a

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NASA Technical Memorandum 100504

(hASA-lPl-1005C4) A N A Z Y S I S OE 7- X 10-FOOT N88- 12496 E I G H SPEED WIND T C N N E L SHAP? 1 C A C S IN SLFPCSI CF P A K k F A D E F A I L U R E I L v E S % I G A T I O N (hASA) 49 p CSCL 1 4 ~ U n c l a s

G3/09 0104492

ANALYSIS OF 7- X 10-FOOT HIGH SPEED WIND TUNNEL SHAFT LOADS I N SUPPORT OF FAN BLADE FAILURE INVESTIGATION

Richard W. Faison

NOVEMBER 1987

.

National Aeronautics and Space Administration

b ~ R o 8 o & c h ~ Hampton, Virginia 23665

INTRODUCTION

Th is a n a l y s i s was prepared t o a i d i n t h e f a i l u r e i n v e s t i g a t i o n o f t h e High-speed 7- x 10-Foot Wind Tunnel. The High-speed 7- x 10-Foot Wind Tunnel a t Langley Research Center, Hampton, V i r g i n i a , exper ienced a c a t a s t r o p h i c f a i l u r e of a l l 18 S i t k a spruce fan blades d u r i n g opera t ion a t 0.8 Mach number on J u l y 9, 1985. The High-speed Tunnel, a c losed-c i rcu i t /s ing le - re turn atmospher ic wind tunne l , has been operated s i n c e 1945 t o suppor t a wide range o f subsonic aerodynamic t e s t s and s tud ies. use s i n c e 1975. I n a d d i t i o n t o b lade loss, t h e most s i g n i f i c a n t damage was a bent main d r i v e s h a f t f o r a t o t a l est imated damage loss o f $1.7 m i l l i o n .

The f a i l e d b lade s e t had been i n

An a n a l y s i s o f t h e n a t u r a l f requency c h a r a c t e r i s t i c s as w e l l as loads, r e a c t i o n s , s t resses and d e f l e c t i o n s of t h e fan d r i v e system r e s u l t i n g from s teady-s ta te and dynamic loads due t o unbalance was performed. T r a n s i e n t l o a d cases were s imu la ted by step i n p u t and ramp i n p u t l o a d i n g f u n c t i o n s in tended t o s i m u l a t e t h e l o s s of one t o n i n e blades (maximum unbalance f o r c e s ) . (Note: The f a c t t h a t t h e fan rpm changes and t h e r e i s a change i n i n e r t i a w i t h t i m e i s n o t s t r i c t l y accounted f o r i n t h i s problem b u t r a t h e r , t h e s o l u t i o n ( s ) a r e in tended t o bound t h e dynamic response).

ANALYS I S

Math Model:

The 7- x 10-Foot Tunnel d r i v e system i s dep ic ted as F igure 1 and c o n s i s t s o f an 18-blade fan d i s k d r i v e n by a 14,000 horsepower motor w i t h 14 p o l e p a i r s winding g i v i n g a top synchronous speed of 514 RPM. The d r i v e system speed i s c o n t r o l l e d by a motor generator set and l i q u i d rheos ta t . For t h i s study, t h e coord ina tes a long t h e s h a f t a re based on t h e fan c e n t e r l i n e a t s t a t i o n 0; t h e forward b e a r i n g a t s t a t i o n 33; and t h e r e a r bear ing a t s t a t i o n 191. P e r t i n e n t p h y s i c a l c h a r a c t e r i s t i c s of t h e d r i v e system a r e t a b u l a t e d as Tab le I and l i s t s weights and i n e r t i a of t h e fan and motor. The a n a l y t i c a l programs u t i l i z e d f o r t h i s s tudy use a cont inuous beam approach and t h e d i s t r i b u t i v e p r o p e r t i e s a re t a b u l a t e d as Tables I1 and I11 f o r t h e l a t e r a l and t o r s i o n a l s tud ies , r e s p e c t i v e l y . Table I 1 l i s t s t h e s t a t i o n s a long t h e s h a f t ( x ) ; t h e d i s t r i b u t e d mass moment of i n e r t i a about a d i a m e t r i c p i t c h a x i s ; t h e mass which i s t h e mass p e r u n i t leng th ; E1 which i s t h e bending s t i f f n e s s ; and ASG which i s t h e shear ing s t i f f n e s s p e r inch. Table I 1 1 g ives t h e t o r s i o n a l p h y s i c a l c h a r a c t e r i s t i c s as a f u n c t i o n o f x ( s t a t i o n a long t h e s h a f t ) where ZR i s t h e r o t a t i o n a l i n e r t i a p e r i n c h and JG which i s t h e t o r s i o n a l s t i f f n e s s p e r inch.

