modal analysis of gear housing and mounts - nasa · modal analysis of gear housing and mounts teik...
TRANSCRIPT
I NASA Technical Memorandum 10 14-45
AVSCOM Technical Report 88-C-041
Modal Analysis of Gear Housing and Mounts
Unclas 63/37 C 1 S E E 3 9
Teik C. Lim and Raj. Singh The Ohio State University Columbus, Ohio
and
James J . Zakrajsek Lewis Research Center Cleveland, Ohio
Prepared for the Seventh International Modal Analysis Conference cosponsored by Union College and the Society for Experimental Mechanics, Inc. Las Vegas, Nevada, January 30-February 2, 1989
US ARM AVlATlO SYSTEMS COMMAND AVIATION RLT ACTIVITY
https://ntrs.nasa.gov/search.jsp?R=19890011873 2018-05-31T12:39:16+00:00Z
MODAL ANALYSIS OF GEAR HOUSING AND MOUNTS
T e i k C . L i m and R a j . S i n g h Depar tment o f Mechan ica l E n g i n e e r i n g
The O h i o S t a t e U n i v e r s i t y Columbus, O h i o 43216
and
James J . Z a k r a j s e k N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n
Lewis Research C e n t e r C l e v e l a n d , O h i o 44135
ABSTRACT
Dynamic f i n i t e e lement a n a l y s i s o f a r e a l gea r h o u s i n g i s p r e s e n t e d . The a n a l y s i s was conduc ted f o r t h e h o u s i n g w i t h o u t t h e r o t a t i n g components ( g e a r s , s h a f t s , and b e a r i n g s ) . B o t h r i g i d and f l e x i b l e m o u n t i n g c o n d i t i o n s f o r t h e gear h o u s i n g a r e c o n s i d e r e d i n t h i s a n a l y s i s . The f l e x i b l e s u p p o r t s i m u l a t e s t h e r e a l i s t i c moun t ing c o n d i t i o n on a r o t o r c r a f t , and t h e r i g i d one i s ana- l y z e d f o r compar i son pu rposes . The e f f e c t o f gear h o u s i n g s t i f f e n e r s i s a l s o e v a l u a t e d . The r e s u l t s i n d i c a t e t h a t t h e f i rst s i x n a t u r a l modes o f t h e f l e x i - b l y mounted g e a r h o u s i n g i n t h e 0 t o 200 Hz range c o r r e s p o n d t o t h e t r a n s l a - t i o n a l and r o t a t i o n a l r i g i d body v i b r a t i o n modes o f t h e h o u s i n g . Above t h i s
r i g i d mount, o n l y t h e h o u s i n g p l a t e e l a s t i c modes a r e o b s e r v e d w h i c h a r e v e r i - f i e d by modal a n a l y s i s e x p e r i m e n t s . P a r a m e t r i c s t u d i e s show t h a t t h e h o u s i n g p l a t e s t i f f e n e r s and r i g i d mounts t e n d t o i n c r e a s e most o f t h e n a t u r a l f r e q u e n - c i e s , t h e l o w e r ones b e i n g a f f e c t e d t h e most.
4 Lo Lo cf
I W range , t h e h o u s i n g p l a t e e l a s t i c modes b e g i n t o o c c u r . I n t h e case o f t h e
INTRODUCTION
Gear n o i s e and v i b r a t i o n i s a m a j o r p r o b l e m i n many power t r a n s m i s s i o n a p p l i c a t i o n s as i s e v i d e n t from t h e l i t e r a t u r e ( r e f s . 1 t o 8 ) . T h i s p r o b l e m becomes more s i g n i f i c a n t i n a p p l i c a t i o n s w i t h h i g h e r o p e r a t i n g s p e e d s w h e r e t h e v i b r a t o r y e x c i t a t i o n , wh ich i s r e l a t e d t o t h e gear t r a n s m i s s i o n e r r o r ( r e f s . 7 , and 9 t o l l ) , o c c u r s a t f r e q u e n c i e s i n t h e o r d e r o f s e v e r a l k i l o h e r t z . Most of t h i s v i b r a t o r y ene rgy g e n e r a t e d a t t h e g e a r s i s t r a n s m i t t e d t o t h e h o u s i n g and a t t a c h e d s t r u c t u r e s t h r o u g h t h e s t r u c t u r e - b o r n e p a t h s i n v o l v i n g t h e s h a f t s , b e a r i n g s , and mounts ( r e f s . 4, 5 , 7 and 1 2 ) . I n r o t o r c r a f t a p p l i c a - t i o n s t h e v i b r a t o r y ene rgy t r a n s m i t t e d from t h e gears t o t h e a i r c r a f t s t r u c - t u r e r e s u l t s i n a h i g h l e v e l o f c a b i n n o i s e . Hence, a fundamenta l knowledge of t h e dynamic b e h a v i o r o f a gearbox and i t s s u p p o r t i n g s t r u c t u r e i s e s s e n t i a l i n t h e o v e r a l l g o a l o f r e d u c i n g gear i n i t i a t e d v i b r a t i o n p rob lems .
