CN114812908A - Eight-branch orthogonal parallel type six-component force sensor and structure optimization method thereof - Google Patents

Eight-branch orthogonal parallel type six-component force sensor and structure optimization method thereof Download PDF

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CN114812908A
CN114812908A CN202210385071.2A CN202210385071A CN114812908A CN 114812908 A CN114812908 A CN 114812908A CN 202210385071 A CN202210385071 A CN 202210385071A CN 114812908 A CN114812908 A CN 114812908A
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骆昕
胡博伦
闫瑞
韩超
杨慧
刘嘉靖
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BEIJING INSTITUTE OF METROLOGY
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01LMEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/16Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring several components of force
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/10Geometric CAD
    • G06F30/17Mechanical parametric or variational design
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/23Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00Details relating to CAD techniques
    • G06F2111/06Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14Force analysis or force optimisation, e.g. static or dynamic forces

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Abstract

The invention discloses an eight-branch orthogonal parallel six-component force sensor and a structure optimization method thereof, which can measure full force information of a certain point in space, namely F x 、F y 、F z 、M x 、M y And M z The sensor comprises eight force measuring branches which are divided into four horizontal and four vertical branches, each force measuring branch consists of a flexible hinge and a pull-press sensor, and all the force measuring branches are uniformly arranged. The upper platform is used for loading force, the lower platform is used for fixing, and the upper platform, the lower platform and the force measurement are carried outThe branches are all connected through bolts. The principle of the invention is that six-component force is converted to eight branches, and the standard single-dimensional tension and compression sensor is adopted to obtain the axial force of each branch, so that compared with a patch type six-component force sensor, the invention avoids errors caused by a patch method. And a multi-objective optimization algorithm is adopted, the characteristic dimension of the flexible hinge part of the sensor is optimized, and the coupling of force among all dimensions is structurally reduced.

Description

Eight-branch orthogonal parallel type six-component force sensor and structure optimization method thereof
Technical Field
The invention relates to the technical field of sensors, in particular to a six-component force sensor capable of reducing crosstalk coupling of components.
Background
Six-component force sensors are sensors for measuring full force information, i.e. F at a point in space x 、F y 、F z 、M x 、M y And M z Three forces and three moments. The method is widely applied to the fields of intelligent robots, intelligent manufacturing, aerospace and the like, and the measurement accuracy directly influences industrial production. At present, various scientific research institutions develop researches on six-component force sensors, the designed six-component force sensors are various and have respective advantages and disadvantages, but the problem of coupling crosstalk among the component forces still needs to be further researched.
The main reason for affecting the accuracy of a six-component force sensor is that there is coupling between the component forces during measurement, so it is critical to decouple the component forces to reduce the coupling. The decoupling is divided into two parts of hardware decoupling and software decoupling, the hardware decoupling is the basis of the software decoupling, the hardware decoupling is to optimize the sensor structure, and the force/moment coupling of the force in the internal transmission process of the sensor is reduced.
Disclosure of Invention
The invention provides an orthogonal parallel six-component force sensor based on a flexible hinge in order to reduce the crosstalk problem of each component force during measurement, and a structure optimization method is explained.
The technical scheme for realizing the invention is as follows: an eight-branch orthogonal parallel six-component force sensor is characterized in that a flexible hinge is connected with a single-dimensional pull pressure sensor to form force measurement branches, wherein the force measurement branches comprise 8 force measurement branches, 4 force measurement branches are vertically arranged, 4 force measurement branches are horizontally arranged and circumferentially uniformly distributed, and the vertical force measurement branches are orthogonal to the horizontal force measurement branches; the lower platform connecting block and the upper platform connecting block are perpendicular to the force measuring branch; the upper platform is parallel to the lower platform. The flexible hinge of the force measuring branch is connected with the single-dimensional tension and compression sensor through a bolt, the lower platform connecting block is connected with the lower platform through a bolt, the upper platform connecting block is connected with the upper platform through a bolt, the horizontal force measuring branch is connected with the upper platform connecting block and the lower platform connecting block through a bolt, and the vertical force measuring branch is connected with the upper platform and the lower platform through a bolt;
the front surface of the flexible hinge is provided with a through forward through hole and a through forward cutting groove, and the side surface of the flexible hinge is provided with a through lateral through hole and a through lateral cutting groove; a countersunk through hole for fixing an upper platform connecting block, a countersunk through hole for fixing a flexible hinge, a positioning hole and a through hole are formed in the corner of the upper platform 4; the lower platform is provided with a countersunk through hole for fixing the hinge connecting block, a threaded through hole for connecting the single-dimensional pull pressure sensor and a through hole for fixing the lower platform.
