123-44-Example of a Gear Design

8/6/2019 123-44-Example of a Gear Design

1/8

NASA AVSCOMTechnical Memorandum 101457 Technical Report 88-C-033

Wear Consideration ih Gear Designfor Space Applications

--- - - -( E A S A - I M - 70 1 4 5 7 )L E S l G h FCfi S P E C k E E F L Z C A T I C B S (AASd) 8 PY E A K C O B S J C E C A 3 X C # IN GEAB t i89- 154 14CSCL 131

Unclas63/37 0 18792 1

Lee S. AkinCalifornia State UniversityLong Beach, Californiaand

Dennis P. TownsendLewis Research CenterCleveland, Ohio

Prepared for theFifth International Power Transmission and Gearhg Conferencesponsored by the American Society af Mechanical EngineersChicago, Illinois, April 25-27, 1989

US ARMAVlATlOSYSTEMS COMMANDAVIATION R6T ACTIVITY


2/8

WEAR CONSIDERATION I N G EAR DESIGN FOR SPACE APPLICATIONSLe e S. A k i nC a l i f o r n i a S t a te U n i v e r s i t yL o ng B ea ch , C a l i f o r n i a 9 08 1 5

andDenn i s P . TownsendN a t i o n a l A e r o n a u t ic s a nd Spa ce A d m i n i s t r a t i o nLewis Res earc h Cente rC l e v e l a n d , O h i o 4 41 35

ABSTRACT. A p r o ce d u r e i s d e s c r i b e d t h a t was d e v e l o p e d fore v a l u a t i n g t h e wea r i n a s e t o f g e a r s i n me sh u n d e rh i g h l o a d a n d low r o t a t i o n a l s pe ed . T he m e th o d c a n b eused f o r a ny lo w- sp ee d g e a r a p p l i c a t i o n , w i t h n e a r l yn e g l i g i b l e o i l f l l m t h i c k n e s s , a n d 1 s e s p e c i a l l y u s e fu li n s p ac e s t e p p i n g m e ch an is m a p p l i c a t i o n s w he re d e t e r m i -n a t i o n o f p o i n t i n g e r r o r due to w ea r i s i m p o r t a n t , s uc has i n l o n g l i f e s e ns or a nt en na d r i v e s.A m e th o d i s d e v e l o p e d for t o t a l w ear d e p th a t t h e

w i t h t h e s l i d e t o r o l l r a t i o V s / V r . A method i s a l s ot r a n s m i ss i o n e r r o r a l s o kno wn as p o i n t i n g e r r o r o f agear mesh.

ends of t h e l i n e o f a c t i o n u s i n g a v e r y s im p le f o r m u l ad e v e lo p e d t h a t u s es t h e w ea r r e s u l t s t o c a l c u l a t e t h e

INTRODUCTIONG ea rs u se d i n sp ac e a p p l i c a t i o n s a r e u s u a l l yt h o u g h t o f a s " in s t r u m e n t g e a r s" w i t h n e g l i g i b l e l o a dt h a t m u s t m a i n t a i n p o s i t i o n a c c u ra c y th r o u gh o u t t h e i ro p e r a t i o n a l l i f e o r a s d e p l o y m e n t l a c t u a t o r g e a rs t h a tmay h av e i n e r t i a l l o a d s b u t a v e r y low number o f d u t yc y c l e s .

