 8.1, The value
of (/] is givcn by 4 < a.! <" 5 m;cording 1.0 thc powcr law creep, a trial vullle a., 4. 5 I~ ~lJggeslC{1
theret(\rc. Manson· Collin low staWs that the li11igue ductility CXPlll"lCril (' - (O.'i 0.7), in thi~
work, C '" -0. ~ is s\lggest.ed.
I'or the determination or the material constant m, experiments were ~an'it;;d out. n\!· th~, same
current hut with dif!(;rt,:Tlt tin times. The number of current pulses which n,ISeS withstand and the
on time ~tHl\lld hnve a lincar relation on a double logllrithrnic scale: the slope 01" the relation is a
tllc,lsurc lilr the value 01" m.
From the experimental !'CSltlts listed ill Table 3.3 of Chapkr :1, three sCrJcs of cxperimt:nts
were us~~cI fi.)J' this purpose. Their values a!'e given in Table XA.
Table 8.4 Oata used for the determination of material constants
f
.. -
1.52 A
1.:')2 ;\
J.52 ;\
ton
I min
."
5mill
10min
filii
Imin
5min
"1';11 in
5%,
mean N
20 ... .. 80
~
3.8
2.1
.. ..,.., ...
19.7
7.9
1)5%
l'iX
._--42.4
I~
According to this wble, Fig. 8.4 gives the results l~)r th~ lime slope. In is 1~)\Jnd to be ·0.5,
therci()re the exponential compom~nt for time is "I ill the lifetime relation. Arlot her tcatllrc of this
evaluation is thilt the determination of constant KIJ From Fig. R.4. the vallie 01' KIl for the mean
[63[ i~ l(lIlTlti to be 3.6* IO~ ( the :'i (X, value is 7.8 * 10\
Liferime Predictions
99
2 Number of current pulses
~
10
1
10 .
~~
~
--;'b'2-~~~~~~~1W03
Time
[s1
Figure 8.4 Determination of material constants m and Ko
"x-x"; mean values; "0--0": 5% values
8.3.5 Discussion
As a final expression tt)r the lifetime consumption by plastic strain, it follows from Eq. 8.7
N = K~ r 17 r l
( 3.3 )
with K(J =3.6~108 , a} = 3, (1] = 4,5, and m = -112. In Fig, 8.5, the relation Eg. 8.3. based on
limited data from Table 8.4 are compared with the whole set of experimental lifetime:>; from
Tables 3.1 and 3.2.
Number of current pulses
106~__~____- .____~____- ,____- ,____~
1'27 r1
Figure B.5 Comparisons of predicted lifetimes and observations
"0" ; for the on time from 10 seconds to 1 hour (see Table 3,3)
"x"; 5% values for the on time of 1 hour (see Table 3.1)
100
- - - - - - - - - - - - - - - ---_..
-...__._- . _ - - - - - - -
Considering the experimental Ii i0times in Table y,), ~howing sueh a wide nllll!C of v"lill,:;~ I{)!
current I, on tirm: "," and otl' (ime '''/f; it is remarkable that thl,; lijdim~s Cill\ be ,'elated with only
one exp!'e.~si()n, even when some pai'amcters wtre determined by u~;ing u part 01" this t<1hk.
For t.he difthsion dominant situation, dilTusion t.hickness is known to he pwportiollal to the
square mot of time and dilTusion coel1icient. The diffusion coeni(;ient 1461 j,; r,~"lt(,!d with the
activation energy Q and t.;mpera(Ure ri~c T. Combining Ihe difrusion with (ile power law creep.
Ih(; (;f/;;I,:;P ra(e Cflrl be npproximatcd by
wh,,;rl.; Q is tht: i~ctiv<lt.i()rl energy fbr diffusion, R i~ gns
r decreases, the Ii fdiml: in(;[t:ases wilh Ko also.
Cl)n~tant.
This m..:ans 111:11
:IS
tt;lIlJ'!eralurc
I'iSt
8.4 Lifetime prediction for a continuous loading
i"or continuous loading, (.he creep accumulation may he di ffe-rent from er(;ep wilh cydi,: loading.
llowcycr, n)[lsider'ing the plastic strain rclation proposed in Scction SJ, thl.; lilt:limt,; )'(;,l(is
n;sultitlg in
<l
rupture time t
" 1 .1)
J-
Kn
I~m /
I
~
III
( 11.9 )
or
Figurc S.O shows l,omparisons of rrcciictions i"rom Eq, g,!) <lod ohservations (rom hg. 3.3.
"-'-'--'i--'---r---' '-r--'"
1"-
.
I
I
:
I
I
\
o
~
10
1 .. _.•.•i_ ...L_J_....I..._Ld.. ___ _
.1
10
10°
Current
10
1
[A]
Figure 8.6 Comparisons of predictions (Eq. 8.9) and obsfJr\mtiotls
for a d. c. current' '" 1.5·'n
!4~fime
Predicfions
]0]
It shows that indications for the minimum melting current which is normally determined
after several hours has lost their relevance in the vcry long time.
8.5 Change of current ~ time characteristics
Up to now, extensive studies have been performed lor lifetimE: determinations for short current
pulses and long current pulses. It is clear that fuses age if creep of the fuse element happens or
elastic fracture is involved.
Because of ageing, current - time characteristics change. They ~hift to faster operating
curves. If a fuse breaks after a number of current pulses, the
value of the last current pulse
before breaking is the momentary I"t value of the fuse, This means that Eq. 8.7 can be uscd 10
dete.rmine the whole shifted 1- t Curve of fuses with the numher of long current r\l!scs N ,IS ,I
parameter. For short current pulses, Eq. 8.] can be \lsed for determining the shift of 1 - t curve.
For the transition from the creep dominant interruption to the elastic fracture, the number
current pulses for fuses to withstand witl be the same. From Fig. 8.2 and Eq. 8.7. for different
current magnitudes, the On time for the transition is estimated to be about 5 seconds tor the time
lag fuses \lnder discussion. Figure 8.7 shows comparison of current - time characteristics for new
products and fuses after subjected to 10000 current pulses. Curve "a" indicates the shifted I - t
characteristic calculated hy creep dependent part and the elastic fracture determined part.
it
or
10
2
1- I limits for virgin fuses
a : N= 10000 - '
Ratio of current to the rated current
Figure 8.7 Comparison of current - time characteristics of virgin fuses
(before current pulses) with that after current pulses (N=10000)
1(12
('flUl'll'l'
S
Phy~ically, (he shin of" CUlTcn( - time characteris(i(; is also directly rc1all.xl with thl: incn;H~c
of" resis(ancc of t'u~c~. In tlu: adiahalie he.ating, (he /1, for the mcltini! is ,I ~~(}nstant whidl is
proportionnl to the invcrs(; or resi~tivity (or resistance). Iinwevcr, (hl.~ 1J1illilnllll\ Itlsing current is
p"oporlional to tlu: inverse square root of the resistivity. Consi(kring the f"ae! tlw( r~~islance
increases aner usc indicated in Chapters 2 ,md 3, the mort.: shiH of / - I curve in (he adiabati(;
range will bl.: cxpected as c()mpar(;d with the shift in the r,tl)ge of the small (;un'cnts 1ll!' the SlIWt.:
amount of resistance intre<1se. In other words, t()r the same amounl of !':OI'rent pulses, (hl.~ shi n or
1- t curve is larger lur snlitil currents, This is nol significant in I'ig. K.7.
