The dynamic loading of spur gear teeth

Report No. 122

jnr

Kluy

THE COLLEGE OF AERONAUTICS

CRANFIELD

THE DYNAMIC LOADING OF SPUR GEAR TEETH

by

OOL aOUWKUNDE ...twatlO - DEJ-FT REPORT NO. •f22, O c t o b e r . 1 9 5 9 . T H E C O L L E G E O F A E R O NJLUJILI_Q_S C R A N F I E L D

The dynamic loading of spur gear teeth

b y

-J, H. Dunmore, B.Sc,, A.C.T.Birm., A.P.Inst.Pet.

SmVMARY

In this report, description of the first stage of some work on the dynainic loading of gear teeth is given. The work has been performed on a power circulating gear rig, using gears of 9 inch P.CD,, li.'D,!'., and 1/2 inch face vri.dth. The rig is capable of running at pitch line velocities up to 20,000 ft/min. with imposed loads of up to 3>000 lbs/ inch of face width. Psirticular reference is made to the instrumentation problems which vrere encountered, and to the neasurement of the shape of the gears sind their associated transmission errors. No attempt is made at a theoretical analysis of the results obtained as this will be

the subject of a future report, along \7ith the publication of more results.

CONTENTS

Page

1• Introduction

2, Description of Test Rig

3.

h-,

5.

6.

7.

8, 9. 10. 11. 2.1, Description of Geaxs

2.2, Description of the Error Measuring Equipment

InstnmientatT on Techniques

The Measurement of the Individual Gears

Method of attaching Lead Zirconate Crystals to the Teeth

Calibration of the Lead Zirconate Crystals

Results and Discussion

Projected Future Work

Immediate Future Work

Acknowledgements

References

Appendix 1

Appendix 2

ApponrJix 3

Tablcjs I, II and III

Photographs Nos. 1 - 1 1 Figures 1 - 3 7 Graphs 1 - 1 2 2

3

k

3

5

6

8

8

8

9

10 12

17

1

-1. Introduction

Vfith the present day demand, in all fields of engineering, for higher speeds and higher working loads, the existence of reliable design criteria becoines important. This is particularly so vdth problems relating to gears tmd bearings. This report describes v7ork which is being carried out in the Department of Aircraft Propulsion at the College of Aeronautics, Cranfield, to establish the magnitufle of the loads imposed on gear teeth under varying speed and loading conditions,

In the design of gears, two main types of tooth failxore have to be considered. These are fracture of the root due to bending fatigue, and failure of the surface, either by scuffing or pitting. Both these types of failure are influenced by tooth loading, and it would appear, therefore, that the accuracy of the estimated life of a gear depends upon the accuracy of the estimated load, for any of the above failures to be avoided. Now, if tlie load is to be estimated accurately, a reliable estimate must be made of the dynamic loading imposed on the teeth. Various mathematical approaches have been made in an attempt to estimate the loading, but they have been contradictory, and further there has been little e3q)erimental evidence to support them. It is the object of this work and its associated research programme to find the effect of several possible variables on the dynaipdc load. Prom the results obtained, it is hoped to either substantiate an existing theory or establish a new one. At the very least, there will be some guidance as to which factors are the most important.

2. Description of Test Rig

As has already been stated, the test rig is of the povTcr circulating type. This uses two sets of gears, in effect driven back to back, so that the povrer requirements are those of the losses encountered in the gears and beaorings. A full description of the rig has been given in College of Aeronautics Note No. 75* but for the sake of sompleteness, vd.ll be repeated,

The general arrangement of the rig is shov/n in Figure 1 , and a general viev/ shovm. in Photograph 1 . Pour separate bearing hoiosings are mounted in pairs on two small bed-plates which are in turn mounted on one large bed-plate. Each housing contains one double roller

bearing and tvro deep groove ball bearings, which support a short, large diameter, shaft as shown in Figure 2. The beariiigs used are "ultra-precision bearings" and by suitable alteration of the split spacing ring length, the radial clearance of the roller bearings

may be adjusted to any amount by forcing it up its tapered seat. This bearing arrangement gives very accurate radial and axial location of

the shaft axis, at the same time giving good accessibility to the test gears. The test gears are housed at (5) (see Pig, 1 ) , and the

- 2

slave gears a t {k) > A f u l l d e s c r i p t i o n of the gears i s given l a t e r .

To i n s u l a t e the t e s t gears from such extraneous t o r s i o n a l v i b r a t i o n s

as do e x i s t , long t o r s i o n shafts (3) are used. They are a l s o u t i l i s e d

t o impart load to the gear t e e t h by means of the loading arm ( 7 ) .

This a c t s on one half of the loading coupling, the other h a l f being

r i g i d l y locked for the purposes of loading. A v e r n i e r dovrel arrangement

i s used i n which one half of the loading coupling has 21 equi-spaced

holes on a 6,3 i n . diameter and the other half has 20 equi-spaced

holes on a s i m i l a r diaaieter. This permits the a p p l i c a t i o n of the Ipad

i n increments of 154- l b s / i n c h of face width,

Tvro separate l u b r i c a t i o n systems are used on the r i g , one for the

bearings aaid one for the g e a r s . The bearings are l u b r i c a t e d by o i l

mist from one l u b r i c a t o r and the gears are supplied id-th o i l from a

combined pressure/scavenge pump. The o i l s used a t present are Gastrol

Hyiooy for the gears and S h e l l Telus 15 for the b e a r i n g s . The r i g i s

driven by a 50 H.P. Schrage motor, through a 3:1 or 6:1 p u l l e y d r i v e ,

using a high speed 'Meteor' b e l t ,

2*1 • De scription_of^ Gears

Test .Gears _

The basic d e t a i l s of the t e e t h are as follows :

-P.G.D, 9 iiich No. of t e e t h 36

Pressure Angle 27 Pace width l / 2 inch

Material S.82

Four t e s t gears have been manufacturc^d up to the p r e s e n t . One

p a i r has a pure involute p r o f i l e ; the other has a. p r o f i l e modified t o

s u i t current p r a c t i c e a.t Rolls Royce. As the gears are r e v a r s i b l e ,

both sides of the t e e t h riiE.y be used as pressure f a c e s . One pressiore side

of each gear has been ground, to give the minii;nam p o s s i b l e p i t c h e r r o r s

as given i n Table 1 . This allows gear faces vj±th nominal tootl'i

spacing to be meshed together i n the pure involute and modified

involute forra. Some of the meshing combinations t h a t can be obtained

with these gea.rs are shown i n Table I I . I t i s seen t h a t the e f f e c t s

of two b a s i c types of e r r o r may be i n v e s t i g a t e d . One i s a sudden

change i n constant adjacent p i t c h e r r o r extendin.g f o r 9 teeth each

side of the i n v e s t i g a t i o n p o i n t , and the other i s an i s o l a t e d e r r o r

with 8 teetli each side a t nominal p i t c h . Photograph No. 2 shows the

gears with the modified p r o f i l e i n p o s i t i o n on the r i g .

