Effect of entrained water on virtual intertia of ship propellers. 1953-06

Effect of entrained water on virtual intertia of ship propellers. 1953-06
Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis Collection
1953-06
Effect of entrained water on virtual intertia of ship propellers.
Price, Robert Ira.
Massachusetts Institute of Technology
http://hdl.handle.net/10945/24687
Uumty
V. S. Naval Postgraduate School
Monterey, Calif^^rnia
.2
EFFECT OF ENTRAir>lED WATER
OF
SlilP
Otl
VIRTUAL INERTIA
PROPELLERS
by
ROBERT IRA ^RICE
Lieutenant, United States Coast Guard
B.B.A.
,
Collev^e of the City of Wew York
(1942)
B.S.
,
United States Coast Guard Acadeny
(1940)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF NAVAL ENGINEER
at the
I^SSACHUSETTS INSTITUTE OF TECl^^aOGY
June, 1953
EFFECT OF ENTRAIHED V.'aTER OM VIRTUAL INERTIA
OF SHIP PROPELLERS
By
Robert Ira Price
Submitted to the Department of Naval Architecture
on May 25, 19^3, in partial fulfillment of the
requirements for the degree of Naval Engineer
In the design calculations of torsional critical frequencies for marine line shafting, it is present practice to
arbitrarily increase the inertia of the propeller by 2^% as
This
an allowance for the effect of the entrained water*
figure is not an experimentally determined one. Rather it
represents a mean of increments to the propeller inertia
which have had to be applied to ships already built in order
to bring the calculated critical frequency into agreement
with the frequency observed. The observed range of these
increments is from 23-32;o, The cause of variation is not
known.
Previous efforts to experimentally determine the virtual
inertia of propellers by tests with models have given results
of oOjj' for the increase, leading to the conclusion that there
was a scale factor for vibrational similitude.
The objective of this thesis has been (1) to develop a
simple, effective method of evaluating the virtual inertia of
a model propeller, (2) to examine the effect of speed of advance upon the virtual inertia, and (3) to investigate the
effect of the propeller pitch on virtual inertia.
The equipment designed for the purposes of this thesis
converted the M,I,T, Propeller Tunnel apparatus into an instrument for the direct evaluation of the combined inertia
of propeller and entrained water.
The inertia acting upon
the system could thereby be found once the resonant frequency
was known. The amplitude at resonance was sufficiently well
defined to permit damping to be ignored. The entrained water
inertia was taken to be the difference between the virtual
inertia and the inertia of the model propeller as evaluated
in air by means of torsion pendulum observations.
The following are the principal results!
1,
2,
3,
4,
Curves of Inertia Increase versus Speed Coefficient J
for three pitch-diameter ratios,
Curves of Inertia Increase versus Slip for three pitchdiameter ratios,
A calibration curve for the experimental apoaratus,
Photographs and sketches of the experL-nentai apparatus.
o
n /r n
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r
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Some conclusions derived from the results arei
1«
There does not appear to be a scale factor between model
and propeller as previous work suggested,
2*
As propeller loading increases, the virtual inertia
increases*
3*
A minimum value of virtual inertia is attained in the
vicinity of J « 0.8.
4.
Virtual inertia increases with increase in pitch.
Additional study and further investigation are believed
warranted. Sofue recommendations are:
1.
More detailed study of the region of minimum virtual
inertia.
2.
Exploration of the effect of other significant geometrical propeller characteristics including area distribution of blades, blade thickness, number of blades.
3.
Comparison of model tests with the values obtained from
the parent propeller as installed.
Thesis Supervisor: Frank M. Lewis
Professor of Marine Engineering
Title:
:5.i':^
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J -x-'V!
•^
•£
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ACKIia';LEDGE^^NT
The author wishes to acknowledge his indebtedness
to Professor Frank M, Lewis for his guidance, interest
and encouragement in the course of this investigation.
CamlDridge, Massachusetts
2b May 19L3
Professor Earl B, Millard
Secretary of the Faculty
Massachusetts Institute of Teclmology
Cambridge 39, Massachusetts
Dear Sir:
I herev/ith
submit the attached thesis entitled
EFFECT OF E14TRAINED WATER ai VIRTUAL INERTL\ OF SHIP
PROPELLERS in partial fulfillment of the requirements
for the degree of Naval Engineer,
Respectfully submitted,
I
II
III
IV
V
VI
VII
Intrcxiuction
1
Procedure
8
Results
19
Discussion of Results
21
Conclusions
26
Rocoramendations
27
Appendix
20
A.
Details of Design
29
D,
Details of Observation
36
C,
Translation
41
D.
Literature Citations
49
I
-
Toi'sion Tenduluin
4
II
-
Simplified Systtm
6
III
-
Variable Inertia Element on Torsion Pendulum
10
IV
-
Variable Inertia Element as Installed for
Calibration
10
V
-
Calibration Curve for 3/8" Dia. Torsion Rod
11
VI
-
Effect of Speed of Advance on Virtual
Inertia at Various ^itch Ratios
12
Effect of Slip on Virtual Inertia at
Various Pitch Ratios
13
Schematic Diagram of Experiment
30
VII
-
VIII
-•
IX
-
Excitation Element Installed
32
X
-
Excitation Element Installed
33
XI
-
Excitation Element Disassembled
34
XII
-
Excitation Element
35
XIII
-
View of Observer's Station
37
XIV
-
Specimen Plot of Response of Inertia Element
38
XV
-
Specimen Plot of Response of Propeller
39
iX
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I.
IMTMBUCTICM
In the design calculations of torsional critical fre-
quencies in marine line shafting, it has been the practice
to arbitrarily increase the inertia of the propeller by
Z:>%
to allow for the effect of the entrained water at the pro-
peller.
