Gearbox Design Principles

7/29/2019 Gearbox Design Principles

1/20

AAG GEARDESIG PRINCIPLES

"MAA&


2/20

MAAG gear design pr inc ip lesDr. P. BlochThe advan t a ges of hardened and ground gears were recognizeda l ready very e a r ly by the founder o f oLir Company,Dr. h . c . Max Maag. The MAAG des ign ph i losophy has s incecen te red on hardened and ground s i ng l e h e l i c a l o r s t r a i g h tspu r gea r s .This pape r i s i n t e n d ~ d to i l l u s t r a t e the appr ec i ab l eadvantages o f the se des ign p r i n c i p l e s .1. Hard e ning and g r i nd i ng1 .1 G r ea t e r l oad c ap a c i tyThe load capac i ty of gears i s determined by th e fo l lowingt h r ee c r i t e r i a :- Bending s t r e s s- Contac t s t r e s s- Carry ing capac i t y of the o i l f i lm between the too th

1'1 anks .The bending s t r e s s a t the r oo t of th e too th i s given bythe fo l lowing s i m p l i f i e d formula :

(j F = Const F . b.mn


3/20

Where

- 2

H c o n t a c t s t r e s sCons tHrt =

a =d l =d2 =u =

Combinat ion of a l l cons t an t o r approximate lycons t an t f 'actors in th e ISO o r AGf.'lA formulaeface widthcen t r e d i s t ancerpin ion diamete rgear d iame te rgea r r a t i o ( ~ l )

The con tac t s t r e s s i s s u b s t a n t i a l l y propor t iona l to th eroo t of the K f ac to r , which accord ing to Lloyd o r API i s

K = F t u+lbd l uThe ca r ry ing capac i ty o f th e o i l f i lm, fo r which a formulahas been proposed in the new ISO s t anda rds (compi led withMAAG c o l l a b o r a t i o n ) i s reduced as the p i t c h i n c r e a se s .The permis s ib l e bending s t r e s s accord ing to MAAG i s- fo r s t ee l s case hardened to HRC = 60: 500 N/mm2- fo r a l loy s t e e l s th rough hardened to HB = 300: 300 N/mm2


4/20

- 3 -hardened to 300 HB i s i n ~ r e a s e d to approx imate ly 2 . 5 . Thisstill l eaves adequa te sa f e ty margin in r e s p e c t o f c o n t a c ts t r e s s .In genera l it may be assumed t h a t the use of case hardeneds t e e l s i n s t ead o f through hardened s t e e l s inc reases theload ( :a r ry ing capac i ty o f gears t,vo- o r t h r e e fo l d.Important in t h i s r ~ s p e c t i s t h a t fo r thruugh hardenedgears the c r i t e r i o n de te rmin ing the p e rm i s s i b l e l()ad i sthe c o n t a c t s t r e s s , ~ w h i l s t fo r case hardened gears the

~ r i t e r i o n i s usua l ly the bending s t r e s s .These r e l a t io l l sh ip s a re shown in Fig. 1. The p en n i s s ib l eload p e r u n i t fac e width Ft i s p l o t t e d ag a in s t the normalmodule . bCurve 1 Permiss i b l e l oad p e r u n i t face width determinedby c o n t a c t s t r e s s fo r a m a t e r i a l through hardenedto HE = 300CUI've 2 Permiss ib l e load p e r uni t face width d ( ~ t e r m i n e d

by c o n t a c t s t r e s s fo r a mate r i a l case hardened toHRC = 60

Curve 3 Pe r m i s s i b l e l oad p er u n i t face width determined bybending s t r e s s a t the roo t o f the t oo th fo r amate r i a l through hardened to HB = 300

Curve 4 Pe r m i s s i b l e load p er u n i t face width determined bybending s t r e s s a t the r o o t o f tho tooth fo r amate r ia l c as e hardened to HRC = 60Curve 5 Permiss ib l e load p e r u n i t face width determined by

the c a r r y i n g c a p a c i t y o f the o i l f i lm (no ti n f luenced by t he cho ice o f m a t e r i a l ) .


