A method for machining error calibration and acceleration readout of a resonant beam accelerometer

Abstract

This paper develops a method for calibrating machining errors and reading acceleration for resonant beam accelerometers. This method addresses the beam width machining errors caused by MEMS processing. By calibrating the actual beam width, this is incorporated into the resonator's internal structural parameters, and the least squares method is used to solve for acceleration and common-mode stress. The proposed method does not require additional equipment and simply uses known parameters and the calculated beam width machining error parameters to enter into a matrix to solve for acceleration and axial force.

Description

Technical Field

[0001] The invention belongs to the technical field of silicon micro-resonant accelerometers, and in particular relates to a method for calibrating machining errors and reading acceleration of a resonant beam accelerometer. Background Art

[0002] Silicon resonant accelerometers (SRAs), a recently developed micromachined accelerometer based on MEMS technology, have found widespread application in communications, computers, earthquake detection, consumer electronics, aerospace, and other fields. These applications each place varying demands on accelerometer performance. Currently, most SRAs are of low to medium precision, but applications in military, navigation and guidance, gravity measurement, and oil exploration require very high precision.

[0003] The resonant accelerometer structure consists of four main components: a sensitive mass, a resonator, a microlever (which amplifies inertial force), and a supporting structure. The resonator uses a differential structure to reduce common-mode error. However, due to the limited precision of MEMS processing, the width of the resonant beam has dimensional errors. The different widths of the two resonant beams lead to inconsistent temperature responses of the two resonator frequencies, reducing common-mode rejection and exacerbating the accelerometer's output errors.

[0004] In the papers "High-Precision Silicon Micro-Resonant Accelerometer Frequency Measurement Output Circuit" (Journal of China Inertial Technology) and "Implementation and Performance Testing of Miniaturized Silicon Micro-Resonant Accelerometers" (Optical Precision Engineering), the acceleration frequency is traditionally determined using the frequency difference method: the difference between the readout frequencies of the two resonators. This method fails to account for minor errors in the internal structure of the resonant beam during machining, which can lead to errors in the accelerometer's output frequency. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calibrating machining errors and reading acceleration of a resonant beam accelerometer, so as to overcome the limitations of MEMS machining technology and make the obtained acceleration value more accurate.

[0006] The technical solutions for achieving the purpose of the present invention are:

[0007] A method for reading acceleration of a resonant beam accelerometer, acceleration a:

[0008]

[0009] Where f1 represents the measured output frequency of resonator 1; f 01 represents the output frequency of resonator 1 in the free state; f2 represents the measured output frequency of resonator 2; f 02represents the output frequency of resonator 2 in the free state; w1 represents the actual width of resonant beam 1; w2 represents the actual width of resonant beam 2; l represents the length of the resonant beam; n represents the lever displacement ratio; ω represents the fundamental frequency of the sensitive mass block.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] This invention overcomes the acceleration reading errors caused by limitations in MEMS processing. This method changes the traditional method of calculating acceleration from the difference in the output frequencies of two resonators. By incorporating internal structural parameters and the calculated actual beam width, the acceleration value is calculated using the least squares method, reducing the accelerometer reading error and improving the accuracy of the accelerometer output frequency. This method is applicable to all resonant beam accelerometers and achieves more accurate acceleration readings by inferring the beam width error. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 A flow chart for calculating the acceleration and axial stress of the accelerometer according to the present invention;

[0013] Figure 2 A flow chart for calculating the machining beam width error of an accelerometer according to the present invention;

[0014] Figure 3 Flow chart of specific steps of the present invention;

[0015] Figure 4 Schematic diagram of the comb structure of the accelerometer resonator of the present invention;

[0016] Figure 4 Where l represents the length of the resonant beam; w represents the width of the resonant beam comb teeth; d represents the length of the overlapping part of the resonant beam comb teeth; V dc is the DC voltage; V ac is the AC voltage; I s is the alternating current;

