Load-sharing measurement platform and calculation method of six-dimensional force

Abstract

The present invention relates to the field of spatial micro-vibration measurement, and in particular to a load-sharing measurement platform and a six-dimensional force calculation method thereof. The load-sharing measurement platform includes a mounting base, a sensor, a load-sharing cylinder, a boss and a load platform. There are at least five bosses on the lower surface of the load platform, which are respectively connected to the load-sharing cylinder and the sensor. They are arranged to avoid the flatness requirements of a large area to reduce processing costs. Two different sensors are used in the sensor part to reduce device costs. The load-sharing cylinder is distributed parallel to the sensor and is located at the center of the lower surface of the load-sharing platform. The load-sharing measurement platform of the present invention has good self-decoupling, static linearity and dynamic linearity, and is excellent in cost, fundamental frequency, load capacity, measurement accuracy, etc.

Description

Technical Field

[0001] The present invention relates to the field of spatial micro-vibration measurement, and in particular to a load-sharing measurement platform. Background Art

[0002] The performance requirements for measurement accuracy, stability, and directivity of the China Space Station's telescopes continue to increase as deep space exploration missions continue to advance. Therefore, ground-based measurement and evaluation of the dynamic disturbance forces that significantly impact telescope performance are essential. Furthermore, as moving parts on spacecraft become heavier and larger, ground-based force measurement platforms are required to possess a large mounting surface, high load capacity, high fundamental frequency, and excellent measurement accuracy.

[0003] Traditional strain-type force measurement devices struggle to achieve both high load and high sensitivity. Increasing the platform's fundamental frequency and load often exposes the platform's measurement signal to noise, necessitating a balance between the two. Piezoelectric ceramics, on the other hand, increase the platform's load capacity while maintaining high sensitivity. Consequently, Stewart platforms have been widely used in previous research on piezoelectric measurement devices. However, their loose structure reduces the platform's stiffness, limiting their application for heavy-load measurements. Furthermore, they suffer from over-constrained instability, difficult installation, and high processing costs. Based on continuous exploration and research, more optimized and improved inventions have been proposed. For example, in the paper YJLi, et al. Dynamic characteristics of piezoelectric six-dimensional heavy force / moment sensor for large-load robotic manipulator. Measurement 45.5 (2012): 1114-1125, a six-dimensional force / moment measurement device similar to the principle of the Kistler-type measurement platform is proposed. The device mainly includes four symmetrically distributed three-dimensional force A-type sensors. They all have the characteristics of high fundamental frequency and low coupling. However, as the mounting surface increases and the load increases, the fundamental frequency of the platform will drop significantly, which will have a significant impact on the measurement results and measurement methods. At this time, a simple four-point support is difficult to meet the measurement requirements. For this reason, a sensor with a load-sharing ring is proposed in patent CN108020355B. However, this invention introduces the equivalent stiffness of dozens of parts in the derivation of the load-sharing rate, making it easy for the calculation to produce a large error with the actual result, so that the mathematical model cannot be directly used for measurement, and it is not easy to see the influence of structural parameters on the load-sharing effect from the mathematical model. On this basis, patent CN109990888B proposes an eight-point support type, with four points located on the horizontal platform and four points located on the vertical surface. The large-scale force measurement mechanism can measure the vibration of large-mass and large-volume vibration sources, but the redundant measurement caused by its measurement principle inevitably introduces systematic errors. There are many similar invention designs. These measurement devices have different structural designs and measurement principles based on different application environments, but the existing measurement equipment is difficult to meet the proposed measurement requirements. For different measurement objects, the fundamental frequency, structural parameters, and calculation process of the measurement platform itself will change significantly, making it difficult for the measurement platform to meet the measurement requirements of different measurement objects. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a load-sharing measurement platform that ensures high fundamental frequency on a large mounting surface. The specific structure includes: a mounting base, a sensor, a load-sharing cylinder, a boss, and a load platform, wherein:

[0005] There are n sensors, where n is an even number greater than 2;

[0006] There is one load-sharing cylinder;

[0007] The load-sharing cylinder has the same height as the sensor. The load-sharing cylinder is located at the center of the lower surface of the load-sharing platform, and the sensors are symmetrically distributed along the load-sharing cylinder.