Previous res~<1rcher:<: considered lhallhe fatigue or ('usc clement was mainly (;(1ntrniled hy thl.~
plastic strain range. [n Section X.2, lifetimes an: predicted according (() lhe clastic J'ml.'lurl.~ i()r short
elllTent pulses. If the rdative r't v<llue ol'thc pulsed (;(IITC!)( is smaller than (),7, clastie strain plllY~
,It\ import.ant role. In the ril.nge of larg(; relative It value :.- OJ, plns!ic stmin l~:\i~(~, ct'ncks
propaga((; in " T)lme or less briHie t:1shion [100 I (or wire elements with small diamder~
(wrresponding \0 the pla((; with ,I lhickness 0('0,254 mm), Eq. fI.1 can still he llSl:d f()J' tht~ rus~
lildime prediction. In Sl:dions 1.\.3 ,md flA, tk litet(me~ arc deterrnilwt\ with the pbsti(; str,lin
(ct~ep) lor long current pube.~ and eontinuou~ loading. ;\t this mOlfwnt tht: reason is s(ill nO! dear
why not all protesses H)llow the ciltSti(; fracture.
Fwm hg. f..7, it is also dear t.hilt the proper protection provided by new il.lses may be not
v,dici fm fuscs after liS!; bcr;~use of the shill of current· time chilrilcteristics. For (hi~ rl!;ISOn, it is
reeommcndd til,lt fuse manuli.ldlm:rs should provide tht~ information 0(' shill ill current - tilT\e
eharaderistics 1'0 avoid unexpect~(i interruption due tn ageing. This rcquit~mcnt. is Hi II nO! yet
~r~~d lied in me Publiultions jhr Ii.lses.
8,6 Lifetime prediction for notched strip fuses
In the pn;vio(ls scctions, lildimG predictions have been prescnted where typical ,:ornfllt;r'clal
minhl1urc Il.lses have been laken as examples, This section describes cffhrts to <lpply the method
of Iifdime prcdi!,:t.iolls t()r semiconductor protection thses subjected to Shott current pulses.
Tlwnnol Imelding or (hr; ~~Iement due (0 electric eurrcn(s is di,~Ctl.~~ed, and thermal fatigue is
considered as the main rC!lson ji)r ageing,
For the commc!'cinl semicondudor protection li.lSI;;S ill te:<:l, tbe rawLi um'0nt nr silver rUS(;
clements was 160 ;\. Tht: ('use construction was ~hown in Fig. 1.1, (lie clcml:nt shapes and
dimension wtre shown in Fig~, 4.4 - 4.7.
8.6.1 Comparisons of calculati()ns and observations
When fllse~ Me subjeewd to currcnt pulst:s, temperaturc ri~e brings abmJi (hernwl stress due 10
thermal expansion. As the thermal stress is above a er.:r\"in value, the 1\I~t~ dement tends t(l m()ve
and lcave~ its pI'evloLis positiorL During post buckling, only ;1 part or the tlwrmal ~train is
nm(rihuted to the rncd)(tnical strain to pmdLlcc stress, Til c rd()J'(; , to pn:did the liktimr.:, tile
temperature distrihut.ion and thl.~ thermlll buckling behaviour wen; ~llld1cd ,md (ks(;rihcd in
Chaptcr~ 4 and o.
Thermal strain induced in the notch region 0(' the Illsc dement dut.: t() " currenl pub: is
proportio[wllO the tempen\(ure rise. The (o(al thermal strain UUl he obtained by irllcgrnting J'ront
:;; I, to 1: and is approximated by
f4"elime Predictions
103
~'\T(x);;:;Ao.T
'-..J
~
(ll'
ITmx
(1:\10 )
where ~ is the thermal expansion coefficient ofsilv(;r (20* 10-\ Ail, I" and 12 al'e cons«lnts,
The mechanical strain is only a fraction of the thermal strain, it is similar to that for fuses
with wire elements in air. Based on the relationship between stress and strain in Ihl;: elastic range
(ilt~ = t..~I1)' th(; number of current pulses N which fuses can with~tand may be predicted 146, 971
according to Eq, 8, I.
For ~dlver fuse elements, modulus of elasticity E = 71 * [0'1 MP II , JitligUI;: sln:ss coefficient cr',
"130 MP" i,;an be u~cd, Fatigue strength exponent b= -0.08 was assumed. For clement~ with I~ve
rows of notches, parameters All , I" ,12 in Fq. 8.10 were determined from the ~imulation to be Au
'. 0.23. I,. = 1,5 mm. 12 = 4 mm, However, the deflection factor y in Eq. R.4 is not known. To
J()ITnulatc the calculations, this factor wa~ assumed to be the same as for the elements with one
row of notches shown in Fig, 4,5, Based on the experimental observations presented in Chapler
4, Y" 0.88 was found.
As it has been indicated in Chapter 4. to study the deformation
mechanism of
semiconductor fuses, lifetime tests were performed with different types of fuse elements (type A.
type C and type D). From th(; experiments, the number of current pulses which fuses withstood
and their mean values were obtained. Comparison of predictions and the mean values of
observations is shown in Fig. 8.8. This figure clearly shows that for pulsed Currents with a
duration of about 10 ms, lifetimes of fuses with sand decrease as the i I value increases.
predictions Hre in (he conservative side of (he number of Current pulses which fuses withstand.
Number of current pulses
10'r-----------------------------------------~~
-it-
1 O~
o
o
x
o
x
Figure 8.8 Comparisons of predictions ~Jnd observations
"x" : type A; I/o" : type C; 1/+" : type D; --: Calculation
104
In Fig. !U( the number of current pulses that Ii.lses withstand has ken rn;~(;)l(~xl tngether
with experimental results i()r short (;lIlTent pubes 01" nbout 10 11K I;nr t'(~iil scmicnnductor I"USl'
applications, cydes lHT olkn with on timos of a(ol1tld :) seconds (mowr starling) or sev.,;ml
rninut(;s (1radion), hom the discussion in Section R.5. it is known llidt tht: I;i,!sti..: fl'iIClIH"C
mechanism mainly determincs liktimes for th~ time lag fuses 1ilt, on lim~> smalkr than 5
seconds. Because thc silver clement cr~eps slower than the clement f()r tht~ tillll.: 1,1i! rllst's, tile
timc limit for thc elastic frnct\lre mechanism is expcctcd to be larglT Il1an ') s~:c{)n(k slIppnse thal
Ii.ISI.:S are properly (ksigncd. Thcrehrc, tht~ resllll~ hen: Me sti II valid for Ihis ~;illlati()n. hlr on
limes in the range 01" several minutes, a further t~XmJli[l,lti()1I i.s Ilcc(1cd to c()I1sidl'r Ihl;
~;I)])lpeti(iol) hetween crcep and elastic I"rm:tllr~.