This value arose as an average of the factors which
experience showed to be necessary to bring into agreement
the calculated and the observed critical frequencies.
factors have been found to run from
These
to 3Zt, the actual
22^i
figure in each case being determined only after the ship was
built and operated,
l^\J
A body moving in
a
fluid medium undergoes an increase
in inertia (apparent mass) whenever there is
a
transmission
of kinetic energy between the body and the fluid.
The mag-
nitude of this effect is of particular interest in oscil-
latory phenomena inasmuch as the amplitude and frequency are
directly affected thereby.
According to classical hydrodynamics,
motion in an ideal fluid gives rite to
a
a
body in steady
streamline flov/
such that the pressure distribution over the body produces
no drag.
Should the motion of the body be unsteady, then,
despite the ideal medium, variation in the momentum of flow
occurs and the inertial resistance of the body to motion
exceeds that due to the body alone by the amount of the
inertia of the entrained fluid.
J^
t^:
J
&i*J
d*-'
The hydrodynamic increase in inertia has been determined
by analytical methods for
a
number of specific shapes under
certain assumptions. Z~^» 3, 4 and
1j
J
,
These analytical
solutions are based upon motion in an ideal fluid and are of
considerable value where the actual flow behavior approxi-
mates potential flow.
A ship's propeller, however, is a
body of complex contour, moving in translation and rotation
in a real medium, in a variable flow.
The three-dimensional
nature of the problem is difficult to approximate.
It is not feasible to evaluate the total or virtual
inertia by
a
direct comparison of the force of acceleration
with the resulting acceleration of the body as the problem
might suggest.
The resistance due to friction is a function
of time in hydrodynamic acceleration and is therefore
difficult to extract from values so obtained, /"6 and
ij*
Experimental efforts to determine the cause of the wide
variation in the value of propeller virtual inertia were
made by C, J. Hawkes in about 1920.
Hawkes never published
his work for his results were so much higher than the figure
of
25/1^
ordinarily employed that he believed that there was
a
scaling effect between the model and the propeller that he
had not taken into account.
His methods of investigation
are not known.
In 1935, H, Guntzberger, Z"8j7, while investigating
propeller damping, obtained an increase in inertia for
steel propeller of
In reference
{XJ
t
60Ji>
from tests made on
a
a
6" diameter model.
Hawliet referred to Guntzberger* s result as
If.
iJL
ilA
consistent with his own.
A translation of Guntzberger*
s
paper
is considered of interest and is included in the Appendix of
this report.
The object, then, of this thesis was to experimentally
evaluate the virtual inertia of model propellers under
dynamical conditions.
The information obtained from explor-
ation into the nature of the increase in propeller inertia
may eventually permit the designer to relate the virtual
inertia to the propeller selected for the ship.
The M,I,T. Propeller Tunnel offered facilities suited
to this purpose, having the proper equipment to vary the
operating conditions of rpm, pressure and water velocity,
Three-bladed destroyer tvpe propellers of pitch-diameter
ratios 0,782, 1,10 and 1,40 were selected for testing from
those available at the Tunnel,
In addition to these three
propellers, some other propellers, including 4-bladed merchant
types, were also tested under conditions of approximately
100^ slip.
A simple, accurate method of determining the polar
inertia of
by means of
body of complex contour such as
a
a
a
propeller i$
torsion pendulum, illustrated by Figure
I.
o^i
Figure
TORSION
I
PENDULUM
The object is supported by strings of equal length, which
are equidistantly spaced about
a
circle of diameter equivalent
to that of the body so that the strings hang vertically.
pendulum is then given
The
small angular displacement and the
a
The polar inertia of
frequency of vibration is observed.
the body may be found by the following expression:
q
W D^
16Tr2 L
f2
^^^
where
g «
acceleration due to gravity (in/sec^)
J « polar inertia (in^-lbs.)
W
*=
weight (lbs.
)
D = diameter (inches)
L = length of suspension (inches)
f «
observed frequency (cycles/sec.)
:'XtJ
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^
.
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o.
At a preliminary stage in this investigation, the nodel
having
a
pitch-diameter ratio of 1.10 was vibrated on
torsion pendulum in air and in water,
frequencies obtained gave
See Appendix,
of 47,5%,
produced
a
a
a
A comparison of the
value for the increase in inertia
The damping effect of the water
rapid decay of amplitude and it cannot be stated
with certainty that the damping was here linear.
Further,
the amount of entrained water is dependent to some extent
upon the amplitude of vibration; consequently comparison of
the free-undamped and free-danped frequencies is not con-
sidered to be a reliable method in this application.
The technique employed in this investigation made use
of the behavior of a vibrating system at the resonance con-
dition.
Except where high damping is present, this is
well-defined point of maximum amplitude.
a
To force the
vibration, an excitation assembly was developed to be fitted
to the M, I,T, Propeller Tunnel equipment.
This element
superposed upon the steady driving torque an alternating
torque having
torque and
a
a
peak amplitude of about one-half the steady
frequency of three cycles per rotation of the
propeller shaft.
The test system, reduced to its simplest form, ignoring
the steady-state rotation, can be illustrated by Figure II,
e
,^
10
t
xci jirc
SIMPLIFIED
-Lx
SYSTEM
K2
«»,
't^
•<3
'«-
i
Approximate Values
Jj,
= inertia of excitation element = 30 in^-lbs.
