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Cyclic stresses in marine propeller shafting Johnson, William James 1949

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CYCLIC STRESSES IN MARINE PROPELLER SHAFTING  William James Johnson and Norman Clement Bruce  A Thesis Submitted Ia P a r t i a l Fulfilmeiit Of The Requirements For The Degree Of MASTER OF APPLIED SCIENCE In The Department Of MECHANICAL AND ELECTRICAL ENGINEERING  THE UNIVERSITY OF BRITISH COLUMBI^ A p r i l , 1949  „V  CYCLIC STRESSES IN MARINE PROPELLER SHAFTING ABSTRACT This project constitutes an attempt to confirm the existence and determine the magnitude of c y c l i c bending stresses thought to be the cause of many of the t a i l s h a f t failures i n the "Victory" type freighters.  Tests with the  stern t h i r d of a 1/22 scale model h u l l supported i n a testing tank were r e l i e d upon to obtain the desired r e s u l t s . Because the maximum water speed through the tank was only one foot per second the experimental results obtained could not be applied to the prototype.  At this water v e l o c i t y ,  however, i t v/as shown that the type or angle of the rudder has l i t t l e effect on the bending stresses i n the t a i l s h a f t and that the bending stresses when the propeller i s "breaking water" (ship running l i g h t ) are about 2§- times as great as when the propeller i s f u l l y submerged (ship at f u l l - l o a d draft). The experimental technique developed i n this project may be used to advantage i n future research on stress determination i n tailshafts of ship models.  vi  ACKNOWLEDGEMENT The writers wish to thank Prof. W. 0. Richmond for his direction and advice during the course of this investigation; Prof. E. S. Pretious for his assistance i n operating the testing tank; and Mr. T. A. McLaren, of West Coast Shipbuilders L t d . , for supplying records of ship trials.  Thanks are also extended to Mr. A. P. Menzies,  Chief Engineer, Burrard Dry Dock Co. L t d . , for supplying blueprints of the boat; to Seaboard^ Shipping Co. L t d . , for supplying the model propeller; and to the Board of Governors for funds ma de available on the recommendation of the University Committee on Research.  CONTENTS Page Abstract  vi  Introduction  1  Model Theory For Marine Propellers  5  Symbols  5  Rotational speed of the propeller  6  Speed of the model  8  Horsepower required  9  Thrust expected  9  Design and Construction of Model  10  The testing tank  10  The model  11  Design and Construction of Measuring Instruments  18  Bending forces  18  Torque.  *  Thrust.  26  Calibrations and Tests  28  Stern tube calibrations Torquemeter calibrations  25  28 •  31  Conditions for tests  31  Observations  37  Results  41  Calculation of results  41  Discussion of results  45  Conclusions and Recommendations  56  Results  56  Equipment  56  Recommendations  57  Appendix A  58  Appendix B  61  Appendix C  .  ••••••  Appendix D Appendix E  6 9  73 .  75  Appendix F  81  Notes  82  Bibliography.  85  ILLUSTRATIONS Page Figure  1. Typical propeller shaft fatigue f a i l u r e * . .  3  2. Bow s e c t i o n . . .  11  3. Flow lines of "Victory" type f r e i g h t e r . . . .  11a  4. Section view of l/22 scale model  lib  5. Model under construction.  •  12  6. Model under construction  12  7. Model before shaping...  13  8. Finished h u l l without stern casting  13  9. Stern casting being f i t t e d into p o s i t i o n . .  15  10. Contraguide rudder  16  11. Propeller driving mechanism  17  12. Testing tank with model i n place.  17  13. Cantilever tube for measuring forces and couples 14. Stern tube and shaft d e t a i l  19 19a  15. Simplified c i r c u i t for amplifying a nd recording strains.  19  16 Components of propeller drive and s t r a i n measuring equipment. 17. Wiring diagram of stern tube and p a n e l . . . .  22 23  18. Drive shaft showing torquemeter and contactor24 19. Units assembled for test  25  20. Torquemeter...  26a  21. Strain gage combination for measuring thrust  27  22. Model i n tank. Thrust measurement by spring balance  27  23. Arrangements for c a l i b r a t i n g stern tube...  27  24. Static and dynamic calibrations of stern tube s t r a i n gages  '  32  25. Static and dynamic calibrations of stern tube s t r a i n gages  33  26. Calibration of stern tube s t r a i n gages....  34  27. Torquemeter c a l i b r a t i o n  35  28. Wake for test no. 1  38  29. Water l i n e for tests no. 3 and 4  38  30. Wake for test no. 4  39  31. Obstruction for test no. 6  39  32. Sample oscillograms  39a  33. Forces and couples at t a i l s h a f t for t r i a l no. 1..  49  34. Forces and couples at tailshaft for t r i a l no. 2  50  35. Forces and couples at tailshaft for t r i a l no. 3  51  36. Forces and couples at tailshaft for t r i a l no. 4  52  37. Forces and couples at t a i l s h a f t for t r i a l na 5  53  3 8 . Forces and couples at t a i l s h a f t for t r i a l no.  6  54  3 9 . Torque-thrust-propeller speed relationship for model propeller  Table  55  40. Wire s t r a i n gage  61  41. Wheatstone bridge  64  4 2 . Bridge with slide wire.  64  4 3 . Strain indicator wiring diagram  64  44. Brush oscillograph  64  4 5 . Free v i b r a t i o n of stern tube and propeller  78  1. Values of Re  7a  2. Kinematic v i s c o s i t i e s of water  7a  3 . Comparison model to p r o t o t y p e . . . .  31  4 . Results  44  5 . T r i a l Results  60a  CYCLIC STRESSES IN MARINE PROPELLER SHAFTING The large number of propeller shaft f a i l u r e s on the American "Liberty" type and the Canadian "Victory" type freighters has caused some concern to the ship owners and to the marine insurance companies.  Some of the failures have  resulted i n loss of propellers at seaj the majority, however, have been detected when the propeller shaft was removed for a routine inspection which i s normally made every three years.  Because of the frequent occurrence of the propeller  shaft f a i l u r e s , the American Bureau of Shipping i n 1947 recommended to the owners of "Liberty" type ships that t a i l shafts be drawn for examination every two years instead of three. The cause of the propeller shaft f a i l u r e s has been the subject of investigation b'y organizations such as the Engineering Research Department of Lloyd's Register of Shipping; the General E l e c t r i c Company, for the American Bureau of Shipping; and the B r i t i s h Columbia Industrial and Scientific Research Council.  In an a r t i c l e e n t i t l e d " ' L i b e r t y ' 1  Ship Propellers and Rudders" we find the following excerpt; "The f i r s t of the'Liberty'ships'was delivered i n 1941, but I t was not u n t i l the end of 1945 that their percentage of propeller shaft failures f e l l into two d i s t i n c t categories. One type was due to corrosion  1  2 fatigue and was indicated by a circumferential groove around the shaft at the end of the l i n e r . This type was caused by a defective seal at the propeller, and the records for 1947 indicated that failures from this cause had been p r a c t i c a l l y eliminated. The other type of f a i l u r e took the form of a fine hair l i n e crack starting from the forward end of the keyway on the driving side. A torsional vibration analysis of the propulsion system was made by the staff, and the General E l e c t r i c Company was retained by the Bureau to carry out torsiograph tests aboard ship, which v e r i f i e d the s t a f f ' s findings. The tests- showed that there was a third-order c r i t i c a l sjoeecL In the normal operating range of about 4 , 5 0 0 pounds per square Inch. This vibratory stress was s u f f i c i e n t l y high to cause the type of f a i l u r e noted, but only after the shafting had been run at, or near the peak for a considerable length of time. As soon as this condition was disclosed by the actual tests the Bureau recommended that the engines be operated at a safe speed of rotation. The staff, as well as the Bureau's special sub-committee on marine engineering, were at present engaged i n working out practicable means for removing this torsional c r i t i c a l from the normal operating range." Many failures of the second type mentioned i n the above quotation have also been attributed to incorrect f i t t i n g of the propeller to the t a i l shaft and to a r e l a t i v e l y high stress concentration at the forward end of the t a i l s h a f t keyway. A l l failures have been at the outboard end of the t a i l s h a f t and i n most cases near the, Tbig end of the taper. Figure 1 i s an example of the type of f a i l u r e found i n the 2 propeller shafts.  It has been suggested  that a torsional  stress should produce a h e l i c o i d a l fracture, whereas the crack shown i n figure 1 i s perpendicular to the axis of the shaft.  Such a fracture might have been caused by bending  stresses instead of torsional stresses. The bending stresses are thought to be caused by p e c u l i a r i t i e s i n the flow of water past the propeller, by  3  P i g . 1. T y p i c a l p r o p e l l e r s h a f t f a t i g u e f a i l u r e . i n t e r a c t i o n between p r o p e l l e r and h u l l o r r u d d e r , and by  the  p r o p e l l e r b l a d e s " b r e a k i n g water" when the s h i p i s r u n n i n g l i g h t o r i n heavy seas.  T h i s t h e s i s r e p o r t s an attempt to  v e r i f y the e x i s t e n c e o f bending s t r e s s e s and  to determine  t h e i r magnitudes. Two  g e n e r a l methods o f attack were p o s s i b l e , namely,  the measurement o f s t r e s s e s i n the p r o p e l l e r s h a f t o f a ship d u r i n g a normal voyage, and the measurement o f s t r e s s e s i n the p r o p e l l e r s h a f t o f a model s h i p i n a t e s t i n g tank.  The  problems i n v o l v e d i n s e t t i n g up measuring equipment on a s h i p made the f i r s t method i m p r a c t i c a l f o r an i n i t i a l i n v e s t i g a t i o n ; t h e r e f o r e model t e s t s were r e s o r t e d to f o r the  information  required. A s c a l e model o f the h u l l o f the " V i c t o r y " type f r e i g h t e r v/as t h e n r e q u i r e d .  I t was  n e c e s s a r y t h a t the model  4  be large enough to minimize scale effect, and yet, small enough to f i t into the University testing tank.  In oper-  ation the model was suspended from the sides of the tank on rollers in  3uch  a way that the thrust produced by the  rotating propeller could be measured.  