[0017] Figure 5 This is the amplitude-frequency curve of the accelerometer resonator oscillation signal in the knocking state. DETAILED DESCRIPTION

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0019] Combine Figure 1-Figure 4This embodiment provides a resonant beam accelerometer machining error calibration and acceleration readout method. By utilizing the actual resonant beam width and internal resonator parameters, the resonant beam accelerometer readout method is modified to effectively improve the resonant beam accelerometer readout error caused by the resonant beam width machining error. The method primarily includes: (1) resonant beam width error calibration of the resonant beam accelerometer; and (2) calculation of the acceleration and axial common mode stress of the resonant beam accelerometer.

[0020] The resonant beam accelerometer has two resonators, respectively marked as resonator 1 and resonator 2. Assuming that the common mode stress of the two beams of the resonant beam accelerometer is equal, combined with the attached Figure 3 and attached Figure 4 , including the following steps:

[0021] S1: Calibrate the actual resonant beam widths w1 and w2 of resonator 1 and resonator 2. The specific steps are as follows:

[0022] S1.1: Obtain the frequency output f of resonator 1 and resonator 2 under +1g and -1g input conditions by gravity field inversion test. 1，out+1g 、f 1，out-1g 、f 2，out+1g and f 2，out-1g , calculate the values of scale factors k1 and k2 of resonator 1 and resonator 2 respectively according to formulas (1) and (2).

[0023]

[0024]

[0025] S1.2: Substitute the scale factor measurement results into formulas (3) and (4) to calculate the actual resonant beam width values w1 and w2 of resonator 1 and resonator 2 respectively.

[0026]

[0027]

[0028] Where, ρ represents the density of single crystal silicon; A comb represents the equivalent area of the resonator comb teeth; l represents the length of the resonant beam; E represents the Young's modulus of the silicon material; n represents the lever displacement ratio; ω represents the fundamental frequency of the sensitive mass block; k1 represents the scale factor of resonator 1 obtained in S1.1; k2 represents the scale factor of resonator 2 obtained in S1.1.

[0029] S2: Calculate the parameters of the resonant beam accelerometer ω, f1, f2, f 01 and f 02 ;

[0030] S2.1: Obtain the fundamental frequency ω of the acceleration-sensitive mass by the tapping method. The specific steps are as follows:

[0031] S2.1.1: Install the signal acquisition equipment of the resonant beam accelerometer, strike the accelerometer fixture to excite the fundamental frequency mode of the accelerometer, and use the data acquisition card to collect the original signal of the output signal. The collected signal includes amplitude and frequency, where the frequency of the resonator is f and the fundamental frequency is

[0032] S2.1.2: Perform Fourier transform on the collected signal to obtain the amplitude-frequency curve of the signal. In the knocking state, the sensitive mass of the accelerometer is excited into an oscillation state. The amplitude-frequency curve is shown in the figure below. Figure 5 As shown in the figure, the frequency values corresponding to the maximum / second / third largest signal amplitudes are taken out, and the fundamental frequency is the difference between the peak frequencies on both sides and the middle peak frequency.

[0033] S2.2: Determine the output frequencies f1 and f2 of resonator 1 and resonator 2 through experiments.

[0034] S2.3: Based on the actual resonant beam widths w1 and w2 of resonator 1 and resonator 2 calculated in S1.2, use equations (5) and (6) to calculate the frequency f of resonator 1 and resonator 2 in the free state. 01 and f 02 .

[0035]

[0036]

[0037] Where ρ represents the density of single crystal silicon; h represents the thickness of the resonant beam; m comb represents the mass of the comb-tooth electrode of the resonant beam; l represents the length of the resonant beam; E represents the Young's modulus of the silicon material; w1 represents the actual beam width value of resonator 1 calculated in S1.2; w2 represents the actual beam width value of resonator 2 calculated in S1.2.

