Error modeling method for asymmetric flexible beam structure of quartz flexible accelerometer

Abstract

The invention belongs to the technical field of accelerometers, and particularly relates to an error modeling method for an asymmetric flexible beam structure of a quartz flexible accelerometer, which comprises the following steps of: calculating a torsion angle generated by additional torque in the direction of a pendulum shaft according to the bending-resistant and torsion-resistant section characteristics of a flexible pendulum beam, and calculating the error of the asymmetric flexible beam structure on the basis of a non-parallel polar plate differential capacitance structure model; a theoretical reference is provided for the structural symmetry and coaxiality design of the quartz flexible accelerometer pendulum assembly by adopting the influence effect of the virtual string method equivalent torsion angle on the accelerometer output. The method comprises the specific steps that S1, the actual action positions of inertia force and electromagnetic force are determined according to the defects of the pendulum assembly; determining the magnitude and direction of the shear force causing the additional torque according to the actual action positions of the inertia force and the electromagnetic force; s2, modeling a torsion angle generated by the flexible swing beam along the direction of the swing shaft under the action of the additional torque; and S3, based on the non-parallel polar plate differential capacitance model, obtaining the asymmetric flexible beam structure error of the quartz flexible accelerometer caused by the torsion angle of the pendulum shaft.

Description

Technical Field

[0001] The invention belongs to the technical field of accelerometers, and in particular relates to an error modeling method for an asymmetric flexible beam structure of a quartz flexible accelerometer. Background Art

[0002] The quartz flexible accelerometer is mainly composed of a mechanical meter head and a servo circuit, which are used for sensitive signals and detection signals respectively. When the accelerometer is working, the pendulum assembly in the meter head can sense the acceleration of the input shaft and drive the pendulum beam to vibrate. The displacement signal generated by the pendulum assembly is equivalently output as a current signal through the differential capacitor detection circuit, thereby completing the detection of the input acceleration. As the core component inside the meter head, the high flexibility of the ultra-thin flexible beam in the input axis direction ensures the high resolution of the accelerometer, while the high strength in the output axis direction limits the freedom of movement of the pendulum assembly. The structural characteristics of the pendulum assembly have an important influence on the output performance of the accelerometer, especially the dynamic performance.

[0003] At present, due to the large discretization error of the production process of the quartz flexible accelerometer head, the differences between the quartz flexible components produced in the same batch are large, resulting in a large degree of discretization of the performance of the assembled accelerometer. Due to the limitations of the manufacturing process, in actual situations, it is difficult to produce a completely symmetrical double beam through chemical etching, laser cutting and other process flows; the axis of the coil assembly is difficult to be completely symmetrical with the axis of the quartz pendulum. When the flexible pendulum beam is asymmetrical, the flexible double beam has different supporting effects on the pendulum mass; when the pendulum and the coil assembly are not coaxial, the lengths of the inertial force arm and the feedback force arm are different. Both situations will cause the pendulum assembly to produce additional torque. In an ideal situation, the differential capacitance detection circuit is sensitive to the rotation angle of the pendulum assembly around the output axis; under the action of the additional torque, the pendulum assembly produces a torsion angle along the pendulum axis direction, and this torsion angle will cause the output error of the accelerometer in the differential capacitance circuit's detection of the pendulum group position.

[0004] In summary, in the processing of the pendulum piece, there is a lack of inspection steps for the symmetry of the pendulum beam, the coaxiality of the pendulum assembly and other performance; there is no means to inspect the structural symmetry quality of the pendulum assembly from the completion of the pendulum assembly production to the packaging of the entire meter; there is no effective equivalent method to study the influence of the additional torque of the pendulum shaft on the output performance of the quartz flexible accelerometer. Summary of the invention

[0005] In view of the above problems, the present invention provides a method for modeling the error of an asymmetric flexible beam structure of a quartz flexible accelerometer. The method calculates the torsion angle generated by the additional torque in the direction of the pendulum axis through the bending and torsion cross-sectional characteristics of the flexible pendulum beam, and based on the non-parallel plate differential capacitor structure model, uses the virtual string method to calculate the influence of the equivalent torsion angle on the accelerometer output, providing a theoretical reference for the structural symmetry and coaxiality design of the pendulum assembly of the quartz flexible accelerometer.