power dr ives are emerging on the space mechanisms schemes uc h as d r i v e s f o r w ea th er s a t e l l i t e s w h ere p o i n t i n ga c c u r a c y ( a s i n i n s t r u m e n t s ) a s w e l l a s s u b s t a n t i a li n e r t i a l l o a d a r e i mp ose d d ue t o momentum compensateda n t e n n a s . T h i s t y p e of d r i v e may a l s o ha v e a c o n t i n u o u sd u t y c y c l e f o r up t o 1 0 y e a r s . S uc h d r i v e s c a n n o t b ec o r r e c t e d b y u s e of a n t i - b a c k l a s h d e v i c e s b e c a u s e t h i sc o n t r i b u t e s t o more wear as a r e s u l t o f t h e a d d i t i o n a la n t i - b a c k l a s h d e v i c e l o a d i n g s p r i n g s . Also " p o s i t i o na c cu r ac y " i s n o t c o r r e c t e d b y su ch d e v ic e s t h a t a r es t i l l s u bj ec te d t o s ev ere wear .m i z e wear e f f ec t s due t o g e a r r a t i o a nd p r o v i d e a dd end umm o d i f i c a t i o n t h a t w i l l m i n i m i z e th e t o o t h w ea r r a t e .Th i s paper des c r i bes a method t ha t has been dev e lopedf o r a n a l y z i n g t h e t o t a l g ea r t o o t h wear a n d i t s e f f e c to n p o i n t i n g a c c u ra c y . The r e s u l t s c an a l s o be u se d t oa n a l yz e t h e r e s u l t i n g e f f e c t o n ge a r dy na mi c l o a d i n g .

M o r e a n d m o r e f r e q u e n t l y t h e c o m b i n e d i n s t r u m e n t /

A g e a r a r r a n g e m e n t m u s t b e d e v i s e d t h a t w i l l m i n i -

APPROACH TO SOLUTIONB e f o re d e s c r i b i n g a d e t a i l e d a n a l y t i c a l a p pr oa ch ,i t i s n e c e s s a r y t o u n d e r s t a n d t h e b a c kg r o u n d a s su m p t io na nd a n a l y s i s c o n d i t i o n s assum ed . F i r s t o f a l l t h er e art h r e e l u b r i c a t i o n s r e gi m es ( P e t e r so n . 1 9 80 ) i n g e a re dd r i v e s : ( 1 ) B ou nd ar y ( a l l a s p e r i t y c o n t a c t - n o f i l m ) ,( 2 ) m i xe d , an d ( 3 ) f u l l f i l m ( n o a s p e r i t y c o n t a c t ) .T h i s p a p e r w i l l d e a l w i t h w ea r i n t h e bo u n da r y l u b r i c a -t i o n re g im e o n l y . Wear i n t h e f u l l f i l m l u b r i c a t i o nr eg im e i s n e g l i g i b l e .Second I t i s p re su me d t h a t p e o p l e d e s i g n i n g g e a r sfo r s p a c e a p p l i c a t i o n s w i l l hav e a gear des ign c omputerp r o g ra m f r o m w h i c h p a ra m e t e rs c a n be p u l l e d fo r u se i nt h e a n a l y s i s p r e se n t e d h e r e i n . T h i s sa ve s c o n s i d e r a b l et i m e a n d a l l o w s u s e o f t h e s i m p l i f i e d m et ho d p r e s e n t e da t t h e e nd o f t h i s p ap e r.

A k i n , 1 9 7 3 ) i s t o c o n s i d e r t h a t we ar c a n c o n s i s t o f oneo r m ore o f t h e f o l l o w i n g m o d e s ( 1 ) l o w s p e e d l u b r i c a t e dw ea r, ( 2 ) p i t t i n g i n i t i a t e d w ea r, ( 3 ) a b r a s lv e w ea r,and ( 4 ) s c u f f i n g o r s c o r i n g t h a t my e v e n t u a l l y l e a d t os e i z u r e . O n l y l u b r i c a t e d l o w s pe e d a d h e s i v e w ea r i sc o n s i d e r ed i n t h i s pa p e r . The s e c t i o n s t o fo l low p r o -v i d e a q u a n t i t a t i v e a n a l y s i s o f low speed adhes ive weari n g e a r s . A l t h o u g h s p u r g e a r s a r e u s ed h e r e a s t h ee xa m pl e c a s e, t h e m e t ho d p r e s e n t e d w o u l d be a p p l i c a b l et o o t h e r t y p e s o f g e a r s .