[0008] The number of mounting bases is 1+n, one of which is connected to the load-sharing cylinder, and the remaining mounting bases are connected to the sensor; the load-sharing cylinder and the sensor are connected between the mounting base and the load platform.

[0009] Preferably, the load platform and the mounting base are made of 304 stainless steel.

[0010] Preferably, the load-sharing cylinder is made of aluminum.

[0011] Preferably, the load platform has 1+n bosses, one large boss is connected to the load-sharing cylinder, and n small bosses are connected to the sensor.

[0012] Preferably, the sensors are divided into two types: type A sensors and type B sensors; type A sensors include piezoelectric ceramics with compression piezoelectric effect and piezoelectric ceramics with shear piezoelectric effect; type B sensors only include piezoelectric ceramics with compression piezoelectric effect.

[0013] Preferably, the number of type A sensors and type B sensors is the same and they are symmetrically distributed along the load cylinder.

[0014] Preferably, the piezoelectric ceramics are sealed with resin to form type A sensors and type B sensors.

[0015] A six-dimensional force calculation method for a load-sharing measurement platform includes the following steps:

[0016] S1: Calculate the six-dimensional force measured by n sensors, where n is 4, including the first A-type sensor, the first B-type sensor, the second A-type sensor, and the second B-type sensor. The calculation formula is as follows:

[0017]

[0018] F x-m 、F y-m 、F z-m 、M x-m 、M y-m 、M z-m It is the force and torque acting on the sensor; Ra represents the torque;

[0019] F x1+2 The vector sum of the forces output by the two A-type sensors in the X direction, F y1+2 Represents the vector sum of the forces output by the two A-type sensors in the Y direction;

[0020] F x1 、F x2 It represents the force acting on the two A-type sensors in the X direction, F z1 、F z2 、F z3 、F z4 represents the force acting on the four sensors in the Z direction;

[0021] S2: Introduce the measurement coefficient μ to calculate the six-dimensional force acting on the load platform. The calculation formula is as follows:

[0022]

[0023] Among them, F x 、F y 、F z 、M x 、M y 、M z are the six-dimensional forces and moments acting on the load platform,

[0024] Indicates the force measurement coefficient of the load platform in the X direction,

[0025] Indicates the force measurement coefficient of the load platform in the Y direction,

[0026] Indicates the force measurement coefficient of the load platform in the Z direction,

[0027] Indicates the moment measurement coefficient of the load platform in the X direction,

[0028] Indicates the moment measurement coefficient of the load platform in the Y direction;

[0029] S3: Establish the energy conservation equation, the formula is as follows:

[0030]

[0031] in, represents the work done by the force acting on the load platform, and the right-hand side represents the sum of the axial strain energy, the sum of the bending strain energy, the sum of the torsional strain energy, and the sum of the shear strain energy on the elastic body;

[0032] S4: Calculating measurement coefficients of six-dimensional forces and moments acting on the load-sharing measurement platform;

[0033] The measuring platform is a symmetrical structure. x and F y 、M x and My The calculation method is the same, μ Fx =μ Fy , μ Mx =μ My , only for μ Fx 、μ Fz 、μ My and μ Mz The specific calculation steps are as follows:

[0034] The calculation formula is as follows:

[0035]

[0036] F zl is the Z-axis force acting on the load-sharing cylinder, F zp is the Z-axis force acting on one of the sensors,

[0037] E l and E p is the elastic modulus of the load-sharing cylinder and the sensor,

[0038] A l and A p is the cross-sectional area of ​​the load-sharing cylinder and the sensor,

[0039] h l and h p is the height of the load-sharing cylinder and the sensor,

[0040] ε l and ε p is the axial translation distance of the load-sharing cylinder and the sensor under the action of force, ε l and ε p Satisfy: ε l =ε p ,

[0041] r l and r p is the cross-sectional radius of the load-sharing cylinder and the sensor;

[0042] The calculation formula is as follows:

[0043]

[0044] Among them, F xl and F xp is the shear force acting on the load-sharing cylinder and the A-type sensor,

[0045] ν l and ν pis the horizontal movement distance of the load-sharing cylinder and the A-type sensor under the action of the tangential force,

[0046] G l and G p is the shear modulus of the material of the load-sharing cylinder and the A-type sensor,

[0047] μ l and μ p is the non-uniformity coefficient of circular cross-section distribution under shear stress, μ l =μ p =10 / 9;

