Capacitive force sensor signal conversion model establishment method

Abstract

The invention discloses a capacitive force sensor signal conversion model establishment method for a sensor structure with an elastomer and a capacitor, and the method comprises the steps: (1) deducing a flexibility matrix of a cantilever beam based on the Cartesian second theorem, analyzing the spatial geometric position relation of an elastic structure, and calculating the flexibility matrix of the cantilever beam; and establishing a conversion matrix between the displacement of the elastomer and the input force / torque. (2) analyzing the geometric arrangement relationship between the elastomer and the capacitor movable pole plate, and establishing a conversion displacement matrix of elastomer deformation and capacitor movable pole plate displacement; and (3) based on the working principle of the differential structure capacitor of the sensor, establishing a conversion capacitance change matrix between the displacement of the movable polar plate of the capacitor and an output capacitance signal. And determining a conversion mathematical model between the input force / torque signal and the output capacitance signal of the capacitive force sensor by combining the steps. According to the method, a mathematical matrix model for signal transmission in a sensor system is established, and a signal conversion mathematical model of the capacitive six-dimensional force sensor can be efficiently solved.

Description

Technical Field

[0001] The present invention relates to the technical field of sensor design and optimization, and in particular to a method for establishing a capacitive force sensor signal conversion model. Background Art

[0002] In the process of optimizing the design of capacitive six-axis force sensors, the signal conversion model is of great significance. However, finite element analysis is usually cumbersome and time-consuming, and the existing analytical methods are still immature and have large errors. When using analytical methods to optimize the design of six-axis force sensors, it is necessary to start with the theoretical model, deeply study and analyze its mechanical model, and finally derive specific mathematical expressions through mechanical principles. However, the implementation of analytical methods also faces certain challenges. On the one hand, it often takes a lot of time to establish analytical models, and for six-axis force sensors of different configurations, it may be necessary to rebuild the corresponding mathematical model; on the other hand, the analytical method limits the flexibility of sensor design to a certain extent because it usually relies on assumptions and simplifications of theoretical models. In this field, many scholars continue to explore and innovate, trying to overcome the limitations of analytical methods. The analytical method has poor versatility in optimizing the design of six-axis force sensors. The establishment of the initial mathematical model is usually time-consuming, and the mathematical model needs to be rebuilt for the optimization design of sensors of different configurations. Therefore, in order to more effectively apply the analytical method to capacitive six-axis force sensors, it is necessary to establish an accurate mathematical model of the conversion matrix between six-axis force / torque and capacitance change. Summary of the invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art. To this end, the present invention proposes a method for establishing a capacitive six-dimensional force sensor signal conversion model for a sensor structure having a capacitor and an elastic body, which can effectively improve the optimization design efficiency of the sensor. To achieve the above objectives, the technical solution adopted by the present invention is:

[0004] The first step is to analyze the stress and deformation of a single cantilever beam structure and establish the flexibility matrix of the single cantilever beam structure using Castigliano's second theorem.

[0005] The second step is to analyze the spatial geometric position relationship of the elastic structure and establish the conversion matrix between the displacement of the elastic body and the input force / torque;

[0006] The third step is to analyze the spatial geometric relationship between the elastic body deformation and the capacitor plate displacement, and establish a conversion matrix between the capacitor plate displacement and the elastic body deformation;

[0007] The fourth step is to analyze the relationship between the capacitor output signal and the displacement of the capacitor plate, and establish a conversion matrix between the capacitor output signal and the displacement of the capacitor plate;

[0008] The fifth step is to determine the specific expression of the conversion model between the output signal and the input signal of the six-dimensional force sensor by combining the above four steps.

[0009] Based on the above steps, the mathematical matrix model of signal transmission within the sensor system is analyzed by mathematical analytical methods, and the signal conversion mathematical model of the capacitive six-dimensional force sensor can be efficiently derived, providing a theoretical mathematical model for the subsequent optimization of sensor performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0011] Figure 1 It is a flow chart of a method for establishing a capacitive force sensor signal conversion model;

[0012] Figure 2 It is a single cantilever beam structure;

[0013] Figure 3 It is the deformation diagram of a single cantilever beam structure under the action of external force;

[0014] Among them, (a) is the deformation diagram of a single cantilever beam under Mx loading, (b) is the deformation diagram of a single cantilever beam under Fz loading, (c) is the deformation diagram of a single cantilever beam under Mz loading, and (d) is the deformation diagram of a single cantilever beam under Fx loading.

[0015] Figure 4 It is a coordinate system diagram of the elastic structure of a single T-beam of the six-dimensional force sensor elastic body;

[0016] Figure 5 It is the xy plane coordinate system diagram of the elastic body of the six-dimensional force sensor;

[0017] Figure 6 It is the structural parameter diagram of the elastic body of the six-dimensional force sensor;

[0018] Figure 7 It is the structural parameter diagram of the capacitor of the six-dimensional force sensor;

[0019] Figure 8 It is a capacitive six-dimensional force sensor capacitor plate displacement diagram.