[0038] S2.4: The values of the remaining parameters l, E, h, and n are small because individual MEMS have small differences, so a unified structural design value can be used;

[0039] S3: Calculate the acceleration a and axial force F, use formula (7) to substitute various parameters, and solve the formula,

[0040]

[0041] Where, l represents the length of the resonant beam; E represents the Young's modulus of the silicon material; h represents the thickness of the resonant beam; n represents the lever displacement ratio; ω represents the fundamental frequency of the sensitive mass block; f1 represents the measured frequency of resonator 1; f 01represents the frequency of resonator 1 in the free state; f2 represents the measured frequency of resonator 2; f 02 represents the frequency of resonator 2 in the free state; w1 represents the actual width of resonant beam 1; w2 represents the actual width of resonant beam 2; F represents the axial force; a represents the acceleration;

[0042] Solve the matrix formula (7) using the least squares method and get:

[0043]

[0044]

[0045] Solved:

[0046]

[0047]

[0048] Calculate the acceleration a and the axial force F.

Claims

1. A method for reading acceleration of a resonant beam accelerometer, characterized in that: Acceleration a: Where f1 represents the measured output frequency of resonator 1; f 01 represents the output frequency of resonator 1 in the free state; f2 represents the measured output frequency of resonator 2; f 02 represents the output frequency of resonator 2 in the free state; w1 represents the actual width of resonant beam 1; w2 represents the actual width of resonant beam 2; l represents the length of the resonant beam; n represents the lever displacement ratio; ω represents the fundamental frequency of the sensitive mass block; The acceleration readout process includes the following steps: S1, calibrating the actual resonant beam widths w1 and w2 of resonator 1 and resonator 2; specifically comprising the following steps: S1.

1. Obtain the frequency output f of resonator 1 and resonator 2 under +1g and -1g input conditions by gravity field inversion method. 1，out+1g 、f 1，out-1g 、f 2，out+1g and f 2，out-1g , calculate the values of scale factors k1 and k2 of resonator 1 and resonator 2 respectively according to formulas (1) and (2): S1.

2. Substitute the scale factor measurement results into formulas (3) and (4) to calculate the actual resonant beam widths w1 and w2 of resonator 1 and resonator 2, respectively: Where, ρ represents the density of single crystal silicon; A comb represents the equivalent area of the resonator comb teeth; E represents the Young's modulus of the silicon material; S2. Calculate the parameters of the resonant beam accelerometer: the fundamental frequency ω of the sensitive mass, the measured output frequency f1 of resonator 1, the measured output frequency f2 of resonator 2, and the output frequency f of resonator 1 in the free state. 01 , the output frequency f of resonator 2 in the free state 02 ; Calculate the acceleration a and the axial force F: Solve the above matrix using the least squares method; Step S2 specifically includes the following steps: S2.1: Obtain the fundamental frequency ω of the acceleration-sensitive mass block by the tapping method; S2.2: Determine the output frequencies of resonators 1 and 2 through experiments. S2.3: Based on the calculated actual resonant beam widths w1 and w2 of resonator 1 and resonator 2, use equations (5) and (6) to find the output frequencies of resonator 1 and resonator 2 in the free state: Where h represents the thickness of the resonant beam; m comb Represents the mass of the resonant beam comb electrode.

2. The acceleration reading method of the resonant beam accelerometer according to claim 1, characterized in that: Step S2.1 specifically includes the following steps: S2.1.

1. Install the signal acquisition equipment of the resonant beam accelerometer, strike the accelerometer fixture to excite the fundamental frequency mode of the accelerometer, and use the data acquisition card to collect the original signal of the output signal. The collected signal includes amplitude and frequency, where the frequency of the resonator is f and the fundamental frequency is S2.1.2: Perform a Fourier transform on the collected signal to obtain an amplitude-frequency curve of the signal. Under the striking state, the sensitive mass of the accelerometer is excited into an oscillating state. The frequency values corresponding to the maximum / second / third largest signal amplitudes are obtained. The fundamental frequency is the difference between the peak frequencies on both sides and the peak frequency in the middle.

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