APPLICATION OF SIGNAL ANALYSIS TO INTERNAL FRICTION MEASUREMENTS

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APPLICATION OF SIGNAL ANALYSIS TO INTERNAL FRICTION MEASUREMENTS

J. Baur, A. Kulik

To cite this version:

J. Baur, A. Kulik. APPLICATION OF SIGNAL ANALYSIS TO INTERNAL FRIC- TION MEASUREMENTS. Journal de Physique Colloques, 1983, 44 (C9), pp.C9-357-C9-361.

�10.1051/jphyscol:1983952�. �jpa-00223402�

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APPLICATION OF SIGNAL ANALYSIS TO INTERNAL FRICTION MEASUREMENTS

J. Baur and A. Kulik

I n s t i t u t de Ggnie Atomique, Swiss Federa2 I n s t i t u t e o f !i'eehnoZogy, PHB-EcubZens, CH- 101 5 Lausanne, SwitzerZand

Rdsum6

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Un systsme entisrement automatis6 de mesure de frottement int6rieur (FI) a 6t6 construit. Ilmesure le FI par analyse de forme de la d6croissan- ce libre. Cette m6thode dlimine les perturbations dues aux mouvements para- sites de 1'6chantillon et pr6sente une faible dispersion mcme aux petites amplitudes de dgformation. Elle permet de mesurer de courtes d6croissances li- bres gardant ainsi 116chantillon en vibrations quasi stationnaires.

Le systsme a 6t6 utilis6 pour mesurer le FI dans des Bchantillons vibrant en torsion dans le domaine du Hz et dans des dchantillons vibrant en flexion dans le domaine du kHz. Un ordinateur de table contr8le tous les paramstres expi5rimentaux et pilote le systsme. Les rdsultats sont affich6s en temps reel sur un 6cran graphique et stock6s sur un support magn6tique.

Des rdsultats expsrimentaux typiques sont pr6sent6s.

Abstract

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A fully automatized internal friction (IF) measuring system was constructed. It measures IF by proceeding a waveform analysis of the free decay vibration. The choosen method eliminates disturbances due to parasitic motions of specimen and shows a weak dispersion even at low strain amplitudes.

It allows to measure short free decay keeping the specimen vibrating in quasi stationnary conditions.

This system was used to measure IF of specimens vibrating in torsional mode in the Hz range and also of specimens vibrating in flexural or cantilever mode in the kHz range. It is driven by a desktop computer which controls all experimental parameters. Results are displayed in real time on a graphic screen and stored on a magnetic medium. Experimental results are presented.

INTRODUCTION

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Many mechanical properties of metals like plastic deformation or damping capacity are due to interactions between dislocations and point defects. A good method to study these interactions is the measurement of internal friction(1F). The- se measurements are particularly difficult due to the fact that very small changes of IF should be detected on a wide range of strain amplitude. Therefore a good accuracy of IF measurements is desired, specially in the interesting region of very small strain amplitudes(+10-7).

Another problem characterizing the study of these interactions is the mobility of the point defects near the dislocations [1,2]. During an IF measurement, the dislocations oscillate around their equilibrium position, which induces a reorganization of the spatial distribution of the mobile point defects surroundingthedislocations.

Using free decay to measure IF will disturb the spatial distributionof these defects.

Therefore it is necessary to keep the strain amplitude as constant as possible during an IF measurement, so that the measured specimen stays in stationary conditions.

Above mentioned contradictory requirements, i.e.

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good accuracy, small strain amplitudes and constant amplitude during measurement

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show that the traditional method using a wave height analysis during a free decay is not suitable for our stu- dies.

A fully automatized IF measuring system using a waveform analysis was constructed.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983952

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C9-358 JOURNAL DE PHYSIQUE

T h i s t e c h n i q u e d e s c r i b e d by Yoshida and a 1 [31 c a l c u l a t e s I F by F o u r i e r t r a n s f o r m o f t h e o s c i l l a t i o n s of t h e specimen v i b r a t i n g i n f r e e d e c a y . The waveform a n a l y s i s g i v e s a v e r y good a c c u r a c y on I F measurements even a t low s t r a i n a m p l i t u d e s where poor s i - g n a l t o n o i s e r a t i o i s a c h i e v e d . The choosen method e l i m i n a t e s p e r t u r b a t i o n s d u e t o p a r a s i t i c motions o f t h e specimen. Furthermore i t a l l o w s t o d e c r e a s e t h e v a r i a t i o n of s t r a i n a m p l i t u d e d u r i n g t h e f r e e decay.

