18 Design and Dynamic Simulation of a Fixed Pitch 56kW Wind Turbine Drive Train With a Continuously Variable Transmission

8/13/2019 18 Design and Dynamic Simulation of a Fixed Pitch 56kW Wind Turbine Drive Train With a Continuously Variable Tr

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DOE/NASA/00063NASA CR-179543555 74K?

Design and Dynamic Simulation ofa Fixed Pitch 56 k W Wind TurbineDrive Train with a ContinuouslyVariable Transmission

C. Gallo, R. Kasuba,A. Pintz, and J. SpringCleveland State U niversity

March 1986NASA-CFI- 1 7 9 5 4 3 ) D L S 3 G N A 6 D C Y N A L I I C N87- 17401S i K U L A T I C N i;J? A E I X E C E I T C k i 5 t k k i i I l DT U R B I N E C R I V f : T f i A X N W X l D A CChllhCOUSLYC l e v e l a n d S t G t c C n i v . ) 4 5 F CSCL 1OB G3/44 43870V A P I A E L E i H A I i 5 M I S S I C K F i n a l beport U I l C l d S

Prepared forNATIONAL AERONAUTICS AND SPACE ADMINISTRATIONLewis Research CenterUnder Cooperative Agreement NCC 3-6forU.S. DEPARTMENT OF ENERGYConservation and Renewable EnergyWind/Ocean Technology Division


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DOE/NASA/0006-2NASA CR-179543

Design and Dynamic Simulat ion ofa Fixed Pitch 56 k W Wind TurbineDrive Train w ith a ContinuouslyVariable Trans m ission

C. Gallo, R. Kasuba,A. Pintz, and J. SpringCleveland State UniversityCleveland, Ohio

March 1986

Prepared forNational Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio 44135Under Cooperative Agreemen t NCC 3-6forU.S. DEPARTMENT OF ENERGYConservation and Renew able EnergyWindlOcean Technology DivisionWashington, D.C. 20545Under Interagency Agreem ent DE-AI01 -76ET20320


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TABLE O F CONTENTS

PageSummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2D e s i g n C o n s i d e r a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . 2Dynamic Mode l o f Sys tem . . . . . . . . . . . . . . . . . . . . . . . . . 6Bo n d Gra p h Mo d e l i n g Te ch n i q u e s . . . . . . . . . . . . . . . . . . . . . . 9Ad va n ce d C o n t i n u o u s S i mu l a t i o n L a n g u a g e P ro g ra m . . . . . . . . . . . . . 1 4S ys te m S i m u l a t i o n R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . 1 4R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3Ap p e n d i x A e s i g n M et h od s f o r D r i v e T r a i n C om po ne nts . . . . . . . . . . 2 4

R o t o r S e l e c t i o n . . . . . . . . . . . . . . . . . . . . . . . 24R o t o r L o a d i n g A n a l y s i s . . . . . . . . . . . . . . . . . . . 27Low Speed Sha f t Des ign . . . . . . . . . . . . . . . . . . . 3 0L o w Sp e e d Sh a f t Be a r i n g s . . . . . . . . . . . . . . . . . . 31D i s k B r a k e . . . . . . . . . . . . . . . . . . . . . . . . . 3 3S p e e d I n c r e a s e r . . . . . . . . . . . . . . . . . . . . . . . 3 3C o n t i n u o u s l y V a r i a b l e T ra n s m i s s io n . . . . . . . . . . . . . 3 4I n d u c t i o n G e ne ra to r . . . . . . . . . . . . . . . . . . . . . 34D r i v e T r a i n C o u p l in g s . . . . . . . . . . . . . . . . . . . . 34

Ap p e n d i x B - ACSL P r o gr am I n p u t L i s t i n g . . . . . . . . . . . . . . . . . 3 8


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S U MMA R Yl h i s r e p o r t c ov e rs t h e dynam ic a n a l ys i s o f a h o r i z o n t a l a x i s f i x e d p i t c hw i nd t u r b i n e g e n e r a to r ( W I G ) t h a t i s r a t e d a t 56 kW. A m e c h a n i c a l C o n t i n u o u sV a r i a b l e l r a n s m i s s i o n ( C V l ) was i nc o rp o ra te d i n t h e d r i v e t r a i n t o p r o v i d ev a r i a b l e sp eed o p e r a t i o n c a p a b i l i t y . One g o a l o f t h e d yn am ic a n a l y s i s was t od e t e r m i n e i f v a r i a b l e s pe ed o p e r a t i o n , b y m eans o f a m e c h a n i c a l C V T , i s capab

o f c a p t u r i n g t h e t r a n s i e n t p ow er I n t h e W TG/wind e n v i r on m e n t . A n ot h er g o a l wt o d e te r m in e t h e e x t e n t o f power r e g u l a t i o n p o s s i b l e w i t h C V l o p e r a t i o n .

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eS

The d yn am ic s i m u l a t i o n o f t h i s d r i v e t r a i n was p e r f or m e d w i t h t h e Ad vancedC o n t i n u o u s S i m u l a t i o n L a n gu ag e (ACSL) co mp u te r p ro g ra m w h i ch i s an improvedv e r s i o n o f t h e o r i g i n a l I B M - C S M P progra m. The lumped par am ete r method was usedt o a cc ou nt f o r t h e i n e r t i a and s t i f f n e s s e f f e c t s o f t h e d r i v e t r a i n c o m p o n e n t si n t he W T G m a t h e m a t i c a l m o d e l . A l s o i n c l u d e d we re t h e e f f e c t s o f a e ro d yn am icd am pin g, g e n e r a t o r s l i p and t h e v a r i a b l e sp eed r a t i o o f t h e C V T . l h e m et ho d o fb ond g r a p h d e f i n i t i o n o f t h e ma t he m a ti ca l m od el was u se d t o g e n e r a t e t h e f i r s to r d e r d i f f e r e n t i a l e q u a ti o n s ( s t a t e e q u a t i on s ) . R o t or t o r q u e , as d e te r m in e df r o m a WTG aerodyn amic p e r fo r man ce compute r code (PROPCODL), and ro t o r speedw er e t h e i n p u t s i n t h e m o de l. The c o r r e s p o n d in g pow er a t t h e g e n e r a t o r wast h e o u t p u t p a r a m e t e r .

The W l G was s u b j e ct e d t o t h r e e d i f f e r e n t w in d gu s t p r o f i l e s and t h e i re f f e c t o n t h e o u t p u t p ow er o f t h e s ys te m was m o n i t o r e d . T he f i r s t p r o f i l e wasa s t e p i n c r e a s e o f t h e w in d v e l o c i t y f r o m z er o t o 30 mph t o v a l i d a t e t h e d r i v et r a i n m o d el . The s ec on d w i n d g u s t was a t r i a n g u l a r p u ls e o f s i x ( 6 ) secondd u r a t i o n t o d e t e rm i ne t h e e f fe c t i ve n e s s o f t h e C V T t o r e g u l a t e p ower o u t p u t .The t h i r d w in d p r o f i l e c o n s is t e d o f a s e r ie s o f i r r e g u l a r t r i a n g u l a r p u ls es t oa c c o u n t f o r t h e r andom c h a r a c t e r i s t i c s o f a n a c t u a l w i nd .The a b i l i t y o f t h e C V T t o i n f l u e n c e pow er g e n e r a t i o n a nd r e g u l a t i o n wasi n v e s t i g a t e d by u s i n g s e v e r a l t i m e spans b et w ee n s u c c e s s i v e C V 1 a d j u s t m e n t s .T he se r a n ge d f r o m a n i n s t a n t a n e o u s c han ge t o z e r o a d j u s t m e n t c o r r e s p o n d i n g t o af i x e d s peed r a t i o o f t h e C V l . C u r r e n t l y , W l G ' s o p e r a t e i n t h e c o n s t a n t spee dmode. T hu s, t h e f i x e d s pee d r a t i o s i m u l a t i o n s e r v e d as a b a s e l i n e f o r t h er e s u l t s i n v o l v e d i n v a r i a b l e speed o p e r a t i o n . The spee d o f t h e g e n e r a t o r w a su se d as t h e s i g n a l f o r a d j u s tm e n t o f t h e C V 1 r a t i o . F o r e xa m ple , i f g e n e r a t o rs peed was t o o h i g h , t h e n t h e r a t i o w a s d e c re a s e d t o s l o w t h e g e n e r a t o r dow n.S i m i l a r l y , i f t h e s pe ed was t o o l o w , t h e n t h e r a t i o was i n c r e a s e d t o ma x i m i zep o w e r o u t p u t f r o m t h e s y s t e m .A s i d e f r o m th e v a l i d a t i o n o f t h e m ode l w i t h a s t e p cha ng e i n w in d v e l o c i t y ,t h e r e s u l t s o f t h e t r i a n g u l a r p u ls e i n d i c a te d t h a t t h e C V l i n t h e s p ee d c h an g emode was c a p a b le o f t r a n s i e n t p ow er r e g u l a t i o n an d c a p t u r e . l h i s c o n c l u s i o np r e v a i l e d e ve n w i t h t h e u se o f t h e r andom w i n d spe ed i n p u t p r o f i l e . F o r t h e s ew i nd g u s t mo de ls , t h e g e ne r a to r power f l u c t u a t i o n s w e re l i m i t e d t o w i t h i n2 p e r c e n t o f t h e n o m in a l va l u e f o r v a r i a b l e s pe ed o p e r a t i o n , w h er ea s o p e r a t i o na t f i x e d speed r a t f o r e s u l t e d i n a maximum power f l u c t u a t i o n o f a b o u t8 p e r c e n t . A l s o , t h e WTG r e sp o ns e t im e was c o n s i d e r a b l y q u i c k e r f o r v a r i a b l es pe ed o p e r a t i o n a s o p p os e d t o t h e f i xe d sp e e d mo d e .R eco mm end ations f o r f u t u r e w or k w ou ld i n c l u d e i n v e s t i g a t i o n s o f t h e t y p eo f c o n t r o l n eed ed f o r t h e C V T a d j us tm e n t , t h e e f f e c t o f speed changes on W l Gl i f e an d a c t u a l t e s t i n g o f t h e WTG c o n c e p t .

