THE

NOVIKOV

GEAR

IN

A. I. Shvarts, I. G. and R. R. Ishmuratov

CENTRIFUGAL Galiakhmetov,

COMPRESSOR

TRANSMISSIONS UDC 6 2 1 . 8 3 1 / . 8 3 3 : 6 2 1 . 5 1

T h e m a j o r i t y of g e a r t r a n s m i s s i o n s f o r d r i v i n g c e n t r i f u g a l c o m p r e s s o r s u s e e v o l u t e g e a r s . T h e s e g e a r s h a v e c e r t a i n t e c h n o l o g i c a l a d v a n t a g e s b u t s u f f e r f r o m a n u m b e r of d e f i c i e n c i e s . T h e i r m a j o r d i s a d v a n t a g e i s l i m i t e d c o n t a c t s t r e n g t h . T h e a c c e p t e d m e t h o d s of i n c r e a s i n g the c o n t a c t s t r e n g t h c o m p l i c a t e the f a b r i c a t i o n of e v o l u t e t r a n s m i s s i o n s and r e q u i r e s p e c i a l e q u i p m e n t . The K a z a n ' c o m p r e s s o r d e s i g n SKB h a s d e v e l o p e d a t r a n s m i s s i o n u s i n g a Novikov c o n t a c t g e a r f o r d r i v i n g a K T K - 1 2 . 5 / 3 5 o x y g e n c o m p r e s s o r ( p o w e r N = 3000 kW, s p e e d n -- 3 0 0 0 / 1 3 , 4 0 0 r p m ) . T h i s i n c r e a s e s i t s t r a n s m i s s i o n c a p a c i t y and e f f i : ciency. T h e t r a n s m i s s i o n w a s f a b r i c a t e d at the K a z a n c o m p r e s s o r f a c t o r y u s i n g a m a s s p r o d u c e d t r a n s m i s s i o n h o u s i n g f o r K T K - 7 t u r b o c o m p r e s s o r s (N = 1500 kW with an e v o l u t e g e a r ) . T h e p a r a m e t e r s of the new t r a n s m i s s i o n w e r e : d i s t a n c e b e t w e e n c e n t e r s A = 350 r a m , width of e a c h h e l i x b = 160 m m , and w e i g h t G = 1934 kg. T h e e v o l u t e g e a r t r a n s m i s s i o n , with the s a m e output, h a s a c e n t e r - t o - c e n t e r h e l i c e s , a g e a r d r i v e with t h r e e s u p p o r t e r s in the h o u s i n g , and a w e i g h t of 3300 kg. The f i r s t Novikov g e a r t r a n s m i s s i o n s w e r e s p i r a l g e a r t y p e s . T h e a x i a l t h r u s t w a s t a k e n up by a j o u r n a l b e a r i n g . H o w e v e r , c o m m e r c i a l t e s t i n g of t h e s e t r a n s m i s s i o n s s h o w e d g e a r t e e t h c o n t a c t w a s l o c a t e d in the a r e a of the j o u r n a l due to the width of the g e a r w h e e l . C o n c e n t r a t e d l o a d i n g in the t e e t h c a u s e d a n u m b e r of g e a r t e e t h f a i l u r e s . A h e l i c a l a r r a n g e m e n t w a s a d o p t e d to e l i m i n a t e such f a i l u r e s . M o r e than 40 such t r a n s m i s s i o n s a r e in s u c c e s s f u l o p e r a t i o n at m a j o r m e t a l l u r g i c a l c o m p l e x e s at the p r e s e n t t i m e . T h e K a z a n c o m p r e s s o r f a c t o r y f a b r i c a t e d s e v e r a l o t h e r t y p e s of Novikov g e a r t r a n s m i s s i o n s in a c c o r d a n c e with S K B - K d e s i g n s . T h e s e a r e l i g h t e r and s m a l l e r in s i z e . F i g u r e 1 s h o w s two t r a n s m i s s i o n s u s i n g e v o l u t e and Novikov g e a r s with i d e n t i c a l c h a r a c t e r i s t i c s (N = 1500 kW, n = 3000 r p m , and t r a n s m i s s i o n ratio i = 4.5). The advantages of Novikov gear transmissions are evident from the operating experience of a TsK100-61G machine compressing casing head gas. Evolute type transmissions, with an adequate safety factor, were failing in this compressor application after a few months due to propagating fatigue cracking. This was a result of the reduction in viscosity of the gas-contaminated oil which was used to lubricate the

F i g . 1. 1500 kW t r a n s m i s s i o n s with e v o l u t e and Novikov g e a r s .