T h e c o n v e n t i o n a l a p p r o a c h t o wear (D ud ley , 1962 an

DEVELOPMENT OF T H E THEORYThe b o u nd a ry l u b r i c a t i o n re g im e i s d e f i n e d q u a n t i -t a t i v e l y as g e a rs o p e r a t i n g a t a spe ed an d l u b r i c a n t

v i s c o s i t y s uch t h a t t h e l am bd a r a t i o ( A ) i s l e s s t h a n0 . 4 ( 0 < X 5 0.4 ) where :L u b r i c a n t EHD f i l m t h i c k n e s sC o m po s it e A s p e r i t a l RMS h e i g h t=

T h i s a l l o w si t e r a c t o nReal i zi s due t o sF i g . 1 , t h e

( 1t h e a ss u mp t io n t h a t s u b s t a n t i a l a s p e r i t ye x i s t s as i t h e c a s e .n g t h a t t h e s u b s t a n c e of we ar i n ge a r a c t i oi d i n g a lo n g t h e l i n e o f a c t i o n , as shown i ns l i d e - t o - r o 1 r a t i o ( a l s o known a s s p e c i f i c

1


3/8

s l i d i n g ) a nd t h e c om p re s si v e s t r e s s m u st be c a l c u l a t e d .The ne ces sary formul as may be found i n Gay (1970) ando t h e r r e f e r e n c e s . t o d e t er m i ne t h e s l i d i n g d is t a n c e p e rp as s a t a ny p o i n t o n th e t o o t h p r o f i l e .wear equa t i on (Rab inow icz , 1965) w i l l be used to c a l c u -l a t e d e p t h w e a r ( h ) a s f o l l o w sThe Archard

KWNXh = -3PAa where

The H e r t z i a n b a nd of c o n t a c t ( b ) m a y b e d e t e r m i n e dby the me thod o f Dudley (1954 or 1984) :

whereK w ea r c o e f f i c i e n t ( d im e n s i o n l e s s )WNX t o t a l s l i d i n g d is ta nc e ( f o r t o t a l l i f e )pAT h e w e a r c o e f f i c i e n t ( K ) i s d e t e r m i n e d e x p e r i m e n t a l l yb u t u s u a l l y f a l l s w i t h i n t h e ra ng e of 3 ~ 1 0 - ~o6 . 7 ~ 1 0 - 5 for l u b r i c a t e d ge a r s an d as h i g h a s 1 . 7 ~ 1 0 - 3for c l e a n u n l u b r i c a t e d s u r f ac e s ( P e t e r s o n , 1 98 0) i n a ne a r t h e n v i r o n m e n t .t h e a p p l i e d t o r q u e ( T I a s f o l l o w s

l o a d no rm al t o t h e t o o t h ( a l o n g l i n e o f a c t i o n )

f low p r e s s u r e o f s u b s t r a t e ( h a r d n e s s )a p p a r e n t a r e a o f c o n t a c t ( H e r t z i a n a r ea )

The normal load WN i s u s u a l l y c a l c u l a t e d f r om

T Tw _ - - -N - R b - R co s @where

( 3 )

RbR p i t c h r a d i u s4 p r e s s u r e a n g le ( t r a n s v e r s e )

D e t e r m i n a t i o n o f t h e t o t a l s l i d i n g d i s t an c e ( x )p a s t a s p e c i f i c p o i n t o f c o n t a c t i s t h e mo st i m p o r t a ntc a l c u l a t i o n t o be made. I t can be de te rm ined as f o l l ows

i s t h e i n v o l u t e base c i r c l e r a d iu s

x = V bC5 s Ywhere( 4 )

V s s s l i d e - to - r o l l r a t i o = V s / V r d e t e r m i n e d a t t h e e n d

V sV r wp = r o l l i n g v e l o c i t yp R s i n $ 1 = r a d iu s o f c u r va t ur e a t p o i n t iw r o t a t i o n a l v e l o c i t y , r a d /s e c

o f a c t i o n w he re i t i s a maximumV r 1 - Vr2 = s l i d i n g v e l o c i t y

$i p r e ss u r e a n g le a t i n s ta n t an e o u s p o i n t o f c o n t a c t ib w i d t h o f H e r t z i a n b an d o f c o n t a c tCy t o t a l number o f c o n t a c t c yc l e s ( l i f e )The s l i d e - t o - r o l l r a t i o V s s may be determined frome q ua t io n s i n K h i r a l l a ( 1 97 6) or from a Gear DesignComputer program.