Furthermore, the number of the force measuring branches is 8, and the vertical force measuring branches are vertical to the horizontal force measuring branches.
Further, the upper platform connecting block is of a U-shaped structure, and the vertical flexible hinge is contained in the opening of the upper platform connecting block but has a gap with the inner wall of the upper platform connecting block and is not in contact with the inner wall of the upper platform connecting block.
Further, the upper platform and the lower platform are arranged in parallel.
Furthermore, the flexible hinge is provided with a through forward through hole and a through side through hole, the forward through hole and the through side through hole are located in the middle of the hinge and are symmetrically distributed by taking the hinge central shaft as the center respectively, and the forward through hole and the through side through hole are orthogonal.
Furthermore, the flexible hinge is provided with a pair of through forward cutting grooves and a pair of through side cutting grooves, the front cutting grooves and the horizontal direction are arranged in a V shape with an angle of 45 degrees and an oblique upward V shape, the side cutting grooves and the horizontal direction are arranged in an inverted V shape with an angle of 45 degrees and an oblique downward V shape, and the central axis of the through hole is positioned on the central plane of the cutting grooves.
Furthermore, the forward through hole and the lateral through hole of the flexible hinge are in a notched perfect circle shape.
Further, the front slot and the lateral slot of the flexible hinge are parallel to each other.
Optimizing the characteristic dimension of the flexible hinge (2), wherein the optimized variables are the hole diameters of the forward through hole (7) and the lateral through hole (9), the groove widths of the forward cutting groove (8) and the lateral cutting groove (10) and the hole distance between each pair of through holes, and the optimizing steps are as follows:
step one, acquiring force measurement branch theoretical value of six-component force sensor
According to the strength limit of the six-component force sensor structure, each force measuring branch is ensured to be in a safe working state, the rated load value of the six-component force sensor is given, the rated load value is used as an input value, and the theoretical value of the axial force borne by each force measuring branch is obtained by using a spiral theory.
Step two, acquiring simulation output values of force measurement branches of six-component force sensor
In practical use, the force measurement branch is not only limited to the axial force in theory, and an axial force simulation value close to a real value needs to be obtained by a finite element simulation method. And (3) taking each characteristic dimension of the flexible hinge (2) as a variable, taking the rated load value given in the step one as an input value, and performing finite element analysis on the six-component force sensor models under different characteristic dimensions by using a finite element analysis method to extract the axial force value of each force measurement branch.
Structure optimization target of step three and six component force sensor
And (3) subtracting the force measuring branch axial force values under different characteristic sizes obtained in the step (II) with the force measuring branch theoretical force value obtained in the step (I) to obtain error values, wherein each characteristic size value corresponds to 8 error values, and multi-objective optimization is carried out by taking the minimum error value of each force measuring branch as an optimization target to obtain the optimal characteristic size value of the flexible hinge (2) so as to reduce the coupling condition of the sensor.
Step four, six component force sensor structure optimization
And (3) respectively normalizing the error values of the 8 force measuring branches corresponding to each characteristic dimension value in the third step by adopting a weighting method in a multi-objective optimization algorithm, wherein the weights of the error values corresponding to the force measuring branches are the same, and the multi-objective optimization is converted into single-objective optimization. And determining a characteristic dimension value which can minimize the target value under the condition of ensuring the conforming strength, namely a final characteristic dimension parameter of the flexible hinge (2).