[0006] The present invention provides a method for modeling an error of an asymmetric flexible beam structure of a quartz flexible accelerometer, and the specific steps are as follows:

[0007] S1. Determine the actual action positions of the inertial force and the electromagnetic force according to the defects of the pendulum assembly; determine the magnitude and direction of the additional torque shear force according to the actual action positions of the inertial force and the electromagnetic force;

[0008] S2. Simulate the flexible pendulum beam of the quartz flexible accelerometer as two parallel rectangular cross-section beams; obtain the cross-sectional characteristics of the flexible pendulum beam; and model the torsion angle of the flexible pendulum beam along the pendulum axis direction under the action of the additional torque;

[0009] S3. Based on the non-parallel plate differential capacitance model, the asymmetric flexible beam structure error of the quartz flexible accelerometer caused by the torsion angle of the pendulum shaft is obtained.

[0010] Optionally, the specific steps of S2 are:

[0011] S21, simulating the flexible pendulum beam of the quartz flexible accelerometer as two parallel rectangular cross-section beams, the two parallel rectangular cross-section beams twist around the twisting center point C; setting the end boundary conditions of the two parallel rectangular cross-section beams;

[0012] S22, determining the equilibrium condition;

[0013] S23, determining physical conditions;

[0014] S24, determining a turning angle condition;

[0015] S25, determining the return boundary conditions;

[0016] S26, combining the boundary conditions in step 25 and the distance equations of the two rectangular cross-section beams;

[0017] S27, bringing the boundary condition of the bending corner into the equilibrium condition in step 22;

[0018] S28. Based on step 27, obtain the pendulum shaft torsion angle.

[0019] Optionally, the specific steps of step S3 are: when the pendulum assembly is subjected to additional torque, the two side plates of the sensitive capacitor are in a non-parallel state; the non-parallel plate differential capacitance is obtained by using a virtual series method; based on the differential capacitance, the asymmetric flexible beam structure error between the pendulum shaft torsion angle and the quartz flexible accelerometer is obtained.

[0020] Optionally, the two side plates of the sensitive capacitor generated by the pendulum plate under the influence of the additional torque are equivalent to the secondary displacement of the two side plates of the sensitive capacitor to obtain the differential capacitance.

[0021] Alternatively, the expression for the differential capacitance is:

[0022]

[0023] Among them, C1 and C2 are two sensitive capacitors in the differential capacitance detection circuit; ε0 represents the vacuum dielectric constant; ε r Represents the relative dielectric constant; s represents the plate area; d0 is the plate spacing when the two side plates of the sensitive capacitor are in equilibrium position; Δd is the displacement of the two side plates of the sensitive capacitor due to the input acceleration; Δd′ represents the additional sensitive displacement caused by the additional torque; C0 represents the capacitance of the two side plates of the sensitive capacitor when they are in equilibrium position; ΔC represents the ideal capacitor output; ΔC′ represents the additional capacitor output caused by the additional displacement; ΔN is the distance of the shear center offset from the ideal symmetry axis.

[0024] Optionally, based on the differential capacitance, the asymmetric flexure beam structure error Y of the quartz flexure acceleration is obtained, and the expression is:

[0025] Y=K C (ΔC+ΔC′)

[0026] Among them, K C It is the amplification factor of the proportional link of the detection circuit.

[0027] Optionally, the end boundary conditions of the two parallel rectangular cross-section beams include boundary conditions of torsion angle, bending deflection and bending rotation angle.

[0028] Compared with the prior art, the present invention has at least the following beneficial effects:

[0029] 1. The method of the present invention uses the equilibrium equation to derive the double beam torsion problem and uses the virtual string method to calculate the non-parallel plate differential capacitor output, which can clearly obtain the mechanical analysis and the obtained results are accurate:

[0030] The present invention adopts the equilibrium equation as the basis, and takes the displacement, deflection and rotation angle of the end of the swing beam as the boundary conditions, which can clarify the force relationship between the double beams; the present invention adopts the virtual string method to calculate the output of the non-parallel plate differential capacitor, and equates the torsion problem to the additional displacement sensitive to the differential capacitor, and connects the relationship between the torsion problem and the output of the accelerometer. The equivalent method in the two steps has clear mechanical analysis, accurate calculation results, saves calculation time, and improves experimental efficiency.

