CN116878704A - Positioning point fastening force calculation method based on fiber bragg grating strain data - Google Patents
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
- G01L1/00—Measuring force or stress, in general
- G01L1/24—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet
- G01L1/242—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet the material being an optical fibre
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Abstract
The invention discloses a positioning point fastening force calculation method based on fiber bragg grating strain data, which comprises the following steps: symmetrically arranging a plurality of fiber grating sensors with single grating measuring points on the surface of the positioning cantilever; establishing a linear equation set of a three-dimensional force mapping relation from each grating strain measurement value on a positioning arm to a workpiece positioning point by utilizing a mechanical principle; calibrating undetermined coefficients in the linear equation set through experiments; and in the service process of the tool, according to the strain data currently measured by the sensor, combining the linear equation set and the calibrated coefficient, and calculating the three-dimensional force of the fastening force of the positioning point of the tool. The invention utilizes the characteristic of tiny volume and mass of the fiber bragg grating sensor to indirectly calculate the three-dimensional force of the positioning point according to the strain data, can lay a foundation for monitoring the internal stress of the assembly, optimizing and adjusting the positioning point position and improving the assembly quality, and simultaneously avoids the problems of additional load and space interference caused by the larger volume and mass of the force sensor, so that the detection result is more accurate.
Description
Technical Field
The invention belongs to the field of optical fiber sensing and mechanical intersection, and particularly relates to a positioning point fastening force calculation method based on fiber bragg grating strain data.
Background
At present, the positioning and fastening functions of the assembly of the aircraft components mainly depend on a tool-shaped frame, so that the tool is flexible to adapt to the gesture-adjusting positioning requirements of different assembly products, and a large number of reconfigurable structures are adopted by the tool, wherein the overhanging positioning arm structure is one of the mainly adopted structural forms. Because of the existence of positioning errors, the fastening force between the tool positioning hole pin and the assembly part can deform the assembly product, so that the assembly part has larger internal stress and the assembly quality is influenced. The monitoring of the fastening force of the positioning point of the fixture is realized, and the method has great significance for the force-position coupling control and the improvement of the assembly quality of the flexible fixture.
The existing method for monitoring the fastening force of the tool mainly adopts a method for directly arranging a force sensor, and the method has the following problems: the force sensor is large in volume and mass, and particularly, a large load is added to a positioning structure in an overhanging form to deform the structure, so that the positioning accuracy of the tool is affected.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a positioning point fastening force calculation method based on fiber grating strain data by taking a cantilever type positioning structure adopted by a reconfigurable tool in a large amount as an application object, and aims to realize the on-line monitoring of the three-dimensional force of a workpiece positioning point in an assembly environment in the service process of the tool.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating is applied to an assembly fixture comprising a cantilever type positioning structure, wherein the cantilever type positioning structure comprises a positioning arm and a tail end connector, and is characterized by comprising the following steps:
step 1: symmetrically arranging a plurality of fiber grating strain sensors with single grating measuring points on the periphery of the positioning arm;
step 2: aiming at a tool positioning point, namely a connecting point of the end connector and a workpiece, a positioning point three-dimensional force calculation model based on strain measurement data of a plurality of grating measuring points is established by using a mechanics principle, and the method comprises the following steps:
the fastening force born by the fixture positioning points is decomposed into three-dimensional force data, namely three orthogonal components F under a three-dimensional rectangular coordinate system x 、F y And F z The three orthogonal components are translated to the position of the center point of the cross section of the tail end of the positioning arm, the z axis of the three-dimensional rectangular coordinate system is parallel to the extending direction of the positioning arm, the y axis is parallel to the vertical direction, the x axis is perpendicular to the z axis and the y axis, and the additional bending moment M of the center point of the cross section of the tail end in two directions is obtained according to the force system translation principle x 、M y And an additional torque M in one direction z ；
Calculating center points of cross sections of the tail ends by using cantilever beam bending models of material mechanics to respectively act on F only x 、F y 、F z 、M x 、M y Or M z The axial strain of each grating measuring point is obtained based on the linear superposition principle of small deformation and simultaneously acts on F at the center point of the end section x 、F y 、F z 、M x 、M y And M z The axial combined strain of each grating measuring point is used for establishing the strain measurement value of the fiber bragg grating strain sensor relative to F x 、F y And F z Is a linear system of equations;
step 3: calibrating undetermined coefficients contained in the linear equation set obtained in the step 2 through experiments;
step 4: and (3) carrying out on-line monitoring on an assembly tool in the service process, and solving three-dimensional force data of the fastening force of the positioning point of the workpiece by utilizing the linear equation set obtained in the step (2) and the coefficient calibrated in the step (3) in combination with the current strain measurement value of each fiber grating strain sensor at the grating measuring point position.