8,6.2 How to ~'Cdtll~C IlgciTlg
Ageing is a time depcndent pro(;(;ss, Effects of long time loads on the Ii Idil11l; cnllsuming ure
mainly to be of crcep nature (including difJ\.Jsion and oxidation), l'"or :;t!oI1 tillll! loads, Ii fetimes
are considered to be um~llmt;!d due tn cyclic fatigue related with ~tr~in variations 1571.
As ageing dUI;: to temperature risc is eonc~rned. per'haps the maximum temperatu[1.: call he
proposed <I.~ one f1letnr Ihr design and application of fuses. According tl) the defor'l1lation
mechanism map 1461, It)r ternp(:T<1ture below 200°C there will n(; no plnstic defhrmation I()j'
silver dements. On this baSIS, fuses should he designed t() (;arry currents which do not produce
overheating. For the ~:1)1l1me1'dal fuses under invl::stiga(ion, when with thc rated eurrent of 160 II.
is (;x~rtcd, the com::sponding temp(;nlt\lr~ rise is found to he 200 0(' liwn tlie I ;M'I'I' simulation,
Thcrei"hre, in theory this rlil;;i1IlS the designed fuses will have inJlnitc lifetimes if the eum.:nt !.lows
through the~e fuses without switching off.
The argument here is that (icl(mnation mechanism Jl\ilPS arc established at a rat iter slow
heating up process, is tlie [e~illt rclevll11t to Ii.lsc applications? According: to onscrvat!nn provided
in 1321, during thl;! l';lpid hcating up dillusion may occur on the gnli)l hO(Jlltiarics, bccaust~ of
illlwlllnginol.1s material construction, (t mcans that the critt~ri'l from the dcfhrmation In,lf) is nnly
vnlid 1'01' t.he small current I,;arrying ,Ibllity and constant loads which do not always [I.~ll~Ci reality.
lkcausc of cyclil,; cffJ;.Cls, temperature variations pl'()duee Jel()[[IHilio{l l.:VL!1\ at the lower
temp(;rature, a~ (I consequence, lifetime reduction can not bl.; aVl)id. Tile question is how tn
lk~igl\ an element shape with the optimallifetinl(;.
Straight fuse ekmI.:TI(..s providc a relative high stress during current !lowing, heeatlsc themw)
expansion Gln not he released ea~ily. In practice, ollen ()riginally bent or waved fuse dements
,II'C used. In the most sitlHltions, the dement notch h~s to withstand th(; IIw,ximllm strcss because
01" the high(;st kmpt)t'aturc risc and the Slwlkst cross sectional 'Irei!. The local stress in Ow fllse
(;](;IIlI;:])t notch b determined by thermal cxpansion, strain due to the displa(;<:lll~:l\t in the axial
dirt)etion and strain due to th~ dhplaeement in the perpendicular i.liredion. Anothcr factor is OIl;
curvature at thl;; nntch due to the vJ;:rt.ical dispiaeeml.;nt. On the one hand, Ih~: Ver1 leal
displacement will release pn((. of thermal expansion, stress dt~cr(;ases. ()I\ the other hand,
bending will increase the stress on the outer surface. The I1nal situation depend~ (Hl thc
compmsation of two factors.
i.~
The hreaking location of f\l~e elements is situated at the pla(;e wher~ m!lximutl1 dc I"ormation
Induced. Experiments indicate the hr~~ilking usually OCUlr~ ilt the notch ncar end (:nps. II.s
Lifetime ['redictions
105
temperature rises near end caps arc not thc highest, stress release is expected 10 be less al these
locations due to the element design,
For very short pulse times, lifetime difference due to demmt shapes, sand and bounded sand
will decrease in theory because of the delay in displacement. The maximum stress imposed
depends mainly On thermal expansion caused by joule heating.
8.7 Application of the method to results from literature
In this scction, results presented in several literature for difli.::renl lypes of fuscs will be examined
with t.he proposl:u lilt:time determination mcthod for miniature fuses. FOI' the power law or crl;;ep
ratc, aJ = 4 ._, 5, the exponent in Eq. 8.7 C<1n thus be from 24 to 30, if T IX
Because of heat
transfer in sand, a I <" 3 ean be expected in thc expression IX: ! "I for low voltage power fuses,
Consequent.ly, the exponent of current in the lifetime relalion can be below 24. Stevenson [97]
obtained experimental results for semiconductor protection fuses with on times from 5 seconds to
10 minuh::s, The curve slope in the fitted function can be found to be 0,045 on a double logarithmic
scale, This value is very close to 1124 and comparable to the slope liZ7. This encourage further
practice of using physical models presented in Section 8,3
r
i.
In 1972, Slettcrink [104] conducted experiments for determining the number of current
pulses that fuses withstood. The tcsted fuse links were made of silver, a spot or pure tin was
positioned be!w~en two rows of notches of the fuse link. The I'ated current of 1hese j~lsc links
was 100 1\.. The number of current pulses with On times from about 10 seconds to 1000 seconds
was presented f()r different current values hetween 160 A and 400 A. From the t~xperimental
results. the C\lrrent. - time characteristics of fuse links were evaluated with the number of cutrerlt
pulses as parameter. As discussed in Section 8.3, for the pure diff\lsion controlled ageing, the
exponent of time is about -I for the lifetime rdation (see Eg. 8..7). Because of stress
concentration near the not.ch, it may be expected that creep increases faster for the notched
clement than for the uniform element due to diffusion, For the same reaSOn as indicated in
Section 8.3, this time exponent has to be determined fl'Orn experimental values, The exponent of
on time! was found to be -4. Following this scheme, calculations were made in use of
N" k
o
!'QI~.(!!,,)~' ~
/4
1
( 8, II )
where kl) = 2.51, In = 100 A. Results from the literature are presented with calculations from Eg,
8.11 in Fig, 8,9, where marks represent the observations for different currents and lines give the
corresponding calculations. From this, again one may conclude that from the determination of
One set of ageing results, all data can be related with the same expression.
I ()()
( '/Wjller
8
"",."--'-~--'------
10
4
'r""'---r"\""""T
'I
'I
160 ;\
<f'!
w
1 O~ ..
100/\
<f'!
"5
c..
C
ID
10~
~
::I
0
~
Q)
J;j
()
10
o
1
400 A
\
E
;;;J
z 10°
10,'1
10
0
250 A
_...L----L...-.~,~,~~'___"'____'_...L,
10'
Time
t
.