5/20

in r e s p e c t o f th e p e r m i s s i b l e c o n t a c t s t r e s s .With dec reas ing c e n t r e d i s t ance however , th e c o n t a c ts t r e s s i n c r e a s e s , as can be seen from th e formula fo r fTHgiven p r e v i o u s l y . The p i t t i n g c r i t e r i o n fo r case hardenedgear s thpn becomes impor t an t . This a p p l i e s p r i m a r i l y toa i r c r a f t , au tomot ive and sma l l i n d u s t r i a l gea r s . Nowadayssuch g ea r s a re i n c o n c e i v a b l ~ w i th o u t ca se h a r d en in g .1 .2 Smal l e r dimensions fo r ~ h e same dutyInc rea s ing the load c a r r y i n g c a p a c i t y by a f a c t o r o f 2 o r3 by the cho ice of case hardened m a t e r i a l s l o g i c a l l ya f f o r d s th e oppor tun i ty o f cor re s pond ing ly r educ ing thedimensions and weight of t he gear s fo r the same du ty .A mar ine r educ t ion g e a r i s shown in Fig . 2, on th e l e f twith hardened and ground gear s and on th e r i g h t with gearso f conven t iona l des ign .

The socond r educ t ion of a r o l l i n g m i l l dr ive t r a n sm i t t i n g10,000 hp a t 28 rpm i s shown in Fig . 3.The co n v en t io n a l double h e l i c a l gears with a p in ionhardened to 260 HB and a g e a r hardened to 230 HB r e q u i r e sa g ea r with a f ace , . ; idth of 2 x 750 mm + 200 mm gap .'I'lle s i n g l e l1eli o a l ve r s ion with a p in ion case hardened to60 HR C and a g e a r th rough ha rdened to 3'10 HB enabl es thetace width o f th e g ea r to be reduced to ROO mm withp r a c t i c a l l y the same c e n t r e d i s t a n c e . The weight i sp r a c t i c a l l y halved from 91 t to 45 t .


6/20

- 5 -

to t r ans mi t very much more power with gears of the samedimensions o r the same power with much s ma l l e r gears andof co r re spond ing ly l e s s weight , hardened and ground gearsalso o f f e r the fo l lowing spe c i a l advantages .- G r ea t e r s t i f f n e s s of ' th e gearbox cas ingThe s ma l l e r dimensions enable apprec iab ly s t i f f e r gearboxcas ings to be des igned withou t exces s ive inc rease inweight . This has a b e n e f i c i a l e f f e c t on the noise l eve land the v i b ra t i on c h a r a c t e r i s t i c s of the t r ans mi s s i on .- Reduct ion of ro to r de f l e c t i onEach r o t o r , e spe c i a l l y the p in ion , d e f l e c t s under too thand t o r s i o n a l l oads , as shown in Fig . 5. For the sameload , t h i s de f l e c t i on becomes s ma l l e r as the span i sreduced . It then becomes e a s i e r to c a l c u l a t e the de-f l e c t i o n in advance and to prov ide compensat ion byappropr ia te l ong i t ud i na l modi f i ca t i ons dur ing gr i nd i ng .- Lower pe r iphe ra l speedsSmall e r dimensions r e s u l t in lower pe r iphe ra l speeds fo rthe same speeds of r o t a t i o n . Lower pe r iphe ra l speeds int u rn r e s u l t in lower windage l o s s e s and t he re fo re s ma l l e rt empera ture r i s e s in th e gearbox r o t o r s .Lower pe r iphe ra l speeds also mean lower c e n t r i f uga lforces in the ro to r s .Smal le r tempera ture r i s e s and lower c e n t r i f u g a l forcesreduce r o t o r de f l e c t i on and t he r e fo re l ead to b e t t e r too thbear ing pa t t e rn s and hence to h i ghe r load c a pa c i ty .


7/20

- 6 -

Max Maag a l ready a dv o ca ted the use of s in g l e h e l i c a l gearsand poin ted the way to t h e i r manufac ture .2.1 Advantages- Simple r manufactureEach gea r has only one se t of t e e th ins tead of two. Thisi s apprec iab ly s imple r f o ~ m a n u f a c t u r e , p a r t i c u l a r l y fo ri lardening and g r in d in g .- A ~ j u s t m e n t of too th be a r ing p a t t e r n i s p o s s i b l eWith s in g l e h e l i c a l gea r s , an accura te too th bear ingp a t t e rn can be ach ieved very e a s i l y by deformat ion of thegearbox cas ing o r by ad ju s t ab l e bea r ings .In the case of double he l i c a l gears t h i s i s apprec iab lylIIore d i f fLc u l t , as the d imensions a re l a r g e r . I f thehe l ix angles uf t he fou r se t s of meshing t e e th a re notexac t ly c u r re c t , an e x a c t ad jus tment o f the too th bear ingp a t t e rn is not p o s s ib l e a t a l l and a t b e s t it i s onlyp o s s i b l e to minimise the e r r o r by a compromise.- Compact cons t ruc t ionSing le h e l i c a l gears do not r e q u i r e a c e n t r a l gap. Thismakes them more compact wi th a l l the consequent advantages.