The water then flowed  past the model to produce the same r e l a t i v e effects as though the ship were moving through s t i l l water. Two main tests were proposed; one at f u l l - l o a d draft, and the other at no-load draft.  In each t e s t , v a r i -  ables such as water speed, propeller speed, and draft were adjusted, as nearly as possible, to values calculated to give dynamic similitude between model and prototype.  The observ-  ations included oscillograms of c y c l i c stresses, measured by s t r a i n gages; and readings of torque, thrust, propeller speed, and water speed.  Bending stresses were calculated, and con-  clusions drawn from the r e s u l t s .  5  Model Theory for Marine Propellers Model tests with marine propellers are subject to 3 the general law of dynamic s i m i l i t u d e . This law states that "...geometrically s i m i l a r systems are dynamically similar when s i m i l a r l y situated p a r t i c l e s under the action of applied forces trace similar paths In proportional times and when the ratios of corresponding forces are equal." P r i o r to designing and constructing a model, certain-basic data should be calculated to insure that the results of the experiment with the model can be applied to the prototype. These data are the rotational speed of the propeller, the speed of the model r e l a t i v e to the surrounding water, the horsepower required, and the thrust developed by the propeller.  Each of these quantities can be estimated by com: -  promising between results of previous experiments and calculations using equations derived from the above mentioned law. Symbols Re  Reynolds number  k  = kinematic v i s c o s i t y i n feet per second  n  revolutions per second of propeller  N  = revolutions per minute of propeller  d  —  diameter of propeller i n feet  R  = radius of propeller i n feet  MIR  = mean width ratio -•• mean developed width of one blade propeller diameter  6  BTP = blade thickness fraction = X V  =  —  maximum blade thickness propeller diameter  r a t i o of large ship to the model velocity of boat i n feet per second  V  velocity of water at propeller i n feet per second  W  wake fraction  g  = density i n pounds per cubic foot  s  = real slip  S  =  apparent s l i p  T  = thrust i n pounds  Q  —  torque i n foot pounds  subscript 1 refers to the ship subscript 2 refers to the model Rotational Speed of the Propeller The second part of the similitude condition states that the ratios of corresponding forces must be equal i f geometrically similar systems are to be dynamically s i m i l a r . Inertia and f r i c t i o n forces are the only forces acting on a f u l l y submerged propeller.  Therefore to satisfy the  similitude law the ratio of f r i c t i o n forces to i n e r t i a forces must be equal for both the model propeller and the ship propeller.  It can be shown that the constancy of this ratio  i s f u l f i l l e d when the Reynolds number i s the same i n both systems.  Reynolds number i s defined as the product of any  characteristic speed and any characteristic length divided by the kinematic v i s c o s i t y of the medium.  This seemingly  simple requirement i s d i f f i c u l t to obtain i n practice inasmuch as i t implies that i n the same medium a model propeller  7  must "be tested at X times as great a speed as the f u l l sized propeller, where X denotes the l i n e a r r a t i o . However, investigations into the effects of blade f r i c t i o n  by  4  "F.Gutsche" overcome.  show that this d i f f i c u l t y can be p a r t i a l l y According to his report a model propeller i s  entirely free from blade f r i c t i o n when the Reynolds number exceeds the c r i t i c a l value given i n table 1 at a l l blade radii.  It i s possible with the use of the following equation,  table l,and table 2 to obtain a value for the rotational speed of the model propeller. Re = rewriting n =  x  k  MWR (1)  R e  d  z  MWR  With a fixed p i t c h propeller and assuming no s l i p i t i s evident that the water speed past the model h u l l i s d i r e c t l y proportional to the propeller speed.  When conducting  tests with models I t i s desirable for p r a c t i c a l reasons to use as low a water speed as possible by using a low propeller speed.  From the above equation I t can be seen that to keep  n low one must t r y to obtain low values of k and Re.  Table 2  shows that k decreases as temperature increases; therefore, as warm water as possible should be used In the testing tank.  It  can be shown by past model experiments that a c r i t i c a l Re corresponding to 0.4R can be j u s t i f i e d .  This value of Re may  give blade f r i c t i o n losses on r a d i i less than O.4R; but, as  Table 1. Values of Re B l Th Fr MWR ~ "  r R  40 x 10 21 13 9.0 7.1  .20 .30  .40  .50  .60 .70  B l Th Fr _ MWR  i  65  4  6.5 6.6 7.6  .80 .90  x 104  34 20 14 10 8.7 8.0 8.5  Table 2. Kinematic V i s c o s i t i e s of. Water ( f t . / sec.) 2  Temperature ° F . 42 44 46 48 50 52 54 56 58 60 62  Salt Water  Fresh Water 1.6068 x 10" 1.5530 1.5021 1.4538 1.4080 1.3646 1.3233 1.2840 1.2466 1.2109 1.1769  5  1.6568 x 10~ 1.6035 1.5531 1.5053 1.4599 1.4188 1.3758 1.3368 1.2996 1.2641 1.2303  5  3  portions of the propeller blades below this r a d i i contribute less than 20% of the t o t a l thrust of the propeller the r e s u l t ing error cannot be large. Speed of the Model with respect to surrounding water The f i r s t part of the law of similitude states that geometrically similar systems are dynamically similar when s i m i l a r l y situated p a r t i c l e s under the action of applied forces trace similar paths i n proportional times.  It can be  shown that i f two propellers work at the same s l i p fractions, the following condition w i l l be s a t i s f i e d .  —fcL. =  rewriting  -)L=-dJL_  rewriting using subscripts 1 and 2  xm  *  v  Since both propellers are working at the same s l i p fractions the s l i p terms cancel out; rewriting 1/ = Mdz substituting n, for N, and n  z  for N  z  therefore,  iY/ V / l /  V =• fir *  2  0,/V,  (2.)  9  Horsepower Required In the paragraph on the rotational speed of prop e l l e r s i t was shown that, blade f r i c t i o n forces can be neglected i f the Reynolds number exceeds a certain c r i t i c a l value.  This conclusion simplifies the equation used to c a l -  culate the torque, as only the i n e r t i a forces need be considered.  An equation r e l a t i n g torque, diameter, and speed  can then be written as follows:  Q._  Q.z  9,N d,> ~ &// 'cT z  rewriting  Q = ^'f'ffiffi-  <3)  z  Ji  ''I  CJ,  The horsepower required can now be calculated by:  ftp "  =  r  ZTTNzQ, 3300O  u  )  As before, these equations only hold when both propellers are working at the same s l i p f r a c t i o n . Thrust Expected The same conclusion can be arrived at for thrust calculations as was obtained under horsepower required. Therefore, i t can be shown that the following equation w i l l hold for propellers working at the same s l i p f r a c t i o n . rewriting  ^^ ,z  '  % M*d*  (5)  10  Design and Construction of the Model The primary object of the investigation reported herein i s to measure the c y c l i c bending stresses produced at the forward end of the propeller shaft keyway.  The essential  equipment for the proposed test includes a model testing basin, a scale model of the "Victory" type freighter h u l l , and sens i t i v e strain-measuring and recording instruments. The basic design data for the model have been c a l culated (appendix A) and are as follows: propeller speed  - 690 RPM  torque  - 33.1 inch-pounds  horsepower (at propeller)- 0.36 thrust  - 18.6 pounds  water speed  - 8.91 feet per second  The Testing Tank The tank i n the Hydraulics Laboratory was made available for the project by the C i v i l Engineering Department. This tank, shown i n figure 12 i s fifteen feet between the baffles and the overflotv weir, four feet wide, and three feet deep.  The greatest water velocity obtainable i s about one  foot per second.  The size of the model i s l i m i t e d , then, by 5  the size of the tank.  11  F i g . 2.  Bow section.  The Model A 1/22 scale model of the "Victory" type ship prop e l l e r , obtained for the project, determined the size of the hull.  A complete h u l l to this scale would be 20 feet long,  30 Inches wide, and 20 inches deep.  This model Is obviously  too long for the tank, so we decided to build only the stern section to scale, and to add a short bow section ( f i g . 2) to " s p l i t " the water and make the flow conform to the scale section of the h u l l . For construction purposes, a f u l l size drawing of 6  the model lines had to be prepared from the drawing supplied. The bulkheads were scaled up with proportional dividers and the water lines were l a i d off every three-quarters of an inch. The water-line spacing was determined by the thickness of the lumber.  Figures 3 and 4 show the lines and dimensions of the  fx  I  T  1  '  f  3  4  2&9  i  $"  HALF  BREADTH  :  hUN  ft£F£P£fi££ J>P6. W B H D . 7093A NORTH VMSH/P f:£PA/PS t$&.  THE WII/ERStTY- OF BRITISH COL &m!' PA-  '"i A Us-i.  44/  F  Fi f)W / A ' — '  %  \''V/u.7?./ry' /:  V  f  r  |  , , 1 .  .  ._  Ckecttea by  .  ,  _  ,  -?/" BEAE1.  •  . . . " •  I-  1 . •  ^—r." ITU  nj  !  LH i j x c h o t f t r r / ?  c  -i :  Xzr  i  ;y-  • I ! !  ; r :i  ll—t  I i  /  V' Y;£W 'A I//  ,\D w /*~\ .ZL,  APPROX.  /L-  SCALE  12  Fig. Model  6.  under construction.  F i g . 8. Finished h u l l without stern casting  14  model. The model was constructed of k i l n - d r i e d f i r . Successive layers were l a i d off from the drawing and handsawed to shape.  Four or five layers at a time were glued and  clamped on a building frame, as shown i n figures 5 and 6 . Figure 7 shows the model before shaping.  A s o l i d bulkhead  was fastened to the forward end of the model.  The details  were arranged so that other lengths of h u l l could be attached i f required. After glueing was completed, the model was shaped with special round-bottomed planes and other finishing t o o l s . The shape of the model was made to conform to templates of the bulkheads.  The h u l l was f i n a l l y scraped and sanded to a  smooth surface, ( f i g . 8) The stern section around the propeller boss and the gudgeon was too weak to be l e f t i n wood.  The section was  therefore cut out and used as a pattern for a bronze casting. Figure 9 shows the finished casting being f i t t e d into place. A boring t o o l was made to bore the ste:m tube hole.  