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I N T R O D U C I IONW i t h h y d ro c ar b on s as e n e rg y s o ur c es b e i n g d e p l e t e d , a l t e r n a t e f o rm s o fpo wer p r o d u c t i o n a r e b e i n g de v el op e d a nd i m p ro v ed t o m ee t t h e i n c r e a s i n g ne ed so f t h e w o r l d t o d a y . One s uc h s o u r c e o f a l t e r n a t e e n er g y i s t h e w i n d , w ho see n e r g y i s c a p t u r e d w i t h m a c hi ne s c a l l e d W ind T u r b i n e G e n e r a t o r s ( W l G ' s ) . T h e r ei s a n ee d f o r r e s e a r c h t o make WTG's c o s t e f f e c t i v e b y means o f d e s i g n s i m p l i -f i c a t i o n , co mpo ne nt im p ro ve m en ts an d a b e t t e r u n d e r s t a n d i n g o f t h e d y n am ic sr e s u l t i n g i n m ore e f f i c i e n t pow er p r o d u c t i o n . One a p pr oa ch c o n s id e r e d t o bea n i mp ro ve me n t t o w i nd p o w er ma ch i n e s i s t o i n c l u d e a m e c h an i ca l C o n t in u o u s l yV a r i a b l e T r a n s m i s s i o n ( C V T ) t o c o n t r o l t h e o u t p u t p o we r o f t h e s y st em a nd t oi n c r e a s e t h e t o t a l am ount o f po we r p r o d uc e d . T he u s e o f C V T ' s i n t h e a uto mot i v e f i e l d i s c u r r e n t l y u nd er i n v e s t i g a t i o n w he re s i z e an d pow er r e q u ir e m e n t s( 4 0 - 7 5 kW) p e r m i t u s i n g C V T ' s c o n s i s t i n g o f a s y ste m o f b e l t s and v a r i a b l es h e a v e p u l l e y s .T h i s p a p er d i s cu s s e s t h e a p p l i c a t i o n o f s uc h a C V T a s p a r t o f a 56 kW( 7 5 h p) w in d t u r b i n e d r i v e t r a i n . One o b j e c t i v e i s t o o p t im i z e t h e c o n f l l c t i n gr e q u i r e m e n t s o f en e rg y c a p t u r e a nd s y s te m d y n am i c s. A n o t h e r o b j e c t i v e i s t h ep o t e n t i a l u se o f l ow c o s t and s im p l e c o n t r o l s r e s u l t i n g f r o m t h e u t i l i z a t i o n o f

a C V T a s co mp are d t o a ero dy na mic c o n t r o l s i n t h e r o t o r . I n t h e ab se nc e o f a nye x t e r n a l c o n t r o l , t h e o u t p u t f ro m t h e g en e r a to r f l u c t u a t e s w i t h w in d s peed .H o p e fu l ly , t h i s i n v e s t i g a t i o n w i l l show t h a t t h e C V 1 w i l l r e d u c e t h e d e g r ee o fp o w e r f l u c t u a t i o n f r o m t h e s y s t e m .I t i s w o r t h n o t i n g t h a t t h e l a r g e r W T G ' s r e q u i r e a C V T w h i c h i s much moreco mp le x t ha n t h e s im p le h y d r a u l i c a l l y c o n t r o l l e d p u l l e y t y p e . A s p l i t p ower

C V T arra nge me nt was used f o r a 400 kW ma chin e ( 1 ) . The s p l i t pow er t y p ei n c l u d e s a m e c h a n i c a l C V T w i t h i n a p l a n e t a r y ge ar t r a i n t o c o n t r o l t h e speedo f t h e p l a n e t a r y o u t e r g e a r. T h i s p r e s e n t s t u d y w i l l d e t e r m i n e i f a s m a l l W T Gs y s t e m ( l e s s t h a n 1 0 0 kW) c an b e c o n t r o l l e d b y a b e l t t y p e C V T a s co mpa re d t ot h e m o r e e l a b o r a t e d e s i g n s .F or t h i s i n v e s t i g a t i o n , a w in d t u r b i n e d r i v e t r a i n i n c l u d i n g a c o n t in u o u s l yv a r i a b l e t r a n s m i s s i o n was d e s ig n e d t o o p e r a te a t 56 kW. A d y n a m i c s i m u l a t i o no f t h i s d r i v e t r a i n w a s p e r f o rm e d t o d e t e r m i n e t h e o u t p u t p ow er r e sp o ns e u s i n gt h e C V T as t h e o n l y m ethod o f c o n t r o l . The m eth od s u se d f o r t h e d r i v e t r a i nc om po ne nt d e s i g n a n d s e l e c t i o n a r e i n c l u d e d i n A pp e nd ix A . Bo n d g ra p h te ch -n i q u e s w er e use d t o m odel t h e s ys te m r e q u i r i n g i n e r t i a , s t i f f n e s s and da mp in gc h a r a c t e r i s t i c s o f t h e c om po ne nts . F rom t h i s m o de l, f i r s t o rd e r d i f f e r e n t i a le q u a t i o n s w e r e g e n e ra t e d as i n p u t f o r t h e A dv an ce d C o n ti n u o us S i m u l a t i o nL an gu ag e (A CS L) c o m pu te r p r o g ra m f o r t h e s i m u l a t i o n o n t h e C l e v e l a n d S t a t eU n i v e r s i t y IBM-370 ma i n f r a me . A l i s t i n g o f t h e ACSL i n p u t i s i n c l u d e d i nAp p e n d i x B.

DESIGN CONSIDERATIONSThe m ai n com ponents i n t h e w i nd t u r b i n e d r i v e t r a i n a r e t h e r o t o r , speedi n c r e a s e r , C V T a nd g e n e ra t o r p r o v i d i n g sy s te m i n p u t , a d j u s t m e n t an d o u t p u t .T a b l e 1 p r e s e n t s t h e d e si gn p a r a m et e rs o f t h e s y st em .

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TABLL 1D e s i g n P a r a m e t e r s f o r 56 kW WTG D r i v e T r a i n

R o t o rS p e e d I n c r e a s e r - G e a r R a t i o o f 1 5 . 1 5 : lc V l - R a t i o R a ng e F ro m 2 : l t o 3.33:lI n d u c t i o n G e ne ra to r - 56 kW, 3 S l i p , 1 8 0 0 - 1854 rpm Range

- Op e ra t i n g R a n g e F ro m 36 t o 60 rpm

The r o t o r was l i m i t e d t o 56 kW power p r o d u c t i o n f o r t h e o p e r a t i n g r a n g e o ft h e WTG. A b l a d e s i z e was s e l e c t e d b as ed on p e r f o r m a n c e a n a l y s e s u s i n g t h eN A S A P R O P C O D E c o m p u te r p r o g ra m . The g e a r r a t i o o f t h e s pe ed i n c r e a s e r wasc ho se n t o p ro d u ce t h e r e q u i r e d speed a t t h e g e n e r a t o r b as ed on t h e r o t o ro p e r a t i n g r a n g e a nd C V l r a t i o r a ng e . An i n d u c t i o n g e n e r a t o r was c ho se n t op r o d u c e 56 kW a t 1854 rpm based on 3 p e r ce n t s l i p . T h is r e l a t i o n d i c t a t e st h a t n o p o w e r i s p ro d uc e d a t z e r o s l i p c o r r e s p o n d i n g t o a g e n e r a t o r s pe ed o f1800 rp m. T he n a r r o w r a t i o r a n g e o f t h e C V 1 r e s u l t s i n a s m a l le r a nd s i m p l ed e s i g n w he re o n l y o ne p u l l e y n ee ds t o be o f a v a r i a b l e r a t i o , t h us r e q u i r i n go n l y one a c t u a t o r s y st em i n s t e a d o f tw o .

The P R O P C O D E p r o g r a m i s a n a e ro d yn a m ic p e r f o r m a n c e co de d e t e r m i n i n g r o t o rp ow er f o r a g i v e n a i r f o i l d e s ig n , w i nd sp ee d, r o t o r d i a m e t e r and r o t o r s pe ed .U s i n g t h e s e r e s u l t s t h e r o t o r speed was d e t e r m i n e d f o r a g i v e n w in d s p ee d t op r o d u c e t h e m a x i m u m p o s s i b l e p o w e r . The p e rf o rm a n c e a n a l y s i s a l s o i n d i c a t e st h a t v a r i a b l e s pe ed o p e r a t i o n com pared t o c o n s t a n t sp ee d r e s u l t s i n m or e p ow erg e n e r a t i o n a t a ny g i v e n w i n d s pee d. F i g u r e 1 p r e s e n t s t h e c a l c u l a t e d p ow erl e v e l s g e ne ra te d by t h i s WTG a t v a r i o u s w in d s pe ed s f o r c o n s t a n t r o t o r s pee dso f 36, 40 and 48 r pm an d a v a r i a b l e s p ee d o p e r a t i o n f r o m 36 t o 60 rpm.T h e c o n t r o l s y s t e m o f t h e w i nd t u r b i n e l i m i t s t h e r o t o r speed t o 60 rpm.However , i f t h e c o n t r o l m a l f u n c t i on s , t h en t h e d i s k b r ak e i s a p p l i e d a nd t h e

WTG i s r o t a t e d o u t o f t h e w i n d . The p u rp o s e o f t h e b r a k e i s t o a ss ur e t h a t t h er o t o r s p e e d l i m i t i s n o t ex ce ed ed . U s i n g t h e b r a k e t o c o n t r o l pow er f l u c t u a -t i o n i s n o t p r a c t i c a l b ec au se o f t he r e s u l t i n g h i g h w ea r an d o v e r h e a t i n g o f t h eb r a k e .T a b l e 2 s um m a ri ze s t h e r e l a t i o n b e tw e en w i n d , r o t o r a nd g e n e r a t o r s p ee d,

C V T r a t i o a nd po we r p r o d u c t i o n . R o t or s pe ed s a r e c h os e n f o r a g i v e n w i n d s pe edt o e x t r a c t t h e m o st pow er f r o m t h e w in d. 1-he r o t o r s pe ed -p ow er r e l a t i o n i sf r o m F i g u r e 1 .

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TABLF. 4S t a t e Eq u a t i o n s f o r W l G D r i v e T r a i n

P1P1dT- 51SE t R 1 * SF - -) - K1 * Q

= K 1 * Ql K 2 * Q 2dTm p3.d7 - 5 2 5 3- -P3 - K 2 * Q 2 - M 1 * K 3 * Q3d T

- M 1 * P3 P4-dT - 5 3 - 54- -P4 - K 3 * 9 3 - K4 * 9 4d T

dP5 = K4 * 94 - M2 * K5 * Q SdT

r * P 7 R2 * PK 5 * Q5 -6 A_--P6dT - Jb * K6 t r * r 5 7 5 6dP7 r * P6dT - 5 6

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ADVANCLD C O N T I N U O U S SIMULATION LANGUAGE P R O G R A Ml h e s y st em s t a t e e q u a t io n s d e r i v e d f r o m t h e b ond g r a p h we re us ed i n t h eAd va n ce d C o n t i n u o u s S i m u l a t i o n L an g ua g e (AC SL) co mp u te r p ro g ra m fo r t h e d yn a m i cs i m u l a t i o n ( 5 ) .g u s t p r o f i l e s was d e t er m in e d .w i n d s pee d b e f o r e b e i n g s u b j e c t e d t o a w i n d g u s t .

The s ys te m o u t p u t r es p on s e ov e r t i m e f o r v a r i o u s i n p u t w i n dThe WTG i s assumed t o be a t a n om in al i n i t i a l

A w i nd g u s t p r o f i l e was i n p u t t o t h e s i r n u la t i o n . The t o r q u e and r o t o rsp ee d c o rr e s p o nd i n g t o a p a r t i c u l a r w in d sp ee d w er e i n p u t t o t h e s ys te m.t o r q u e a t t h e g e n e r a t o r was o b t a i n e d f r o m t h e s o l u t i o n o f t h e s ys te m e q u a t i o n s .l h e g e ne r a to r s peed was c a l c u l a t e d f r o m t h e s l i p r e l a t i o n p r es e n te d i n F i g u r e 5a nd t h e r e s u l t i n g o u t p u t pow er was c a l c u l a t e d .b as ed on t h e s ys te m o u t p u t p a ra m e te r s t o r e g u l a t e t h e po we r f l u c t u a t i o n f r o mt h e s y s t e m . V a r i a b l e C V T a d j u s t m e n t o r c o n t r o l t i m e s b e tw ee n s u c c e s s i v e C V Tr a t i o ch an ge s w ere i n t r o d u c e d t o s t u d y t h e s ys te m o u t p u t power c h a r a c t e r i s t i c s .A b l o c k d i a g ra m o f t h e p r og ra m s t r u c t u r e i s g i v e n i n F i g u r e 7 .

