SU1326931A1 - Method of determining parameter of attenuation and resonant frequency of mechanical system with turbulent friction - Google Patents

Abstract

The invention relates to the study of the dynamic characteristics of mechanical systems with turbulent friction, for example hydro and pneumatic dampers. The purpose of the invention is to improve the accuracy and reduce the time spent on determining the attenuation parameter and the resonant frequency. The essence of the invention is the excitation of free vibrations of the system under study and the measurement of five instantaneous values of vibration displacement over a time interval that is an order of magnitude smaller than the calculated value of the oscillation period. The attenuation parameter S and the resonant frequency o) of the system are calculated by the formulas, which include the measured vibration displacement and the time interval between measurements. The invention provides the possibility of determining the specified characteristics in a short (within the half-period of oscillations) time. In one or two oscillation periods, multiple measurements can be made. Averaging the results of multiple measurements makes it more accurate to determine the desired characteristics.

Description

The invention relates to the study of the dynamic characteristics of mechanical systems with nonlinear dissipative forces such as turbulent (hydrodynamic) friction, for example, structural materials, hydraulic and pneumatic dampers. The aim of the invention is to improve the accuracy and reduce the time spent determining the attenuation parameter and the resonant frequency.

The essence of the invention lies in the fact that they measure over a period of time less than the calculated value of the oscillation period, five instantaneous values of vibratory mixing with free oscillations and determine the attenuation parameter and the resonance frequency from them.

 The method is carried out as follows.

When excited, for example, by a blow or a breakdown of the established forced oscillations, the free oscillations of the system under study are measured, starting

I () + YV3 () .4 (ЗУг.) G 2У „,, (, У„ ,, + У „,, У„,.,) - 2У „,, ((У„ ,,,)

thirty

For mechanical systems with nonlinear dissipative forces such as turbulent (hydrodynamic) friction, damped free oscillations in discretization with a period of & 35 will be presented as a time sequence

where L -5Ad4; cosWA; A j 2cobU4 S-AO L

,one , .

The relation (2) -will be with and for any other example values, (n + 1), (n + 2), and so on, on the time axis relative to the n-th, taken as the initial one, it is easy to form a system of relation equations. well known, 2 solutes, taking into account the accepted threshold, 45 determines the parameter S when the resonant frequency W

U (pl) „

(one). where b) is the resonant frequency of the system;

S is the attenuation parameter; A, H d - the amplitude of the envelope and the phase of the oscillations corresponding to the initial moment of time accepted for zero,,

1 jL f J "a

For any values of A, S, ul, 4 for the samples using formula (1), the following relations between the individual samples Y,, + 4

DPU „+ () U„ ,,,, - 1 / п + 1) U ,, - (Y. + Y “,,), (2)

- Ih-M Yn.3 (..i) -bYf., 3 (3yn + yn a) -Yt (3ynM) - 2Yn.3 (Y "y" .i + YnYn.3) -2Y ,, (( „. + U, +,)

from an arbitrary point in time, five instantaneous values of vibration displacement over an interval of an order of magnitude less than the calculated value of the oscillation period, and the attenuation parameter S and the resonant frequency and systems are determined by the relations:

I,

-.1 2 (ND,) Y,.,

A V f

v) - arcos -, L /

de y.yft ,,,.

, (measured instantaneous values of vibration displacement;. (time interval between measurements;

  ntg

Release

2y

11 “4.

.

where L -5Ad4; cosWA; A j 2cobU4 S-AO L

,one , .

The relation (2) is also valid for any other values of n (for example, (n + 1), (n + 2), etc.) shifted along the time axis of the relative n-th, taken as the initial, t . It is easy to form a system of three linear equations for three unknowns, 2 of which, taking into account the accepted notation, determines the attenuation parameter S and the resonance frequency W

WITH -

.. 2 (1 + YAU,., - ;;, y „y +

with I arccos f l /

Where

-3 P Yh-fZ Y, .l

 2U „,, -, У„ ,,

The small required measurement time (from 4 to 4 I) allows to increase the accuracy of determining S and S by repeated measurements of rhenium and averaging of the results obtained. In addition, it provides an opportunity to determine parameters for a fraction of the oscillation cycle, and with the introduction of averaging, one or two oscillation cycles, thereby reducing the requirements for technical means that determine the mode of free oscillations (fastening, excitation of a mechanical system), possibility of analyzing systems with a large attenuation (or with a small excitation force). The choice of time for the initial p-th reference of the vibration displacement is arbitrary.

 and

conducted through

Jt ". . . 1st

Definition

the ratio of Y,, and - samples, which eliminates the multiplicative measurement errors.

Claims (1)

Formula invented The method of determining the attenuation parameters and the resonant frequency of a mechanical system with turbulent training 71 ,, + Y „, Y ,,) - 2y ,, (y, 4Y,) Make V. V. Semenychev. Editor Y. Sereda Tekhred L. Oliynyk Proofreader V. But ha Order 3273/37 Circulation 776 Subscription VNIIPI USSR State Committee for inventions and discoveries 113035, Moscow, Zh-35, Raushsk nab.,, d. 4/5 Production and printing company, Uzhgorod, st. Project, 4 It is used to excite free oscillations of the system under study and measure several instantaneous values of vibration displacement, characterized in that, in order to increase accuracy and reduce time costs, five instantaneous values of vibration displacement are measured at intervals the dock is smaller than the calculated value of the oscillation period, and the attenuation parameter S and the resonant frequency W of the system are determined from the relations: I, with - 20 where U „, U„ +,, V y Y p + a n 25 and measured instantaneous displacement values; time interval between measurements; Yn + Yn-fi