RU2624411C1 - Method of determining the valuability of a mechanical vibrational system - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method for determining the quality factor of a mechanical oscillatory system equipped with a position sensor is that the frequency of natural oscillations of a mechanical oscillatory system ω₀ from the phase-shift condition between the driving force and the output signal of the position sensor equal to π/2, experimentally establish the frequency ω_1. The driving force from the phase-shift condition between the driving force and the output of the position sensor equal to π/2+ϕ₁. Phase Shift Module |ϕ₁|<π/2, and the quality factor Q of the mechanical oscillatory system is determined by a known formula that takes into account the tangent of the phase shift, the frequency of the natural oscillations of the mechanical system, and the frequency of the driving force.

EFFECT: increase of accuracy, simplification and acceleration of the Q-factor determination procedure.

Description

The invention relates to the field of measuring equipment, namely to measuring the quality factor of mechanical oscillatory systems with one degree of freedom. This problem often arises when using various vibrometric sensors: vibro viscometers, vibrobalances and others.

There is a method of determining the quality factor of a mechanical oscillatory system that oscillates under the action of a periodic driving force, according to which the following sequence of operations is performed:

- remove the amplitude-frequency characteristic of the oscillating mass of a mechanical oscillatory system equipped with a position sensor;

- taking into account the speed and acceleration of forced oscillations, a resonance curve is calculated that characterizes a mechanical oscillatory system, the maximum of which corresponds to the natural frequency ω _{0 of the} oscillatory system;

- conditionally determine the width of the resonance curve at half its height. The width of the resonance curve identifies the frequency region Q ₂ -Q ₁ lying respectively before and after the resonance;

- the Q factor of a mechanical oscillatory system is determined by the formula Q = ω ₀ / Ω ₂ -Ω ₁ (hereinafter, the commonly used designation "ω" is used for frequency) [Yu.I. Iorish, Vibrometry, Ed. second.- M .: State. publishing house of engineering literature, 1963. - S. 179].

The known method has the following disadvantages: a sufficiently high complexity and duration of the measurement procedure. Removing with sufficient accuracy the amplitude-frequency characteristics of the oscillatory system requires numerous steps of discrete changes in the frequency ω of the driving force. Measurement with sufficient accuracy of the amplitude of the output signal of the position sensor and storing in memory of each measurement result. The number of these steps is proportional to the frequency range from ω ₁ to ω ₂ . The complexity and duration of the known method is especially noticeable when organizing the automatic time-continuous determination of the quality factor of a mechanical oscillating system during its operation, which significantly limit the speed and time of determining the quality factor.

The technical task of the invention is to reduce the time to determine the quality factor of a mechanical oscillatory system while maintaining the accuracy of the measurements.

A method for determining the quality factor of a mechanical oscillatory system is proposed, in which under the action of a periodic driving force, the frequency of the forced oscillations of the oscillating mass of the mechanical oscillating system equipped with a position sensor is changed, characterized in that the frequency of the forced oscillations is changed and experimentally determine the natural frequency of the mechanical oscillatory system ω ₀ from the condition phase shift between the driving force and the output signal of the position sensor equal to π / 2, experiment no determine the frequency ω ₁ of the driving force from the condition of phase φ shift (ω ₁₎ between the driving force output signal and the position sensor equal to π / 2 + φ _1, wherein the phase shift module | φ ₁ | <π / 2, and Q-factor Q mechanical oscillatory system is determined by the formula:

.

.

The proposed method is based on the fact that for mechanical oscillatory systems with one degree of freedom at the natural frequency ω _{0, the} phase shift ϕ at the output of the position sensor relative to the driving force is always π / 2 for any value of the quality factor of the oscillatory system Q [ibid. 173]. This follows from the theoretically known phase-frequency characteristic of such a system [ibid. P. 170, equation (5.15), taking into account (4.90), (5.13)]:

или

или

or

or

where ω is the frequency of forced oscillations; ξ = ω / ω ₀ ; Q = 1 / ε.

When the frequency changes from ω ₀ to ω _{1, the} phase shift between the driving force and the output signal of the position sensor will change and becomes equal to π / 2 + ϕ ₁ , and in accordance with (1), the following expression will be valid:

As known,

From (2) and (3) the quality factor is defined as:

where ω ₁ is the frequency of the forced oscillations at which the phase shift is π / 2 + ϕ ₁ .

In view of the foregoing, the claimed method is implemented as follows.

Experimentally determine the frequency of the driving force for a mechanical oscillatory system equal to ω ₀ at which the phase shift ϕ between the driving force and the output signal of the position sensor is π / 2 based on the known phase-frequency characteristic (1). Next, the frequency of the driving force for the oscillatory system is changed to a value of ω ₁ , at which the phase shift between the driving force and the output signal of the position sensor becomes π / 2 + ϕ ₁ and ϕ _{1 is} arbitrarily selected by the operator from the condition | ϕ ₁ | <π / 2 . For example, ϕ ₁ can be chosen equal to π / 4, with tg (ϕ ₁ ) = 1. By decreasing the set value ϕ ₁ , the frequency tuning range decreases from ω ₀ to ω ₁ , which increases the efficiency of determining the current quality factor Q of a mechanical oscillatory system. Therefore, it is advisable to set the minimum value of ϕ ₁ at which the error in determining the quality factor remains valid.

Knowing the values of ω ₀ , ω ₁ and tg (ϕ ₁ ), according to equation (4), the quality factor of the mechanical oscillatory system Q is calculated by calculation, mainly by software. Thus, the determination of the quality factor of the present method requires only two experimental operations for determining the frequencies ω ₀ and ω ₁ .

When implementing the proposed method to improve the accuracy of determining the quality factor, it is advisable to use digital methods of measuring and controlling the frequency and phase.

The inventive method allows to significantly simplify the process of determining the quality factor by eliminating measurement operations and storing the current values of the amplitude of the output signal of the position sensor of the oscillating mass, excluding operations to find the derivative, maximum amplitude and boundary values of the amplitude of the output signal of the position sensor of the oscillating mass. Efficiency is also improved by reducing the required tuning range of the frequency of the driving force.

The inventive method can be automated using microprocessor technology and allows the determination of the quality factor of a mechanical oscillatory system in the process of its operation.

Claims (2)

A method for determining the quality factor of a mechanical vibrational system, in which under the action of a periodic driving force, the frequency of the forced vibrations of the oscillating mass of the mechanical vibrational system equipped with a position sensor is changed, characterized in that the frequency of natural vibrations of the mechanical vibrational system ω ₀ is determined experimentally from the phase shift between the driving force and the output signal of the position sensor equal to π / 2, experimentally set the frequency ω _{1 of the} driving force from the condition phase shift between the driving force and the output signal of the position sensor equal to π / 2 + ϕ ₁ , while the phase shift modulus | ϕ ₁ | <π / 2, and the quality factor Q of the mechanical oscillatory system is determined by the formula: