T-shaped mode coupling resonant accelerometer

Abstract

The invention relates to a T-shaped modal coupling resonant accelerometer, which comprises a sensitive mass block, the sensitive mass block is connected with an anchor point through a T-shaped resonator, and the T-shaped resonator is used for realizing acceleration detection and an early warning function; the T-shaped resonator comprises a horizontal beam and a vertical beam, one end of the horizontal beam is fixed on the anchor point, the other end of the horizontal beam is connected with the sensitive mass block, one end of the vertical beam is vertically connected at the midpoint of the horizontal beam, and the other end of the vertical beam is in a suspended state; the driving electrodes are distributed on one side of the horizontal beam, the regulation electrodes are distributed on the two sides of the horizontal beam, the horizontal beam induction electrodes of the horizontal beam are distributed on one side of the horizontal beam, and the vertical beam induction electrodes of the vertical beam are distributed on the two sides of the vertical beam. The sensitivity of the accelerometer is improved, and the high-resolution acceleration early warning effect is achieved.

Description

Technical Field

[0001] The invention belongs to the field of micro-electromechanical systems (MEMS), and in particular relates to a T-type modal coupling resonant accelerometer. Background Art

[0002] MEMS (micro-electromechanical system) accelerometers have become an indispensable component in key fields such as consumer electronics, earthquake monitoring, and aerospace due to their miniaturized design and high integration. Based on their unique detection mechanism, MEMS accelerometers can be subdivided into multiple types, including resonant, capacitive, and piezoresistive. Among the many types, MEMS resonant accelerometers play an irreplaceable role in fields that require high-precision and high-reliability measurements due to their significant advantages such as wide measurement range, high accuracy, and strong anti-interference.

[0003] MEMS resonant accelerometers mainly change the axial force of the resonator by applying acceleration. According to different detection methods, they can be divided into two categories: one is to detect acceleration by using the offset of the resonant frequency, and the other is to detect acceleration by using the change of the amplitude ratio based on modal localization. There is little research on the use of bifurcation frequency offset in detecting acceleration sensitivity, but this principle has been widely used in mass sensors.

[0004] In the prior art, some resonant accelerometers improve the sensitivity of the accelerometer by reducing the structural size and introducing an amplification mechanism. However, due to the constraints of the processing technology, the size of the accelerometer cannot be infinitely reduced; and the introduction of the amplification mechanism greatly reduces the detection sensitivity of the accelerometer and the amplification factor is unstable. In view of the above problems, a solution is proposed below. Summary of the invention

[0005] In order to solve the technical problems existing in the background technology, the present invention provides a T-type modal coupling resonant accelerometer, which improves the sensitivity of the accelerometer and achieves a high-resolution acceleration warning effect.

[0006] The technical solution adopted by the present invention to solve its technical problem is: A T-type modal coupling resonant accelerometer includes a sensitive mass block, the sensitive mass block is connected to an anchor point via a T-type resonator, and the T-type resonator is used to detect acceleration and realize an early warning function; The T-type resonator includes a horizontal beam and a vertical beam, one end of the horizontal beam is fixed on an anchor point, and the other end is connected to a sensitive mass block, one end of the vertical beam is vertically connected at the midpoint of the horizontal beam, and the other end is suspended; The driving electrodes are distributed on one side of the horizontal beam, the regulating electrodes are distributed on both sides of the horizontal beam, the horizontal beam sensing electrodes of the horizontal beam are distributed on one side of the horizontal beam, and the vertical beam sensing electrodes of the vertical beam are distributed on both sides of the vertical beam.

[0007] Furthermore, the sensitive mass block is supported by four folding beams, which are fixed on anchor points and are symmetrical in pairs along the X-axis direction.

[0008] Furthermore, the driving electrodes, the regulating electrodes, the horizontal beam sensing electrodes and the vertical beam sensing electrodes are all equal in size and are at equal distances from the resonant beam.

[0009] Furthermore, the length of the horizontal beam is 300 , the width of the horizontal beam is 3 ; The length of the vertical beam is 189 , the width of the vertical beam is 3 .

[0010] Further, the driving electrode is located at one end of the horizontal beam close to the anchor point; The regulating electrode is located at one end of the horizontal beam close to the sensitive mass block; The horizontal beam sensing electrode is located between the driving electrode and the regulating electrode.