F i g . 2. T e s t b e d f o r Novikov c o u p l i n g t r a n s missions.

T r a n s l a t e d f r o m K h i m i c h e s k o e i N e f t y a n o e M a s h i n o s t r o e n i e , No. 8, pp. 2 9 - 3 1 , A u g u s t , 1970. 9 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 77th Street, New York, l N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without ] permission of the publisher. A copy of this article is available from the publisher for $15.00.

679

F i g . 4. C a l c u l a t i o n of the c o r r e c t i o n to b e a p p l i e d to the g e a r gage reading.

I

t r a n s m i s s i o n (gas c o n t a c t e d t h e oil due to l e a k a g e of c o m p r e s s o r end s e a l s ) . T h e Novikov g e a r is l e s s s e n s i t i v e to oil q u a l i t y . T h e e v o l u t e g e a r s w e r e r e p l a c e d b y a p a i r of Novikov g e a r s . T h e s e h a v e b e e n in o p e r a t i o n s i n c e A p r i l 1963 and a r e in e x c e l l e n t c o n d i t i o n .

F i g . 3. Method of f i n d i n g the d e s i r e d c h o r d .

T h e a c c u m u l a t e d e x p e r i e n c e p o i n t e d to the s i g n i f i c a n t a d v a n t a g e s of the N o v i k o v g e a r . S K B - K c a r r i e d out t e s t s t a n d i n v e s t i g a t i o n s of g e a r t r a n s m i s s i o n of v a r i o u s p r o f i l e s [1} to d e t e r m i n e the o p t i m u m . S i n c e both t h e o r y and p r a c t i c e h a d shown the m o d i f i c a t i o n of t h e N o v i k o v g e a r to b e s u p e r i o r , o n l y v a r i o u s p r o f i l e s of t h i s m o d i f i c a t i o n w e r e t e s t e d . T h e s e v a r i e d in t h e r / t n r a t i o ( w h e r e r i s the p r o f i l e r a d i u s , t n = v m n i s the p i t c h , and m n i s the t r a n s m i s s i o n m o d u l e ) : U r a l - 2 N , D Z P - 0 5 , and Y u T z - 6 3 . F o u r p a i r s of e a c h p r o f i l e w e r e t e s t e d and two p a i r s with e v o l u t e - s h a p e d g e a r s w e r e a l s o t e s t e d f o r comparison. A l l Novikov g e a r p a i r s w e r e h e l i c a l and h a d m n = 4 r a m , z w = 68, Zd = 18, b = 42.5, and rid = 0.44 r a d i a n s ( w h e r e z w and z d a r e the n u m b e r of g e a r teeth in the d r i v e w h e e l and the d r i v e n g e a r , r e s p e c t i v e l y , and fld i s the a n g l e of the t e e t h of the f i r s t c y l i n d e r ) . T e s t s w e r e c o n d u c t e d on a t e s t b e d o p e r a t i n g on the c l o s e d loop p r i n c i p l e ( F i g . 2). T h e d i s t a n c e b e t w e e n c e n t e r s of the t r a n s m i s s i o n f r a m e s w a s 190 r a m . At s p e e d s of nw = 3000 r p m (low s p e e d d r i v e w h e e l ) and nd = 11,300 r p m ( d r i v e n g e a r ) the c a l c u l a t e d m a x i m u m p o w e r w h i c h c a n b e t r a n s m i t t e d b y t h i s f r a m e u s i n g the e v o l u t e c o n f i g u r a t i o n i s 100 kW, which c o r r e s p o n d s to a c a l c u l a t e d m o m e n t on the d r i v e n g e a r N Mc = 97,500 - - =- 867 kg-cm. nd All p a i r s w e r e t e s t e d u n d e r i d e n t i c a l c o n d i t i o n s with s t e p l o a d s equal to 1.5, 2.2, 3, and 4 t i m e s M c o p e r a t i n g a b a s e n u m b e r of c y c l e s in e a c h r e g i m e . T h e s t r e n g t h of the w h e e l m a t e r i a l w a s 75 k g / m m 2. The sound p r e s s u r e (noise) l e v e l and p o w e r c o n s u m p t i o n (for e f f i c i e n c y d e t e r m i n a t i o n ) w e r e m e a s u r e d d u r i n g the t e s t i n g of e a c h p a i r . T h e r o u n d e d s e c t i o n s of the p r o f i l e s w i t h s t o o d l o a d s e x c e e d i n g the c a l c u l a t e d m a x i m u m f o r the e v o l u t e c o u p l i n g : 2.2 t i m e s ( U r a l - 2 N p r o f i l e ) , 3 t i m e s ( D Z P - 0 . 5 ) , and 4 t i m e s ( Y u T Z - 6 3 ) . T e s t i n g of the e v o l u t e p a i r s c o n f i r m e d that the c a l c u l a t e d l o a d w a s a c t u a l l y the m a x i m u m . At l o a d s equal to 1.52 M c both t e s t pairs were damaged by progressive cracking. T h e D P Z - 0 . 5 and Y u T Z - 6 3 p r o f i l e g e a r s e x p e r i e n c e d f a t i g u e c r a c k i n g at t h e e v o l u t e s e c t i o n s , which j o i n the c o n v e x c i r c u l a r s e c t i o n of the s h a n k . T h i s w a s c a u s e d b y the c o r r e c t i n c i s i o n depth of the c u t t i n g tool not b e i n g m a i n t a i n e d in s h a p i n g the t e e t h . In addition, c e n t e r i n g two t r a n s m i s s i o n s s i m u l t a n e o u s l y with r e s p e c t to the d r i v e n g e a r and t h e g e a r w h e e l c o m p l i c a t e d the e l i m i n a t i o n o f the i n i t i a l c o n t a c t f r o m the e v o l u t e s e c t i o n of the t e e t h . C r a c k s o c c u r at t h e s e p o i n t s at high (for e v o l u t e s ) l o a d s . A f t e r r u n n i n g in, the r o u n d e d s e c t i o n o f t h e p r o f i l e t o o k the m a j o r p a r t of the l o a d f r o m the e v o l u t e s e c t i o n s and c r a c k p r o p a g a tion s t o p p e d . A n a l y s i s of t e s t r e s u l t s l e a d s to the f o l l o w i n g c o n c l u s i o n s .