A 1.375  inches inside diameter brass l i n e r was f i t t e d into the hole between the casting and a brass bulkhead plate, and the unit was cemented and pulled up t i g h t l y to the h u l l with long bolts ( f i g . 4 ) . The casting was faired to the h u l l and the model was finished with marine enamel. A model of the "contra-guide" rudder, shown i n figure 10, was made to scale.  The rudder was constructed so  that i t could be locked at any desired angle.  15  F i g . 9.  S t e m c a s t i n g being f i t t e d into  position.  A f- horsepower v a r i a b l e - s p e e d motor, t o d r i v e the p r o p e l l e r , was mounted on the h u l l , as shown i n f i g u r e 11. A v e e - b e l t d r i v e was a r r a n g e d  t o g i v e maximum speed o f  700 RPM. F i n a l l y , t h e model was suspended i n the t e s t i n g tank from c r o s s beams, as shown i n f i g u r e 12.  F o r reasons  w h i c h w i l l be d i s c u s s e d i n the s e c t i o n on t h e measurement o f t h r u s t , b a l l - b e a r i n g r o l l e r s were a t t a c h e d t o t h e ends o f t h e beams.  The r o l l e r s r e s t e d on s h o r t t r a c k s a t t a c h e d t o t h e  top o f the tank w a l l s ( f i g . 4.).  The t r a c k s a l l o w e d a l o n g -  i t u d i n a l m o t i o n o f about f o u r i n c h e s . t r a c k was t o p r e v e n t  The upper member o f the  t h e model f r o m f l o a t i n g o u t o f p o s i t i o n .  SCALE  0T\  8  r  or SECT/OA/5  " 1 T  £ 8  £'  2>'  -9' i  1  a' 1  Y  B'  C'2' — UNI VERS/TY  SCALE  °r JUDDER  OF  gR/T/S/1  COLI/M3M  -/  REEERE/VCE DC-R. A/° '•/-./£/-3 ey: W.J.J. FIGURE - 10 TODD-BATH /ROM SMPBI//LD/NC CORP.SCAie: As shaw/i'  18  Design and Construction of Measuring Instruments Hooke's Lav/ states that i f a material Is stressed within i t s e l a s t i c range the force producing the stress i s proportional to the resulting deformation.  If the deform-  ation or s t r a i n can be measured, the force can be calculated. This p r i n c i p l e can be applied to the measurement of forces acting on the propeller of the model.  I f the applied force  i s c y c l i c , the stress and s t r a i n i n the material w i l l be cyclic. The Baldwin SR-4 e l e c t r i c s t r a i n gage (Baldwin Locomotive Works, Southwark Division) was the basis of the design of the strain-measuring devices for the project. Steady strains are detected by the SR-4 s t r a i n gage and measured by the SR-4 s t r a i n indicator.  Cyclic strains are  detected by the SR-4 s t r a i n gage through a suitable e l e c t r i c a l c i r c u i t and recorded by a Brush pen-and-ink oscillograph (Brush Development Company) (appendix B ) . Bending Forces Two methods of applying SR-4 s t r a i n gages to the problem are considered.  The more obvious method i s to cement  s t r a i n gages to the propeller shaft at the location of the shaft f a i l u r e s , and thereby measure the stresses.  Here,  current must flow to the gages through s l i p rings on the  shaft.  This method was discarded because of anticipated d i f f i c u l t i e s  P. -WW-  -vwv  Oscil/ojr-aijeh  F~IG.  15. *S/m/oJifiecl recording  Circuit  -for strains  am/olifymj  and  J.  i_3 16  S+r-<y,n  20riC  on 2->  £~Q Holes on 3g /  i  X  F  "ZZ2  'mi* inn hn'i  i i J  ii u i  U]  4  n  3 '-4  X  Y  v  c  n  *2  * 8  6  TT  3?  Sec X-X  Sec.  Y-Y.  °4 /5-  STEf?n  7 -20HC 5eiJ>cre*/-  4  TUBE  DETAIL.  &  Sr/^Ain  GAPE  LAYOUT  .  Bearincj Retainer IO-24HC  Set  spacers  Sere*/ Curtis  -4 - S/rr~ Searinjs -Key  Universe/ Joint  ££48  T - * H  6—  Toper- Bushmj to Propeller-.  Suft  PeoPELLEP  SHAFT  f ' C B U f f E  DETAIL  14  .  ^co/e  One-ha/f~ full size.  M.C.B. 2b-3-49.  20  i n eliminating small changes of resistance through the brushes and s l i p rings. 8 In the second method of s t r a i n gage application the propeller i s supported at the end of a fixed cantilever tube ( f i g . 13).  A f l e x i b l e shaft inside the tube transmits  torque to the propeller.  Forces and couples acting on the  propeller are transmitted through the stern bearing to the tube .where the resulting strains are measured by SR-4 s t r a i n gages.  By this method s l i p rings are eliminated, and the  bending moments measured may be resolved into forces and couples acting In the horizontal and v e r t i c a l planes. We selected this method as the more p r a c t i c a l for the proposed investigation. Figure 14 i s a drawing of the s t e m tube, bearings, and shaft i n d e t a i l .  The shaft i s f l e x i b l e so that i t w i l l  not absorb forces and couples but w i l l transmit only torque. The stern pair of b a l l bearings forms a r i g i d connection between shaft and tube.  The bearings are a tight f i t - t o the  shaft and tube, and the spacers between the bearing races preload the bearings when the unit Is assembled.  The r i g i d i t y  between the shaft and tube w i l l guarantee the accurate transfer of couples from the propeller to s t r a i n gages. We were unable to predict the magnitude of the forces to be encountered, and to design accordingly; consequently, the size of the tube was determined by the size of the shaft, f l e x i b l e couplings, bearings, and the materials 9  available.  The most suitable b a l l bearing  had an outside  21  diameter of 1.125 Inches.  The tube was turned from seamless  steel tubing 1.375 inches diameter and 1.0 Inch bore.  The  active length of the stern tube was turned to give a wall thickness of 0.020 inches. The arrangement of s t r a i n gages i s i l l u s t r a t e d i n figure 14.  Sight gages (type C-l) were cemented to the tube  i n the horizontal and v e r t i c a l planes, with their measuring axes p a r a l l e l to the axis of the shaft.  The gages operate i n  p a i r s , as follows: two diametrically opposite gages ( e . g . , gages A and C, f i g . 14) are connected i n series as shown i n figure 15.  A r a d i a l force appled to the propeller shaft i n  the plane of the gages produces tension i n one gage and compression i n the other.  A voltage V applied to the gages  drives a constant current I through both gages (the current to the amplifier Is n e g l i g i b l e ) . ' The changes i n resistance due to the tension and compression of the gages r e s u l t , fore, i n a change i n the voltage E across one gage.  there-  This  change i n voltage can be amplified and recorded by an oscillograph.  The amplitude of the oscillograph wave i s then  proportional to the bending moment at the gage.  By suitable  c a l i b r a t i o n the magnitude of the bending moment can be determined.  The bending moments measured by the four pairs  of gages are then substituted into equations which are solved for the horizontal and v e r t i c a l forces and couples acting i n some convenient plane through the propeller, normal to the shaft axis (appendix C ) .  The forces and couples acting  through the propeller can be combined to give the bending  22  P i g , 16. Components of p r o p e l l e r d r i v e and s t r a i n measuring equipment. moment at the forward end of the t a i l s h a f t keyway. The four s t r a i n gage records were timed by means of a contactor  ( f i g . 16) on the d r i v e shaft.  The contactor, i n  s e r i e s with a s u i t a b l e resistance (appendix D) made a mark on the o s c i l l o g r a m at the same point In each r e v o l u t i o n of the shaft.  A f t e r several timing marks were recorded, the con-  t a c t o r was switched o f f to allow the true wave to be recorded ( f i g . 32).  In order to c a l c u l a t e the forces and moments at  the p r o p e l l e r , the four separate o s c i l l o g r a p h waves were assumed to have been recorded at the same time. Steady r a d i a l f o r c e s , exclusive of the p r o p e l l e r weight, a c t i n g on the p r o p e l l e r shaft during a t e s t , were  e3  b  I'M'h To Volt meterSter-n A  B  T  D  1c  Tube G  cam  H  <<<<<<<<<<<<<<<<  < < < <  <  u>4  U/  P^nel  V  s  \ Patch  Cord± To <~  I 7)  FIGURE  — WiGiriG  OFSTERn  DIAGRAM  TUBE  AND  Ampli-fier Oscillograph PACJEL  Legend. A  to  b  -  ft  -58-4  "3"  battery  C  - Contactor- Open  J  t  -la  - Pesistor  P  - (?es»s  *S  - Tojjle  *  fain  22.4  Jack  circuit  Open  220,000 tor-  Example^ osci //oy-ap  j a j es  500,  fy/°<?  C/  500  A.  v.  on propeller-  ~ *S/nj/e  P, z  si  shaft.  .  circuit  jack  .  si.  OOO Si. .  switch. str-arin  aaae  p>c*ir  A  £  connected  -to  h.  n.c.8  €-4  -4-9  24  F i g . 18. Drive shaft showing torquemeter and contactor.  measured with the SR-4 s t r a i n indicator.  A reading was taken  on each pair of gages, f i r s t with the propeller stopped, and then with I t running at test speed. To f a c i l i t a t e the operation of the equipment, a panel hoard was f i t t e d to the side of the model.  A l l electri  cal leads were brought out to the panel where any desired combination of gages could be had.  A tachometer to indicate  propeller speed was also f i t t e d into the panel. a l i n e diagram of the e l e c t r i c a l components.  Figure 17 i s  Figures 11 and  18 show the arrangement of the driving mechanism i n the h u l l , and figure 19 shows the recording instruments set up for test  25  P i g . 19.  U n i t s assembled f o r t e s t .  Torque The  torquemeter, i l l u s t r a t e d i n f i g u r e s 16 and  c o n s i s t s of a h e l i c a l s p r i n g mounted between two  flanges.  Each f l a n g e i s f i x e d to the d r i v e s h a f t by set screws. i n c h diameter d i s c which has periphery i s fastened fastened  a centimetre  The  open-coiled  inches o u t s i d e diameter, has 8 turns o f 0.134 s t e e l wire.  The  A 6  s c a l e on i t s  to the forward f l a n g e , and  to the a f t e r f l a n g e .  20,  a pointer i s  s p r i n g , !§• inches  diameter  c a l c u l a t i o n s to check t h i s s p r i n g f o r the  26  application are given i n appendix F.  The rotating scale can 10  be read when illuminated by a stroboscopic l i g h t  synchro-  nized to the propeller shaft by the contactor. Thrust Two methods were used to measure the steady thrust. The strain gages, which measured bending moments, were also i n compression under the action of propeller thrust.  The  forward pair of bearings i n the stern tube "floated" i n the tube, therefore the thrust was transmitted from the s t e m bearings through the active length of the tube to the h u l l . Gages A-G and E-G were connected In a s e r i e s - p a r a l l e l arrangement ( f i g . 