200 ;\
.L.L...J..!
I,l .
10'
[s
10
'1
1
Figure 8.9 Comparisons of calculations (Eq. 8.11) and observations
after S/etterink [104]
--- : Calculation: x, * + 0 . Observations
For the h.v. motor protcdi(lll~. Ossowieki 1105] presenkd experimental r'esuhs of copper
fuse clements for cyclic loading. In a similar way, rc~ulls thcr<: t;(lrl ,llso he cnrapolatd on tht:
basis of e1astil.: Ir(l~:1\II'e mcchanisms.
8.8 Recommendations
In the cxi~ting ~t.andard lEe Publit,ation 127, pulse tests and cndllrmll.;t: {t;sls hillie been spcciiicd
Ihl' small amounts or cydil.; 1.;1Irreots_ 1\ very limikd number (1000 Pllises in ILC 127) or puhed
current is applied hl th.: fil~e to examine the quality of fllses. On the one hum!. Ihc magnitudc or
pulsed e(lw~nt will be too low to givt: <I indication of pulse withstand ahility of Il.lses; on tht, ollH,;r
hand, from this inve~tigatinn it. is clear that f\m:s may with~tand some th()lIsand~ oi"puhi;;d cUI'rents,
but they may still hil ,lncr a long run in ~crvi~e, Results from thc tcsb Ciln not give expectations
how long foses operate according to thdl' characteristics, Th.: nnly tiling known is that i"u~<:~ can
withstand the specilicd nurnner.~ of current pubes. Nevertheless, this mt:a~ure il\d~ed is ertcctivc
to remove Iht: iTlitial Tn;)nuillcturing lililurl;:s of the produets. Th":r<;;i()rc, the requirement in IL~C is
unsure I:n guarantee the long t~rm hehaviour of fust:~. more specific values or Ii idiTlIC shlluld be
carried out as a guidm\l;c orsdectivity.
In conlrast t.o these, for both pulse t.ests and emlurance tests it is suggested Ihnl ruses are
for two values of spc(;ilJi.: current pulses until their operation. High eurrent vidovs may be
lI~ed to reduce the testing time. For long current pulses according to Eq. '!l.,7. constant K/i and 1"/"1
can be determined. H;)sed on these known fnctors, Ii retime~ om (H~ predicted tilr gcner,il
(;onditions, 1"<)1' short current pubes, because the slope is approximately constant lilr dll'lcrCni 1"1
Vilh.lcs of current pulses. liretimes e[lI1 also be de1(!l'rlllncc\ as a linear rUll~:lillll Dr I Ill: relative (I
k~led
Llletime: Predi(:fions
107
value. On the basis of lifetime information, thl;: shiH of current· time chawcteristics can bl.:
determined. The similar issues can be made also for semiconductor protection fuses.
8.9 Conclusions
In this chapter, physical models for lifetime predictions have been established lur short currcnt
pulse and long I.:urrcnt pulses. Possibilities to extend the model for continuous 10ilding are also
discussed. Predictions for typical time lag fuses have been demonstrated and wmpared with
experiment<ll ob5ervations; agreement has heen found, The work is developed purdy on tile
physil.:al basis and results obtained so far therefore provide a significant understanding of fuse
ageing pwblern~ compared with previous investigations, Methods proposed arc also sup]'lnr'h~d
by previous contributions which cover topics of semiconduetOl' protection fuses, low voltage
fuses and high voltage fuses. For short current pulst:s, the exponent of It in lifetime relation
depends On the ekmcnt materials, typically -12.5. For long current pulses, the exponent of
current I is from 24 - 30 and the exponent of time I may vary from ·1 to -4. In general
applications of the methods, only a few of experiments are needed to determine fuse liJdimes for
cyclic loading. Therefore, it assists the evaluation of commercial products, new developments
and applications of fuses. Also this work offers a basis for more powerful tests for detecting
fuse ageing.
Part V
General Conclusions
Chapter 9 Conclusions
TiliS tilesis deals with ageing prohlems of electric fuses in service and descrihcs methods to
prcdic! lifdimes fur these fuses. "I"ypicaJ miniature fuses and semiconductor protection tbse~ at·c
used as examples to demonstrate the application of proposcd methods. This work has been
carried out in co-operation with SIBA GmbH. Uinen, Germany and Linelfuse BY. Utrech!. the
Netherlands. In particular. attention has been paid to relations between motion and lifetime for
different types of fuse elements. Simulations of non-linear thermal and mechanical responses
duc to electric current are performed. Deformation is studied for notched fust: clements by using
a scanning electron microscope and an optical microscope.
9.1 Main results
( I)
During the lifetime of miniature fuses, measured resistance shows a gradual increase fix
short, long eUITcnt pulses and continuous loading. As a meaSUre for the reached lifetime
consumption. it is recommended to check the voltage drop.
Aller semiconductor protection fuses subjected to current pulses, damage of tile fuse
elements has been examined by using a scanning electron microscope and an optical
microscope. Significant deformation was found in the notch of the element. However,
resistance remains more or less the same. Resistance measurements can only indicate the
spread of new products and provide a little guidance for the lifetime consumption for short
CUiTent pulses.
(2)
The temperature distribution within a fuse is simulated by using the electrical analogue
method for both miniature fuses and semiconductor protection fuses. Voltage responses of
current pulses and current • time characteristics have been found in agreement with
experimental observations. For semiconductor protection fuses, numerical results of the
current density distribution can also be obtained with EMTP fTom three dimensional nonlinear transient simulations.
( 3 ,)
For straight wire elements, the average temperature rise can be obtained from resistance
determinations for arbitrary temperature distributions with an acceptable accuracy. !-"rom
the average temperature rise or the temperature distribution, the displacement and
corresponding stress are calculated On the basis of thermal post buckling analysis. The
displacement perpendicular to the element is proportional to the square root of the average
temperature rise. The stress along the element is approximately the same and proportional
to the total thermal expansion.
(4)
The previously suggested empirical value of the deflection factor for considering: fuse
element buckling has been determined experimentally and given a theordi,"al ba~i~ flu'
both miniature fuses and semiconductor protection fuses.
109
110
(5)
('hap/a <)
For short current pulses, the lildime i~ predict.ed hased on the clastic ti'adurc Il1cdl,lnism
in llgrc;;emt;n( with experiments. The lif(~time can be approximllted ,I~ ,I lineal' n.lIlCtion 01"
thc /2/ valuc of a current pulse on the double logarithmic scale for minilitulT fU~t;s ,Inl!
semit;"(lfl(hJct.ll1' protection fI.lses.
The exponent in the lil\;tirne function may vary (i"mn -1; to -20 for dirkr~:!lt types of
miniature nl.~CS; the wave (orm of the cum:nt pube has a secondary in!lucncc on th~:
lifetime.
