POLYMER

MECHANICS

593

INSTRUMENT F O R RESONANCE TESTS ON P O L Y M E R M A T E R I A L S A. A. B a l o d i s and V. A. L a t i s h e n k o M e k h a n i k a P o l i m e r o v , Vol. 2, No. 6, pp. 9 2 3 - 9 2 6

1966

UDC 678:626.1.05 The operating principles and technical characteristics of a new testing instrument, the IChZ-7F, are briefly described. This imtrumen~, developed at the Institute of Polymer Mechanics of the Academy of Sciences of the Latvian SSR, Riga, measures the various natural frequency modes and the logarithmic decrement of intermediate products and finished parts made of polymer and other materials. Its specific advantages over similar instruments are discussed. In r e s e a r c h o r g a n i z a t i o n s t h e v i s c o e l a s t i c p r o p e r t i e s of p o l y m e r m a t e r i a l s a r e f r e q u e n t l y s t u d i e d by d y n a m i c m e t h o d s , in p a r t i c u l a r , t h e r e s o n a n c e m e t h o d , i n v o l v i n g d e t e r m i n a t i o n of the c o m p l e x m o d u l i of e l a s t i c i t y and t h e i r c o m p o n e n t s f r o m m e a s u r e d v a l u e s of the n a t u r a l f r e q u e n c i e s of v a r i o u s m o d e s of v i b r a tion of the t e s t p i e c e s and the l o g a r i t h m i c d e c r e m e n t of the v i b r a t i o n s [1]. I n v e s t i g a t i o n s at the I n s t i t u t e of P o l y m e r M e c h a n i c s of the A c a d e m y of S c i e n c e s of the L a t v i a n SSR [2] h a v e shown t h a t the r e s o n a n c e m e t h o d can be w i d e l y u s e d to d e t e r m i n e the p h y s i c o - m e c h a n i c a l p r o p e r t i e s of p o l y m e r m a t e r i a l s and f o r continuous n o n d e s t r u c t i v e q u a l i t y t e s t i n g of t e s t p i e c e s , i n t e r m e d i a t e p r o d u c t s , and v a r i o u s f i n i s h e d p a r t s e v e n u n d e r p r o d u c t i o n c o n d i t i o n s . The r e s o n a n c e m e t h o d m a k e s i t p o s s i b l e to r a p i d l y d e t e c t s t r u c t u r a l c h a n g e s that s e r i o u s l y a f f e c t s e r v i c e p r o p e r t i e s y e t a r e d i f f i c u l t o r i m p o s s i b l e to d e t e c t by o t h e r m e t h o d s . T h e w i d e r u s e of the r e s o n a n c e m e t h o d in s c i e n t i f i c r e s e a r c h and i n d u s t r y would m a k e it p o s s i b l e to a c c e l e r a t e the d e v e l o p m e n t and i n t r o d u c t i o n of new m a t e r i a l s , i m p r o v e the q u a l i t y of p a r t s m a d e of p o l y m e r m a t e r i a l s , m a k e s a v i n g s in m a t e r i a l s t e s t i n g , and p r o d u c e p a r t s of g u a r a n t e e d q u a l i t y . The chief r e a s o n f o r d e l a y in the m o r e g e n e r a l adoption of t h i s m e t h o d i s the l a c k of s u i t a b l e c o m mercial equipment.

F i g . 1. G e n e r a l view of i n s t r u m e n t .

The instruments presently in use in various organizations are '~home-made" and were developed principally for solving particular problems [3-5]. The shortcomings of existing equipment, especially that used

for measuring the decrement, include unsatisfactory accuracy and complicated circuitry which reduces the reliability of the equipment and makes it difficult to use by people who are not specialists in radio engineering. In a number of cases the broader use of the eqilipment is limited by the narrow range of measurement of natural frequencies and decrement or by the possibility of obtaining individual comparative characteristics only on test p~eces of a particular shape and size. i

I

I

I

L-";-~I

t~'-r'~l

lf~-!