P Pp = = r e l a t i v e r a d i u s of c u r v a t u r epP + p9F = f a c e w i d t h g e arE' =- nd when El = E2 : E ' - E/ 2

E 1 + E2v = P o i s s o n ' s r a t i o

The c o n t a c t c o m p r e s s iv e s t r e s s c a n b e us e d t o c a l c u -l a t e b as f o l l o w s :3.63 Scp

Eb = , (for s t e e l g e ar s o n l y ) (6)where

0.35 WNE' 1/2Fp 1 = c o m p r e s s i v e s t r e s s ( A G MA . 1982)=C

The f l o w p r e s s u r e o r hardness can be app rox ima ted by :p = 1500 BH(ps i )

whereBH B r i n e l l ha rdness number

Then the apparen t a rea o f c o n t a c t c a n b e c a l c u l a t e d from(7)

where: F = g e a r f a c e w i d t h , i n c o m bi n i n g E qs . ( 2 ) . ( 4 ) ,a nd ( 7 ) . t h e w e ar f o r m u l a c a n b e p r e s e n t e d as :

A = b F = H e r z ia n c o n t a c t a r e a

KWN(VSSbC )3PbF

so t h a t t h e b ' s c an b e c a n c e l l e d=r e s u l t i n g i n t h e f o rm ul a:

K W N V ~ s C y3PF= (8)p r o v i d i n g a v e r y s i m p le f o r m u l a w i t h o n l y o n v a r i a b l e( V s s ) a s a f u n c t i o n o f p o s i t i o n on t h e l i n e o f a c t i o n .c a l c u l a t e t h e V s s v a l ue s a t t h e e xt re m e p o s i t i o n s o nt h e l i n e o f a c t i o n a s s hown i n T a b le I . The normal

I n p r a c t i c e a g e a r c o mp u te r p r o g ra m may b e us e d t o

2


4/8

wear on t he p i n i o n mus t be added t o t h e w e a r o n t h egear t o o b t a i n t h e t o t a l w ea r a t a s p e c i f i c p o i n t ont h e l i n e o f a c t i o n .Thus , i f we obs erv e i n Eq. (8) h a t t h e g r o u p e dparameter s-F form a c o n s t a n t for a g i v e n g e a r s e t a nd t h a tt h e t o t a l w e a r c a n b e f o r m u l a t e d a s :

KWNIh l h p l + h g l = 3pF ( V s s l C y l + Vss2Cy2)

F u r t h e r , t h e co n t a c t c y c l e s fo r t h e p i n i o n c a n bec a l c u l a t e d f r o m :

cy1 = "g cy2wheremg g e a r r a t i o . T hu s:

K W N C 2E h l = -g# (m g V s s p l + Vssgl)l a t OD of gear , and

( 9 )

Eh5 =&W NC 2 (m g V S s p 2 + V s s 9 2 ) 5 a t OD o f p i n i o n .The task now i s t o b a l a n ce t h e w e ar a t t h e e x tr e meends o f t h e l i n e o f a c t i o n ( se e F i g . 2 ) so t h a tEh l = Ehg.addendum o f t h e p i n i o n a nd g e a r o n s t a n d a r d c e n t e r s .Thus Aap = -h ag i s a d j u s t e d u n t i l :