[0031] 2. The method of the present invention proposes an equivalent method between the torque of the quartz flexible pendulum assembly along the pendulum axis and the output of the accelerometer, and provides an evaluation method for the structural error of the quartz pendulum assembly:

[0032] The flexible pendulum is an important structure for sensitive acceleration input in quartz accelerometers. Currently, there is no quality inspection of the symmetry and coaxiality of the pendulum assembly structure in the production and assembly process of quartz flexible accelerometers; there is also a lack of evaluation methods for the symmetry and coaxiality of the pendulum assembly structure. The present invention provides an equivalent output calculation method for the accelerometer when the input error source is the asymmetric or non-coaxial structure of the quartz pendulum assembly, provides an evaluation method for the structural error of the quartz pendulum assembly, and provides a theoretical reference for the structural optimization design of the pendulum assembly of the quartz accelerometer. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic cross-sectional view of the quartz double pendulum beam of the present invention;

[0034] Figure 2 It is a schematic diagram of the differential capacitor torsion of the present invention;

[0035] Figure 3 A schematic diagram of the offset of an example coil assembly in the present invention;

[0036] Figure 4 Schematic diagram of the quartz double pendulum beam structure of the present invention;

[0037] Figure 5 The simulation result of calculating the torsion angle of the pendulum assembly in the present invention;

[0038] Figure 6 This is the error value simulation result under the action of additional torque of the differential capacitor in the present invention. DETAILED DESCRIPTION

[0039] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0040] A specific embodiment of the present invention, as Figure 1-6 , discloses a method for modeling the error of an asymmetric flexible beam structure of a quartz flexible accelerometer, the specific steps are as follows:

[0041] S1. Determine the actual action positions of the inertial force and the electromagnetic force according to the defects of the pendulum assembly; determine the magnitude and direction of the additional torque shear force according to the actual action positions of the inertial force and the electromagnetic force.

[0042] For example, the asymmetry of the flexible pendulum beam will cause the shear center of the cross section of the flexible pendulum beam to deviate; the non-coaxiality of the quartz pendulum piece and the coil assembly in the pendulum assembly will cause the center of mass of the pendulum assembly to not coincide with the center of force of the coil. When the shear center of the cross section of the flexible pendulum beam, the center of mass of the pendulum assembly and the center of mass of the coil are not coaxial, the pendulum assembly will be subjected to an additional torque along the pendulum axis.

[0043] S2. The flexible pendulum beam of the quartz flexible accelerometer is simulated as two parallel rectangular cross-section beams; the cross-sectional characteristics (section moment of inertia and section polar moment of inertia) of the flexible pendulum beam are obtained; the pendulum axis torsion angle generated by the flexible pendulum beam along the pendulum axis direction under the action of the magnitude and direction of the additional torque shear force is modeled, the steps are as follows:

[0044] S21, two parallel rectangular cross-section beams such as Figure 1 As shown, N is the distance between the centers of the two rectangular cross-section beams, and the pendulum beam is assumed to twist around the torsion center point C; the end boundary conditions of the two parallel rectangular cross-section beams are set, including the boundary conditions of the pendulum axis torsion angle, bending deflection and bending rotation angle.

[0045] (1) The boundary conditions of the torsion angle are:

[0046]

[0047] in, is the torsion angle at the end of the first rectangular cross-section beam 1, is the torsion angle at the end of the second rectangular cross-section beam 2, is the pendulum shaft torsion angle.

[0048] (2) The boundary conditions for bending deflection are:

[0049]

[0050] Among them, ω1 is the deflection of the end of the first rectangular section beam 1, ω2 is the deflection of the end of the second rectangular section beam 2, N1 is the distance from the centroid of the cross section of the first rectangular section beam 1 to point C, and N2 is the distance from the centroid of the cross section of the second rectangular section beam 2 to point C.

[0051] (3) The boundary conditions of the bending corner are:

[0052] θ1=θ2=θ

[0053] Among them, θ1 is the bending angle of the end of the first rectangular cross-section beam 1, θ2 is the bending angle of the end of the second rectangular cross-section beam 2; θ represents the bending angle of the swing tongue.

[0054] S22. Determine the equilibrium condition, the expression is:

[0055]

[0056] Among them, ∑F y represents the resultant force of the first rectangular cross-section beam 1 and the second rectangular cross-section beam 2 in the y-axis direction; F1 and F2 are the forces of the first rectangular cross-section beam 1 and the second rectangular cross-section beam 2 relative to the linear displacement, respectively; represents the sum of the bending moments of the first rectangular section beam 1 and the second rectangular section beam 2. M1 and M2 are the bending moments of the first rectangular section beam 1 and the second rectangular section beam 2 relative to the bending angle, respectively; M0 represents the magnitude and direction of the additional torque shear force on the pendulum assembly; ∑M x represents the sum of the torques of the first rectangular cross-section beam 1 and the second rectangular cross-section beam 2; is the torque of the first rectangular cross-section beam 1 and the second rectangular cross-section beam 2 relative to the torsion angle.