S i m i l a r l y ,

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Governing Equations For Oynamic Response Analys is

The l a t e r a l d e f l e c t i o n can be represented i n rllodal f a r m s o l u t i o n as:

The governing d i f f e r e n t i a l equation f o r t he genera l i zed coord ina te q n ( t ) i s (assuming i n i t i a l cond i t i ons = 0)

where aD

Qn = 1 P i ( t ) +,,(xp) = genera l i zed force i =1

P i ( t ) = f o r c i n g f u n c t i o n on s h a f t a t blades

$,,(xP) = modal d e f l e c t i o n a t fan blades, s t a t i o n 0

Mn = general i z e d mass

OJ,, = modal frequency, rad lsec

cn = modal dampening (assume .Ol)

Equat ion ( 2 ) w i l l be so lved f o r two types o f genera l i zed force, (a ) a s tep f u n c t i o n and (b ) a ramplstep funct ion.

The magnitude o f t h e fo rc ing f u n c t i o n i s dependent upon t h e number of b lades l oss . The f o r c e per b lade i s

F = mri l l 2 ( 3 )

The f o l l o w i n g assumptions are made:

18 blades t o t a l

Shaf t speed = 465 HPM = 48.69 rad/sec

Weight o f blade loss = 250 l b / b l a d e

c.g. o f b lade = 105 inches f rom c e n t e r l i n e

b lade spacing = 20'

.

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The f o r c e f o r one b lade loss i S

- 250 x 105 x 48.692 = 1.612209 EO^ i b = 386

The fo rce f o r l o s s o f n i n e blades l o s s i s

F = 1.612ES [ s i n 90 + 2 { s i n 10 + s i n 30 t s i n 50 t s i n T O ) ]

F = 9.283E5 l b = f o r c e of 1 / 2 blades loss .

U n i t Step Funct ion - Forc ing - The Laplace equat ion f o r the u n i t s tep

f o r c i n g w i t h 1/2 t h e b lade loss and i n i t i a l c o n d i t i o n s qn(O) = {n(O) = 0 i s :

i s t h e damped n a t u r a l frequency. The t i n e domain s o l u t i o n o f equat ion ( 4 ) i s

Equation ( 6 ) i s the genera l ized coord ina te f o r t h e n t h mode. response due t o a s tep f u n c t i o n force a p p l i e d w i t h zero i n i t i a l c o n d i t i o n s i s :

The moment

4

where ~ l ~ ( x ) i s the modal moment f o r the n t h mode and M ( x , T ) i s t he sha f t moment.

The sha f t s t ress i s given by:

where i) i s the sha f t diameter a t x .

.

1.439E7E t (Pn ( x p ) - - ' U ( t ) i - u ( t - T ) j

A p l o t o f t h e f i r s t f i v e genera l ized coord inates i s g iven as F igures 2a A p l o t o f t he maximum moments along the sha f t , t h a t i s the maximum t o 2e.

values o f equat ion (8) i s y iven as Figure 3. shear i s given as F igure 4. hear ing i s g iven as Figures 5a and 5b. i s g iven as F igu re 6.

