CN118032006A - Method for separating quadrature coupling errors and identifying structural errors of silicon micromechanical gyroscope - Google Patents
Method for separating quadrature coupling errors and identifying structural errors of silicon micromechanical gyroscope Download PDFInfo
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Abstract
The invention provides a method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope, which comprises the following steps: establishing a model comprising driving beam width inequality, driving comb tooth gap inequality, driving detection comb tooth gap inequality and detection comb tooth gap inequality of a silicon micro-gyroscope coupling error, measuring orthogonal coupling errors by respectively adjusting driving comb tooth direct current bias voltage, driving detection comb tooth direct current bias voltage and detection comb tooth direct current bias voltage, and linearly fitting the square of the orthogonal coupling errors and the direct current bias voltage to obtain corresponding linear fitting coefficients, thereby obtaining the orthogonal coupling errors caused by three parts of comb tooth gap inequality when the gyroscope normally works, and calculating the driving comb tooth gap inequality, the driving detection comb tooth gap inequality and the detection comb tooth gap inequality; and the total orthogonal coupling error during normal operation of the gyroscope is combined, and the orthogonal coupling error caused by uneven gaps among three comb teeth is removed, so that the orthogonal coupling error caused by unequal widths of the driving beams and the unequal widths of the driving beams are obtained.
Description
Technical Field
The invention belongs to the technical field of silicon micromechanical gyroscopes, and particularly relates to a method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope.
Background
The silicon micromechanical gyroscope is a miniature angular velocity detection sensor manufactured by an MEMS process and has the characteristics of small volume, light weight, mass production and the like. With the improvement of MEMS technology, the performance of the silicon micromechanical gyroscope gradually approaches the navigation level, and the silicon micromechanical gyroscope has wide application prospect in the fields of civil use, military use, aerospace and the like.
The MEMS technology manufacturing defect causes the asymmetry of the gyro mechanical sensitive structure, thereby causing the interference force/moment in the detection axis direction to generate coupling errors, including in-phase coupling errors and quadrature coupling errors. The coupling error is a main component of zero bias of the gyroscope, and the influence of the installation error and the ambient temperature on the coupling error can be reflected in the zero bias stability. The current research considers that the rigidity coupling caused by unequal beam widths is a main source of gyro quadrature coupling errors. To this end, university of Zhejiang (202310407455.4, 202310407486. X) proposes a coupling coefficient identification method based on frequency domain and quadrature demodulation, and french CEALETI laboratory characterizes beam width discretion (Bias Contributions in a MEMS Tuning Fork Gyroscope, 2013) by a test structure named "beam width discretion (DELTA WIDTH)". In fact, not only is the beam width unequal to generate an orthogonal coupling error, but also the driving comb teeth, the driving detection comb teeth and the detection comb teeth are uneven, and the orthogonal coupling error is generated, and meanwhile, the coupling error generated by the comb tooth structure has a strong temperature characteristic and has a great influence on the temperature performance of the gyroscope. Therefore, in the prior art, all the quadrature coupling errors are generated by unequal beam widths, so that deviation is brought to understanding of the coupling errors, and large deviation is generated to identification of gyro structure errors and correct evaluation of gyro performance.
Disclosure of Invention
The invention aims to provide a method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope, which is used for separating quadrature coupling errors caused by unequal widths of driving beams and uneven gaps between teeth (comprising driving comb teeth, driving detection comb teeth and detection comb teeth) and identifying corresponding structural errors based on the separation results of the quadrature coupling errors.
The technical solution for realizing the purpose of the invention is as follows:
A method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope comprises the following steps:
Establishing a model comprising driving beam width inequality, driving comb gap inequality, driving detection comb gap inequality and silicon micro-gyroscope coupling errors caused by four sources of the driving comb gap inequality and the detection comb gap inequality based on an interference force/moment generation mode, measuring quadrature coupling errors based on a phase-sensitive demodulation method by respectively adjusting driving comb DC offset voltage V DCd, driving detection comb DC offset voltage V DCds and detection comb DC offset voltage V DCs, and linearly fitting the quadrature coupling errors and the squares of the DC offset voltages to obtain linear fitting coefficients of the coupling errors generated by the three parts of comb gap inequality, thereby obtaining the quadrature coupling errors caused by the driving comb gap inequality, the driving detection comb gap inequality and the detection comb gap inequality when the gyroscope works normally, and calculating the driving comb gap inequality, the driving detection comb gap inequality and the detection comb gap inequality; and the total orthogonal coupling error during normal operation of the gyroscope is combined, and the orthogonal coupling error caused by uneven gaps among three comb teeth is removed, so that the orthogonal coupling error caused by unequal widths of the driving beams and the unequal widths of the driving beams are obtained.