[0057] S23. Determine the physical conditions, the expression is:

[0058]

[0059] Among them, l represents the length of the first rectangular section beam 1 and the second rectangular section beam 2; I1 and I2 are the section moments of inertia of the first rectangular section beam 1 and the second rectangular section beam 2 respectively; E is the elastic modulus of the material; It1 and It2 are the section polar moments of inertia of the first rectangular section beam 1 and the second rectangular section beam 2 respectively; G is the shear modulus of the material.

[0060] S24, determine the corner condition, the expression is:

[0061]

[0062] Furthermore, F1=F2, so M1=M2.

[0063] S25. Determine the boundary conditions, the expression is:

[0064]

[0065] S26, combine the boundary conditions and equations N1+N2=N in step 25:

[0066]

[0067] Wherein, N represents the distance between the centroid of the cross section of the first rectangular cross-section beam 1 and the centroid of the cross section of the second rectangular cross-section beam 2;

[0068] S27, bring the boundary conditions of the bending corner into the equilibrium conditions in step 22, and we have:

[0069]

[0070] S28, based on step 27, obtain the pendulum shaft torsion angle, the expression is:

[0071]

[0072] Wherein, b1 represents the width of the first rectangular cross-section beam 1 ; b2 represents the width of the second rectangular cross-section beam 2 .

[0073] S3. Based on the non-parallel plate differential capacitance model, the asymmetric flexible beam structure error of the quartz flexible accelerometer caused by the torsion angle of the pendulum shaft is obtained.

[0074] Furthermore, when the pendulum assembly is subjected to an additional torque, the two side plates of the sensitive capacitor are in a non-parallel state. The virtual series method is used to calculate the differential capacitance of the two non-parallel plates to obtain the equivalent relationship between the pendulum shaft torsion angle and the accelerometer output.

[0075] Specifically, see Figure 2 , the pendulum shaft torsion angle generated by the two side plates of the sensitive capacitor under the influence of the additional torque Equivalent to the secondary displacement of the two plates on both sides of the sensitive capacitor, the differential capacitance is obtained, and the expression is:

[0076]

[0077] Among them, C1 and C2 are two sensitive capacitors in the differential capacitance detection circuit; ε0 represents the vacuum dielectric constant; ε r Represents the relative dielectric constant; s represents the plate area; d0 is the plate spacing when the two side plates of the sensitive capacitor are in equilibrium position; Δd is the displacement of the two side plates of the sensitive capacitor due to the input acceleration; Δd′ represents the additional sensitive displacement caused by the additional torque; C0 represents the capacitance of the two side plates of the sensitive capacitor when they are in equilibrium position; ΔC represents the ideal capacitor output; ΔC′ represents the additional capacitor output caused by the additional displacement of the two side plates of the sensitive capacitor; ΔN is the distance of the shear center of the two side plates of the sensitive capacitor offset from the ideal symmetry axis.

[0078] Based on the differential capacitance, the asymmetric flexure beam structure error Y of the quartz flexure acceleration is obtained, and the expression is:

[0079] Y=K C ·(ΔC+ΔC′) (9)

[0080] Among them, K C It is the amplification factor of the proportional link of the detection circuit.

[0081] S4. Example verification:

[0082] In this embodiment, the double flexible pendulum beam has an asymmetric thickness, and the thickness distribution is h1=22μm, h2=20μm respectively. The quartz pendulum piece and the coil assembly in the pendulum assembly are not coaxial, and the coil assembly is offset along the output axis by Δx=0.01mm. The structure is shown in the figure. Figure 3 As shown, the point of action of the feedback force F is offset from the original symmetry axis by Δx, and the center of mass offset of the swinging part is Δx':

[0083]

[0084] Among them, m 线圈组件 is the total mass of the coil assembly, m 摆组件 is the total mass of the pendulum assembly, and is the sum of the masses of the coil assembly and the quartz pendulum.

[0085] The structure of the flexible double beam is set as Figure 4 As shown in the figure, l is the length of the pendulum beam, b is the width of the single-side pendulum beam, and h1 and h2 are the thickness of the pendulum beam.

[0086] Then the additional torque on the swing beam is: M0 = m 摆组件 a(Δx-Δx′)=3.4×10 -5 N·mm, where a=9.8m / s 2 is the input acceleration.

[0087] According to formula (7), the torsion angle can be calculated as Through ANSYS finite element simulation, the torsion angle of the asymmetric structure model under 1g acceleration is calculated to be 7.9×10 -6 rad, it can be seen that the calculation results are basically accurate, and the simulation results are as follows Figure 5 shown.