Slave Geo.rs

The slave gears cure helical gears of 8 D,P, and three times the face v/idth of the test gears. This increase in D,P, aaid face -^-iddth was chosen

- 3

in order that the amount of vibration arising from the slave gears could be kept to a minimum. Pliotograph No, 3 shows the slave gears mounted in position,

2.2, Description of the_Error Ivfcasuring Equipirent

An ideal pair of gears, operating under ideal conditions, m i l transfer rotation about the axis of the driving gear into rotation about the axis of the driven gear in a pei-fectly linear manner. When considering a set of gears operating tinder varying conditions

of load and speed, it is very important to knov: the deviation from linearity of transfer of angular movement.

In order to measure this deviation, the follovring device v/as

designed and developed, general views of which are shown in Photographs 7j 8 and 9. Two pulleys, each of 9 inch outside diameter, are mounted, one on each test gear. One of the pulleys consists of a solid circular disc viiich is mounted rigidly to the gear and the other consists of an annulus of 9 inch outside diameter and a solid circular disc of outside diameter less than the inside diameter of the annuliis. The annulus was attached to the disc by means of four radial leaf springs incorporating means for adjustment of the coaxiality of the gear and pulley. A steel flexible belt is arranged, in the manner shoirn in Photographs 7, 8, and 9 to transfer motion of the first pulley, perfectly linearly

to the motion of the second pulley. During the motion of the two test gears, the driving gear of the two test gears will drive the driven gear and consequently any deviation betvveen the motion of the driven pulley and the driving pulley will indicate the ma^gnitude of the lack

of linearity in the transfer of angular movement, by the gears.

This deviation is shovvn by movement of the annulus with respect to its solid circular disc. The movement is measured v/ith the aid of a

Southern Instruments Magna Gauge, and a galvanometer recorder. The probe of the Magna Gauge, wiiich is in fact an inductive pick-up, is fixed to the annulus and the tip of the probe allowed to rest against a plate fixed to the smaller disc. Early tests fed the output from the Gauge to an iiltra-violet galvanometer recorder. The advantage of using the ultra-violet galvanometer recorder was that the paper

sensitive to liltra-violet light could be attached to one of the

couplings of the rig, and this would serve as the drive for the paper, This avoids any errors arising from changes in velocity whilst turning the rig. This has to be done slowly by hand, as the rig could not be 3run at very low speeds. It was found that to obUjain clear traces

suitable for reproduction, a photographic paper, sensitive to white light, had to be used. Another method for measuring these transmission errors is being considered. This consists of using two Southern

Instruments Torsiographs fixed to each shaft, and feeding the differential output from each torsiograph to a recording oscilloscope. It is

important that the reference position is known accurately, and use is made of the triggering device for the instrumentation. This will be eacplained in detail in another section,

2^.

-3 , In_strignentation Tecliiiiques

At f i r s t , t\70 mctliods for measuring the deflection of the gear

t e e t h r e l a t i v e t o the gear shaft

YIGTB

used; f i r s t l y movement of the

gear t e e t h r e l a t i v e t o the shaft wa.s made -to vary the capacity of a

small condenser, one p l a t e of which was attached to the tooth and the

other fixed r i g i d l y to the shaft (Figure 7 and Photograph No. 4-),

and secondly a s t r a i n gauge was fixed t o both sides of a sniall beam

v/hich was made t o bend should a tooth move r e l a t i v e t o the shaft (see

Photograph No. 5 ) . I n i t i a l l y the s i g n a l from the condenser was

detected by means of a conventional g r i d - d i p o s c i l l a t o r arrangement

(Figure 9) but d i f f i c u l t y v/as experienced Td.th the d r i f t of the

o s c i l l a t o r and an a l t e r n a t i v e method of t r a n s m i t t i n g t h i s capacity..'"

s i g n a l was designed. This used another p a r a l l e l p l a t e condenser, of

much g r e a t e r capacity than the pick-up to transmit the sign.al to a

Southern Instrument P,M, System. A disc i s fixed r i g i d l y t o the

shaft of the instrumented gear and can r o t a t e between tvTO p l a t e s with

about 0,010 inch clearance betvTuen each side of the r o t a t i n g d i s c ,

Figure 8 shows the method used. I t i s f e l t t h a t both these methods

s^uffer from lack of high frequency response, due to compliance of the

small beam supporting the condenser p l a t e from the t o s t t o o t h .

The s i g n a l from the s t r a i n gauges \7as detected by a normal D.C,

Bridge and airrplifier feeding i n t o an o s c i l l o s c o p e , Difficul'cy was

experienced using t h i s method, owing to d i f f i c u l t i e s of s t i c k i n g

the gauges t o 'tiie beam, and more e s p e c i a l l y t o the problem of mercixry

s l i p r i n g s and the a s s o c i a t e d noise l e v e l . The output from the s t r a i n

gauge was very small, and t h i s r e s u l t e d i n a low s i g n a l to noise r a t i o

from the s l i p r i n g . YJith the high amplifications v/hich had t o be used

t o obtain s u i t a b l e deflections on a recording o s c i l l o s c o p e , t h i s

became a problem. I t vrcis decided, t h e r e f o r e , to use lea.d zirconate

c r y s t a l s as s t r a i n transducer elements. HigJ'i outputs can be obtained

from these p i e z o - e l e c t r i c elem.ents and, t h e r e f o r e , the s i g n a l to

noise r a t i o 1,10.11 be higli. F u r t h e r , the high frequency response i s

good. These elements vrere very successfxjl; they may be attached

d i r e c t l y t o the side of the gear, i f nocessaiy, and have been chosen

f o r f u r t h e r use on the r i g .

Another problem a.rose; t h a t of adjequate recording of the phenomena

under observation. Y/ith the use of a six-chai:nel recording oscilloscope

and i t s recording camera, the important p a r t of the t r a c e , t h a t on

which the gear tooth i s under load, i s vers'" small, even a t modest

speeds. This i s due t o l i m i t a t i o n s of film speed - a mtociraum of 1200

i n c h e s / s e c . would be obtained. I n view of t h i s , another method of

p r e s e n t a t i o n of the phenomena was designed and developed. This system

uses a Shackman Camera v/hich takes shots every 0,5 seconds. A t r i g g e r i n g

s i g n a l i s taken from the i-ig, by means of a hole i n a disc i n t e r r u p t i n g

a beam of l i g h t focussed on t o a p h o t o - c e l l , and fed i n t o an e l e c t r o n i c

g a t e . At the same time a 24-volt s i g n a l evcTy 0,5 seconds i s fed i n t o

-5

-the gate and -the electronics is arranged so that after -the arrival of the first 22f.-volt pulse, the next signal from the triggering device triggers the oscilloscope and the trace is arecorded. The film is then moved on automatically, and nothing happens until the next 24-volts pulse is received, and then the next trigger signal again triggers

the oscilloscope beam. This process is repeated throughout the test run, Thijs, approximately every •|--second a record is taken as the test tooth meshes. Details of the electrcnic circvdts used are given in Figures 3> 4» 5 and 6, It is seen that a delay is incorporated in

order that some compensation for the lead of the triggering signal at different speeds may be given,

The speed of the idg is measiored with the aid of a photo-cell and a disc with éO holes equi-spaced around its circumference. A light source is focussed on to the cell and hence a signal may be obtained from the cell. The signal from the photo-cell is fed to a Dekatrcn Counter and also to the second beam of the double beam

oscilloscope. A signal of known frequency is superimposed on this second beam in order that a time marker may be obtained, A full block diagram of the instrumentation is given in Figure 10.