8/20

- 7 -cance l t hemse lves ou t . This i s not the case on s i ng l ehe l i c a l g e a r s . This can r e s u l t in poor t oo th bea r ingp a t t e r n s where t he re a r e l a rg e d i amet e r gears combinedwith smal l bea r i ng spans . In such cases the use o f pin iont h r u s t c o l l a r s , which w i l l be d i scussed s u b s e q u e n t l y , i srecommended. T i l t i n g moments a re i n S i g n i f i c a n t where t he rea re la rge face width to d i amet e r r a t i o s .- A xia l t h r u s tThe ax ia l t h r u s t r e s u l t i n g from s i n g l e h e l i c a l gea r s i s initself no d i sadvan t a ge. I t even can be e x p lo i t e d as anadvantage by s p e c i a l a r rangements of dr iv ing machine -gearbox - dr iven machine . I f an a x i a l t h ru s t i s undes i rab leo r no t pe rmisS ib le , then the des ign u t i l i z i n g p in ionth rus t co 1 laIc; i s recommended.These t h r u s t c o l l a r s not only e l im in a t e a l l t i l t i n gmoments, but a lso malee the p ro v i s io n o f t h r u s t bea r i ngson the p in ion and gea r s ha f t s capab l e o f s us t a i n i ng thee n t i r e t h r u s t unnecessa ry and so l e ad to improvede f f i c i e n c y .The p in ion t h r u s t c o l l a r s a lso make it pos s i b l e to t r a n s -mi t a x i a l t h rus t from one gearbox s h a t t to the 0 theI ' , Wi thdouble h e l i c a l gea r s t h i s i s only p e rm i s s ib l e tu a veryl im i t e d ex t en t .2 .3 Examples o f hardened and ground s i ng l e h e l i c a l gearsA dnal t a ndem a r t i c u l a t e d marine r educ t ion gea r i s shownin Fig . b. The ax ia l t h r u s t of the l a rg e gea r ac t s inoppos i t i on to the p r o p e l l e r t h r u s t .The t h ru s t s from the second r educ t ion p in ion and the firstr educ t ion gea r a re o f equa l magni tude and opposed and


9/20

- 8 -

The g e n e r a t o r i s connec ted a x i a l l y to the g e a r by af l ex i l l l e s h a f t .The connec t ion between th e p in ion and th e t u rb ine i s a l soby f l e x i b l e s h a f t , so t h a t th e e n t i r e i n s t a l l a t i o n onlyr e qu i re s a s i n g l e t h r u s t bea r ing , namely t h a t o f th egas t u r b i n e . This improves ~ h e e f f i c i e n c y .A type G D - ~ 7 speed i n c r e a s i b g gearbox between a gas t u r bine and compressor fo r t r a n sm i t t i n g 2LJ iviW a t LJ670/101")0 rpm i s shown in Fig . 8 .The gearbox i s connec ted to th e t u r b i n e and compressor byt oo thed coup l ings .

T i l t i n g pad t h r u s t b ea r in g s t ake th e t h r u s t s from th es h a f t s .The type GO-Q 8 gearbox shown in Fig . 9 i s a lso a s tep-upd r i ve and t r ansmi t s 31,500 hp a t 1200/5830 rpm. The poweri s p r o v i ~ e d lly a synchronous motor in t h i s case . A too thedCIJUP 1 i ng i s [i te d to bo th gearbox s h a f t s .The t h r u s t ()l1 th e h igh speed p .in ion s ha f t i s t aken by at i l t i n g pad t h r u s t bea r ing , whi le a s imple t a p e r l andc o l l a r bear ing s u f f i c e s on the slow speed gea r s h a f t .

3. Spur gear sSpur gear s have become very f a s h ionab l e ag a in r e c e n t l y .They a re very s imple to produce and do n o t r e s u l t in any


10/20

- 9 -3 .2 Spur gea rs in marine propu l s ionA s im i l a r des ign o f gearbox i s a l s o s upp l i e d by MAAG fo rmarine propu l s ion fo r use with medium speed Diese l eng ines .Two such mar ine ge arboxes mounted on a back- to -back t e s tr ig a re shown in Fig . 11.