In addition to the above, the improved or preferred solution further includes:
further, the cross section of the positioning arm is a symmetrical rectangular cross section, and the strain neutral layer in the x-axis direction of the positioning arm is assumed to be overlapped with the transverse geometric center layer, and the strain neutral layer in the y-axis direction of the positioning arm is assumed to be overlapped with the vertical geometric center layer.
Further, in step 1, two fiber bragg grating strain sensors with single grating measuring points are respectively arranged on the surfaces of the left side and the right side of the positioning arm, so that the grating measuring points located on different sides of the positioning arm are bilaterally symmetrical with the vertical geometric center layer of the positioning arm as a center, the grating measuring points located on the same side of the positioning arm are vertically symmetrical with the horizontal geometric center layer of the positioning arm as a center, the axial distances from the four grating measuring points to the center point of the cross section of the tail end of the positioning arm are equal, the vertical geometric center layer is parallel to the y axis, and the horizontal geometric center layer is parallel to the x axis.
Further, in step 2, the strain measurement value of each fiber grating strain sensor is related to F x 、F y And F z The linear equation set of (2) is:
in the formula (1), c 1 、c 2 、c 3 、c 4 And c 5 Five constants related to the section size and the material property of the positioning arm are coefficients to be determined, and the calculation method comprises the following steps:
in the formula (2), E is the elastic modulus of the positioning arm, I x And I y Moment of inertia of the strain neutral layer in the x-axis direction and the y-axis direction of the cross section of the tail end of the positioning arm; a is the cross section area of the positioning arm, L is the axial distance from the center of four grating measuring points to the center point of the cross section at the tail end of the positioning arm, and r 1 And r 2 The distances from the four grating measuring points to the strained neutral layer in both the y-axis and the x-axis directions are respectively.
Further, the step 3 includes:
installing a three-dimensional force sensor on the cross section of the tail end of the positioning arm, loading concentrated forces in different directions and in different sizes for a plurality of times at a preset tool positioning point under the condition that a workpiece is not connected, and recording three-dimensional force data measured by the three-dimensional force sensor when the concentrated force is loaded each time and strain measurement values of all grating measuring points on the positioning arm; and (3) taking the three-dimensional force data and the strain measurement value corresponding to the three-dimensional force data as sample data into the linear equation set obtained in the step (2), constructing an overdetermined non-homogeneous linear equation set related to the undetermined coefficients, and solving all the undetermined coefficients by a least square method.
Further, in step 3, the coefficient c is determined 1 、c 2 、c 3 、c 4 And c 5 The overdetermined non-homogeneous linear equation set of (2) is:
in the formula (3), n is the number of loading experiments, namely three-dimensional force data and the number of samples of the strain measurement value corresponding to the three-dimensional force data; f (F) i And epsilon i Respectively representing a matrix and a vector shown in formula (4):
in the formula (4), F ix 、F iy And F iz Is three-dimensional force data acquired by the ith experiment, epsilon i1 、ε i2 、ε i3 And epsilon i4 Is the strain measurement value of the four grating measuring point positions acquired by the ith experiment, i is 1 to nIs any natural number of (a);
c in formula (3) 1 、c 2 、c 3 、c 4 And c 5 The least square solution formula of (2) is:
in the formula (5) (. Cndot. + Moore-Penrose generalized inverse matrix representing the matrix.
Further, in step 4, three-dimensional force data F of the fastening force of the workpiece positioning point x 、F y And F z The solution formula of (2) is:
epsilon in formula (6) 1 、ε 2 、ε 3 And epsilon 4 Is the current strain measurement at four grating measurement points.
Further, the signal output end of the fiber grating strain sensor is connected with a lower computer of the fiber grating demodulator, the data directly read from the lower computer is the wavelength offset of the corresponding grating measuring point, and the relation between the wavelength offset delta lambda of any grating measuring point and the strain measuring value epsilon of any grating measuring point is as follows:
ε＝k 1 Δλ (7)
k in formula (7) 1 Taking 1.2X10 6 pm -1 。
Further, the end connector is arranged at one end of the positioning arm, the other end of the positioning arm is a fixed end connected with the supporting structure, and the grating measuring point is arranged at a position close to the fixed end of the positioning arm.
