SU1399708A1 - Device for determining nonlinear characteristics of oscillatory systems - Google Patents

Abstract

The invention makes it possible to increase the accuracy and performance of a device for determining the nonlinear characteristics of an oscillating system during vibration tests and examination of instruments and machines by eliminating the need to realize resonant vibrations. At the outputs of the resistor 10 and the integrator 11, the cosine and sinusoidal components of JUP are obtained (not a phase-shifted harmonic signal of the disturbing process equal to the amplitude of the sensor 8 signal. Using blocks 12, 13 and 9, this signal is adequately decomposed and thus the balance its cosine component with the sum of the signals coming from the output 4 of source 1 and from the outputs of the raising block 7 to the power when the controls for adjusting their proportionality coefficients are set to the desired position. The coefficients of the potential characteristic are decomposed in a power series. At the same time, the sinusoidal component of this signal is balanced with the dissipative member of the motion equation, therefore by translating switch 5 into three positions on the indicator 14, data is obtained for calculating the dissipative characteristic. 1 ill. $ (L

Description

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with

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The invention relates to test instruments and can be used in instrument making, in vibration testing and investigation of nonlinear oscillatory systems.

The purpose of the invention is to increase the accuracy and performance of the device. properties.

The drawing shows a block diagram of the proposed device.

The device contains a source of 1 voltage proportional to offset, qxopocTH and acceleration with outputs 2, 3 and 4, respectively, a four-position switch 5 having an output and four inputs, the first of which is connected to the output of the first adder 6, whose single input Connection with output 4 of source 1 is direct, and group of inputs with output 2 of source 1 through block 7 to the power of the group. The device also contains a disturbing process sensor 8, an amplitude comparison unit 9 having two inputs, one of which is connected directly by sensor 8, and the other through an adjustable resistor 10, 1 tag; tor 11, and a second adder 12, the second input of which as the first one of the first adder 6, is connected to the INPUT of the resistor 10, and the output is additionally 1: it is connected to the first input of the phase meter 13, the second input of which is connected to the output 2 of source I. The device is also equipped with an indicator 14, which is connected to you sudom switch 5, fourth ld to It is connected to the output of the integrator 11, and the second and third to the YYKHOD 3 of the source 1 directly AND through the unit 15 for estimating the average value of the module, respectively.

The device works as follows.

The operation of the device is based on the transformation of the differential equation of forced oscillations of a nonlinear system in a standard form.

+ r (x) f (x) e cos cot

(one)

Mind X + r (x) + bgsin at.

f (x)

 CO t +

(2)

which is equivalent to transferring the time point to the phase angle (f between the perturbing and oscillatory processes. The transformed equation (2) splits into two independent equations

X f (x) a coscot; (3)

g (x)

bgSin cot.

(four)

5 about 5

0

five

0

five

0

five

The first of them is valid at any moment in time and allows one to determine the potential characteristic f (x) from a single realization of non-resonant oscillations, and the second, valid only on average over a period, the dissipative characteristic r (x) from several realizations of forced oscillations (various levels ).

Before starting operation, the adjustment knobs of blocks 10 and 11 are set to their original position, which corresponds to zero resistance of resistor 10 and zero proportionality factor of integrator 11, which provides the sinusoidal component of the right side of equation (2). After the realization of the established oscillations of the system, the phase meter I3 shows the magnitude of the phase angle if, which in the case of resonance oscillations is within O, ..., Tc / 2 rad, and in the case of resonant oscillations within ii / 2, ..., IT. By rotating the proportional control knob of the block 11, the phase meter reads respectively O or li. Then, by adjusting the resistance of the resistor 10, a zero indication of the amplitude comparison unit 9 indicator is obtained and thereby completes the formation of the transformed disturbance process corresponding to the right side of equation (2). The device is ready to determine both characteristics.

I -

The potential characteristic f (x) is defined as its decomposition in a power series. Dp finding the decomposition coefficients at the first (far right) position of the switch 5 performs the adjustment of the power units 7 to the power of the group by adjusting their proportionality coefficients while on the indicator 14 (for example, on the screen of the cathode oscilloscope) a zero signal will be received according to equation (3). The position of the adjustment knobs corresponds to the values of the required decomposition coefficients.

To determine the dissipative characteristic, the r (x) switch is sequentially switched to the second, third, and fourth positions, while recording the indicator readings. 14, respectively, the amplitude of the speed of the oscillatory process x

mako

the average

module value (absolute value)

portioned according to the speed offset and acceleration, the first adder, a group of inputs of which is connected to the outputs of a group of raising blocks to the extent that, in order to increase the accuracy and performance of the device, it contains a disturbance sensor

speed XSR and the amplitude of the sinusoidal process, adjustable resistor.

part of the transformed perturbed process b. Then, the value 2bgK f.) Is calculated, which is the value of the required function r (x), when its argument x is equal to x,;. .

The measurements are repeated several times at different values in this way to obtain the desired function in a tabular form, which, if necessary, can be approximated by analytical expression.

The use of the proposed device makes it possible to increase the accuracy and speed up the process of identifying nonlinear dynamic systems by forced oscillations with harmonic perturbation due to the fact that there is no need to perform hardly realizable resonant oscillations.

Ula Invention Form

A device for determining the nonlinear characteristics of oscillating systems, comprising a switch, an indicator, a voltage source, having first second and third outputs, about 5

0

the integrator, the second adder, the amplitude comparison unit, the phase meter and the module for estimating the average value of the module, the switch being four-positional, having an output connected to the pincher, and four inputs, the first of KOTOpbDc connected to the output of the first adder, the first voltage source output connected with the first input of the phase meter and with the input of a group of blocks of exponentiation, the second output with the first single input of the first adder, the third output with the second input of the switch directly, and with the third input of the switch the module for estimating the average value of the module, the output of the disturbing process sensor is connected to the first input of the amplitude comparison unit directly and via an adjustable resistor to the second single input of the first adder, to the first input of the second adder and to the integrator input, the output of which is connected to the fourth switch input and with the second input of the second adder connected by the output to the second inputs of the phase meter and the amplitude comparison unit.

five

Claims (1)

Claim Device for determining nonlinear characteristics of vibrational 35 systems, comprising a switch, an indicator, a voltage source having first first second and third outputs, proportional to speed offset and acceleration, respectively, a first adder, the group of inputs of which is connected to the outputs of a group of power raising units, characterized in that, in order to increase accuracy and performance of the device, it contains a disturbing process sensor, an adjustable resistor, an integrator, a second adder, an amplitude comparison unit, a phase meter, and an average value estimator for the module, and switch It is made four-position, having an output connected to the indicator, and four inputs, the first of which is connected to the output of the first adder, the first output of the voltage source is connected to the first input of the phase meter and to the input of the group of power raising blocks, the second output with the first single input of the first adder , the third output is with the second input of the switch directly, and with the third input of the switch is through the unit for estimating the average value of the module, the output of the disturbing process sensor is connected to the first input of the amp comparison unit itud directly and through an adjustable resistor - to a second single input of the first adder, the first input of the second adder to the input of the first integrator, the output of which is connected to a fourth input of the switch and to the second input of the second adder output is connected to second inputs of phase meter and amplitude comparator unit. Compiled by A. Lashchev