Three-dimensional force measurement method and system based on normal pressure array

Abstract

The application relates to the technical field of pressure sensors, and provides a three-dimensional force measurement method and system based on a normal pressure array, which comprises the following steps: arranging an elastic layer with preset model parameters on a normal force array sensor, and applying preset pressure to the elastic layer, so as to obtain the pressure resultant force and pressure center offset amount of the normal force array sensor, and obtaining the corresponding tangential force according to the pressure resultant force and pressure center offset amount; and in order to ensure the measurement accuracy of the tangential force, the preset model parameters are calibrated and corrected, so that the model parameters are more accurate, the three-dimensional force measurement accuracy is improved, and the thickness of the whole sensor measurement mode can be effectively controlled, the sensor is convenient to install in a narrow space such as a foot bottom to measure relevant parameters, and the application range is wide.

Description

Technical Field

[0001] This invention relates to the field of pressure sensor technology, and in particular to a three-dimensional force measurement method and system based on a normal pressure array. Background Technology

[0002] Three-dimensional force sensors are used to measure the contact force on an object in three-dimensional space, typically comprising three orthogonal force components. Most existing three-dimensional force measurement methods require special structures, such as hemispherical junctions, and these methods require pressing into specific locations to correctly interpret the three-dimensional force. Alternatively, they may be implemented using magnetic induction or longitudinal structures, but this results in excessively thick sensors, making them unsuitable for installation in confined spaces. Summary of the Invention

[0003] The purpose of this invention is to provide a three-dimensional force measurement method and system based on a normal pressure array, so as to solve the technical problem of low measurement accuracy in existing three-dimensional force measurement methods.

[0004] In a first aspect, the present invention provides a three-dimensional force measurement method based on a normal pressure array, comprising: S100, an elastic layer with preset model parameters is arranged on a normal force array sensor; wherein, the preset model parameters are determined by test data calibration; S200, apply a preset pressure to the elastic layer and obtain the resultant pressure force and pressure center offset of the normal force array sensor; S300, based on the resultant pressure force and the offset of the pressure center, the corresponding tangential force is obtained.

[0005] Optionally, in step S100, the preset model parameters of the elastic layer include a first model and a second model; The first model includes: the formula for the offset of the pressure center after applying tangential force is d = (F 切 / S)*e / G, where e is the thickness of the elastic layer, G is the shear modulus, S is the area of ​​pressure applied, and F 切 It is a tangential force; The second model includes: F 法 *d=F 切 *e, where F 法 Let d be the resultant pressure force, and d be the offset of the pressure center. Combining the first and second models, we get: F 切 =(A(F 法 / e)+B(S*G / e))*d;where A is the first coefficient of the first model and B is the second coefficient of the second model.

[0006] Alternatively, the shear modulus G is calculated using the following formula: ; Where E is Young's modulus. ν It is Poisson's ratio.

[0007] Optionally, in step S200, the resultant pressure force is obtained by measuring each detection point of the normal force array sensor, and the pressure center offset is calculated by the pressure value at each detection point.

[0008] Optionally, before step S100, the method further includes: calibrating the preset model parameters using test data, wherein the calibration process specifically includes: S101, Obtain two test samples of the same size in the elastic layer with preset model parameters; S102, the two test samples are placed in the preset position of the calibration device and horizontal pressure is applied so that weights of different masses are clamped between the two test samples respectively. S103, obtains the horizontal pressure corresponding to weights of different masses through a spoke force gauge; S104, taking the horizontal pressure and the mass of the weight as variables, and obtaining the first coefficient corresponding to the first model and the second coefficient corresponding to the second model through regression algorithm and data fitting; S105, calibrate the first model and the second model according to the first coefficient and the second coefficient respectively, so as to obtain the calibrated preset model parameters.