680

C o n t a c t s t r e n g t h is the l i m i t i n g f a c t o r in high s p e e d g e a r t r a n s m i s s i o n s with " d o z a p o l y u s n o e " Novikov g e a r s . T h e c o n t a c t s t r e n g t h of Novikov t r a n s m i s s i o n s i s 2 - 3 t i m e s h i g h e r than that of e v o l u t e transmissions. T h e c o n t a c t s t r e n g t h of d i f f e r e n t s h a p e s of Novikov g e a r s i n c r e a s e s with the r / t n r a t i o . A s t a r t i n g s h a p e with a r a t i o of r / t n -> 0.5 s h o u l d be u s e d to m o r e e f f e c t i v e l y u t i l i z e the l o a d c a p a b i l i t i e s of the N o v i kov g e a r . T h e s o u n d p r e s s u r e l e v e l in t r a n s m i s s i o n s u s i n g Novikov g e a r s d o e s not e x c e e d that in e v o l u t e t r a n s m i s s i o n s when Novikov g e a r s a r e o v e r l o a d e d b y a f a c t o r of 2 - 2 . 5 c o m p a r e d to e v o l u t e t r a n s m i s s i o n s . T h e e f f i c i e n c y of t r a n s m i s s i o n s with Novikov g e a r s , at 2 . 5 - 3 t i m e s the l o a d s on e v o l u t e t r a n s m i s s i o n s i s 2 - 3 % h i g h e r than that of e v o l u t e t r a n s m i s s i o n s . One of the a d v a n t a g e s of the Novikov g e a r i s that t e c h n o l o g y d e v e l o p e d f o r f a b r i c a t i n g e v o l u t e t r a n s m i s s i o n s c a n b e u s e d . H o w e v e r , it i s n e c e s s a r y to m a i n t a i n m a x i m u m a c c u r a c y of the depth of the i n c l u s i o n b y the c u t t e r to a c h i e v e i n i t i a l c o n t a c t on the r o u n d s e c t i o n s of the p r o f i l e . The e d g e g e a r g a g e u s e d f o r m e a s u r e m e n t d o e s not f u l f i l l t h i s r e q u i r e m e n t . T h e r e f o r e , w o r k w a s u n d e r t a k e n to d e v e l o p the u s e of a t a n g e n t i a l g e a r g a g e to m e a s u r e the g e a r w h e e l s with Novikov g e a r i n g . T h e l o c a t i o n of c h o r d s , f o r m e d b y the p o i n t s of c o n t a c t of the tooth with the r e f e r e n c e j a w s of the g e a r g a g e , c a n b e d e t e r m i n e d when the t a n g e n t i a l g e a r g a g e i s l a i d on the h e a d of the tooth of the Novikov g e a r . S i n c e the jaw o p e n i n g a n g l e of a s t a n d a r d g e a r g a g e i s 2 a d = 40 ~ the p o s i t i o n of t h i s c h o r d s h o u l d b e l o c a t e d b e t w e e n t a n g e n t s d r a w n to the c o n v e x s e c t i o n o f the t e e t h and t h o s e f o r m i n g an a n g l e of 20 ~ with the a x i s of s y m m e t r y of the tooth. S i n c e m e a s u r e m e n t s a r e t a k e n in the n o r m a l c r o s s s e c t i o n of the t o o t h , a l l d i m e n s i o n s a r e d e t e r m i n e d in the p l a n e p e r p e n d i c u l a r to i t s a x i s . In this c a s e the tooth i s s h a p e d on the c o r r e c t e d i n i t i a l c i r c u m f e r e n c e [2], w h o s e r a d i u s e q u a l s Ri ces2~d