The corresponding maximuni sha f t The shear t ime h i s t o r y a t each s i d e o f t h e

The moment t ime h i s t o r y a t t h e bear ing

Ramp/step f o r c i n f u n c t i o n - The sha f t speed o f 465 RPM has a p e r i o d o f ,129 s e c o n d s z r r e v o 9- utKn.f t h e f o r c i n g peaks i n 1/2 of a r e v o l u t i o n , the racnpjstep f u n c t i o n f o r loss o f one-hal f o f the blades can be assumed as fo l lows:

-F(t) = 1.439E7t 9. F ( t ) = 9.283E5

--_ - F ( t ) p /-" T i me

The govern ing d i f f e r e n t i a l equat ion i s :

The Laplace equat ion i s :

l.433E7 $,, (x,)

Mn Let An =

Then the s o l u t i o n o f equat ion (11) i s :

For t < T

For t > T

Equations (13) and (14) are t h e genera l i zed coord ina tes f o r t h e rarnp/step i n p u t and are p l o t t e d on Figures 7a t o 7e f o r genera l i zed coord ina tes 1 through 5, respec t i ve l y . TI/T~ = 0.6. ramp/step i n p u t i s p l o t t e d as F igures 8 and 9, respec t i ve l y . The t ime h i s t o r y o f t he shear a t each s ide of t he bear ing i s given as F igure 10a and Ilk and t n e t ime h i s t o r y o f the moment i s g iven as F igure 11.

F igures 7a-7e are f o r a r i s e t ime t o f i r s t mode p e r i o d ra tes , The s h a f t bear ing maximum moment and maxivum shear f o r t h e

Load cases s tud ied :

S t a t i c loadings o f (a ) g r a v i t y , ( b ) an unbalance load due t o one b lade loss, ( c ) an unbalance load d u e - t o n ine blades l oss were evaluated. The app l i ed l oad ing f o r t h e s t a t i c b lade loss was t h e c e n t r i f u g a l force imbalance o n l y and

6

d i d not i nc lude t h e aerodynamic unbalance which i s a small e f f e c t (adds approx imate ly 10% t o a l l loads) . and the weight o f b lade loss was 250 pounds a t a center o f g r a v i t y d i s tance o f 105 inches from a x i s o f r o t a t i o n .

The s h a f t was assumed t o r o t a t e a t 465 RPY

Dynamic response s tud ies fo r n ine blades l oss were run f o r a step f u n c t i o n and f o r a ramp/step f u n c t i o n where t h e r i s e t ime was var ied. Le t t h e r i s e t ime be def ined as TI and t h e s h a f t f i r s t mode pe r iod as r; then the r a t i o T / r 1 v a r i e d 0, .6, l., 1.5, 2 f o r t he dynamic runs.

RESULTS AN0 OISCUSSION

0 namic C h a r a c t e r i s t i c s o f D r i ve System. The l a t e r a l and t o r s i o n a l modal Z?hjFi3 of t h e f X 10 Y n m r u n on LRC programs LATVIB and TORVIB ( r e f s . 1 and 2), respec t i ve l y . These programs use a t r a n s f e r m a t r i x approach f o r t he s o l u t i o n and t h e r e f o r e use a continuous beam d e s c r i p t i o n . Table I V l i s t s t h e l a t e r a l and t o r s i o n a l modal f requencies i n u n i t s o f h e r t z and t h e genera l i zed masses i n u n i t s o f l h -sec2 / in f o r t h e f i r s t f i v e modes.

A Campbell diagram f o r t he 7 X 10 tunne l d r i v e i s g iven as F igu re 12. inodes ar2 s i g n i f i c a n t l y above t h e 1 per r e v o l u t i o n e x c i t a t i o n . l a t e r a l o f 15.5 h e r t z corresponds t o t h e 2 per r e v o l u t i o n e x c i t a t i o n a t t h e s h a f t speed o f 465 RPM. The 7 X 10 tunnel d r i v e should not , however, have a h i g h 2 per r e v o l u t i o n e x c i t a t i o n which might e x i s t i n an asymmetric shaf t des ign o r a s h a f t d r i v e w i t h s e l f a l i g n i n g coupl ings.