I n t h i s s t u d y , t h e dynamic p r o p e r t i e s o f a r e a l gea r h o u s i n g a r e p r e - d i c t e d u s i n g t h e f i n i t e e lemen t method (FEM) and v e r i f i e d u s i n g e x p e r i m e n t a l modal a n a l y s i s ( E M A ) . The f i n i t e e lemen t p rog ram ANSYS ( r e f . 13) was used t o c a l c u l a t e t h e n a t u r a l f r e q u e n c i e s and modes o f a r e a l gea r h o u s i n g and mounts w i t h o u t t h e g e a r s , s h a f t s and b e a r i n g s . A d e s c r i p t i o n o f t h e a c t u a l gearbox and t h e FEM model used t o model i t a r e g i v e n . R e s u l t s o f t h e FEM a n a l y s i s as compared t o t h e e x p e r i m e n t a l modal a n a l y s i s r e s u l t s f o r t h e r i g i d l y mounted
s t i f f e n e d gearbox case a r e a l s o p r e s e n t e d . F i n a l l y , r e s u l t s a r e g i v e n on t h e e f f e c t s of t h e mounts and s t i f f e n e r s on t h e dynamics o f t h e h o u s i n g , as p r e d i c t e d by t h e FEM model .
F I N I T E ELEMENT MODEL
The FEM model was c o n s t r u c t e d t o s i m u l a t e t h e e x p e r i m e n t a l gearbox a t NASA Lewis Research C e n t e r . The s i m u l a t e d gearbox , as shown i n f i g u r e 1 , i s a p p r o x i m a t e l y 0 .254 by 0.279 by 0 .330 m (10.0 by 11.0 by 13 .0 i n . ) , and a l l o f i t s p l a t e s a r e 0.006 m ( 0 . 2 5 i n . ) t h i c k made o f 1020 s t e e l . The r e g i o n s n e a r t h e b e a r i n g s a r e 0.025 m (1 .0 i n . ) t h i c k . There a r e f o u r c i r c u l a r h o l e s f o r t h e b e a r i n g s , two a t each s i d e p l a t e s u p p o r t i n g t h e s h a f t s . F i g u r e 2 i l l u s - t r a t e s t h e 0 .254 m (10.0 i n . ) t a l l f l e x i b l e mount f rame wh ich i s c o n s t r u c t e d from e i g h t 0 .006 m (0 .25 i n . ) t h i c k , 1020 s t e e l a n g l e beams. The f u s e l a g e shee t i s a 0 .006 m (0 .25 i n . ) t h i c k a luminum p l a t e o f d imens ions 0 .762 b y 0 . 6 6 0 m (30.0 b y 26 .0 i n . ) , and i s a t t a c h e d h o r i z o n t a l l y t o t h e f l e x i b l e mount s t r u c t u r e . The h o u s i n g i s s u p p o r t e d a t each c o r n e r o f t h e base p l a t e f o r a l l moun t ing c o n d i t i o n s , and t h e mounts a r e a t t a c h e d t o a r i g i d f o u n d a t i o n .