Further, the structure optimization method of the eight-branch orthogonal parallel type six-component force sensor is characterized in that a Cartesian coordinate system is established on a loading plane of a platform on the six-component force sensor, and theoretical force values of force measurement branches of the six-component force sensor, which are obtained by a spiral theory, are as follows:
Figure BDA0003593278090000041
wherein the content of the first and second substances,
F x 、F y 、F z 、M x 、M y and M z The load is the rated load value of the six-component force sensor, h is the distance between the axis of the horizontal force measurement branch and the upper platform, b is the distance between the vertical force measurement branch and the x axis or the y axis, and a is the distance between the horizontal force measurement branch and the x axis or the y axis.
The invention provides an eight-branch orthogonal parallel six-component force sensor which has the following beneficial effects:
1. the standard single-dimensional pull pressure sensor is adopted to measure each branch force value, and compared with a common external patch type six-component force sensor, the system error caused by manually attaching a strain gauge on an elastic body is avoided.
2. The flexible hinges of the force measuring branches are provided with the through holes and the cutting grooves, so that the bending rigidity of the flexible hinges is reduced, the flexible hinges can be elastically bent around two mutually vertical shafts, the interference of non-axial force on the force measuring branches is reduced, namely, the coupling crosstalk of force between dimensions is reduced, and the measuring precision is improved.
3. According to the eight-branch orthogonal parallel six-component force sensor, each single-dimensional pull pressure sensor in the structure is a calibrated sensor, so that the force value measured by the six-component force sensor can be traced.
4. The upper platform is provided with a plurality of positioning holes and threaded holes, so that the upper platform can be conveniently and fixedly connected with the tested equipment and the loading equipment.
5. And a multi-objective optimization algorithm is adopted to optimize the size of the flexible hinge structure of the six-component force sensor, so that the coupling is further reduced structurally.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a front view of the structure of the present invention;
FIG. 3 is a cross-sectional view at A-A of the present invention;
in the figure:
1. an upper platform; 2. a flexible hinge; 3. a single dimensional pull pressure sensor; 4. a lower platform connecting block; 5. a lower platform; 6. an upper platform connecting block; 7. a forward via; 8. cutting a groove in the forward direction; 9. a lateral through hole; 10. laterally grooving; 11. the upper platform is connected with a countersunk through hole for quick fixation; 12. positioning holes; 13. the flexible hinge is fixed by a countersunk through hole; 14. a threaded through hole; 15. the hinge connecting block is fixed with a countersunk through hole; 16. the single-dimensional pull pressure sensor is fixed by a threaded through hole; 17. the lower platform is fixed with the through hole.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1 to 3, the structural relationship is as follows: the flexible hinge 2 is connected with the one-dimensional tension pressure sensor 3 to form force measuring branches, wherein the force measuring branches comprise 8 force measuring branches, 4 force measuring branches are vertically arranged, 4 force measuring branches are horizontally arranged and circumferentially and uniformly distributed, and the vertical force measuring branches are orthogonal to the horizontal force measuring branches; the lower platform connecting block 4 and the upper platform connecting block 6 are perpendicular to the connected force measuring branches; the upper platform 1 is parallel to the lower platform 5. The flexible hinge 2 of the force measurement branch is connected with the one-dimensional tension and compression sensor 3 through a bolt, the lower platform connecting block 4 is connected with the lower platform 5 through a bolt, the upper platform connecting block 6 is connected with the upper platform 1 through a bolt, the horizontal force measurement branch is connected with the upper platform connecting block 6 and the lower platform connecting block 4 through a bolt, and the vertical force measurement branch is connected with the upper platform 1 and the lower platform 5 through a bolt;
the front surface of the flexible hinge 2 is provided with a through positive through hole 7 and a positive cutting groove 8, and the side surface is provided with a through lateral through hole 9 and a lateral cutting groove 10; the rigidity of the flexible hinge is reduced, the crosstalk coupling of each component force can be reduced, the measurement sensitivity of the sensor is improved, and an upper platform connecting block fixing countersunk through hole 11, a flexible hinge fixing countersunk through hole 13, a positioning hole 12 and a threaded through hole 14 are formed in the positions of 4 corners of the upper platform 1; the lower platform 5 is provided with a countersunk through hole 15 for fixing the hinge connecting block, a threaded through hole 16 for fixing the one-dimensional pull pressure sensor and a through hole 17 for fixing the lower platform, and is used for assembling the sensor and mounting the sensor and the tested equipment.