Riw h e r e R i i s the r a d i u s of the i n i t i a l c i r c u m f e r e n c e .

T h e l e n g t h of the d e s i r e d c h o r d , a c c o r d i n g to F i g . 3, i s found f r o m the e x p r e s s i o n S=2(DaC2--OIC2)

=2Jr cos (a+y)-R i sin y].

(1)

T h e d i s t a n c e f r o m the top of the tooth to the c h o r d i s d e t e r m i n e d f r o m the e x p r e s s i o n H = R e -- OOx--DaDI = R e

--Ri cos "/--r sin (~+'0.

(2)

F r o m the c o n d i t i o n s of the p r o b l e m ~ (ol + 2/) = 20 ~ T h e c o r r e c t e d r a d i u s of the w h e e l p r o j e c t i o n s i s

Re=R i q-(Re--R i). 8 u b s t i t u t i n g t h e s e v a l u e s into f o r m u l a e (1) and (2) w e f i n a l l y get S = 2 (r cos 20~ - - Ri sin "0; H = (Re

]

--Ri ~q- Ri (1 - - cos ~/)--r sin 20~

/

(3)

T h e t a n g e n t i a l g e a r g a g e m u s t b e a d j u s t e d to t h e p r o p e r d i m e n s i o n b e f o r e m e a s u r i n g . A r e f e r e n c e r o l l e r i s r e q u i r e d f o r c a l i b r a t i n g the g e a r g a g e . The d i a m e t e r of this r o l l e r is c h o s e n so that it c a n fit into the tooth to b e m e a s u r e d , t a n g e n t to it at the c a l c u l a t e d p o i n t s ( F i g . 4). T h e d i a m e t e r of t h i s r o l l e r s h o u l d e q u a l dr --

s cos 20~

(4)

If the i n d i c a t o r of the g a t e i s s e t to z e r o w h e n i t i s c a l i b r a t e d with a r o l l e r of this d i a m e t e r , a c h e c k of a c o r r e c t l y f a b r i c a t e d g e a r w h e e l u s i n g the t a n g e n t i a l g e a r g a g e s h o u l d indica*e A mhi

= H--

hp,

w h e r e ZXmh] i,s t h e c a l c u l a t e d v a l u e of the i n d i c a t i o n of the t a n g e n t i a l g e a r g a g e .

681

T h e d i s t a n c e f r o m c h o r d S to the v e r t e x of the r o l l e r h r i s equal to hr

=dr

1--cos20 ~ 2 _ 0.329 dr.

(5)

U s i n g e x p r e s s i o n (3)-(5) we f i n d t h e r e a d i n g of the t a n g e n t i a l g e a r g a g e w h e n i t h a s b e e n a d j u s t e d u s i n g a r o l l e r with d r : A m hi = (Re--Ri:) -t- Ri (1 - - cos "{+0,70022. sin T) - - r.