4, The Measurement of the Individual Gears

This was done by Rolls-Royce, and a chart showing the errors is given in Table 3 and Graphs 1 to 8. As a check, the gears were measured on the Sigma Instrument Company Gear Measuring Device, and the results are shovm in Graphs 9 to 12, This machine was described in a paper presented by PiHDfessor Loxham (Head of the Department of Economics & Production

at the College) to the International Conference on Gearing (Ref, 7 ) . Up to the present, only the pure involute set of gears have been measured

on this machine, as the modified profile gears are on the rig, and it was felt desirable to complete the preliminary running on them before disturbing them. Maag profile diagrams for the gears were obtained and are presented following Table 3,

An interesting point arises in that whilst with the bioilt-in

errors the measurements from Rolls-Royce and Signa Instrument Co. agree fairly v/ell, those with the 'perfect' gears show differences. These are being investigated,

5, Method, of attaching lead zirconate crystals to the teeth

The lead zirconate crystals were attached to the teeth of the test gear with the aid of Araldite and Hardener, Aluminiiim powder was mixed into some Araldite and Hardener, in order to make it slightly

conducting, and the resiolting mixture applied to one side of the crystal which was then fixed and clanped in position on the side of the gear. This was allowed to harden over a period of 24 hours. The appropriate leads can then be soldered to the visible face of •fee

6

-crystal. Crystals have been attached to the mid point of the strain gauge beam and to the side of the tooth carrying the beam, the crystal being fixed near to the root. The tooth preceding this tooth has a

similar crystal attached. Photograph No. 6 shows the position of the crystals.

6, Calibration of the Lead Zirconate Crystals

This may lead to some difficulty, but it is hoped to overcome this by direct comparison with strain gauges. The lead zirconate crystals are an A.C. device, and so tha problem resolves into a

comparison with a D.C, device. Strain gauges will be stuck on either side of a fairly stiff beam, and crystals will be stuck by the side of the gauges. The beam will be clamped at one end and calibrated at various amplitudes and frequencies. If the amplitude is known, the stress may be calculated and a direct comparison made between crystals and strain gauges over a range of frequencies. Hence a deflection against output calibration may be made.

7. Results and Discussion

¥/ith the gears having the modified profile, corrected to a maximum load of 3,000 lbs/inch face width in position, the follov/ing

tests have been performed

:-(1) Test using the grid-dip principle for transmitting the capacity signal

(2) Test using the capacity slip ring for transmitting the capacity signal

(3) Test using lead zirconate crystals and the signal from these transmitted by means of a mercury slip ring.

The transmission errors of the gears were measured over a range of loads and the results shown in Appendix 3, The calibration is done in steps of 0.0005 inch.

It is emphasised that this report is preliminary in that it presents only the tjrpe of recording that is being obtained from the

instrumentation, and that a full theoretical treatment involving a comparison between Professor Tuplin's and Earle Buckingham's methrd of calculating the dynamic load will be presented at a later date.

Figure 11 shows two capacity transducer records, using the grid-dip method of detecting capacity change, taken with the aid of a drum camera. The traces from left to right on the records are speed marker fr«Hn the Dowty Tachometer, signal from the capacity transducer, time marker ( .^1-. second) and strain gauge signal. The single peak in

7

-the capacity signal record represents -the meshing of -the test tooth.

Figures 12 - 16 inclusive show reaords, again taken with the aid of a drum type camera, of capacity signal transmitted using the

"capacity slip ring". The load has been kept constant at 750 lbs/inch face v/idth, and the speed varied. The traces, reading from left to right, are speed, capacity signal and time ma.rker (0.001 sees.). It will be noted that as the speed is varied, the transducer signal changes in amplitude during the meshing period of the test tooth, For instance, at 1200 r.p.m, the signal is approximately half that at

712 r.p.m. This shows that even with a constant load, there can be marked variations in gear stress with changes in speed. There is also a change in shape of the record with speed, FiJrther, even when the test tooth is not in mesh, it shows a periodic deflection at most of the speeds shown. The reason for this is not yet known.

Considering Pig\ares 1 8 - 22, these show signals obtained frcm the lead zirconate crystal, fixed to the side of the tooth having the

strain gauge beam attached to it. The signals were obtained by the method described at the bottom of page 4. The loading in this oase is the design value of 3,000 lbs/inch face width. Again a marked change in amplitude and shape of the trace is apparent as the speed is changed. The top trace is of pulses representing 6 revolution, the angular pitch of the teeth being 10 . Figures 23

-29 show the signal recorded in a similar manner, but with the load at 1500 lbs/inch face width. In spite of the load being halved, the transducer signals are little reduced and this would indicate that a large part of the strain at reduced load is due to the dynamic effect of the gears meshing at a load not suited to the profile modifications. Further tests, especially those using involute gears should throw

light on the variation of tooth strain with load. A study of Figures 28 and 29, 'w^ere the records were taken during a run dovm frcxn

maximum speed show that even with small changes in speed, large changes in dynamic load may occur.

Ttirning now to a study of the error measurements &a shown in Appendix 3, it would appear that the profile modification is not

quite so good as was at once hoped. Preliminary results, using a system not quite so sensitive as described in this report, had shown better conformity in involute profile at maximum load. It is seen

that application of the load has had the effect of reducing the peak of the change period and the change is more gradual but has not brought the gears into involutg profile. The bottom trace on the records represents pulses of 6 rotation. It is intended to check the involute gears with the error measuring equipment as soon as possible to check this conclusion.

8

-8. Projected Future Work

(1) Design of a system of loading such tliat load may be applied whilst the rig is in motion.

(2) Design of a brush type slipring having at least six separate channels.

(3) Development of a pystem of measuring alternating torque using Moire Fringe Techniques.

9. Immediate Futtxre YiTork

(1) Check rvins with the test gears lonmeshed to determine the magnitude of any tpsjrious signal.

(2) Completion of the results from the gears with the profile modification at vai:-ious speeds and loads.

(3) Results from the involute profile gears at various speeds and loads.

(4) Investigation into the theoretical and practical implications of the results.