For the practical interest., combination or good h(:ut condut;tinn from thc dement to its
sUITOlmding and (he stress release due to dement wave sh(lpcs may signitlcantly in(;rc(!~~:
(ile ruse lifetimes.
( (l )
For long current pulses, the lifetime of miniature fuses is prediut:d hy t;lJ!ddcring thl~
thermally activakJ creep rrocess. The IiI-dime can hc rt;pr~~scntcd ;Is an cxponential
(tmction 01" current !Ind on time. Exponents of I,;urrtnt ,\[\(1 on time depend on desipls and
Illateriah of the fuse clement; they can b~ determined by a ftw cxperimcllts, Thi~ (unction
has been con(irrned by experimental results for H typi(;aJ (im!; lng. miniature fuse.
Application of thc lifetime relation is also addressed for other types of ru~t:~ with and
without M-cnt:l,;t~,
(7)
I'"or continuous current, tht: li1etime of miniature fuses is approximak:(] (In the k,,,is of the
thermally 11t:tivated creep model (hr long ClllTent pube~.
(g)
In existing Sl,mdal'ds related with luses. there Me no systematic methods hlr lkt(;rrnil1lllg
(he hlse Hfetimc or the number of current pulses that fuses withstood and tlw deterioration
of current· time characteristics, Jfthe lifetime is required. a lot oj" expetlments should Ix:
realised,
In (Ilis work, aft.cr lil\;time determinations for shott and long cum:nt pulses. (he shilt of
current - time characteristics can he determined eith!;;r experimentally or thcoretieally with
the number or current pulses as parameter. This has heen demonstrated (or a typical time
Jag mini,llUre fhsc. Usc of the methods pmpo~ed here will thcn:rorc ht.= ,Ihle to provIde the
innml1lHion ((Ir rt:placing aged fuses in the installations and greatly rl~duee uncxpt:I,;!t;!d
intcrruptions in the systems.
9.2 Suggestions for future work
{I)
For fi..lses subjected 1.0 5h0l1 current puls!;;$. lifetime predictions have been pre~t:oted. The
graphiC presentation uses the minimum melting it value of fuses iI( lO 1m as a base. In
theory, this minimum melting (I valuc ean be replaced at d1fkl'ent melting times t(l
provide guidance for practice as long as the pulse time is within a certain limit ("hOllt :;
seconds l<x AglSnln wire clements).
For silver dements used in high vollilge, low voltage and scmiconduct.or prot cellon ltl~~:s.
no enough experimental data of lifetime~ are available (It t.his moment ((Ir different pulse
times. Precautions should be taken for u8ing thb limit. In addition. sorm: mort;! t:xrcriments
are still needed to solve the problem of lifetime prediction in continuous loading.
(2)
To improve reliability of fuse~, both good ht;:at !.ranste.1' and stress rcka~l; (Ire rt:4uil'cd. For
cxample, Sllhstl'ate (hses may provide excellent heat tran~l(;:r media. Ikl'<luse of mislIl,11Ch
Conclusions
III
of thermal expan~ion, howev~r. extra stress ean be induced for current pulses ilnd lead 10
eracks in the interface hetween conducting materials and the silver base. Therefore further
studies arc desired.
(3)
For designing optimal shapes of fuse elements, the proposed finite dement tormulation
can be extended to include the inlluence of sand, clement notches and the initial shape of
the elemen!.
(4)
To assist applications of fuses, the work of this thesis can he further implemen1ed
software to help application engineers to control and examine: reliability of fuses.
in10 a
Appendix Photos of Fuses and Experiment Setup
Fuses used in experiments
Test circuits a : for miniature fuses ;
b : for semiconductor protection fuses
Experimental setup for measuring displacements
112
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/i)r pr(J!r;.Clion
(j'
Summary
This the~is covers the work carried out in Eindhovm University or Teehnolof!.Y during the
period from Octo her t 99! to S()ptcmher 191:lj, l'rol'essor dr. -ing, II, Ri.ianto. proi(;ssor ir. (i.e.
!);")mstra ~lnd asso(;ialc professor ir. J.ei.J. Sloot arc thesi~ dircetor~.
Among many electrical devices, I'ust;:s Me well knowll for 1l1l:ir popularity ill 1l0U:;l~ apparatlls
nnd industrial installations. Because or ageing effects, eharacterislks nf I!ISt:S \vil! dl:lcri()r"lt: in
scrvice. In ol'der to improve the rdiability or ekdrical systems, liktime l~stimation of !\.lses arl~
required by both L1sers and manubeturer~. LiteratUl't studies silow lil,,1 preVi()IIS wmk and
eXi'il ing standards do not provide gt~neral valid mclhods (0 give Ii ktimc eXI)l~l'tanc.y 01" I"uses.
For the~c rensons, Ihis work Wils initiated in (;o-()p~~nlti()fl wit!) Li((ell"llse I\V ll(rcdil. tl1(;
Ncll"wrlands and Siha GmbH Uinen. Germany.
This the.sis dl;)s(;rib~s ~rrorts (0 predi,;t lii"dimcs or Illinia(un.~ i"uscs <llld st~JlliconduclOr
protcetinl1 fuses, I'MMllcters in the models for predicting rlls~ liktiIlll'S arc ddined with ckar
physical meaning; mcthnds for deu)J'!nining these pal'anll;'lers iii'(':: pl'~S~llt\~d I\\~hll~~d topi~s,
su~~h a~ ekdrit~ curren( distribution. heal transfer. thermal buckling and pla::iic dcl()l"malioll.
(Ir~ ,ll~o dis~;ussed, In existing manutildurer cala[ogues. current - (ime charae((:-ristic~ arc
normally provided. I-'!'Om the Hfclime predictions presented in this Ih~sis, ~hin oi'clll'renl - time
(;lwraderis(i(;s can be calculated with the number of current pulses as parameter.
1.
Studies for miniature fuses
Experimental delerminations or Ii Cetimes were perforL1lI.:d I()r short and long time CUITl~l1t
p\lls~~. Th~~se (~~~h alT comparahle (0 thc surge wi(hshllld Hnd ~~lIdllr'ITKe d('stTihed in ! LC
publicatioll 127. Resllits shnw I.hal. litctimc follows Ihe Wdbull di::i.ribut inn: il dcU'ca~cs with
current and eurrenl conducting time (or 011 time). During tht~ t~urren( pulses, tllermal huekling
of fuse win: dements has been obs!;;rv!;;d, ]{\:sistmH;e of fuses t~nds (0 in~rc,~s~ duriIlg (h~ ruse
Ii k in gcneml, <ll1ho\lgh it may have Slll<lll vill'iations.