The

The C V T r a t i o was a d j u s t e d

SYSTEM SIMUI-A1 ION RESULlST h e r e s u l t s o f t h e i n v e s t i g a t i o n i n d i c a t e t h a t t h e u se o f a c o n t i n u o u s lyv a r i a b l e t r a n s m i s s i o n o f t h e b e l t - v a r i a b l e s he av e p u l l e y t y p e f o r t h i s 56 kWw in d t u r b i n e d r i v e t r a i n p r o v id e s a p r a c t i c a l means o f c o n t r o l l i n g power o u t p u tf l u c t u a t i o n s a nd m a x i m i z in g p ow er p r o d u c t i o n . The r e as o ns f o r t h i s c o n c l u s i o na r e d i s c us s e d i n d e t a i l b elo w.T hre e d i f f e r e n t w in d g u s t p r o f i l e s were i n v e s t i g a t e d . 7-he f i r s t p r o f i l ewas a s t e p i n c r ea s e o f t h e w i nd v e l o c i t y f r o m ze r o t o 30 mph t o v a l i d a t e t h ed r i v e t r a i n m o de l. The se co nd w i nd g u s t was a t r i a n g u l a r p u l s e o f s i x ( 6 )s eco nd d u r a t i o n t o d e t er m in e t h e e f f e c t i v e n e s s o f t h e C V T t o c o n t r o l p o w e r .The t h i r d w in d p r o f i l e c o n s is t e d o f a s e r i e s o f uneven t r i a n g u l a r p u ls e s t oa c c ou n t f o r t h e random c h a r a c t e r i s t i c s o f an a c t u a l w i n d . The f o l l o w i n g p ar a -

g ra ph s p r e s en t t h e s i m u l a t i o n r e s u l t s o b t a i n e d f o r e ac h w in d g u s t p r o f i l e .Power g e n e r a t i o n an d c o n t r o l was i n f l u e n c e d b y t h e t i m e d u r a t i o n b e tw ee ns u c c e s s i v e C V l speed r a t i o a d j u s t m e n t s . The l e n g t h o f t i m e b e tw e en s pe ed r a t i oa d j u s t m e n t s was v a r i e d f r o m v e r y s h o r t ( n e a r l y i n s t a n t a n e o u s C V l r e s p o n s e ) t ov e r y l o n g ( c o n s t a n t s pe ed WTG w i t h o u t a C V1 ). T he n ee d f o r a d j u s t m e n t s i s d i c -t a t e d by t h e c o n d i t i o n o f t h e w i nd . I n a s t e ad y e n v ir o nm e n t , t h e C V T speedr a t i o i s a d j u s t e d t o c o r r e s p o n d w i t h o p ti m um a e ro d yn a m ic p e r fo r m a n ce o f t h er o t o r . I n g u s t y w in ds , t h e de gr ee o f a d j us t m e n t d u r a t i o n depends on t h e i n t e n -s i t y a nd f r e qu e n cy o f t h e g u s t s .I n i t i a l l y , a w in d gu s t s t e p f u n c t i o n was i n v e s t i g a t e d t o v a l i d a t e t h e d r i v et r a i n m od el as shown i n F i g u r e 8 . T he r e s u l t i n g mean p ow er l e v e l s h o u l d

s t a b i l i z e a t 56 kW and r em a in c o n s t a n t f o r t h e d u r a t i o n o f t h e w in d f u n c t i o n asp r e d i c t e d b y t h e p er fo rm a nc e a n a l y s i s . T he c o r r e s p o n d i n g pow er v s . t i m e r e l a -t i o n i s shown i n F i g u r e 9 f o r v a r i a b l e speed o p e r a t i o n w i t h a C V T s p e e d r a t i oa d j u s t m e n t t i m e i n t e r v a l o f 0.0 1 s e c on d s. T he r e s p on s e o f t h e W T G due t o t h i ss t e p i n p u t f o r f i x e d speed o p e r a t i o n i s a l s o i l l u s t r a t e d . A s te ad y o u t p u t o f56 kW i s r ea ch e d i n a b o u t 6 seconds when the WTG i s o p e r a t i n g i n t h e v a r i a b l es pe ed m ode. F o r f i x e d s pe ed o p e r a t i o n , t h e W I G r e q u i r e s a b o u t 30 s e co n ds t or e s u l t i n a c o n s t an t power o u t p u t c o n d i t i o n . Thus t h i s v a r i a b l e speed W T G

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Figure 8 Step Function Wind Profile

60-POWER(kw) 5o -

4 0 -

30W I ND

Fixed Speed - - - -1-

Variable Speed, 0.01 secAdjustment Time Interval --- 1

I0 l b 2 b 4TIME (sec)

Figure 9 Power Output for Step Wind IncreaseFrom Zero to 30 mph Comparing VariableSpeed Operation with a 0.01 SecondAdjustment Time Interval to Fixed Speed

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r e s p o n d s a b o u t 5 t i m e s q u i c k e r when co mp are d t o f i x e d spe ed o p e r a t i o n f o r t h i sw i n d p r o f i l e . B o t h t h e v a r i a b l e and f i x e d s p ee d r e s u l t s c o n ve r ge t o 56 kW a ndt h u s t h e s i r n u l a t i o n m o d e l i s c o r r e c t . The f l u c t u a t i o n o f pow er a t t h e b e g i n-n i n g o f t h e g u s t i s due t o t r an s i e n t s i n t h e s ys te m w h ic h a r e d i s s i p a t e d a f t e ra few seconds .The n e x t p r o f i l e i n v e s t i g a t e d was a t r i a n g u l a r w i n d g u s t p re ce de d and

f o l l o w e d b y c o n s t a n t w i n d s pe ed c h a r a c t e r i s t i c s , a s shown i n F i g u r e 1 0 . Thec o n s ta n t p o r t i o n s o f t h e w in d p r o f i l e a r e b e lo w t h e r a t e d w in d s peed o f 2 4 mpha n d o u t p u t i s c o r r e s p o n d i n g l y b elo w r a t e d pow er w h i c h i s e x p e c t e d .i l l u s t r a t e s t h a t a s m a l l t i m e i n t e r v a l b etw e e n C V T sp ee d r a t i o c ha nge s r e s u l t si n m i n i m a l pow er f l u c t u a t i o n , d e s i r a b l e f r o m a dy na mic s t a n d p o i n t . A f i x e d C V 1r a t i o r e s u l t s i n an i n s i g n i f i c a n t in c r ea s e i n power w h ic h f l u c t u a t e s f o r t h ed u r a t i o n o f t h e w i n d p r o f i l e i m p os i ng dy na m ic w ea r o n t h e s y s t em . The speedi n c r e a s e r i s s u b je c t e d t o a l t e r n a t i n g l oa d s r e s u l t i n g f r om t h e power f l u c t u a -t i o n . T h e C V T m u st m e c h a n i c a l l y a d j u s t f o r t h i s c h an ge and t h e g e n e r a t o r mayo v e r h e a t i f p ow er p r o d u c t i o n f r e q u e n t l y e xc ee ds t h e r a t e d v a l u e . A s y s t e m w l t ht h e C V 7 i n a c t i v e p r o d uc e d m ore power b u t t h i s was n o t c o n s t a n t a n d t h e o b j e c -t i v e was t o o p t i m i z e pow er p r o d u c t i o n and re du ce f l u c t u a t i o n . The r e s u l t si n d i c a t e a n o t i c e a b l e im pro ve me nt i n pow er o u t p u t w i t h t h e C V T c o n t r o l l i n gp o w e r a s comp a re d t o a f i x e d spe ed W T G.

F i g u r e 1 1

A m ore c o m pl ex w i n d g u s t was i n p u t i n t o t h e s i m u l a t i o n b y means o f a s e r i e so f u n ev en t r i a n g u l a r p u l s e s , as shown i n F i g u r e 1 2. T he p a t t e r n f o r t h i s w in dg u s t p r o f i l e was o b t a in e d f r o m ( 6 ) . The c o r r es p o n d in g po wer v s. t i m e r e l a t i o ni s shown i n F i g u r e 1 3 . The C V l m u s t b e a d j u s t e d f r e q u e n t l y f o r m i n i m a l pow erf l u c t u a t i o n w h i l e t h e W 1 G i s s u b j e c te d t o d r o p s i n w in d s pe ed b e lo w 2 4 mph.A t t h e s e l o w w i n d s p e ed s , t h e W T G i s n o t a b l e t o p r o d u c e r a t e d p ow e r o f 56 kW,c a u s in g pow er t o f l u c t u a t e .

A n o th e r n o t i c e a b l e f l u c t u a t i o n o c c u r s when w in d d ec r ea s es t o 1 5 mph a ro u n dt h e c u t - i n w in d s peed o f t h e W T G c o r r e s p o n d i n g t o t h e s pe ed w h e re p ow er i sf i r s t p ro d u ce d .a t n e a r i n s ta n t a n e ou s i n cr e m e nt s a t t h i s w i n d s pe ed , a s shown i n F i g u r e 1 3 f o ra 0 . 01 s e co n d a d j u s t m e n t . I t i s t h e r e f o r e n ec es sa ry t o o p e r a t e a t f i x e d speeda ro un d c u t - i n speed u n t i l w in d speed i n c re a s e s t o e l i m i n a t e p o s s i b l e d yn am icf l u c t u a t i o n s i n t h e sys te m. The r e s u l t s i n d i c a t e t h a t v a r i a b l e speed o p e r a t io nw i l l r e s u l t i n maximum power g e n e r a t i o n w i t h m i n im a l f l u c t u a t i o n f o r t h e d u r a- -t i o n o f t h i s c o mp le x w in d g u s t p r o f i l e .

T he s y s t e m t e n d s t o beco me u n s t a b l e wh en t h e C V T i s a d j u s t e d

A s w i n d s p e e d d i m i n i s h e s , power o u t p u t de cr ea se s as was i l l u s t r a t e d i nF i g u r e 1 r e p r e s e n t i n g p ow er p r o d u c t i o n f r o m t h e a e r od yn a m ic a n a l y s i s o n t h eW T G r o t o r w i t h o u t a ny d yn am ic e f f e c t s . F i g u r e 14 shows a c o m p a r is o n o f powerp r e d i c t e d by t h e p e rf or m an ce a n a l y s is and t h a t o b t a i n e d f r o m t h e s i m u l a t i o n f o rt h e w i n d g u s t p r o f i l e o f F i g u r e 12. The s i m u l a t i o n i n c l u d e s s y st e m d yn am ic sr e s u l t i n g f r o m e ne rg y s to r a g e and r e l e a s e w i t h i n t h e d r i v e t r a i n s ys te m. T h ise f f e c t i s m ost p ro m in e nt f ro m th e h i g h i n e r t i a o f t h e r o t o r r e s u l t i n g i n en erg yb e i n g s t o r e d a nd t h e n r e l e a s e d t h r o ug h t h e s y st em when o p e r a t i n g b e lo w r a t e dw i n d s pe e d. T h i s e n e r g y p r o v i d e s m o re p ow er o u t p u t a t lo w w i n d s pe e d s. T h i se x p l a i n s w hy, f r o m F i g u r e 14 , t h e r e s u l t i n g po we r was h i g h e r t h a n p r e d i c t e d byt h e p e r f o r m a n c e a n a l y s i s w he n w i nd s p e ed s w e r e r e d u c e d t o 1 5 an d 20 mph f o rs h o r t p e r i o d s of t i m e .t h e d r i v e t r a i n com po nen ts and t h e r e i s a r e d u c t i o n i n power g e n e r a t i o n a t l oww i n d s p e e d s . T hu s, d e c r e as e s i n o u t p u t a r e e x p e c t e d w hen w i n d s p ee d i s n o ts u f f i c i e n t t o p ro du ce r a t e d power f o r e xt en de d p e r i o d s o f t i m e .