The beneficial effects of the invention are as follows:
the invention relates to a method for calculating the fastening force of a positioning point based on fiber bragg grating strain data, which is realized based on a plurality of fiber bragg grating sensors with single grating measuring points symmetrically distributed on the surface of a positioning cantilever. The method utilizes the characteristic of tiny volume and mass of the fiber bragg grating sensor, indirectly calculates the three-dimensional force of the positioning point according to the strain data, can lay a foundation for monitoring the internal stress of the assembly, optimally adjusting the positioning point and improving the assembly quality, and simultaneously avoids the problems of additional load and space interference caused by the use of larger volume and mass of the force sensor, so that the detection result is more accurate.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a model diagram of an example verification platform of the method of the present invention;
FIG. 3 is a schematic diagram of a fiber grating strain sensor layout method and a mechanical model according to the method of the invention;
FIG. 4 is three-dimensional force data for each loading experiment collected to verify the method of the present invention;
FIG. 5 is a graph of wavelength shift data for four grating measurement points per loading experiment collected by the method of the present invention;
FIG. 6 shows the relative error between the three-dimensional force result calculated from the strain data of the grating measuring points and the experimental data.
In the upper graph, a center point of a section at the 1-tail end, a positioning point of a workpiece, a 3-grating measuring point, a 4-bottom plate, a 5-positioning arm and a 6-workpiece.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings.
The invention aims to provide a positioning point fastening force calculation method based on fiber bragg grating strain data, which is used for realizing real-time monitoring of a fastening force of a reconfigurable assembly tool to an assembly workpiece in an actual assembly scene.
As shown in fig. 2 and 3, in one embodiment, the assembly tool is provided with a pair of cantilever type positioning structures on two sides of the workpiece, and the cantilever type positioning structures mainly comprise positioning arms and end connectors. The positioning arm is of a beam structure with a symmetrical cross section, and in the embodiment, the positioning arm is made of square tubes, and the cross section of the positioning arm is hollow rectangular. In the service process of the assembly fixture, the positioning arm is horizontally placed, one end of the positioning arm is a fixed end and is connected with the support upright post on the outer side, and the other end of the positioning arm is connected with the end connector so as to position the workpiece through the end connector.
The specific implementation process of the positioning point fastening force calculation method based on the fiber bragg grating strain data is as follows:
s1, symmetrically arranging a plurality of fiber bragg grating strain sensors with single grating measuring points on the peripheral side of a positioning arm, wherein the fiber bragg grating strain sensors specifically comprise:
the rectangular hollow section positioning arm of the reconfigurable assembly tool shown in fig. 2 and 3 is used as a specific application object, fiber bragg grating strain sensors with four single grating measuring points are prepared, and the fiber bragg grating strain sensors are symmetrically distributed on the surfaces of the left side and the right side of the positioning arm along the axial direction, and are preferably arranged at positions close to the fixed ends so as to improve strain response. The grating areas of the four fiber bragg grating strain sensors are axially aligned along the positioning arm, so that the strain of the positioning arm along the axial lines at four positions can be respectively perceived, more specifically, grating measuring points positioned at different sides of the positioning arm are bilaterally symmetrical by taking a vertical geometric center layer of the positioning arm as a center, grating measuring points positioned at the same side of the positioning arm are vertically symmetrical by taking a transverse geometric center layer of the positioning arm as a center, and the axial distances from the four grating measuring points to the center point of the cross section of the tail end of the positioning arm are equal. The end section, i.e. the positioning arm, connects the end faces of the end connectors.
S2, establishing a locating point three-dimensional force calculation model based on strain measurement data of a plurality of grating measuring points by using a mechanical principle aiming at a tool locating point, namely a connecting point of the end connector and a workpiece, namely a strain-three-dimensional force linear equation set, wherein the method specifically comprises the following steps:
firstly, the fastening force born by a tool positioning point is decomposed into three-dimensional force data, namely three orthogonal components F under a three-dimensional rectangular coordinate system x 、F y And F z Then three orthogonal components F at the workpiece positioning point x 、F y And F z Translating to the position of the center point of the tail end section of the positioning arm;
the z axis of the three-dimensional rectangular coordinate system is parallel to the extending direction of the positioning arm, the y axis is parallel to the vertical direction, and the x axis is perpendicular to the z axis and the y axis. The vertical geometric center layer is parallel to the y-axis, and the horizontal geometric center layer is parallel to the x-axis. In this embodiment, the cross section of the positioning arm is a symmetrical rectangular cross section, so it may be assumed that the strain neutral layer in the x-axis direction of the positioning arm coincides with the vertical geometric center layer, and the strain neutral layer in the y-axis direction of the positioning arm coincides with the vertical geometric center layer.