To analyse (h(;: ini1ut:nce or Cll1'rent pulses, electrical analogue method was \lsed to
simulate lhermal responses of wire clcments. I-Icat conduction along Ihe wir~' l'icmc[ll,
convection and radia(iol1 of the I;;krnent w(;:rC ~oilsidcred in p!'Op[)sed heal Irall~!cr models. h)r
allY (;orr~n( pulses, (Cmpet'il(llI'e l'ise could he calculated. Simulations 0 I" vo]wge " curn:nt trac~~s
and current - time characteristics have been compared with exrerirncnlill (\h~l~rV,l(i(Jll<; I()I' two
(ypical (yp~s 0[' l1liIli,llure flJses.
To explain thermal bu(;kling of wir!;; ckrncn(s d\l~ing d.c. CIlt'renl <ll1d Cllrrcnt pulscs, the
analYlic approu~h and (he nnlte element formulatioJl were developed. Theor,'lieal rt~~l1l(~ ()1"
displacemenls calculated from both methods have bc!;:!) !()\Ind in <12.1'eCIllCIlI "'III h observatlolls
i"rom high ~pce:d photogr,lrhy <"In(1 opt.icnl microscope.
III (k(~rmining (he lil~time or miniature fuses Ihr short elll"lTn( pub.~,. 1~'lI)p~~r,I(\lru
distribution ,md di~placement of wire elcments were (<lkl;;l1 in\(! 'Knllll)l. I iI(:IIIlIC I'dation
hased on the clastie fraetun; mJ;;l,;hani~m has b~erl introduced. I ,i fdime predici ions 111 theory
un
121
and experimental evaluation from high speed photography have been compared with rcsults or
lifetime tests.
For long current pulses, the plastic dc!ormation was assumed to be related wilh power law
creep. Material and configuration constants of fuse wire clements were determined by using a
few lifetime data with different On times. Afterwards, the number of current pulses that fuses
withstand has been calculated based on Manson - Coffin law. Predictions have been compured
with various experimental results which are related with current magnitudes below the
minimum fusing current and conducting times lrom several seconds to one hour.
For both short and long current pulses, predictions have been found in reasonable
agreement with expedmental results. From the lifetime predictions, deterioration of current time characteristics ean be calculated which may provide the inrormation for the fuse
replacement.
2.
Studies for semiconductor protection fuses
In experiment.s of lifetimes for short current pulses, typical ~emiconduC[ur protection fuses
with the same current rating (l60A) and different element shapes wCre taken as objects.
Results show that lifetime obeys the Weibull distribution; it decreases with the fit valu!: of
current pulses. Resistance changes during the fuse life are comparable with the spread of new
products.
For the fuse clements with the curved and straight shapes, thermal buckling was confirmed
by high speed photography in spite of existence of sand.
After fuses are submitted to current pulses, the surface of the dement notch becomes
rough, This plastic deformation will increase gradually according to the observation of
scanning electron microscope, Considering the local deformation, lifetimcs of commercial
products have been improved more than ten times for short current pulses.
For analysing the temperature distribution of the notched fuse element, EMTP was used to
solve the resulting networks of electrical· thermal problems. In forming nctworb, non-linear
properties of materials can be taken into account by using point by point functions (or look up
tables). Simulated results have been compared with melting characteristics and measured
voltage time traces. It is concluded that EMTP is a suitable tool for the analysis of three
dimensional time dependent modelling offuses,
In the way similar to that for miniature fuses, the number of short current pulses that
semiconductor protection fuses withstand has been predicted. At the moment, th~ denection
lor the straight element was assumed. Predictions have been compared with experimental
results of [USI;;S with three different curved element shapes. To improve the accuracy of
predictions, further investigations are recommended,
Samenvatting
[)it rroe1\chrifl, leven~duur-v()mspcllingen van sl11eHvcilighedm voor LI..: he"ciligillg v,11l
apparaten en vcrl11ogens-halrgdcidcr~, bdwndclt het werk dat i~ llilgcvO~l'd a~1I1 de i'ec.hnischc
Uni\l~rsiteit Eindhoven gedurcnde de periodc van oktohcr 1991 lOt ~I:pkmhcl" 19')5 DIHI~r leiding
van prof. dL -ing ]-[, Ri.ian(o, proC ir, (i.c. ])iltmtra en il' . .f.(; ..1. Sinot.
I"emidden van vclc clektri~chc apparatcn zijn smeltveiligheden I,cer bc~cnd dDI)!' hun
populariteit vom huishoudclijkc apparatuur en industrii.!lc inst(llJatie.~. Tijtlens hct gebruik van
~md(vcilighI:Jen trtedt cen veroudering op w(l..ardom de karaktcristiekcll vemnJcrcll. Olll de
bet.ro\lwbaat'heid van clektrisehe ~ystemcn te vcrbctcren. l.ijn ~eha((inge[l y(11) ~k Ievcllsdllill' vall
smcltvcilighcdcn gcwenst vonr zowel gebruihr~ als Cabrikanten. Uit litct'alllllr.~IIJ(lie voigt dM
~~cnlcr oTldcrl..ock en hC~t,l(lIldl,': nnrmen niet voorzicn in algemccn gekligl~ Illt'thodcn \,(Ior dc
bcpaling van de Icvensduur van smeltveiligheden. Om dezc reLlencn w(:nl dil w,~rk gl~'lnit ieel'd ill
samenwcrking met Littclli.lse te Utrecht (;11 Siba le LCmen (Did),
Dit procfsehri fl besehrij fl pogingcn om de levensdlHlt' van miniatullr patronen l~1l
smcllveilighcden voor halfgekiderhcvciliging te voorspellen. PaJ'amc.tcrs in dc Illodellcn voor tk
vuorspclling van d.; l!:v.;osdlJl.lr van ~meltveilighedcn worden gedcfinieerd nwt ~~';11 d\lideli.ikc
fysisehc bctckcnis; methoJen voor d(; hepaling van dt:I..(; paWlllctel's WOI'dCIl aangcgcven.
I'iiermcl~ ~amcllhangemlc omkrwJ;;rpJ;;ll %()~ls de clektrischc. strooll1vcrdelillj2.. warll1t . .~ (lvcrdracilt,
lhermi~ehe bllckling Cll plastisehe dc.formatie komcn cvcnCCfl~ ,1,1)) (II,': Ol'tlc.
1.
Onderzoek van rniniatuursmeltveiligheden
Exp~Ti[llI.;nt~lc levensdllurbepalingcn werden uitgevoerd voor stroomplIlscll Ilkt ec:n korle Cil
lange tijdsdllur. [)cze tcstcn zijn vergdijkbaar met de II 'k' 127 tcsten v()or lk hcstendighcid
tcgcn pil;;k- t;[] langdurige hela~ting. lilt de resliltatcn voigt Llat hct statist iSI;l! g~drag van de
!cvcll~duur Ie bcsehrijven is met Weibull ycrdding~l\: de levc-nsduur nccmt af met de
stroomstel'kte en de dUlIr van de slroumbelasting, Tijdcns dc st)'()ompuisen \Verd thermis(;h(;
opkrulling van srndlgcleidcl's w'l~rgenomen. De wcerstand van smcltgdci(kr~ heen in het
algcmeen de nelging om toe Ie IlCl11cn tijdcns de lcvensduur, nl kunnen de vct'andcringcn klein
7.ljn.