J^ = inertia of lucite disk = 40
in-^
-lbs«
Ki = ilt = 3880 in-lbs/radian (Propeller Shaft)
= propeller damping
B
K3 = 1222 in-lbs/radian (Torsion Rod)
The general equation for the free vibration of such
a
system
can be approximated by
(J +
Jj^
+ Jo)
2-
0)20 .
jB^Q . ^ a
(2)
from which the frequency at resonance is very nearly
f
K
=-12ir
^
(3)
(J + Jl + J2)
Since the total inertia values of the propellers tested
were all of about the same magnitude, the angular speed at
which resonance occurred depended upon the stiffness of the
torsion rod, K3.
The heaviest (3/8" dia.
)
rod of those
available at the Tunnel was installed to bring the resonance
(s)
V 11 6 or
-."T.
(
+
rl,
+
v/
J.
J*
•>>
2nl SBW
X^
condition about at as high an angular speed as possible.
the 11.82" diameter aluminum models tested, the range of
resonance was from 140 to 16& rpm.
For
II. PP.OCEDURE
The excitation element designed for this investigation
converted the M, I.T, Propeller Tunnel equipment into an instrument for the evaluation of conibined inertia of the pro-
peller and the entrained water, i.e., the virtual inertia
Prelininary to the application of this
of the propeller.
"instrument" a series of calibration runs (Table lb) were
made employing
a
specially designed device, the polar inertia
of which could be changed by varying the distance of
from the axis of rotation.
\.^N^ights
As it is necessary that the
propeller tunnel bearings be kept water lubricated, and to
avoid any entrainment of water, this variable inertia element
was run dry inside of
a
The
box immersed in the tunnel.
element was designed to substitute in the system for the
propeller and utilized the propeller fairwater and keying
collar, consequently nothing else in the system was changed.
See Figures III and IV.
The resonant angular speed of the system was obtained
for six settings of the variable inertia element.
The polar
inertia of the variable inertia element was found at each
setting by means of
a
torsion pendulum.
(Table lb).
Plot-
ting the polar inertia versus the revolutions per minute at
resonance gave the calibration cur'/e of the "instrument".
Figure Y.
The propellers were then tested for resonance at various
values of water velocity by holding the flov/ rate constant
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and varying the angular speed until the rpm for resonance
v/ere
found.
Entering the calibration curve vdth the value
of the rpm at resonance then gave directly the virtual inertia
of the propeller.
The polar inertia of the propeller alone
wae evaluated by torsion pendulum.
Table 1(a).
Tne dif-
ference between the virtual inertia and that of the propeller
alone was taken as the entrained water inertia.
The increase in inertia due to the entrained water was
plotted for each propeller as
ficient J, Figure VI, and as
a
a
function of the speed coeffunction of slip. Figure VII.
To put the value of the increase into
a
percentage form
as it is customarily thought of, the polar inertia of the
aluminum models as determined by torsion pendulum was multiplied by 3.02.
This value was taken
gravity ratio of manganese bronze,
a
.is
the specific
common propeller
material, to that of aluminum, the material of the models.
The percentage of the increase
v/as
then calculated on the
inertia of a manganese bronze propeller^ Tables II, III and
IV.
To establish the region of interest prior to the cali-
brating of the "instrument", several propellers, including
those mentioned, were tested.
For these tests, the water
velocity was that due to the propeller action alone, i.e.,
very nearly lOO^o slip.
This information is incorporated in
Tables II, III and IV as Run Number 1.
propellers so tested, see Table V.
For the other three
ili;!!^
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19
III. RESULTS
The results of this investigation are included in the
following form:
1.
Curves of the Inertia Increase versus the Speed Coefficient J, Figure VI, for three values of pitch-diameter
ratio.
The propellers are all three bladed destroyer
types,
2.
Curves of
tlie
Inertia Increase versus Slip for three
values of pitch-diameter ratio. Figure VII.
The in-
formation from which both of these figures were derived
appears in Tables II, III, and IV.
3.
Data on the inertia increase at zero speed of advance
(100^ slip) for six propellers of various types.
This
information appears as Run No. 1 in Tables II, III» IV
and V,
4.
Data on the percentage increase in inertia as Tables
II, III, IV and V.
5.
Photographs and sketches of the equipment developed
for the purposes of this investigation* and
plot for the testing apparatus.
a
calibration
et
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90'
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a
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TAIILE VI
Comparison of Free -Undamped and Free-Damped Vibration
Evaluation by Torsion Penauiun
Propeller No. 44
p/d
=1.10
Fret Damped Vibration
L * 36.5 inches
f »
5/8 cycles/sec.
W « 2.83 X Xa2 s 1,78 lbs.
1.7/2.7 = factor to correct for specific gravity in water,
J .
WDi^
. 41.9 in.2.1bs.
16ir2Lf2
From Table 1(a)
J (Free undamped) « 17.2 in.^-lbs.
Entrained V/ater Inertia = 41.9 - 17.2 = 24.7 in.^-lbs.
3.02 X 17.2 » 51,94 in.^lbs. = inertia of Manganese
Bronze Propeller
Increase = 5^*94 x
100 »
47.551^
.-':
ir-
1.
,.-c,
(
9&lH
.
o ai
.
.
i?.ia
« S.VX x £
.
1
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IV.
PlXUSSigJ OF RESLLTS
The data wat put into percentage forn to present the
results obtained in this investigation in the manner in which
inertia increase is usually considered.
However, the ordi-
nate in Figures VI and VII was plotted as the absolute
increase in inertia rather than as
done because there is
soine
a
percentage,
T;.-^
.
-.s
doubt as to the purity of the
propellers selected for the pitch study at a pitch series.
A plot of percentage increase would show the curve for
pitch-diameter ratio of 0.732 as having a generally greater
percentage increase in inertia than for the pitch-diameter
ratio of 1.10.
Considering the manner in v^iich the percen-
tage is evolved, i.e., the ratio of the difference of two
readings of inertia to the multiple of the propeller inertia,
(See Table VI), it is essential that the inertia values of
the individual propellers in the series differ by the effect
of pitch alone.