T h i s c a n b e a c c o m p l i s h e d b y a d j u s t i n g t h e

E V 1 = ( m gV ssp1+ vs sg l ) l= (mgVSsp2+ vssg2)5= Ev5 (10)fo r t h e o p p o s i t e e n d s o f t h e l i n e o f a c t i o n w he reAap a dd en du m m o d i f i c a t i o n o n p i n i o n = ANp/2PdAag addendum mo d i f i c a t i on on gear = ANg/2PdA N p , g v i r t u a l c ha ng e i n num ber of t e e t hp d d i a m e t r a l p i t c hwould be ANp an d ANg a n d t h e o u t s i d e d i a m e t e rs doan d Do c a l c u l a t e d from

T h e r e f o r e , t h e o n l y s p e c i a l d a t a ne ed ed f o r i n p u t s

N + 2 + A N'dd = *0

an dN + 2 - A N b o t h o n s t a n d a rd c e n t e r s .D o = 'd

F i n a l l y , a s a n e n d r e s u l t t h e d e s i g n e r w o u l d w a n tt o kno w t h e c ha ng e i n p o i n t i n g a c cu r a cy a s a r e s u l t o fw e a r. T h i s c a n b e c a l c u l a t e d f rom:Eh,

or18 0 Chl

nRbel =- egrees , ande5 =-h5 r a dRb

or180 Lh5- egrees , so t h a t b y d e s i g nnRb5

( 1 2

( 1 3

e l e 5I f Eq. (10) i s n o t t r u e , t h e a dde ndu m m o d i f i c a t i o n sAap = -Aag a r e i t e r a t e d u n t i l E q. (10) i s t r ue w i t h i na n a c c e p t a b l e t o l e r a n c e ( s a y 1 p e r c e n t ) .A SPECIFIC EXAMPLEL e tD i a m e t r a l P i t c h Pd I 48Number of t e e th i n p i n i o nP r e s s u r e a n g l e 41 = 20"Number o f t e e th i n g ea r Ng = 120Gear bas e r ad iusG e a r r a t i o = 5A dd en du m m o d i f i c a t i o nO u t s i d e d i a m e t e r o f p i n i o nO u t s i d e d i a m e t e r o f gear Do = 2.54166The r e s u l t s o f t h e se i n p u t s t o a gear computer programp r o v i d e d t h e o u t p u t s hown i n T a b l e 1 . T h e u n d e r l i n e do u t p u t v a lu e s V s s l a nd V ss 2 a r e s u b s t i t u t e d i n t oE q. ( 1 0 ) a s f o l l o w s

Np = 24

Rb = 1.1746

A Np = -ANg = 0do = 0.54166

E V 1 = (51-2.47011 + 0.7118)1 # ( 5x .4386+ 1-0.78141)5 = EV5 13 .0623 12 .9 74 4

a c o n s i d e r a b l e m i sm a tc h r e s u l t s h e r e . The p o i n t i n ge r r o r s d ue t o we ar t h a t r e s u l t h e r e wo u ld b e (fromEas . ( 12) and ( 13) ) : KW C1l = Zhl/Rb wh ere Ehl 3 3PF

5 ~ 1 0 - ~1 1 . 1 2 5 ) 1 2 . 6 ~ 1 0 - ~ 13.0623 o.024913 x 980 250 x 0.125hl =e, = 0.02491/1 .1746 = 0.0212 rad . o r 1.2"

KW Ce5 = Eh5/Rb where h5 -e V 5 0.005671e5 = 0.005671/1.1746 = 0 . 0 0 4 8 r a d . or 0.28Or a d ( 1 1 )el 3

3


5/8

a l s o t h e t o p l a n d of t he p in io n wou ld have been reducedwou ld have been reduced by wear 0 .0236 i n . (66 pe rc en t )o f t h e t o o t h t h ic k n es s . A f t e r s e ve r a l i t e r a t i o n s t hefrom 0 . 01 4 4 t o 0. 01 0 9 a nd w or se t h e p i n i o n root (LPC)

f i n a l d e si gn r e s u l t e d . L e t :Np = 24, Ng = 120, ANp = 0.96, ANg = -0 .96O u t s i d e d i a m e t e r o f p i n i o n do = 0.561666O u t s i d e d i a m et e r o f g e a r Do = 2.521666