Compared with the prior art, the invention has the remarkable advantages that:
(1) The drive, drive detection and detection comb tooth pressure difference are respectively adjusted, orthogonal coupling errors caused by all parts of the gyroscope mechanical structure are separated, and the method comprises the following steps: orthogonal coupling errors caused by unequal beam widths and uneven comb tooth gaps;
(2) Based on the separation of the orthogonal coupling errors generated by all parts of the gyroscope mechanical structure, and combining a coupling error theoretical model, the mechanical structure errors causing the coupling errors are identified, wherein the mechanical structure errors comprise unequal beam widths and uneven comb tooth gaps;
(3) The invention is realized by an electrostatic method, has the characteristics of no damage and in situ, and can be applied to the coupling error identification of the packaged silicon micromechanical gyroscope structure and the wafer level coupling error separation;
(4) The invention can realize the gap error generated by MEMS technique for the chip on the wafer; the invention further adopts the packaged silicon micromechanical gyroscope to realize the identification of the gap errors of the packaged structure, and the difference between the two identification results is the gap errors generated by packaging, so the invention can also judge the packaging process.
Drawings
FIG. 1 is a flow chart of an identification method of the present invention.
Fig. 2 is a schematic diagram of a gyro structure according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of the relationship between the quadrature coupling error and the square term of the regulated DC bias voltage according to an embodiment of the present invention. (a) To adjust the quadrature coupling error and the direct current bias V DCd of the driving electrodeIs a linear fit of L 1; (b) To adjust the quadrature coupling error and/>, when the DC bias V DCds of the detection electrode is drivenIs a linear fit of L 2; (c) To adjust the quadrature coupling error and/>, when the DC bias V DCs of the detection electrodeIs a linear fit of curve L 3.
Detailed Description
The invention is further described with reference to the drawings and specific embodiments.
Referring to fig. 1, the quadrature coupling error separation and structure error identification method of the present embodiment provides a model of quadrature coupling error caused by four sources of unequal beam width, uneven drive and detection comb teeth gaps, and uneven detection comb teeth gaps, and obtains a linear fitting coefficient of quadrature coupling error and direct current bias square term by respectively adjusting the drive and detection comb teeth direct current bias voltage V DCd, the drive and detection comb teeth direct current bias voltage V DCds, and the detection comb teeth direct current bias voltage V DCs, according to the principle of detecting signal output caused by axial direction interference force/moment, as shown in fig. 2, and finally calculates quadrature coupling error caused by four sources in normal power supply V DCd＝VDCds＝VDCs＝VDC0 by combining with the quadrature coupling error model, as shown in fig. 3. Referring to fig. 2, the structure of the i-shaped silicon micromechanical gyroscope of the present embodiment includes: driving structure 1, detecting structure 2. The driving structure 1 comprises a driving electrode 101, driving comb teeth 102, a driving detection electrode 103 and driving detection comb teeth 104; the detection structure 2 comprises detection electrodes 201 and detection combs 202.
The specific implementation steps are as follows:
S1, establishing a silicon micro-gyroscope coupling error model based on a generation mode of interference force/moment, wherein sources of coupling errors comprise: the width of the driving beam is not equal to delta w, the driving comb gap is uneven delta d d, the driving detection comb gap is uneven delta d ds and the detection comb gap is uneven delta g;
The quadrature coupling error model for the gyro mechanical structure of fig. 2 includes: the drive beam width is unequal and Deltaw causes the quadrature coupling error to be Wherein eta is the attenuation coefficient of the force load on the driving structure transmitted to the detection structure, m d、ms is the driving mass and the detection mass respectively, L y、LC is the elastic restoring moment of the driving beam and the arm of force of the unit Coriolis moment respectively, f d is the driving frequency, and w d is the average value of the driving Liang Liangkuan; drive comb gap non-uniformity Δd d causes quadrature coupling error/>Wherein n d is the number of teeth of the driving comb of the movable structure, epsilon is the dielectric constant, h is the thickness of the mechanical sensitive structure, omega d is the driving angular frequency, d d is the average value of the gaps between the driving comb teeth, L dx is the arm of force for driving the electrostatic moment of the capacitance of the comb teeth, omega dQ and/>In a linear relationship, the linear coefficient/>Drive detection of comb gap non-uniformity Δd ds causes quadrature coupling error/>Wherein n ds is the number of teeth of the drive detection comb of the movable structure, d ds is the average value of the gaps between the drive detection comb, L dsx is the arm of force for driving the electrostatic moment of the capacitance of the drive detection comb, and Ω dsQ and/>In a linear relationship, the linear coefficient/>The quadrature coupling error caused by detecting the uneven delta g of the comb teeth is as followsWherein n s is the number of teeth of the movable structure detection comb, g 0 is the average value of small gaps of the driving detection comb teeth, and Ω sQ and/>In a linear relationship, the linear coefficient/>