Figure VI shows the effect on the Inertial increment
of the speed coefficient J.
The values are noted as being
high at high values of propeller loading
(lov/ J).
increases, the inertial increment decreases to
the vicinity of J
=0.3
and then rises again.
a
As J
minimum in
In attempting
to determine the reason for this behavior, the values of
inertial increase v^ere plotted as
Figure VII.
a
function of slip.
!»
ill
9fii
»5 tr
He
,^SJ^'^.:Ji:
tl3J^»
olq A
.Jiij^xiff^
I J.
ic
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-»;
«:
.£i
.to 3"^
.•IX
SISi
«'•
J
J. CJ
1
IV
fo^^trts
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ic
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on.T
X
:.
J'i'iS
J '* «J O J
Tel J"?
Slip is a factor embodying both the pitch and tht Wtt^V
velocity.
Slip
«
1
-
«Peed of advance
pitch X ros
Positive values of slip indicate that the propeller is driving
the water; negative values indicate that the propeller is
being driven by the water.
It would seem that if a minirnutn
exists it should coincide with the condition of zero slip,
i.e., zero loading of the propeller.
As Figure VII shows,
this does not appear to be the case.
More detailed experi-
mentation is required in the vicinity of the minimum values.
As to the effect of pitch on virtual inertia. Figure VI
shows that the tendency, at the same speed coefficient J, is
an increase vdth increasing pitch.
The effect is relatively
low between 0.782 and 1.10 pitch-diameter ratios.
Between
1.10 and 1.40 pitch-diamster ratios, liowever, the effect at
constant J is
a
sharp increase.
Comparison is not made at
constant slip from Figure VII since this would take the
pitch parameter into account tv/ice.
Viom the appearance of
the curves in Figure VI it is apparent that the spread in
pitch-diameter ratio selected for the study leaves too much
unexplored.
Further
v/ork is
necessary at interim values,
particularly between 1.10 and 1.40.
Six propellers were tested at conditions of approxi-
mately zero speed of advance to determine the region of
interest for calibration purposes.
The results of these
runs appear in Tables II, III, IV, and V as Run No. 1.
.3CJ.a?V
«»
v ao
Y-
nis Xiv
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9rf*
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2t
..'X
Si.
il
asXdsT iU
-
>
enuT
Comparison of the values obtained with those for the sam«
propeller at higher water velocities confirms the tendency
mentioned above for the increase in inertia to be generally
Two propellers, of
higher witn higher propeller loading.
the four-bladed merchant type, were anwng those so tested.
These are Propellers Nos. 73 and 74,
Comparison of the
values oi^tained for these two propellers with the taree
bladed propellers indicates
generally higher absolute value
a
of inertial increase for the same pitch diameter ratio.
The
percentage ccmiparison shows a four bladed propeller as having
nearly twice the increase of
three bladed propeller of
a
equivalent pitch-diameter ratio*
Notice here, however, that
these four bladed propellers have
a
Table I, than the three bladed.
lower propeller inertia.
This indicates that basing
the increase in inertia upon the propeller's inertia in the
form of
a
percentage is not
a
particularly good treatment.
The absolute increase as a function of the most significant
geometrical characteristics of the propeller would be
better method.
a
It is believed that future work on this sub-
ject should incline toward producing curves of this type.
This will require experimentation with other propeller
properties such as the area distribution of the blades,
blade thickness, number of blades, etc.
The result with Propeller Ho. 27 is not highly regarded.
Difficulty was experienced in supporting this propeller concentric with the shaft as it did not fit the keying piece
properly.
Inclusion of the result is warranted only to
.n—.-'iii
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+ «;-.- If
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^"9qoa:q
<i4
point out the necessity of careful installation in furtl^er
work with the method described.
Much of the time available for this thesis was given to
the development of a satisfactory method of excitation and
observation,
Tlie
fact that the excitation element had to be
designed to fit existing equipment, viz,, the ^A,I,T. PropellDr
Tunnel, presented considerable difficulty due to close
clearances,
Kence the apparatus and the method are con-
sidered to be
a
result of the investigation.
The calibration plot for the "instrument". Figure V,
is of the sliape to be expected.
As shown by Equation (3),
the resonant frequency is proportional to the reciprocal
of the square root of th© polar inertia.
This is
a
hyper-
bolic form.
It is of interest that the method employed is in
principle the same as that used by Guntzberger, /^^J.
He,
however, provided excitation by means of a gravity unbalance,
and determined the resonant frequency by the maximum angular
deflection as taken from high speed photographs, see Appendix,
In the discussion v^ich followed the presentation of his
paper, it was noted that the v;ater was accelerated from rest
by the propeller itself and that no means were employed to
control the velocity.
Yet Guntzberger achieved a speed of
flow of one meter per second with a b" diameter model.
This
suggests that perhaps the diameter of the tunnel in which
the test was made was small with respect to the diameter of
the propeller.
Proximity of
a
solid boundary would cause an
ts*-
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.
CfcVy
2X3 3;13'
3.
asii.
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One other possible
incrtase in tne entrained water.
nation for Guntzberger's result of
605^
ex,:
la-
is that the centri-
fugal force of the gravity unbalance in rotation clso
induced
a bov/ing of
th© propeller snaft such tiiat tne pro-
peller was not actually rotating in its own plane*
eommtnt on Propeller No, 27 above.
the propeller is also a factor in
Note
The loaded condition of
trie
direction of an in-
creased value.
The results of tests with the experimental apparatus
developed for this thesis do not indicate
a
scaling effect
between model and propeller such as was suggested by the
work of Hawkes and Guntzberger,
The results percentage-wise
are too close to the values ordinarily observed.