O n ly a r e l a t i v e l y s m a l l am ount o f e n e r gy i s s to re d i n

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Figure 10 Triangular Wind Pulse of Six Second Duration

50-40-WIND 30-

b P hSPEED 20

10 t I I t I .2055 10TIME (sec)

Figure 1 1 Comparison Between Power Response of a Fixed Speed RatioCVT and Variable Speed with an Adjustment Time Intervalof 0.01 Seconds for a Triangular Wind Pulse

60

40

30

Variable Speed with a0.01 sec. Adjustment Interval

0 5 10 1 5 20TIME (sec)

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A n o th e r m e th od o f c o n t r o l was i n v e s t i g a t e d w h i c h i n v o l v e d r e d u c i n g t h e CV1r a t i o by a c o n s ta n t p e rc e nt ag e o f t h e p r e s en t s e t t i n g i f power i s t o o h i g h o ri n c r e a s i n g t h e r a t i o i f power i s l ow . P e r c e nt a g e c ha ng es r a n g i n g f r o m 0.01 t o10 p e r c e n t we re i n v e s t i g a t e d a l o n g w i t h t i m e sp an s f r o m 0 .0 1 t o 1 s ec on dbe t ween C V 7 a d j u s t m e n t s . The b e s t p ow er o u t p u t o b t a i n e d i s shown i n F i g u r e 1 5f o r t h e w i nd g u s t p r o f i l e o f F i g ur e 1 2 w he re t h e C V T r a t 4 0 was a d j u s t e d b y 0.1p e r c e n t a t 1 s ec on d i n t e r v a l s . T hi s m eth od o f c o n t r o l i s s lo w i n r e du c in gpo we r f l u c t u a t i o n , a s s ee n f r o m F i g u r e 1 5 . F o r r e f e r e n c e , t h e 0.01 seconda d ju s tm e n t t im e i n t e r v a l c u r v e o f F i g ur e 13 i s r ep e at ed on t h i s f i g u r e .R e s u l t s o b t a i n e d f ro m t h i s m e th od ar e s i m i l a r t o f i x e d r a t i o o p e r a t i o n o f t h eC V l . T h e re fo r e , t h i s t y p e o f C V l c o n t r o l i s e f f e c t i v e i f wind speed i s n o tc h a n g i n g v e r y m u c h s i n c e o p t i m u m p o w e r p r o d u c t i o n w i l l n o t r e s u l t .

I n summary, f o r a c t u a l w i n d p r o f i l e s w i t h c h a n g in g w i n d s pe ed s, p ow er o u t -p u t i s o p t i m i z e d w i t h f r e q u e n t a d j u s tm e n ts o f t h e C V l a t a v a r i a b l e r a t e t om i n i m iz e f l u c t u a t i o n . The b e l t - v a r i a b l e p u l l e y C V l has t h e c a p a b i l l t y o fi m p r o v i n g p ow er p r o d u c t i o n f r o m t h l s 56 kW W l G w hen c o mp ar ed t o a f i x e d s pe edr a t i o d es ig n .

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REFERENCES1. " P o t e n t i a l Use o f a C o n t i n u o us l y V a r i a b l e T r a n s m i s s i o n ( C V l ) i n MediumPow er W i nd Tu rb i n e A p p l i c a t i o n s " , R omua ld as Kasu ba , Adam P i n t z a n d Jo h nS p r i n g , P r e s en t e d a t t h e I n t e r n a t i o n a l C o n fe r en c e on S o l a r a nd W ind E n e rg y,B e i j i n g C hin a, NASA P I H # 271, Augus t , 1985 .2 . " I n t r o d u c t i o n t o P h y s i c a l System D yn am ic s" , R o n a ld C . Rosenberg andDean C . Karnopp, McGraw H i l l Book Company, New Y or k, 19 83 .3 . "The E N P O R l U s e r s M a n u a l " , R os en co de A s s o c i a t e s , I n c . , L a n s i n g M i c h i g a n ,1984 .4 . " P r e d i c t e d T o r s i o n a l V i b r a t i o n s f o r t h e MOD-0 w i t h a l h re e - B l a d e d1 . 9 M e t e r T i p - C o n t r o l R o t o r " , J oh n S p r i n g an d Adam. P i n t z , N AS A P I R # 2 7 4 , 1 9 8 5 .5. " A dv a nc e d C o n t i n u o u s S i m u l a t i o n L an gu ag e U s e r s G u i d e / K e f e r e n c e M a n u a l " ,M i t c h e l l an d G a u th e r A s s o c i a t e s , I n c . , Concord Mass , 1981 .6 . " Th e E f f e c t s o f T u r b u l e n c e on t h e P e r fo r m a nc e o f B o t h V a r i a b l e an d Con-s t a n t R o t o r S p e e d W i n d T u r b i n e s " , A. S w i f t a n d M . K i r k l a n d , A S M E W i n d T u r b i n eC o n f e r e n c e , D a l l a s T e x as , F e b r u a r y , 1 98 5 .7 . " MO D -O A 200 KW W in d T u r b i n e G e n e ra t or D e s i g n an d A n a l y s i s R e p o r t " ,T . S . Anderson , C . A . Bo d e n sch a tz , A . G. Eg g e rs , P . S . Hughes, R . F . Lampe, M.H . L i p n e r a nd J . R . Schornhors t , Augus t , 1980 , NASA CR-165128 .8 . " P r e d i c t e d Loads f o r t h e M O D - 0 w i t h T h r ee - B la d e d 1. 9 M e t er T i p C o n t r o lR o t o r " , Adam P i n t z an d C h r i s t o p h e r G a l l o , NASA P I R # 273 , 1985 .9 . N o te s on I n e r t i a a nd W e ig h t D e t e r m i n a t i o n o f M O D - 0 Th re e -B l a d e d H u b b yS t e v e K o z e l k a , CSU I n t e r n a l R e p or t, 1 98 5.

1 0. " l h e o r y o f V i b r a t i o n w i t h A p p l i c a t i o n s " , T h i r d E d i t i o n , W i l 1 ia m . T .T ho mp so n, P r e n t i c e H a l l , I n c . , 1 98 1.1 1. " E n g i ne e r in g C o n s i d e ra t i on s o f S t r e s s , S t r a i n a nd S t r e n g t h " , R o b e rt C .J u v in a l , McGraw H i1 1 Book Company, 1967 .1 2 . " D r i v e T r a i n N o r m a l M odes A n a l y s i s f o r t h e ERDA/NASA 1 0 0 K i l o w a t t W in dT u r b i n e G e n e r a t o r " , T. L . S u l l i v a n , D . R . M i l l e r and D . A . Sp e ra , NASATM-73718 , J u ly , 1977 .

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APPLNDIX A - D E S IGN M t l H O D S F O R D R I V E T R A I N COMPONENTS

D a ta was a v a i l a b l e f o r a 50 f o o t b l a d e c o n s i s t i n g o f a b a r g ra ph i l l u s -t r a t i n g lum ped mass d i s t r i b u t i o n a t s p e c i f i e d b la d e l o c a t i o n s . An e q u i v a l e n tg r a p h f o r a 2 6 f o o t b l a d e was o b t a i n e d b y r e d u c i n g t h e 50 f o o t b l a d e g r a p h bya p p r o p r i a t e s c a l e f a c t o r s . The r a d i a l d i s t a n c e s w er e r ed uc ed b y a l i n e a r r a t i oo f t h e b l a d e r a d i i w h i l e t h e d i s t r i b u t e d mass v a l u e s w e re r e d u ce d by t h e samer a t i o sq ua re d r e s u l t i n g f r o m a c o n s e r v a t i v e v o l u m e t r i c r e d u c t i o n . A d i r e c td e t e r m i n a t i o n o f t h e i n e r t i a and s t i f f n e s s v a lu e s f o r t h e b l a d e w o uld be v e r yi n v o l v e d s i n c e t h e t y pe o f m a t e r i a l s and m et ho d o f c o n s t r u c t i o n o f t h e b l ad em u s t b e c o n s i d e r e d . A g r ap h r e p r e s e n t i n g t h e lum ped mass d i s t r i b u t i o n v s .r a d i a l d i s t a n c e f o r t h e 26 f o o t b l ad e i s shown i n F i g u r e 1 7 . A s i m p l e c o m p u t e r

A number o f a p p r o p r i a t e c om p on en ts h ad t o b e d e s i g n e d f o r e s t a b l i s h i n g t h es ys te m p ar am e te rs ( i n e r t i a , s t i f f n e s s a nd f a t i g u e l i f e ) . S u b s e q u e n t s e c t i o n sd e a l w i t h t h e d e s ig n o r s e l e c t i o n o f t h e r o t o r , l ow speed s h a f t , b e a r i n g s ,s p ee d i n c r e a s e r , CV1, g e n e r a t o r a n d c o u p l i n g s .

R O T O R SELCl I O NA w i n d t u r b i n e r o t o r was c h o se n t o p r o d u c e r a t e d po we r o f 56 kW w h i l eo p e r a t i n g w i t h i n a spe ed r a n g e co mp are d t o t h a t o f W T G ' s c u r r e n t l y i n p ro du c-t i o n .a n d a c o n s t a n t o f 275 w h i c h i s t h e p r o d u c t o f r o t o r s pe ed and b l a d e l e n g t h .P r e v io u s h o r i z o n t a l a x i s w i n d t u r b i n e r e s e a r c h has d e t e rm i n ed t h a t o pt im ume n e r g y c a p t u r e i s a ch i e ve d w h e n th e se va l u e s a re u ' se d ( 7 ) . E q u a t i o n 3 r e l a t e st h e s e f a c t o r s t o g e t h er a nd t h e r a t e d w i n d spee d o f 2 4 m p h ( 3 4 . 4 f p s ) i s d e t e r -m i n e d w h i c h i s t h e min im um w in d s pe ed n ee de d t o p r o d u c e r a t e d p o w e r .