[0009] Optionally, in step S104, the horizontal pressure and the mass of the weight are used as variables, and a first coefficient corresponding to the first model and a second coefficient corresponding to the second model are obtained through regression algorithm and data fitting, including: The mass of the weights is taken as the tangential force, and the horizontal pressure is taken as the resultant pressure force, so the tangential force and normal force are taken as two variables, and the derivation and analysis are carried out through regression algorithm. The first and second coefficients are calculated using the actual data obtained from the calibration, thus obtaining the corresponding first coefficient A and second coefficient B.

[0010] Optionally, in step S105, the first model and the second model are calibrated according to the first coefficient and the second coefficient respectively to obtain the calibrated preset model parameters, including: substituting the first coefficient A and the second coefficient B into the comprehensive model: F 切 =(A(F 法 In the formula / e)+B(S*G / e))*d, the calibrated preset parameter model is obtained.

[0011] Optionally, the calibration device specifically includes: a U-shaped support, a pressure block, a weight, a connecting rod, and a handle; the connecting rod is horizontally positioned and threadedly connected to the side wall of the U-shaped support, one end of the connecting rod is connected to the pressure block, and the other end of the connecting rod is connected to the handle; of the two test samples, one test sample is located on the side of the pressure block away from the connecting rod, and the other test sample is located on the inner side wall of the U-shaped support. By rotating the connecting rod, the pressure block is moved, thereby clamping the weight between the two test samples; wherein, the tightness of the connecting rod determines the magnitude of the horizontal pressure.

[0012] Optionally, when the shear pressure is less than 0.5 MPa, the elastic layer is made of a material with a hardness of 10-30A and a Young's modulus of less than 1 MPa. When the shear pressure is greater than 0.5 MPa, the elastic layer is made of a material with a hardness of 40~100A; where the shear pressure = F 切 / S.

[0013] Secondly, the present invention also provides a three-dimensional force measurement system based on a normal pressure array, comprising: A normal force array sensor with an elastic layer is provided, wherein the elastic layer has specific preset model parameters; A pressure application unit is used to apply a preset pressure to the elastic layer; The control unit is connected to the normal force array sensor and the offset detection unit, respectively. It is used to apply a preset pressure to the elastic layer, obtain the resultant pressure and the pressure center offset applied to the normal force array sensor, and obtain the corresponding tangential force based on the resultant pressure and the pressure center offset. The preset model parameters are stored in the control unit in advance. The normal force array sensor is used to obtain the pressure at each detection point. The sum of the data at all detection points can be regarded as the resultant pressure. The pressure center offset is obtained by the change of the data at each detection point.

[0014] This invention has at least the following technical effects: The present invention provides a three-dimensional force measurement method and system based on a normal pressure array. This method involves arranging an elastic layer with preset model parameters on a normal force array sensor and applying a preset pressure to the elastic layer to obtain the resultant pressure force and pressure center offset of the normal force array sensor. Based on the resultant pressure force and pressure center offset, the corresponding tangential force is obtained, thus achieving the decomposition and measurement of three-dimensional force. Furthermore, to ensure the accuracy of the tangential force measurement, the preset model parameters are calibrated to make them more precise, thereby improving the accuracy of the three-dimensional force measurement. Moreover, since the thickness of the entire sensor measurement method can be effectively controlled, it is convenient to install in confined spaces such as the sole of the foot for measuring relevant parameters, making it widely applicable. Attached Figure Description

[0015] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 A schematic diagram of the structure of an elastic layer in a three-dimensional force measurement system based on a normal pressure array, provided for an embodiment of the present invention; Figure 2 Provided for embodiments of the present invention Figure 1 A schematic diagram showing the intermediate elastic layer after pressure is applied; Figure 3 Provided for embodiments of the present invention Figure 1 A schematic diagram of the pressure and tangential force after the intermediate elastic layer is compressed; Figure 4 This is a schematic diagram of the calibration device provided in an embodiment of the present invention; Figure 5 A flowchart illustrating a three-dimensional force measurement method based on a normal pressure array, provided as an embodiment of the present invention; Figure 6 The following is a flowchart of step S100 in a three-dimensional force measurement method based on a normal pressure array provided in an embodiment of the present invention.