S2: the silicon micromechanical gyroscope and the testing equipment thereof are arranged on a speed turntable, the direct-current bias voltage on a driving detection electrode 103 and a detection electrode 201 is set to be a normal working voltage value V DC0 through a gyroscope measurement and control circuit, the direct-current voltage V DCd on the driving electrode 101 is regulated to be 10-20V, the speed turntable is used for calibrating a gyroscope scale factor SF in the state every 2V, the quadrature coupling error omega Q is measured through phase-sensitive demodulation, and omega Q and the quadrature coupling error omega Q are drawnA scatter diagram is obtained by using least square method to linearly fit to obtain a linear fitting curve L 1, as shown in fig. 3 (a), a linear fitting coefficient xi 1 (linear fitting slope) is obtained, and the size of quadrature coupling error caused by drive comb gap non-uniformity in normal power supply is calculated and obtainedAnd calculates the drive comb gap unevenness/>
S3: setting the DC bias voltage on the driving electrode 101 and the detecting electrode 201 as V DC0 through a gyro measurement and control circuit, adjusting the DC voltage V DCds on the driving detecting electrode 103 to be 10-20V, simultaneously adjusting the driving closed-loop reference voltage V ref to keep the driving amplitude unchanged, enabling the V DCds to change every 2V, calibrating the gyro scale factor SF under the state through a rate turntable, measuring the quadrature coupling error omega Q through phase-sensitive demodulation, and drawing omega Q and the phase-sensitive errorA scatter diagram is obtained by using least square method to linearly fit to obtain a linear fitting curve L 2, as shown in fig. 3 (b), a linear fitting coefficient ζ 2 (linear fitting slope) is obtained, and the size of quadrature coupling error caused by drive detection of comb gap unevenness in normal operation of the gyroscope is calculated to be/>And calculates the drive detection comb gap unevenness/>
S4: setting the DC bias voltage on the driving electrode 101 and the driving detection electrode 103 as V DC0 through a gyro measurement and control circuit, adjusting the DC voltage V DCs on the detection electrode 201 to be 10-20V, calibrating a gyro scale factor SF in the state through a rate turntable every 2V change, measuring a quadrature coupling error omega Q through phase-sensitive demodulation, and drawing omega Q and the direct current voltageA scatter diagram is obtained by using least square method to linearly fit to obtain a linear fitting curve L 3, as shown in fig. 3 (c), a linear fitting coefficient ζ 3 (linear fitting slope) is obtained, and the size of the quadrature coupling error caused by detecting the uneven comb teeth gaps during normal power supply is calculatedAnd calculates and detects comb gap unevenness/>
S5: when the DC bias voltages on the driving electrode 101, the driving detection electrode 103 and the detection electrode 201 are set as V DC0, the gyro is driven to oscillate stably in a closed loop state, the scale factor SF is calibrated through the turntable, the measured quadrature coupling error is omega Q0, the quadrature coupling error caused by unequal beam widths is omega bQ＝ΩQ0-ΩdQ0-ΩdsQ0-ΩsQ0, and the unequal beam widths are omega bQ＝ΩQ0-ΩdQ0-ΩdsQ0-ΩsQ0
The above examples only represent embodiments of the present invention, and the gyro structure described is more specific, but should not be construed as limiting the gyro structure to which the present invention is directed. It should be noted that: modifications and alterations to this method will be apparent to those skilled in the art without departing from the principles of this invention.
Claims (6)
1. The method for separating the quadrature coupling errors and identifying the structural errors of the silicon micromechanical gyroscope is characterized by comprising the following steps of:
Establishing a model comprising driving beam width inequality, driving comb gap inequality, driving detection comb gap inequality and silicon micro-gyroscope coupling errors caused by four sources of the driving comb gap inequality and the detection comb gap inequality based on an interference force/moment generation mode, measuring quadrature coupling errors based on a phase-sensitive demodulation method by respectively adjusting driving comb DC offset voltage V DCd, driving detection comb DC offset voltage V DCds and detection comb DC offset voltage V DCs, and linearly fitting the quadrature coupling errors and the squares of the DC offset voltages to obtain linear fitting coefficients of the coupling errors generated by the three parts of comb gap inequality, thereby obtaining the quadrature coupling errors caused by the driving comb gap inequality, the driving detection comb gap inequality and the detection comb gap inequality when the gyroscope works normally, and calculating the driving comb gap inequality, the driving detection comb gap inequality and the detection comb gap inequality; and the total orthogonal coupling error during normal operation of the gyroscope is combined, and the orthogonal coupling error caused by uneven gaps among three comb teeth is removed, so that the orthogonal coupling error caused by unequal widths of the driving beams and the unequal widths of the driving beams are obtained.