21) and the unit compressive s t r a i n was measured by the SR-4 s t r a i n i n d i c a t o r .  In subsequent  c a l i b r a t i o n s , large thrusts produced only small strains, and so a supplementary method was devised. The method of suspending the h u l l i n the tank has been described on page 15. measure thrust.  The reason for this method was to  In operation, the model was weighted so that  i t floated with l i t t l e pressure being exerted on the r o l l e r s , consequently the resistance to motion was small.  A spring  balance upstream from the boat measured the force to move the boat against the flow of water (propeller stopped); and a spring balance downstream from the boat measured the p u l l of the boat when i t was just moving ahead (propeller running at test speed). readings.  The thrust was taken as the sum of the two  The arrangement Is i l l u s t r a t e d i n figure 22.  TORQUE-METER Itf4r/// Br: .vs. J.J. Ch>£CX£t-8Y: A/. C.J. FIGURE-20 SCAIE:  FULL  i  ^7  Combination  ~fO r~  meas  ct/—/r>  a  f In t- u s f.  Connper>sa t/ny  Baffle  Core/  Sprmj f l 6 . .  balance Model  ha/once  in tank.  "Thrust  measurement  by Sf>rmj  balance.  Sea le • J  E 3  375  7777?  |  IAI  Bending  moment  I  0"  L  s  '"A  4 0  'to  \  Wejhr  = 3 75 W  or 7- 75 W in.-lb. Weight  w Bendmy  f~i<3 £3. Arrangements for- calibrgliny  moment  stcrn  - /2W  in-lb.  lube. n.c e io 4  28  Calibrations and Tests After assembly of the equipment, tests were made for s e n s i t i v i t y and operational d i f f i c u l t i e s .  When a l l units  were functioning s a t i s f a c t o r i l y , the measuring devices were calibrated.  After a l l tests were completed, a l l Instruments  were re-calibrated. Stern Tube Calibration The s t r a i n gages were cemented to the tube and the leads were brought forward along slots i n the tube.  Each  gage was tested for leakage to ground and for perfect bonding to the metal.  The tube was then heated slowly to 175 degrees  P. over a period of forty-five minutes, after v/hich, a coating of Petrosene wax was applied to waterproof the gages. The gages were again tested for leakage to ground.  The leak-  age resistance for the c i r c u i t should not be less than 500 megohmsj and for a single waterproofed gage should not be 11 less than 1000 megohms. The stern tube was calibrated by applying known static bending moments and measuring the unit s t r a i n i n microinches with the SR-4 s t r a i n indicator.  For measuring  variation i n bending forces, only gages A,B,C, and D were calibrated. i n figure 23.  Both forces and couples were applied as shown The unit strains were converted to millimetres  deflection of the oscillograph pen (appendix ifi).  The c a l -  culations are based on 22.5 volts across the gages, an  29  amplification of 1000 (attenuator setting 0.001), an o s c i l l o graph c a l i b r a t i o n of 4 v o l t s , and a gain of 12.5 millimetres amplitude.  This procedure was repeated after the tests.  Some d i f f i c u l t y v/as encountered i n obtaining satisfactory s t a t i c measurements of s t r a i n because of the s e n s i t i v i t y of the type C s t r a i n gages to change i n temperature. The stern tube was calibrated for measuring steady bending forces.  The same method of applying s t a t i c bending  moments was used, but i n this case, one gage was the "active gage", and the diametrically opposite gage was the "compensating gage"; e.g. gage A - active, gage E - compensating.  The c a l i b r a t i o n constants are:  gages A-E  0.2112 inch-pounds per microinch  B-P  0.1883  C-G  0.2165  D-H  0.1850  The stern tube was calibrated to read thrust by measuring the compressive s t r a i n with the SR-4 s t r a i n indicator.  The s t r a i n gages were connected i n a  series-  p a r a l l e l arrangement, so that an average value of thrust could be determined.  The c a l i b r a t i o n constant for this ar-  rangement of gages i s 0,6 microinches per pound thrust. A dynamic c a l i b r a t i o n of the stern tube for measuring c y c l i c stresses was suggested as being more desirable than a s t a t i c c a l i b r a t i o n . were t r i e d .  The following three methods  30  1.  F i r s t dynamic c a l i b r a t i o n : a s i x inch diameter  disc with a 0.25 pound weight at a radius of 2.51 inches was attached to the shaft i n place of the propeller. Oscillograms were taken at speeds from 250 to 800 RPM.  The bending moment  and the u n i t s t r a i n at each gage were calculated (appendix E ) . The amplitude corresponding to a value of unit s t r a i n could then be plotted against bending moment at the gage. 2.  Second dynamic c a l i b r a t i o n : a weight of 0.12  pounds was attached to one blade of the propeller at a radius of 4.36 inches.  Oscillograms were then taken at speeds from  250 to 800 RPM and calculated*as i n 1. 3.  Third dynamic c a l i b r a t i o n : the graphs for the  second c a l i b r a t i o n ( f i g . 24 and 25) curve away from the s t a t i c c a l i b r a t i o n l i n e as the bending moment Increases, i . e . , as the speed increases.  We believe this to be caused by the approach  of the shaft speed to the natural frequency of the propeller 12 shaft assembly.  The stern tube was calibrated again by  holding the speed constant at 580 RPM and changing the weight attached to one blade of the propeller.  Oscillograms were  taken and the results calculated and plotted as before. Of the different calibrations shown i n figures 24 and 25, the t h i r d dynamic c a l i b r a t i o n most nearly approaches the conditions of the tests, and Is therefore the most r e l i a b l e . The calibrations were subsequently used i n analysing the oscillograph records of the tests.  31  Torquemeter Calibration The torquemeter was calibrated by applying a steady torque to the end of the shaft.  A balanced arm was attached  to the shaft and weights were hung on the arm at a 12 inch radius.  The large driving sheave at the forward end of the  shaft was turned u n t i l the arm was h o r i z o n t a l .  Weights were  added i n increments of about 0.15 pounds u n t i l a torque of 41.8 inch-pounds was reached.  This torque gave a reading of  20.0 centimetres on the torquemeter scale.  The weights were  removed and the pointer returned to i t s o r i g i n a l mark denoting zero torque.  Figure 27 i s the c a l i b r a t i o n curve of torque  against scale reading. Conditions for Tests The p r i n c i p a l test (Test No. 1) was designed to simulate f u l l - l o a d , i . e . , greatest draft and greatest speed. The values defining f u l l load for the prototype and model (appendix A) are compared i n table 3. Table 3 Prototype  Model (ideal) Model  Draft (aft) (ft.) 26.9 1.23 21.4 8.91 Speed (ahead)(ft. per sec.) (12.7 knots) 75.6 690 Propeller speed (RPM) 2500 0.36 Horsepower -6.5 -6.5 Apparent s l i p (percent) Torque ( i n . - l b . ) 2,090,000 33 53,400 Thrust (lb) 18.6  I.23 0.93 580 0.39 87.0 42  28  3Z  FiGUQE  2 A  33  FlQ>U&E  £5  35 L-  — ' V"  4  "f  "r  'T y.\.  7 .•" '  •.  ... j. .{-  L  f  i  .v  T  '"•>_'.' 1  t-~ •  H  rr.  j*l  •( |-  T  .  T"*"i~!  '•!• • !  :  >'.-  rrf  •j.  -'•  --  : .L  , , '  •  1  ..—o>— ,o  ••.:,-.  -i  ';  :  -j  :  t.  j-  -  i  i^f j ia/ * • : -"  • ;  -  j  i  i  '  \  -  i•  ^  i  i  i  " 1 ... . O  -:  ~f  ••• •  ._ b .  • 4.  i  •1  i  IfOGQueMEfER. ^  . -  i  ii i  -" •.  • i• r  ''.!-•"••' • 1 • .  V'  •  i  i  !  !  J . ••  i  1  :  I !•• !- ;i  - I ,  \  r  .  i  .  • i  i  r  i •  i ,  fJ  H— i  ..1T.-  '"U:J . . . ....; i  'j  !  !  ;  i  i  I  i  ;  f-l'  -  i  L.....:  JT  'i  rT^~  - -pif  - -- i i !  i  • -r  :  .g:  xrtv  -,-!.;-  ..r  •- (••:-•-  -Vi'4-f  '.;"!7l..f'  "  :  J  ••  i  I  i  ; • i  •  > i  ••i  - ' • •"•  ' •! FI6UPE  27  .j  !  - •  •••  1  1 .-•. -  -  - -j'.:r''1  0  1-.  f  •••-|! • i  r  r  -|....- -.:  ! •••.*! . -  .  -i-  i '  ';  -  z5 Poano 5  -h. H: I-". ! ••-:.] • f r  .• I  •ri • .!  :  ' ' i.•L  ••' !  ':-]'. • { ' -  •  i  '-^Jiffl  -  -  |i  •>.- '•  ' • • !.  •I  -Li  j  "  htj - /  i  V..- , •  j  ;  ©•  G •I-.-  I  i  "  ". r r  I  |  i  -'  •.vj,:i'-;  0  i  "! •  1 •"  •/ 1  s  .  i ••  !  j.• i  •  I"!-"'  ;  y  .; f,  -•.v:'i:  • !  •Sri  . -•- >.  •r- . -  ..'J'S L ..L  v.;  '•rot  r-'-Ti"  ''•r. ~  r r'rr -:,:<; <-M )':•:  -/--7-r  /-  ^ w.  !• '• "' '!  its  '"/* >lir>i  Li.  IT .". , -• -t  I f  I  i  U>  f-TT-r  -; ;• t--  "!  i  !  1 1  I i  !  i  ... -i-'r' ' '•:  •0--T-  > 'i t  '.j±d.  !  i  rr'r-  i . : 1  '  J  !  u T " _  ..V  \. . I i  '  1.%  -H '•  :g B ~ . 'XZ  "L'.'r  1  1  &AL <3£AflQd 1. j — j 1—r y -  i  i  J  ->  :  ¥  i  VV:--'  "H -(  ,  t-'+i  ' i •  •ttff  kit' • !•!  •  i : 1 ''-!" I )  -  -r'Tfi-i-<-;-r ifi£ :'d±i  .!  i  !  • i • •  _*...' >  1  l  ;  i '  Hfi:  ... - _t-  j  \ c/w * '  .i  •..!:•,.  '•.,'r.  f£l -£P :  !  !.  •"•'•'TT  J _.• v . :  : !1 • !  i  READING * !  i •  .-  .'! " 1 1 • T - -1 i  -  V!-'"  ' i•  ' ' '  '  - i . i •  a j'Calibration ' j i | before ! i i-trials. . i i. .A \Collbrqtion after trials,' |  i  '  -  ;  : 1 : .... , '  •* Ii -  j  i  ;'"  !  • !  •  \  |-".f  •!  •  i  r—j  t  •  i•  •  i •! i i  ""1  ,  . ! •  • •._; -; j • _ |  r  '  J  1  i  -  :  .:.Z  J  . i  !  ]  i  !  i j  1  j' - ! > !  I  j  i ".zl'. • i-  • i  V  y^\,  j  -in »-*-  ••  -'ri.  --. t  —  ••f  ..!  .:: •  .  !  ;.. i  . • •. -  :  l-rf—• t • • •4.'.-"  •  ••'Li i  r  i.  :  "  .  .-!-• •  f  •S  ' ' I- •  i.- '.  :  F  '  :  :  -f-.4'."  •,•<oi-.-• -.<a -•  • f  ?r-  -'•  ', ••! -• I--.- i • IS  - ' •  •Hr*  ! "  ••. -"i-  -  i  I  I  t  -  I - I _!:::,!  Hi-\m  • •('  •  |  ;• M  !  '•I  3 t  I  •  J  \  j  |  J.  i  i .  j  9  i  !  36  Obviously, the conditions of the actual model test did not approach the calculated conditions.  The speed of  water flow i n the tank (0.93 feet per second) prevents the achievement of i d e a l conditions.  A second test (Test No. 2)  was made with a propeller speed of 395 RPM, the lowest speed at which the oscillograph wave had any appreciable amplitude. The ships often "travel l i g h t " for considerable distances with the propeller "breaking water".  Severe bend-  ing moments are set up In the shafts by the uneven d i s t r i b u t i o n of thrust between the propeller blades.  Some marine engineers  think that the resulting stresses may be of sufficient magnitude to start a fatigue f a i l u r e .  Two tests were made at  "no-load" draft so that the bending moments at " f u l l - l o a d " and "no-load" might be compared.  