(5) Investigation into the torsional vibrations existing in the rig.

(6) Exploration of the shape and size of the strain traces.

10, Acknowledgement s

Acknov/ledgement is made to the following people who have assisted in this work :

-Professor A. G. Smith, Head of the Department of Aircraft Propulsion, for his encouragement and advice.

Professor J. Loxham, Head of the Department of Economics and Production, and the Signa Instrument Company for measuring the involute profile gears.

Rolls-Royce Ltd., for providing the gears,

Mr. G. YiT, Jackman and Mr. E. C. Sills of the College of Aeronautics for valuable assistance with the instrrimentation.

9

-11, References 1. 2,

3.

5.

6,

7.

College of Aeronautics Note No. 75,

Merritt, H.E, Buckingham, E. Tuplin, Prof, Wilson, Ker, Timoshei±o, Prof.S. Loxham, J. Gears, Pitman,

Analytical Mechanics of Gears, McGraw Hill.

Torsional Vibrations. Chapman & Hall.

Practical Solution of Torsional Vibrations Problems, Vol,I, Chapman & Hall.

Vibration problems in engineering. Van Nostrand,

Inspection of Cumulative Circular Pitch on High Precision Gears.

International Conference on Gearing. Inst. Mech, Engs.

10

-APPENDIX 1

Maximvim Sliding Velocity of Test Gears

Sliding Velocity V^ = V ! i- ^. ^ U^ r^ - R^_^^ - R sin jÓ )

R and Rp are radius of pitch circle of gears

V = pitch circle velocity

r = any radius on the gear

R, = radius of base circle

0 = pressure angle Now R^^ = R^2^ = R^ cos^ }6 = 4.5^ cos^ 27° '' •••:^ •• : = 16,076 for max V r. = 4.75 s 1

and so Vg = 20,000 x — 4.75^ - 16.O76 - 4 . 5 cos 27°

= 74.6 f t / s e c .

Determination of the length of p a t h of c o n t a c t

Length of path of contact = 2 l J ! f + a j - l - l c o s j Z ) j - | s i n J 2 5

^)^(f.)Y-l-. 1

^

v/here d. = top diameter

d = base circle diameter o

Length of path of contact = 2 4.7505^ - 4.0095^ j 2 _ 4.5 sin 27°

11 -•

Determination of the change points

Base circle diameter = 8,01906

Base pitch = Q^0^^06 ^ «r - 0.6998

Assuming oorrect profile modification then the change points will be approximately 0,2" from the pitch point,

Pitch point

0.3 0,2 0,2 0.3

Double Single Double Contact Contact Contact

Contact R a t i o

Contact R a t i o = l e n g t h of path of c o n t a c t base p i t c h

1,009 . , , .

12

-APPENDIX 2

Torsional Vibration and Resonant Frequency of the ,Gear Rig

The diagram of the shafting of the rig, with the inertias involved and the equivalent lengths, is as

below:-Inertias

r

lbs,ins,

Test Gears

Slave Gears

If each line of shafting is considered to be a three mass system, i,e, masses due to the test gears, loading coijpling and slave gear, then one line of shafting may be considered. As a first approximation, consider a two mass system as shown below. This is allo\'7able because the equivalent length betvroen the coupling and the test gear is small compared vri.th the equivalent length between the coupling and the slave gear. For this case the inertias of

531

Inertias

—

-29.3—-533

Test Gears Slave Gears

13

-Tuplin (Ref, l) gives

Spring Constant C = G I L

C = torsional rigidity of shaft G — modiolus of rigidity

p = polar moment of inertia of the corss-section of the shaft

L = equivalent length of shaft

For this case

P _ •I^IJ-.-X 1_0 X 32,2 X 12 24,3

= 1,82*8 X lo"^ lbs,ins.^ sec,

Now, for a two mass system

Frequency constant n 2ir N

C I

L^l

\

/sec, i-- 1.82f8 X 1 o'^r J _ •>

J

= 9.55 6.97 X 10^ /mir^s, = 2520 /min.

If the system is considered as a three mass system, we have

240 , 280 533 Inertias

Test

Gear

O,106

l r

Coupling

24,25

Slave

Gears

14

-One t h i r d of the i n e r t i a of the smaller shaft has been added t o

each of the main i n e r t i a s ,

6 ?

n 1,16 X 10 X 32,2 X 12 , _, .„9 l b s , i n s ,

C^ = — — o ; y Q ^ - ^ = ^-23 X 10 - ^ - . . ^ ^

s e c ,

6 P

r. 1 .16 X 10 X 32.2 X 12 . 0 , / - ^rJ l b s . i n s .

°2 = 24:25 = 1 . 8 2 ^ x 1 0 ^.-^^.^^

s e c .

N - ^ = ° l / i n e r t i a = ^ \ T O ~ = ^ . 7 6 x 1 0 ^

S i m i l a r l y b^

= G ^ ^ ^ ^ ^ ^ . ^

i t ^ J ^ O - . 1 . 5 1 x 1 0 ^

= G,/. , . i ^ % ^ ^ = 6 . 6 x 1 0 ^

2 2 / i n e r t i a 280

V r. 1.846 X lo"^ , ,^ .„4

^2 = ° 2 / i n e r t i a — ^ 3 3 ™ ^ = 3,^6 x 10

Now Tuplin shows t h a t

u + (a^ + b^ + a^ + b^) u + (a^ + b^) (a^ + b^) - a2b^ = 0

2 7 1? 1?

u^ + 3.28 X 10' u + 3.27 X 10 - 10 '^ = 0

u' + 3.28 X 10''' u + 2.27 X lo""^ = 0 Solving this in the usual way leads to :

-6,543 X 10"^ -1_J,0_xA0^

2 Subs n = -^

and hence n = 5720 or 292 vibs/sec, or 54600 or 278O vibs/min,

If the case is now considered in which the two lines of shafting act together, a three mass system as sha\vn below may be obtained. It is assumed here that any forcing of vibration comes from the test gears and none from the helical gears.

- 15

Test Gear

Slave Gear

24.3

-531

Test Gear

-<!f-

•24.3

- ^ M

1066

_53'S Inertias lbs,ins

7 2

Spiing constant f o r shaft = 1,82*8 x 10 l b s , i n s , / s e c ,

a^ = b^ = 3.hS X 10^

ag = bg = 1.735 X 10^

Therefore u^ + 10.43 x 10^ u + (5.215^ - 1.135^) 10^ = 0

u^ + 10,43 X 10^ u + 24,2 X 10^ = 0

This leads t o u = 3,2*8 or - 6 . 9 4 x 10^

giving n = JJZ22 °^ 2520 vibs/min,

I f t h i s l a s t case i s taken a s t e p f u r t h e r by considering a five

mass system, the configuration below i s obtained :

I n e r t Las

Ibs.ifle—

280

'^ o - i - ï ^

-24.25

1066

• < 3

24,25

-280

240

—fes.