Assuming that the offset of the workpiece positioning point relative to the center point of the end section in three coordinate directions is deltax, deltay and deltaz respectively, the bending moment in the x and y axis directions obtained after the force system translates is:
due to F x 、F y And F z Additional end torque after translation M z No axial line strain is imparted to the positioning arm, which does not contribute to the response of the fiber bragg grating strain sensor, and is therefore ignored. Calculating the center point of the end section to be respectively only loaded with F x 、F y 、F z 、M x Or M y The magnitude of the axial strain perceived at four grating measurement points at an axial distance L from the end cross-section:
according to the bending principle of the material mechanics, when only M is applied x When four grating measuring points sense axial strain (epsilon) 11 、ε 21 、ε 31 And epsilon 41 ) The method comprises the following steps:
when only M is applied y When four grating measuring points sense axial strain (epsilon) 12 、ε 22 、ε 32 And epsilon 42 ) The method comprises the following steps:
when only F is applied x When four grating measuring points sense axial strain (epsilon) 13 、ε 23 、ε 33 And epsilon 43 ) The method comprises the following steps:
when only F is applied y When four grating measuring points sense axial strain (epsilon) 14 、ε 24 、ε 34 And epsilon 44 ) The method comprises the following steps:
when only F is applied z When four grating measuring points sense axial strain (epsilon) 15 、ε 25 、ε 35 And epsilon 45 ) The method comprises the following steps:
because the deflection of the positioning arm is smaller, based on the small deformation assumption, the combination strain perceived by the four grating measuring points is as follows according to the superposition principle:
thereby establishing a sensor strain measurement ε 1 ～ε 4 With respect to the three-dimensional force component F x 、F y 、F z Is a linear system of equations of (2).
E, I in the above formula (7) x 、I y The modulus of elasticity of the positioning arm and the moment of inertia of the stress neutral layer with the end section in both the x and y directions, respectively. And (3) making:
c, recognizing that the offset of the workpiece positioning point relative to the center point of the end section is unchanged, and the geometric dimension of the positioning arm is also unchanged 1 、c 2 、c 3 、c 4 、c 5 Is constant. The system of linear equations (7) can be written in matrix form:
or:
s3, calibrating equation set coefficient c through experiments 1 ～c 5 ：
And under the condition that a workpiece is not connected, loading concentrated forces in different directions and in different sizes for multiple times at a preset tool positioning point, and recording three-dimensional force data measured by the three-dimensional force sensor and strain measurement values of each grating measuring point on the positioning arm when the concentrated force is loaded each time. Assuming a total of n experiments were performed, n different sets of three-dimensional force and strain data samples were obtained, each set of samples corresponds to equation (9). And (3) making:
there is a large set of linear equations:
bold italic F in formula (12) above i And epsilon i Moment array F and the strain direction of the formula (11) corresponding to the i-th group sample respectivelyAn amount epsilon. When n is>1, the formula is about c 1 、c 2 、c 3 、c 4 、c 5 In general, there is no strict solution to the overdetermined non-homogeneous linear system of equations (the number of independent equations is greater than the number of unknowns). For this purpose, let a= [ F 1 T ,F 2 T ,…,F n T ] T ,c＝[c 1 ,c 2 ,c 3 ,c 4 ,c 5 ] T ,b＝[ε 1 T ,ε 2 T ,…,ε n T ] T Consider a least squares optimization objective:
partitioning A into blocks according to columns: a= [ alpha ] 1 ,α 2 ,α 3 ,α 4 ,α 5 ]Ac is the vector b at the vector α 1 ～α 5 Projection vectors of the tensed subspace, which are equivalent to Ac- ε and α 1 ～α 5 Orthogonalization, i.e. Ac- ε with α 1 ～α 5 The inner products of (2) are all zero:
the formula (14) is written as a matrix form:
A T Ac＝A T b (15)
then the formula (15) is:
c＝(A T A) + A T b (16)
thereby obtaining coefficient c in equation set (7) 1 ～c 5 Is a value of (2).