[0048] The calculation formula is as follows:

[0049]

[0050] The second A-type sensor and the second B-type sensor are subjected to Y-direction pulling pressure (F api ,i=1,2) and bending force, M yl Indicates the moment in the Y direction acting on the load-sharing cylinder, M ypi (i=3,4,5,6) represents the Y-direction torque acting on the four sensors, M yp1 and M yp2 It represents the tensile force in the Y direction acting on the second A-type sensor and the second B-type sensor multiplied by the moment arm,

[0051] I yl and I yp is the moment of inertia of the load-sharing cylinder and the A-type sensor in the Y-axis section;

[0052] The calculation formula is as follows:

[0053]

[0054] Wherein, the second A-type sensor and the second B-type sensor are subjected to the Z-direction pulling force (F tpi ,i=1,2) and pressure, M zl represents the moment in the Z direction acting on the load-sharing cylinder,

[0055] I zl is the moment of inertia of the loaded cylinder in the Z-axis section.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] The installation of the load-sharing cylinder increases the platform's fundamental frequency and significantly improves its load capacity. The installation of two different sensors reduces the platform's manufacturing cost while ensuring full measurement of six-dimensional forces. The load-sharing measurement platform of this invention exhibits excellent self-decoupling, static linearity, and dynamic linearity, offering superior performance in terms of cost, fundamental frequency, load capacity, and measurement accuracy.

[0058] The six-dimensional force calculation method of the load-sharing measurement platform has the advantages of simple calculation and small error, and the established mathematical model can be directly used for measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a structural diagram of a load-sharing measurement platform provided according to an embodiment of the present invention;

[0060] Figure 2 is a cross-sectional view of a type A sensor provided according to an embodiment of the present invention;

[0061] Figure 3 is a cross-sectional view of a type B sensor provided according to an embodiment of the present invention;

[0062] Figure 4 is a measurement principle diagram of a load-sharing measurement platform provided according to an embodiment of the present invention;

[0063] Figure 5a The F of the load-sharing measurement platform provided in the embodiment of the present invention z force diagram;

[0064] Figure 5b The F of the load-sharing measurement platform provided in the embodiment of the present invention x force diagram;

[0065] Figure 5c is the M of the load-sharing measurement platform provided according to an embodiment of the present invention. y force diagram;

[0066] Figure 5d is the M of the load-sharing measurement platform provided according to an embodiment of the present invention. z Force diagram.

[0067] Reference numerals include:

[0068] Mounting base 1, sensor 2, load-sharing cylinder 3, boss 4, load platform 5, type A sensor 201, type A sensor 203, type B sensor 202, type B sensor 204, type A mounting housing 2011, type A insulating layer 2012, type A wire hole 2013, type A piezoelectric ceramic 2014, type B mounting housing 2021, type B insulating layer 2022, type B wire hole 2023, type B piezoelectric ceramic 2024. DETAILED DESCRIPTION

[0069] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, identical modules are denoted by identical reference numerals. In the case of identical reference numerals, their names and functions are also identical. Therefore, their detailed description will not be repeated.

[0070] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0071] In this embodiment, the mounting base is fixed on the vibration isolation platform, and the load platform is used to place the vibration source to measure the disturbing force.

[0072] Figure 1 A schematic structural diagram of a load-sharing measurement platform provided according to an embodiment of the present invention is shown.

[0073] like Figure 1 As shown, the load-sharing measuring platform provided by the embodiment of the present invention includes: a mounting base 1, a sensor 2, a load-sharing cylinder 3, a boss 4 and a load platform 5. There are five bosses 4 on the lower surface of the load platform 5, four smaller bosses 4 are located at the four corners of the load platform 5, and are connected to the sensor 2; a larger boss 4 is located at the center of the load platform, and is connected to the load-sharing cylinder 3. The load-sharing cylinder 3 is distributed parallel to the sensor 2 and is used to share the load and improve the fundamental frequency of the load-sharing measuring platform. The design of the boss 4 avoids the flatness requirement of the entire lower surface of the load platform, reducing the process difficulty and processing cost. The mounting base 1 is connected to the lower surface of the sensor 2 to improve the fundamental frequency.

[0074] Figure 2 A cross-sectional view of a type A sensor provided according to an embodiment of the present invention is shown.