The c o m pu te r o u t p u t i s sho wn i n T a b l e 11. Theu n d e r l i n ed o u t p u t v a lu e s a r e s u b s t i t u t e d i n t o Eq. ( 10 )as fol lowsE V 1 = (51-0.67251 + 0.4021) Z (5x.5332

+ 1-1.14221)2 = LV5 3.7646 z 3 .8 08 2 w i t h i n 1 p e r c e n t .A good match i s p r o v i d e d h e r e . T h e p o i n t i n ge r r o r s t h a t wo ul d r e s u l t a r e:

e l = 0 .00718 /1 .1746 = 0.00611 rad, or 0.350"e5 = 0 .00726 /1 .1746 = 0 . 0 61 8 r a d , o r 0 .3 5 4"

T h i s i s a s u b s ta n t ia l r e d uc t i on i n p o i n t i n t e r r o re l c au se d b y wear f r o m t h e o r i g i n a l s t a n d a r d g e arde s i n .I t s h o u l d be no t e d h e r e t h a t t h e a b ov e e r r o r s e land e5 ar e due t o w e a r o n l y a n d m u s t be added t o t h eo r i g i n a l b a s ic e r r o r due to b a c k l a s h a n d t o o t h - t o - t o o t hc o mp o si te e r r o r s t o g e t a t o t a l p o i n t i n g e r r o r a t t h eend o f l i f e a f t e r C y l and Cy2 c yc le s of t h e p i n i o na n d g e a r r e s p e c t i v e l y .The ge ar wear l i f e ca n be t he c r i t i c a l f a i l u r ec r i t e r i a . A s a n e x am p le . c o n s i d e r a n i n s t r u m e n t t h a t i sc o n s i d e r e d i n o p e r a b l e i f i t s p o i n t i n g e r r o r exce eds0.2". We w ould c a l c u l a t e i t s l i f e as f o l lo w s . L e t ' ssay t h e d es i r ed l i f e i s 1 5 000 00 0 c y c l e s ( C ) o v e rt h r e e y e a r s a nd we d e t e r m i n e t h a t a l l o w a b l e g a c k l a s h i sea = 0 . 2 " x n / 1 8 0 x Rbea = 0.00349 x 1.1746 = 0.0041 i n . a t wear o u t .

S u b t r a c t 0. 00 18 i n . for i n i t i a l b ac kl as h p l u st o o t h - t o - t o o t h c o m p os i t e e r r o r ( wh en n ew ) t o g e t0 .0 02 3 i n . a l l o w a b l e fo r wear. Us ing fo r mu la (9 ) we

d e t er m i n e t h a t c a l c u l a t e d w ea r d ep t h h o v e r 3 y e a r si s 0 . 04 9 i n . Thus t h e p r e d i c t e d w ea r l i f e w i l l be0.0023/0.0049 x 3 y e a r s = 1 . 4 y e a r s or 1 6 . 9 m n t h s .S i nc e t h i s i s l e s s t h a n i s d e s ir e d , a d e s i g n m o d i f i c a -t i on wou ld be necessa ry .I t s h o u l d a l s o b e n o t e d t h a t t h e c h o i c e o f geara r r an g e m en t c a n a l s o b e v e r y i m p o r t a n t i n m i n i m i z i n gg e ar d r i v e p o i n t i n g e r r o r . b u t t h i s i s be yo nd t h e sco peof t h i s p ap er .CLOSURE