S4, on-line monitoring is carried out on an assembly tool in the service process, and the three-dimensional force data of the fastening force of the locating point of the workpiece is solved by utilizing the linear equation set obtained in the step 2 and the coefficient calibrated in the step 3 by combining the current strain measurement value of each fiber grating strain sensor at the grating measuring point position, wherein the three-dimensional force data specifically comprises the following steps:
combining the scaled c based on equation set (10) derived in step S2 1 ～c 5 Based on strain measurements epsilon of four gate regions 1 ～ε 4 Can solve the three-dimensional force F x ，F y And F z Solving method and pair c in S3 1 ～c 5 The solving method is the same as that:
the signal output end of the fiber grating strain sensor is connected with a lower computer of the fiber grating demodulator, and the strain measurement value epsilon 1 ～ε 4 The linear relation between the optical fiber grating demodulator and the wavelength offset delta lambda directly read from the lower computer program of the optical fiber grating demodulator is satisfied:
Δλ＝kε
wherein ε is ε 1 ～ε 4 K is an intrinsic parameter of the grating, typically: 1.2X10 6 pm。
And (3) experimental verification:
as shown in fig. 3, 20 groups of tensile forces in different directions and in different sizes are applied to the locating points of the tool, on one hand, three-way components of the tensile force of the tail end are collected through a three-dimensional force sensor arranged on the section of the tail end of the locating arm, on the other hand, offset of reflection wavelength of each grating measuring point of the tool layout relative to a reference value during each loading is recorded, and the three-dimensional force and sensor experimental data are shown in fig. 4 and 5 respectively.
According to the strain value calculated by the three-dimensional force data of the previous ten experiments and the four grating measuring point data, five constants c are calibrated by the formula (16) 1 ～c 5 And then applying the calculation model, substituting strain data of four measuring points of the rest ten experiments into the formula (17) to solve the corresponding terminal three-force component, comparing the result with load data measured by the experiments, wherein the relative errors of the three force calculation along the coordinate direction are shown in fig. 6, and the relative errors have certain fluctuation but are controlled in a smaller range.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the invention without departing from the principles thereof are intended to be within the scope of the invention as set forth in the following claims.
Claims (9)
1. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating is applied to an assembly fixture comprising a cantilever type positioning structure, wherein the cantilever type positioning structure comprises a positioning arm and a tail end connector, and is characterized by comprising the following steps:
step 1: symmetrically arranging a plurality of fiber grating strain sensors with single grating measuring points on the periphery of the positioning arm;
step 2: aiming at a tool positioning point, namely a connecting point of the end connector and a workpiece, a positioning point three-dimensional force calculation model based on strain measurement data of a plurality of grating measuring points is established by using a mechanics principle, and the method comprises the following steps:
the fastening force born by the fixture positioning points is decomposed into three-dimensional force data, namely three orthogonal components F under a three-dimensional rectangular coordinate system x 、F y And F z The three orthogonal components are translated to the position of the center point of the cross section of the tail end of the positioning arm, the z axis of the three-dimensional rectangular coordinate system is parallel to the extending direction of the positioning arm, the y axis is parallel to the vertical direction, the x axis is perpendicular to the z axis and the y axis, and the additional bending moment M of the center point of the cross section of the tail end in two directions is obtained according to the force system translation principle x 、M y And an additional torque M in one direction z ；
Calculating center points of cross sections of the tail ends by using cantilever beam bending models of material mechanics to respectively act on F only x 、F y 、F z 、M x 、M y Or M z The axial strain of each grating measuring point is obtained based on the linear superposition principle of small deformation and simultaneously acts on F at the center point of the end section x 、F y 、F z 、M x 、M y And M z The axial combined strain of each grating measuring point is achievedEstablishing a strain measurement value of the fiber bragg grating strain sensor about F x 、F y And F z Is a linear system of equations;
step 3: calibrating undetermined coefficients contained in the linear equation set obtained in the step 2 through experiments;
step 4: and (3) carrying out on-line monitoring on an assembly tool in the service process, and solving three-dimensional force data of the fastening force of the positioning point of the workpiece by utilizing the linear equation set obtained in the step (2) and the coefficient calibrated in the step (3) in combination with the current strain measurement value of each fiber grating strain sensor at the grating measuring point position.
2. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating according to claim 1, wherein the cross section of the positioning arm is a symmetrical rectangular cross section, and the strain neutral layer in the x-axis direction of the positioning arm is assumed to coincide with the transverse geometric center layer, and the strain neutral layer in the y-axis direction of the positioning arm is assumed to coincide with the vertical geometric center layer.
3. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating according to claim 2, wherein in the step 1, two fiber bragg grating strain sensors with single grating measuring points are respectively arranged on the surfaces of the left side and the right side of the positioning arm, so that the grating measuring points on different sides of the positioning arm are bilaterally symmetrical by taking a vertical geometric center layer of the positioning arm as a center, the grating measuring points on the same side of the positioning arm are vertically symmetrical by taking a horizontal geometric center layer of the positioning arm as a center, the axial distances from the four grating measuring points to the center point of the cross section of the tail end of the positioning arm are equal, the vertical geometric center layer is parallel to a y axis, and the horizontal geometric center layer is parallel to an x axis.
4. The method for calculating fastening force of positioning point based on strain data of fiber grating according to claim 3, wherein in step 2, the strain measurement value of each fiber grating strain sensor is related to F x 、F y And F z The linear equation set of (2) is:
in the formula (1), c 1 、c 2 、c 3 、c 4 And c 5 Five constants related to the section size and the material property of the positioning arm are coefficients to be determined, and the calculation method comprises the following steps:
in the formula (2), E is the elastic modulus of the positioning arm, I x And I y Moment of inertia of the strain neutral layer in the x-axis direction and the y-axis direction of the cross section of the tail end of the positioning arm; a is the cross section area of the positioning arm, L is the axial distance from the center of four grating measuring points to the center point of the cross section at the tail end of the positioning arm, and r 1 And r 2 The distances from the four grating measuring points to the strained neutral layer in both the y-axis and the x-axis directions are respectively.
5. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating according to claim 4, wherein the step 3 comprises:
installing a three-dimensional force sensor on the cross section of the tail end of the positioning arm, loading concentrated forces in different directions and in different sizes for a plurality of times at a preset tool positioning point under the condition that a workpiece is not connected, and recording three-dimensional force data measured by the three-dimensional force sensor when the concentrated force is loaded each time and strain measurement values of all grating measuring points on the positioning arm; and (3) taking the three-dimensional force data and the strain measurement value corresponding to the three-dimensional force data as sample data into the linear equation set obtained in the step (2), constructing an overdetermined non-homogeneous linear equation set related to the undetermined coefficients, and solving all the undetermined coefficients by a least square method.
6. The method for calculating anchor point tightening force based on fiber grating strain data according to claim 5, wherein in step 3, the coefficient c is determined as 1 、c 2 、c 3 、c 4 And c 5 The overdetermined non-homogeneous linear equation set of (2) is:
in the formula (3), n is the number of loading experiments, namely three-dimensional force data and the number of samples of the strain measurement value corresponding to the three-dimensional force data; f (F) i And epsilon i Respectively representing a matrix and a vector shown in formula (4):
in the formula (4), F ix 、F iy And F iz Is three-dimensional force data acquired by the ith experiment, epsilon i1 、ε i2 、ε i3 And epsilon i4 The strain measurement value is obtained by the ith experiment and is obtained at the positions of four grating measuring points, wherein i is any natural number from 1 to n;
c in formula (3) 1 、c 2 、c 3 、c 4 And c 5 The least square solution formula of (2) is:
in the formula (5) (. Cndot. + Moore-Penrose generalized inverse matrix representing the matrix.
7. The method for calculating a positioning point fastening force based on fiber bragg grating strain data according to claim 6, wherein in step 4, the three-dimensional force data F of the workpiece positioning point fastening force is obtained x 、F y And F z The solution formula of (2) is:
epsilon in formula (6) 1 、ε 2 、ε 3 And epsilon 4 Is the current strain measurement at four grating measurement points.
8. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating according to claim 7, wherein the signal output end of the fiber bragg grating strain sensor is connected with a lower computer of the fiber bragg grating demodulator, the data directly read from the lower computer is the wavelength offset of the corresponding grating measuring point, and the relation between the wavelength offset Δλ of any grating measuring point and the strain measuring value epsilon is:
ε＝k 1 Δλ (7)
k in formula (7) 1 Taking 1.2X10 6 pm -1 。
9. The method for calculating the fastening force of the positioning point based on the strain data of the fiber bragg grating according to any one of claims 1 to 8, wherein the end connector is installed at one end of the positioning arm, the other end of the positioning arm is a fixed end connected with the supporting structure, and the grating measuring point is arranged at a position close to the fixed end of the positioning arm.
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