The FEM models o f t h e r e c t a n g u l a r gearbox w i t h t h e g e a r s , s h a f t s , and b e a r i n g s removed a r e shown i n f i g u r e 3 f o r t h e r i g i d l y and f l e x i b l y mounted h o u s i n g s . These FEM models c o n s i s t o f fou r -noded q u a d r i l a t e r a l p l a t e e lemen ts w i t h b e n d i n g and membrane c a p a b i l i t i e s f o r t h e h o u s i n g and f u s e l a g e a t t a c h e d , and two-noded beam e lemen ts w i t h shear d e f o r m a t i o n and r o t a r y i n e r t i a c a p a b i l i - t i e s f o r t h e f l e x i b l e mount s k e l e t o n and h o u s i n g p l a t e s t i f f e n e r s . The boundary c o n d i t i o n s a r e : ( 1 ) z e r o d i s p l a c e m e n t s and r o t a t i o n s a t each c o r n e r o f t h e base p l a t e f o r t h e r i g i d mount and ( 2 ) s i m i l a r c o n d i t i o n s a t each foo t o f t h e f l e x i b l e mount . The i n t e r f a c e between a d j a c e n t h o u s i n g p l a t e s a r e assumed t o be c o n t i n u o u s . About 100 dynamic degrees o f f reedom a r e s p e c i f i e d t o m i n i m i z e c o m p u t a t i o n a l e f f o r t w h i l e s t i l l m a i n t a i n i n g s u f f i c i e n t a c c u r a c y . N a t u r a l f r e q u e n c i e s a r e e x t r a c t e d up t o a t l e a s t 4 kHz t o i n c l u d e t h e gear mesh f r e q u e n c y reg ime .
E X P E R I M E N T S AND MODEL VALIDATION
Modal e x p e r i m e n t s were p e r f o r m e d on t h e NASA h i g h p r e c i s i o n gearbox w i t h t h e g e a r s , s h a f t s , and b a l l b e a r i n g s i n s t a l l e d . An a p p r o x i m a t e c o n f i g u r a t i o n o f t h e NASA gearbox i s shown i n f i g u r e 4 . The nomina l d imens ions o f t h e gear h o u s i n g have been g i v e n i n t h e p r e v i o u s s e c t i o n . The v a r i a b l e c e n t e r d i s t a n c e g e a r - s h a f t p a i r i s s u p p o r t e d by f o u r b a l l b e a r i n g s . The f o u r s i d e p l a t e s and base p l a t e a r e welded t o g e t h e r , w h i l e t h e t o p p l a t e i s b o l t e d t o t h e s i d e p l a t e s . The h o u s i n g p l a t e s a r e s t i f f e n e d i n t e r n a l l y , and t h e gear h o u s i n g sys- tem i s mounted r i g i d l y t o a mass ive f o u n d a t i o n . Dynamic t r a n s f e r f u n c t i o n s w e r e o b t a i n e d o n l y on t h e e x t e r i o r o f t h e gear h o u s i n g s t r u c t u r e u s i n g a two channe l dynamic s i g n a l a n a l y z e r . F o r t h e s e e x p e r i m e n t s , 154 degrees o f f reedom w e r e s e l e c t e d i n t h e d i r e c t i o n t r a n s v e r s e to t h e p l a n e o f t h e h o u s i n g p l a t e , w i t h t h e r e f e r e n c e p o i n t b e i n g a p p r o x i m a t e l y nea r t h e c e n t e r o f t h e t o p p l a t e t o a v o i d noda l p o i n t s o f i n t e r e s t . N a t u r a l f r e q u e n c i e s and modes were e s t i - mated u s i n g a c o m m e r c i a l l y a v a i l a b l e modal a n a l y s i s p rogram. Here , t h e expo- n e n t i a l method was used t o e x t r a c t modal pa ramete rs and g e n e r a t e a n a l y t i c a l f u n c t i o n s f o r t h e t r a n s f e r f u n c t i o n s , w h i l e t h e c i r c l e f i t method was used t o c o n s t r u c t t h e modal v e c t o r s .
.