[0020] Among them, (a) force Fz causes the displacement of plate C1; (b) torque Mx causes the displacement of plate C1; (c) force Fx causes the displacement of plate C4; (d) torque My causes the displacement of plate C2; ​​(e) torque M Fy This causes displacement of plate C2; ​​(f) Torque Mz causes displacement of plate C4. DETAILED DESCRIPTION

[0021] The present invention is further described below with reference to the accompanying drawings. A method for establishing a capacitive force sensor signal conversion model proposed in the present invention is shown in the flowchart. Figure 1 , the method comprises the following steps:

[0022] In the first step, according to Castigliano's second theorem, the relationship between strain energy and displacement of a cantilever beam with equal cross-section under external force is analyzed, and the flexibility matrix of a single cantilever beam structure is established.

[0023] A. One end of a cantilever beam of uniform cross-section is fixed by a constraint, while the other end can move freely under the action of an external force. Figure 2 , where the area size is , the length is , is the width of the beam and is the thickness of the beam; coordinate system Located at the free end of a beam of uniform cross-section, the small deformation of the free end can be expressed by torsion. To express, is the force acting on the free end of a cantilever beam of uniform cross-section.

[0024] According to the linear elastic beam theory, the relationship between the external force and the deformation of the free end of the cantilever beam with uniform cross-section is:

[0025] (1)

[0026] In the formula, is the flexibility matrix of the cantilever beam structure with uniform cross-section.

[0027] In order to more accurately calculate the stress state of the flexible beam structure, the external load is decomposed into the coordinate system , In the a and z directions, the strain energy generated by each component force on the beam element is analyzed in turn.

[0028] (1) Under the action of Fy / My, the beam element is compressed / stretched along the y-axis

[0029] The beam unit structure is compressed along the y-axis under the action of the external load Fy. The strain energy stored inside the beam structure can be expressed as

[0030] (2)

[0031] Based on Castiglione's second theorem, the first-order partial derivative of the strain energy function with respect to the force Fy is equal to the displacement caused by the force in the direction of Fy. In the first-order partial derivative function, let the force be equal to the unit force (Fy=1N), then the value of the partial derivative function is equal to the value of the flexibility element of the beam structure

[0032] (3)

[0033] The beam produces an angular deformation at the free end under the action of the torque My , its torsional flexibility can be expressed as

[0034] (4)

[0035] (2) The beam bends around the x-axis under the action of Mx and Fz

[0036] See Figure 3 As shown in (a), the beam structure diagram on the yz plane bends around the x-axis under the action of the external load Mx to produce a rotation angle ;See Figure 3 As shown in (b), the beam unit structure on the yz plane bends around the x-axis under the action of the external load Fz and produces displacement. , then the strain energy stored in the beam structure when it bends around the x-axis under the action of external force can be expressed as

[0037] (5)

[0038] Similarly, calculate the partial derivatives of the strain energy function with respect to Mx and Fz, and let Mx=1 , Fz=0 and Mx=0, Fz=1 N

[0039] (6)

[0040] (7)

[0041] Under the action of Fz, the beam structure will produce a deflection angle with the x-axis, and under the action of Mx, the beam structure will be accompanied by a certain z-direction displacement.

[0042] (8)

[0043] (3) The beam bends around the z-axis under the action of Mz and Fx

[0044] See Figure 3 (c) Schematic diagram of the beam structure in the xy plane. The beam is bent around the z axis under the action of the external load Mz, resulting in a rotation angle ;See Figure 3 (d) In the xy plane, the beam unit structure bends around the z axis under the action of the external load Fx and produces displacement , the strain energy stored in the beam structure when it bends around the z-axis under the action of external force can be expressed as

[0045] (9)

[0046] Similarly, calculate the partial derivatives of the strain energy function with respect to Mz and Fx, and let Mz=1 , Fx=0 and Mz=0,Fx=1 N

[0047] (10)

[0048] (11)

[0049] Under the action of Fx, the beam structure will produce a deflection angle with the z-axis, and under the action of Mz, the beam structure will be accompanied by a certain x-direction displacement.

[0050] (12)

[0051] Among them, E and μ are the elastic modulus and Poisson’s ratio of the material respectively; and are the moments of inertia of the rectangular cross section about the x-axis and z-axis, respectively. ; ; Shear modulus of the material ; Shear influence coefficient ; Torsional moment of inertia of rectangular cross section .

[0052] From formulas (1-12), the flexibility matrix of the cantilever beam with equal cross-section can be expressed as

[0053] (13)

[0054] The second step is to analyze the spatial geometric position relationship of the elastic structure and establish the conversion matrix G1 between the elastic body displacement and the input force / torque.