The l i m i t i n g f a c t o r s u se d t o s i z e a b l a d e w ere a t i p s peed r a t i o o f 8

R o t o r R a d i u s * R o to r Sp e e dW i n d V e l o c i t yi p S peed R a t i o = 3 )l h e s e p ara me te rs a i d i n de v e lo p i ng t h e i n p u t t o t h e P R O P C O D t p e r f o r m a n c ec od e n ec es sa ry f o r s e l e c t i o n o f a b l a d e s i z e . P R O P C O D E r e q u i r e s , a s i n p u t ,b l a d e d a t a s uc h as a i r f o i l l i f t and dr a g c o e f f i c i e n t s , c h o rd l e n g t h and b la d er a d i u s c o r re s p o n d in g t o ea ch c h o rd l e n g t h . l h i s pr og ra m was r u n a t d i f f e r e n tb l a d e r a d i i t o d e t er m i n e a b l a d e t h a t p r od u ce s r a t e d pow er a t a w i n d s pe ed o f2 4 mph. F i g u r e 1 6 shows t h e r o t o r l e n g t h a nd c h o r d v a l u e s a t s p e c i f i e d r a d i a ls t a t i o n s o b t a i n e d fro m t h i s a n a l y s i s .A 26 f o o t t h r e e b l a de d r o t o r c o n s t r u c t e d o f a N A C A 23024 a i r f o i l d e s i g n wasused a t f i x e d p i t c h . The W T G was o p e r a te d i n t h e u p win d p o s i t i o n w i t h a z e ro

d eg re e c o n in g a n g l e s i n c e t h i s r e s u l t s i n t h e l o w e s t d yn am ic l o a d i n g f o r t h eu p w i n d c o n f i g u r a t i o n ( 8 ) .Th e o p e ra t i n g sp e e d ra n g e o f t h e s ys te m was d e t e r m i n e d u s i n g r e s u l t so b t a i n e d f r o m P R O P C U D t . F o r a g i v e n w in d s p ee d, r o t o r s pe ed was d e t e r m i n e d t oe x t r a c t t h e m axim um p o s s i b l e p o w er . A s w i nd v e l o c i t y i n c r e a s e s , r o t o r s peed

i s i n c re a s e d u n t i l r a t e d p ower i s r e a c h e d a n d t h e n t h e r o t o r i s slowed down t o" l e v e l o f f " power p r o d u c t i o n and l i m i t i t t o 56 kW f o r an y f u r t h e r i n c r e a s e i nw i n d s pe ed . l h e r e s u l t i n g o p e r a t f n g ra ng e o f t h e W T G i s f r o m 36 t o 6 0 r pm .The s e l e c t e d r o t o r s peed f o r e a ch w i n d s pe ed an d t h e r e s u l t i n g p ow er p r o d u c t i o ni s p r e s e nt e d i n F i g u re 1 .

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p r og r am was u s ed t o d e t e r m i n e t h e w e i g h t an d i n e r t i a v a l u e s a t e ac h r a d i a ls t a t i o n b a se d o n t h e a r e a an d d i s t a n c e t o e a ch b a r on t h e g r a p h . A r e s u l t i n gs i n g l e b l a d e w e i g h t o f 424 l b s . and a n i n e r t i a o f 2 8,3 00 i n - l b - s e c 2 wasd e t e r m i n e d .T he b a s i c s ha pe o f t h e MOD-0 t h r e e - b l a d e d h ub was u s ed w i t h d i m e n s i o n sr e d u c ed t o a cc om mo da te f o r t h e s m a l l e r d e s i g n . Th e h ub w e i g h t was c a l c u l a t e d

a l o n g w i t h t h e i n e r t i a u s i n g a m ethod d on e p r e v i o u s l y f o r t h e MOD-0 h u b. Ad e t a i l e d p r e s e n t a t i o n o f t h i s method a l o n g w i t h a b re ak do wn o f t h e h ub s e c t i o n sa nd t h e i n e r t i a and w e i g h t e q u a t i o ns f o r e ac h p i e c e i s g i v e n i n ( 9 ) . The hubc o n t r i b u t e s 2500 l b s t o t h e r o t o r w e i gh t and 2300 i n - lb - s e c 2 t o t h e i n e r t i a .

R O T O R LOADING ANALYSISA d yn am ic l o a d i n g a n a l y s i s u s i n g t h e M O S l A B com pu t e r p rog ra m was pe r f o r m e don t h e w in d t u r b i n e r o t o r so t h a t a l o w s pee d s h a f t , c o n n e c t i n g t h e r o t o r h ubt o t h e f i r s t c o u p l i n g , c o u l d be d e s ig n e d. T he l o a d s a c t i n g o n t h e WTG hub,w h i c h a r e r e l a t e d t o w i n d and r o t o r s pe ed , w ere a p p l i e d t o t h e l ow s peed s h a f tt o o b t a i n t h e s i z e n ec es sa ry f o r i n f i n i t e l i f e . The MOSlAB a n a l y s i s d e t e r m i n e st he s e l o a d in g c h a r a c t e r i s t i c s . The i n e r t i a and s t i f f n e s s v a lu e s o f t h e lo wsp eed s h a f t , a s d e te r m i n e d f r o m t he d i m e n s io n s , a r e n ee de d as i n p u t t o t h ed y n a m ' i c s i m u l a t i o n .D i s t r i b u t e d mass and r a d i a l d i s t a n c e ne c e s sa r y f o r i n p u t t o M O S T A B a r eo b t a i n e d f r o m F i g u r e 1 7 an d t h e c h or d l e n g t h comes f r o m t h e P R O P C O O E i n p u t .The f i r s t f l a p p i n g mode s ha pe o f t h e b l a d e i s a l s o n eeded f o r i n p u t t o MOS IA B .T h is i n v o lv e d p e r fo r m i ng a n a t u r a l f re q ue n cy a n a l y s i s u t i l i z i n g M y k l e s t a d 'sm e th od f o r r o t a t i n g beams ( 1 0 ) . The M y k l e s t a d p r og r am r e q u i r e s i n p u t a t ea chr a d j a l s t a t i o n c o n s l s t in g o f t h e lu mp ed m as s, l e n g t h b et w e en s t a t i o n s a n d ab l a d e s t i f f n e s s v a l u e s c a l e d down f ro m 50 f o o t b l a d e d a t a . I h e n a t u r a l f r e -quency o f t h e b l a d e as o b t a i n e d f r o m t h i s p ro g ra m f o r a n o p e r a t i n g r an g e o f 3 6

t o 60 r p m v a r i e s f r o m 4 . 5 t o 5 .0 Hz.MOSTAB was r u n a t v a r i o u s r o t o r sp ee ds and w i nd v e l o c i t i e s t o d e t e r m i n e t h em a g n i t u de o f t h e l o a d s on t h e W l G hub r e a c t i n g o n t h e l ow sp ee d s h a f t t o d e t e r -m i n e a s h a f t s i z e . The d e s i g n v a lu e s w e re o b t a i n e d f o r a r o t o r sp ee d o f 80 rpmand wind speed o f 50 mph. I t i s i m p o r t a n t t h a t t h e l o w sp eed s h a f t i s o v e rd e s ig n e d t o c a r r y h i g h lo a d s t o p r e ve n t c o s t l y b re ak ag e . S i n c e t h e o p e r a t i n gr a n g e o f t h e WTG s h o u l d n o t e x c e e d 60 rp m, a 33 p e r c e n t m a r g i n o f s a f e t yr e s u l t s f r o m t h j s d e si g n r o t o r speed. T a b l e 5 p r e s e n t s t h e dy na mic l oa d s a tt h e r o t o r h ub o b t a i n e d f r o m M O S l A B a n d F i g u r e 18 i l l u s t r a t e s t h e p o s i t i v e s i g nd i r e c t i o n and c o o r d i n a t e s y ste m o f t h e s e l o a d s . I h e m o st p r o m i n e n t l o a d i n g ont h e W T G hub was t h e mean f l a t w i s e moment. F i g u r e 19 i l l u s t r a t e s t h e v a r i a t i o no f t h i s l o a d v s . w i n d a nd r o t o r speed.

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Figure 18 Positive Sign Direction of Hlade Loads

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TABLE 5Dynamic L o a d i n g a t R o t o r H ub O b t a i n e d f r o m MOSTAB f o r aDes ign Ro to r Speed o f 80 rpm and Wind Speed o f 50 mph

A x i a l F o rc e i n X - D i r e c t io n : Mean = - 9 7 0 0 l b sH o r i z o n t a l F or c e i n Y - D i r e c t i o n : Mean = 3 9 0 l b sV e r t i c a l S hea r i n Z - D i r e c t i o n : Mean = - 1 6 0 0 l b sF l a t w i s e Moment i n X - Z Plane: Mean = - 3 2 7 0 0 0 i n - l b sC y c l i c = 1 7 6 0 0 i n - l b sChordwise Moment X - Y Plane : Mean = - 8 9 0 0 0 i n - l b sC y c l i c = 5 3 8 0 0 i n - - 1 b sT w i s t T orq ue i n Y - Z Plane: Mean = 9 4 0 i n - l b sC y c l i c = 4 6 0 i n - l b s

C y c l i c = 4 1 0 l b sC y c l i c = 4 1 0 l b sC y c l i c = 8 0 l b s

LOW SPEED SHAFI DESIGNA l o w sp ee d s h a f t was d e s i g n e d u s i n g t h e l o a d s p r e s e n t e d i n T a b l e 5 a l o n gw i t h a d e s i g n t or q u e o f 2 6 4,0 00 i n - l b s d ue t o a 50 mp h w i n d a n d 8 0 rp m ro to ra c t i n g i n t h e Y - Z p l a n e a s d e t e r m i n e d b y P R O P C O D E .Z - d i r e c t i o n r e s u l t i n g f r o m t h e w e i g h t o f t h e b l a d es an d h ub was a l s o c on -s i d e r e d . T he se f o r c e s , m om ents a nd t o r q u e s w er e c o n v e r t e d t o s t r e s s e s w h i c hw e r e c o m b i n e d b y a d d j t i o n i f a c t i n g i n t h e same d i r e c t i o n . R e s u l t i n g v a l ue sw e re o b t a i n e d f o r s t r e s s e s i n t h e same p l a n e . A s e xp e c te d , t h e momen t a n dt o r q u e v a l u es d om in at e and t h e r e f o r e r e p r e s e n t t h e c o n s t r a i n t f o r t h e s h a f ts i z e .r e s u l t i n g s t r e s s r e l a t i o n s and th e s e f i n a l v a lu e s a r e shown i n E q u a ti on s 4 and5 w i t h d i a m e t er as a v a r i a b l e . F o r a h o l l o w s h a f t , t h e d i a m e t e r t e r m i s e q u a lt o E q u a t io n 6

A f o r c e o f 4000 l b s i n t h e

An e q u i v a l e n t mean a nd a l t e r n a t i n g s t r e s s was d e t e r m i n e d f r o m t h e

E q u i v a l e n t M e a n S t r e s s = 4,200,000 psiDi met e r 3

581,000 psiE q u iv a le n t A l t e r n a t i n g S t r e s s = Di me t e riu t s i d e D i a m e t e r 4 - - I n s i d e D i a m e te r 4O u t s i d e D i a m e t e ri a m e t e r 3 =

( 4 )

( 5 )

A I S 1 4340 s t e e l w i t h a y i e l d s t r e n g t h o f 9 9 k s i and an u l t i m a t e t e n s i l es t r e n g t h o f 1 11 k s i was c h o s e n a s a m a t e r i a l f o r t h e l o w s pe ed s h a f t be ca us eo f t h e h i g h s t r en g t h c h a r a c t e r i s t i c s .s he ar s t r e n g t h s s i nc e t o r s j o n a l s t r e s s was t h e l i m i t i n g f a c t o r d ue t o t h e h i g ht o r q u e on t h e s h a f t .u l t i m a t e s t r e n g t h i s 8 0 p e r c e n t o f t h e n o r m a l v a l u e s .s t r e n g t h f o r i n f i n i t e l i f e was t ak en f r o m E q u a t io n 7 w i t h a s u r f a c e f a c t o r (CS )o f 0 .7 3, f o r m a c hi ni ng , a l o a d f a c t o r ( C L ) o f 0 .5 8 f o r t o r s i o n an d a d i a m e t e rf a c t o r ( C D ) o f 0 . 9 .