A l l The f i r s t

A p l o t o f t he l a t e r a l mode shapes i s g iven as F igu re 13 and t h e t o r s i o n a l mode shapes i s g iven as F igu re 14 f o r t h e f i r s t f i v e modes.

A dynamic response f o r a s tep func t i on to rque o f 1.E6 inch - lb . app l i ed a t t he f a n c e n t e r l i n e was accomplished. The genera l ized coord ina tes are def ined s i m i l a r t o equat ion (6 ) o f ana lys i s sec t i on except t o r s i o n a l f requencies, mass and d e f l e c t i o n s were used. The maximum torque was c a l c u l a t e d and tabu la ted as Table I. The maximum torque and maximum t o r s i o n a l s t r e s s f o r t h e s tep e x c i t a - t i o n occurs a t s t a t i o n 8 which i s i n t he reg ion o f t he fan keyway.

Steady s t a t e response:

The s t a t i c steady s t a t e response was accomplished by a two p o i n t boundary va lue prograin a t LaRC. at tached t o ground a t s t a t i o n 33 and t h e two boundaries were t h e f r e e end a t t h e fan and t h e s imply supported r e a r bearing. t h e s t a t i c problem were t h e same as l i s t e d p rev ious l y f o r t h e dynamic s tud ies .

The forward bear ing was s imu la ted by a l a r g e s p r i n g

The phys i ca l p r o p e r t i e s f o r

The r e s u l t s f o r g r a v i t y load; l - b lade loss (F = 1.6122ES l b ) ; and 9-blade l o s s (F = 9.283E5 l b ) a re g iven as F igures 15, 1 6 , and 1 7 , r e s p e c t i v e l y . For t h e tab les , y represents the d e f l e c t i o n ( inches) ; a lpha t h e s lope i n u n i t s o f rad ians; m t h e moment i n u n i t s o f inch-pounds; v t h e shear i n u n i t s o f pounds.

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tlnbalance fo rce requ i red _____ to d e f l e c t -. --- blade center1 -- i n e _--- 0.11) __- inches - _-- (steady __ __ ___ s t a t e response)

The d e f l e c t i o n a t t h e b lade c e n t e r l i n e ( s t a t i o n 0) due t o one b lade loss ( fo rce = 1.6122E5 l b s ) was .Os88 inch. This would i n d i c a t e t h a t a s t a t i c force o f (.1/.0589) X 1.6122E5, o r a l o s s of 1.7 blades would be requ i red f o r w a l l contact , where 0.10 i n c h has been assumed t o he t h e b lade clearance.

-- -

L n a m i c response f o r loss o f up t o n ine blades

The dynamic response f o r nine-blade loss and hav ing a s tep func t i on ( T / P ~ = O), where TI = r i s e t ime and T i s the f i r s t mode pe r iod and f o r a ramp/step f u n c t i o n was presented i n ana lys is sect ion. A p l o t o f t he maxiwm moment f o r t h e s tep and ramp/step func t ion was g iven as F igures 3 and 8, respec t i ve l y , t h e l a t t e r be ing presented f o r the parameter ~ / r 1 = .6, o r t h e r i s e t ime equal t o one-half t he f i r s t mode per iod. S i m i l a r p l o t s were g iven f o r t h e maximum shear i n F igures 4 and 9. F igure 6 d e p i c t s t h e r e s u l t i n g moment t ime h i s t o r y a t t he forward bear ing s t a t i o n 33 and i t i s ev ident t h a t t h e modal p a r t i c i p a t i o n i s almost e n t i r e l y t h a t o f t he f i r s t mode. The shear h i s t o r y g iven as F igures 5a and 5b, however, shows s i g n i f i c a n t t h i r d inode pa r - t i c i p a t i o n . The dynamic response h i s t o r y f o r t h e ramp/step funct ion, F igures l o a , lob, and 11 show almost e n t i r e l y f i r s t mode p a r t i c i p a t i o n .