One can
only conclude at this point that similitude of vibration has
been achieved and that the method developed is satisfactory.
To properly evaluate the results of this investigation
further work is necessary.
that
a
It is particularly important
comparison be made of the results of model tests
with the increase in inertia obtained for the parent pro-
peller as installed in the ship.
E»
(
«' t-
-i.
i;
.j..;i.>-
•;
..A
>
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The conclusions drawn from this investigation are as
follows:
1«
A satisfactory method of evaluating the virtual inertia
of model propellers has been developed.
appear to be
a
There does not
scaling effect between model and pro-
peller.
2,
As propeller loading increases, the virtual inertia of
the propeller increases.
3,
A minimum value for the virtual inertia is attained
in the region of J = 0.8.
4,
There is relatively little variation in the increase
in inertia between pitch-diameter ratios of 0,782 and
1.10.
Between 1.10 and 1.40, the inertial increment
rises sharply.
5,
In general, four bladed propellers show a greater
increase in inertia than three bladed.
•t
;li
frS-
'<?7
VI.
RECCMOOATigJS
The following suggestions are offered concerning the
course of future investigation of this subject:
!•
More detailed study of the region of minimum virtual
inertia,
2.
Further work on the effect of pitch-diameter ratio,
particularly between 1,10 and 1.40,
3.
Exploration of the effect of other significant
geometrical propeller characteristics including area
distribution of blades, blade thickness, number of
blades,
4.
Comparison of the model tests with the results of
actual installation of the parent prq^eller.
^s
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,
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si
T or: ;v,
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(jT'
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02
l.'j'cairiC-O
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«
VII
APPEMPIX
&...^.^..^^
2^3
A.
DETAILS OF DE5IQI
Th« M.I.T, Propeller Tunnel equipncnt tonether with the
excitation apparatus developed for this investigation is
shovwi scheraatically in
Figure VIII.
The basic tunnel equip-
ment for the evaluation of torque nay be traced through as
The motor is belt-connected to the hollow driving
follows.
shaft, to which is fixed the torque disk housing.
The
hollow driving shaft is fastened to the propeller shaft
through
a
calibrated torsion rod,
of the system, Figure II.
Tliis
rod is the "spring"
The graduated lucite disk is
attached to the propeller shaft and is therefore free to
move with respect to the disk housing.
The propeller shaft
runs through sealing glands to the propeller in the test
section of the tunnel.
Bearings are not shown.
The stroboscope circuit is closed once per revolution
of the hollow driving shaf t^ illuminating the indicator arrow
on the disk housing port and the lucite disk inside.
The
light is reflected into the telescqpe by the mirror enabling
the viQ\tex to read the relative position of disk to housing
in tenths of degrees of angular deflection.
The difference,
at the same rpm, between the readings with the propeller
installed and the propeller removed represents the torque
absorbed by the propeller.
The stroboscope phasing control
shifts the position of contact to insure that the housing
port is in line v/ith the mirror and telescope.
A more de-
tailed description of the Tunnel equipment has been
published C'^J^
•ciuro
fr,
«£>
^iii
af
o^
:f-
^i/-^'
tj'.-,-^
TCSMl ftOJiO
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iv
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X
FIGURE
VIII
i
<
3
X
UJ
UJ
_l
_l
it!
o
<
O
Q.
P
O
liJ
o
ftJJ
Upon this basic system is installed the excitation
apparatus. Figures IX, X and XI, developed for this experiA sleeve, supported concentric with the propeller
ment,
shaft, bears two 6" gears, one of which is the driving gear
and the other the phasing gear.
Three
2**
gears, meshing with
the 6" driving gear, rotate the 1/4" shafts in bushings
pressed into the arms of the three-armed carrier.
An 18 gram
lead v;eight is clamped 2" off-center to each of the three
1/4" gear shafts.
The three-armed carrier is fastened to
the propeller shaft.
When the shaft is turned, the small
gears are forced to rotate, executing three rotations with
respect to the propeller shaft for each revolution of the
The lead weights are placed in identical
propeller shaft.
positions relative to their respective carrier arms.
The
centrifugal forces developed by the lead weights add vec-
torially to superpose upon the steady driving torque of the
system
a
sinusoidally alternating torque having
a
frequency of
three times the propeller shaft rotation.
The peak magnitude of this torque is given by the
following expression:
Qe
-
^
where L
RjL
(3w)2 R^(L)
""
^i
"*"
^2
= 3 inches
R2 -
1
inch
W
« 18 gms « .0396 lbs.
u)
« angular speed of propeller shaft (radians/sec)
9tiS
*«
.f
P'*'i^'^-V/\
*'^^'
flifi^l^
T
i'^
oniric fei.
81 nA
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32
Figure
Excitation
i;<
I£lew2r.t
Installed
(^r
-33
Figur e X
Excitation Eleneat Installed
?%>-
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3^
Excitation Element Disasseubled
ff-
•^>r.
i5
FiQtft XXI
EXCITATION
ELEMENT
The phasing gear mounted on the concentric sleeve en-
gages
a
small structure- supported gear.
by a ratchet lever permitting the viewer
relation of the exeitation.
This gear is turned
to alter the phase
By simultaneously shifting the
phase of excitation and stroboscope, the observer is able to
read through the telescope maximum and minimun values of
angular deflection on the lucite disk.
•J
4
no
The technique of observation is as follows for each con-
dition of operation, i»e», whether
a
calibrating run using
th* variable inertia element or a propeller test.
The ob-
server sets the rpm of the propeller shaft by manipulating
the drive motor rheostat.