The b a s i c t o o l s h av e b ee n p r o v i d e d i n t h i s p a pe rfo r t h e m i n f m i z a t i o n of p o i n t i n g e r r o r due t o weart h r o u g h m o d i f i c a t i o n of s t a n d a r d g e a r t o o t h g e o m e t r y ,a l s o an examp le has been p ro v id ed t o c l e a r l y i l l u s t r a t et h e u s e o f t he me thod .T h i s m e th od i s e a s i l y a d a pt ed t o o t h e r t y p e s o fg e ar s u s i n g t h e same p r i n c i p l e s . T h i s i s a f i r s ta t t em p t a t q u a n t i z a t i o n o f g e ar we ar an d e s p e c i a l l y i t se f f e ct o n g ea r l i f e i n ter ms o f a n a l l o w a b l e p o i n t i n gi n a c c u r a c y .REFERENCESAGMA, 1 98 2, " R a t i n g t h e P i t t i n g R e s is t a n c e an d B e nd i ngS t r e n g t h of S p ur a nd H e l i c a l I n v o l u t e Ge ar T ee t h, "Stan dard 218.01, Amer ican Gear Man ufa ctu rer sA s s o c i a t i o n , A l e x a n d r i a , V A .A k i n . L.S. , 1 9 7 3 . " EHD L u b r i c a n t F i l m T h i c k n e s sFormu las for Power Tran smi ss i on Gears." -ASME Paper73-LUB-21.Dud ley , D.W., 1962, Gear Handbook. McGraw H i l l , NewYork.Dud ley , D . W . , 1954 , P r a c t i c a l Gear Des iqn , McGraw H i l l ,New York.Dud ley , D . W . , 1984 , Handbook o f P r a c t i c a l Gear Des ign ,McGraw H i l l , New York.Gay, C . E . . 1970, How t o D e s i g n t o Min im ize Wear i nGears , Mach ine Des ign , Vol . 42 . No. 29, Nov. 26,

DD . 92-97.K h i r a i l a . T . W . , 1976, On th e Geometry o f E x t e r n a lI n v o l u t e S pu r G e ar s , T.W. K h i r a l l a , N o r t hH o l l y w o o d , C A .Pete rson , M.B. and Winer , W.O. , 1980, Wear ControlR a b i n o w i c z , E . , 1 96 5, F r i c t i o n a nd Wear o f M a t e r i a l s ,Handbook, ASME. New York.John Wi le y & Sons, New Yo rk.

4


6/8

TABLE I. COMPUTER PRINTOUT FO R SLIDING AND HERTZ STRESS A T 5 POINTS ON TH E TOOTHPROFILE

6.8217.8720.8521.8232.87

L o c a t i o n ont o o t h p r o f i l e( a )

1 .22 4 .23 - 3 .01 3 .01 50 808 -2 .4701 0 .711 83 . 2 0 3 . 8 4 - 0 . 6 4 0 . 6 4 57 094 - 0 . 2 0 0 5 0 . 1 6 7 03 . 7 3 3 . 7 3 -0.00 0.00 53 600 0.0000 0.00003 . 9 0 3 . 7 0 0 . 2 1 - 0 .2 1 52 646 0 .053 1 - 0 .0560

0 . 4 3 8 6 - 0 . 7 8 1 4. 8 8 3 . 3 0 2 . 5 8 - 2 . 58 2 6 2 0 6 ~~

R o l l i n g S l i d i n gv e l o c i t y , v e l o c i t y ,i n . / s i n . / sH e r t z i a n S p e c i f is l i d i n g r a t i o

aCode f o r l o c a t i o n s o n t o o th p r o f i l e :1 = S t a r t o f A c t i v e P r o f i l e (SAP)2 = L o w es t P o i n t o f S i n g l e T o o t h C o n t a c t (LP STC )3 = P i t c h p o i n t (P )4 = H i g h e s t P o i n t o f S i n g l e T o o t h C o n t a c t ( H P S T C )5 = End o f A c t i v e P r o f i l e (EAP)

TABLE 11. - COMPUTER PRINTOUT FOR SLIDING AND H E R T Z S T R E S S A T 5 POINTS ON T H E TOOTHCONTACT

L o c a t i o n o nt o o t h p r o fi e( a )