Preferably, the number of the force measuring branches is 8, and the vertical force measuring branches are perpendicular to the horizontal force measuring branches.
Preferably, the upper platform connecting block 6 is a U-shaped structure, with the vertical flexible hinge 2 contained within its mouth but spaced from and not in contact with its inner wall. In practical use, the specific form and size of the upper platform connection speed are designed according to the sizes of the flexible hinge and the single-dimensional pull pressure sensor.
Preferably, the upper platform 1 is arranged in parallel with the lower platform 5.
Preferably, the flexible hinge 2 is provided with a through forward through hole 7 and a through lateral through hole 9, the forward through hole 7 and the through lateral through hole 9 are located in the middle of the hinge and symmetrically distributed by taking the center axis of the hinge as the center, and the forward through hole and the through lateral through hole are orthogonal.
Preferably, the flexible hinge 2 is provided with a pair of through-going forward slots 8 and a pair of through-going lateral slots 10, the forward slots 8 are arranged in a V shape inclined upward at 45 degrees to the horizontal direction, the lateral slots 10 are arranged in an inverted V shape inclined downward at 45 degrees to the horizontal direction, and the central axis of the through-hole is on the central plane of the slots.
Preferably, the forward through hole 7 and the lateral through hole 9 of the flexible hinge are in a perfect circle with a gap.
Preferably, the front slots 8 and the lateral slots 10 of the flexible hinge are parallel to each other in the slots.
As shown in fig. 1, when the lower platform connecting block 4 is actually used, as long as the rigidity is large enough to effectively support the horizontal force-measuring branch, the specific structural form is not strictly limited.
Optimizing the characteristic dimension of the flexible hinge (2), wherein the optimized variables are the hole diameters of the forward through hole (7) and the lateral through hole (9), the groove widths of the forward cutting groove (8) and the lateral cutting groove (10) and the hole distance between each pair of through holes, and the optimizing steps are as follows:
step one, acquiring force measurement branch theoretical value of six-component force sensor
According to the strength limit of the six-component force sensor structure, each force measuring branch is ensured to be in a safe working state, the rated load value of the six-component force sensor is given, the rated load value is used as an input value, and the theoretical value of the axial force borne by each force measuring branch is obtained by using a spiral theory.
Step two, acquiring simulation output values of force measurement branches of six-component force sensor
In practical use, the force measurement branch is not only limited to the axial force in theory, and an axial force simulation value close to a real value needs to be obtained by a finite element simulation method. And (3) taking each characteristic dimension of the flexible hinge (2) as a variable, taking the rated load value given in the step one as an input value, and performing finite element analysis on the six-component force sensor models under different characteristic dimensions by using a finite element analysis method to extract the axial force value of each force measurement branch.
Structure optimization target of step three and six component force sensor
And (3) subtracting the force measuring branch axial force values under different characteristic sizes obtained in the step (II) with the force measuring branch theoretical force value obtained in the step (I) to obtain error values, wherein each characteristic size value corresponds to 8 error values, and multi-objective optimization is carried out by taking the minimum error value of each force measuring branch as an optimization target to obtain the optimal characteristic size value of the flexible hinge (2) so as to reduce the coupling condition of the sensor.