The propeller speed for the  f i r s t test (Test No. 3) was 810 RPM and for the second test (Test No. 4) was 530 RPM.  The conditions calculated for the  " f u l l - l o a d " test are based on the assumption that the propeller i s f u l l y submerged.  The conditions justifying a comparison  of the results of Tests No. 1 and No. 4 were assumed to be the same propeller speed and the same water v e l o c i t y . One object of the project was to investigate i n t e r action between propeller and ship.  More failures have  occurred i n tailshafts of ships having the "contraguide" type of rudder than on ships having the "plate" type rudder.  The  o r i g i n a l plan for this part of the test was to use the stern tube to measure the difference i n bending moment, i f any, with the two types of rudders.  In subsequent tests, however, no  37  difference i n bending moment could be detected when the rudder was straight astern, when i t was turned t h i r t y degrees to either side, or when i t was removed. plate type rudder was not b u i l t .  As a r e s u l t , the  Because of the apparent  insensitiveness of the stern tube, a test was made by exaggerating the effect of an obstruction near the propeller i n the path of the water flow by locating an obstruction as close to the propeller as possible i n the horizontal plane (fig.  31). The obstruction, a ij- inch square piece of wood,  projected from one side of the tank.  The f i r s t test (Test  No. 5) was made with the obstruction  inch astern of the  propeller.  The second test (Test No. 6) was made with the  obstruction  inch ahead of the propeller.  The propeller  speed v/as 580 RPM and the water speed 0.93 feet per second for both tests. The l a s t test (Test No. 7) was made to determine the relationship between propeller speed, torque, and thrust (water speed constant at 0.93 feet per second). Observations In each test the following readings were taken: 1. An oscillograph record for each of the pairs of gages, A-E, B-P, G.-G, and D-H. connected to the amplifier.  Gages A,B,GI, and B were  The voltage applied across the 13  s t r a i n gages v/as kept constant at 22.5 v o l t s .  The amplifier  settings were c a l i b r a t i o n voltage, 4 v o l t s ; gain, 12.5 millimetres;, attenuator 0.001; and paper speed, 125 m i l l i -  38  P i g . 3 1 Obstruction for test no. 6 .  39a  jI  - i I •• ' i j  I  !  I  I  C.HART  !  i  tt I  NO. 3 L  908  rtyi  t  / / / / Hi  JUJ-J  r! i  i  THE  • i i  M  i  ITHJITTZ  ti  l  \_\ \ \\ \\\ \\ \\\ BRUSH DEVELOPMENT C O  PRINTED  E  O-tL  IN -.S.A.  BRUSH  Pig. 3 2 . Sample Oscillograms  DEVELOPh  40  metres per second.  In taking each oscillogram, the timing  marker was s .itched on for the f i r s t 6 inches of paper t r a v e l off for the next 18 inches, and on for the .last 4 inches. 2.  An SR-4 Strain Indicator reading on each p a i r  of gages to' determine the steady force.  One gage of a p a i r  was connected to the active terminals and the other gage to the compensating terminals of the s t r a i n indicator. 3. thrust.  An SR-4 s t r a i n Indicator reading to determine  The gages and Indicator were connected as shown i n  figure 21. 4.  A spring balance reading of thrust.  5. The shaft speed i n RPM. 6. A torquemeter reading. 7.  The water v e l o c i t y .  were taken with a current meter  Five readings of v e l o c i t y at a depth of 6 inches.  One reading was taken at the bow, two amidships and two 6 inches from the h u l l and 6 Inches ahead of the propeller.  The  water v e l o c i t y waa taken as the average of these readings. 8. of the tank.  The draft, as measured by a scale on the side  41  Results Calculation of Results The results of the tests are given i n table 4. Oscillograms for each test were analysed for horizontal and v e r t i c a l forces and couples acting at the propeller.  The  forces and couples were then combined to give the v a r i a t i o n of bending moment at the forward end of the t a i l s h a f t keyway. In each calculation of forces and couples acting at the propeller, one revolution (from peak to peak of the timing mark) from each of the four wave® (one for each p a i r of gages) was required.  The timing marks were continued into the un-  disturbed section of wave with d i v i d e r s .  An average wave was  selected from each record, and the amplitude was measured every 30 degrees. measured.  Peaks occurring at other angles were also  The four samples were assumed to have been recorded  together, and to represent the same revolution. wave samples for each test were analysed.  Two sets of  The bending moments  corresponding to the amplitudes of the waves were obtained from the c a l i b r a t i o n curve ( f i g . 26). The bending moments were converted to forces and couples acting i n an arbitrary plane through the propeller hub, and normal to the shaft axis (appendix C).  The equations  for finding forces and couples from bending moments at the gages are:  42  M - M_ = — c  Px  (6)  4  Py  - Mo  M  A  = —  (7)  4  7M - 3M Mx = — B  .  A  (8)  4 7M  My = where  - 3M  D  C  •  (9)  Px = horizontal force (pounds) Py  = v e r t i c a l force (pounds)  Mx = moment i n v e r t i c a l plane (inch-pounds) My = moment i n horizontal plane (inch-pounds) M  A  = bending moment at gage A (Inch-pounds)  M  R  = bending moment at gage B (inch-pounds)  M  c  = bending moment at gage C (inch-pounds)  M  D  = bending moment at gage D (inch-pounds)  A l l forces and moments are recorded graphically i n figures 32 to 37. Forces and couples were resolved into a force P and a couple M i n the a x i a l plane of the keyway by substituting i n the equations  M  P = Py cos (30+a) - Px s i n (30+a)  (10)  M = Mx cos (30+a) - My s i n (30+a)  (11)  K  » =  -(P d #  +  M)  (12)  43  where  M ' = bending moment at the forward end of the t a i l s h a f t keyway. a = angle (degrees) at which the amplitude Is measured on the oscillogram. K  d  = distance from arbitrary plane to forward end of keyway. = 1 inch.  When M ' i s p o s i t i v e , the keyway Is i n tension, (appendix C) K  The bending moment M  f K  Is caused by the varying or  c y c l i c forces acting on the propeller as a result of i r r e g u l a r i t i e s i n the water flow, and interaction between h u l l and propeller.  Tests for steady forces acting on the prop-  e l l e r have been described (page 2 2 ) . The s t r a i n indicator readings were converted to bending moments by the c a l i b r a t i o n constants (page29)«  The results were substituted into  equations (6) to ( 9 ) . The weight of the propeller, which also produces a reversing bending moment at the keyway, was added to Py calculated above. Weight of f u l l size propeller - 23,000 pounds  15  23000  5- = 2.16 pounds  Weight of model propeller  122K  Actual weight of model propeller - 2.25 pounds The propeller weight 2.16 pounds was added to Py.  The  forces and moments, thus calculated, were substituted into • equations (10), (11), and (12) to give M " .  The graphs of  K  M ' and M " were added to give M , the net bending moment k  K  K  acting at the forward end of the keyway.  M  f K  was calculated  for a l l tests, but M " and M were calculated for tests No. 1 K  and 4 only.  K  44 ~T7\BLE Test  —  1  No.  :  42.0  Torquet  /n.-/b. 21 Tube compression uin./in. 35.0 Thrust (rube) lb Thrust (^pr/no b<a/) lb. 28.5 Maximum cyclic -forces (f couples ( Oscil/oyraph recora/s fiiy. 33 +0 33) J 1 Sample rv"ave~ -n.c Px lb. Pu  lb. in, lb.  /Vfy Steo/oly  in. -lb.  -forces  Couples  (sir-am  1 n <rJ 1 c cyfor  J  395  530 1.23  0.93  1. 09  1.09  0.93  0.93  6.3  II. 0  1  1  2  24  17  ^3.3  4O.0  28.4  4.5  2  -1-9.0+C3  z  I  2  2  /  +2.6 +3.4.+•2.4 +0.8 +2.5 + S.O  -0  -&Z  +0.3  -t-4.6, +6./  -3.3 •2.3 -1.4 -1.4 -2.0 -2.3 +2.1 -2-3 +-2.0 -+•/.£> +2.9 +2.0,  -7.5  -3.3 + 1.0, -2.0 -2.1 -3.3 -3.3  -1.0 -o.e +4.0  lb.0  24.0 7 11.7 7.5  +1.4-T/.O -/.<&  4.5  9.0  -+&.i  S.5 -8.5  +24.0 *34.5 •+IZ.h + 11.0+6.5 -6.0  +/Z.8 +14.4 +15.1 -8.8 -5.4  -&.0 -2.3 +0 ->S .O + 7-Z  -I9.0  >24.5 +20.5 -15.3  +14.1 +10.3 +10.3 +14.0 +/5.i>  -4.5  -33.0 -14.0  -10.8 -7-0  -6.7  -4.5  - 3 . 6  - 5 - 6  -12.0  -5-3  -0  -17.5  -4.4  -17.5  <:  + 0.15  + 0.03  - 0. 55  -O.IQ  + 0.5  4.48  + 1.4.1  -t  My  + 0. 43  -1.95  -  rVf. (add-to  f§)  Maximum bend my nyonjenl at key^/cy C+M - KnS<j. in -rensiffn.) MK' in.-lb.  2.  m-lb-  2.l<o  5.15 1.62  2.1 <o  + Q-ZQ -0.25  054  -0.0,4  -0.47  -+4.5  -+2.3 8  -+ 5.18  + 3.0'5  - 1. 6  TO. 9 8  2.l<6  2.1  •+8.0 + 11.0+8-5  + 1.1  -fll.O  -3.5 - 4 . 5  -S.5  -17-5-21. 5 -12.3  -rlo.O  +  t o . 03  ->/./ -Kc.O  in-lb  / 6  A  -+ 1.105  +  MK  530  1.32  M*  MK"  540  0.82  3 /S.O  2  8IO  6  0.8G  -4.4  P,  Prop.  5  1.36  19.5  + 1.7 +•/. to -I.I -tS-O  4  3  Propeller speed (PPM 530 Dm-ft ft. 1.41 Water- velocity ft./jec 0.93 20.0 Torquemeter t~dq. cm. /  4  d  2  2./&  +3.o- +•(,.5 + 7.1 +IZ.4  -11.3 -8.7 -11.7 -9.Q  -14.6  + 7.4 -7.4.  -<°.0 -(o.O  -7.4 -7.4  1-8.O + 6.8  +17.5 + 1Z.0  -8.0 -9.2  -19.4 -17-0 ff. ",4,19-  45  Discussion of Results Test No. 1. Table 3 shows that the calculated conditions for similitude were not met i n the test.  The  water v e l o c i t y was too small, and the s l i p too great.  The  forces and moments cannot therefore be correlated to the prototype.  In finding the bending moment from the c a l i b r a t i o n  curve ( f i g . 26), an inaccurate region of the curve was used, for oscillograph amplitudes of one millimetre or l e s s .  Forces  and couples calculated cannot then be considered p a r t i c u l a r l y accurate.  The curves are Irregular i n shape and not consis-  tent for the two samples.  Because the oscillograph wave i s  not consistent throughout i t s length, and because the wave samples were selected at random, any number of wave shapes could be expected for M ^ . 1  The accuracy of the steady, or  "deadweight", forces and couples acting on the propeller shaft i s questionable because of the small magnitude of the strains (3 to 15 microinches), and because of the unsuita b i l i t y of the type C s t r a i n gage for s t a t i c measurements. For the same reasons, the accuracy of the thrust measured by s t r a i n gages i s also questionable. Test Ho. 2.  The amplitudes of oscillograph waves  ( f i g . 33) are too small to give accurate bending moments. The results of the test are consequently of l i t t l e s i g n i f icance. Test No. 3« The bending moments calculated for t h i s test are probably quite accurate because of the r e l -  46  atively large amplitudes of the oscillograph waves.  