Test

Gear

Coupling

Combined

Slave Gears

0.106

Coupling Test

Gear

Considering one half of the system,

For an even mode v i b r a t i o n , we have the following configuration :

240^

'280

<a33

24.25 16 24.25

-This system has been considered, giving frequencies of n = 54>600

or 2780 vibs/min. For an odd mode v i b r a t i o n

I n e r t i a s

2

l b s , i n s

240

280

g ^ ^ = 1

-0,106

-24.25

—•n^'O

i2f

'^

The c e n t r a l i n e r t i a i s now i n f i n i t e , and so bp = 0,

P

Therefore u + (a^ + b^ + a^) u + (a^ + b^) a^b^ = 0

u^ + 3.277 X 10"^ u + 2,155 X l o ' ' ^ - 9.98 X 10'''' = 0

u^ + 3.277 X 10^ u + 1,157 X lo""^ = 0

Giving u = -3,27 x 10' or 6,9 x 10^

n = 54,700 or 2,500 vib/rain,

I t would appear t h a t the f i r s t and second and the t h i r d and fourth

n a t u r a l v i b r a t i o n s are close t o g e t h e r . Prom consideration of the

above c a s e s , i t appears t h a t the modes of v i b r a t i o n are as follovvs :

-1 s t mode

2nd mode

3rd mode

4th mode

1790 vibs/min.

2,520 vibs/min.

54,600 vibs/min.

54,700 vibs/min.

17

-- AEPEII^roiX j

Dynamic Load on Spur Gear T e e t h ,

Specimen T e s t s R e s u l t s from the E r r o r Measuring Equipment.

Gears Used - Modified P r o f i l e , v/ith minimum e r r o r s .

H»! 9O00 o JO Sd^lS

Nouvöanvo

HiaiM 3DVd iJ3U|/ïqi OOOE

HiaiM 30Vd H3U.I/Ï1I OSZS

HIOIM 3DVd 43U|/«1I OOSI

TABLE I • Showing Controlled E r r o r s manxifactured i n Test Gears

Gear

I d e n t i f i c a t i o n

No.

1/1 2/1

P r o f i l e

Modified t o Norma.!

R.R. P r a c t i c e

Pure involute

Spacing on one Pressure Side

P i t c h e s 36/1

" 9/10

" 18/19

" 27/28

8/9 — «0008 i n , g r e a t e r than nominal

17/18 - noiidnal

26/27 - ,0011 i n , l e s s than nominal

35/36. ** ,0003 i n , g r e a t e r than nominal

1/2

2/2

Modified t o Normal

R.R, P r a c t i c e

Pure involu-be

P i t c h 36/1 — ,0005 g r e a t e r "than nominal

P i t c h e s 1/2 -. 8/9 i n c l , - nominal

P i t c h 9/10 ~ .0008 l e s s than nominal

P i t c h e s 10/11 - 17/18 i n c l , - nominal

P i t c h I8/19 - .0011 l e s s than nominal

P i t c h e s 19/20 - 26/27 i n c l . - n o m i n a l

P i t c h 27/28 - ,0014 g r e a t e r than nondnal

P i t c h e s 28/29 - 1)3/% " nominal

Gear Teeth Numbere 1 - 3 6

TABLE II, Showing Type and Magni-tude of Errors available for investigation "srlMi Test Gears,

Driver Gear Profile No, Tooth Spacing

Driven Gear

No, Tooth Spacing

Controlled Errors Available for Inve stigation Modified o r Pxjre I n v o l u t e Modified o r P u r e I n v o l u t e Modi f i e d o r P u r e I n v o l u t e Modi f i e d o r P u r e I n v o l u t e 1/2 o r 2 / 2 1/2 o r 2 / 2 1/1 o r 2/1 1/1 o r 2/1 Nominal Nominal Gconstant E r r o r s Nominal 1/1 o r ~2/l 1/1 o r 2/1 1/2 o r 2/2. 1/2 o r 2 / 2 Nominal Cons tan-Nominal -I s o l a t e Nil + ,0005 i n . chaxige - .0008 i n , " - .0011 i n , " + ,0014 i n . " - ,0005 i n , change + ,0008 i n , " + ,0011 i n . " - .0005 i n . " + .0005 i n . - .0008 i n , - .0011 i n . + .0014 i n .

IABU! 3 . Individual tooth enXMM. (Detenriiied a t Rolls^oTCel G e a r N o . S p a c e N u n b e r 3 6 - 1 1-2 2 - 3 3 - ! ^ V-5 5 - 6 6 - 7 7 - 8 8 - 9 9 - 1 0 10-11 1 1 - 1 2 1 2 - 1 3 13-11f 1V-15 1 5 - 1 6 1 6 - 1 7 1 7 - 1 8 1 8 - 1 9 1 9 - 2 0 2 0 - 2 1 '21-22 2 2 - 2 3 2 3 - 2 4 2V-25 2 5 - 2 6 2 6 - 2 7 2 7 - 2 8 2 8 - 2 9 2 9 - 3 0 30-31 3 1 - 3 2 3 2 - 3 3 3 3 - 3 4 3 4 - 3 5 3 5 - 3 6 1 s t I S . 1 5 5 6 / 5 2 A 1/1 S i d e T a r g e t + . 0 0 0 8 n H H n n If n tt . 0 0 0 0 ti II " n " n It •• - . 0 0 1 1 n " II 11 11 II " n + . 0 0 0 5 II It II " " " " A c t u a l + . 0 0 0 6 + . 0 0 0 9 2 5 + . 0 0 0 8 2 5 + . 0 0 C 7 + . 0 0 0 9 5 + . 0 0 0 9 2 5 + . 0 0 0 8 + . 0 0 1 0 + . 0 0 1 0 2 5 - . 0 0 0 0 6 + . 0 0 0 0 5 - . 0 0 0 0 2 5 , - . 0 0 0 1 7 5 . 0 0 0 0 . 0 0 0 0 r . 0 0 0 3 2 5 - . 0 0 0 1 7 5 - . 0 0 0 2 5 - . 0 0 1 1 5 - . 0 0 1 0 5 - . 0 0 0 8 7 5 - . 0 0 0 9 - . 0 0 0 8 2 5 - . 0 0 0 7 5 - . 0 0 0 9 7 5 - . 0 0 1 0 2 5 - . 0 0 1 2 + . 0 0 0 2 2 5 + . 0 0 0 2 7 5 + . 0 0 0 1 5 + . 0 0 0 2 5 + . 0 0 0 1 2 5 + . 0 0 0 3 + . 0 0 0 1 7 5 + . 0 0 0 2 5 + . 0 0 0 2 SM.SUG. T a r e o t

