RESONANCE

P H E N O M E N A IN D Y N A M O M E T E R S Y S T E M S

OF T E S T M A C H I N E S UDC

A. B. S h a g i n y a n

620.1.052

The sluggish pendulum dynamometers of static test machines are now being successfully replaced by quickresponse meters (of the spring, torsion, electronic, and other types). However, the parameters of dynamometers are often chosen arbitrarily. It was found in testing specimens of low-carbon steel on rigid machines of the type UMM-5 in the laboratories of the Armavir Special Design Office of the Institute of Metals (SKBIM) that in certain sections of the tensile test diagram the loading of the specimen changes repeatedly not only in value, but also in direction. This is particularly noticeable on the yield plateau. In measuring specimens of low-carbon steel, the variations of loading at the yield plateau consist of a transient oscillatory process whose amplitude and frequency depend entirely on the properties of the combined system of the machine and the specimen. The static balance between the efforts exerted on the dynamometer and the specimen, and required for precise evaluation of the load applied to the latter, is disrupted in principle as soon as the limit of proportionality is reached. In order to avoid considerable dynamic errors at the transitional sections of the tensile diagram [1-2], and especially for resonance phenomena, it is necessary to specify the frequency range of dynamometer devices. Assuming conditionally that the variations of the load on the specimen at the yield plateau are harmonic* and having set a point on the diagram at the level of the elastic limit as the beginning of counting for the system, let us write the dynamometer's movement equation:

md~t + ( a s +

a t t a2r

(1)

) X1 "~ Ck.sX1 = A1 sin % t,

where m d is the mass of the dynamomemr referred to its pendulum rolle/; a s is the resistance coefficient of the supports; a r is the resistance coefficient of the damper; Ck.s is the dynamometer's kinematic stiffness; A 1 is the maximum (amplitude) variation of the load in the specimen at the yield plateau, w0 is the frequency of load oscillations in the specimen; X t is the current displacment of the dynamometers referred mass. The dynamometer movement equation can be represented for a forward displacement (loading) as:

X f r f- - - e - nl l t ( ~ x~ 1 7 6

VnX /r/llX~~

n2l-l-p2

" sin - ~ / 1 - - n 2 / pl ~

p

AI

+

p2 ~ too 2

+

AI

t

1--pT

2ni w o

+

"

<2)

* For the present investigations such an approximation is permissible, since in specifying the frequency parameters of dynamometers it is sufficient to know precisely the frequency or the frequency range of the load oscillations on the specimen. Translated from Izmeritel'naya Tekhnika, No. 1, pp. 34-36, January, 1971. Original article submitted December 8, 1968.

9 1971 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

52

Pl ,Resonance

2

t c

Fig. 1. Oscillogram of a simultaneous recording of the load on the specimen; 1) and the pendulum dynamometer; 2) of the UMM5 machine. and for a backward displacement as:

Xbkx=e-n~t (Xo cos P ~ I -

2o + n2 Xo

- ng~ -p2 't-k

V r p

p~ __ ~2

•

(p~

co~)2_t_4n~%2

" sino)o/

-

-

n~ 1 -- p2

_/

tl. 2

--

-- p ~ . t +

.sin ~ / 1

A1

2n2 ~

rod

(p _o b +44o4

-

A1 m---d

OS ot,

(s)

where

2n1 = - as

= 8.10-4 see-t; p2 =

Ck's = 8 , 4 sec-Z; 2he-- - - a s @C~r -- 0.31 sec-l; md md

md

X0 is the initial displacement of the dynamometer's referred mass for t = 0; 20 is the initial displacement velocity of the referred mass; p is the natural oscillation frequency of the dynamometer. The processing of numerous oscillographic recordings of load variations on the specimen in testing low-carbon steels shows that the value of w0 varies within the limits of 3-25 rad/sec. This range of frequencies almost coincides with the free oscillation frequencies of dynamometers which are used at the present time. In this connection even the pendulum dynamometers display at the transition sections of the diagram batches of resonance (Fig. 1), which substantially distort the measurement results. In order to determine the range of the most rational frequencies for dynamometer devices, let us write on the basis of (2) and (3) the values of the dynamic load factors in loading and unloading, without damping, but taking into consideration only the resistance of the dynamometer's kinematic pairs: 1 p~

) 2-1-

(4)

p4

and with damping by means of an equivalent viscous resistance [3]: 1

1

p~

-t

-}-

p4.

(5)

Let us also plot a graph of the relationship of Kd to frequency w0/p for various Values of resistance in the dynamometer links (Fig. 2). The condition for ensuring the precise evaluation of the load on the specimen (for standard machines) at the yield plateau with equivalent damping, i.e., for 2neq/P ~ 0.1, can be expressed in the following manner:

53

J

2

:

a

y

B

I I I I

I

,;0 P

Fig. 2. Graph of the dynamic load coefficient's relationship to the frequency ratio % / p . A) Range of the high-frequency spring and torsion dynamometers; B) range of the low-frequency pendulum dynamometers. K

I =

~

1,Ol.

The solution of (6) provides the frequency ratio % / p for which the rise in the amplitude of forced oscillations does not exceed 1% (~0/ph = 1.41 and (~0/P)2 = 0.1. The above frequency ratios determine the range of highfrequency (spring and torsion) dynamometers (for ~0/p -< 0.1) and the range of low-frequency (pendulum) dynamometers (for w0/P --- 1.41). In testing 150 specimens of low-carbon steel, it was found that at the yield plateau the presence of highfrequency transient processes with load oscillation frequencies of ~o0 = 10-25 rad/sec is more probable (90% of tests). It is quite obvious that the pendulum dynamometers with natural oscillation frequencies of p = 1.5-3 rad/sec vibrate on the yield plateau at frequencies very close to those of free oscillarions, whereas the spring and torsion dynamometers (p -- 65-95 rad/sec) acquire forced oscillations with a considerable effort. Thus, in order to meet the requirements of the All-Union State Standard (GOST) 7855-61 referring to static test machines, it is advisable to consider the range of p = 100-250 rad/sec as the most rational for the natural oscillation frequencies of the newly produced quick-response dynamometers. LITERATURE

1. 2. 3.

84

CITED

A. KochendSrfer und W. Wink, Archiv far das EisenhUttenwessen, 2, No. 28 (1957). A. 8. Shaginyan, "Investigation of universal test machines with pendulum and torsion dynamometer devices," in: Works of the RISKhM [in Russian], Rostov-on-Don (1966). 8. P. Timoshenko, Oscillations in Engineering ~n Russian], Fizmatgiz, Moscow (1959).