[0075] like Figure 2 As shown, the A-type sensor 201 provided by the embodiment of the present invention includes: an A-type mounting housing 2011 , an A-type insulating layer 2012 , an A-type wire hole 2013 and an A-type piezoelectric ceramic 2014 .

[0076] In this embodiment, there are two A-type sensors 201 and 203, which are located on the two diagonal bosses 4 of the load platform 5. The A-type piezoelectric ceramics of the A-type sensors 201 and 203 have both compression piezoelectric effect and shear piezoelectric effect, and are used to measure forces in the X, Y, and Z directions.

[0077] Figure 3 A cross-sectional view of a B-type sensor provided according to an embodiment of the present invention is shown.

[0078] like Figure 3As shown, the B-type sensors 202 and 204 provided in the embodiment of the present invention include: a B-type mounting housing 2021 , a B-type insulating layer 2022 , a B-type wire hole 2023 and a B-type piezoelectric ceramic 2024 .

[0079] In this embodiment, there are two B-type sensors 202 and 204 located on the two bosses 4 on the other diagonal line of the load platform 5. The piezoelectric ceramics of the B-type sensors 202 and 204 have only compression piezoelectric effect and are used to measure the force in the Z direction.

[0080] Figure 4 The measurement principle of the shared-load measurement platform provided according to an embodiment of the present invention is shown.

[0081] According to the measurement principle, the calculation method of the six-dimensional force applied on the load-sharing measurement platform is as follows:

[0082] like Figure 4 As shown,

[0083] S1: Calculate the six-dimensional force acting on the sensor:

[0084]

[0085] F x-m 、F y-m 、F z-m 、M x-m 、M y-m 、M z-m It is the force and torque acting on the sensor; Ra represents the torque;

[0086] F x1+2 represents the vector sum of the forces output by the two A-type sensors 201 in the X direction, F y1+2 represents the vector sum of the forces output by the A-type sensor 201 in the Y direction;

[0087] F x1 、F x2 represents the force acting on the two A-type sensors 201 in the X direction, F z1 、F z2 、F z3 、F z4 Represents the force acting on the four sensors in the Z direction.

[0088] Due to the presence of the load platform, the sensor measurement result is not equivalent to the force acting on the load platform.

[0089] S2: Introduce the measurement coefficient μ to calculate the six-dimensional force acting on the load platform. The calculation formula is as follows:

[0090]

[0091] Among them, F x 、F y 、F z 、M x 、M y 、M z are the six-dimensional forces and moments acting on the load platform;

[0092] represents the force measurement coefficient of the load platform in the X direction;

[0093] represents the force measurement coefficient of the load platform in the Y direction;

[0094] It represents the force measurement coefficient of the load platform in the Z direction;

[0095] represents the moment measurement coefficient of the load platform in the X direction;

[0096] represents the moment measurement coefficient of the load platform in the Y direction;

[0097] S3: Establish the energy conservation equation, the formula is as follows:

[0098]

[0099] The left-hand side of the equation represents the work done by the force acting on the load platform, and the right-hand side represents the sum of the axial strain energy, the sum of the bending strain energy, the sum of the torsional strain energy, and the sum of the shear strain energy on the elastic body, respectively.

[0100] S4: Derive the measurement coefficients of the six-dimensional forces and moments acting on the load-sharing measurement platform.

[0101] The split-load measuring platform is a symmetrical structure. x and F y 、M x and M y The calculation method is the same, μ Fx =μ Fy , μ Mx =μ My , only for μ Fx 、μ Fz 、μ My and μ Mz Calculate the .

[0102] Figure 5a The F of the load-sharing measurement platform provided in the embodiment of the present invention is shown. z Force.

[0103] like Figure 5a As shown, Fz Acting on the load-sharing measuring platform, the load-sharing cylinder 3 and the sensor are subjected to force in the same way.

[0104] F z =4F zp +F zl ;

[0105] Among them, F zl is the Z-axis force acting on the load-sharing cylinder, F zp is the Z-axis force acting on an A-type sensor.

[0106] Combined with the law of conservation of energy, we can get:

[0107]

[0108] Among them, E l and E p is the elastic modulus of the load-sharing cylinder and the A-type sensor, A l and A p is their cross-sectional area, h l and h p is the height of the cylinder. l and ε p is the axial translation distance of the load cylinder and the A-type sensor under the action of force, ε l and ε p Satisfy: ε l =ε p

[0109] From the above derivation, we can get:

[0110]

[0111] Among them, r l and r p is the cross-sectional radius of the load-sharing cylinder and type A sensor.

