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 /s r /i:^ T t£JXi w^iU sx«* ll *? /x r» 1L r\ o 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':^ -. J -x-'V! •^ •£ .L 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 0£ ijv ^ iox? xr. 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 -LI I ^ . J5£- \O^0' 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 SJv* 0* 3:0 -'^^ 3ei3.:u..-.. ii- r'fjJ">'Si[ brsr •nlJv ;r^ .V -w-j.:) to -a rH 0) 8- -f* ^ M iH 0)04 c MM r^"* 00*vO • • if) a 4 (« •H 01 .H-P XH • r- (^ p tn C c n n-1 o <WCN] rH c 4 «TJ o M ^ •H CO SOO CO ^ ••••• CM O O fO <> O «X) u") • 04 CM ro CO CO lO o: u • • > o « 3 «) M S cr • CMroco -t <t u 'sr oo-c O o ^o <V M ^^^ ooo O vO ^o g-8 O vO li^ • if ) •£> • « • C> vO .H O O »0 O hOO lO O vo vO a") r* h- r^ \D c g V) OJ ex: C3> D.G C «» -H OJ 3 js 6 -J iH iD ul (D ••••• CM CM CM uO ^ '^r sr "^ "^ rj"^ jf) • • • rO c*) CO • • • CO pS <T> • lO if) W >• CQ oi s s Q s s s CO I CO ^ tn cocM a, r* • g > » CO • s E o nj G • • CMiH—J • « • CM CM CO CO CM CM cooo if> •p e • • • o« CO c>r^ CO (> o ooc^ • • • o r- lO iH vO u) O u) f^iH r^ tH »H fH a tO li) 2 Ht CO CO CO CO 5t" if) '^^ ^ CQ rH CM CO M O a ^o cott CMr- t*- r- ^ aO O •-,.« \ 'U t. o d u ^ Variable Inertia Hlement on Torsion Penduljm Variable Inertia Element as, Installed for Calibration V' m- V»ij l_[ 1^1 1 !_|,j M [_Mj !__!_!_! ! 1 M CALIBRATION FOR 3/8" TORSION ROD 1 ! ! | DIA. POLAR INERTIA t LB. -IN V 60 i \ 1 i ^ ^. m ^ ^ A« 4 5- ---j- ^^ ^ J ^»^ •s; L_ 5 it L. 5 : ^ it.*«- ^^ : ^^ ^ ^^ %^ ^r 5^ ji - ^ ^ ^ ' — v ' ' ^ ' »* it ^ _ ^ ~ rZ S S-i_ -^ it it -.1 _ _ FIGURE V 1 I I . , _^^_ it S^ > , ^. »/\ . 1 ,^0 1 1 1 . , J , ., . , \ \^^ I I- 4- -^ . IK . s -t- ^. ^^^ Si % ^vN^ 9tt sq ^V , 1 V I "S V - mt K> 1^9 14 KO 196 l^0 ~^ 166 ' i' 1 ifeAiJA*iPff%^A^\&i&&i^%i* 11 rM -..!! _,___,' . AT RESONANCE - - , 1 1 1 1 i"*/ 1 it^Dil'^llTiM *./^k|.ll3r.A titf r I 1 . . , .. ,_J . , '/^ilCfV/CT v/UrCV 1 ' . L ' ^ 1 . -J ' , ' ' 1 ' ' 1 1 ' i ' ' ' ^i^^tTt^ ^^~-JLly - _ __ . . ,_ .._±_ ^ ~S7if^ TT " riourwi Mil VI 1 1 1 1 I EFFECT OF SPEED OF ADVANCE ON VIRTUAL INERTIA AT VARIOUS RTCH RATIOS ^ \ \\ \ X , L . ' ^A\ ^N "" '' \ , ' ': ±1 . i '^. :, , : : -^ . M i .1 1 " • 1 '^S *C^ \^^ I .^ _.-.- i vO *>• ^k. Vv ^'^ V^4» \^ - / e^ _ • V^^ t - '» o f -4 7 r y J^ t J 2 it ^^ /^ - - J ^ ! - / / 1 *% A *-|* /y ^^ T ^ * ^ 1/ / L + i/ 2 "' " / :-T liN*. / j! 