[0055] A. The elastic structure includes a cross beam (denoted as P) and a longitudinal beam (denoted as U). The P beam is composed of a beam He Liang Combined together in parallel; see Figure 4 , cross-section of the upper and lower symmetric planes of the elastic structure and schematic diagram of each coordinate system. The sensor elastic body is composed of three T-shaped deformable beams that are distributed in parallel and rotationally symmetrically around the z-axis, see Figure 5 .

[0056] B. Elastomer structural parameters of the sensor, see Figure 6 , including: outer ring, elastic structure, force measuring platform, measuring block, relative position coordinates of the elastic structure and the central force measuring platform. The elastic structure parameters l1, l2, b1, h p , h and the radius of the force measuring platform r; the structural parameters of the capacitor moving plate of the sensor are shown in Figure 7 The capacitor structure parameters include the area S1 facing the horizontally arranged capacitor group, the area S2 facing the vertically arranged capacitor group, the initial pole distance d0 of the horizontally arranged capacitor, the initial pole distance d1 of the vertically arranged capacitor, and the position parameters a0, a1 of the sensor measurement block and the capacitor group.

[0057] In complex spatial multi-DOF connection structures, forces and deformations need to be calculated from the coordinate system. Convert to another coordinate system To do this, we need to apply the coordinate transformation matrix

[0058] (14)

[0059] In the formula, yes Relative to The coordinate rotation matrix of the system, is the antisymmetric operator matrix, for The origin is The expression in the system, is a zero matrix.

[0060] External forces and deformations The coordinate transformation in the coordinate system can be calculated as

[0061] (15)

[0062] Substituting formula (15) into formula (1), we can get Flexibility matrix in coordinate system for

[0063] (16)

[0064] Assume that n branch unit combinations are fixed on the central force measuring platform, and establish a reference coordinate system at the force acting point j=(1, 2, ..., n). Using the principle of virtual work, consider the total displacement of the output of the force measuring platform The deformation of the top of the basic flexible unit caused by the deformation can be obtained by formula (1, 14~15). The stiffness matrix of the elastic structure of the multi-branch force sensor can be expressed as

[0065] (17)

[0066] Assume that m branches are connected in parallel and fixed on the force measuring platform. The reference coordinate system is established at the top of each branch chain. According to the deformation law of the top of the i-th branch chain and the force measuring platform under the action of six-dimensional load, the displacement output generated by the central force measuring platform Displacement with the top of the i-th branch The mathematical relationship between

[0067] (18)

[0068] In the formula, is the coordinate system O at the top of the i-th branchi -xyz relative to coordinate system O f -xyz coordinate transformation matrix.

[0069] A separate force analysis is performed on the force measuring platform, and the six-dimensional load and the force vectors F1 to F1 at the top of the m branches can be listed. m The static equilibrium equation between

[0070] (19)

[0071] Using the relationship between force and deformation, the overall stiffness matrix of the multidimensional force sensor can be obtained as follows:

[0072] (20)

[0073] See Figure 4 , P beam is composed of beam He Liang Combined in parallel, the stiffness matrix at the top It can be expressed as

[0074] (twenty one)

[0075] Among them, C i3 , C i4 is the short beam A in the i-th branch chain i and B i The flexibility matrix. The top two short beams of the crossbeam in the i-th branch Relative to The pose transformation matrix of the system can be expressed as

[0076] (twenty two)

[0077] The posture matrix in formula (22) can be expressed as

[0078] (twenty three)

[0079] The coordinate transformation formula (around the x, y, and z axes) in formula (23) can be expressed as

[0080] (twenty four)

[0081] In formula (24), The origin of the coordinate system is The system can be expressed as

[0082] (25)

[0083] The T-shaped elastic structure is composed of a crossbeam P and a longitudinal beam U in series. Combining formula (21-22), the stiffness of a single branch of the six-dimensional force sensor elastic structure can be obtained as follows:

[0084] (26)

[0085] In the formula, is the U-side flexibility matrix of PU branched chain, is the coordinate transformation matrix, which can be expressed as

[0086] (27)

[0087] In the formula, is the unit matrix, The origin of the coordinate system is Representation in the system i1 and r i2 They can be expressed as

[0088] (28)

[0089] Combined with the above analysis, the overall stiffness of the elastic body of the six-axis force sensor can be expressed as

[0090] (29)

[0091] In the formula, is the top of the i-th PU branch Relative to the force measuring platform The coordinate transformation matrix of the system can be expressed as

[0092] (30)

[0093] In the formula, , , , , , .

[0094] According to the calculated stiffness matrix of the overall elastic body of the sensor, the elastic displacement matrix of the elastic body end point under the action of external force F can be expressed as:

[0095] (31)

[0096] The third step is to analyze the spatial geometric relationship between the elastic body deformation and the capacitor plate displacement, and establish an expression between the capacitor plate displacement and the elastic body deformation.