[0017] In the diagram: 1-Elastic layer; 2-Normal force array sensor; 201-Detection point; 3-U-shaped support; 4-Pressure block; 5-Weight; 6-Connecting rod; 7-Handle; 8-Test sample. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein. It will be understood by those skilled in the art that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms.

[0020] Combination Figures 1 to 5 As shown, the present invention provides a three-dimensional force measurement method based on a normal pressure array, comprising: S100, an elastic layer 1 with preset model parameters is arranged on a normal force array sensor 2; wherein, the preset model parameters are determined by test data calibration.

[0021] Specifically, the preset model parameters corresponding to elastic layer 1 can be selected and determined according to its material properties. Different thicknesses and materials of elastic layer 1 determine the corresponding preset model parameters. In the specific calibration process, the correspondence between tangential force and pressure center offset is calibrated, and the preset model parameters are calibrated based on the calibration results. Before calibration, the preset model parameters can be initially set. After calibrating the model using specific test data, the specific parameter values ​​in the preset model parameters are adjusted to improve the accuracy of the preset model parameters.

[0022] S200, apply a preset pressure to the elastic layer 1, and obtain the resultant pressure force and pressure center offset of the normal force array sensor 2.

[0023] Specifically, when detecting the pressure center offset, for example, four measurement points corresponding to a cross on the normal force array sensor below the elastic layer 1 can be identified. A simple coordinate system can be established using these four measurement points; for example, the line connecting the two points in the vertical direction represents the Y-axis, and the two points in the horizontal direction represent the X-axis. When the pressure percentage of the four points is the same (25% each), the pressure center is the exact center of the four points. If the percentage of one point is 100%, then the center of this point is considered the pressure center. Therefore, the pressure center can be calculated using the different percentages of the data from each measurement point. The resultant pressure force refers to the sum of the normal pressures at each measurement point.

[0024] Optionally, in step S200, the resultant pressure force is measured by each detection point 201 of the normal force array sensor, and the pressure center offset is calculated by the pressure value of each detection point 201.

[0025] S300, based on the resultant pressure force and the offset of the pressure center, the corresponding tangential force is obtained.

[0026] Specifically, the resultant pressure force and pressure center offset obtained in step S200 are used as input variables and solved using the preset model parameters corresponding to elastic layer 1 to obtain the corresponding tangential force. This enables the decomposition and measurement of three-dimensional force. The three-dimensional force measurement method based on a normal pressure array provided in this invention involves arranging an elastic layer 1 with preset model parameters on a normal force array sensor 2, and applying a preset pressure to the elastic layer 1 to obtain the resultant pressure force and pressure center offset of the normal force array sensor 2. Based on the resultant pressure force and pressure center offset, the corresponding tangential force is obtained, thereby achieving the decomposition measurement of three-dimensional force. Furthermore, to ensure the accuracy of tangential force measurement, the preset model parameters are calibrated to make the model parameters more precise, thus improving the accuracy of three-dimensional force measurement. Moreover, since the thickness of the entire sensor measurement method can be effectively controlled, it is convenient to install in narrow spaces such as the sole of the foot for measuring relevant parameters, and has a wide range of applications.

[0027] Optionally, in step S100, the preset model parameters of the elastic layer 1 include a first model and a second model; The first model includes: the formula for the offset of the pressure center after applying tangential force is d = (F 切 / S)*e / G, where e is the thickness of elastic layer 1, G is the shear modulus, S is the pressure area, and F is the shear modulus. 切 It is a tangential force; The second model includes: F 法 *d= F 切 *e, where F 法 The resultant force is the pressure force, and d is the offset of the pressure center. Combining the first and second models, we get: F 切 =(A(F 法 / e)+B(S*G / e))*d;where A is the first coefficient of the first model and B is the second coefficient of the second model;where A and B are unknown parameters before calibration, that is, the initial values ​​can be given in advance according to the material properties of the elastic layer 1 before calibration, and the specific values ​​of the first and second coefficients can be determined after calibration by measurement data, thereby improving the accuracy of three-dimensional force measurement.