A Goodman D iagr am was p l o t t e d based onThe sh ea r y i e l d s t r e n g t h i s 58 p e r c e n t a nd t h e s h e a rThe 1 0 m i l l i o n c y c l e

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P S iU l t i m a t e S t r e n g t h * C S * C L * C D2n f i n i t e L i f e S t r en g t h = ( 7 )E q u a t i o n s 4 t h r o u g h 6 w e re us ed t o d e te r m i n e s t r e s s v a l u e s f o r v a r i o u ss h a f t d i a m e t e r s . T he r e s u l t s w e re c om p ar ed on t h e Goodman D i a g r a m show n i nF i g u r e 20 t o d et e r m in e t h e f a c t o r o f s a f e t y a nd a l s o t o c he ck f o r a n i n f i n i t el i f e e xp ec ta nc y ( 1 1 ) - O u te r d la m et er s o f 5, 6, 7 a nd 8 i n c h e s w ere i n v e s t i -

g a t e d c o r r e s p o n d i n g t o s a f e t y v a lu e s o f 1 .3 , 2 .3 , 3 .6 a n d 5.4 r e s p e c t i v e l y . As h a f t w i t h o u t s i d e d ia m e te r o f 7 i n c h e s an d i n s i d e d ia m e t e r o f 3 i n c h e s wass e l e c t e d t o p r o v i d e a f a c t o r o f s a f e t y o f 3 .6 . T h i s v a l u e i s v e r y c o n s e r v a -t i v e s i n c e t h e s h a f t was d e s i gn e d f o r w i n d an d r o t o r s pee ds a bo ve t h e o p e r a t i n gr a ng e o f t h e W l G .The i n e r t i a and s t i f f n e s s o f t h e l o w s pe ed s h a f t w er e c a l c u l a t e d u s i n gE q u a t i o n s 8 a n d 9 w i t h a s h a f t l e n g t h o f 65 i n c h e s wh ere G i s t h e t o r s i o n a lm od u lu s o f r i g i d i t y . I n e r t i a and s t i f f n e s s v a l ue s f o r a l l t h e components a r ei n c lu d e d i n T a b le 7 .

G * P i p *S t i f f n e s s = 32 * L e n g t h ( O D 4 - ID 4 ) i n - l b / r a d

LOW S P E E D S H A F l BEARINGSB e a r i n gs we re s e l e c t e d t o s u p p or t t h e l o w sp ee d s h a f t s o t h a t a l l compon e n t s a r e co nn e ct ed t o t h e b e d p l a t e . D o ub le ro w t a p e r e d s p h e r i c a l r o l l e rb e a r i n g s w ere use d b ec au se o f t h e i r h i g h l o a d c a r r y i n g c a p a b i l i t y . Twob e a r i n g s w ere c ho se n w h i c h i n t r o d u c e t w o v a r i a b l e d i s t a n c e s :f r o m t h e hub c e n t e r t o t h e f i r s t b e a r i n g an d t h e d i s t a n c e b e tw ee n b e a r i n g s .l h e f i r s t was c h o se n t o b e 32 i n ch e s a l l o w i n g f o r h a l f t h e h ub an d t h e l o w

s pe ed s h a f t f l a n g e w h ic h f a s t e n s t o t h e h u b . Th e se co nd was d e t e rm i n e d b a se do n l o a d a nd s i z e r e s t r i c t i o n s . The r e a r b e a r i n g was s u b j e c t e d t o b o t h a r a d i a land t h r u s t l o a d and t h e f r o n t b e a r i n g was r e q u i r e d t o c a r r y o n l y a r a d i a l l o a d .T h i s a r r a n g e m e n t a d j u s t s m a i n l y f o r s h a f t e x p a n s i o n d ue t o t e m p e r a t u r e c h a ng esand a l s o t o p r o v i d e a n a ll o w an c e f o r m i s a l i g n m e n t .

t h e me a su re me n t

Moments a nd s he ar f o r c e s a c t i n g o n t h e s h a f t i n b o t h t h e r a d i a l Y and Zd i r e c t i o n s we re t ak en i n t o ac co un t i n a d d i t i o n t o an a x i a l t h r u s t f o r c e . Thesel oa d s w ere c o n ve r te d i n t o e q u i v a l e n t d e s i g n v a l u e s a s g i v e n i n E q u at io n s 1 0t h ro u g h 1 3 w i t h a B r e p r e s e n t i n g t h e u n k n o w n d i s t a n c e b e t w e e n b e a r i n g s .O u t b o a r d B e a r i n g :

-6 300V e r t i c a l F o r c e = IB 4 0 0 l b s

5 6 9 ' 6 0 0 t 7 6 0 0 l b so r i z o n t a l F o r c e = B

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I n b o a r d B e a r i g :V e r t i c a l F o r c e = 27 6 300 t 30 , 000 l bs

5 6 9 ' 6 0 0 t 3 0 , 0 0 0 l b so r i z o n t a l F or ce = BA d i s t a n c e o f 25 i n c h e s was c h os en f o r B b e c au s e t h i s r o v i d e d a com-prom Sse b e tw e en b e a r i n g l o a d s an d s h a f t l e n g t h . B o t h t h e f r o n t an d r e a rb e a r i n g s a r e SKF-SDAF 2 26 38 c o m p l et e p i l l o w b l o c k a s s e m b l i e s . T he f r o n tb e a r i n g w i l l have p ro v i s io n s i n t h e p i l l o w b l oc k t o a l l o w f o r t he f l o a t i n gc a p a b i l i t y .

D I S K B H A K EA d i s k b ra k e i s c o n n ec t e d t o t h e l ow s pe ed s h a f t t o i n c l u d e t h e i n e r t i ae f f e c t s f r o m t h e d i s k i n th e s im u l a t io n . l h e b ra ke i s p l a c e d b e f o r e t h e s p e e d

i n c r e a s e r t o r e du ce t h e r e s u l t i n g r o t a t i o n a l dynam ic e f f e c t s as an a l t e r n a t i v et o a d i s k o n t h e h i g h spe ed en d. l h e d i sa d v an t ag e o f t h i s i s t h a t a l a r g e rb r a k e i s n ee de d t o o ve rc om e t h e l a r g e t o r q u e r e s u l t i n g f r o m t h e w in d o n t h eb l a d e s .A W i c h i t a ATD-130-H a i r d i s k b r a k e was c h o se n w h i c h i s r a t e d a t 193,000 i n -l b s o f t o rq u e . T h i s i s d o u b l e t h e maxim um t o r q u e t h e WTG g e n e r a t e s w i t h i n t h en o r m a l o p e r a t i n g r a n g e . I t i s a s s u m e d t h a t t h e b r a k e i s engaged i f r o t o r s p e e de x c e e d s 60 rpm a nd t h u s s h o u l d t h e o r e t i c a l l y n e v e r be s u b j e c t e d t o a t o r q u en e a r t h e r a t e d v a l u e . D im e ns io n s w ere o b t a i n e d f o r t h e b r a k e hub a nd d i s k f r o mm a n u f a c t u re r ' s l i t e r a t u r e t o d e te rm in e an i n e r t i a v a l u e . The h o l l o w f e a t u r e o ft h e d i s k n ec es sa ry f o r c o o l i n g a nd l ow i n e r t i a c h a r a c t e r i s t i c s was c o ns id e re di n t h i s c a l c u l a t i o n a l s o .

S P tD IN OK LA S E KA g e a r b o x s i z e was c h o s e n b as ed on t h e o p e r a t i n g s p e ed r a n g e an d t o r q u er e q ui re m e n ts . l h e r o t o r o p e ra t es f ro m 36 t o 60 r p m a n d t h e C V l r a t i o ra ng esf r o m 2 : l t o 3. 3 3: l . I n o r d e r t o p ro du ce a speed r a ng e a t t h e g e n e r a to r f r o m1 80 0 t o 1 85 4 rp m f o r 3 p e r c e n t s l i p , t h e g e a rb o x m u st s u p p l y a g e ar r a t i o o fa b o u t 1 5 : l . A d e s i g n t o r q u e o f 1 53 ,0 00 i n - l b s was o b t a i n e d f r o m P K O P C O D E f o ra 60 rpm r o t o r and 50 mph w ind speed . Th i s v a l ue was doub le d t o im p lem en t al o a d s a f e t y f a c t o r o f 2 f o r c o n t i nu o us o p e r a t i o n . A C r i c h t o n 2 4,0 00 s e r i e ss pe ed i n c r e a s e r c a p a b l e o f 3 23,000 i n - l b s o f t o r q u e was s e l e c t e d w i t h a 1 5 . 1 5 : lr a t i o . The p l a n e t a r y sp eed i n c r e a s e r i s p r e f e r r e d f o r t h i s a p p l i c a t i o n be ca use

t h e d r i v e t r a i n c e n t e r l l n e i s n o t a l t e r e d d ue t o o f f c e n t e r i n p u t and o u tp u ts h a f t s .The i n e r t i a a nd s t i f f n e s s o f t h e spe ed i n c r e a s e r was d e t e r m in e d by a p p r o x i -m a t i n g t h e d im e n si on s o f t h e g ea rs and c a r r i e r s w i t h i n t h e p l a n e t a r y s peedi n c r e a s e r . T h i s was a c c o m p l i s h e d b y t h e u s e o f t h e g ea .r bo x o u t e r d i m e n s i o n sa nd a p i c t o r i a l ex p lo d e d v i e w o f t h e i n t e r n a l c om po ne nts . T h i s was n ec e s s a rys i n c e d e t a i l e d i n f o r m a t i o n was n o t a v a i l a b l e f o r t h i s c om po ne nt.

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The gearbox I s a t w o s t a g e d e v i c e i n c l u d i n g t wo s e p a r a t e p l a n e t a r y s peedi n c r e a se s . The s t i f f n e s s and i n e r t i a o f t h e s e pa r a te i n t e r n a l p i e c e s w er ec om b in ed i n t o t h r e e d i s t i n c t g r ou p s d e t e rm i n e d by t h e m a g n it u de o f t h e speedi n c r e a s e e ac h g oe s t h r o u g h . T he se w e re t h e n c om b in ed i n t o e q u i v a l e n t s i n g l ev a lu e s f o r t h e e n t i r e spe ed i n c r e a s e r . T h i s f o l l o w s t h e m e th od ol og y f o r t h eg e a r b o x p a r a m e t e r s a s p r es e nt e d i n ( 1 2 ) . The t o t a l s t i f f n e s s f q r t h e g ea rb oxwas r e du ce d b y a bo ut 25 pe r c en t t o a d j u s t f o r f l e x i b i l i t y i n t h e g ea r t e e t h .

CONllNUOUSLY VARlABL 1RANSMISSIONl h i s c om po ne nt i s t h e m o s t i m p o r t a n t i n t h e s y st em b ec au se t h e i m pl em e n ta -t i o n o f a C V T i n a win d t u r b i n e d r i v e t r a i n i s t h e pu rp os e o f t h i s p r o j e c t . A

C V l w i t h a s i m p le method o f r a t i o c o n t r o l was u se d h e r e t o k ee p c o s t t o a m i n i -mum. The 7 5 horsepower C V T m a n u f a c t u r e d b y Kumm I n d u s t r j e s hi js a s pe ed r a t i ov a r i a t i o n f ro m 2 :l t o 3 . 3 3 : l . The i n p u t p u l l e y o f t h e t ra n s m i s s i o n i s o f af i x e d r a d i us w h i l e t h e o u t p u t p u l l e y d ia m e te r i s v a r i e d b y means o f h y d r a u l i cc o n t r o l p r o d u c i n g a n e ar in s t a n t a n e o u s a d ju s t m e n t o f t h e speed r a t i o . The C V Tb e l t i s m a n u f a c t u r e d o f n eo pr en e an d i n c l u d e s c h o rd s c o n s i s t i n g o f K e v l a rr e s u l t i n g i n a s t i f f p l a s t i c - r u b b e r c o m p os i t io n . F i g u r e 21 i s a sk e tc h o f t h ei n t e r n a l p a r t s o f t h e C V l .