Viie
value of the rpm is deterrnined
by taking stopwatch readings against the readings of a
Veeder-Root turn counter.
The flov/ rate is set by adjusting
the speed of the tunnel impeller until the desired value is
The water speed is evaluated by a pitometer in-
obtained.
stalled in the tunnel.
colunn.
Readings are taken from
a
water
The observer then notes the maximum and minimum
readings of the lucite disk, operating the phasing controls
of excitation and stroboscope as necessary.
a view taken of the observer's station,
Figure XIII is
showing the relative
position of the telescope, the phasing controls and the
rheostats.
The response of the system to variation in rpm in terms
of the total angular deflection of the lucite disk, that is,
the difference between the raaximum and minimum readings, is
presented in Figures XIV and XV,
Figure XIV shows the be-
havior for the variable inertia element installed and
Figure XV shows the behavior with a propeller installed.
The peak value, corresponding to resonance, is sufficiently
well-defined to permit damping to be ignored.
ts
r
-no 3
ig ai
iioi^e
n<
,^,
m
ai
« L
4
.nr.?:Jf
ltr;i:;t
sitfii
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ii:'T
^
:^
f\^^a €,('•
"."i -^r-r
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?>,v
V.
Vr r.v
3
-^
H-.
"-«<;?
.
-•
,^
*^r\r
-.-i^,
-,-
',-1
.-'^iiirf'f
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'"k
•
t
<i\.
Tpi?
»"»
I
.'irifiVfi'
o
fit
XOxVoit
J«
\rtn^^
or Objcrvcr'?
""'^tion
•SiTU^W*
i
J
•J
1
1
^^^^^^
r
..i' .;::•
lllfc'
jh^^Z^a*
fj^^
'i^^^^^^^^^^^^^^^^^B.
.
HHBJ
a^H^^^^^^^^^^^^^^^&
1
T*
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i^
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^
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IS
I^K
[
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__
1
1
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FIGURE XIV
'
I
'
'
'
M
'
'
'
'
'
1
!
'
'
1
'
'
L
'
SPECIMEN PLOT
ILLUSTRATING RESPONSE
WITH INERTIA ELEMENT INSTALLED
=;
1
1
'
'
!
::
i
'
'
1
1
!
:
:
TOTAL ANGULAR
-T
_
DEFLECTION
/Ilk
1
[
1
1
1
1
1
1
1
M
1
^6
1
Ii
.
i
III
1
1
.
1
1
1
1
1
1
•
M
1
1
1
1
1
1
-
1
1
'
'
'
-
,
,
1
I
1
1
'
,
1
I
!
\
~'^
i
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it
H'
"
1
*
-.
it IT
J
/
T
^
..-.,.-
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-Ihr
^5
It
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\
^
^t
7
L
5
L
fr
*
^
^^-
j-
-<»--L
-<h-»-
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-,1-
7
.^
it
^s.
^
n^
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o
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;
'^
a
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:
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/
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it
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1
.
1
1
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1
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5C
1
rc
J
C
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it
_
z''
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L jUf
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1
^fj/^
i
-vVi^
n-n-rnr-TTT FIGURE KV^
:
L!
!
!
!
I
Tnr
SPECIMEN PLOT
ILLUSTRATING RESPONSE
WITH PROPELLER
INSTALLED
H
TOTAL ANGULAR
4 DEFLECTCH
-
(
•
)
tttr
i
i
3?;
2
j-j^
140
ISO
i-in>
tTD^
*h
^<r
40
Until the observer becomes accusto.aud to
the system near resonance, it
raay
tlie
behavior of
be necessary to plot the
data after the fashion of Figures XIV and XV, fron which tht
rt80nanu
v/ill
rpr.i
can be aeteriuined.
In practice, xae ojserver
be able to recognize the resonant condition by the
thumping note which the system produces only at this state*
It is then only required that the observer confirm by stop-
watch and by telescope the resonant rpm.
By this method,
the observation of resonant rpm should be correct within
one-half
a
revolution per minute*
ot
v
oiiJ"
djii^
^y^ii^lulH
yd fiolil
,bod:^9m
aid:*'
yfi
ill
v. 3.:
.mqct
Bil
.
I
9r{.t
>i oJ
es;
j-nfinoe©^ 9d:t
i<
oqci
.1©^
sXds
Y<^
dt
''"^
dad-sw
Danping Effect of the Screw Propeller on the
Torsional Vibrations of Line Shafting
by
Guntzberger
Ingeniear du Genie Maritime
H.
We have sought to determine the value of the daciping
force as
a
f jnction of
the variation of the angular speed
and the slip; we have been led in the course of this study
to determine the increase in inertia due to the entrained
water in
1»
a
rotating propeller,
Experimental Apparatus
The apparatus consists of two shafts - the driving shaft
A, and the propeller shaft B, joined by a spring connection.
The driving ohaft is turned by an electric motor by means of
a
worm gear driving tangentially
a
heavy
flyi'4ieel
insures that the speed of rotation is constant.
which
An annular
plate C is also mounted on the driving shaft.
The shaft B carries
a
disk D located in the same plane
as C, also an unbalanced mass and the propeller,
Tlie
annular
plate C and the disk D are joined by two metal springs
(figure I),
duces
a
When the shafts turn, the off center mass pro-
sinusoidal irregularity in the speed of rotation of
the propeller.
The entire apparatus is enclosed in an open box placed
in a propeller tunnel.
*x
SU(iB
.rt;
.
1C*2^
X
Cii-
'V
^
r/O
on*
Ji».-
2
i
•Xii
prf.t
ts-l.t
-4.