2
The FEM model p r e d i c t i o n s were compared w i t h EMA t e s t s pe r fo rmed on t h e NASA e x p e r i m e n t a l gearbox . Tab le I l i s t s t h e r e s u l t i n g n a t u r a l f r e q u e n c i e s and mode shapes. A s d e p i c t e d i n t h i s t a b l e , FEM p r e d i c t i o n s a r e i n good ag ree - ment w i t h €MA. The r e s u l t s i n t a b l e I a l s o sugges t t h a t t h e g e a r s , s h a f t s , and b e a r i n g s p r e s e n t i n t h e a c t u a l h o u s i n g have no a p p r e c i a b l e a f f e c t on t h e dynamics o f t h e hous ing , s i n c e t h e FEM modeled t h e h o u s i n g w i t h o u t t h e s e compo- n e n t s . T h i s may n o t be t r u e f o r t h e f l e x i b l y mounted case , where t h e added mass and s t i f f n e s s o f t h e g e a r s , s h a f t s , and b e a r i n g s c o u l d r e s u l t i n an a p p r e c i a b l e d i f f e r e n c e i n t h e r i g i d body modes o f t h e a c t u a l sys tem as com- p a r e d t o t h e FEM p r e d i c t i o n s . mount case, a r e i l l u s t r a t e d i n f i g u r e s 5 and 6 . I d e n t i f i c a t i o n of a mode shape i s based on i t s most dominant f e a t u r e due t o i t s c o m p l e x i t y . For each mode, two s i m p l i f i e d i l l u s t r a t i o n s a r e shown: ( 1 ) mode shape o f t h e t h r e e v i s - i b l e p l a t e s , and ( 2 ) mode shape o f t h e t h r e e n o n v i s i b l e p l a t e s i n an a p p r o x i - mate i somet r ic v i e w . F i g u r e 5 compares t h e s i m p l i f i e d mode shape t o t h e a c t u a l one f o r t h e t h i r d mode. The f i rs t mode i s b a s i c a l l y a f i r s t t r a n s v e r s e mode of t h e t o p h o u s i n g p l a t e w i t h sma l l a m p l i t u d e s o f v i b r a t i o n a t t h e s i d e p l a t e s . Second t o f o u r t h modes a r e g i v e n b y d i f f e r e n t c o m b i n a t i o n s of f i rs t t r a n s v e r s e h o u s i n g p l a t e modes. For example, i n t h e second mode, t h e s i d e p l a t e s s u p p o r t i n g t h e b e a r i n g s a r e in-phase ( i . e . , b o t h p l a t e s a r e mov ing i n t h e same d i r e c t i o n w i t h r e s p e c t t o t h e g l o b a l c o o r d i n a t e s ) . T h i r d and f o u r t h modes a r e g i v e n by ou t -o f -phase t r a n s v e r s e v i b r a t i o n o f t h e s e s i d e p l a t e s , b u t w i t h d i f f e r e n t c o m b i n a t i o n s f o r t h e o t h e r p l a t e s . The f i f t h mode c o n s t i t u t e s a second t r a n s v e r s e p l a t e mode a t t h e t o p p l a t e combined w i t h f i r s t and second t r a n s v e r s e p l a t e modes a t t h e s i d e p l a t e s . The h i g h e r modes, n o t shown h e r e , a r e a l s o g i v e n by s i m i l a r c o m b i n a t i o n s o f p l a t e modes. e r modes a r e made on t h e b a s i s o f modal d e n s i t y f o r o n e - t h i r d o c t a v e band cen- t e r f r e q u e n c i e s i n t h e 500 t o 4000 Hz range , as shown i n f i g u r e 7 , because of t h e h i g h number o f p a r t i c i p a t i n g modes obse rved . The r e s u l t s a g a i n i n d i c a t e t h a t FEM i s i n good agreement w i t h EMA.