[0011] Furthermore, the kinetic model is:

[0012] in and denote the amplitudes of the vertical beam and the horizontal beam, respectively, and is the damping ratio; is the driving force, which is proportional to the product of the AC driving voltage and the DC driving voltage; and are the first and second natural frequencies of the resonator; is the geometric nonlinear stiffness coefficient caused by axial stress; Cubic nonlinear stiffness coefficient caused by large deformation; is the damping nonlinear stiffness coefficient caused by large deformation; is the square coupling stiffness coefficient; is the damping coupling stiffness coefficient.

[0013] Beneficial effects of the present invention: (1) The natural frequency ratio of the vertical beam and the horizontal beam of the sensitive resonant structure of the resonant accelerometer is close to 1:2, which realizes the modal coupling phenomenon. By detecting the semi-harmonic signal of the vertical beam, the sensitivity of the accelerometer is improved.

[0014] (2) The electrode distribution of this resonant accelerometer effectively overcomes the phenomenon of frequency ratio disproportion caused by processing errors. The introduction of regulating electrodes makes the modal coupling phenomenon adjustable and controllable.

[0015] (3) The folded beam of the resonant accelerometer is mainly used to support the sensitive mass block, and has a smaller stiffness along the sensitive axis and a larger stiffness along the non-sensitive axis, which can improve the sensitivity of the accelerometer and reduce the cross-sensitivity.

[0016] (4) When modal coupling occurs, this resonant accelerometer detects the change in the natural frequency of the vertical beam and uses the detection electrodes on both sides of the vertical beam to capture the semi-harmonic vibration signal, thereby achieving a high-resolution acceleration warning effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0018] Figure 1 It is a schematic diagram of the overall structure of the present invention; Figure 2 It is a schematic diagram of the structure of a T-type resonator; Figure 3 Schematic diagram of electrode distribution of T-type resonator; Figure 4 It is a partial schematic diagram of the folded beam; Figure 5 This is the COMSOL simulation diagram of the T-type resonator working mode, with the vertical beam vibration being the main one; Figure 6 This is the COMSOL simulation diagram of the T-type resonator working mode, with the horizontal beam vibration being the main one; Figure 7 This is a COMSOL simulation diagram of the effect of the control voltage on the natural frequency of the horizontal beam and the vertical beam; Figure 8 The experimental results of the effect of the control voltage on the natural frequency of the horizontal beam and the vertical beam are shown in the figure; Fig. 9 This is the experimental result diagram of quantitative detection of acceleration when no modal coupling occurs; Fig.10 This is the experimental result diagram for quantitatively detecting acceleration through the shift of bifurcation frequency caused by modal coupling; Fig.11 is the amplitude-frequency response curve of the vertical beam when the acceleration a=0g; Fig.12 It is the amplitude-frequency response curve of the vertical beam when the acceleration a=-0.5g; Fig.13 is the effect of acceleration on the vertical beam frequency; Fig.14 is the T-type resonator and coordinate system under the influence of acceleration.

[0019] Reference numerals A101, anchor point; F101, horizontal beam; F201, vertical beam; C101, folding beam; B101, sensitive mass block; D101, driving electrode; D201, horizontal beam sensing electrode; D401, vertical beam sensing electrode; D301, control electrode. DETAILED DESCRIPTION

[0020] The present invention is further described in detail below with reference to the accompanying drawings.

[0021] In the description of the embodiments of the present invention, it should be recognized that the directions or positional relationships represented by the terms such as "upper", "lower", "left", "right", "X", "Y", etc. are defined based on the perspective of the drawings, for the purpose of simplifying and clearly explaining the present invention, rather than stipulating or implying that the devices or components must strictly follow these specific directions or positions. Therefore, the use of these terms should not be interpreted as any limitation to the present invention.

[0022] In order to illustrate the purpose, technical solutions and advantages of the present invention, the present invention will be described in detail with reference to the accompanying drawings and embodiments. It should be noted that the embodiments are only used to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features described in the various embodiments of the present invention can be freely combined without contradicting each other.