% od e f o r l o c a

Rolla n g l e ,c ,de g

13.3622.5320.852 8 . 3 637.53

R o l l i n gv e l o c i t y ,i n . / sV r 1

2.394 .033 . 7 35 . 0 76 .71

V r 24 . 0 03 . 6 73 . 7 33 . 4 63 . 1 3

on s o n t o o th p r o f i l e :

S 1 i i ngv e l o c i t y ,i n . / s

0 . 3 6 - 0 . 3 6-0.00 0.00

1.61 - 1 .613 . 5 8 - 3 . 5 8

1 = S t a r t o f A c t i v e P r o f i l e . (SAP)2 = L o w e s t P o i n t o f S i n g l e T o o t h C o n t a c t (L PS TC )3 = P i t c h p o i n t ( P )4 = H i g h e s t P o i n t o f S i n g l e T o o t h Co n t a ct (HPSTC)5 = End o f A c t i v e P r o f i l e ( EAP)

H e r t z i a ns t r e s s ,1 by n .

051 98844 85847 71016 479

s l i d i n g r a t i o

" s s l- 0 .6725

0.0892-0.0000

0 . 3 1 7 70.5332

0.4021-0 .09800.0000

- 0 .4657-1 .1422

5


7/8

\ISTANCE ILINE OF ACTION

FIGURE 1. - SLIDE DISTANCE ON LINE OF ACTION.

IA L I ION

FIGURE 2. - WEAR DEPTH ON LINE OF ACTION.

6


8/8

National Aeronautics and Report Documentation PageSpace AdministrationI - i t Accession No.' ' Report No' NASA TM-101457

17. Key Words (Suggested by Author(@)

I z. Laovernrnen

18. Distribution Statement

~ . - -~AVSCOM TR-88-C-033 I4. Title and Subtitle

Wear Consideration in Gear Design for Space Applications

Wear; Lubrication; Gears; Space; Transmission error

7. Author(@Lee S. Akin and Dennis P.Townsend

Unclassified-UnlimitedSubject Category 37

9. Performing Organization Name and Address

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pagesUnclassified Unclassified 8

NASA Lewis Research CenterCleveland, Ohio 44135-3191andPropulsion DirectorateU.S. Army Aviation Research and Technology Activity-AVSCOMCleveland, Ohio 44135-3127

12. Sponsoring Agency Nam e and AddressNational Aeronautics and Space AdministrationWashington, D.C. 20546-0001andU.S. Army Aviation Systems CommandSt. Louis, Mo. 63120-1798

22. Price'A02

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

8. Performing Organization Report No.E4532

10. Work Unit No.505-63-5 11L1622mA47A

11. Contract or Grant No.

13. Type of Report and Period CoveredTechnical Memorandum

14. Sponsoring Agency Code

15. Supplementary NotesPrepared for the Fifth International Power Transmission and Gearing Conference sponsored by the American Society ofMechanical Engineers, Chicago, Illinois, April 25-27, 1989. Lee S.Akin, California State University, Long Beach,California 90815 (work funded under Grant NAG3-20) and Dennis P. Townsend, NASA Lewis Research Center.

16. AbstractA procedure is described that was developed for evaluating the wear in a set of gears in mesh under high load andlow rotational speed. The method can be used for any low-speed gear application, with nearly negligible oil filmthickness, and is especially useful in space stepping mechanism applications where determination of pointing errordue to wear is important, such as in long life sensor antenna drives. A method is developed for total wear depthat the ends of the line of action using a very simple formula with the slide to roll ratio V,/V,. A method is alsodeveloped that uses the wear results to calculate the transmission error also known as pointing error of a gearmesh.

I I I'For sale by the National Technical Information Service, Springfield, Virginia 22161AS A FORM 1626 CCT 86

123-44-Example of a Gear Design

Documents

Transcript of 123-44-Example of a Gear Design