Mode shapes p r e d i c t e d by FEM, for t h e r i g i d
Compar ison o f t h e h i g h -
PARAMETRIC STUDIES
E f f e c t s O f Mounts
The FEM model was used t o i n v e s t i g a t e t h e e f f e c t s o f moun t ing f l e x i b i l i t y on t h e dynamics o f t h e gear h o u s i n g system. The r i g i d l y mounted gear h o u s i n g i s obse rved t o possess o n l y h o u s i n g p l a t e e l a s t i c modes. On t h e o t h e r hand. FEM model o f t h e f l e x i b l y mounted gear h o u s i n g i n d i c a t e s t h a t t h e f i r s t s i x n a t u r a l modes a r e t h e t r a n s l a t i o n a l and r o t a t i o n a l r i g i d body modes of t h e gear h o u s i n g as shown i n f i g u r e 8. For example, t h e f i r s t n a t u r a l f requency a t 54 Hz co r responds t o t h e gear h o u s i n g v i b r a t i o n i n t h e Y - d i r e c t i o n as shown. I n a d d i t i o n , t h e n a t u r a l f r e q u e n c i e s a r e c o n s i d e r a b l y lower, by approx - i m a t e l y one o r d e r o f m a g n i t i d e , as compared t o t h o s e o f t h e r i g i d l y mounted gear h o u s i n g . These r i g i d body v i b r a t i o n modes r e s u l t from t h e complex e l a s t i c d e f o r m a t i o n o f t h e f l e x i b l e mount s k e l e t o n and f u s e l a g e s h e e t . The h o u s i n g p l a t e n a t u r a l f r e q u e n c i e s a r e a l s o l owered , e s p e c i a l l y t h e f i r s t few, when t h e box i s mounted f l e x i b l y . F i g u r e 9 compares t h e modal d e n s i t y f o r o n e - t h i r d o c t a v e band c e n t e r f r e q u e n c i e s o f t h e f l e x i b l y mounted gear h o u s i n g t o t h a t of t h e r i g i d l y mounted one. The modal d e n s i t y a t f r e q u e n c i e s above 1 kHz i s seen to be h i g h e r for b o t h c o n d i t i o n s . F i g u r e 10 compares t h e n a t u r a l f r e q u e n c i e s of t h e f 1 e x i : b l e mount , r i g i d l y mounted h o u s i n g , f l e x i b l y mounted h o u s i n g , and t h e g e a r - s h a f t s y s t e m . The modal d i s t r i b u t i o n o f t h e g e a r s h a f t system i s seen t o be s i g n i f i c a n t l y l o w e r t h a n t h a t o f t h e h o u s i n g and mounts . The
n a t u r a l f r e q u e n c i e s o f t h e gear s h a f t sys tem were added i n f i g u r e 10 t o compare t h e modal d e n s i t i e s o f t h e m a j o r components o f t h e t e s t gea rbox . Here i t i s assumed t h a t t h e modes o f t h e gear s h a f t sys tem a r e i ndependen t o f t h e h o u s i n g p l a t e modes; c o u p l i n g i s s u e s a r e c u r r e n t l y b e i n g i n v e s t i g a t e d . A s expec ted , t h e n a t u r a l f r e q u e n c i e s o f t h e f l e x i b l e mount a r e l owered when t h e h o u s i n g i s added t o i t , as shown i n f i g u r e 10.
E f f e c t O f S t i f f e n e r s
The i n t r o d u c t i o n o f h o u s i n g p l a t e s t i f f e n e r s , as shown i n f i g u r e 4, do n o t change t h e n a t u r e o f t h e mode shapes p r e d i c t i o n s . f r e q u e n c i e s f o r t h i s case a r e h i g h e r as i l l u s t r a t e d i n f i g u r e 1 1 . The l o w e r n a t u r a l f r e q u e n c i e s a r e a f f e c t e d more by t h e s t i f f e n e r s t h a n t h e h i g h e r f r e - q u e n c i e s . wh ich reduce t h e modal d e n s i t y f u r t h e r i n t h e h i g h e r f r e q u e n c y bands.