Step four, six component force sensor structure optimization
And (3) respectively normalizing the error values of the 8 force measuring branches corresponding to each characteristic dimension value in the third step by adopting a weighting method in a multi-objective optimization algorithm, wherein the weights of the error values corresponding to the force measuring branches are the same, and the multi-objective optimization is converted into single-objective optimization. And determining a characteristic dimension value which can minimize the target value under the condition of ensuring the conforming strength, namely a final characteristic dimension parameter of the flexible hinge (2).
Preferably, the structure optimization method of the eight-branch orthogonal parallel type six-component force sensor is characterized in that a cartesian coordinate system is established on a loading plane of an upper platform of the six-component force sensor, and the theoretical force values of the force measurement branches of the six-component force sensor, which are obtained by a spiral theory, are as follows:
Figure BDA0003593278090000091
wherein the content of the first and second substances,
F x 、F y 、F z 、M x 、M y and M z The load value is the rated load value of the six-component force sensor, h is the distance between the axis of the horizontal force measurement branch and the upper platform, b is the distance between the vertical force measurement branch and the x axis or the y axis, and a is the distance between the horizontal force measurement branch and the x axis or the y axis.
The embodiments described above are intended to facilitate one of ordinary skill in the art in understanding and using the present invention. It will be readily apparent to those skilled in the art that various modifications to these embodiments may be made, and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the embodiments described herein, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.

Claims (10)

1. An eight-branch orthogonal parallel type six-component force sensor is characterized in that: the flexible hinge (2) is connected with the one-dimensional tension pressure sensor (3) to form force measurement branches, wherein the force measurement branches comprise 8 force measurement branches, 4 force measurement branches are vertically arranged, 4 force measurement branches are horizontally arranged and circumferentially and uniformly distributed, and the vertical force measurement branches are orthogonal to the horizontal force measurement branches; the lower platform connecting block (4) and the upper platform connecting block (6) are perpendicular to the force measuring branch; the upper platform (1) is parallel to the lower platform (5); the flexible hinge (2) of the force measuring branch is in bolted connection with the one-dimensional tension and compression sensor (3), the lower platform connecting block (4) is in bolted connection with the lower platform (5), the upper platform connecting block (6) is in bolted connection with the upper platform (1), the horizontal force measuring branch is in bolted connection with the upper platform connecting block (6) and the lower platform connecting block (4), and the vertical force measuring branch is in bolted connection with the upper platform (1) and the lower platform (5);
the front surface of the flexible hinge (2) is provided with a through forward through hole (7) and a through forward cutting groove (8), and the side surface is provided with a through lateral through hole (9) and a through lateral cutting groove (10); a countersunk through hole (11) for fixing an upper platform connecting block, a countersunk through hole (13) for fixing a flexible hinge, a positioning hole (12) and a threaded through hole (14) are formed in the positions of 4 corners of the upper platform (1); lower platform (5) are equipped with fixed countersunk head through-hole (15) of using of hinge connection piece, and the fixed screw thread through-hole (16) of using of single dimension pressure sensor, and fixed through-hole (17) of using of lower platform.
2. The eight-branch orthogonal parallel six-component force sensor of claim 1, wherein: the number of the force measuring branches is 8, and the force measuring branches are vertical to the horizontal force measuring branches.
3. The eight-branch orthogonal parallel six-component force sensor of claim 1, wherein: the upper platform connecting block (6) is of a U-shaped structure, and the vertical flexible hinge (2) is contained in the opening of the upper platform connecting block but has a gap with the inner wall of the upper platform connecting block and is not in contact with the inner wall of the upper platform connecting block.
4. The eight-branch orthogonal parallel six-component force sensor of claim 1, wherein: the upper platform (1) and the lower platform (5) are arranged in parallel.