ë

a

f^

i

Ö '•^

i

A c t u a l - . 0 0 0 0 2 5 + . 0 0 0 1 + . 0 0 0 0 2 5 + . 0 0 0 1 + . 0 0 0 0 5 + . 0 0 0 0 2 5 . 0 0 0 0 0 . 0 0 0 0 + . 0 0 0 0 7 5 . 0 0 0 0 0 - . 0 0 0 0 5 . 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 1 7 5 - . 0 0 0 0 2 5 - . 0 0 0 0 7 5 - . 0 0 0 0 7 5 . 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 1 - . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 0 5 - . 0 0 0 0 2 5 - . 0 0 0 0 5 - . 0 0 0 0 5 - . 0 0 0 0 2 5 + . 0 0 0 0 7 5 - . 0 0 0 7 5 + .0O0O5 + . 0 0 0 0 7 5 + . 0 0 0 0 2 5 + . 0 0 0 0 5 + . 0 0 0 0 5 + . 0 0 0 1 2 5 + . 0 0 0 0 7 5 I S . 1 5 5 6 / 5 2 A 1 / 2 1 « t Rirt» T a r g e t + . 0 0 0 5 . 0 0 0 0 0 n H " II w II " - . 0 0 0 8 . 0 0 0 0 0 " n It II II n II - . 0 0 1 1 , 0 0 0 0 0 II 11 II n n n n + . 0 0 1 4 . 0 0 0 0 H " " It " tl It A c t m l + . 0 0 0 6 + . 0 0 0 0 5 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 0 7 5 - . 0 0 0 0 7 5 - . 0 0 0 9 2 5 - . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 0 2 5 - . 0 0 0 0 7 5 - . 0 0 0 0 7 5 + . 0 0 0 1 5 - . 0 0 0 0 2 5 + . 0 0 0 1 2 5 - . 0 0 1 0 7 5 . 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 1 2 5 + . 0 0 0 0 2 5 . 0 0 0 0 0 + .0001 - . 0 0 0 0 5 - . 0 0 0 0 5 + . 0 0 1 4 5 + . 0 0 1 5 - . 0 0 0 2 5 + . 0 0 0 0 2 5 + . 0 0 0 0 5 . 0 0 0 0 0 - . 0 0 0 0 5 - . 0 0 0 1 - . 0 0 0 2 2 5 P i t c h D i f f e r e n c e T a r g e t ^ p

H

Ö ft A c t u a l - . 0 0 0 0 7 5 + . 0 0 0 0 2 5 . 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 0 5 - . 0 0 0 1 2 5 - . 0 0 0 0 2 5 . 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 1 5 - . 0 0 0 1 . 0 0 0 0 0 - . 0 0 0 0 2 5 - . 0 0 0 0 7 5 - . 0 0 0 1 - . 0 0 0 0 2 5 - . 0 0 0 0 5 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 1 5 + .0001 - . 0 0 0 1 - . 0 0 0 0 2 5 + . 0 0 0 0 2 5 + . 0 0 0 1 5 + . 0 0 0 1 5 + .0001 . 0 0 0 0 0 + . 0 0 0 0 5 . 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 0 2 5 I S . 1 5 5 6 / 5 1 S t S i d e ftxoi E a u a . T a r g e t + . 0 0 0 8 " II n n n n II II . 0 0 0 0 0 n II II n n n II n - . 0 0 1 1 It n II " II ft II " + . 0 0 0 3 + . 0 0 0 3 II H II H tl II " 3 2 / 1 2 n a S i d e L S s a c i i m A c t u a l + . 0 0 0 9 + . 0 0 1 0 + . 0 0 0 8 + . 0 0 0 9 2 5 + . 0 0 0 8 2 5 + . 0 0 0 7 5 + . 0 0 0 9 7 5 + . 0 0 0 8 2 5 + . 0 0 1 0 - . 0 0 0 0 2 5 JXXXX . 0 0 0 0 0 - . 0 0 0 0 5 — 0 0 0 0 7 5 . 0 0 0 0 0 - . 0 0 1 . - . 0 0 0 1 2 5 + . 0 0 0 1 - . 0 0 1 3 - . 0 0 1 2 - . 0 0 1 0 5 - . 0 0 1 1 7 5 - . 0 0 1 1 5 — 0 0 1 0 5 — 0 0 1 0 5 - . 0 0 1 2 7 5 - . 0 0 1 1 2 5 + . 0 0 0 3 5 + . 0 0 0 2 + . 0 0 0 3 + . 0 0 0 2 7 5 + . 0 0 0 3 + . 0 0 0 2 7 5 + . 0 0 0 5 5 + . 0 0 0 5 + . 0 0 0 3 T a r g e t

u

i

pi S A c t u a l - . 0 0 0 2 5 - . 0 0 0 2 7 5 + . 0 0 0 1 2 5 - . 0 0 0 1 7 5 . 0 0 0 0 0 - . 0 0 0 0 5 - . 0 0 0 1 5 - . 0 0 0 1 . 0 0 0 0 0 - . 0 0 0 0 7 5 + . 0 0 0 0 2 5 + . 0 0 0 0 7 5 - . 0 0 0 0 2 5 , 0 0 0 0 0 + . 0 0 0 1 5 . 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 1 + . 0 0 0 1 5 + . 0 0 0 1 5 , 0 0 0 0 0 + . 0 0 0 1 5 + . 0 0 0 1 0 + . 0 0 0 1 + . 0 0 0 1 - . 0 0 0 1 5 + .0001 - . 0 0 0 0 7 5 - . 0 0 0 0 2 5 + . 0 0 0 0 2 5 + . 0 0 0 0 2 5 . 0 0 0 0 0 , 0 0 0 0 0 . 0 0 0 0 0 + . 0 0 0 0 7 5 - . 0 0 0 1 I S . 1 5 5 6 / 5 3 2 / 2 l B + Ri^« T a r e e t + . 0 0 0 5 . 0 0 0 0 0 " M " 11 n II A c t u a l + . 0 0 0 5 + . 0 0 0 1 - . 0 0 0 1 + . 0 0 0 1 5 + . 0 0 0 2 . 0 0 0 0 0 + . 0 0 0 0 5 + . 0 0 0 0 5 . 0 0 0 0 0 - . 0 0 0 8 - . 0 0 0 7 5 . 0 0 0 0 0 II II " II " " " - , 0 0 1 1 , 0 0 0 0 0 II II " II II " " + . 0 0 1 4 . 0 0 0 0 0 . " II II II " II II - . 0 0 0 0 5 + .0001 - . 0 0 0 1 - . 0 0 0 0 2 5 - . 0 0 0 1 7 5 - . 0 0 0 1 7 5 . 0 0 0 0 0 - . 0 0 0 0 2 5 - . 0 0 1 3 5 , 0 0 0 0 0 - , 0 0 0 0 7 5 + , 0 0 0 1 2 5 - . 0 0 0 0 5 - . 0 0 0 0 5 - . 0 0 0 0 5 + . 0 0 0 0 5 - . 0 0 0 0 2 5 + , 0 0 1 2 2 5 . + . 0 0 0 0 2 5 + . 0 0 0 1 7 5 - . 0 0 0 1 . 0 0 0 0 0 - . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 0 2 5 + . 0 0 0 1 5 T a r g e t É É