However, t h e n a t u r a l
Also, some o f t h e h i g h e r modes a r e suppressed b y t h e s t i f f e n e r s
CONCLUSIONS
Based on t h e a n a l y t i c a l and e x p e r i m e n t a l r e s u l t s o b t a i n e d i n t h i s s t u d y , t h e f o l l o w i n g c o n c l u s i o n s can be made:
I ( 1 ) The FEM model used a c c u r a t e l y p r e d i c t e d t h e dynamic c h a r a c t e r i s t i c s
1 o f an e x p e r i m e n t a l gea r h o u s i n g , as v e r i f i e d w i t h modal a n a l y s i s e x p e r i m e n t s on t h e a c t u a l hardware .
( 2 ) The f l e x i b i l i t y o f t h e gear h o u s i n g mount d i r e c t l y i n f l u e n c e s t h e I n t h e r i g i d l y mounted t y p e and f r e q u e n c i e s o f t h e p r i m a r y h o u s i n g modes.
case t h e p r i m a r y modes c o r r e s p o n d t o t h e e l a s t i c p l a t e modes of t h e h o u s i n g . I n t h e f l e x i b l y mounted case t h e p r i m a r y modes o c c u r r e d a t f r e q u e n c i e s l o w e r t h a n t h e r i g i d mounted case, w i t h t h e mode shapes c o r r e s p o n d i n g t o r i g i d body modes of t h e h o u s i n g .
( 3 ) The a d d i t i o n o f h o u s i n g p l a t e s t i f f e n e r s d i d n o t s i g n i f i c a n t l y change t h e n a t u r e o f t h e mode shape p r e d i c t i o n s . However, t h e mode shapes of t h e h o u s i n g w i t h s t i f f e n e r s o c c u r r e d a t h i g h e r f r e q u e n c i e s t h a n t h e c o r r e s p o n d i n g mode shapes o f t h e h o u s i n g w i t h o u t s t i f f e n e r s .
REFERENCES
1 . Badg ley , R . H . ; and L a s k i n , I.: Program f o r H e l i c o p t e r Gearbox Noise P r e d i c t i o n and R e d u c t i o n . USAAVLABS-TR-70-12, Mar . 1970. ( A v a i l . N T I S , AD-869822.)
2 . Badg ley , R . H . ; and Chiang, T . : R e d u c t i o n o f V i b r a t i o n and N o i s e Genera ted by P l a n e t a r y R i n g Gears i n H e l i c o p t e r A i r c r a f t T r a n s m i s s i o n . J . Eng. I n d . , v o l . 9 5 , no. 4, Nov. 1973, pp . 1149-1158.
3 . Badg ley , R . H . ; and Hartman, R . M . : Gearbox Noise R e d u c t i o n : P r e d i c t i o n and Measurement o f Mesh-Frequency V i b r a t i o n s W i t h i n an O p e r a t i n g H e l i c o p t e r R o t o r - D r i v e Gearbox. J . Eng. I n d . , v o l . 96, no . 2 , May 1974, pp . 567-577. i
4
4 . Bowes, M . A . ; and Berman, A . : P r e d i c t i o n o f V i b r a t i o n and Noise o f a T r a n s m i s s i o n U s i n g a Dynamic Model P a r t i a l l y D e r i v e d from T e s t D a t a . E n v i r o n m e n t a l Techno logy ' 7 7 , I n s t i t u t e o f E n v i r o n m e n t a l S c i e n c e s , Mount P r o s p e c t , IL, 1977, p p . 334-338.
Mode shapea
F i r s t t o p p l a t e mode In-phase f i r s t s i d e p l a t e s mode
Second t o p p l a t e mode
Out-of-phase f i r s t s i d e p l a t e s mode I Out-of-phase f i r s t s i d e p l a t e s mode I 1
5 . Bowes, M . A . : Development and E v a l u a t i o n o f a Method fo r P r e d i c t i n g t h e V i b r a t i o n and N o i s e C h a r a c t e r i s t i c s o f H e l i c o p t e r T r a n s m i s s i o n s . T h i r t y - T h i r d Annual N a t i o n a l Forum, Amer ican H e l i c o p t e r S o c i e t y P r e p r i n t 77-33-76, May 1977.
t o t h e Source R e d u c t i o n o f N o i s e and V i b r a t i o n i n H i g h l y Loaded M e c h a n i c a l P o w e r - T r a n s m i s s i o n Systems. F i f t h W o r l d Congress o n t h e T h e o r y o f Machines and Mechanisms, Vol. 2 , ASME, 1979, p p . 910-913.