The  c a l i b r a t i o n curves should be most accurate for amplitudes greater than one millimetre.  The wave forms of a l l forces  and moments are extremely i r r e g u l a r , and the peaks show no relationship to the position of the propeller blades. No regular wave pattern could be expected because of the turbulence of the water around the propeller when i t "breaks water". Test No. 4.  The discussion of the results of Test  No. 3 apply to Test No. 4.  A comparison of the results  indicates that by increasing the propeller speed 1§ times (540 to 810 RPM), the bending moment M ' at the keyway i s i n K  creased by 1 1/3.  The c y c l i c bending moment M " caused by the K  steady or "deadweight" force acting <3>n the shaft was added to M  K  !  t o  give the net bending moment Mj< at the keyway. Com-  parison of the results of Test No. 1 and Test No. 4 indicates that the bending moments caused by water flow effects with the propeller "breaking water" are about 2^ times as great as when the propeller i s f u l l y submerged. Tests No. ,5 and 6.  The tests were carried out to  determine the effect of an obstruction i n the flow of water past the propeller. as for Test No. 1.  The conditions of the tests are the same The effect of placing the obstruction  after the propeller on one side only was to increase the bending moments M ' by 1,7; and of placing i t ahead of the proK  p e l l e r was to increase the bending moment by 2,5,  The obstruc-  t i o n i n the flow of water to the propeller produces a greater bending moment i n the shaft than- the obstruction after the  47  propeller.  In preliminary tests no effect on bending moments  was noticed when the rudder was turned to right or l e f t of center, or was removed altogether.  This fact, together with :•  the fact that a r e l a t i v e l y large obstruction caused a r e l a t i v e l y small increase i n bending moment, would indicate that the rudder has l i t t l e or no effect on the bending forces and moments acting on the propeller shaft. In general, the method of applying SR-4 s t r a i n gages to the measurement of bending forces and moments acting on the propeller Is satisfactory.  The advantages of the method are  that the forces and couples may be resolved Into horizontal and v e r t i c a l components; the components thus resolved, are free of the effect of the weight of the propeller, and therefore represent only the effects of water flow about the propeller.; and there are no harmful effects of s l i p r i n g r e s i s t ances on the accuracy of the records. The main disadvantage's that, with the single channel oscillograph, the strains from only one p a i r of gages at a time can be recorded.  The assumption that a l l sample  waves selected were recorded simultaneously i s not j u s t i f i a b l e In view of the fact that the waves for successive revolutions are not i d e n t i c a l .  Furthermore, orienting the wave samples  by a timing mark which i s part of the s t r a i n wave i s unsatisfactory i n that accumulative errors may be introduced i n using dividers to produce the timing marks into the undisturbed portion of the wave.  The solution to both problems appears  to be i n the use of a multi-channel oscillograph, with a  48  channel for each p_air of gages and one for the timing mark. The stern tube i s not sensitive enough for the forces acting In Tests No. 1 and 4; however, we think that, i f the correct water v e l o c i t y (table 3) were available, the forces acting would be greater and the tube might be sensitive enough as i t i s .  4 9  360  ffd' F/QUQE  33  lb-3-49  50 ,  . . . .  •  n 3r  C •  — - >  >**  ±|ij  rff"ff  . . . .  . .- . - \ r-i  :  —  •  11  0  —: :  to  i  V  V  j  : :: : :  j  1. •  • rr*[ - — "*  • •  -]--  —  —--i  '—  :  .  ST  2X1  J *  /  w  f  • •  •  -r: J—i  :-  Hi  -  iii  :  \  ; ..  ...  —  •i —Ii  :  • : : . ] . : : .  : :. ::::  -4-  •••• \ :  •  :::!;:  .I-  •  : :  .:..]:'  1-o  -.  — T T T —  . .  —  rr  1  -t-: •: 11"' i—.  -  m  •-. r—•  • ' • : • • • •  ' f  •*  r  —  —  -  .....  :—rfr " 1  .  tS :':|.::.  .  —_  /»  fr  .  .. •':  •  1  • ri  ::-•;);;  to  I  g  O  ees  AfV<3Z.£ -  *l  *  :  . f t  e  .1  i• :'  • . . . .  h  '.  Tl K . 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J7± x t + -~f ... -i - L i . . "- + ! + . . . 4. 4 -  . 1.1 :  TH-:;:.: j  h  t]ll  I'iLi tj::-; 1  i-;: j  ri-  H-fr- J  :  • • •: 1 . : : ;  c  : . . .  if: •::..:  '• i • • •  ;;: : i ' : •••'!'•••'  ::\:  Hr III:Til] ::::\  - -  ::.;: j : : •:  ii  •H  ...{.;. Li|:L._ ~::""{H:~:"~ r:  : : : r  ;•;:]..:.:  :\\ f  ... i . . .  t  •  :T  HTH-  :  • : -. | . : • .  :  ; j ' i • l i  -"• •~:\\  :;•.  H.H-Ll:i  \Tj;  •rrh-  :::'  ill-  !:• i .; . j . .  |L tfff • ::i  1  :  ill  ' IH  : i L Hi!.  ;:!:  ' j . 1  :. i • : : - •. •  ;.: j I : : :  :  •i» ' -Mi  ' i:.:  fffH -HHt:  -r-r  ...; .  .i.i  ::]:•: •: i  i  ' ' : '•  I : . . '.1 '. W  -1-  . . ' i.:.;  HH'  ill':  .. ( .. :: i:".  . .  :  :  j  ]  !  !" L !  r  •HIIJI-  \--\-'  Conclusions and Recommendations The Results Conclusions regarding results are summarized as follows: 1.  The bending moments at the keyway are not  applicable to the prototype; 2. c y c l i c bending forces and moments do e x i s t , although their magnitudes do not appear to be large; 3.  the rudder has l i t t l e or no effect on the bend-  ing stresses i n the propeller shaft; 4.  a member or obstruction ahead of the propeller  does have an effect on the bending moment.  The fact that  the propeller shaft receives an impulse as the blade passes the lower stern frame and the gudgeon i s borne out by the appearance of the oscillogram ( f i g . 38); 5.  the magnitude of the bending stresses set up  i n the t a i l s h a f t when a ship i s "running l i g h t " i s greater, by about 2§- times, than when the ship i s f u l l y loaded. The Equipment Conclusions regarding equipment and measuring devices are summarized, as follows: 1,  the methods and techniques developed during the  investigation for measuring bending moments are satisfactory and sound;  57  2.  the stern tube, although i t functions w e l l , i s  not sensitive enough; 3.  the testing tank i s not suitable, for testing  model ships; 4.  the method of measuring torque i s r e l i a b l e ;  5.  the method of measuring thrust with spring  balances could be improved upon. Recommendations For further investigations into the determination of stresses and vibrations i n the propeller shaft due to water flow, the following recommendations are made: 1.  that a h u l l model of greater length be towed  i n a model-testing basin at the required v e l o c i t y , and with the required s l i p ; 2.  that, f a i l i n g t h i s , the model be mounted i n a  flume where the water can be flowed past the model at about the required v e l o c i t y ; 3.  that the stern tube be redesigned for greater  s e n s i t i v i t y i n bending and i n compression i f i t i s to be used for measuring strains at water speeds as low as one foot per second. 4.  that oscilloscopes or a multi-channel o s c i l l o -  graph be used to record the v a r i a t i o n of strains i n a l l strain gages simultaneously, and to record the timing mark separately.  58  APPENDIX A PROPELLER  "  5PEED  =  - - , J * A ?  CALCULATION  Equation  ^  E  fi.W.R.  = .7936  (l)  )  } Kef. /£> Bl. Th-Pr. _ -Q4Z9 PI. W.K.  _  ' -793C  Re = 73 «70 * .  Ta67e /. f>- &  if' = 7-211« 70'*@ CO°E  r*67e z.  d-- dj * 78. S = .844 feet TahleS. n  s  Q*»*VX'3*'°V_ (••844) .793Q  _  / . / I / - (//>?) 60  WATER  -  5PEED  MZ  /  /  ~ ^  z  y  /  P  P  S  " -  A/  J  C90 Rrrfi. CALCULATION  < dxTVid,N,  Equaf/on  V  pg a  e  (2)  S.  I/, = 72.7 faffs =274 feet/sec. d = 78-S feef 77,  =-  -fable S'  RFA7.  Table S'  dz = 70.///?c7?es =.844- feef A i - C30 -•- * -  -  8.9,  R Pff. feet/stc.  e uat7o»(7) 9  S3  Q  _  3~30OOff.Hr?)  27T/V, H P = ' '  2TfA/g.Qi33000  Ffuaf'a* ^f e  C4) 9  1.H.P = indicated H/P = 2SOO  Table S  - 64 founds f^er cu. fir, j?  z  C2-4 pound's /Oer  M * 7X 6  /?./?/?.  Nt  H,P.A7  &90  2  n  Q  '  =  0.i ,\  frf?  3 3ooo  i-28  fzs-oe)  (7*4)  :  Tzhle S  - /O./ /ncAes =  Table S ' equation (I)  :  d, = /S'S~ feet d  cufi/,  .844  /74,000 r  feet  ,  , •  foot  f o u  /2f2.7C^ - 33 inch ^our/da , (Q>Z8) &90(2>7£) 33000  _  up =  •  n  (  /  S  GO  PROPELLER  THRUST  CALCULATION oaf/on  77  =  =  -R(i-ty b -  'B/iL  3SD  D 3  MO-jsa)  =  '*  0 0  (s)  P  ounds  /e  '  D - d/sp/acer,:er/f - 73700 Lang tons 7a hie $ B i-beam ~ E~C-3 feet H* draftr.  26.9  Tah/ef  feet  Tab/e E  •L - fen gib - 4-1C feet  feb/e^  f, 6/ocA coefficient  = 3^0 / \ 3  oo  ^  =  SC9fZ&.S)4l£  then t=f/irusf  deduct/on coefficient  when- C = constant •  and  s  cW = .60(3/4) =.08  =•  cfeperfd/n^ or, sd/yo ~ .3/4  Wr wake- tract-on  A= ship P = shaft  /  speed  in /wots  T*6te S  - 12.7  horsepower ^ .90(ffip) ^ .3o(2$~0o) where -triech. eff, = .90  =- 2 2 EC € = propufs/ve  efficiency - .7f  Cj =- C4 pounds per c.u. ft. t  Cj = z  £2.4-pjoxnds per  N, = 7S~.t> A7  Z  R.P71.  Table *T  - 690 R.R71-  d, = 7S-S feet  T -- S'ZiooCc2.4)(C9P) .&44 * Z  Efuaton  .  d* = .84-4 feet •  cu- ff,  0)  Table f ..  1  J  60  Table 5 T r i a l Results MP  Speed  App arent Slip (%)  65  1662  10.83  -5.6  71  2090  11.76  -4.7  75.8  2497  12.70  -6.5  RPM  70.3  2025  12.5  -12.6  66.4  1865  12.18  -16.1  70.3  2112  12.63  -13.1  79.0  2742  13.51  -8.3  Details S.S. Arlington Beach Park Feb. 19, 1944. mean draft 26' 10|" 13,700 tons displacement S.S. Quetico Park Mar. 30, 1944. ' mean draft 18' 0 | " 8725 tons displacement S.S. Willowdale Park Mar. 10, 1944. mean draft 16» 0 | " 7600 tons displacement  a  61  Appendix B 21  The Baldwin SR-A Strain Gage "SR-4 gage" i s the trade name of the resistanceatrain-sensitive wire gage manufactured by the Baldwin Locomotive Works, Philadelphia, P a . .  The gage i s made of  0.001 inch diameter wire arranged as shown i n figure 40.  P i g . 40.  Wire-strain gage.  The wire i s bonded to a thin paper c a r r i e r by a cellulose cement for temporary or low-temperature i n s t a l l a t i o n s ; and by a phenol r e s i n cement for permanent or high-temperature i n s t a l l a t i o n s (up to 300 P . ) .  Strain i n the surface layer of  the material to which the gage i s bonded i s transferred to the wire v i a the cement.  