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78 PRIKLADN AYA MEKtlANIKA

A METHOD OF COMPENSATING TEMPE RAT URE -DEP ENDE NT CHANGES IN THERESISTANCE OF STRAIN GAUGE SENSING ELEMENTSL. A. Ch erk aso v and N. V. Skvo rtsov aPr ik la dn ay a Mekhani ka, Vol. 2, No. 7, pp. 135- 137, 1966

The mea sure men t o f s t a t i c therma l s t r a ins by meansof s t ra in gauges i s compl ica ted by the need to es t imatethe ef fec t o f pure ly the rmal expans ion on the therma ls t re ss da ta ob ta ined . Sens ing e lements p laced d i rec t lyon the heated par t exper ience changes in res i s -tance due both to the s t rai n in the part and to the in-c r eas es i n t h e i r o wn t em p era t u re . T h e i n c reas e s i ns en s i n g e l em en t r e s i s t an ce w i t h r i s i n g t em p era t u recan be expre ssed in re la t iv e un i t s ,

where fl is the thermal resistance coefficient of thesensing element wire; At is the temperature increment.mm

10T~30 50 ItTO lgO ]80 Z2u

Fig. 1I f the sens ing e lement i s cemented on to a par t whose

mate r ia l has a t emper a tur e expans ion coeff i c ien t d i f -feren t f rom that of the sens ing e lement wi re , then thela t t er exper ience s add i t ional s t ra in dur ing the f reethe rmal expans ion of the par t , so tha t i ts re s i s t ancechanges by the re la t ive amount

the l imit s ARTW /R - 9 10 -~ as the t emp er atu re va r-ie s fr om 20 ~ to 210 ~ C [1].

In a sens ing eleme nt with a compe nsat ing loop thet em p era t u re -d ep en d en t i n c reas es i n t he r e s i s t an ce ofthe sens ing wi re are correc te d for by the res i s t anceincr emen ts o f the compensa t ing loop connected as anaddi t ional res i s t ance in to the compensa t ing branch ofthe measur i ng br idge . The compensat ing loop mus t bemade of wi re hav ing a t emperat ure incr eme nt of thesame sign as that of the sensin g element grid under thesame condi t ions . In the 20o-240 ~ C tempe ratu re ranget he m ax i m u m t em p era t u re -d ep en d en t r e s i s t an ce i n c re -men t is i60 " 10 -5 [1].

Sen s in g e l em en t s wi t h t em p era t u re - c o m p en s a t edwi res and wi res se l f - compe nsate d by anneal ing whichhave a zero t emper atur e coeff i c ien t g ive read ingswhich do not depend great ly on t emp era tur e in therange from 20 ~ to 2000-270 ~ C. If the elast i c s t r ainbeing mea sure d i s suf f i c ien t ly l arge to make an er r orof AR/R = +2 9 10 -~ in the re sis tan ce change acce pt-ab le , then c i rcu i t compensat ion need no t be employedin this rang e [2].

Exper iments show, however , tha t c i rcu i t compen-sa t ion i s no t a lways feas ib le , whi le co rrec t ion for there s i s t a n ce i n c reas e a f t e r t he ex p e r i m en t h as a m ark edadver se ef fec t on the accurac y of s t re ss meas ure -ments , s ince in th i s case the s t r a in gauge g ives theto ta l therm al expans ion of the par t wi th a l lowance forthe thermal expans ion of the sens ing e lement . Thi sled us to develop a new technique of t em per a tur e com-p en s a t i on b as ed o n an e l ec t ro m ech a n i ca l p r i n c i p l e .

Her e ozM is the t emp era ture expans ion coeff i c ien t ofthe par t mate r ia l ; c~WR i s the t emper atur e expans ioncoeff i c ien t o f the wi re ; At i s the t emperature incre-ment; SWR is the s t rai n se nsi t ivi t y of the wire.