[0112] Figure 5b The F of the load-sharing measurement platform provided in the embodiment of the present invention is shown. x Force.

[0113] like Figure 5b As shown, F x Acting on the load-sharing measurement platform, same as F z The derivation process is similar to that of

[0114]

[0115] Among them, F xl and F xp is the shear force acting on the load-sharing cylinder and an A-type sensor, ν l and νp G is the horizontal movement distance of the load-sharing cylinder and type A sensor under the action of tangential force, l and G p is the shear modulus of the material of the load-sharing cylinder and the A-type sensor. l and μ p is the non-uniformity coefficient of the circular cross-section distribution under shear stress. Since the cross-sections are all circular, μ l =μ p =10 / 9.

[0116] By the same logic, we can deduce:

[0117]

[0118] Figure 5c The M of the load-sharing measurement platform provided in the embodiment of the present invention is shown. y Force.

[0119] like Figure 5c As shown, M y Acting on the load-sharing measuring platform, the load-sharing cylinder 3, type A sensor 201 and type B sensor 202 are only subjected to bending force, while type A sensor 203 and type B sensor 204 are subjected to axial tensile pressure (F pi ,i=1,2) and bending force. yl To express the moment acting on the load-sharing cylinder, use M ypi (i=3,4,5,6) represents the torque acting on the four sensors. M yp1 and M yp2 It represents the tensile force acting on sensor 203 and sensor 204 multiplied by the moment arm. Therefore, we can get:

[0120]

[0121] Among them, I yl and I yp is the moment of inertia of the load-sharing cylinder and A-type sensor in the Y-axis section.

[0122] After finishing, we can get:

[0123]

[0124] Figure 5d The M of the load-sharing measurement platform provided in the embodiment of the present invention is shown. z Force.

[0125] like Figure 5d As shown, the torsional force M z Acting on the load-sharing measuring platform, the load-sharing cylinder 3 is subjected to a torsional force M zl , and the four sensors are subjected to shear force F along the tangent linetp , we can get:

[0126]

[0127] Among them, I zl is the moment of inertia of the loaded cylinder in the z-axis section.

[0128] After finishing, we can get:

[0129]

[0130] In summary, μ is calculated based on the measurement results of two A-type sensors 201 and 203 and two B-type sensors 202 and 204. Fx 、μ Fz 、μ My and μ Mz , because the load-sharing measurement platform is a symmetrical structure, F x and F y 、M x and M y The calculation method is the same, so μ Fx =μ Fy , μ Mx =μ My The measurement coefficient μ of the six-dimensional force and moment acting on the load-sharing measurement platform Fx 、μ Fy 、μ Fz 、μ Mx 、μ My and μ Mz All are obtained through calculation, through the calculated measurement coefficient μ Fx 、μ Fy 、μ Fz 、μ Mx 、μ My and μ Mz The six-dimensional forces and moments of the load-sharing measurement platform can be calculated.

[0131] Although the embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0132] The above specific embodiments of the present invention do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A load-sharing measurement platform, characterized in that it includes a mounting base, a sensor, a load-sharing cylinder, a boss, and a load platform, wherein: There are n sensors, where n is an even number greater than 2; There is one load-sharing cylinder; The load-sharing cylinder has the same height as the sensor, the load-sharing cylinder is located at the center of the lower surface of the load-sharing platform, and the sensors are symmetrically distributed along the load-sharing cylinder; The number of the mounting bases is 1+n, one of which is connected to the load-sharing cylinder, and the remaining mounting bases are connected to the sensor; the load-sharing cylinder and the sensor are connected between the mounting base and the load platform; The sensors are divided into two types: type A sensors and type B sensors; the type A sensors include piezoelectric ceramics with compression piezoelectric effect and piezoelectric ceramics with shear piezoelectric effect; the type B sensors only include piezoelectric ceramics with compression piezoelectric effect.

2. The load-sharing measurement platform according to claim 1, wherein: The load platform and the mounting base are made of 304 stainless steel.