Om de invloed van ~(r(l()mpuh.;n te ondel'",ocken, werden elektrisl,;he allulog,~ l1)oddlen
gcbruikt om de (hermische respnl1s van draaddementcn k sim\llcrcn. In de voorgesleldc
warmt.eoverdrachtl11odcllen werJ rckcning gehollden met. warmtegelcidin)!.. eonv(Ttil,; en stl'i1lillg.
Voor willekeurigc stroompulscn bleek het mogdi.ik om d~ telllpel'atllllrtoenal1ll~ te hepaic[1.
Simub("ies van het tijdsverloop Vml stroom en spanning zijn vl,;rgc!cken m~1 ~xperi mentcle
obsevaties vom Iwee lypische minbtumpatronen.
Orn (herrni~cllc opkrulling van draadclemcnten tijdclls gclijkstro(lill ~~II ~tr'(l(lll\plllscn te
ytrU(lr'cn, wU'd ccn analytisehe benmkrlng met de eindige elcmenkll m~~(hj)dc olliwikkcld.
Thcoretisehe rC~lIlta(!;;n Van vet'Plaatsingen, berekeml volgel\s bdde mcthoden bkken
overeenstcmming met wilarnemingcn door rniddcl I/(ln hoge snelheidsi()to.I!.r,iliJ:
microscoopopnamcs.
122
III
~n
123
Bij de bepaling van de levensduur vom k0l1e stroompulsen, werd rekening gchllllden met de
t.emperalulIrvcrdeling en de uitwijking van draadclemcnten. Voor de leveIlS(!llUi' is eeo
uitdrukking voorgesteld, gebaseerd op elast.ische breuk. Voorspcllingen van de levensduur,
zowcl gebaseerd op een semi empirische rdatie als vanuit een zuiver theoret.isch model zijn
vergeleken met de experimentele result.aten van levensdullrbepalingcn.
Voor langdurigc stroompulscn werd verondersteld dat de plastische deiormatie ~amenhangt
met exponentii:!le kruip. De benodigde materiaal- en con/iguratiealhankclijkc comtanten van
smcltgelciders werden afgeleid ult enkele experimentele verbanden van de levcnsduur bij een
beperkt aantal verschillende waarden vOOr de plilsduur. Vervolgens is een algemeen geldig~
uitdrukking voor de 1evensduur afgeleid Ult de Manson-Coffin-betrekkin/t. Dc hicrmec gcdane
voorspdlingcn zijn vergekken met een groot aantal experimentele resultaten mel cen groot
bereik van de stroomsterkte en pllIstijden van enkcle sccond~~ tot een uur.
Voor pulsen met zowel een korte als lange tijdsduur, bleken
met cxperimcntcle reslIltaten.
voor~pcllingcn
in
overeen~lemming
2.
Onderzoek van smeltveiligheden voor halfgeleiderbeveiliging
De levensduur werd experimenteel bepaald vOOr slroompulsen met een korte tijdsduur. Hiervoor
werden typisehe halfgeleiderpatronen met dezelfde nominale stroom (160 A) maar verschillend..:
elementconfiguraties beproefd als testobject. Uil de resultaten voigt dat de Icvensduul' voldoct
aan een Weibull verdeling. De levensduur neemt af met de it waarde horende bi; de
stroompulsen. Dc vcranderingen van wcerstandswaardc gedurende de levensduur waren
vergetijkhaar met de spreiding van nieuwe produkten.
Voor de smeHgdciderelcmenten mct gebogen en rechte vorm, werd met snelle fotografie het
optreden van thermische opkrulling vastgesteld, ondanks de anwezigheid van zand. Uit opnames
met een scanning mieroseoop volgde dat het oppervlak van de smeltgeleider ter plaatse van de
verjongingen rtlW was na atloop van een langdurige pllisbelasting, des te ruwer naarmate de
aantal pulsen toenam. Dil duidt op een geleidelijk toenemende plastische vervorming. Door de
nadere beschouwing van lokale vel'vOl'wing kon worden bereikt dat. de levensduur van
eommerciele produkten, bclast met pulsvormige stromen, een factor tien werd verlengd.
Voor de analyse van de temperatulIrverdeling van slripdemenlcn melllil~paringcn, werd het
programma EMTf> gebrulkt om de resulterende netwerken horende bij elektdsche en thermische
problemen op te lossen. Hierbij kan n::kening worden gehouden met niet·lineaire materiaal
eigenschappen door middel van gedefinieerde tuncties of opzoektabellen, Simulatieresulwlen
zijn vergelekcn met smeltkarakteristicb::n en gcmelen spanning.tijd verbandcn. Hieruit kan
worden geconcludeerd dat EMTP een gesehlkt instrument is voor de analyse van driedimensionale tijdsafhankelijkc modellering van smeltgcleidcrs.
Op een soortgelijke manier als die bij miniatuursmeltveiligheden werd het aantal
stroompulsen herekend, waartegen een smeltveiligheid hestand is. Wei werd hierhij ui!gcgaan
van een vcrondcrstelling vOOr de optredende lIitbuiging. Voorspellingen zijn vcrgclekcn met
experimentele resultaten vool' smeltveiligheden met dde verschillende gebogen configuraties.
Oln de betrouwbaarheld van deze laatste voorspellingen te verbeteren wordt verder onderzoek
aanbevolen.
124
Acknowledgements
In accomplishing this thesis, I have benefited f)'om the advice and help of 1Il,'I1)'
Eindhovl,;n Univl,;r~ily, in industril,;s. and in thl;; stutimt training, I would lik>' I,)
thanks t.o all of you f()t' your cxpCrl ise, eont.ribution, encouragement., and support.
pL'()pl~
"'.\prl'S~
- in
Illy
!-"irs( ()r (Ill, 1 wi~h (0 rl~cord my lll<lI)b (0 ()H~sis supervisors pl'()lessor llendro I~ i}lrllo, (lct:rl
Damstra and .loop Sioot. for thei!' valuable guidance. Lspccially . .loop, he limmilaled Ihe proposal
fbr this thesis, stimulated impressive discussion, and provided constanl help in my daily Ii k. I wish
to thank prokssor .rimei Wang f()r introducing me to the lidd or electrical switcliinf:( componenls
(In(i ins(lllatiuns, <llld prokssor Wilh.:m van deo Heuv~1 .l()r inviting I)l{; (ojoin n;s~'(lrdl (1~;livili~s in
the Seelion of Electrical Energy Systems.