[0023] The T-type modal coupling resonant accelerometer includes a sensitive mass block B101, wherein the sensitive mass block B101 is connected to an anchor point A101 through a T-type resonator, and the T-type resonator is used to detect acceleration and realize an early warning function; The T-type resonator includes a horizontal beam F101 and a vertical beam F201. One end of the horizontal beam F101 is fixed on the anchor point A101, and the other end is connected to the sensitive mass block B101. One end of the vertical beam F201 is vertically connected at the midpoint of the horizontal beam F101, and the other end is in a suspended state. The driving electrode D101 is distributed on one side of the horizontal beam F101, the regulating electrode D301 is distributed on both sides of the horizontal beam F101, the horizontal beam sensing electrode D201 of the horizontal beam F101 is distributed on one side of the horizontal beam F101, and the vertical beam sensing electrode D401 of the vertical beam F201 is distributed on both sides of the vertical beam F201.

[0024] Furthermore, the sensitive mass block B101 is supported by four folding beams C101 , which are fixed on the anchor point A101 and are symmetrical in pairs along the X-axis direction.

[0025] Furthermore, the driving electrode D101 , the regulating electrode D301 , the horizontal beam sensing electrode D201 , and the vertical beam sensing electrode D401 are all equal in size and are at equal distances from the resonant beam.

[0026] Furthermore, the length of the horizontal beam F101 is 300 , the width of the horizontal beam F101 is 3 ; The length of the vertical beam F201 is 189 , the width of the vertical beam F201 is 3 .

[0027] Further, the driving electrode D101 is located at one end of the horizontal beam F101 close to the anchor point A101; The regulating electrode D301 is located at one end of the horizontal beam F101 close to the sensitive mass block B101; The horizontal beam sensing electrode D201 is located between the driving electrode D101 and the regulating electrode D301 .

[0028] Furthermore, the kinetic model is:

[0029] in and denote the amplitudes of the vertical beam and the horizontal beam, respectively, and is the damping ratio; is the driving force, which is proportional to the product of the AC driving voltage and the DC driving voltage; and are the first and second natural frequencies of the resonator; is the geometric nonlinear stiffness coefficient caused by axial stress; Cubic nonlinear stiffness coefficient caused by large deformation; is the damping nonlinear stiffness coefficient caused by large deformation; is the square coupling stiffness coefficient; is the damping coupling stiffness coefficient. Specific embodiments like Figure 1 As shown, this embodiment is a T-type modal coupling resonant accelerometer, which includes an anchor point A101, a horizontal beam F101, a vertical beam F201, a folded beam C101, a sensitive mass block B101, a driving electrode D101, a horizontal beam sensing electrode D201, a vertical beam sensing electrode D401, and a control electrode D301.

[0031] Specifically, the sensitive mass block B101 is connected to the anchor point A101 via a folded beam C101, and the folded beam C101 and the anchor point A101 are symmetrically distributed on both sides of the sensitive mass block B101 about the X-axis.

[0032] like Figure 2As shown, the T-shaped sensitive structure includes a horizontal beam F101 and a vertical beam F201. One end of the horizontal beam F101 is connected to the anchor point A101, and the other end is connected to the sensitive mass block B101. One end of the vertical beam F201 is in a suspended state, and the other end is vertically connected to the horizontal beam F101 at the midpoint of the horizontal beam F101. The frequency ratio of the vertical beam F201 and the horizontal beam F101 is close to 1:2.

[0033] like Figure 3 As shown, the driving electrode D101 is distributed on one side of the horizontal beam F101, the regulating electrode D301 is distributed on both sides of the horizontal beam F101, the horizontal beam sensing electrode D201 is distributed on one side of the horizontal beam F101, and the vertical beam sensing electrode D401 is distributed on both sides of the vertical beam F201. It should be noted that the electrodes are of the same size and are at an equal distance from the resonant beam, not less than 3um.

[0034] like Figure 4 As shown, the folding beam C101 is used to connect the sensitive mass block B101 and the anchor point A101. The folding beam C101 can keep the sensitive mass block B101 in the XY plane and provide the detection sensitive mass block with the freedom of movement along the X-axis direction; at the same time, the folding beam C101 plays a role in adjusting the torsion pendulum mode of the detection sensitive mass block, which can reduce the cross-axis sensitivity.

[0035] like Figure 5 As shown, through COMSOL modeling and simulation, the first-order natural frequency of the T-type sensitive resonator in this example is 87506 Hz, mainly vertical beam vibration.