3. The load-sharing measurement platform according to claim 1, wherein: The load-sharing cylinder is made of aluminum.

4. The load-sharing measurement platform according to claim 1, wherein: The load platform has 1+n bosses, one large boss is connected to the load-sharing cylinder, and n small bosses are connected to the sensor.

5. The load-sharing measurement platform according to claim 1, wherein: The number of the A-type sensors and the B-type sensors is the same and they are symmetrically distributed along the load cylinder.

6. The load-sharing measurement platform according to claim 1, wherein: The piezoelectric ceramics are sealed with resin to form the A-type sensor and the B-type sensor.

7. A six-dimensional force calculation method for a load-sharing measurement platform according to claim 1, characterized in that: The following steps are involved: S1: Calculate the six-dimensional force measured by n sensors, where n is 4, including the first A-type sensor, the first B-type sensor, the second A-type sensor, and the second B-type sensor. The calculation formula is as follows: F x-m 、F y-m 、F z-m 、M x-m 、M y-m 、M z-m are the forces and moments acting on the sensor; Ra represents the moment; F x1+2 The vector sum of the forces output by the two A-type sensors in the X direction, F y1+2 represents the vector sum of the forces output by the two A-type sensors in the Y direction; F x1 、F x2 The force acting on the two A-type sensors in the X direction, F z1 、F z2 、F z3 、F z4 represents the force acting on the four sensors in the Z direction; S2: Introduce the measurement coefficient μ to calculate the six-dimensional force acting on the load platform. The calculation formula is as follows: Among them, F x 、F y 、F z 、M x 、M y 、M z are the six-dimensional forces and moments acting on the load platform; represents the force measurement coefficient of the load platform in the X direction; represents the force measurement coefficient of the load platform in the Y direction; It represents the force measurement coefficient of the load platform in the Z direction; represents the moment measurement coefficient of the load platform in the X direction; represents the moment measurement coefficient of the load platform in the Y direction; S3: Establish the energy conservation equation, the formula is as follows: in, represents the work done by the force acting on the load platform, and the right-hand term represents the sum of the axial strain energy, the sum of the bending strain energy, the sum of the torsional strain energy, and the sum of the shear strain energy on the elastic body; S4: Calculating measurement coefficients of six-dimensional forces and moments acting on the load-sharing measurement platform; The measuring platform is a symmetrical structure. x and F y 、M x and M y The calculation method is the same, μ F x =μ F y , μ M x =μ M y , only for μ F x 、μ F z 、μ M y and μ M z The specific calculation steps are as follows: The calculation formula is as follows: F zl is the Z-axis force acting on the load-sharing cylinder, F zp is the Z-axis force acting on one of the sensors, E l and E p is the elastic modulus of the load-sharing cylinder and the sensor, A l and A p is the cross-sectional area of ​​the load-sharing cylinder and the sensor, h l and h p is the height of the load-sharing cylinder and the sensor, ε l and ε p is the axial translation distance of the load-sharing cylinder and the sensor under the action of force, ε l and ε p Satisfy: ε l =ε p , r l and r p is the cross-sectional radius of the load-sharing cylinder and the sensor; The calculation formula is as follows: Among them, F xl and F xp is the shear force acting on the load-sharing cylinder and the A-type sensor, ν l and ν p is the horizontal movement distance of the load-sharing cylinder and the A-type sensor under the action of the tangential force, G l and G p is the shear modulus of the material of the load-sharing cylinder and the A-type sensor, μ l and μ p is the non-uniformity coefficient of circular cross-section distribution under shear stress, μ l =μ p =10 / 9; The calculation formula is as follows: The second A-type sensor and the second B-type sensor are subjected to Y-direction pulling pressure (F api ,i=1,2) and bending force, M yl Indicates the moment in the Y direction acting on the load-sharing cylinder, M ypi (i=3,4,5,6) represents the Y-direction torque acting on the four sensors, M yp1 and M yp2 I represents the Y-direction tensile force acting on the second A-type sensor and the second B-type sensor multiplied by the moment arm, yl and I yp is the moment of inertia of the load-sharing cylinder and the A-type sensor in the Y-axis section; The calculation formula is as follows: Wherein, the second A-type sensor and the second B-type sensor are subjected to the Z-direction pulling force (F tpi ,i=1,2) and pressure, M zl It represents the moment in the Z direction acting on the load-sharing cylinder, I zl is the moment of inertia of the loaded cylinder in the Z-axis section.

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