2. The method for separating the quadrature coupling error and identifying the structural error of the silicon micro-mechanical gyroscope according to claim 1, wherein the modeling of the coupling error of the silicon micro-mechanical gyroscope comprises:
The drive beam width unequal Δw causes quadrature coupling errors:
the drive comb gap unevenness Δd d causes a quadrature coupling error:
The drive detection comb gap unevenness Δd ds causes a quadrature coupling error:
Detecting comb gap unevenness Δg causes a quadrature coupling error:
Wherein xi 1、ξ2、ξ3 is a linear fitting coefficient; η is an attenuation coefficient of force load on the driving structure transmitted to the detecting structure, m d、ms is driving mass and detecting mass respectively, L y、LC is an elastic restoring moment of the driving beam and a moment arm of a unit coriolis moment respectively, f d is driving frequency, and w d is driving Liang Liangkuan mean value; n d is the number of teeth of the driving comb of the movable structure, epsilon is the dielectric constant, h is the thickness of the mechanical sensitive structure, omega d is the driving angular frequency, d d is the average value of the gaps between the driving comb teeth, and L dx is the arm of force for driving the electrostatic moment of the capacitance of the comb teeth; n ds is the number of teeth of the drive detection comb of the movable structure, d ds is the average value of the gaps between the drive detection comb teeth, and L dsx is the arm of force for driving the electrostatic moment of the capacitance of the drive detection comb teeth; n s is the number of teeth of the movable structure detection comb, and g 0 is the average value of small gaps of the driving detection comb.
3. The method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope according to claim 2, wherein the driving comb tooth gaps and the corresponding quadrature coupling errors are:
The acquisition process of xi 1 is as follows: setting V DCds＝VDCs＝VDC0, marking a plurality of voltage points as the values of V DCd, calibrating a gyro scale factor SF, measuring a quadrature coupling error omega Q through phase-sensitive demodulation, and drawing omega Q and the quadrature coupling error And (3) a scatter diagram, wherein a linear fitting curve is obtained by using a least square method to obtain a linear fitting coefficient xi 1;VDC0 as a normal working voltage value.
4. The method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope according to claim 2, wherein the driving detection of comb tooth gap unevenness and corresponding quadrature coupling errors is:
The acquisition process of xi 2 is as follows: setting V DCd＝VDCs＝VDC0, marking a plurality of voltage points as the value of V DCds, simultaneously adjusting the drive closed-loop reference voltage V ref to ensure that the drive amplitude is kept unchanged, calibrating the gyro scale factor SF, measuring the quadrature coupling error omega Q through phase-sensitive demodulation, and drawing omega Q and the quadrature coupling error omega Q And (3) a scatter diagram, wherein a least square method is used for linear fitting to obtain a linear fitting curve L 2, and a linear fitting coefficient xi 2;VDC0 is obtained as a normal working voltage value.
5. The method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope according to claim 2, wherein the driving detection of comb tooth gap unevenness and corresponding quadrature coupling errors is:
The acquisition process of xi 3 is as follows: setting V DCd＝VDCds＝VDC0, marking a plurality of voltage points as the values of V DCs, calibrating a gyro scale factor SF in the state, measuring a quadrature coupling error omega Q through phase-sensitive demodulation, and drawing omega Q and the quadrature coupling error omega Q And (3) a scatter diagram, wherein a least square method is used for linear fitting to obtain a linear fitting curve L 2, and a linear fitting coefficient xi 2;VDC0 is obtained as a normal working voltage value.
6. The method for separating quadrature coupling errors and identifying structural errors of a silicon micromechanical gyroscope according to claim 2, wherein the drive beam widths are unequal and the corresponding quadrature coupling errors are:
ΩbQ＝ΩQ0-ΩdQ0-ΩdsQ0-ΩsQ0
Wherein Ω Q0 is a measurement quadrature coupling error, and the acquisition process is: v DCd＝VDCds＝VDCs＝VDC0 is set, the gyroscope is driven to oscillate in a stable amplitude under the closed loop state, the scale factor SF is calibrated through the turntable, and the quadrature coupling error omega Q0 is measured; wherein omega dQ0、ΩdsQ0、ΩsQ0 is the orthogonal coupling error caused by uneven drive comb teeth gap, uneven drive detection comb teeth gap and uneven drive detection comb teeth gap respectively; v DC0 is the normal operating voltage value.
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