I ¢o II

II

o II

F i g . 2. B l o c k d i a g r a m of i n s t r u m e n t . The u s e of h o m e - m a d e i n s t r u m e n t s t e n d s to c r e a t e s e r i o u s d i f f i c u l t i e s in c o n n e c t i o n with the c o m p a r i s o n of d a t a o b t a i n e d on d i f f e r e n t i n s t r u m e n t s , e v e n when the t e s t p i e c e s a r e i d e n t i c a l . T h i s a p p l i e s p a r t i c u l a r l y to d e t e r m i n a t i o n of the l o g a r i t h m i c d e c r e m e n t , s i n c e in the p r o c e s s of m e a s u r e m e n t i t i s d i f f i c u l t to t a k e into a c c o u n t the e f f e c t on t h a t q u a n t i t y of d i f f e r e n t e x c i t i n g , r e c e i v i n g , and r e f e r e n c e s y s t e m s and o t h e r factors. R e s o n a n c e i n s t r u m e n t s of f o r e i g n m a n u f a c t u r e , f o r e x a m p l e , t h o s e m a d e by the F o r s t e r I n s t i t u t e (West G e r m a n y ) , C a w k e l l R e s e a r c h E l e c t r o n i c s (England), J a p a n E l e c t r o n i c s I n s t r u m e n t s Co. (Japan), e t c . , a l s o p o s s e s s a n u m b e r of s i m i l a r s h o r t c o m i n g s . At the I n s t i t u t e of P o l y m e r M e c h a n i c s we h a v e d e v e l o p e d an e x p e r i m e n t a l m o d e l of an i n s t r u m e n t f o r m e a s u r i n g v i b r a t i o n f r e q u e n c i e s and d a m p i n g c h a r a c t e r i s t i c s , the I C h Z - 7 F , which can be u s e d to d e t e r m i n e , c o n v e n i e n t l y and with high a c c u r a c y , the f r e q u e n c y of v a r i o u s m o d e s of v i b r a t i o n and t h e i r a t t e n u a t i o n both on t e s t p i e c e s and on a s e r i e s of i n t e r m e d i a t e p r o d u c t s and p a r t s . The c o n s t r u c t i o n of the i n s t r u m e n t i s u n i t i z e d . The basic instrument has very simple circuitry, is reliable, and c a n b e u s e d w i d e l y both in s c i e n t i f i c r e s e a r c h and in i n d u s t r y . A s p e c i a l f r e q u e n c y d e t u n i n g m e c h a n i s m m a k e s p o s s i b l e d i r e c t d i a l r e a d o u t of the d e c r e m e n t . A u x i l i a r y u n i t s and d e v i c e s m a k e i t p o s s i b l e to i m p r o v e the a c c u r a c y of the m e a s u r e m e n t s and a l s o to r e g i s t e r the a m p l i t u d e of the v i b r a t i o n s and the r e s o n a n c e curve° A s a r e s u l t of c o m b i n a t i o n with o t h e r s p e c i a l l y d e s i g n e d units, the i n s t r u m e n t can a l s o be a d a p t e d to the