A general statement about the modal p a r t i c i p a t i o n a long t h e d r i v e s h a f t i s t h a t t he modal p a r t i c i p a t i o n cons is t s o f severa l modes bu t most of t he shaf t can be descr ibed v i a the f i r s t mode.

The s t r e s s i n the s h a f t i s g iven by equat ion ( 9 ) which i s

10.18591 M( xlt) ( 9 )

The s t ress a t the forward bear ing ( x = 33) i s obta ined w i t h 0 = 16 inches.

The r e a c t i o n o f t he forward bear ing i s g i v e n by the d i f f e r e n c e between the shear a t s t a t i o n x = 33.

The d e f l e c t i o n and s lope a t t h e forward bear ing i s g iven as Table V I f o r t h e s tep and ramp/step func t i on .

As has been mentioned e a r l i e r , t h e dynamic s tudy f o r t he parameter r / q was run fo r T / T ~ = 0, .6, O., 1.5 and 2. Only t h e p l o t s f o r T / T ~ = .6 have been inc luded i n t h i s repo r t . A t a b u l a t i o n of t h e r e s u l t s f o r t h e complete para- m e t r i c study has been presented as Table V I I . The aerodynamic moment was no t inc luded i n t h i s study, as has been mentioned e a r l i e r . Tho aerodynamic unba- lance would c o n t r i b u t e approx imate ly 10 percent the e f f e c t o f t h e c e n t r i f u g a l f o r c e unbalance. The r e s u l t s o f the c e n t r i f u g a l force have been increased by

’ 10 percent for Table V I I . The values have been nor mal ized by t h e i r respec t i ve s t a t i c values and presented as Table V I 1 1 w i t h a p l o t shown as F igure 16. On F igu re 18 i s shown t h e dynamic f a c t o r f o r a s i n g l e degree of freedom s y s t e i . A s mentioned e a r l i e r , t he dynamic response a t t h e forward bear ing was most ly t h e f i r s t mode. curves would have been as per the s i n g l e degree of freedom curve.

Had the p a r t i c i p a t i o n been e n t i r e l y t h e f i r s t mode, t h e

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The ana lys i s r e s u l t s presented have been f o r t he c e n t r i f u g a l force c rea ted by the b lade loss. 4n a d d i t i o n a l moment load i s due t o t h e aerodynamics unbalance due t o the b lade loss and i s approx imate ly 10 percent of moment c rea ted by t h e c e n t r i f u g a l force a t t he forward bear ing. sented i n Table V I 1 f o r t he moment and s t r e s s a t t h e forward bear ing account f o r t h e aerodynamics unbalance.

The r e s u l t s p re -

A comparison o f t h e c a l c u l a t e d bending s t resses a t t h e bear ing (h ighes t s t ress p o i n t ) g iven i n Table V I 1 i n d i c a t e t h a t p a r t i a l t o t o t a l y i e l d i n g o f t h e shaf t would occiir (see Table 1-A f o r s t reng th va lues) . s h a f t , t he modulus o f y i e l d ( o r rup tu re ) would be 1.6 t imes t h e t e n s i l e capa- b i l i t y . 1.6 x Sy ie ld Inspec t i on o f t he d r i v e s h a f t does show t h a t i t i s bent and t h e r e f o r e y i e l d e d p a r t i a l l y so t h a t t h e s o l u t i o n r e s u l t s in Table V I 1 are be l ieved t o bound t h e loads t h a t t h e d r i v e system experienced due t o b lade f a i l u r e .

A d d i t i o n a l l y , based on t h e estimated shear s t reng th p r o p e r t i e s (see Table 1-6) f o r t h e f o u r bear ing pedasta l t ie-down b o l t s which f a i l e d i n shear, a r e a c t i o n a t t h e hear ing o f approximately 854,000 lbs . would be s u f f i c i e n t t o shear t h e b o l t s . Table V I 1 shows t h a t t he peak unbalance r e a c t i o n load f o r a l l cases s tud ied i s g r e a t e r than 854,000 lbs.