The bond between wire and cement i s  of sufficient strength that the wire deforms i n both tension and compression as directed by the cement. When the wire i s strained i n tension i t s length Increases and i t s diameter decreases.  Its e l e c t r i c r e s i s t -  ance increases by virtue of the change i n length and diameter. The relationship between "change i n resistance" and "change i n strain" i s a r a t i o called the s t r a i n - s e n s i t i v i t y factor  62  or gage factor.  Symbolieally, A  where  R /  A  L  R i s the resistance change i n the t o t a l gage resistance  R (ohms) and  L i s the change i n length i n the t o t a l conductor  length L (inches).  If e i s the unit s t r a i n (inches per inch  of length), then 1  L  f  P  A H  R  The basic standard gage resistance of 12G ohms i s obtained with a five inch length of wire.  Many types of gages  are made i n various shapes and gage lengths, and with various resistances. i»  Two main c l a s s i f i c a t i o n s of gages are: Type A. Constantan wire (Cu-Ni), cellulose  bonded, gage factor about 2.0, negligible temperature coefficient of resistance. 2. Type C.  Iso-elastic wire (Ni-Cr-Mo), cellulose  bonded, gage factor about 3.5, high temperature coefficient of resistance. Type A gages, because of their negligible temperature coefficient of resistance, are used for dynamic and s t a t i c testing.  Type C gages, though more sensitive (high gage factor)  are suitable only for dynamic testing where the high temperature coefficient of resistance i s not disturbing.  Because  of the higher s e n s i t i v i t y , type C - l s t r a i n gages were used for the project.  The particulars on the type C - l gage are:  63  effective gage length.  - 1 l / l 6 inches,  trim width  - 9/32 inches,  resistance  - 500 ohms,  gage factor  - 3*34  The Baldwin SR-4 Strain Indicator  t  1  percent.  2 2  The SR-4 s t r a i n indicator i s p r i m a r i l y a four-arm Wheatstone bridge.  The SR-4 s t r a i n gage i s always used i n  such a way as to unbalance the bridge c i r c u i t when i t s r e s i s t ance i s changed by stress.  Balance or zero potential across  the two resistances, C and A ( f i g . 41), i n p a r a l l e l , i s regained by changing resistance D u n t i l the galvanometer G shows zero current, thus establishing the fundamental r e l a t i o n between the resistances A*D = B*C To obtain the effect of a variable resistance G and D, a slide wire P can be introduced as shown i n figure 42. It Is necessary to amplify the weak but precise signal produced by the unbalance of the s t r a i n gage bridge to obtain from I t enough power to put I t to p r a c t i c a l use for driving indicating meters, oscillograph galvanometers,  cathode  ray oscilloscopes, and pen and Ink recording oscillographs. Alternating current amplification i s preferred over direct current means because i t i s simple and accurate, and because I t automatically eliminates the contact potential or thermal e.m.f.'s i n the gage because of constantly changing p o l a r i t y .  6 4  Fo  41  Wheat stone  A  bridge.  -  a c  J  D -  F  Flo  Fie 4 2 . Br  idae  with  slide  43 b. Strain  indicator  panel  wire-  PHAS£ 4  DlSceiHtirtATOf?  etcr/nt'i?  uniT,\  K t>HAT.±r_AgAT.  1/000 CP5 \osciLLkTOe  FlCs  A-3c*  indicator  Strain  wiriny  diagram.  Legend A-B  Actn/C  yaye  C - D  Lorn pens  tlinoiiny  at my  posts  yaye  bmcdmy  posts F  -  6  - Reference  Balancing mx.roinch  ti - Oaae J  ~ Battery  M " Balance knob switch  (P ' Panje ~ IOOO  ^>teps  factor  jetf/no  177 h>2ZO  jsm/tch i nolo-  ator  extender  20 OOO m,<.ro  inches  - by . /ICS  ic-4-49  65  Figure 43a i s the wiring diagram for the SR-4 s t r a i n Indicator and the panel face of the instrument.  The l e t t e r s  on the diagram refer to the corresponding components on the meter ( f i g . 43b)•  The active and compensating gages are two  arms of the bridge and are the only components i n the c i r c u i t outside the instrument.  The t h i r d and fourth arms are fixed  resistances N and P and the point-by-point variable resistance for coarse balancing i s at G, supplementing F, the main s l i d e wire, for fine balance, Indicating strains on the scale above It.  The meter M serves as a n u l l balance i n d i c a t o r .  gage factor adjuster slidewire.  H is a  The amount of movement of F  for balance Is read on the scale i n microinches per inch, the s t r a i n i n the active gage. Direction of unbalance which determines whether the s t r a i n i s tension or compression Is determined by the phase discriminator whose function i s to reveal the phase difference between the amplified bridge unbalance voltage and the o s c i l l a t o r voltage.  The coupling between the bridge and  o s c i l l a t o r i s shown at K.  The meter thus shows both magnitude  and d i r e c t i o n (tension or compression) of unbalance. The nameplate data on the s t r a i n indicator used for the tests are, as follows: Baldwin SR-4 Strain Indicator Type K Serial D 95335 Baldwin Southwark D i v i s i o n , Baldwin Locomotive Works, Philadelphia, Pennsylvania. Made by Foxboro Company.  66  Brush Oscillograph  J  The Brush pen-and-ink oscillograph has three main components; a magnetic pen motor, a recording oscillograph, and "an amplifier.  The magnetic pen motor i s an Instrument  designed to make direct inked records of the e l e c t r i c a l potentials from D.C. to 120 cycles per second.  I t consists  of a D Arsonval moving c o i l galvanometer element suspended 1  i n the f i e l d of a powerful Alnico magnet.  The inking pen Is'  attached to the upper end of the moving c o i l system.  Ink Is  supplied to the pen from an inkwell through a f l e x i b l e p l a s t i c tube behind the pen.  This penmotor, Model BL-902, i s mounted  i n the Model BL-201 Direct Inking Oscillograph.  The o s c i l l o -  graph provides a chart drive mechanism for p u l l i n g the r a d i a l l y ruled paper at constant speed under the pen.  The three speeds  available are 5> 25, and 125 millimetres per second. The penmotor Is driven by an amplifier, Model BL905.  The amplifier has a self-contained power supply operat-  ing from 105-125 v o l t s , 50-60 cycles.  A calibration circuit  i s included i n the c i r c u i t so that the pen deflection of the oscillograph can be correlated to the input voltage of the amplifier.  The panel and controls of both amplifier and  oscillograph are shown i n figure 44.  The amplifier i s equip-  ped with an adjustable high frequency boost so that the o s c i l l o graph-amplifier combination has an essentially uniform response from 0.5 to 100 cycles per second.  The maximum  voltage gain of the amplifier i s about 2000 times.  6,  Stjna/ Input F i g . 44.  Brush O s c i l l o g r a p h  I n o p e r a t i o n t h e a t t e n u a t o r must be s e t on "100" p r i o r t o making any e x t e r n a l adjustment t o t h e i n p u t c i r c u i t , otherwise  the a m p l i f i e r may t e m p o r a r i l y p a r a l y s e .  Pressing  the b u t t o n marked " c a l i b r a t e " i m p r e s s e s a 60 c y c l e A.G. v o l t a g e on the Input o f the a m p l i f i e r . moves the i n p u t j a c k from the c i r c u i t , c a l i b r a t i o n I s a m p l i f i e d and r e c o r d e d . age can be s e t a t some c o n v e n i e n t  This operation r e so t h a t 60 c y c l e The c a l i b r a t i o n v o l t -  v a l u e I n d i c a t e d by the  c a l i b r a t i o n v o l t m e t e r , and the d i s p l a c e m e n t a d j u s t e d by the " g a i n " Input v o l t s  o f t h e pen  control.  (peak) = a t t e n u a t o r s e t t i n g x pen d i s p l a c e -  ment (mm. from c e n t e r ) x c a l i b r a t i o n ( v o l t s p e r mm.) In o p e r a t i o n , t h e pen s h o u l d n o t d e f l e c t more t h a n 20 mm. from t h e c e n t e r f o r f r e q u e n c i e s up to 70 c y c l e s p e r second;  68  and not more than 10 mm. at 120 cycles per second.  Signals  giving less than 2 mm. per deflection may he affected by pen friction.  This effect i s reduced by operating at higher  paper speed. The nameplate data on the oscillograph used for the tests are, as follows: Amplifier Oscillograph  - Type BL 902 Volts 115 - Type BL 201  S e r i a l 829 Frequency 60 S e r i a l 259  Volts 110  Frequency 60  The Brush Development Company, Cleveland, Ohio.  G3  APPENDIX CA LCUL  AT/077  OF  C  FORCES  AND  24  COUPLES  Assume J • plane.  On  the 05Ci//oc?ram  the  h/ave  are  a 60re  tbe  /si tens/on  ves  O-60Ue  ¥v7>e* co*„ectect  center-Axe  and centsr  -7/rt e  /) and a re  P«'X  A  77a. f  are  p>/i/S and  x  + fix = A1A. a  beta*/  B-f E  and' s$/On  t  E  .  tn/ntss.  1  MA-ft*  q  =MA-(MA-M*\XA  1  the sberri fube  flA-flrs fix.  gayes  //? cam/jre  Pufx^ -x ) ~A? -71 B  a>id  3  fixx-=  For  75  PcfX +- Rl = t1 B  subtract  /tiE/cat?*  i  gajes  fo<?a<fe>sA-E  =  771s-37in 4  Xs.~  3/ncbes  Xfix -  7/ncfies  70  c  A  Assume (J p/ane  On the osc///ojran? wAen c, ortnecfec7 fo c?a<fes the  CO-n <f  wave 6e/oW 77 e cenfre -77ne /nd/cafes that gajes Cane/  D cere /n ~7en5/on &n <f<ja^e*rG- an Waves a7>ove f>e7aw ane  Cen7er-7/ne  at re  /r? com p.  are? <^<a//ed p7u-?r and  byav  mtrtus .  S/m/far-fy fa ff?e /?r<ecec///}<2 Proof fitc-f1z> ' ' r  =  4 M  7f1* -3Afc  Note:c~e fen 5 ru/e  for  to r/j>ftf f an c7 /vomer?f$  71  f-OW  Anj/e f  of  fades  Anyway  a n cf propedfer  respecf  wv///  fo  far  S/tSr/'l  ward  dm/ricy  War/<er>  a. - anyfe  l e t  fese/v/nj  fro/r?  cos (so  fcti/ures way  ffiroo<jf aire  fhrouoAouf  //? ffe  of  cffrecf/0/7  fhe  >  an  a_f  - f?> s/n^P-f  forces  a) - ffy at fit.  arlifrary ar?cf ffe  a  a)  c  occur"  re sofcref  aef/n<y  Coup>fes  -t- &y  cc5(3o+  . f i f i x S/nce  /varfer  feyway  P f y  Hey  and  forces f/ie  f//n//?y  ff?e j  (So-ta)  s/rt  forw  / y , / / * > ffy  p/are  rero/ufo/7  fo of  er/d  of  of  e?n d fcK^^d  /r> ff?e  c o/? vc* A fg d  fortrvO' r d  arcf  atfr/cf  /oroyve//er~  J>  f>endir< cy rn f/te  ffe  f<?y  o/»enfk  vsoy  sStotff pro  fspS/o/7  tie  of  d^ce^ S feyway^j  7?  APPENDIX D 77min/f  of  24  RecorJs  / - amy>f/f/er ,tocut. ja/n osc///oyrapA , 3ens/f/v/fy  0-  *3 -Vww--  for  tcnr. SiA//r;y &fpen  2 - c on factor po/nf  0  /OOO fo t  K-fo  F  .  which cfoses of one  offte  shaft  strait?  -  <4rotts  refa.for?. $&je.  SOO JX  - cxy>f>f/etf in?ftape - 2 0  ft  3  =  £2l2,ooo  M-  as  ca/cufafef  fof/ows. K  ~ Corthh/necf  factor cfases pen W/ien coin  must  /  With Wifh  con factor  open  factor  COM  /  /id f cf effect  v efface  on  _L^-L  r  #,  / r o m  £  "  /  p?  /  &#2-  X,+t?