?i'
SI
^r.
a
r,ri.^:^:-\.t.'""r
"^r
o ns
c
"-0
Tlie
shaft A»
Ua^/xxv-^
the irre<j(ularity of
a
ii:otior»
^
L
*
uniform rotation » one can measure
of shaft B by the variation in
the course of rotation of the angle between
tvfo
radial
vectors, one representing snaiii n and the other shaft B,
One can materialize these two vectors by two fixed bright
radial lines, one on annulus C and the other on disk D.
The
angle of dispiaceneni can be recorded pjioLograpniCiiJ-xy under
stroboscopic light, the speed of which is about four times
tliat
of shsfts A and B»
The cx^jcrir^isntai apparatus does not
Mm
aini
at reproducing
phenomena which in actual shafting give rise to the
It has been designed in the
irregularities of rotation.
ftanner described to accorxiodate it to the production and
OMMSurement of irregularity in the pri^eller rotational i^edd*
II,
>tudy of Motion
Let us consider the radial vector passing through the
center of gravity of the unbalanced suits and let f(t} be the
law of variation of the angle it makes with the horizontal
f(t) •
<*>t
d (t)
lJ.h
•m
iju^
•lU
ttfC
'..
•;^»ji.i:.
.'
,!••')
vviij.
43
CO
being the speed of rotation of shaft
ularity of rotation.
and 9(t) the irreg-
>\
Let us call
the polar moment of the masses (disk, unbalanced
I,
mass, propeller and shaft) held by shaft B.
I2
the inertia of the water entrained by the propeller,
C
the spring constant,
mga
the maximum moment of the mass with respect to the
axis of rotation,
A
the damping constant of the propeller at the
variation of angular speed **
dt
,
Let us suppose that the frictional couple of the pro-
peller shaft on the bearings is proportional to the angular
speed
B (w +
^
).
Then the equation of the irregularity of motion is
(Ij^
+ I2)
^
= - ce - mga cos
ot 4^(t)
-A
^D ^
To solve this equation we limit ourselves to a first
approximation in writing the moment exercised by the unbalanced mass in the form
mga cos
cat.
The equation becanes
di+I^)
*•
^
^
= - Ce - mga cos ot - A j2£ - B
•"
dt2
The solution is
© « 9q cos
where 9
«
o
(ojt
+ o^
)
{li^l2W
-
C
^ + (a + B)2 0.2
I
mga
I
..
ilfi
dt
dt
.1
.1
i)k
c
3/!;f
or,
^
Ilk
44
tan
^
«
(A
BIm
+ l2)o2 - C
-*•
di
Analysis of the photographs shows
tiiat
the angular dis-
placement follows the law at stated,
9 = 00 cos (wt + <^
)
The plot of the values of ©q and ©C
permits the calcu-
lation of the unknowns A, B and I2 by the formulae above.
The numerical values of the known quantities by measure
or by direct calculation are
1^ « 0.0000b85 in M.K.S,
inga
x
m^ units of mass
« 2,26 x 10"'^ Kg - m
C = 0,079
Kg-rr/radian
The screw characteristics are:
dia, = 0,156m
geometrical pitch » 0,1904m
pitch of center of pressure = 0,137m
polar inertia = 0.000153 in M,K, S, x m^ units
Material « aluminum
III, Experimental Determinations
We have determined by separate experiment the values of
the unknowns A, B and l2»
1,
Determination of the damping coefficient of friction-B,
We replaced the propeller with a cylinder having the
same inertia and w» measured the amplitude 9q of the vibrations
from 3 to 7 rps.
We found B » 4 x 10"^ Kmg/radian/sec.
This value is within 25^,
hi;-
A-'.
.9V0d6
»•
ii, dkiJiil
\-xs.
iiy^.
..u
.rji ,iis_j.
js.
XVsFM'v
A er
JJ, JO. - Xti-
•Hi
.)
'
•
d«s
-i
2,
Determination of the increase in inertia duo to the en-
trained water - l2.
We made use of the relation
tan
oC
=
(A
PK^
- C
+
I2)w2
dx
•»•
noting that for
= 900, (l^ +
cv:
l2)«^i^ -
C = o.
We found, the value of the phase of the sinusoidal ir-
regularity from 3 to 7 rps and for water speeds of
0,60 rr/sec and for the still condition,
variation in
<3C
as a function of the rps.
Plate
I
1
n/sec,
gives the
The number of
turns at which o^ « 90° is 4,80,
TLATE X
PCTERMINATION OP CRiTiCAL
PERW
<<
y
tsc
-^
'
/
/
s
<*
0*ie
/
no
90
/
tiO
30
\
5
\t
rt>S
f
can deduce from this that the total inertia of the
masses and the entrained v/ater is
1^+12=
0,0000870 in M.K,S, x m^ units.
The increase in inertia of the propeller is 183, 55y,
a steel
3,
propeller this would be
For
609^,
Determination of the damping due to the propeller - A,
We made a series of determinations of the rps in the
vicinity of critical speed for water speeds of from
1 m/sec.
to
The results are given in the following table where
01
I
o^tii^
.r.oi
^
zo
.C
.SJir.ii
-i^
X
^•-^•.is
;.
.li;ov/
o
jiv
.1^
;.
we indicate the value of the coefficient K such that
A »
h^^1
S2^
27rno
Cq being the torque on the propellor corresponding to
the steady state speed Hq.
Snftad
n/sec
.17
.21
.215
.40
.62
.62
.61
.61
.02
.825
1.0
1.0
1.03
4.
fits
Bjac*"^
4.56
4.90
4.56
13.2
10.5
13.2
14.7
5.