- Oynamic b lade loss f o r .1 i n c h d e f l e c t i o n

The f o r c i n g f o r one-blade l o s s i s 1.6122E5 and f o r n ine-b lade l o s s i s 9.283E5. For t h e s tep input , t h e n ine-b lade loss gave a fan c e n t e r l i n e d e f l e c t i o n of .a228 inch . Thus

I n t h e case o f a c i r c u l a r

Thus t h e s t r e s s requ i red t o form a p l a s t i c h inge would be o r f o r f r a c t u r e 1.6 x SUIt.

Comparison o f t h e requ i red r e a c t i o n load t o t h e c a l c u l a t e d loads i n

.1" d e f l e c t i o n = FORCE .8228" de f 1 e c t i on 9.283E5

o r FaRCE = 1,1728E5 or 70% o f one b lade

F o r t h e ramp/step using T / T ~ = 0.6,

.l" d e f l e c t i o n - FORCE .61752' d e f l e c t i o n 9.283E5

o r FORCE = 1.503E5 o r 93% of one blade.

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CONCLUSIONS

(1) No i n s t a b i l i t i e s o f opera t iona l resonances f o r t h e d r i v e system were i d e n t i f i e d .

( 2 ) Upset (unbalance) loads due t o b lade(s ) f a i l u r e f o r a l l cases s tud ied are s u f f i c i e n t t o p a r t i a l l y o r g ross ly y i e l d t h e d r i v e shaf t , f a i l the bear ing pedestal b o l t s , and b r i n g the blades i n t o contact w i t h the tunnel s h e l l which would r e s u l t i n almost instantaneous d e s t r u c t i o n o f the h l ades.

( 3 ) Transient s o l u t i o n r e s u l t s c o r r e l a t e w i t h t h e damage susta ined due t o t h e mishap.

( 4 ) The ana lys is i n d i c a t e s t h a t the loss of approximately 70% t o 93% o f t h e mass o f one blade would d e f l e c t t h e c e n t e r l i n e o f t h e fan 0.1 i n c h which i s t h e minimum measured opera t ing gap between t h e b lade t i p s and t h e tunnel she1 1.

RECOMMENOAT IONS

(1) Upon complet ion of repa i rs , t h e d r i v e s h a f t should be instrumented and v i b r a t i o n measurements taken d u r i n g shakedown.

(2) Permanent d r i v e system moni tors should be i n s t a l l e d t o t r i p the system o f f l i n e i f excessive v i b r a t i o n s occur.

( 3 ) I f t h e present d r i v e shaf t i s reused, hardness checks should be made and very thorough inspec t ions completed before i n s t a l l a t i o n .

( 4 ) Because o f t h e f l e x i b i l i t y o f the d r i v e s h a f t r e s u l t i n g i n h i g h sens i - t i v i t y t o unbalance loads, cons idera t ion should be g iven t o i n s t a l l i n g f r a n g i b l e t i p s on t h e new b lade se t and opera t ing w i t h a l a r g e r gap between the blade t i p and tunnel w a l l .

REFERENCES

1. Harkins, Barbara; and Geiger, Thomas T.: Computer Program f o r Natura l Modes and Frequencies o f a Branched Beam i n Transverse V ib ra t i on . ER-14441, M a r t i n Company, Bal t imore, Mary1 and. December 1966.

Davis, Robert B; and Stephens, Maria V.: A Recurrence M a t r i x Method f o r t h e Ana lys i s o f Long i tud ina l and Tors iona l V i b r a t i o n s i n Non-Uniform Mu l t i b ranch Beams w i t h Var iab le Boundary Condi t ions. NASA TMX-71973 dated May 6, 1974.

2.

