CN-116499665-B - Nonlinear stiffness dynamic measurement system and method for reed return mechanism of low-frequency vibrating table

Abstract

The invention belongs to the technical field of nonlinear stiffness identification of vibration excitation devices, and particularly relates to a system and a method for dynamically measuring nonlinear stiffness of a reed return mechanism of a low-frequency vibrating table. Through accurately testing the vibration displacement signals with different amplitudes in the working frequency range of the low-frequency vibration table, the data processing unit performs FFT analysis on the output vibration displacement signals and the input standard sinusoidal voltage signals to obtain corresponding signal amplitudes and phases, and then the transfer function calculation unit calculates and obtains transfer functions in the form of first-order inertia links of the low-frequency vibration table corresponding to all the output vibration displacement signals with selected amplitudes in the working frequency range. And finally, performing power series fitting by a nonlinear stiffness fitting unit to obtain a power series expression representing nonlinear stiffness, and completing dynamic measurement of nonlinear stiffness of the reed return mechanism of the low-frequency vibrating table. In general, the measuring system has simple structure composition, simple and convenient operation flow and wide application range, and can realize accurate dynamic measurement of the nonlinear rigidity of the reed return mechanism of the low-frequency vibrating table.

Inventors

• ZHANG XUFEI
• ZHANG FENGYANG
• DU TAOTAO
• ZHANG JINKAI

Assignees

• 太原理工大学

Dates

Publication Date

20260508

Application Date

20230506

Claims (2)

1. 1. The method is realized based on a low-frequency vibration table reed return mechanism nonlinear stiffness dynamic measurement system, and the system comprises a program-controlled signal generator, a power amplifier, a low-frequency vibration table provided with a reed return mechanism, an eddy current displacement sensor, a data acquisition card, a computer and a software analysis module, wherein the program-controlled signal generator is used for generating an input standard sinusoidal voltage signal, driving the low-frequency vibration table to generate an output vibration displacement signal after being amplified by the power amplifier, the eddy current displacement sensor is used for detecting the output vibration displacement signal in real time, the data acquisition card is used for acquiring the output vibration displacement signal and the input standard sinusoidal voltage signal and sending the acquired signal into the computer, and the software analysis module is arranged in the computer and comprises a data processing unit, a transfer function calculation unit and a nonlinear stiffness fitting unit and is respectively used for carrying out FFT analysis, transfer function calculation and nonlinear stiffness fitting on the output vibration displacement signal and the input standard sinusoidal voltage signal, and the low-frequency vibration table reed return mechanism nonlinear stiffness dynamic measurement method based on the system is characterized by comprising the following steps: Step one, a program-controlled signal generator generates an input standard sinusoidal voltage signal with a certain set frequency omega i in the working frequency range (omega A ～ω B ) of a low-frequency vibrating table The time t is the time, the amplitude and the frequency of the input standard sine voltage signal are respectively U a 、ω i , and the input standard sine voltage signal is amplified by a power amplifier and then drives a low-frequency vibration table to generate an output vibration displacement signal X a 、φ i is the amplitude and phase of the output vibration displacement signal respectively; The electric vortex displacement sensor is arranged above the working table surface of the low-frequency vibration table, the output vibration displacement signal is detected in real time, and then the data acquisition card acquires the output vibration displacement signal and the input standard sinusoidal voltage signal and sends the acquired signal into the computer; performing FFT analysis on the output vibration displacement signal and the input standard sinusoidal voltage signal by the data processing unit to obtain corresponding signal amplitude and phase; step four, repeating the testing process from step one to step three by changing the amplitude of the input standard sinusoidal voltage signal with the frequency of omega i , and obtaining output vibration displacement signals corresponding to different amplitudes under the same frequency and the amplitude and phase of the input standard sinusoidal voltage signal; selecting other different frequency points in the working frequency range, and repeating the testing process in the first to fourth steps to obtain output vibration displacement signals and input standard sine voltage signal amplitude and phase corresponding to different frequencies and different amplitudes; Step six, outputting vibration displacement signals and corresponding input standard sinusoidal voltage signals based on a certain amplitude value of the low-frequency vibration table corresponding to each frequency point obtained through testing, comparing corresponding amplitude values and phases by a transfer function calculation unit, and fitting to obtain an experimental transfer function in a first-order inertia link form of the low-frequency vibration table corresponding to the amplitude values, so that the experimental transfer function in the first-order inertia link form of the low-frequency vibration table corresponding to other amplitude value output vibration displacement signals can be obtained based on the same method; And step seven, simplifying and expressing a theoretical transfer function of the low-frequency vibration table into a first-order inertia link in a low-frequency range based on an electromechanical coupling equation, further obtaining nonlinear stiffness values corresponding to different amplitudes through comparison calculation based on turning frequency of the theoretical transfer function and turning frequencies of experimental transfer functions corresponding to different amplitudes by a nonlinear stiffness fitting unit, and finally fitting to obtain a power series expression capable of accurately representing nonlinear stiffness characteristics, thereby realizing dynamic measurement of nonlinear stiffness of a reed return mechanism of the low-frequency vibration table.
2. 2. The method for dynamically measuring nonlinear stiffness of a reed return mechanism of a low-frequency vibrating table according to claim 1, wherein the specific principle of the nonlinear stiffness fitting unit for calculating nonlinear stiffness values corresponding to different amplitudes and fitting a nonlinear stiffness characteristic power series expression is as follows: (a) The electromechanical coupling equation for a low frequency vibrating table can be expressed as: (1) wherein m is the mass of a moving part of the low-frequency vibrating table, k and c are the rigidity and the damping of the reed return mechanism respectively, 、 And Respectively outputting vibration displacement signals, vibration speed signals and vibration acceleration signals of the low-frequency vibration table, wherein L, L and R are respectively the length, inductance and resistance of a driving coil in a moving part of the low-frequency vibration table, B is the air gap magnetic induction intensity, and u a and i are respectively input standard sinusoidal voltage signals and corresponding driving currents of the low-frequency vibration table; (b) Based on the formula (1), a voltage-displacement transfer function corresponding to the low-frequency vibration table can be calculated: (2) Wherein X a (s) and U a (s) are respectively Law transformation of an output vibration displacement signal X a and an input standard sinusoidal voltage signal U a , and s is a Law operator; (c) The spring return mechanism damping c of the low-frequency vibrating table and the inductance L of the driving coil in the moving part are small and ignored, meanwhile, in the low-frequency range, the high-order term of the transfer function in the formula (2) is also small and ignored, and based on the fact, the formula (2) can be simplified into a theoretical transfer function in a first-order inertia link mode: (3) (d) The theoretical transfer function turning frequency f d described by equation (3) can be expressed as: (4) Because parameters R, B, l and the like in the formula (4) can be approximately constant in a low-frequency range, the turning frequency f d of the theoretical transfer function in the formula (4) is respectively and correspondingly equal to the turning frequencies of the experimental transfer functions corresponding to different amplitudes, and the nonlinear stiffness values k corresponding to different amplitudes can be approximately calculated; (e) Considering that the rigidity of the reed return mechanism of the low-frequency vibrating table is periodically and continuously changed along with the change of an output vibration displacement signal x a , the nonlinear rigidity can be fitted through a finite power series, and the nonlinear rigidity k (x a ) is assumed to be fitted through an n-order power series, and the corresponding expression is as follows: (5) in the formula, Respectively taking the coefficients of power series of each order, when x a respectively takes the different amplitudes described in the fourth step, combining the nonlinear stiffness values corresponding to the different amplitudes calculated by the principle (d), and performing polynomial fitting on the formula (5) to determine And waiting for the power series coefficients of each order, further obtaining a power series expression representing the nonlinear stiffness characteristic, and completing the dynamic measurement of the nonlinear stiffness of the reed return mechanism of the low-frequency vibration table.