[0036] like Figure 6 As shown, through COMSOL modeling and simulation, the second-order natural frequency of the T-type sensitive resonator in this example is 180570 Hz, mainly horizontal beam vibration.

[0037] like Figure 7 As shown in the figure, through COMSOL modeling and simulation, when the control voltage is between 0V and 220V, the relationship between the natural frequency ratio of the horizontal beam and the vertical beam and the control voltage is plotted. According to this example, the control voltage has a greater impact on the natural frequency of the horizontal beam, and the impact on the natural frequency of the vertical beam is almost negligible. By controlling the voltage, the ratio of the natural frequency of the vertical beam to the horizontal beam can be close to 1:2.

[0038] like Figure 8 As shown in the figure, through experimental verification, when the control voltage is between 0V and 220V, the relationship between the natural frequency ratio of the horizontal beam and the vertical beam and the control voltage is plotted. The experimental results are almost consistent with the finite element simulation results. The modal coupling phenomenon can be adjusted and controlled by regulating the voltage.

[0039] like Fig. 9As shown in the figure, under a small excitation, the acceleration of -g-+g is applied to the accelerometer by controlling the rotation angle of the stepper motor. When the applied acceleration is -g, the T-type resonator is subjected to pressure, and vice versa, when the applied acceleration is +g, the T-type resonator is subjected to tension. As the acceleration increases, the natural frequency of the T-type resonator increases linearly.

[0040] like Fig.10 As shown in the figure, when modal coupling vibration occurs, the horizontal beam exhibits obvious forced vibration behavior, and its response frequency is consistent with the driving frequency. At the same time, the vertical beam exhibits significant parametric vibration behavior, and its response frequency is only half of the driving frequency. The semi-harmonic vibration signal is captured by using detection electrodes on both sides of the vertical beam. According to this example, the sensitivity of the accelerometer is 52.84Hz / g through experimental measurement.

[0041] like Figure 11-13 As shown in the figure, when the acceleration increases from -0.5g to 0g, the bifurcation frequency of the vertical beam jumps from 176.955kHz to 178kHz, and the bifurcation frequency shifts by 1045Hz. At the same time, when the acceleration gradually increases from 0g to g, the bifurcation frequency of the vertical beam hardly changes. Therefore, we use the mutation of the bifurcation frequency to achieve acceleration warning. It should be noted that this warning phenomenon is caused by frequency locking. When the applied acceleration reaches a critical value, the amplitude and bifurcation frequency of the vertical beam will increase sharply, thereby achieving the acceleration warning effect.

[0042] like Fig.14 As shown in Figure 2, in order to explain the acceleration sensing mechanism based on the bifurcation caused by modal coupling, we theoretically derived a dynamic model. The dynamic model of the distributed electrostatically driven T-type resonant accelerometer can be expressed as:

[0043] in and denote the amplitudes of the vertical beam and the horizontal beam, respectively, and is the damping ratio; is the driving force, which is proportional to the product of the AC driving voltage and the DC driving voltage; and are the first and second natural frequencies of the resonator; is the geometric nonlinear stiffness coefficient caused by axial stress; Cubic nonlinear stiffness coefficient caused by large deformation; is the damping nonlinear stiffness coefficient caused by large deformation; is the square coupling stiffness coefficient; is the damping coupling stiffness coefficient. The quality factor and natural frequency can be measured experimentally. The nonlinear stiffness coefficient can be obtained by theoretical method. The specific derivation process is as follows.

[0044] The simplified model of the accelerometer is as follows Fig.14 As shown in the figure, by using Hamilton's principle and considering the dissipative force caused by the sliding film damping and the air film damping, the control of the lateral deflection and the control of the lateral displacement are and The equation of motion is written as: (A1) in, represents the resonator density, represents the length of the horizontal beam, represents the length of the vertical beam, represents the cross-sectional area of ​​the resonator, represents the moment of inertia of the resonator, represents the Young's modulus of the resonator.

[0045] (A2) The boundary conditions are:

[0046] For lateral loads, only the distributed electrostatic driving force is considered, which can be defined as: (A3) (A4) in, represents the DC voltage applied to the regulating electrode; represents the DC voltage applied to the driving electrode and the detection electrode; represents the AC voltage applied to the driving electrode; represents a step function; represents the dielectric constant of vacuum; Indicates the driving frequency; represents the thickness of the resonator; represents the starting position of the vertical beam sensing electrode; represents the end position of the vertical beam sensing electrode; Indicates the starting position of the driving electrode; Indicates the end position of the driving electrode; Indicates the starting position of the horizontal beam sensing electrode; Indicates the end position of the horizontal beam sensing electrode; Indicates the starting position of the control electrode; Indicates the end position of the control electrode.