T h i s measuring s y s t e m i s d r i v e n by a d e s k t o p computer which d i s p l a y s t h e experimen- t a l r e s u l t s i n r e a l t i m e . I t was u s e d t o measure t h e I F of specimens v i b r a t i n g i n t o r s i o n a l mode i n t h e Hz r a n g e and a l s o of specimens v i b r a t i n g i n f l e x u r a l o r c a n t i - l e v e r mode i n t h e kHz r a n g e .

WAVEFORM ANALYSIS OF FREE DECAY SIGNAL

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The method of I F measurement by a waveform a n a l y s i s i s based on t h e f a c t t h a t t h e f r e q u e n c y spectrum of damped o s c i l l a t i o n s shows a n e n l a r g e d peak. The s t u d y of t h e peak s h a p e p e r m i t s t o c a l c u l a t e t h e I F . During a f r e e decay, t h e specimen motion c a n b e assumed t o b e :

where f , ( t ) i s t h e main component of t h e damped o s c i l l a t i o n and can be w r i t t e n : f 1 ( t ) = A exp ( - t / t l ) c o s (mot + Arg A)

=

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^[A exp ( j w l t ) + A* exp ( - j w l t ) )

where t l i s t h e t i m e c o n s t a n t of damping and wl i s t h e complex a n g u l a r frequency d e f i n e d a s :

I F i s t h e n simply :

f 2 ( t ) r e p r e s e n t s c o n t r i b u t i o n s due t o p a r a s i t i c motions s u c h a s e . g . a p r e c e s s i o n a l one i n t h e c a s e of t o r s i o n a l v i b r a t i o n s . These motions a r e supposed t o c o n s i s t of se- v e r a l s i m p l e harmonic motions w i t h a n g u l a r f r e q u e n c i e s f a r away from wo.

The t h i r d term f , of e q . (1) r e p r e s e n t s a l l components of t h e specimen m o t i o n o t h e r t h a n f ( t ) and f a ( t ) . I t i s c o n s i d e r e d a s a s m a l l random n o i s e .

The d i s c r e t e F o u r i e r t r a n s f o r m (DFT) of f ( t ) r e v e a l s a main peak a t t h e a n g u l a r f r e - quency wo and s e v e r a l o t h e r peaks due t o p a r a s i t i c motions f 2 ( t ) . Yoshida and a 1 [ 3 ] have shown t h a t i n t h e v i c i n i t y of t h e main f r e q u e n c y peak t h e DFT bf f ( t ) i n a f i - n i t e time i n t e r n a l t g i s approximated by :

assuming t h a t 2n >> wot3/2n >> 1 where 2n i s t h e number of t i m e domain samples. T h i s assumption means t h a t t h e number N of samples p e r p e r i o d of v i b r a t i o n s a t i s f i e s t h e c o n d i t i o n : 2n >> N >> 1.

The term B + C's r e p r e s e n t s a l i n e a r a p p r o x i m a t i o n f o r t h e c o n t r i b u t i o n s of p a r a s i t i c motions f 2 ( t ) and f 3 ( t ) t o t h e main peak of t h e f r e q u e n c y spectrum. Using f o u r conse- c u t i v e v a l u e s of F ( s ) (3'(sl? t o ~ ( s , , ) ) around s % w o t 3 / 2 n w e c a n e l i m i n a t e t h e cons- t a n t s B and C . I F i s t h e n given by r r e f . 3 1 :

F ( S ~ ) - ~ . F ( S > ) + F ( ~ ~ ) where R = F ( S , ) - ~ . F ( S , ) + F ( S , )

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bances whose frequency is fairly distant from the main one. This is very frequent in practice. In some cases, however, the parasitic motions can give additional peaks very close to the main one. It happens particularly when parasitic motions induce an amplitude modulation of the free decay signal. In these cases, the above described method calculates too large values of IF and then must be used with caution.

Thegreatadvantage of the waveform analysis for calculating IF is that the effecti- ve signal to noise ratio is highly improved by effect of statistical treatment of noise. This method calculates IF from several data per period of specimen vibration.