The i n e r t i a and s t j f f n e s s o f t h e C V 7 was d et e r m in e d i n a manner s i m i l q r t ot h a t o f t h e s pe ed i n c r e a s e r e x c e p t a s c a le d b l u e p r i n t d r a w i n g a nd a s k e t c h o ft h e i n t e r n a l p a r t s o f t h e C V T w er e a v a i l a b l e . P u l l e y and s h a f t v a l u e s w e red e t e r m i n e d u s i n g E q u a t i o n s 8 a nd 9 - w i t h d im e n si on s o b t a i n e d f r o m t h e d r a w i n g s .The b e l t i n e r t i a was r e p r e s e n t e d as a dde d w e i g h t on t h e p u l l e y s a nd t h e s t i f f -n es s was d e t e r m i n e d f r o m Yo un g's m o du lu s, t h e l e n g t h o f t h e b e l t i n t e n s i o n an dt h e i n p u t p u l l e y r a d i u s , s qu ar ed .

I N D U C l I O N G E N E H A I O RThe ge n e r at o r chosen f o r t h i s a p p l i c a t i o n i s a t h r e e p h as e R e l i a n c e - X T3 6 5 1 s p r o d u c i n g an o u t p u t o f 56 kW ( 7 5 h p ) a t 460 v o l t s . T h i s g e n e r a t o ri n c l u d e s a f a n f o r c o o l i n g and a sp ac e h e a t e r f o r l o w t e m p e r a t u r e o p e r a t i o n .Th is componen t i s an e xt r e m e h e a v y d u t y m o d e l s i n c e i t i s s u b j e c t e d t o a n ea rc o n s t a n t m o d e o f o p e r a t i o n .l h e ge n e r at o r c o n t r i b u t e s a n i n e r t i a a nd s t i f f n e s s due t o b o t h t h e mechan-i c a l and e l e c t r i c a l a s pe c ts . The m e ch an ic a l i n e r t i a a nd s t i f f n e s s o f t h eg e n e r a t o r s h a f t w e r e o b t a i n ed by a p p ro x im a t in g t h e i n t e r n a l r o t o r s i z e f r o me x t e r n a l d im e n s io n s . The e l e c t r i c a l c h a r a c t e r i s t i c s w er e d e te r m in e d by u s i n ga n e q u i va l e n t f i e l d s t i f f n e s s and g r i d i n e r t i a . An e s t im a t e d v a lu e f o r t h ef i e l d s t i f f n e s s was o b t a in e d f r o m ( 7 2 ) . l h i s f i n a l s t i f f n e s s v a lu e wasc o n n e c t e d t o an e l e c t r i c a l g r i d o f i n f i n i t e i n e r t i a w here a l a r g e f i n i t e v a l u ewas u s e d f o r c o m p u t a t i o n a l p u r p o s e s .

D R I V E 1-HAIN COUPLINGST h re e c o u p l i n g s a r e n e ce s s a ry t o c o n n e c t t h e l o w sp ee d s h a f t , s pe edi n c r e a s e r , C V l a nd g e n e r a t o r t o g e t h e r i n s e r i e s . D o u bl e e ng ag em en t g e a rc o u p l i n g s w e r e s e l e c t e d f o r e ac h l o c a t i o n t o a d j u s t f o r m i s a l ig n m e n t b etw ee n

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I

9 67

Dimeni n inc

F i g u r e 21 Diagram of CVT

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c om po ne nt s o r f o r e x p a n s io n a nd c o n t r a c t i o n o f s h a f t s d ue t o t e m p e r a t u r ech a n g e s .t h e a mo un t o f t o r q u e e a ch c a n w i t h s t a n d a nd t h e m axim um a l l o w a b l e b o r e b a s e do n c o u p l i n g s t r e n g t h .a nd t o a s s ur e a se cu re a tt a ch m e n t. I n f o r m a t i o n on p ow er and s i z e r e s t r i c t i o n so b t a i n e d f r o m c a t a lo g u e s a r e u se d t o s e l e c t t h e s e c o m po ne nt s.

The d e si g n c o n s t r a i n t s n e ce s sa ry t o d e t er m i n e a c o u p l i n g s i z e a r eI n some cases, a spacer i s needed t o f a c i l i t a t e a sse mb ly

620-w a rT he c o u p l i n g b e tw ee n t h e l o w sp ee d s h a f t a n d sp ee d i n c r e a s e r i s a F a l k1 05 0 6 i n c l u d i n g a 6 i n c h s p a c e r ..box and C V 1 . T h i s i s e s s e n t i a l l y t h e same as t h e p r e v i o u s c o u p l i n g e x ce p tA F a l k 6 20 -1 03 06 c o u p l i n g c o n n e c t s t h ei n a s m a l l e r v e r s io n s i n c e t r a n s m i t t e d t o r q u e i s l ow e r due t o t h e speedI n c r e a s e .s u p p l i e d b y t h e m a n u f a c tu r e r .A p p r o pr i a t e i n e r t i a and s t i f f n e s s v a l u es w ere o b t a in e d f r o m t a b le s

The f i n a l c o u p l in g c o n n e c ti n g t h e C V 7 t o t h e g e n e ra t o r i s a Zurn F101.5w i t h a 3 i n c h s p ac er n e c e s s a r y f o r a s se m bl y.s u p p l i e d b y t h e m a n u f a c tu r e r a r e s hown i n T a b l e 7 .The i n e r t i a and s t i f f n e s s v a lu e s

l a b l el i s t s t h e

6 r e p r e s e n t s a summary o f t h e d r i v e t r a i n co m po ne nt s a nd T a b l e 7i n e r t i a and s t i f f n e s s d a t a c a l c u l a t e d f o r e ach .

TABLE 6C om po ne nt S p e c i f i c a t i o n s i n 5 6 kW W l G D r i v e T r a i n

R o t o r -Th re e - B l a d e d wi th a B l a d e L e n g t h o f 2 6 .3 f e e t , Z e r o C o n i n g, U p w in dP o s i t on, N A C A 23024 A i r f o i l7 i n . O u t s l d e , 3 i n . I n s i d e D i am e t e r, A I S 1 4 3 4 0 S t e e lSKF S D A F 2 26 38 P i l l o w B l o c k A s se m b lyF a l k 6 2 0 - 1 0 5 0 6 D o u b l e Eng ag eme nt Ge a r , 6 i n . Sp a ce rC r i c h t o n 24 ,0 00 M od el Two S t ag e P l a n e t a r y , 1 5 . 1 5 : l O v e r a l l R a t i oF a l k 6 2 0 - 10306 Dou ble Engagement Gear TypeKumm I n d u s t r i e s , 7 5 HP, 2 : l - 3 . 3 3 : l S peed R a t i oZu rn F1 0 1 .5 Ge a r C o u p l i n g , 3 i n . S p a c e rRe l ia nc e XT-365TS, 56 kW, 460 V o l t O u tp u t , Th ree Phase , Coo l . ing Fan, SpaceH e a t e r

Low Speed Shaft -B e a r i n g s -C o u p l i n g 1 -S p e e d I n c r e a s e r -C o u p l i n g 2 -C o n t i n u o u s l y V a r i a b l e T r a n s m i s s io n -C o u p l i n g 3 -G e n e r a t o r -

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TABL 7C om ponent I n e r t i a an d S t j f f n e s s V a lu es

C O M P O N E N l

3 B la d e sHubLow S p e e d S h a f tB r a k eC o u p l i n g 1GearboxC o u p l i n g 2C V 1 I n p u t S h a f tC V T I n p u t P u l l e yC V T I d l e r sC V 1 B e l t ( o n i n p u t )

( o n o u t p u t )C V T O u t p u t P u l l e yC V T O u t p u t S h a f tC o u p l i n g 3G e n e r a t o r R o t o r / S h a f tG e n e r a t o r F i e l dE l e c t r i c a l G r i d

R O T A 1 IONAL I N E H T I A TORSIONAL STIFFNESS( i n - l b - s e c 2 )48 . 4 9 x 1 032 .30 x 1 011 .04 x 1 0

4.50 x 10 3 .20 x l o 1

31 . 6 1 x 1 03 .83 x 10 - 17 .50

2.703 . 9 01 . 3 0

7 .50

4.80 x 10-1

2.85 x 10-1

13 .10 x 10 -07 .80 x 10

-201 . 0 x 1 0

( i n - l b / r a d i a n )

-73 .9 x 10

-87

76

6 .1 x 1 09 . 5 x 1 08.1 x 101 .7 x 10

66

1 . 8 x 1 01 . 8 x 1 0

-61 . 3 x 1 062.5 x 1 0

7 .0 x l o 641 . 2 x 1 0

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APPENDIX B - ACSL PROGRAM INP UT L IS TI NG

/ / VM#R0000 J OB ( R0000, 000000000, 5, 3OO) , ACSL, CLASS=L// EXEC ACSLCLG/ / ACSL. SYSI N DD *PROGRAM 5GKW W ND TURBI NE DRI VE TRAI N DYNAMI C SI MULATI ON' - - - - - - - - - - - - - - - - - - DEFI NE ALL THE PRESET V A R I A B L , E S - - - - - - - - - - - - - - - 'I NI TI ALCONSTANT J 1 = 87200. 0 , 5 = 864. 0 I 53 = 804. 0CONSTANT 54 = . 872 , 55 = . 296 I J 6 =I 8. 11 , 57 = l.OE+lSCONSTANT K l = 3. 66Ef 07 , K2 = 9. 54E+07 I K3 = 1. 2GE+06CONSTANT K4 = 7. 48Ei 05 , K5 = 5. 46E+05 , K 6 = 1. 2E+O4

CONSTANT CVADJ = l o o . , WNOT = 30. SL I P = . 03 TSTP = 43. 999CI NTERVAL CI NT = . 01CONSTANT R = - 13. 14 , M1 = 15. 15 , PI = 3. 14155' 265

TI CNT = 0. 0' - - AT THE END OF EACH CI NT, GENERATOR T@RQUE AND RPM IS CALCULATED- - '' - - AT THE END OF EACH CVADJ , THE CVT RATI O IS ADJ USTED - - '' - - - - NPUT FUNCTI ON FOR AERODYNAMI C DAMPI NG BASED ON PJ I ND SP EED- - - - 'R1A = 18417. 0- 3896. 4* WNOT+139. 8~ WNOT 2+3. 102~~~~~~~@T~R1B = - 0. 12048 WNOT~ 4+0. 24939E- O4* ~~NOTx 5+O. l 4Z8~~- O4xWNO~R 1 = R1A + R1B' - - - - - - - - - SET I NI TI AL CONDI TI ONS FOR ROTOR SPEED OI.iEC,.L.--- 'TNOTl = - 43686. + 12700. * WNOT - 1265. 7* WNOT+ ZTNOT2 = 65. 165* WNOT* 3 - 1. 0652* WNOT* 4TNOT = TNOTl + TNOT2I F ( WNOT .GT. 30. ) TNOT = 97509.I F ( WNOT . LE. 6. 0) TNOT = 0 0' - - - - - - - - - - - CALCULATE ROTOR SPEED FOR I NI TI AL W ND SPEED- - - - - - - - - - - - 'I F ( WNOT . LE. 10. ) OMRPM = 36.I F ( WNOT . GT. 10. . AND. WNOT . LE. 18. ) OMRPM = 3. O WNOT f 6 0I F ( WNOT .CT. 18. . AND. WNOT .L,E. 22. OMRPM = 60.I F ( WNOT . GT. 30. ) OMRPM = 48. 5OMEGA = OMRPM*PI / 30.POW = TNOT* OMEGA/ 8843. 6GENRAD = ( ( POW*SLI P / 56. ) + 1. ) +188. 49556GENRPM = GENRADk30. / PIM2 = GENRAD/ ( l S. l 5 0MEGA)