5. The eight-branch orthogonal parallel six-component force sensor of claim 1, wherein: be equipped with on flexible hinge (2) through-going forward through-hole (7) and side direction through-hole (9), two pairs forward through-hole (7) and side direction through-hole (9) all are located the middle part of hinge, use the hinge center pin to be symmetric distribution as the center respectively, and forward through-hole and side direction through-hole quadrature.
6. The eight-branch orthogonal parallel six-component force sensor of claim 1, wherein: the flexible hinge (2) is provided with a pair of through forward cutting grooves (8) and a pair of through lateral cutting grooves (10), the forward cutting grooves (8) are arranged in a V shape with an angle of 45 degrees and inclined upwards with the horizontal direction, the lateral cutting grooves (10) are arranged in an inverted V shape with an angle of 45 degrees and inclined downwards with the horizontal direction, and the central axis of the through hole is positioned on the central plane of the cutting grooves.
7. An eight-branch orthogonal parallel six-component force sensor according to claim 1 or 2, wherein: the positive through hole (7) and the lateral through hole (9) of the flexible hinge are in a notched circular shape.
8. An eight-branch orthogonal parallel six-component force sensor according to claim 1 or 3, wherein: the flexible hinge comprises a positive cutting groove (8) and a lateral cutting groove (10), and two planes in the cutting grooves are parallel.
9. Optimizing the characteristic dimension of the flexible hinge (2), wherein the optimized variables are the hole diameters of the forward through hole (7) and the lateral through hole (9), the groove widths of the forward cutting groove (8) and the lateral cutting groove (10) and the hole distance between each pair of through holes, and the optimization steps are as follows:
step one, acquiring force measurement branch theoretical value of six-component force sensor
According to the strength limit of the six-component force sensor structure, ensuring that each force measuring branch is in a safe working state, giving a rated load value of the six-component force sensor, taking the rated load value as an input value, and calculating an axial force theoretical value borne by each force measuring branch by using a spiral theory;
step two, acquiring simulation output values of force measurement branches of six-component force sensor
In practical use, the force measuring branch is not only subjected to axial force in theory, and an axial force simulation value close to a real value is obtained by a finite element simulation method; taking each characteristic dimension of the flexible hinge (2) as a variable, taking the rated load value given in the step one as an input value, and respectively carrying out finite element analysis on the six-component force sensor models under different characteristic dimensions by using a finite element analysis method to extract the axial force value of each force measuring branch;
structure optimization target of step three and six component force sensor
Subtracting the force measuring branch axial force values under different characteristic sizes obtained in the step two from the force measuring branch theoretical force value in the step one to obtain error values, wherein each characteristic size value corresponds to 8 error values, and performing multi-objective optimization by taking the minimum error value of each force measuring branch as an optimization target to obtain the optimal characteristic size value of the flexible hinge (2) so as to reduce the coupling condition of the sensor;
step four, six component force sensor structure optimization
Respectively normalizing the error values of the 8 force measuring branches corresponding to each characteristic dimension value in the third step by adopting a weighting method in a multi-objective optimization algorithm, wherein the weights of the error values corresponding to the force measuring branches are the same, and converting multi-objective optimization into single-objective optimization; and determining a characteristic dimension value which can minimize the target value under the condition of ensuring the conforming strength, namely a final characteristic dimension parameter of the flexible hinge (2).
10. The method for optimizing the structure of an eight-branch orthogonal parallel six-component force sensor according to claim 9, wherein a cartesian coordinate system is established on a loading plane of an upper platform of the six-component force sensor, and theoretical force values of the force-measuring branch of the six-component force sensor, which are obtained by a spiral theory, are:
Figure FDA0003593278080000041
wherein the content of the first and second substances,
F x 、F y 、F z 、M x 、M y and M z The load value is the rated load value of the six-component force sensor, h is the distance between the axis of the horizontal force measurement branch and the upper platform, b is the distance between the vertical force measurement branch and the x axis or the y axis, and a is the distance between the horizontal force measurement branch and the x axis or the y axis.
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