[0028] Alternatively, the shear modulus G is calculated using the following formula: ; Where E is Young's modulus. ν For Poisson's ratio, E and ν All of these are determined by the material of elastic layer 1.

[0029] Optionally, such as Figure 6 As shown, before step S100, the method further includes: calibrating the preset model parameters using test data. The calibration process specifically includes: S101, Obtain two test samples 8 of the same size from the elastic layer 1 with preset model parameters. The test samples 8 use the same elastic layer 1 as in the actual three-dimensional force measurement process.

[0030] S102, the two test samples 8 are placed in the preset position of the calibration device and horizontal pressure is applied so that weights 5 of different masses are clamped between the two test samples 8 respectively.

[0031] S103, the horizontal pressure corresponding to weights 5 of different masses is obtained by using a spoke force gauge. S104, taking the horizontal pressure and the mass of the weight 5 as variables, the first coefficient corresponding to the first model and the second coefficient corresponding to the second model are obtained through regression algorithm and data fitting.

[0032] Specifically, the mass of weight 5 is taken as the tangential force, and the horizontal pressure is taken as the resultant pressure force, thus treating the tangential and normal forces as two variables, and deriving and analyzing them through a regression algorithm. The first and second coefficients are calculated using actual data obtained from calibration, thereby obtaining the corresponding first coefficient A and second coefficient B. The specific calculation process can be achieved by jointly calculating the unknown first and second coefficients using different test data.

[0033] S105, calibrate the first model and the second model according to the first coefficient and the second coefficient respectively, so as to obtain the calibrated preset model parameters.

[0034] Specifically, substituting the first coefficient A and the second coefficient B into the comprehensive model: F 切 =(A(F 法 In the formula / e)+B(S*G / e))*d, the calibrated preset parameter model is obtained.

[0035] In some embodiments, the calibration device mentioned in step S102 specifically includes: a U-shaped support 3, a pressure block 4, a weight 5, a connecting rod 6, and a handle 7; the connecting rod 6 is horizontally arranged and threadedly connected to the side wall of the U-shaped support 3, one end of the connecting rod 6 is connected to the pressure block 4, and the other end of the connecting rod 6 is connected to the handle 7.

[0036] Specifically, one test sample 8 is located on the side of the pressure block 4 away from the connecting rod 6, and the other test sample 8 is located on the inner side wall of the U-shaped support 3. By rotating the connecting rod 6, the pressure block 4 is moved, thereby clamping the weight 5 between the two test samples 8. The tightness of the connecting rod 6 determines the magnitude of the horizontal pressure.

[0037] It should be noted that the horizontal pressure is perpendicular to the test sample 8, which is equivalent to the normal pressure in the actual measurement process.

[0038] Optionally, when the shear pressure is less than 0.5 MPa, the elastic layer 1 is made of a material with a hardness of 10-30A and a Young's modulus of less than 1 MPa.

[0039] When the shear pressure is greater than 0.5 MPa, the elastic layer 1 is made of a material with a hardness of 40~100A; where the shear pressure = F 切 / S.