[0088] Then we can get: ΔN = 0.46 mm, Δd′ = 4.14 × 10 -6 mm.

[0089] When the pendulum assembly is in equilibrium, the static capacitance C0 = 30.9pf, and the plate spacing d0 = 0.02mm at equilibrium, we can get Through MAXWELL electric field simulation, the error capacitance of the asymmetric structure model under torsion is calculated to be 0.012pf. It can be seen that the calculation results are basically accurate. The simulation results are as follows Figure 6 shown.

[0090] Finally, it can be calculated that under the action of additional torque, the output error value of the accelerometer can be equivalent to Y′=K C ·ΔC′.

[0091] It can be concluded that the output equivalent method of the asymmetric flexible beam structure of the quartz flexible accelerometer can effectively calculate the influence of the additional torque on the accelerometer output, has a clear mechanical concept, and greatly saves calculation time.

[0092] Therefore, the present invention adopts the above method to provide an equivalent output calculation method of the accelerometer when the input error source is the asymmetric or non-coaxial structure of the quartz pendulum assembly, provides an evaluation method for the structural error of the quartz pendulum assembly, and provides a theoretical reference for the structural optimization design of the quartz accelerometer pendulum assembly.

[0093] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for modeling the error of an asymmetric flexible beam structure of a quartz flexible accelerometer, characterized in that: The specific steps are as follows: S1. Determine the actual action positions of the inertial force and the electromagnetic force according to the defects of the pendulum assembly; determine the magnitude and direction of the additional torque shear force according to the actual action positions of the inertial force and the electromagnetic force; S2. Simulate the flexible pendulum beam of the quartz flexible accelerometer as two parallel rectangular cross-section beams; obtain the cross-sectional characteristics of the flexible pendulum beam; and model the torsion angle of the flexible pendulum beam along the pendulum axis direction under the action of the additional torque; S3. Based on the non-parallel plate differential capacitance model, the asymmetric flexible beam structure error of the quartz flexible accelerometer caused by the torsion angle of the pendulum shaft is obtained.

2. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 1, characterized in that: The specific steps of S2 are: S21, simulating the flexible pendulum beam of the quartz flexible accelerometer as two parallel rectangular cross-section beams, the two parallel rectangular cross-section beams twist around the twisting center point C; setting the end boundary conditions of the two parallel rectangular cross-section beams; S22, determining the equilibrium condition; S23, determining physical conditions; S24, determining a turning angle condition; S25, determining the return boundary condition; S26, combining the boundary conditions in step 25 and the distance equations of the two rectangular cross-section beams; S27, bringing the boundary condition of the bending corner into the equilibrium condition in step 22; S28. Based on step 27, obtain the pendulum shaft torsion angle.

3. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 1, characterized in that: The specific steps of step S3 are: when the pendulum assembly is subjected to the additional torque, the two side plates of the sensitive capacitor are in a non-parallel state; the non-parallel plate differential capacitance is obtained by using the virtual series method; based on the differential capacitance, the asymmetric flexible beam structure error between the pendulum shaft torsion angle and the quartz flexible accelerometer is obtained.

4. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 3, characterized in that: The two side plates of the sensitive capacitor generated by the swing plate under the influence of the additional torque are equivalent to the secondary displacement of the two side plates of the sensitive capacitor to obtain the differential capacitance.

5. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 4, characterized in that: The expression for differential capacitance is: Among them, C1 and C2 are two sensitive capacitors in the differential capacitance detection circuit; ε0 represents the vacuum dielectric constant; ε r Represents the relative dielectric constant; s represents the plate area; d0 is the plate spacing when the two side plates of the sensitive capacitor are in equilibrium position; Δd is the displacement of the two side plates of the sensitive capacitor due to the input acceleration; Δd′ represents the additional sensitive displacement caused by the additional torque; C0 represents the capacitance of the two side plates of the sensitive capacitor when they are in equilibrium position; ΔC represents the ideal capacitor output; ΔC′ represents the additional capacitor output caused by the additional displacement; ΔN is the distance of the shear center offset from the ideal symmetry axis.

6. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 5, characterized in that: Based on the differential capacitance, the asymmetric flexure beam structure error Y of the quartz flexure acceleration is obtained, and the expression is: Y=K C ·(ΔC+ΔC′) Among them, K C It is the amplification factor of the proportional link of the detection circuit.

7. The method for modeling the asymmetric flexible beam structure error of a quartz flexible accelerometer according to claim 2, characterized in that: The end boundary conditions of two parallel rectangular cross-section beams include boundary conditions of torsion angle, bending deflection and bending rotation.

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