Description

Nonlinear stiffness dynamic measurement system and method for reed return mechanism of low-frequency vibrating table Technical Field The invention belongs to the technical field of nonlinear stiffness identification of vibration excitation devices, and particularly relates to a nonlinear stiffness dynamic measurement system and method of a reed return mechanism of a low-frequency vibrating table. Background Along with the development of intelligent technology, vibration sensors are increasingly widely used in various fields of industrial production and life. In order to ensure the detection precision of the vibration sensor, the development of the vibration calibration device and the related technology is more and more important. According to the international and domestic standards of vibration calibration, a steady-state sinusoidal excitation signal is required to be applied to the vibration sensor by the vibration table in the process of calibrating the vibration sensor. Based on the above, the distortion degree of the output vibration waveform is an important index for measuring the performance of the vibrating table, and the vibration calibration accuracy is seriously affected. In order to simplify the structural composition and save the cost, a flexible reed is usually used as a restoring mechanism of the vibrating table. To meet the calibration requirements of the low-frequency vibration sensor, the stroke of the corresponding low-frequency vibration table is usually increased so as to generate a large-displacement vibration signal with enough signal-to-noise ratio. However, with the increase of the vibration stroke, the reed restoring mechanism inevitably generates nonlinear characteristics under the condition of large deformation, so that the vibration signal output by the low-frequency vibration table generates serious waveform distortion, and the calibration precision of the low-frequency vibration sensor based on the low-frequency vibration table is further affected. Based on the method, the nonlinear stiffness characteristic of the reed return mechanism under low-frequency large deformation needs to be accurately obtained, a parameter basis is provided for constructing a motion waveform control system of the low-frequency vibration table, the low-frequency vibration table generates a low-distortion vibration excitation signal, and the low-frequency vibration calibration precision is effectively improved. At present, in order to obtain the nonlinear stiffness characteristic of the large deformation of the reed return mechanism, a static test method for testing displacement deformation under the action of a certain force is mostly adopted. The method generally adopts a direct current power supply to drive a low-frequency vibrating table, so that the reed return mechanism generates a plurality of static displacements along the bending deformation direction of the reed return mechanism, and the displacement value is detected by a displacement sensor and then compared with the static force generated by input current to approximately obtain the nonlinear rigidity characteristic parameter of the reed return mechanism. The method has the defects that the obtained nonlinear rigidity can only reflect the static characteristic of the reed return mechanism, and the dynamic nonlinear rigidity characteristic of the reed return mechanism can not be represented when the low-frequency vibration table generates a vibration excitation signal. In addition, the method has the problems of complex testing process, complex system composition and the like. In addition, some scholars have conducted research work on stiffness property tests of other nonlinear structures and systems. The representative method comprises the following steps of China patent 201310507793.1 discloses a nonlinear stiffness test method for a hard coating composite structure, wherein the primary values of the inherent frequencies and modal damping ratios of all orders and the primary values of the linear stiffness of all orders of the hard coating composite structure are obtained through a pulse excitation device. And then, based on the nonlinear stiffness type judgment standard of the hard coating composite structure, acquiring a frequency response curve corresponding to the inherent frequency of each step through frequency sweep test identification, and calculating to obtain corresponding nonlinear stiffness parameter values of each step. And finally, respectively calculating to obtain the strong nonlinear stiffness value and the weak nonlinear stiffness value of the hard coating composite structure by superposing the nonlinear stiffness values of each step and the linear stiffness values of each step. The method has the defects of complicated parameter testing process, complex system and high cost, and the nonlinear stiffness testing result of the method has higher requirements on the frequency sweep test and the frequency response characteris