g

%\ A c t u a l - . 0 0 0 1 5 + . 0 0 0 0 5 + . 0 0 0 1 - . 0 0 0 1 5 - . 0 0 0 1 - , 0 0 0 0 5 , 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 0 5 - . 0 0 0 1 .C-J-JOO + . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 0 5 . 0 0 0 0 0 + . 0 0 0 1 + . 0 0 0 1 - . 0 0 0 0 5 + . 0 0 0 1 + , 0 0 0 0 5 + . 0 0 0 0 5 + . 0 0 0 0 2 5 + . 0 0 0 0 5 + . 0 0 0 0 5 + . 0 0 0 0 2 5 . 0 0 0 0 0 - . 0 0 0 0 2 5 . 0 0 0 0 0 + . 0 0 0 0 2 5 + . 0 0 0 0 2 5 - . 0 0 0 1 2 5 . 0 0 0 0 0 . 0 0 0 0 0 . 0 0 0 0 0 - . 0 0 0 0 5 . 0 0 0 0 0 1 »-T

HIOTOGRmiS

General view of the test rig

General view of the test gears

General view of the slave gears

The capacity piok-vtp

Strain gauge beam attached to a gear tooth

The position of tho lead zirconate crystsils

The general view of the Error-Measuring Equipment

The Error-Measuring Equipm.ent with the Magna Gavige in position

The Error-Measuring device with clock gauge in position

The rig showing the loading coupling, etc,

PHOTOGRAPH NO. I.

PHOTOGRAPH SHOWING GENERAL VIEW OF THE GEAR TEST RIG.

PHOTOGRAPH NO. 2 .

PHOTOGRAPH SHOWING GENERAL VIEW OF TEST GEARS (MODIFIED PROFILE.)

PHOTOGRAPH NO. 3.

GENERAL VIEW OF HELICAL SLAVE GEARS WITH

ONE LOADING COUPLING IN P O S I T I O N . PHOTOGRAPH N O - 4 . PHOTOGRAPH SHOWING CAPACITY

PHOTOGRAPH NO. 5.

PHOTOGRAPH SHOWING STRAIN GAUGE BEAM ATTACHED TO GEAR TOOTH

PHOTOGRAPH N O - 6 .

PHOTOGRAPH SHOWING POSITION OF LEAD

PHOTOGRAPH NO. 7.

PHOTOGRAPH SHOWING GENERAL VIEW OF THE

' E R R O R MEASURING EQUIPMENT*

PHOTOGRAPH NO. 8 .

PHOTOGRAPH OF THE ' E R R O R MEASURING DEVICE

PHOTOGRAPH NO. 9.

PHOTOGRAPH OF THE ERROR MEASURING DEVICE* WITH CLOCK GAUGE IN POSITION

PHOTOGRAPH NO. lO.

PHOTOGRAPH OF RIG SHOWING LOADING COUPLING, PHOTO CELL AND DISC FOR MEASURING SPEED, AND RECORDER

PHOTOGRAPH NO. I I .

PHOTOGRAPH SHOWING PHOTO-ELECTRIC TRANSDUCERS FOR SHAFT-SPEED AND TRIGGERING SIGNAL.

I2;CT5EJ

1 . Diagrajamatic Arrangem-int of Test E i g 2 . Typical Bearing Arfangeraent

3 . Block diagram of 1 s t E l e c t r o n i c Tincr for Goat Test Rig 4 . Block diagz'am of 2nd E l e c t r o n i c Tinier for Gear Test Rig 5 . C i r c u i t diagram of i s t E l e c t r o n i c Timer

6 . Ciitjuit diagram of 2nd E l e c t r o n i c Timer 7 . Capacity Pick up

8 . P r i n c i p l e of the Capacity S l i p Ring 9. P r i n c i p l e of the Grid-dip system

10, Block diagram showing instrumentation en^iloyed on tlie gpar r i g 11 >- 29 i n c l . Test R e s u l t s

( i ) Specimen r e s u l t s using the Capaci-ty Pick-Up and the Grid-dip O s c i l l a t o r

( i i ) Specimen r e s u l t s using tho Capacity Pick-Up and the Capaci-ty Transmitter

( i i i ) Spociinen r e s i i l t s using the Lead Zirconate C r y s t a l and the Mercury S l i p Ring, ( C r y s t a l cemented t o the side of t o o t h ) .

I n a l l the abo\ro t e s t s the follovidng conditions T/ore s t a n d a r d i s e d . O i l C a s t r o l Hypoy 90

O i l tomperatuTG éO C,

O i l pressiire 30 Xbs/sq.inoh Oil flow 22 gallons/hour 30 - 37 i n c l . Maag P r o f i l e Diagrams f o r the t e s t gears

I '

( ! )

STRAN GAUGE

PLATE. DOUBLE ROW CYLINDRICAL

ROLLER BEARING. SINGLE ROW DEEP GROOVE _{BALL BEARING.}

TORSIOGRAPH COUPLING DISTANCE PIECES.

SYN PULSE PULSE SHAPER I 2 0 m sec. DELAY GATE ^ RESET SIGNAL GAS TRIODES VARIABLE DELAY PULSE SHAPER

+

~ 1

TRIGGER

FIG. 3 . DIAGRAM OF 1st ELECTRONIC TIMER FOR THE GEAR TEST R I G . 24 VOLT PULSE _njuT-1 I I _njuT-1 M _njuT-1 PHOTO CELL GATE

Y

INVERTING STAGE A MONO-STABLE ECCLES JORDAN WITH VARIABLE DELAY AMPLIFIER AND PULSE SHAPER TRIGGER

+ 300

+ 24V«- - l O O

V | V j V 2 V3 V 7 V4 V 5 ECC.8I. 6F.33. EF. 91. GTE. I75.M.

RELAY • Y =

CAMERA

F I 6 . 5. CIRCUIT DIAGRAM OF 1st ELECTRONIC TIMER +

— • A

Vi

EF80 >56K

V2

EF80 gECCfll 2ECC8I

• I M F 56K 270K • 01 MF >33K I MEG

} r >

i

IMEG ^ • I M F 6DS

u-.^

28K > 50K 5K Bleeder Rciistor iO Watts approx v47Kn. - • 1 0 0 - V V| V2 EF a o V3 ECC8I V4 EF9I Output *

FIG. 6. CIRCUIT DIAGRAM OF 2nd ELECTRONIC TIMER

CAPACITY PLATE FIXED TO GEAR TOOTH,

TUFNOL INSULATING SLEEVE INSTRUMENTATION RING. PYC. DIAPHRAGM MICA STRIP

FIG. 7. CAPACITY PICK - UR

CLEARANCE BETWEEN REVOLVING DISC S FIXED ENVELOPE OF THE ORDER

o - o o s " - oio" INSULATOR^ SIGNAL ^ r^ FROM — • - V ^ PICK-UP

£

REVOLVING SHAFT DISC FIXED TO REVOLVING SHAFT

y

/•^ F M . SYSTEM OSCILLOSCOPE FIXED ENVELOPE

RING-STATIC ROTATING c n i D MP OSCILLATOR :— — 1

s e

S B

ff ^

^ AMPLIFIER

k 4

O

OSCILLOSCOPE

FIG. 9. GRID DIP SYSTEM FOR MEASURING CHANGES OF CARACtTY

SLIP f RING - _{0 9} PULSE SHAPER OSCILLATOR PHOTO ELECTRIC CELLS

>4> SIGNAL FROM CRYSTAL

TIMING PULSE SPEED CATHODE FOLLOWER DOWTY COUNTER PHOTO TIMER ELECTRONIC ^ ^ " DOUBLE BEAM OSCILLOSCOPe •DIFFERENTIAL AMPLIFIERS

TT

CAMERA 2 4 VOLTS

FIG. lO. BLOCK DIAGRAM SHOWING INSTRUMENTATION EMPLOYED ON GEAR RIG.

RESULTS OF TESTS USING THE CAPACITY P I C K - U P AND THE GRID - DIP OSCILLATOR GAIN X 10

T^

CAPACITY SIGNAl

SPEED 732 P.RM. SPEED 812 R.RM.

TESTS UilNG THE CAPAOTY PICK-UP AND THE CAPACITY TftANSMITT EB

GAIN (XISS) _{GAIN [ x 155)}

CAPAOTY SIGNAL

SPEED e i s RPM

CAPAaTY SGNAL SPEED 1 0 0 0 RPM.

FIG. 12. LOAD 7SOLBS / INCH FACE WIDTH

SPEED 1 2 0 0 R.BM. SPEED 1574 RP.M

GAIN (x I55j _{GAIN (XISS)}

SPEED 1765 R.PM. SPEED 2 0 0 e P.PK

FIG. 14. LOAD 7 5 0 LBS. / INCH FACE WIDTH

SPEED 2 3 0 2 PPM. SPEED 2601 R R M .

GAIN (XISS) GAIN (x IS5]

( 1

SPEED 2905 RJ>M SPEED 3759 nP.M. SPEED 4 0 0 0 RRM.

TESTS USING LEAD ZIRCONATE CRYSTAL CEMENTED TO SIDE OF TOOTH AND SIGNAL TRANSMITTED ETC MEANS OF A MERCURY SLIP -RING

UDAD 3 , 0 0 0 LBS / INCH FACE WIDTH

1

1 .^

^ %««

1?

- ^ I

1^

«

ui y ^

M i l f\ \

i

J

V

V-i j

f

• ' • : J

J

; 1 ^ ^ • ^

X

^ ^

a

• ^

SPEED B U R.PM. LOAD 3 , 0 0 0 L B S / I N C H FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X 5 TIME BASE 5 MILLISEC/CNIS

SPEED I0O2 R.PM. LOAD 3,0OO LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X S TIME BASE S MILLISEC /CMS

FIG. 16

SPEED IS40 RRM LOAD 3 , 0 0 0 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CM5 HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 5 MIL.YSEC/CMS

k—H

H ^

^ ^ « ^

-T

t\

I

J

j^

1

1

':

J

: '• %

\i

\

L^

J

Jl

"-*" ^

Ul

• — —

SPEED 2 0 0 0 RPM. LOAD 3 , 0 0 0 LBS/ INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 5 MIULISEC/CMS

y^lft

^4^fWrgtf

'm

1

ijtjt

$ • «NtX ^ " p *

1 •,

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f^ _^ k

M

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A/

j / ^

ƒ :

A

4

• : . \

_J

" "

•

-\ - . - ^ ^ ^ w '

J

^ K ^

SPEED 2529 R.BM. LOAD 3 , 0 0 0 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CMS SPEED 3499 RRM, LOAD 3 , 0 0 0 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 5 MILUSEC /CMS HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 2 MILUSEC/CMS

\ ^^ r * * N ^

r--J

\ A \ _ i

w

J"l

:

"V/

_{V ;} f

r

r-^ ^

v

k j

_"U

r-\

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1 < - *

SPEED 3 0 I 0 RRM. LOAD 3 . 0 0 0 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT /CMS HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 2 MILUSEC/CMS

SPEED 4 0 4 0 R.P.M. LOAD 3,000 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X 10 TIME BASE 2 MIUISEC/CMS

^ r^ r\. e^ H L - ^ ^

. \^ y \ j J ^ ^ p U ^ U ^

- -^•^-r

1

'A

• •-• mmm^ * * * *

SPEED 4S24 R.P.M. LOAD 3 , 0 0 0 LBS / INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIFICATION X lO TIME BASE 2 MILLISEC /CMS

> i \ ^/»A "\ /

V

wA

> (

AJ

n

f\ 1

\J

i

J

' ^

'vi

J

r \ /

AJ

\ i 11

T

u

V ,

VJ

r ^ ,_ /

vi

'T^ \ t

\J

' V ^ ^ / \ - , ' *tr^

SPEED SOOO R.RM. LOAD 3 , 0 0 0 LBS/INCH FACE WIDTH. SENSITIVITY I VOLT/CMS HORIZONTAL SWEEP MAGNIRCATION X lO TIME BASE 2 MIUISEC/CMS

FIG 2 2

TESTS USING LEAD ZIRCONATE CRYSTAL CEMENTED TO SIDE OF TOOTH AND SIGNAL TRANSMITTED BY MEANS OF A MERCURY S L I P - R I N G

LOAD 1 5 0 0 LBS/INCH FACE WIDTH

^ALF LOAD)

SPEED 7 6 4 ( I B M . LOAD I S O O LBS/INCH FACE WIDTH SENSITIVITY 2 VCuTS/CMS HORIZONTAL SWEEP MAGNIFICATION X S TIME BASE 5 MILLISEC / CMS

^t^t;f'Crü^:?'::nnrV^

t t I I ; I I

SPEED I 0 0 2 H.fiM. LOAD ISOO LBS/INCH FACE WIDTH, SENSITIVITY 2 VOLTS/CMS HORIZONTAL SWEEP MAGNIFICATION X 10 TIME BASE lO MILuiSEC/CMS

\\^,:^xx^::];^:t^X

• < t < 1 ; < t < t

I -4 t « 4 M «

^^^^^^v^4

rtt^F

SPEED IS20RBM. UOAD ISOO LBS / INCH FACE WIDTH. SENSITIVITY 2 VOLTS/CMS HORIZONTAL SWEEP MAGNIRCATION X IO TIME BASE IO MILUSEC /CMS

•> r^ n ^ n "> y.

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