[0047] For convenience, we introduce dimensionless variables: , , , , Substituting the dimensionless variables into the equations, (A1)-(A2), we obtain: (A5) (A6) in represents acceleration, Indicates the detection quality.

[0048] Under boundary conditions:

[0049] in , , is the thickness of the resonant beam, The distance between the parallel plate electrode and the resonant beam.

[0050] It should be noted that since the DC voltage applied to the driving electrode and the detection electrode is relatively small, the influence of the driving electrode and the detection electrode on the static displacement of the resonant beam is ignored. ,get:

[0051] Here, we only consider the first-order bending vibration of the horizontal beam and the vertical beam. Then, the solution of Eq.

[0052] (A1-A2) can be expressed as ,in denote the first-order linear undamped modes of the vertical beam and the horizontal beam respectively. The linear undamped eigenvalue problem can be obtained as: (A7) in:

[0053] Substitute equation (A7) into the resulting equation (A5-A6), multiply by , and x i =0 to 1, we get: (A8) (A9) Then, the two-degree-of-freedom dynamic model can be obtained (A10) in: (A11) (A12) (A13) (A14) (A15) (A16) (A17) Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. T-type modal coupling resonant accelerometer, characterized in that: It comprises a sensitive mass block (B101), wherein the sensitive mass block (B101) is connected to an anchor point (A101) via a T-type resonator, wherein the T-type resonator is used to detect acceleration and realize an early warning function; The T-type resonator comprises a horizontal beam (F101) and a vertical beam (F201), one end of the horizontal beam (F101) is fixed on an anchor point (A101), and the other end is connected to a sensitive mass block (B101), and one end of the vertical beam (F201) is vertically connected to the midpoint of the horizontal beam (F101), and the other end is in a suspended state; The driving electrode (D101) is distributed on one side of the horizontal beam (F101), the regulating electrode (D301) is distributed on both sides of the horizontal beam (F101), the horizontal beam sensing electrode (D201) of the horizontal beam (F101) is distributed on one side of the horizontal beam (F101), and the vertical beam sensing electrode (D401) of the vertical beam (F201) is distributed on both sides of the vertical beam (F201).

2. The T-type modal coupling resonant accelerometer according to claim 1, characterized in that: The sensitive mass block (B101) is supported by four folding beams (C101), and the folding beams (C101) are fixed on the anchor points (A101) and are symmetrical in pairs along the X-axis direction.

3. The T-type modal coupling resonant accelerometer according to claim 1, characterized in that: The driving electrode (D101), the regulating electrode (D301), the horizontal beam sensing electrode (D201) and the vertical beam sensing electrode (D401) are all of equal size and are at equal distances from the resonant beam.

4. The T-type modal coupling resonant accelerometer according to claim 1, characterized in that: The length of the horizontal beam (F101) is 300 , the width of the horizontal beam (F101) is 3 ; The length of the vertical beam (F201) is 189 , the width of the vertical beam (F201) is 3 .

5. The T-type modal coupling resonant accelerometer according to claim 2, characterized in that: The driving electrode (D101) is located at one end of the horizontal beam (F101) close to the anchor point (A101); The control electrode (D301) is located at one end of the horizontal beam (F101) close to the sensitive mass block (B101); The horizontal beam sensing electrode (D201) is located between the driving electrode (D101) and the regulating electrode (D301).

6. The T-type modal coupling resonant accelerometer according to claim 1, characterized in that: The kinetic model is: ； in and denote the amplitudes of the vertical beam and the horizontal beam, respectively, and is the damping ratio; is the driving force, which is proportional to the product of the AC driving voltage and the DC driving voltage; and are the first and second natural frequencies of the resonator; is the geometric nonlinear stiffness coefficient caused by axial stress; Cubic nonlinear stiffness coefficient caused by large deformation; is the damping nonlinear stiffness coefficient caused by large deformation; is the square coupling stiffness coefficient; is the damping coupling stiffness coefficient.

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