I F ( WNOT . GT. 22. . AND. WNOT . LE. 30. ) OMRPM = - 1. 4375 WN@T+91. 625' - - - -CALCULATE VALUES F O R SYSTEM BASED ON I NI TI AL CONDI TI ONS- - - - - - - - '

R2 = - 1. O R' - - - - - - - - - - - CALCULATE I NTEGRATI ON I FI I TI AL COFI EI TI ONS - - - - - -Ol I C = TNOT/ Kl42 C = TNOT/ K2Q3 I C = TNOT/ K3Q4I C = TNOT/ K4Q5I C = TNOT/ K5Pl I C = J l * OMEGAP2 C: = J2"OMEGl iP3I C = J 3* OMEGAP4I C = J 4 OMEGAP SI C -= ,I.5"OMEGP,P G T C = J G+OMEGAP7I C = 57* OMEGAEND $' OF I NI TI AL 'DYNAMI C 38


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I ' - - - - - - - - - - - - - - - - - I NPUT W ND FUNCTI ON OVER TI ME- - - - - - - - - - - - - - - - - - '' - - - -TRI ANGULAR PULSE STARTI NG AT T=O FOR TNI TI AL W ND OF 20 MPH---I F ( T . GE. 0. 0 . AND. T . L T . 10. 0) W ND = 20.I F ( T . GE. 10. 0 . AND. T . L T. 13. 0) W ND = 10. O T - 80.I F ( T . GE. 13. 0 . AND. T . L T . 16. 0) W ND = - 10. O T + 180.I F ( T . GE. 16. 0) W ND = 20.I F ( W ND . L E. 10. ) OMRPM = 36.I F ( W ND . GT. 10. . AND. W ND . LE. 18.) OMRPM = 3. 0 W ND + 6. 0I F ( W ND . GT. 18. . AND. W ND . LE. 22 . ) OMRPM = 6 0 .I F ( W ND . GT. 30. ) OMRPM = 48. 5OMEGA = OMRPM* PI / 30.

' - - - - - - -CHANGE ROTOR SPEED DUE TO CHANGI NG W ND- - - - - - - - 'I F ( W ND . GT . 22. . AND. W ND . LE . 30 . ) OMRPM = - 1. 4375* W ND+91.

- - - - - - -CALCULATE AERODYNAMI C DAMPI NG EASED QN NEW W ND SPEED- - - - -R1A = 18417. 0- 3896. 4 W MD+139. 88~W MD*+2+3. 1024xW ND~*3R1B = - 0. 12048*W ND 4+0. 24~39E- O4~~~I ND~~5+0. 14284E- O4' - - - - - - - -CALCULATE TORQUE FROM W ND FOR MAXI MUM POWER EXTRACTI ON- - -TORQl = 38456. - 11028. XW ND + 951. 78 W ND* * 2 - 11. 554*W ND 3TORQZ =- . 59013*W ND* * 4 + . 16891E- O1 W ~D * 5- . 12249E- O3*W ND1 - - _ - _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~ - ~ - - - - - - - - - - - - - - - - - - - - - - - -DERI VATI VE' - - - MAXT I S THE I NTEGRATI ON TI ME I NCREMENT - - - - 'I - - - NUMBER OF I NTEGRATI ON STEPS TO NEXT CI NT==> NSTP=CI NT/ MAXT - - -' - - - - - - - - - - - STATE EQUATI ONS - - - - - - - I

R1 = R1A + R 1 j 3

TORQ = T O R Q l + T O R 9 2MAXTERVAL MAXT = 0005

PDOTl = TORQ + Rl ( 0MFGA - Pl / J l ) - K1* Q1QDOTl = Pl j J l - P2/ J 2PDOT2 = I ; l *Q1 - K2*Q2QDOT2 = P2/ J 2 - P3/ J 3PDOT3 = K2 Q2 - Ml *K3*Q3QDOT3 = ( Ml / J 3) * P3 - P4/ J 4PDOT4 = K3* Q3 - K4 Q4QDOT4 = P4/ J 4 - P5/ J 5PDOTS = K4 Q4 - M2* KSXQ5Qr j OT5 = ( M2/ J 5) *P5 - Pb/ J bPDOT6 = ( J 6 / ( J 6 + R R/ K6) ) ( I ; S*Q5 - ( R/ J 7) F' 7 - ( R2, , ' J 6) *PG)PDOT7 = ( R/ J 6) PG

1 - - - - - - . - - - I r ~I TEGRATE STATE EQIJAT I O N S -- - - - - - 'P1 x I NTEG( PDOT1 I Pl I C)Ql = I NTEG( QDOT1 , Ql I C)P 2 = I NTEG( PDOT2 , PZI C)Q2 = I NTEG( QDOT2 , Q2I C)P3 = I NTEG( PDOT3 , P3I C)P4 = I NTEG( PpOT4 , P4I CjQ4 = I NTEG( ODOT4 , Q4I C)P5 = I NTEG( PDOT5 , P 5 I C95 = JNTEC,(QD[: T5 Q S I C : )Pb = I NTEG( PI ?OTG , PSI C)P7 = I NTEG( PDOT7 I P7I C)

Q3 = I NTEG( QDOT3 Qz I C)

END ' O F DERI VATI VE- - '' - - - - - - - - - - - CALCULATE OUTF' UT PARAMETERS AT GENERATOR - - - - - - - - - - '39


44/45

G E N R A D = 1 8 8 . 4 9 5 5 6 * ( 1 . - P D O T 7 x S L I P / 2 5 5 1 . )G E N R P M = G E N R A D * 3 0 . / P I' -- -- - - -A D J U S T C V T A T I N T E R V A L S E V E R Y C V A D J S E C O N D S - - - - - - -- - - - -- 'C ONSM = T I C N T + C V A D J - C I NT; ' 2 .C O N S P = T I C N T + C V A D J + C I N T / 2 .

I ( T . G T . C O N S M . A N D . T . L T . C O N SP ) T I C N T = TI F ( T .G T . CONSM .A N D . T .L T . C O N S P ) M = GEP RkD,/( 1 5 . 15 'kOMEGE.)' C A L C U L A T E PO WE R AN D U P D A T E P A R A M E T E R S F O R I N T E G R A T I O N IPOW = P D O T 7 * G E N R P M , , ' 8 4 4 5 0 .PPS = P O W " ( - 1 . 0 )R2 = ( 2551. ' SLI P) ( 1 . ' 188. -39556 - 1 . C;EI.JRAD)' _-- - - - - - - - - - S P E C I F Y T E R M I I \I A T I O ~ J C O N D I T I O N - - - - - -- - - - - '

END $' OF D Y N A M I C 'END $' OF PR OGR AM'/ / G O . S Y S I N DD *S E T T I T L E = ' D' IP I AM I C S I M U L A T I O N O F A 5 6 K W W I N D T U R B I N E D R I V E T R A I N 'S E T DI S=99 $ ' FOR C E 3 C O L F OR MA T F O R O U T P U T 'S E T N D B U G = 0O U T P U T T I O M R P M , C V A D J , Q D O T 2 , F5 , . . .

T E R M T ( T .G E .T S T P )

W I N D , R1 , P D O T 1 , QDOT3, F 6, . . .T O R Q , E2, P D O T 2 , QDOT.2, P 7 , . . .PI OT7, M2, P D O T 3 , Q D O T 5 , Ql , . . .G E N R P M , MI , I 'DOT4, P 1 , Q2, . . .T N O T , K 6 , P D O T G , P 3 , Q 4 , . . .POW , R P D O T 5 , P 2 , Q 3 . . .WNOT, TI CNT, Q D O T 1 , P4 , o s , ' N C I O U T ' = 5 0P RE PA R T I P n O T 7 , G E N R P ~ , P O W , W I N D

STP i TPLQT W I N DP I , O T POWS T O P/ / G O . FT99FC701 DE S'J'SOIJTI=A/ */ /

S E T N G X P F ' L = 5 0 , ? JI ;I 'P P L= 20 , N P X P P L = 1 0 0 , N P Y P P L - 1 0 0

40

~~


45/45

1 Report NoNASA CR-179543

D e s i g n an d D yn am ic S i m u l a t i o n o f a F i x e d P i t c h 56 kWW ind T u r b l n e D r i v e T r a i n w i t h a C o n t in u o u s lyV a r i a b l e T r a ns m i ss i on~7. Author@)

2 Government Accession No_ _

C . G a l l o , R . Kasuba, A . P i n t z , a n d J . S p r i n g

_____ -.5 Report DateMarch 1986

6 Perforrriiriy Orydnization Code

8 Performing Organization Report No

9. Performing Organization Name and AddressC l ev e la n d S t a t e U n i v e r s i t yC l e v e l a n d , O h i o

2 Sponsoring Agency Name and AddressU. S. D e p a r t m e n t o f E n e r g yW in d/O ce an T e c h n o lo g y D i v i s i o nWash ing ton , D . C . 20545

3. Type of Report and Period CoveredC o n t r a c t o r R e p o r t

DOE/NASA/000635 Supplementary Notes

F i n a l R e p o r t . P r e p a re d u n d e r I n t e r a g e n c y A g re e m en t D E -A I0 1- 76 ET 20 32 0. P r o j e c tM an age r, 0. M i l l e r , P ow er S y st em E n g i n e e r i n g D i v i s i o n , N A S A L e w i s R e s e a r c h C e n t e r ,C l e ve l a n d , Oh i o 4 41 35 .,6 Abstract

T h i s r e p o r t c o v er s t h e dynam ic a n a l y s i s o f a h o r i z o n t a l a x i s f i x e d p i t c h w in dt u r b i n e g e n e r a t o r (WTG) t h a t i s r a t e d a t 56 kW.a b l e T r an sm i ss io n (CVT) was i n c o r p or a t e d i n t h e d r i v e t r a i n t o p r o v i d e v a r i a b l es p e e d o p e r a t i o n c a p a b i l i t y .v a r i a b l e s pe ed o p e r a t i o n , b y m eans o f a m e c h a n i c a l CVT, i s c a p ab le o f c a p t u r i n gt h e t r a n s i e n t p ow er i n t h e W TG/wind e n v i r o n m e n t . A n o t h er g o a l was t o d e t e r m i n et h e e x t e n t o f power r e g u l a t i o n p o s s i b l e w i t h C V T o p e r a t i o n .

A m e c h a n i c a l C o n t i n u o u s l y V a r l -One g o a l o f t h e d yn am lc a n a l y s i s was t o d e t e r m i n e i f

m e c h a n i c a l- -______ - __ _ - ~7 Kry Words (Suqqf.stcd b y Author(5)) __

m i e d

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