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CO C •0 4 (0 « •i Mc ^c 19 Ml H.Q -3 -P-H uO c CM c •H 5- C <u IBM .H M +> G U4 c< • * if) r^ 4 (0 <a-H^ 3 -pinl +J MCNI M a> J •H c d '. M c 4 uj >M^ r«»HX :3 s -P +> HU »H » nj « (tJ.HX -pfH flS «M •H O ^ •P M O G C C 0) c D -PrH +J MN M O •H C C « O• ^ CM >M'H M »4 •2 & o ao 0) D. ao u (X a* -p (0 « s (0 J3 C (0 cs o (A o & -a « c o XI U) » O vO O a: rt a > M-P > rt r- O o iJ-H P < •P <J SH o (Q M O > re a o !l^ > Jh 03 > M-P ©•H -{J U <5 3h« > 1 r-t a 0) g M o. c -^ cS § u 01 c M ex: %:.. I & i*~' o t:? fc^i e 'c O •* |6 00 f-t- ki u Si' F;'; ^^ h 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;!!^ '•jv.^i... fpAiV U IS J few A r»'u/ i; *i; ';} orf* -jv ty,-, .-> I'i-dj..- •VI -f *V .:>-f^tv lidi^cw »*n^T'W ^rr-: oT'-t 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 OaJ- sv"icO 90' %«^s .a « J. a ^4. X nolisixiilBD B bns , I O.i^JS'QIiJLjvjij ^iixJ'Bi'w Sj'iJ" o-0 1 j'OXCj •£ «> 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 «! 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 »/- -»; «: .£i .to 3"^ .•IX SISi «'• J J. CJ 1 IV fo^^trts c5UJ.i-V ic 1 IaU-.^ 9S£-o >o i.pi.;. » •^vf 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 -9-: 9rf* ;t< 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 ? JLii -./T i«. + «;-.- If .->•' ^ >.vn r-- J O * -f -f _- -nr. iTi'XO A T>n*^'r') <ii«W . ^"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*- g; . CfcVy 2X3 3;13' 3. asii. 3*.X3 .<-" <i£ 18L^'. VI 'to .?i £}< . &iu .fc ti: ah "0 o S^ v> X 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 > »>/ 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 •.r>lfp.o\-rL!: , o -? t K -r :: si T or: ;v, 1 b- (jT' i tl^f:.: •ijI'xJ'Gr.tjaD Id >C' 02 l.'j'cairiC-O »A « 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 !..iri-i » , , T ;-*r.'-. 7'..-, ^ilt .'.. t>5{if .-.V I J -V iv . -• ^fi «". .( .. •> .\S^~\ k oV .J i ' 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 XXftflit •fit ^0 ,0; :•-.>,_ ' fi/i •. .:. r^M/o t-^ yetc'T *-"igqq£ .--^ , *{if ,^ «fo euptoj i^^^c (J) ,nla 6 iHsd-aY* fiS^ r>F ^ « ,1? ai3»i;»i:j: .-^i a (3«8\S< fie xSiX :o j^- iii* = C3 ^P 32 Figure Excitation i;< I£lew2r.t Installed (^r -33 Figur e X Excitation Eleneat Installed ?%>- ^«> 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 ;5':ffsv ii:'T ^ :^ f\^^a €,('• "."i -^r-r % ?>,v V. Vr r.v 3 -^ H-. "-«<;? . -• ,^ *^r\r -.-i^, -,- ',-1 .-'^iiirf'f \y ' '"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* ^Kl^^^^^^^^^^^^^^^^^^^Sl i^ ^^ ^ S^ ^*> • IS I^K [ - v^- __ 1 1 ' ' ' ' ' ' ' 1 i ' ' ' ' ' ' ' ' 1 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 L it H' " 1 * -. it IT J / T ^ ..-.,.- \t -Ihr ^5 It V \ \ ^ ^t 7 L 5 L fr * ^ ^^- j- -<»--L -<h-»- V^ -,1- 7 .^ it ^s. ^ n^ Si o ^ / 1 / TT X ^T ^ Ijl -^ ; '^ a ' ' X .._._. V / < : J ^ ^^k- / ' ' V^ ^ "^"^ i ^^ it ' " \ i\ ... ' " ! ' , 1 . 1 1 \z 1 5c 5C 1 rc J C 1 J B^E^A. it _ z'' -., «t L jUf -jf^^y 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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