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I TABLE I

PHYSICAL CHARACTERISTICS OF 7 X 10 TUNNEL

, Tota l d r i v e weight = 79451 l b .

Fan blade and hub weight = 2800 lb .

Motor r o t o r weight = 30396 lb .

To ta l d r i v e i n e r t i a = 437995 i n lb . set' Fan b lade and hub i n e r t i a = 252787 i n lb . sec2

Motor r o t o r i n e r t i a = 182112 i n lb . sec2

TABLE I - A

SHAFT STRENGTH PROPERTIES

(ESTIMATES FROM HARDNESS CHECKS)

Room Temperature Values

Suit = 95 k s i

S y i e l d = 70 kSi

TABLE I - R

BEARING TIE-DOWN BOLTS ULTIMATE STRENGTH PROPERTIES

(ESTIMATED FROM HARDNESS TESTS)

Tens i le U l t i m a t e - 117 k s i

Shear U l t i m a t e - 94 k s i

12

TABLE I 1 ORIGINAC PAGE ‘31: POOR QUALITY P t i Y S I C A L C H A R A C T E R I S T l C 5

X

(INCHES) --

-. 0 17.006

-- 11 . 000 -- - - ii . o oo--

0.000 _ _ T L o o o . 13.000

- - 19.000 19.0 00 24.750 24.7 50

--

- - 7xib TUNNEL L A T E R A L M O I M

--- 33.000 330 000

~ 42.625 .

1 7 4 2 . 6 2 5 5 0 . 6 2 5

.-_. ‘56.000 ~

56.000 82.00!J 82.000 83.004 96. 500 96.500

I O ~ . S C O ~ -109.500 I 130.500 ~ . 130.500

~ 148.500 I 1 7 4 * 5 0 6

1800 500 - 1 8 5 . 8 1 3

185.813 191.000

-.

1 4a . 5 03

_ _

’ *-. 191.000 . 196 188

*ld219E+oL. ldL19t +Gl ~18219E*OA 39923E+01 399231: +01 .1134Ok+O2 17295E+04

-0 1 7 2 9 5 E + 0 4 A 7295E + 0 4

0 17L93E+OI; 17293t+o4 .172‘J5E+04 172 95E +O 4

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-. 196.188 ~74627t+00 207.938 .74627E+OO ,

. 207.v39 .35989t+03 217.000 035989E*00

- 229.000 . _ _ _ _ 035989i+OO’ .

--

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I . CENTER O F G R A V I T Y X = I

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-- -

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13

7 x 1 0 TUNNcL fURS1l)N M o o t 3

S T A T I O N

14

TABLE I V

MODE LATEHAL

( W MASS FREQUENCY GENERALIZED

15.517 ,9477058E2

41.505 .989O 384E 2

71.782 .1650873E3

116.054 .7522273E1

131.51 .1084724E2

TORSIONAL

(Hz 1 MASS FREQUENCY GENERALIZED

18.015 .1865477€6

55.555 .1336389€6

96.238 .e2300 74E5

104.498 .1312093€6

150.1341 .9236134E5

15 ORIGINAL PAGE 1s TABLE V OF POOR QUALITY MAXIMUM TORSIONAL RESPONSE DUE TO STEP FUNCTIONS

16

TABLE V (CONT'D)

X T I M E i MAX TORQUE

I

I

-

ORIGINAL PAGE IS OE POOR QUALIm

.

17

TABLE V I

DEFLECTION AND SLOPE AT FAN CENTERLINE

Mode

1

2

3

4

5

Mode

1

2

3

4

5

- .01081068 -e044972 -.0083563 8.14299-4 1.513058-4

.04782744 .98205 .O 16846 4.696893-2 8.05701-4

- a002432855 -.023794 -.0016474 5.788735-5 4.007885-6

.(3061097 6.1326 7 1-3 2.206 122-4 Y'I = -2.7849-2

--- .03610952 .16984 yn = .8228

= -1 A9566 deg.