The power t r a nsm i t t e d i s 13,200 kW and the speed r a t i o js[100/122 rpm. '}'11i5 speed r a t i o of approximate ly 4:1 c a l l sfo r a des ign with s t a t i o n a r y annu l a r gea r and r o t a t i n gp l a n e t c a r r i e r . For s ma l l e r speed r a t i o s , such as encoun-t e r e d with s lower speed engines , t he des ign o f p l a ne t a rygearbo xe s with s t a t i o n a r y p l a n e t c a r r i e r and r o t a t i n gannu l a r gea r i s more advantageous . Such a p l a ne t a ry gearboxa l lows t rue power s p l i t t i n g and i s t he r e fo re apprec iab lymore compact than a cor responding p a r a l l e l s h a f t gearbox .3.3 The usc of sp u r gear s in high speed gearboxesA gas t u rb ine double r e duc t ion gea r with spur gears i sshown in Fig . 12. A deep too th p r o f i l e was chosen in thei n t e r e s t of ach iev ing a high c o n t a c t r a t i o . The powert r a nsm i t t e d i s 1700 hp and the speed r a t i o is ]7100/1208 rpm.A p l a ne t a ry s p l i t t e r gearbox , .. i t h "Flexpin" f l e x ib l ep l a n e t wheel pins b u i l t under l i c e nc e from Vickers Sh ip bu i l de r s Limi ted , Bar row- in-Furness , England , i s shown inF ig . 13. The Flexpin ar rangement makes exac t load sha r ingbetween the i nd i v i dua l p l a n e t wheels , which may number 5o r more, p o s s i b l e . The power t r a nsm i t t e d i s 4050 kW withspeed r a t i o s of 12020/17412/1500 rpm.


11/20

- 10 -

which, compared with conven t iona l double h e l i c a l g ea r s ,havp. the advan tage of s imp le r manufac ture as wel l asnumerOllS o t h e r des ign and f u n c t io n a l advantages d iscussedin d e t a i l in t h i s pape r , namely:

- F a c i l i t y fo r too th bea r ing p a t t e r n ad jus tment- Compact c o n s t r u c t i o n- Simple g r in d in g o f l o n g i t u d i n a l and p r o f i l emo d i f i ca t i o n s- El imina t ion of a x i a l v i b r a t i o n s- Ca p a b i l i t y o f t r a n s m i t t i n g a x i a l t h r u s t s- Explo i t a t i on o f th e a x i a l t h r u s t- Use o f p in ion th ru s t c o l l a r s- Simple r des ign o f p l a n e t a r y gea rboxes .


12/20

- 11 -

E~ z

- - - - - i . ~ m mm

Fig. 1 Cr i t e r i a fo r gear design: Tangent ia l p i t ch l i neload pe r un i t face width in r e l a t i on to module.


13/20

EEooU1-oJ

EEo(T )

800

t. 5 000 kg

f\28rpm \ ~ 0340 BHN

~lD-oJ

E.EolD

- - - . ;;;...;.;;;=r 60 Rc~. -

- 12 -

91000 kg

230 BHN260 BHN

Fig . 3 Second s t age o f a r o l l i ng mi l l r educ t ion gea r ,l e f t ha r d ened and ground; r i gh t unhardened


14/20

- 13 -

f

Fig . 5 Ela s t i c de f l e c t i on o f p in ion

,,,__ _ L ____ _,


15/20

- 14 -

Fig. 7 Gearbox fo r a gas t u rb ine -genera to r dr ive40 ~ n v , 4500/3600 rpm o r 35 MW, 4500/3000 rpm.


16/20

- J5 -

Fig. 9 Speed i nc reas ing gearbox between synchronous motorand compressor . 31500 hp, ]200/5830 rpm.


17/20

77Sx;QO/.O_ _17lIINll1l1 ____ ! F ' = d . ! : = = = " " " o : f ~17lI2J1J,OU : : : ; : ~ _ ~ ~ ~ ~ ~ ~ ~ ~ ~ : ; : ; :77Sl5illOll77Sl51SfIlJ17lIl5XIIIJ

71S151lf1l1 = = f = = t i = ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

775,11711114

16_775;WI010_775151flOll

/ _77515160/.3./ ' / / / _77S.l5I1S.011

_7751


18/20

- 17 -

Fig . 11 Mari n e plane ta ry gearbox on t e s t r i g .13 ,200 kW, 400/122 rpm.


19/20

- 18 -

Fig. 13 Sp l i t t e r p lane ta ry gearboxgas tu rb ine - compressor - genera to r~ 0 5 0 kW, 12,020/17 ,412/1500 rpm.


20/20

- 19 -

Fig . 14 Single reduc t ion plane ta ry gearbox5420 hp, 13,4 71 /5 ,271 rpm.

Documents

Gearbox Design Principles