*  d , c k  £f#, + R3)  / c ' on  a rh p// T/e r  J ^ ( R + 2 R ^ ^ f )  Change  /ri  vat  fa ye  f>y  Sf?3  c/os/nef  C  /fj  spa/e  &/>y?f/rf,er - ~~  =  Hte  off ftie  c/osect  7T*7t  Vol fag*  off?, artcf  res/stance  74  For  /c/n. Jump for  Vo/fs  *»«  A  £  m  of pen  / c/n. sen-s/fiv/'fy.  2(K +2ft) /?  5  -  af" /OOO X Seff/ny art  °  2o(s~oo)  <12-3-4  r  K  "  s  4AE  P'oO.,  ?~  - czs:ooo JTL  ~ T  75  Appendix B Static Calibration  2 4  Let  v  I = current. ww\ — I  1  Maximum recommended current is 30 milliamp. R l = SR - 4 s t r a i n gage type C - l = 500 ohms. P = Gage Factor = 3*34  A  Maximum voltage = 2(500)(30)/lQ00 = 30  V = applied voltage = 22.5 v o l t s . E = voltage on amplifier. A = amplifier. 0 = oscillograph. The tube i s bent so that (R-j_)^ i s lengthened; the resistance becomes R + A R.- Since ( R I ) E i s diametrically opposite, i t s resistance becomes R - A R . Before s t r a i n i n g , 1  =  E  =  V/2R  and  E  = IR  V/2  After s t r a i n i n g , E + A E = I (R+&R) A  E  =  I ' A R  76  Now  P=  * t  R  L  iL  .A , • e  where e = unit s t r a i n (micro-inches per inch).  R  =  = 3.34 Therefore AE  = V (3.34 e)/2 =  =  22.5 (3.34)e/2  37.6 e  With an amplification of 1000 and an oscillograph s e n s i t i v i t y of 4 volts to 13.5 mm. amplitude, 1mm. = 0.004/13.5 = 0.000296 v o l t s . Therefore, the unit s t r a i n represented by 1 mm. amplitude on the oscillograph record e = A S/37.6 =0.000296/37.6 = 0.00000788 inches per inch. = 7 . 8 8 micro-inches per inch. Sample calculation: In the second s t a t i c c a l i b r a t i o n of gage A, a weight of 1.96 l b . gave a reading of 33 micro-inches on the s t r a i n indicator (gage factor setting 2.20) e =  2.20(33)/3.34 = 21.7 micro-inches.  Bending moment at A ( f i g . 2 3 ) = 1.96 (7.75) =15.2  in.-lb.  Deflection of oscillograph pen f o r a bending moment of 15.2 inch-pounds a t  ga ge A  = 21.7/7.88 = 2.75 millimetres or, a deflection 2.75 mm. indicates a bending moment of 15.2 inch-pounds. This i s one point on the c a l i b r a t i o n curve for gage A ( f i g . 24).  77  Dynamic Calibration Sample calculation for t h i r d dynamic c a l i b r a t i o n : Voltage applied to gages = 22.5 Calibration voltage 0.296 volts per m i l l i m e t r e . Attenuator setting = 0.001 F = force N = propeller speed RPM. R = 4.28 i n . g = 32.2 f t . per sec. per sec.  P =  2TT  N  -6tr  2  R = WN (2rr/60) 2  (4.28/32.2(12))  2  = 0.0001215 WN . For a weight W = 0.04459 l b . and N = 600 RPM, the pen 2  deflection was A E = 3 mm. for gage pair A - E. F = 1.95 l b . Bending moment at A - E = 1.95(2.17+1.75+4.0) = 15.44 i n . - l b . By this method, a deflection of 3 mm. indicates a bending moment of 15.44 i n . - l b .  This i s a point on the c a l i b r a t i o n  curve. Calculated Calibration s = 5ji£ where s - stress M = bending moment I = moment of i n e r t i a of tube cross-section n =  < o d  4  -  64 = 0.0114  d  i ) 4  =  n  (U.141) -(1.101) ) 64 4  4  78  c = d /2 = 0.570 In. Q  E = 30,000,000 l b . per sq. i n . for steel. Let  M =15.44 i n . - l b . s = 15.44(0.570)/0.0114 = 772 l b . per sq. i n .  Now e = unit s t r a i n = s/E = 772/30,000,000 .= 25.7 micro-inches per inch, and 1 mm. deflection = 7.88 micro-Inches per inch (p.76). Therefore  A E = 25.7/7.88 = 3.26 mm.  By this method, a deflection of 3.26 mm. indicates a bending moment of 15.44 i n . - l b . c a l i b r a t i o n curve.  This i s a point on the  The discrepancy between the s t a t i c  c a l i b r a t i o n and the calculated c a l i b r a t i o n for gage A Is due to the fact that the inside diameter of the tube was measured at the end of the tube and not at gage A. The inside diameter of the tube Is not pa r a l l e l . Influence of Natural Frequency of Tube on Dynamic Calibration Curve To find the natural frequency of the cantilever tube and propeller, the propeller was "plucked" and the free vibration recorded by the oscillograph.  The resulting  wave i s shown i n figure 45. From the wave the natural frequency i s f  n  =  73.7 cycles per second.  w = 2TT f n  n  = 2n (73.7)  = 463 radians per second.  79  Assuming forced vibration without damping, we maywrite the equation  28  sin  x = c  st  i  -  u)  t  (u)/u) )2 n  where x r a t i o of the ordinate of the wave st to the s t a t i c deflection. The ratio of amplitudes i s greatest when s i n ^ t = 1. .x . . 1 *st Sample calculation f o r gage pair A - E, second =  x  1  dynamic c a l i b r a t i o n : N = 708 RPM  e = 0.0001192 i n .  = 2 TI 708 = 74.1 cycles per second 60 = 74.1 = 0 . 1 6 WT  -  1 = 1- (0.16T 2  1.027  Prom the s t a t i c c a l i b r a t i o n curve ( f i g . 24) at M = 61 inch pounds, e = 94 micro-inches The effect of the approach of the propeller speed (708 RPM) to the natural frequency would increase the force acting, and hence the s t r a i n , by micro-inches.  1.027,  or to 96.5  The s t r a i n of 116 micro-inches for the  same moment on the second dynamic c a l i b r a t i o n curve Is not accounted for by the forced v i b r a t i o n effect. Damping, as shown by the decreasing amplitude of the free v i b r a t i o n ( f i g . 4 5 ) , has l i t t l e effect on the force m u l t i p l i e r  (1.027),  calculated "above.  The  80  logarithmic decrement, & , i s calculated from the amplitudes and Xn+i of two successive waves by the equation 2 TT  8  C  where C i s the ratio of the coefficient of damping to the c r i t i c a l coefficient of damping.  Xr,  ;  From figure 45 x  .7 CHAHT NO BUi  = 8.2 mm.  n  XjQ—- 7 « 7  I  mm.  0 = 8.2 - 7 . 7 C" 8.2 (2)tr  m 1. ,  -  0.0097  \ •• i  c  VieexTton OF PHOPOLIB, 5H*#T  f Tfagit  nLLL  F i g . 45  For this r a t i o -  £ 1  -  •  where cj i s the damped natural  therefore  frequency. From the previous example, = 0.16 x  _C_ _ ^ _ \  2  y 0.9 53 I  = 1.024 The damping, therefore, acts to reduce the effect of the approach of the propeller speed to the natural frequency of the system. For the t h i r d dynamic c a l i b r a t i o n , the model was moved from a r e l a t i v e l y "springy" support to a r i g i d support.  The result was a noticeable reduction i n the  forced vibration effect on the bending moment at the higher speeds.  31  APPENDIX TORQUERjETER  SPRING  CALC  UL  AT/OR  DIMENS/O/VS  SPRING  /it " outside  diawzfc'  8 separated  turns  . /34 O  -  £  33OOP  _  /&8/V2)  W  ~  23  diameter  wire  (rip) 12  27TR  Ed*2fTR  nl  povsepovyer* - acT/ve  /V  Turns  D-mean  .73 {motor  ofco//-/.3C6  E - Youngs tnodu/us d ~ d/am efey~ of ti „ n  -  -  '  3  3  0  0  at  T~he above Otf  r~  fwtsf  £ V O /6<  tf/Op// cat/  T/o  of  Or? .  - '  ^Z8f700)  /R  5half  fotr^ns  8  ^  Z  ~«r>ll_  3C y,.82Z = .39T  t*rr,5  •7S  f  IA/OU/C/  wfl/C  c  .  .3C ffP ^pri^.cj  30*/O \A//rc? - ./J34 —  of shaft = 700  ° frs-)nf/o-8)8Q.3CC)  30* /0*f./3*)1  fur,is  -  /  — S  diamefer  ft-RPrl  outfit•71  R  IrV  a  fAe  fo^j  cs-<?/*t <? fer-  d<? S /r~£& f>/&  Ror—  82  NOTES 1 " ' L i b e r t y ' Ship Propellers and Rudders", The Syren and Shipping, p. 337, Feb. 18, 1948. 2 Richmond, W. 0 . , Progress Report on Research Project  Cyclic Stresses i n Ship Propeller  Shafting,  Feb. 12, 1949. 3 Rossell, H. E. and Chapman, L . B . , Principles of Naval Architecture, v o l . 2, The Society of Naval Architects and Marine Engineers, New York, 1947, PP» 138-140 4 I b i d . , p. 192 (141). 5 I b i d . , p. 89, tank cross section should be not less than 100 times the submerged cross section of the model. 6 Lines Plan, Standard Cargo Steamer Victory Type, B.D.D. No.  7 0 9 3 A  North Van. Ship Repairs L t d . ,  North Vancouver, B. C. 7 Baldor, Type W1B, 60 cycle, single phase, va riable speed motor, f- horsepower, 110/220 v o l t s , S e r i a l No. J30551, Baldor E l e c t r i c Co., St. Louis, U. S. A. 8 Method suggested by W. 0. Richmond . 9 SKF Bearing EE4B. 10 Strobotac, type No. 631-B, S e r i a l No. 8296, General Radio. Co., Cambridge, Mass. 11 Instructions for Securing SR-4 Gages to  - 83  Structures using SR-4 Cements, The Baldwin Locomotive Works, Philadelphis 42, Penn. 12 Appendix E, p. 78. 13  Weston D.C. Voltmeter, Model  45,  No.  26631,  Weston E l e c t r i c a l Instrument Co., Newark, N. J . 14 Midget Current Meter no. 17, Le.upold Volpel and Co., Portland, Oregon. 9° blade, c a l i b r a t i o n curve dated Aug. 9, 1946. 15 Richmond, W, 0., Failure of T a i l Shafts of Victory Type Steam Cargo Ships, May 2 3 , 1947, p. 9. 16 Drawing No. 7595-A, Details of Bronze Propeller, Burrard Dry Dock Co. L t d . , March 30, 1944. 17 Seward, H. L . , Marine Engineering, V o l . 1, New York, The Society of Naval Architects and Marine Engineers, 1942, p. 284. 18 Marks, L. S., Mechanical Engineers' Handbook, !  New York, McGraw - H i l l , 1941, p. 1501. 19 Rossell, op. c i t . , p. 149. 20 I b i d . , p. 121. 21 T a t n a l l , F . G . , SR-4 News Letter, v o l . 1, no. 2, Oct. 1944, Baldwin Locomotive Works, Southwark D i v i s i o n , Philadelphia, P a . , 22 Tatnall, F . G . , SR-4 News Letter, v o l . 1, no. vol.  3,  2,  Nov. no.  1944; 4,  no  Jan.  4,  Dec.  1944;  no.  5,  Jan.  1945;  1946  23 The Brush Development Co., Cleveland, Ohio,  84  Operating Information,  Brush Oscillograph Equipment,  F-401, 402, 403.  24 Richmond, W. 0 . 25 R o s s e l l , op. c i t . , p . 139. 26 I b i d . , p. 114. 27 West Coast Shipyard Drgs. No. 135, 136, 137. 28 Den Hartog, J . P . , Mechanical Vibrations, New York, McGraw - H i l l , 1947, pp. 57-67. 29 Mechanical Springs, Their Engineering and Design, The Wallace Barnes Co., L t d . , Hamilton, Ont., p. 55-  85  BIBLIOGRAPHY Barnaby, S. W., "Marine Propellers", New York, Spon and Chamberlain, 1921. Den Hartog, J . P . , "Mechanical Vibrations", New York, McGraw - H i l l ,  1947.  " ' l i b e r t y * Ship Propellers and Rudders", The Syren and Shipping, p. 337, Feb. 18, 1948. Marks, L . S . , "Mechanical Engineers' Handbook", New York, McGraw - H i l l , 1941. Richmond, W. 0 . , "Failure of T a i l Shafts of Victory Type Steam Cargo Ships",  Vancouver, May 2 3 , 1947  Rossell, H. E. and Chapman, L. B . , "Principles of Naval Architecture", The Society of Naval Architects and Marine Engineers, New York, 1947, 2 vol.. Seward, H. L . , "Marine Engineering", New York, The Society of Naval Architects and Marine Engineers, 1942, 2 v o l . Tatnal, F. G . , "SR-4 News Letter Philadelphia, Baldwin Locomotive Works, 1944, 1945 Wallace Barnes Company, "Mechanical Springs", B r i s t o l , Connecticut, Associated Spring Corporation, 1944.  

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