SU1633281A1 - Method for determination of natural frequency of elastic system - Google Patents

Abstract

This invention relates to instrumentation technology. The aim of the invention is to increase the accuracy by reducing the effect on the measurement result of the nonlinearity and the hysteresis loop characteristics of the elastic element of the system. The method is carried out by measuring the angular velocities of the centrifuge, on which a pre-deformed elastic system with different values of static displacement is attached to the radius. It is shown that the value of the natural frequency of the elastic system is related to the measured parameters by the relation f0 1 I (Og-OYJ Ј T) Where the given static displacement of the elastic system is, we; from a hard stop and according to a given value. The essence of the method consists in using a linearized stiffness of the elastic system. Specifying the values of pre-warp and static displacement allows the linearization error to be significantly reduced. The use of a hard stop for pre-deformation contributes to an increase in accuracy, since in this case, only the own elastic force of the system acts. The method according to claim 2 is distinguished by a value ij equal to twice the amplitude of the oscillations of the elastic system at its own frequency and the fact that the value of COi corresponds to the moment that the elastic system is placed on a rigid support. The method also eliminates the uncertainty associated with the ambiguity of the CGu parameter corresponding to the same static displacement value, which is typical for systems with significant damping. 1 hp ff, 2 ill. F (L and with with ISD 00

Description

The invention relates to instrumentation engineering and can be used in mechanical engineering to determine the vibration parameters of elastic systems.

The aim of the invention is to improve the accuracy by reducing the effect on the measurement result of the nonlinearity and the hysteresis loop characteristics of the elastic element of the system.

FIG. Figure 1 shows the loading diagram of an elastic system; Fig. 2 is a diagram of an apparatus for carrying out the proposed method.

The method for determining the natural frequency of an elastic system consists in pre-deforming the elastic system in the direction of its static displacement by means of a hard stop, and the elastic

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the system on the centrifuge at radius R with the possibility of moving in the radial direction from the centrifuge axis, gradually increasing the angular velocity of the centrifuge, fixing the value of CO and the angular velocity of the centrifuge corresponding to the preliminary displacement (the moment of removing the system from the stop), fixing it with 00 corresponding to a given static offset determine the natural frequency

Ј elastic system of the ratio

one

u

(GjJ-G & R

 T,

(one)

The method is based on the use of linearized stiffness, defined (Fig. 1) as the ratio of DGII Mo, where is the elastic loading force

system (in this case, the force of inertia); - static system displacement (strain value). The concretization according to the method of the values of pre-deformation and static displacement L allows to significantly reduce the error of linearization of the stiffness of the elastic system. Providing a pre-deformation using a hard stop also contributes to an increase in accuracy, since with a static displacement of an elastic system only its own elastic force acts (the stop is considered absolutely rigid)

For elastic systems with significant damping, i.e. For those in which the characteristic of the elastic element has a noticeable hysteresis loop, there is an error associated with the ambiguity of the parameter G) u corresponding to the same static displacement value (Fig. 1, i points a and c). In the method according to claim 2, the indicated error is also eliminated. After fixing the SOch value, the angular velocity of the centrifuge is gradually reduced, and the CO value of the angular velocity of the centrifuge is fixed at the time of setting the elastic system to a rigid stop (Fig. 1, point c), the static offset «is set equal to the doubled amplitude of the system oscillations at its own frequency determined, for example, by calculation.

The choice of magnitude and equal to twice the amplitude of oscillations brings the conditions for determining the natural frequency to

conditions of loading of the elastic system during oscillations, which also contributes to an increase in accuracy.

The ratio (1) is obtained as follows. The force of energy Rin is determined by the known ratio

F "H - Rmu,

where m is the concentrated mass of the elastic

systems;

G) is the angular velocity of the centrifuge. The inertia forces with CO COi, and

Ј balanced by Hz force

 with v

where c is the linearized stiffness of the elastic system at static displacement O.

Then, taking into account (2) and (3)

Taking into account the known ratio

get

0

five

,

0

0

five

-

UЈ (u}) R

| - t,. - 1fly

The device (Fig. 2) contains a centrifuge 1, a screw 2 with a nut 3, mounted on the table of a centrifuge 1 using a bracket 4 and electrically isolated from the latter, an adjustable micrometer screw 5, also mounted on a table of a centrifuge 1 using a second bracket 6 and also electrically insulated from the bracket 6, with the screws 2 and 5 arranged coaxially one towards the other and radially with respect to the centrifuge axis of rotation, the power source 7, two lamps 8 and 9, each of which is connected to screws 2 or 5, respectively, and stvuyuschim outlet of the power source 7.

The device works as follows.

An elastic system consisting, for example, of elastic elements 10 (e.g., shielding insulators) and a concentrated mass 11 (for example, a protected object) is placed on the table of the centrifuge 1 so that the movement takes place in the radial direction relative to the axis of rotation of the centrifuge 1. Screw 2 pre-deformation of the elastic system is provided, after which screw 2 is supported with nut 3. After that, the adjustable micrometer screw 5 is installed-. The specified displacement 8 is equal, for example, to twice the amplitude value of the oscillations of the elastic system at its own frequency.

The mass 11 is electrically connected to the common terminal of the power source 7. Then turn on the centrifuge 1 and smoothly increase the speed of rotation. The moment of removal of the system from the fixed stop (screw 2) is determined by the indicator of the breaking of the electric circuit (at the moment of turning off the light bulb 8 connected to the electric circuit with the power source 7, weight 11 and screw 2). When the light bulb 8 goes out, the angular velocity value is fixed (0, .... With a further increase in speed, the current in the electric circuit is determined by the indicator (by the light of the light bulb 9 connected to the electrical circuit with the power source 7, weight 11 and screw 5 at the moment when moving elastic

the system has reached the value

V

In that

the moment is fixed at 63. Then the speed of rotation is reduced and at the time the lamp 8 lights up, the value of the angular velocity Ou is fixed. According to the data obtained, using the relation (1), the natural frequency is determined

formula

the invention

r

Claims (2)

1. The method for determining the natural frequency of an elastic system, which consists in fixing the elastic system in a centrifuge at radius R, increases the angular velocity of the centrifuge until a given static displacement $ is obtained. systems, fix the value b), the angular velocity of the centrifuge, corresponding to the value of d, determine the natural frequency of the centrifugal system by the value of COi and the angular velocity of the centrifuge, characterized in that, in order to improve the accuracy, the elastic system is preliminarily deformed in the direction of its static 0, when the angular velocity of the centrifuge is changed, its value Ј0. Corresponding to the preliminary deformation is also fixed, and the natural frequency Ј0 of the elastic system is determined 5 of the ratio  1 huJ-e R Go 2fl | - $} - 2. The method according to claim. Characterized in that the static offset of about 1 is set equal to twice the amplitude of the system oscillations on its own elastic system. At the same time use the frequency defined, for example, races / 1 / JJ value of CO 0) ju if in a characteristic way, after fixing the sign of the elastic element of the system without having ffl / i, the angular velocity of the centrifuge em noticeable hysteresis loop, or low melting, and the value of The value of 03 Sch., if the hysteresis loop - the speed of the centrifuge is fixed in the brain, neglecting the measurement conditions of the setting of the elastic system is unacceptable. hard stop. Fm Rma} 2