6 . Drago, R.J. ; L e n s k i , J.W., J r . ; and R o y a l , A . C . : An A n a l y t i c a l Approach
N a t u r a l f requency , Hz
FEM EMA
50 1 497 598 584 627 639 752 781 889 877
7 . Drago, R . J . : Gear System D e s i g n f o r Minimum N o i s e . Gear N o i s e Seminar , G e n e r a l Motors, Feb. 1986.
8 . S c i a r r a , J . J . , e t a l . : H e l i c o p t e r T r a n s m i s s i o n V i b r a t i o n and N o i s e R e d u c t i o n Program. A p p l i e d Techno logy L a b o r a t o r y , USARTL-TR-78-2A,-2B, Mar . 1978. ( A v a i l . N T I S , AD-A055104, AD-A054827.)
9 . Mark , W.D.: Gear N o i s e O r i g i n s . Gears and Power T r a n s m i s s i o n Systems for H e l i c o p t e r s and T u r b o p r o p s , AGARD CP-369, AGARD, N e u i l l y - S u r - S e i n e , F r a n c e , 1984, p p . 30-1 t o 30-14.
10. D a l e , A . K . : Gear N o i s e and t h e S ideband Phenomenon. ASME Paper 84-DET-174, O c t . 1984.
1 1 . Mark , W.D. : Gear N o i s e E x c i t a t i o n . E n g i n e N o i s e : E x c i t a t i o n , V i b r a t i o n , and R a d i a t i o n , R . H i c k l i n g and M . M . Kamal, e d s . , Plenum P u b l i s h i n g , 1982, p p . 55-93.
12. B a d g l e y , R . H . ; and C h i a n g , T . : I n v e s t i g a t i o n o f Gearbox D e s i g n M o d i f i c a t i o n s for Reduc ing H e l i c o p t e r Gearbox N o i s e . E u s t i s D i r e c t o r a t e , USAAMRDL-TR-72-6, Mar . 1972. ( A v a i l . N T I S , AD-742735.)
13. Ansys U s e r ' s Manua l . Swanson A n a l y s i s Systems I n c . , Houston, P A , 1987.
5
- INPUT SHAFT
SOUSING
OUTPUT SHAFT & RIGID
MOUNTS .3;
FIGURE 1 . - GEARBOX WITH R I G I D MOUNTS. FIGURE 2 . - GEARBOX ON FLEXIBLE MOUNTS.
box on rigid mount (Fig. 1)
box on flexible mount (Fig. 2) F I G U R E 3 . - F E N MODELS OF THE GEARBOX.
C
7
0.006m thick 1020 steel plate
SECTION A-A
SECTION B-B I
0.006 m b- 0.330 m -4 FIGURE 4. - SCHEPMTIC OF THE NASA GEARBOX.
.
Actual
visible plates nonvisible plates FIGURE 5. - THIRD MODE SHAPE OF THE RIGIDLY MOUNTED GEARBOX.
f 1=501 Hz f2=598Hz
f 3= 627 Hz f4=752Hz
f5=889Hz
FIGURE 6. - M O M SHAPES OF THE RIGIDLY MOUNTED. STIFFENED NASA GEARBOX SHOWN IN FIGURE 4. BOLD SIGN IMPLIES LARGER AMPLITIDE. ACTUAL BOX ORIENTATION IS THE SAME AS SEEN IN FIGURE 5.
9
12
10- v1 Q)
TJ 8 - 2 ru 0 6 - Id
E g 2 4P" . ,'
measured (EXVIA) - - - - - - predicted (FEM)
/
I ,'
n ! " I
0.50 0.63 0.80 1.00 1.25 1.60 2.00 2.50 3.15 4.00
One-Third Octave Band Center Frequency (kHz) FIGURE 7. - PREDICTED AND EASURED MODAL DENSITIES.
FIGURE 8. - R I G I D BODY MODES OF THE FLEXIBLY MOUNTED GEARBOX.