4.80
4.55
4.85
4.55
4.35
5.05
4.56
4.95
4.55
4.82
5.0
a
^liQ
0.505
.68
.43
.415
.38
.366
.328
,278
15.1
11.3
9.45
9.7
7.55
8.8
8.1
8.8
8.5
4.55
i
1
.8
.776
.76
.53
.315
.271
.33
.39
.39
.166
,
5
.031
.11
.22
-.0285
-.175
-.1
.08
.051
8.
3.'.)
-.1
Experiment compared with the theory.
M. Bara, Ingonieur du Genie Maritine, indicated in a
paper (AT?M 1934) the formula A « -tl^ « i
2Trdn
r^,
£a
2?TnQ
iNhere Ko = r^
r^
**
the slip with respect to zero torque.
Let us put the torque in the form analogous to Froude*6
formula
C^ = F(r) n^^ d^
r = slip with respect to the point of zero thrust as
generally considered.
I
»V/
l.J*» •-' J.
ccc«
xeo.
-"O
0,1
C.I
evx.'
V
^w
r
.
>©r!t
•
a..
,{^
L'ii^v
iq
I'J
j;i.ii'J':
J
if
L:'.!-,
dC
Cq
^
2rfdn
+ (1 - r)
2nrn/
f
K3 = -
2+
(1
-r)f
Plate II gives the values of K^ and
of r as vvell as of the experimental value
K-,
as a function
Kj^,
c
Plate
K
10
^ >-
as
f^
^^
-0A
t>
^^
t
Of
V*>LUE
Curve
1
Curve 2
—
X•
i^
r
A\
ik
K AS
FUMCTION
^^2
= ^c
!'
»
_
.....
1»
^
.,„..,...„<-
,
F
o = Experimental Points
Kj^
The curve of K3 averages the experimental values,
"At
high slip it is much nearer the experimental points
than the curve of K2»
the experimental.
At lov; slip the two carves approximate
,1.
1-1
d-
i
Conclusion
1,
The increase in inertia due to entrained water for
steel model is equal to
One usually uses
2,
The formula
a
of the inertia of the propeller,
60Jto
25?o.
-^
2jrdn
=
Ss^
2Trn-,
°
2 + (1-r)
'
^^
4^
d£
F
gives the value of the propeller damping for first node
vibrations.
3,
By experiment, the damping force was found to be de-
pendent on the speed of advance and the angular speed and
independent of the angular acceleration.
In the discussion following this paper, M. Guntzberger
states that water velocities v/ere read by pitot tube, and
also that the water velocity was not controlled.
The
velocity obtained was that resulting from the acceleration
of the v;ater from rest caused by the propeller itself.
Jl,
dbOO
j-8'-
a©Ii;
.>nn?.tf,-fi'.*v
'*L>
(1)
Brown, T, W, F, - "Vibration Problems from the Marine
Engineering Point of View," Transactions of the North
East Coast Institution of Engineers and Shipbuilders,
Volume bb, 1938, pg. 127.
(2)
Lamb, H, - "Hydrodynamics," Dover, 1932 Edition.
(3)
Lewis, F. M. - "The Inertia of the Water Surrounding
a Vibrating Ship," Transactions of the Society of
Naval Architects and Marine Engineers, Volume 37,
1929, pg. 1.
(4)
Greenhill, A. G. - "The Motion of a Solid in Infinite
Fluid," American Journal of Mathematics, Volume XXVIII,
1906, pg. 71.
(5)
Taylor, J. L. - "Some llydrodynarnical Inertia Coefficients"
Piiilosophical Magazine, Series 7, Volume IX, 1930.
(6)
Abell, T. B, - "A Note on the Direct Measurement of
the Virtual //ass of Ship Models," Transactions of the
Institution of Maval Architects, Volume 72, 1930.
(7)
Baumann, H. - "Tragheitsmoment und Dampfung belasteter
Schiff sc^.rauben" (Danping and Moment of Inertia of
Loaded Ship Propellers) - Werft - Reederei-Hafen,
Volume 20, No. 16, 1939.
(3)
Guntzberger, H. - "Effet Amortisseur de I'helice sur
1«8 oscillations de torsion des lignes d'arbres*
(Buffer effect of the Propeller on Torsional Vibrations
of Line Shafting) - Bulletin de 1* Association Technique
Maritime et Aeronautique, Volume 39, 1935.
(9)
Lewis, F. M. - "Propeller Testing Tunnel at the
Massachusetts Institute of Technology" - Transactions
of tne Society of Naval Architects and Marine Engineers,
Volume 47, 1939, pg. 9.
(10) Brahmig, R. - "Die Experimentelle Bestimraung des
Hydrodynamischen Massenzuwachses bei Schwingkorpern"
(Experimental Determination of the Hydrodynamic Increase
in Mass in Oscillating Bodies), Schiffbau, Nos. 11 and
12, June 1940 (Translation 118 of David Taylor Model
Basin).
ijiiit
4.^ j.v-/ivLv
uqii::^
:jai.
.
,
.
lA
.z'sim.
•niix^
.
.:;?vcu
' ,3j(a.;:*Jij:.\'
,5i
,l;.
e)
"•tn©
r-.'0»^,.
jj
^i.i^i^^ijj'A
V)
A«X
c
«nc
i-^!)
9'
X»i-)0:4
r'-i-r .-far-
'
-f
;.
.;''
,.s
f
'-. ->;k'^..
?
\%
JUL
2
25 MAY 67
25 MAY 67
BINO^CRY
c n Q »
1"5 9 fl 3
1
20520
^.
fl
Thesis
^'
wa"'meet of entrained
of
inertia
ter on virtual
ship propellers.
*
..
aSMAt 67
1 5 9
fl
^
P94
/CUOA^Vi
Price
Effect of entrflined. vnter on
virtual inertia of ship propeller e.
Library
U. S. Naval Postgraduate School
Monterey, Cahfomia
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