(6)

N a t u r a l l y , t h e c a l c u l a t e d d i a m e t e r of the r e f e r e n c e r o l l e r d r g e n e r a l l y d o e s not e q u a l the d i a m e t e r of the r e f e r e n c e r o l l e r s u s e d with s t a n d and t a n g e n t i a l g e a r g a g e s . T h e r o l l e r c l o s e s t in d i a m e t e r to that of t h e c a l c u l a t e d s t a n d a r d r o l l e r c a n b e u s e d to e l i m i n a t e the r e q u i r e m e n t f o r f a b r i c a t i o n of v e r y a c c u r a t e l y s i z e d r o l l e r s . A c o r r e c t i o n m u s t t h e n b e a p p l i e d to the i n d i c a t i o n of the t a n g e n t i a l g e a r g a g e . T h i s c o r r e c tion i s , a c c o r d i n g to [1], u=0.962 ( d r - - dst ),

w h e r e d s t i s the d i a m e t e r of the s t a n d a r d r o l l e r , o r u s i n g e x p r e s s i o n s (3) and (4), u~1.924

Ri sin'/ 0.9397

i

dst _) 2 "

I n t r o d u c i n g t h i s c o r r e c t i o n into f o r m u l a (6) we find the g e a r g a g e r e a d i n g when i t i s c a l i b r a t e d u s i n g the s t a n d a r d r o l l e r ZXmhi = (Re-- Ri ~ + Ri (l - - cos "/q- 2. 7485 sin ~') - - 2,924r q- 0,962 d st

(7)

T h u s , a t a n g e n t i a l g e a r g a g e , u s e d f o r m e a s u r i n g the g e a r w h e e l of a Novikov g e a r , s h o u l d h a v e i t s z e r o a d j u s t e d u s i n g a s t a n d a r d r o l l e r with a d i a m e t e r c l o s e to t h a t c a l c u l a t e d by f o r m u l a (4). The r e a d i n g of the c a l i b r a t e d i n s t r u m e n t a f t e r g a g i n g i s c o m p a r e d to that c a l c u l a t e d b y f o r m u l a (7). F o r m u l a (7) i s u n i v e r s a l and c a n b e u s e d to m e a s u r e the teeth of any i n i t i a l p r o f i l e and any m o d u l e . T h e t e r m s of f o r m u l a (7), w h e n it i s u s e d f o r a s p e c i f i c p r o f i l e , c a n b e r e p r e s e n t e d a s R e - - Ri = a m i ;

Ri - - cos "f+2.748 sin'/) = m /

z

1 - - cos -b cos 3 ~o ; -z a ~o + 27.48 sin b cos z

2.924r = c m i , 0.962dem = c m i

(if a s t a n d a r d r o l l e r , c o r r e s p o n d i n g to the m o d u l e of the w h e e l b e i n g m e a s u r e d , i s s e l e c t e d ) , w h e r e a, b, c, and d a r e c o n s t a n t s f o r t h i s p r o f i l e ; and z i s the n u m b e r of t e e t h . In t h i s c a s e f o r m u l a (7) a s s u m e s the f o r m [ Amh i =m i a+

z ( 2cos3~,d 1 - - c o s

b cos'Bd z +2.748sin

b'cos'Bd ) z --c+d

]

.

(8)

It i s e v i d e n t f r o m f o r m u l a (8) that the r e a d i n g of the t a n g e n t i a l g e a r g a g e v a r i e s only a s a f u n c t i o n of m o d u l e m i and the c o m p l e x z / c o s ~ rid" T h i s p e r m i t s the d e v e l o p m e n t and s i m p l i f i e s c a l c u l a t i o n of A m h i . LITERATURE 1. 2.

682

CITED

D e s i g n and I n v e s t i g a t i o n of C o m p r e s s o r s [in R u s s i a n l , I s s u e 1, B. V. S h n e p p a ( e d i t o r ) , M a s h i n o s t r o e nie, M o s c o w (1967). M . S . t~idinov, D e s i g n of G e a r and W o r m T r a n s m i s s i o n s [in R u s s i a n ] , M a s h g i z , S v e r d l o v s k (1961).