RAMP/STEP FUNCTION t = .0387

q n ( t = .0387 4n(Xp = 0) '+'n(Xp = 0) Yn = qn4n yn = qn'Jln - .97 .60162 -.(I22707 .583571 - -022026

----. -

- .0076 -.044972 -.(IO83563 3.41787-4 6.351-5

.0302 .98205 .016846 .02966 5.0875-4

- .00615 -.023794 -moo16474 1.4633-4 1.01315-5

.0061097 3.83838-3 1.3808-4 --- - .0226 .16984 Yn = e617519 yn = -2.13-2

= -1.2207 deg.

18

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F i g u r e 12. - Campbell Diagram f o r 7 X 10 Tunne l .

42

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X I INCHES

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43

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. .. -

\

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Bearing r e a c t i o n

4 ’4

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1.2 I

Figure 18. - Dynamic Factor as a Funct ion o f Rise Time.

1. Report No. NASA TM-100504

13. Type of Report and Period Covered

Technical Memorandum 12. Sponsoring Agency Name and Address

14. Sponsoring Agency Code Nat iona l Aeronaut ics and Space A d m i n i s t r a t i o n Washington, DC 20546

15. Supplementary Notea

2. Government Accession No. 3. Recipient's Catalog No.

16. Abstract

1. Title and Subtitle Ana lys i s o f 7- X 10-Foot High Speed Wind Tunnel Sha f t Loads i n Support of Fan Blade F a i l u r e I n v e s t i g a t i o n

~

Th is r e p o r t was accomplished t o a i d i n t h e f a i l u r e i n v e s t i g a t i o n o f t h e High-speed 7-x 10-Foot Wind Tunnel. a t Langley Research Center, Hampton, V i r g i n i a , exper ienced a c a t a s t r o p h i c f a i l u r e o f a l l 18 S i t k a spruce fan blades d u r i n g opera t i on a t 0.8 Mach number on J u l y 2, 1985. The High-speed Tunnel, a closed-circuit/single-return atmospheric wind tunne l , has been m e r a t e d s ince 1945 t o support a wide ranqe

The High-speed 7-x 10-Foot Wind Tunnel

5. Report Date November 19 87

6. Performinp Code

o f subson use s ince ben t main

7 Author(s) Richard W. Faison

'

3. Performing Organization Name and Address

NASA Langley Research Center Hampton, VA 23665-5225

An analys r e a c t i on s

8. Performing Organization Report No.

1 10. Work Unit No.

505-61-01-07 1

11. Contract or Grant No.

c aerodyanmic- tes ts and s tud ies . The f a i l e d b l a d e ' s e t had been ii 1975. I n a d d i t i o n t o blade loss, t he most s i g n i f i c a n t damage was a d r i v e s h a f t f o r a t o t a l es t imated damage l o s s of $1.7 m i l l i o n .

s o f t h e n a t u r a l frequency c h a r a c t e r i s t i c s as w e l l as loads, s t resses and d e f l e c t i o n s of t h e fan d r i v e system r e s u l t i n g from

steady -s ta te and dynamic loads due t o unbalance was performed. l o a d cases were s imu la ted by step i n p u t and ramp i n p u t l o a d i n g f u n c t i o n s in tended t o s imu la te t h e l o s s o f one t o n i n e blades (maximum unbalance

T r a n i i e n t

fnrrnc \ .

17. Key Words (Suggested by Authors(s))

D r i v e s h a f t dynamic response Shaft s t resses Dynamics of blade l o s s Dynamic system response to fan

U n c l a s s i f i e d - U n l i m i t e d

Cllh;ne+ ratnnnmi I blade failure I I -

19. Secur:tv Classif.(of this report) i 20. Security Cl.usif.(of this page) 131. No. of Pages 22. Price

U n c l a s s i f i e d - - I U n c l a s s i f i e d 1 48 A03

For sale by the Sational Technical Information Service. Springfield, i'irginia 22161 h4S.A ia:.qley F,,rrn . 1 J i n e 1 3 3 5 )