I would like to gratitude Leen Vermij for his practical, concise, valuahle adviee. and
I am imkhkd to l\;kr van Ridschokn and DipJ. -illg, II.l J. 11:l;IS I(lr 1i1(.!ir ~:()lIlrihllli(Jn
in lifetime tests or fi.lses. I am gratcfhl to Dr. C. M. Menken fbI' his discussion (In lhe hu(,kling
Conl,:~p(, Thailb ;!lso gl) (0 Xill\il\g ./jl(lng kH' his help in scanning ciccI fOil Inkroscope
photography.
<.:Olnrnm(s,
1"0 nil fhe Olhel' ml;mh~I'~ of group H'i, lowe many thanks i"or theIr hl,lp of any kind
whal,soevcr 1 have received. II. is a pleasure 10 mention my E)rmer rO()lTllluill' Mall! Ilolkn, illY
colleagues Rene Smeets and Vlastimil Kalasek I()r alway~ willing (I) hdp, Sp~~,:i<d (lianks go 10
Hans Vossen tur his assis(ancc in high speed phOl.Ogl"lphy, Ton Wi Imcs il)r his support in
ekc(rnnic circuits and soil ware development, ;\ric van Staalduinen for his tl'c.hnical work if!
preparing experimental samples, and Gerard Jacobs l(lr his support in I~M'I r simlll;I(.iO\ls.
i"l\ank$ M~ given 10 .Ieroen van f lc.rcl, Arcnd van de Poll and Rid1clH.~J Bulb,I;11 jl)l'
eonlributions during their studies. who conducted soH ware prognlnHning and network simulalions.
[ am also gratdi.i1 (0 many pl.:opic who made Ihe inlmduclion of laljl (juan and
or (jigl)!lg inln (his !l!livc!,~ity p()~~ib1c.
Chinl'~1.:
rm~di(a(i()ll
I would like to I,;xprl;;ss my ;Ipologies to those whom I may havt: ilwtivl'rtcnlly I;lilcd In
nlention, (:in(llly I t.hank my nlmily. particularly my wife Yillg und illy dallghlN Nancy fhr lheir
suppml lhroughout this thesis.
125
Curriculum Vitae
The author was hom in Ningxia, China. on 06 June 1903.
In July 1979 he finished his high school education. After travelling one thousand kilometres hy
train. on a heavily rainy day September 1979. he a.rrived at Xi 'an to continue his education, III
Xi'an Jiaotong University, he obtained his Bachelor's Degree in July 1983 and Master's Degree in
April 1986 in Electrical Engineering with the specialisation of electrical components and
installations. Afterwards. he worked in the same university as a teat;her until October 1987, Then,
he began his study as a research assi~tant.
In Novt;mber 1989 he came to work in Eindhoven University of Technology, lie involved in a
number of activities which covcr dectrit; fuses, arcing studies, protection of transformers and
motor control ccnWrs. During the period from October 1991 to December 1995 he has worked on
the reliability or electric fuses in the Section of Ekctrical Energy Systems. The project was in cooperation with Uttelfusc BY, the Netherlands and Siba GmbH, Germany, Some results orthe work
during this period lead to this thesis. The thesis directors are professor dr. -ing. H. Rijanto,
professor ir. (J,e. Damstra and ir. 1.G.1. Sloot.
Statements
accompanying the dissertation
Lifetime Predictions of Miniature Fuses and
Semiconductor Protection Fuses
X.Z. Meng
1
Large mechanical structures such as oil rigs. bridges, pipelines. chemic["ll plants. 11\lclear
installations and aircraft may in the i"ulurc be ~quipped wilh "fuses", which will give early
warnings about stre~scs in the structure that cDuld lead to cata~trophic failures. Different
from electric fuses. these "mechanical fuses" dQ not ch:arthe possible damage however.
• A. Coghlan, 'Fatigue: fuses' blow (In' whjstle on structural stress, Ncw scientist. Vol. 131.
pp. 25-25, Sept. 1991.
2
Electrical analogue methods can be used to predict declrical and thermal
rcspon~es
of
fuses which form the basis ofli1etime determination.
- This thesis
3
For fuses wilh and without sllnd, thermnl buckling of the [lise ekment takes
temperature oflhl::: clement exceeds a certain limit.
- This
plac~ liS
1I1c
lhe~i S
4
In electric distribution networks, UPS inverters, conHouous goncratol"S, large motors and
electronic relay systems have the shortest ETTF (e~pectcd time to thilure). Fuses Ol"d
MVILV circuit breakers have a relatively long ETTf. In conclusion, performance of
inverters, generators, motors and relay systems should be improved to increase Ihe reliability
of systems .
• M.H.J Bollen. '"Li(er(Iture sewell/or reliability data ojccmponems in electt·jc dis(ribZltion
networks." EUr Report 93·E·276, Cindhoven: TU Eindhoven, August 1993.
5
In distrihution systems, numerical relays capable of C0n111lUnic,lI.ing with management
SYS(I;;TI1S can be designed to enable sdl~m()nitoring for better availahility and les.~
maintenancc. Thereforc, they may provide possible advantages in reliability
costs over traditional electromechanical and electronic protection rclays.
iHld
lifetime
6
Power quality is dlanlctcriscd by several indices, Some (l[ these indices ,)rc dcfinl.:d by
the utility <'lnd others by eustOnll;rs. Therefore, agreement between utilities and i[Hlustrie.~ is
needed to improve the overall power quality.
7
BecUlISc of 'H..Ivanecd /l;;chnology, the average lifctiml) of people l1il~ illeJ'ea~cJ
dramatically, However, the maximum lifetime is still more Or less the same. So, the need to
investigate the mechilllism oCtbe maximum lifetime \ViII inct>.:asc in Hu: future.
8
To pursue a high economy growth r,lle the na~ural resources should be considered, such
as willer, air, food and space, Otherwi~e, people have to pay back irl the long run.
9
Whenever a govemmcnt stuy~ in power for too long 0, too shorl a period. lhe government
will attempt to view thc country ,Is its Own propt:rly. To minimi:-;e COl'l'Uj"ltilJn, the
govcmment should he renewed l'egularly without military interference.
10
lhl;; Tao (':<In be cxpressl;;d (abstnl(.:t nom nature), hut words Me never sulliciell!, Names
bc given (to describe cxistenu:), hut descriptions are nC\i\:r cOI11]'lkte. Wh,)( docs not
existln though 1 prepares lhe beginning ofhcavCJl and cal'~h; what docs exist i11 thought is the
mother of lhe world. It is with I}O mind that miracles arc to b~ observed. It is will) mind th:1t
I,;hanges arc to be examined. Both are from the same sourl:C ,mJ with /,liffcl'cnt descriptions.
Continuous repetition of being with mind and with no mind leads to (he cxp<;rkncc of the
Tao.
Ciln
- Lao Zi, "Dao De ling (Tao Te Ching)," EditiOJl of Lou Guan Tai, Chapter one. aboul 10
century R.t.
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