[0040] In this embodiment, elastic layer 1 with different material properties is selected according to different shear pressures. This is beneficial to improve detection sensitivity because if the material hardness is too high when the shear pressure is low, the detection result will be too blunt, while if the material hardness is too low when the shear pressure is high, the detection result will be too sensitive. Secondly, embodiments of the present invention provide a three-dimensional force measurement system based on a normal pressure array, comprising: A normal force array sensor 2 with an elastic layer 1 is arranged, wherein the elastic layer 1 has specific preset model parameters; A pressure application unit is used to apply a preset pressure to the elastic layer 1; Offset detection unit, the offset detection unit is used to obtain the offset of the pressure center of the elastic layer 1 after applying a preset pressure; The control unit is connected to the normal force array sensor 2 and the offset detection unit, respectively. It is used to apply a preset pressure to the elastic layer 1, obtain the resultant pressure and the pressure center offset applied to the normal force array sensor, and obtain the corresponding tangential force based on the resultant pressure and the pressure center offset. The preset model parameters are stored in the control unit in advance. The normal force array sensor 2 is used to obtain the pressure at each detection point 201. The sum of the data of all detection points 201 can be regarded as the resultant pressure. The pressure center offset is obtained by the change of the data of each detection point 201.

[0041] The three-dimensional force measurement method and system based on a normal pressure array provided in this invention involves arranging an elastic layer 1 with preset model parameters on a normal force array sensor 2, and applying a preset pressure to the elastic layer 1 to obtain the resultant pressure force and pressure center offset of the normal force array sensor 2. The corresponding tangential force is then obtained based on the resultant pressure force and pressure center offset. Furthermore, to ensure the accuracy of the tangential force measurement, the preset model parameters are calibrated to make them more precise, thereby improving the accuracy of the three-dimensional force measurement. Since the thickness of the entire sensor measurement method can be effectively controlled, it is convenient to install in confined spaces such as the sole of the foot for measuring relevant parameters, thus having a wide range of applications. Those skilled in the art will understand that the steps, measures, and schemes in the various operations, methods, and processes discussed in this invention can be alternated, modified, combined, or deleted. Furthermore, other steps, measures, and schemes in the various operations, methods, and processes discussed in this invention can also be alternated, modified, rearranged, decomposed, combined, or deleted. Furthermore, steps, measures, and schemes in the prior art that are similar to those disclosed in this invention can also be alternated, modified, rearranged, decomposed, combined, or deleted.

[0042] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0043] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more pieces.

[0044] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0045] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A three-dimensional force measurement method based on a normal pressure array, characterized in that, include: S100, an elastic layer with preset model parameters is arranged on a normal force array sensor; wherein, the preset model parameters are determined by test data calibration; S200, apply a preset pressure to the elastic layer and obtain the resultant pressure force and pressure center offset of the normal force array sensor; S300, based on the resultant pressure force and the offset of the pressure center, the corresponding tangential force is obtained; In step S100, the preset model parameters of the elastic layer include a first model and a second model; The first model includes: the formula for the offset of the pressure center after applying tangential force is d = (F 切 / S)*e / G, where e is the thickness of the elastic layer, G is the shear modulus, S is the area of ​​pressure applied, and F 切 It is a tangential force; The second model includes: F 法 *d=F 切 *e, where F 法 Let d be the resultant pressure force, and d be the offset of the pressure center. Combining the first and second models, we get: F 切 =(A(F 法 / e)+B(S*G / e))*d;where A is the first coefficient of the first model and B is the second coefficient of the second model.

2. The three-dimensional force measurement method based on a normal pressure array according to claim 1, characterized in that, The shear modulus G is calculated using the following formula: ； Where E is Young's modulus. ν It is Poisson's ratio.

3. The three-dimensional force measurement method based on a normal pressure array according to claim 1, characterized in that, In step S200, the resultant pressure force is obtained by measuring each detection point of the normal force array sensor, and the pressure center offset is calculated by the pressure value at each detection point.