594

MEKHANIKA POLIMEROV

determined of the mbove-mentionedcharacteristics under optimal measuring conditions for various special cases. A g e n e r a l v i e w of the b a s i c i n s t r u m e n t i s shown in F i g . 1, the c o r r e s p o n d i n g b l o c k d i a g r a m in F i g . 2. V i b r a t i o n s a r e e x c i t e d in the t e s t p i e c e by m e a n s of an e l e c t r o m e c h a n i c a l t r a n s d u c e r 1 s u p p l i e d through a m p l i f i e r 4 by a s i n u s o i d a l o s c i l l a t o r 3 with tunable f r e q u e n c y ; they a r e then r e c e i v e d by a s e c o n d e l e c t r o m e c h a n i c a l t r a n s d u c e r 2, a m p l i f i e d by a b a l a n c e d a m p l i f i e r 6, and fed to the v e r t i c a l d e f l e c t i n g p l a t e s of a c a t h o d e - r a y tube 7. The a m p l i t u d e of the v i b r a t i o n s and the e x c i t i n g f o r c e can a l s o be c h e c k e d f r o m v o l t m e t e r 9. The i n s t r u m e n t t u b e s a r e s u p p l i e d f r o m l o w - and h i g h - v o l t a g e r e c t i f i e r s 10 and 8. In the e x t e r n a l e x c i t a t i o n r e g i m e the n a t u r a l f r e q u e n c i e s of the t e s t p i e c e a r e d e t e r m i n e d f r o m the m a x i m u m a m p l i t u d e and a r e r e a d f r o m the s c a l e of the m a s t e r o s c i l l a t o r g r a d u a t e d in h e r t z . In o r d e r to c h e c k the c o r r e s p o n d e n c e of the t e s t p i e c e v i b r a t i o n f r e q u e n c y and the f r e q u e n c y of the e x c i t i n g f o r c e f r o m L i s s a j o u s f i g u r e s , the o s c i l l a t i o n s f r o m the o s c i l l a t o r a r e a l s o fed v i a a m p l i f i e r 5 to the h o r i z o n t a l d e f l e c t i n g p l a t e s of the c a t h o d e - r a y tube. In m e a s u r i n g n a t u r a l f r e q u e n c i e s in the s e l f - e x c i t a t i o n r e g i m e m a s t e r o s c i l l a t o r 3 is d i s c o n n e c t e d , and the output of a m p l i f i e r 6 is c o n n e c t e d a c r o s s a p h a s e s h i f t i n g c i r c u i t with the input of a m p l i f i e r 4. In t h i s c a s e the n a t u r a l f r e q u e n c y can b e found f r o m the s c a l e of the m a s t e r o s c i l l a t o r using L i s s a j o u s f i g u r e s , m e a s u r e d with an a u x i l i a r y f r e q u e n c y m e t e r o r a u t o m a tically recorded. The l o g a r i t h m i c d e c r e m e n t is d e t e r m i n e d f r o m the width of the r e s o n a n c e c u r v e and i s r e a d f r o m a s p e c i a l detuning scale, which is graduated directly in decrement units relative to the 0.5 level of the resonance curve. For this purpose a rotary capacitor is employed as frequency tuning element in the master RC oscillator 3 to ensure a logarithmic relation between frequency and rotor angle,

f=f0e~,

(1)

w h e r e f i s the f r e q u e n c y , f0 the m i n i m u m f r e q u e n c y of the r a n g e at cz = 0, c~ is the angle of r o t a t i o n of the r o t o r , and a a c o e f f i c i e n t d e p e n d i n g on the r a n g e o v e r l a p f a c t o r and the c o r r e s p o n d i n g t o t a l angle of r o t a t i o n of the r o t o r . The d e t u n i n g s c a l e i s coupled with a v e r n i e r m e c h a n i s m which e n a b l e s the r e l a t i v e p o s i t i o n of the r o t o r and s t a t o r of' the r o t a r y c a p a c i t o r to be a d j u s t e d at any f r e q u e n c y in the w o r k i n g r a n g e in the d i r e c t i o n of e i t h e r a d e c r e a s e o r i n c r e a s e in f r e q u e n c y . The d e c r e m e n t i s d e t e r m i n e d a s the s u m of the two r e a d i n g s 6_ and 6+ o b t a i n e d f r o m the detuning (dec r e m e n t ) s c a l e by e s t a b l i s h i n g , with the h e l p of the d e t u n i n g m e c h a n i s m , the f r e q u e n c i e s c o r r e s p o n d i n g to the 0.5 l e v e l of the r e s o n a n c e c u r v e b e f o r e and a f t e r resonance,

where

6-=~-~p_;~ 6 + = ~-~ p+, and p_ and p+ a r e t h e r e l -

a t i v e detunings c o r r e s p o n d i n g to 6_ and 6+. The d e t u n ing s c a l e i s g r a d u a t e d in units p r o p o r t i o n a l to the d e tuning with a c c o u n t f o r t h e c o e f f i c i e n t 7r/(3)t/2 . In t h i s e a s e t h e r e a d i n g s 5_ and 5+ on the dettming s c a l e c o r r e s p o n d to detuning a n g l e s A s and Aoz+ r e l a t e d to 5_ and 6+ by t h e e x p r e s s i o n s ah~.