V ar i o u s co m p en s a t i o n m e t h od s ex i s t f or e l i m i n a t i n gthe ef fec t of t emper a tur e on changes in sens ing e le-ment res i s tm~ce. These inc lude the use of two-wi resens i ng e lement s in which one wi re has a negat ive , andt he o t h er w i r e a po s i t iv e t em p era t u re -d ep en d en t r e s i s -t ance inc reme nt when cemented on the par t. Such two-w i re s en s i n g e l em en t s r e t a i n t he s am e r e s i s t a n ce w i thch an g es i n t em p era t u re i f t h e i r co n s t i t u en t w i r e s eg -m en t s h ave r e s i s t an c es w h i ch a r e i n v e r s e l y p ro p o r -t i o n al t o t h e i r r e l a t i v e r e s i s t an ce i n c rem e n t s fo r t em -pera ture changes wi th in the same in ter val f rom t 0 to t,and i f the incre ment s th emse lves are o f oppos i t e s ign.For th i s reason one mus t know in advance the t em-p e ra t u re -d ep en d en t r e s i s t an ce i n c rem en t s o f t h e w i r es eg m en t s cem en t ed s ep a ra t e l y o n t he m a t e r i a l o nwhich the actual sen sing elem ent wil l be used. The re-s i s t an ce o f t w o -w i re s en s i n g e l em en t s v a r i e s w i th i n

- ~ 5~J~ - - _ _ ~

Fig. 2Essen t ia l ly , the t echnique cons i s t s in rep lac ing the

s ignal f rom the opera t ing sens ing e lement occas ionedby the he at ing of the par t under in ves t iga t io n by thes i g n a l f ro m a co m p en s a t i n g s en s i n g e l em en t o cca -sioned by a specific deformation of an elast ic plate.The circui t is designed in such a way that the s ize ofthe s ignal f rom the compen sat ing sens in g e lement de-pends on the t emper atu re o f the par t , s ince the t em-p e ra t u re m eas u r i n g d ev ice co n t ro l s t he d e fo rm a t i o nof the plate.

The technique was tested as fol lows. The S1D-1rec ord er des igned a t the Ins t i tu te o f Mechanics , AS

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S O V I E T A P P L I E D M E C H A N I C S 79UkrSSR, had a resolution of ~ = 1 9 0 - 5 . Speciallymade sensing elements bonded with BF-2 cement on aplate made of ~'45" steel were wired into the operatingand compensating circuits. The temperature was mea-sured with a chromel-alumel therrnoeouple connectedt o a n E P P - 0 9 p o t e n t i o m e t e r . T h e h o t j u n c t i o n o f t h et h e r m o e o u p l e w a s a t t a c h e d t o t h e p l a t e t o w h i c h t h eo p e r a t i n g s e n s i n g e l e m e n t w a s u e m u n t e d ; t h e c o l dj u n c t i o n w a s k e p t a t r o o m t e m p e r a t u r e . T o e n a b l e u st o i n t r o d u c e c o r r e c t i o n s i n m e a s u r i n g t h e e l a s t i c s t r a i no f t h e p a r t b y t h i s m e t h o d w e f i r s t d e t e r m i n e d t h e c h a r -a c t e r i s t i c A R / R = ( o~ - ~ W R ) S A t + f i a t f o r t h e g i v e nb a t c h o f s e n s i n g e l e m e n t s c e m e n t e d t o a p l a t e m a d eo f t h e m a t e r i a l o f t h e p a r t t o b e i n v e s t i g a t e d .

T o t h i s e n d t h e o p e r a t i n g p l a t e w i t h s e n s i n g e l e -m e n t s w a s p l a c e d i n a n o v e n a n d h e a t e d g r a d u a l l y . T h ed e f o r m a t i o n s d u r i n g t h e h e a t i n g p r o c e s s w e r e r e c o r d e dw i t h t h e S I D - I s t r a i n g a u g e a n d t h e t e m p e r a t u r e s w e r er e a d o f f t h e E P P - 0 9 p o t e n t i o m e t e r .

T h e r e s u l t i n g d a t a w e r e u s e d t o p l o t t h e r e l a t i o n