In the classical method using wave height analysis only one point per period is con- sidered. This fact explains why the waveform analysis allows to measure shorter free decay to obtain similar precision to the one in the traditional method. The du- ration of free decay - i.e. variation of strain amplitude - and the number of samples per period cannot be choosen arbitrarily. They are limited by the assumption in equation (2). This condition, however, is not very restrictive. Generally the sampling of free decay during 10 periods of specimen oscillation satisfies this assumption. A free decay of 10 period means for example that strain amplitude decrea- ses 15% in case of an IF equal to 5.10-~.

REALISATION OF MEASURING SYSTEM

The main part of the system is a rapid DC Voltmeter which samples the free decay signal with sufficient rate. The data are then transmitted from the voltmeter to a BA- SIC programmable desktop computer where a Fast Fourier Transform (FFT) is proceeded.

Consequently the frequency domain results are used to calculate the IF. All the experimental results like IF, frequency, temperature and others are then displayed on the graphic screen of the computer and stored on a magnetic medium. The computercon- trols entirely all experimental parameters. The use of standard interconnection bus (IEEE 488-HPIB) greatly simplifies main part of the development.

Our measuring system was connected to an inverted torsional pendulum. Fig. 1 shows the block diagram of the system. The choosen FFT algorithm using 256 time domain data allows to calculate IF each 40 s.

the IF results can be estimated as lo-'+.

For this application, additional connections were added to the measuring system which allow to measure the electrical resistivityofthe specimen. This enhancement in con-

TORSIONAL - nection with a measurement of the

torsional component of the shape change of the specimen is particularly useful for studying phase transitions. Typical experimental results without post-processing are shown in Fig. 2. Fig. 2a gives results for a precipitation peakinan Ag A1 13% alloy and Fig. 2b for a Fig. 1 : Block diagram of electronic part for

martensitic transformation in a torsional pendulum

Ti Ni alloy. The weak dispersion of

HP 85 COMPUTER PERIPHERIALS HP 3L97A

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Fig.2 : Results obtained in torsional pendulum :

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a) Precipitation peak in Ag-A1 13% alloy (heating and cooling)

b) Martensitic transformation in Ti Ni alloy (note torsional component of the shape change).

Different mechanical set-ups using free flexural or cantilever vibrations were connected to the measuring system. The relatively high vibrating frequencies of these set-ups implied the choice of a rapid waveform recorder (see condition for the approximated equation (2)). Figure 3 shows the configuration of system for kilohertz range.

VIBRATING

Fig. 3 : Block diagram of electronic part for kilocycle range apparatus.

HP 3497A DATA ACQ UNIT

FFT was performed on 1024 time domain data. The choice of a more efficient desktop computer than for torsional pendulum allows to obtain experimental results each 30s.

Figure 4 shows typical experimental results in case of a gold specimen at different strain amplitudes. It can be seen that even at very low amplitude . ( 6 x loM8) disper- sion of IF is less than lo-'. For strain amplitude higher than 5

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dispersion becomes very small (in the order of loW5). It should be noted that figure 4 gives raw experimental values without post processing. In these experiments variation of strain amplitude due to free decay was always smaller than 20%.

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Fig. 4 : Results obtained in kilocycle range apparatus :

Bordoni peak in Au 6N -50 ppm Pt at different strain amplitudes : a) 8

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CONCLUSION

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The above described measuring system enables measurements of IF with a good accuracy by use of a waveform analysis. This method eliminates disturbances due to parasitic motions and gives weak dispersion even at low strain amplitudes. It allows to measure IF during short free decay.

REFERENCES

1 GREMAUD G., Proc. ICIFUAS-7, Lausanne, J. Physique

42,

(1981) C5-369 2 SCHWARTZ R.B., FUNK L.L., Acta met.

21,

(1983) 299

3 YOSHIDA I., SUGAI T., TAN1 S., MOTEGI M., MINAMIDA K., HAYAKAWA H., Proc. ICIFUAS-7, Lausanne, 3 . Physique

2,

(1981) C5-1123

ACKNOWLEDGEMENTS

The authors are grateful to G. Gremaud for conception of auxiliary electronics.

This work was partially supported by the Swiss National Science Foundation.