10
4
25 i
20 - v) Q) a 2 15- 0
P
I
b-4
k3 10- E
5-
flexible rigid
- I J / - '. *
Y
0 I
.05 .08 .125 .2 .315 .5 .063 .I .160 .25 .4 .63 1.0 1.6 2.5 4.0
One-Third Octave Band Center Frequency (kHz) FIGURE 9. - MODAL DENSITIES FOR RIGID AND FLEXIBLE MOUNTING CONDITIONS.
I I I GEAR-SHAFT
SYSTEM X l[xx x x x x x x X X A
I I
xxxxxxxxx I GEARBOX ON ! x x x x x x x x x x x x ~ ~ ; x x x ) ( x x x ~ m x x x I
I
FLEXIBLE MOUNTS
I
FLEXIBLE MOUNT -=xx4 xxxx xxxxx xx m xXXXXx)(xx & v
- GEARBOX ON RIGID MOUNTS
I I I I 100 1 0 0 0 10000 1 0
(Computed up
to 4000 Hz) NATURAL FREQUENCY (HZ)
FIGURE 10. - MODAL DISTRIBUTION FOR THE MAJOR COMPONENTS OF THE GEARBOX.
4 0
0 != I 1 1 I 1 1 I 1 I
0.4 0.5 0.63 0.8 1.0 1.25 1.6 2.0 2.5 3.15 4.0
One-Third Octave Band Center Frequency (kHz) FIGURE 11. - RODAL DENSITIES FOR THE STIFFENED AND UNSTIFFENED, GEARBOX ON R I G I D ROUNTS.
Naiinal A t n m U 1 ~ s and 1 %ace Administration
2. Government Accession No. NASA TM-101445
Report Documentation Page 3. Recipient's Catalog No.
AVSCOM TR-88-C-041 4. Title and Subtitle 5. Report Date
I Modal Analysis of Gear Housing and Mounts
6. Performing Organization Code
10. Work Unit No.
505-63-5 1 9. Performing Organization Name and Address
L
I Teik C. Lim, Raj. Singh, and James J. Zakrajsek
Propulsion Directorate U.S. Army Aviation Research and Technology Activity-AVSCOM Cleveland, Ohio 44135-3127
12. Sponsoring Agency Name and Address
E-455 1
13. Type of Report and Period Covered
Technical Memorandum
17 Key Words (Suggested by Author@))
Modal analysis Gear housing
NASA Lewis Research Center Cleveland, Ohio 44135-3191 and
18 Distribution Statement
Unclassified - Unlimited Subject Category 37
I 1 L 162209A47A I
19 Security Classif (of this report)
Unclassified
1 11. Contract or Grant No. I
20 Security Classif. (of this page) 21 No of pages 22. Price'
Unclassified 14 A03
National Aeronautics and Space Administration Washington, D.C. 20546-0001 and U.S. Army Aviation Systems Command
14. Sponsoring Agency Code
I St. Louis, Mo. 63120-1798 I 15. Supplementary Notes
Prepared for the Seventh International Modal Analysis Conference cosponsored by Union College and the Society for Experimental Mechanics, Inc., Las Vegas, Nevada, January 30-February 2, 1989. Teik C. Lim and Raj. Singh, Dept. of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43216; James J. Zakrajsek, NASA Lewis Research Center.
I 16. Abstract
Dynamic finite element analysis of a real gear housing is presented. The analysis was conducted for the housing without the rotating components (gears, shafts, and bearings). Both rigid and flexible mounting conditions for the gear housing are considered in this analysis. The flexible support simulates the realistic mounting condition on a rotorcraft, and the rigid one is analyzed for comparison purposes. The effect of gear housing stiffeners is also evaluated. The results indicate that the first six natural modes of the flexibly mounted gear housing in the 0 to 200 Hz range correspond to the translational and rotational rigid body vibration modes of the housing. Above this range, the housing plate elastic modes begin to occur. In the case of the rigid mount, only the housing plate elastic modes are observed which are verified by modal analysis experiments. Parametric studies show that the housing plate stiffeners and rigid mounts tend to increase most of the natural frequencies, the lower ones being affected the most.