-R- t =f (0 'which was then used to construct the function h = f(t)describing the deformation of the plate with the com-pensating sensing element cemented on it. Both plates(i, e,, the compensating and operating plates) werekept at room temperature. The plate with the compen-sating sensing element was gripped in a vise at oneend and bent by applying a load to its free end. The.displacement h of the free end was read off an indica-tor. The reading of the SID-I strain gauge was notedfor each bending deflection. A temperature was thenassigned to this reading in accordance with the rela-tion I / k ( A R / H ) = ( t ) .Lu t h i s w a y , i . e . , b y t a k i n g v a r i o u s d e f l e c t i o n s , w eo b t a i n e d a w h o l e s e r i e s o f p a i r e d h a n d t v a l u e s . T h er e s u l t s w e r e t h e n u s e d t o p l o t h - f ( t ) . T h e s c a l e o ft h e a x i s o f a b c i s s a s a l o n g w h i c h t h e v a l u e s o f t w e r ep l o t t e d w a s c h o s e n e q u a l t o t h e t e m p e r a t u r e s c a l e o ft h e E P P - 0 9 . T h e h v a l u e s w e r e p l o t t e d a lo n g t h e o r -d i n a t e a x i s . T h i s y i e l d e d t h e c u r v e s h o w n in F ig . 1 .

T h e c u r v e w a s e n g r a v e d o n a t h i c k d u r a l u m i n u mp l a t e w h i c h w a s th e n c u t al o n g t h e c u r v e . T h i s t e m -p l a t e e n a b l e d u s t o v a r y t h e d e f l e c t i o n o f t h e p l a t e w i t h

c o m p e n s a t i n g s e n s i n g e l e m e n t s y n c h r o n o u s ly w i t hchanges in temperature. The synchronizing devicetook the form of the kinematic arrangement shown inFig. 2. Plate 2 with compensating sensing element 3was attached at one end to carriage 4 of the EPP-09potentiometer; the other end of the plate slid alongtemplate 1 mounted rigidly in front of potentiorneterscale 5. At room temperature the plate with the com-pensating sensing element lay at the beginning of thecurve and the potentiometer carriage was set at the20 ~ C position (the plate was not deformed in the initialposition).

In order to enableplate 2 to slide over template 1more easily the surface of the latter was polished andthe free end of plate 2 was fitted with a freely- rollingball tip.

The apparatus was tested over the 20~ ~ Ct e m p e r a t u r e r a n g e . A s t h e o v e n t e m p e r a t u r e r o s e t h ec a r r i a g e o f t h e E P P - 0 9 s h i f t e d ; t h e p l a t e w i t h t h e c o m -p e n s a t i n g s e n s i n g e l e m e n t c e m e n t e d t o i t s l i d o v e r t h et e m p l a t e a n d w a s d e f o r m e d a c c o r d i n g t o t h e l a w h == f ( t ) , b a l a n c i n g t h e m e a s u r i n g b r i d g e . T h e m e t h o dy i e l d e d a d e v i a t i o n o f n o t m o r e t h a n a = = ~ 3 0 9 1 0 - 5f r o m c o m p l e t e b a l a n c e o f t h e m e a s u r i n g b r i d g e .

T h e a b o v e e l e c t r o m e c h a n i c a l t e c h n i q u e o f c o m p e n -s a t i n g t h e t e m p e r a t u r e - d e p e n d e n t i n c r e a s e s i n s t r a i ng a ug e s e n s i n g e l e m e n t r e s i s t a n c e a t e le v a t e d t e m p e r a -t u r e s i s s u i t a b l e f o r u s e w i th s e n s i n g e l e m e n t s w i t hp r a c t i c a l l y a l l c h a r a c t e r i s t i c s b y s t r e n g t h t e s t in gl a b o r a t o r i e s a n d o t h e r d e p a r t m e n t s i n v o l v e d i n t h em e a s u r e m e n t o f s t a t ic t h e r m a l s t r a i n s .R E F E R E N C E S

I . N . P . K l o k o v a , " S t r a i n g a u g e s e n s i n g e l e m e n t sf o r m e a s u r i n g s t a t i c s t r a i n s a t e l e v a t e d t e m p e r a t u r e s , "i n S t r a i n M e a s u r e m e n t w i t h W i r e E l e m e n t s [ i n R u s -s i a n ] , ] z d - v o L D N T P , L e n i n g r a d , 1 9 5 8 .

2 . E . Y u . N e k h e n d z i a n d N . P . K h a r i t o n o v , " C o n -s t a n t a n w i r e s t r a i n g a u g e s e n s i n g e l e m e n t s f o r e l e -v a t e d t e m p e r a t u r e s , " I z m e r i t e l ' n a y a t e k h n i k a , n o , I ,1 9 6 2 .

26 March 1966 Institute of Mechanics, AS UkrSSR