4. The three-dimensional force measurement method based on a normal pressure array according to claim 1, characterized in that, Before step S100, the method further includes: calibrating the preset model parameters using test data. The calibration process specifically includes: S101, Obtain two test samples of the same size in the elastic layer with preset model parameters; S102, the two test samples are placed in the preset position of the calibration device and horizontal pressure is applied so that weights of different masses are clamped between the two test samples respectively. S103, obtains the horizontal pressure corresponding to weights of different masses through a spoke force gauge; S104, taking the horizontal pressure and the mass of the weight as variables, and obtaining the first coefficient corresponding to the first model and the second coefficient corresponding to the second model through regression algorithm and data fitting; S105, calibrate the first model and the second model according to the first coefficient and the second coefficient respectively, so as to obtain the calibrated preset model parameters.

5. The three-dimensional force measurement method based on a normal pressure array according to claim 4, characterized in that, In step S104, the horizontal pressure and the mass of the weight are used as variables, and a first coefficient corresponding to the first model and a second coefficient corresponding to the second model are obtained through regression algorithm and data fitting, including: The mass of the weights is taken as the tangential force, and the horizontal pressure is taken as the resultant pressure force, so the tangential force and normal force are taken as two variables, and the derivation and analysis are carried out through regression algorithm. The first and second coefficients are calculated using the actual data obtained from the calibration, thus obtaining the corresponding first coefficient A and second coefficient B.

6. The three-dimensional force measurement method based on a normal pressure array according to claim 5, characterized in that, In step S105, the first model and the second model are calibrated according to the first coefficient and the second coefficient, respectively, to obtain the calibrated preset model parameters, including: Substituting the first coefficient A and the second coefficient B into the comprehensive model: F 切 =(A(F 法 In the formula / e)+B(S*G / e))*d, the calibrated preset parameter model is obtained.

7. The three-dimensional force measurement method based on a normal pressure array according to claim 4, characterized in that, The calibration device specifically includes: a U-shaped support, a pressure block, a weight, a connecting rod, and a handle; the connecting rod is horizontally arranged and threadedly connected to the side wall of the U-shaped support, one end of the connecting rod is connected to the pressure block, and the other end of the connecting rod is connected to the handle; Of the two test samples, one test sample is located on the side of the pressure block away from the connecting rod, and the other test sample is located on the inner side wall of the U-shaped support. By rotating the connecting rod, the pressure block is moved, thereby clamping the weight between the two test samples. The tightness of the connecting rod determines the magnitude of the horizontal pressure.

8. The three-dimensional force measurement method based on a normal pressure array according to claim 1, characterized in that, When the shear pressure is less than 0.5 MPa, the elastic layer is made of a material with a hardness of 10-30A and a Young's modulus of less than 1 MPa. When the shear pressure is greater than 0.5 MPa, the elastic layer is made of a material with a hardness of 40~100A; where the shear pressure = F 切 / S.

9. A three-dimensional force measurement system based on a normal pressure array, characterized in that, include: A normal force array sensor with an elastic layer arranged thereon, wherein the elastic layer has preset model parameters; A pressure application unit is used to apply a preset pressure to the elastic layer; The control unit is connected to the normal force array sensor and the offset detection unit, respectively. It is used to apply a preset pressure to the elastic layer, obtain the resultant pressure and the pressure center offset applied to the normal force array sensor, and obtain the corresponding tangential force based on the resultant pressure and the pressure center offset. The preset model parameters are stored in the control unit in advance. The normal force array sensor is used to obtain the pressure at each detection point. The sum of the data at all detection points can be regarded as the resultant pressure. The pressure center offset is obtained by the change of the data at each detection point. The preset model parameters of the elastic layer include a first model and a second model; The first model includes: the formula for the offset of the pressure center after applying tangential force is d = (F 切 / S)*e / G, where e is the thickness of the elastic layer, G is the shear modulus, S is the area of ​​pressure applied, and F 切 It is a tangential force; The second model includes: F 法 *d=F 切 *e, where F 法 Let d be the resultant pressure force, and d be the offset of the pressure center. Combining the first and second models, we get: F 切 =(A(F 法 / e)+B(S*G / e))*d;where A is the first coefficient of the first model and B is the second coefficient of the second model.

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