6 _ = } ~:~( 1 --e-~--)," aA%

e i

(2)

),

(4)

w h e r e i i s the r a t i o of the detuning m e c h a n i s m . A c o n v e n i e n t d e c r e m e n t s c a l e f a c t o r can be obtained by a s u i t a b l e choice of i. B r i e f t e c h n i c a l d e s c r i p t i o n of i n s t r u m e n t ( m a i n

uuits): Range of m a s t e r o s c i l l a t o r : 100 to 12 000 Hz. M a x i m u m f r e q u e n c y r e a d i n g e r r o r : =L(2% + 1) Hz. Scale l i m i t s of d e c r e m e n t m e a s u r e m e n t : 0.28. A c c u r a c y of d e c r e m e n t r e a d i n g s f r o m s c a l e : 2-5%. I n s t r u m e n t d i m e n s i o n s : 57 x 38 x 38 cm. I n s t r u m e n t p o w e r supply: ac 5 0 - c y c l e , 1 2 7 / 2 2 0 - v o l t . P o w e r input: 140 W. When a u x i l i a r y units a r e e m p l o y e d f o r s c a l e c a l i b r a t i o n it is p o s s i b l e to r e d u c e the f r e q u e n c y and d e c r e m e n t r e a d i n g e r r o r s to 0 . 1 - 0 . 5 and 1%, r e s p e c tively. A f u r t h e r d e c r e a s e in f r e q u e n c y and d e c r e m e n t r e a d i n g e r r o r s (to 10 -4 o r t e s s and 10-2%, r e s p e c t i v e l y ) c a n be a c h i e v e d by u s i n g s c a l e r s . The a c c u r a c y of d e t e r m i n a t i o n of the a m p l i t u d e of the t e s t p i e c e v i b r a t i o n s with an a u x i l i a r y c a l i b r a t i o n unit is about 5%. E x p e r i e n c e with the i n s t r u m e n t at the I n s t i t u t e of P o l y m e r M e c h a n i c s and r e s u l t s of t e s t s u n d e r i n d u s t r i a l c o n d i t i o n s have shown it to b e a highly e f f i c i e n t ins t r u m e n t f o r s t u d y i n g the effect of c h a n g e s in c o m p o s i t i o n and p r o d u c t i o n p a r a m e t e r s on the p h y s i c a l s t r u c t u r e and s e r v i c e p r o p e r t i e s of m a t e r i a l s and a l s o f o r t h e continuous c o n t r o l of the the q u a l i t y of i n t e r m e d i a t e p r o d u c t s and f i n i s h e d p a r t s .

REFERENCES I. J. Ferry, Viscoelastic Properties of Polymers [Russian translation], Moscow, 1963. 2. V. V. Dzenis and V. Ya. Lipovskii, Mekh. polim. [Polymer Mechanics], 4, 557, 1966 3. Yu. G. Yanovskii and G. V. Vinogradov, Mekh. polim. [Polymer Mechanics], 4, 106, 1965. 4. V. M. Degtev, N. Sh. PinskiiandB. V. Vasil'ev, "Instrument for measuring the natural resonant frequency and decrement of sheet insulating materials and plastics," Report 32, no. P-61-56/6 TsITEIN, 1961. 5. V. S. Sbitnev and G. I,. Tsikolin, "The IKVT-2 instrument for determining the coefficient of internal friction," no. 32-63-491/6 GOSINTI, 1961. 29 June 1966

8=8-+6+,

--1

(3)

Institute of Polymer Mechanics, AS Latvian SSR, Riga