[0097] Six-dimensional force sensor capacitor plate displacement, see Figure 8 ; represents the normal displacement of the elastic body exerting force and torque; It represents the horizontal displacement of the elastic body's force torque. The horizontal plate moves upwards and moves downwards, which is positive, while the vertical plate moves closer to the right plate and moves away from the right plate, which is negative. The relationship between the displacement of the elastic body's endpoints and the displacement of the six capacitor electrodes is expressed as:

[0098] (32)

[0099] The mathematical relationship between the displacement of the central force measuring platform and the displacement of the capacitor moving plate can be expressed as

[0100] (33)

[0101] In formula (33), The displacement matrix of the capacitor moving plate is represented by the mapping relationship matrix G between the displacement of the central force measuring platform and the displacement of the capacitor moving plate. d It can be expressed as

[0102] (34)

[0103] The fourth step is to analyze the changing relationship between the capacitor output signal and the capacitor plate displacement, and establish an expression between the capacitor output signal and the capacitor plate displacement.

[0104] Under the action of six-dimensional force / torque, the relationship between the capacitance change and the pole distance change of the six sets of differential structure capacitors can be expressed as

[0105] (35)

[0106] In the formula, , , , , , Respectively represent the capacitance change values ​​of six groups of differential capacitors.

[0107] The mathematical relationship between the displacement of the capacitor plates and the change in capacitance can be expressed as

[0108] (36)

[0109] In the formula, is the six sets of differential capacitance change matrix of the sensor, .

[0110] (37)

[0111] The fifth step is to determine the specific expression of the conversion model between the output signal and the input signal of the six-dimensional force sensor by combining the above four steps.

[0112] In the capacitive six-dimensional force sensor measurement system, the relationship between the six-dimensional force / torque and the capacitance change can be expressed as

[0113] (38)

[0114] The mapping matrix G of the six-dimensional force sensor is

[0115] (39)

[0116]

Claims

1. A method for establishing a capacitive force sensor signal conversion model, for a sensor structure having a capacitor and an elastic body, characterized in that: The specific steps of this method are as follows: The first step is to analyze the stress and deformation of a single cantilever beam structure, use Castigliano's second theorem to perform static analysis on the single cantilever beam structure and establish its flexibility matrix; The second step is to analyze the spatial geometric position relationship of the elastic structure and establish the conversion matrix between the displacement of the elastic body and the input force / torque; The third step is to analyze the spatial geometric relationship between the elastic body deformation and the capacitor plate displacement, and establish a conversion matrix between the capacitor plate displacement and the elastic body deformation; The fourth step is to establish a conversion matrix between the capacitor output signal and the capacitor plate displacement according to the changing relationship between the capacitor output signal and the capacitor plate displacement; The fifth step is to determine the specific expression of the conversion model between the output signal and the input signal of the six-dimensional force sensor by combining the above four steps.

2. The method for calculating a capacitive six-dimensional force sensor signal conversion model according to claim 1, characterized in that: The specific method of analyzing the intrinsic relationship between the displacement and strain of the single cantilever beam structure and the elastic body as a whole under the action of six-dimensional force in the first and second steps and establishing the flexibility matrix of the elastic body is: A. Calculate the flexibility matrix of the single elastic beam structure of the sensor according to the calculation method of the flexibility matrix of the single cantilever beam structure; B. Based on the calculated flexibility matrix of the single elastic beam structure, establish the flexibility matrix of the entire sensor elastic body.

3. The method for calculating the capacitive six-dimensional force sensor signal conversion model according to claim 1, characterized in that: The second, third and fourth steps analyze the conversion relationship between the elastic body displacement and the input force / torque, the elastic body displacement and the capacitor plate displacement, and the capacitor plate displacement and the sensor capacitance output signal. The specific method is: A. Analyze the structural features and spatial geometric position relationship of the elastic body and the capacitor; wherein the elastic body includes a loading platform, a T-shaped beam and a measuring block; the capacitor includes a horizontally arranged capacitor and a vertically arranged capacitor, the capacitor includes a moving electrode plate and a static electrode plate, and the measuring block serves as the moving electrode plate of the capacitor; B. Based on the analysis of the flexibility matrix and input force / torque of the elastic body, calculate the displacement expression of the entire elastic body ; C. Calculate the expression between the elastic body deformation and the capacitor plate displacement according to the sensor capacitor arrangement structure; D. According to the working principle of capacitor, calculate the expression between the capacitor output signal and the displacement of the capacitor plate; E. Substitute the expression of the overall displacement of the elastic body into the expression of the displacement of the capacitor plate and the deformation of the elastic body and the capacitor output signal and the displacement of the capacitor plate, and calculate the conversion relationship between the sensor output force and the capacitor output signal.

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