Position-independent contour error modeling method for five-axis measurement workstation

Abstract

The invention discloses a position-independent contour error modeling method for a five-axis measurement workstation. The position-independent contour error modeling method comprises the following steps: S1, assembling error modeling; s2, performing differential kinematics mapping on the assembly error; s3, kinematic modeling of the five-axis measurement workstation; and S4, mapping assembly errors of the five-axis measurement workstation. Through the steps, position-independent contour error modeling of the five-axis measurement workstation is achieved, the relation between the assembly error and the tail end error is established through the error model, and the problems of contour errors and the like caused by factors such as manufacturing precision, assembly precision and use abrasion of all parts in the manufacturing process of the five-axis measurement workstation are solved. The work precision of the five-axis measurement work station is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of precision measurement in hydropower engineering, and in particular to a position-independent contour error modeling method for a five-axis measurement workstation. Background Art

[0002] Under the development background of hydropower machines in the field of hydropower engineering, the demand for precision measurement of unit components is becoming increasingly prominent. During the overhaul process of hydropower units, the measurement of geometric dimensions and form and position tolerances of some precision components, such as guide vanes, water guide bearings, thrust bearings, etc., is a key task. In order to achieve high-precision and high-efficiency measurement of these components, the relevant measurement equipment must have a contour measurement ability at the micron level.

[0003] The five-axis measurement workstation, with its multi-degree-of-freedom motion ability and high precision, has become an ideal equipment for measuring such precision components. However, in actual applications, the measurement accuracy of the five-axis measurement workstation is significantly affected by contour errors, that is, when the equipment executes a predetermined measurement trajectory, there will be a deviation between the actual motion path and the theoretical path. This kind of contour error mainly stems from factors such as manufacturing precision deviations of various components of the workstation, precision errors during the assembly process, and wear during the equipment use process, resulting in deviations between the actual positions and postures of the various motion axes of the workstation and their nominal values.

[0004] In order to improve the measurement accuracy, developing a position-independent contour error modeling method that can effectively solve the above problems is of great significance for improving the overall operation accuracy of the five-axis measurement workstation. Summary of the Invention

[0005] In order to solve the current technical problems, the main purpose of the present invention is to provide a position-independent contour error modeling method for a five-axis measurement workstation, which is used to solve problems such as contour errors caused by manufacturing precision, assembly precision, and use wear of various components during the manufacturing process of the five-axis measurement workstation, so as to improve the operation accuracy of the five-axis measurement workstation.

[0006] The technical solution adopted by the present invention is: a position-independent contour error modeling method for a five-axis measurement workstation, including the following steps: S1. Assembly error modeling; S2. Differential kinematic mapping of assembly errors; S3. Kinematic modeling of the five-axis measurement workstation; S4. Assembly error mapping of the five-axis measurement workstation.

[0007] In S1, the assembly error modeling includes the following steps: S11. Homogeneous coordinate transformation, and the homogeneous coordinate transformation matrix between coordinate system i and coordinate system j is: ; In the formula: and respectively represent the rotation transformation matrix and the translation vector from coordinate system i to coordinate system j; , , represent the elements of the first row of the rotation matrix from coordinate system i to coordinate system j; , , represent the elements of the second row of the rotation matrix from coordinate system i to coordinate system j; , , represent the elements of the third row of the rotation matrix from coordinate system i to coordinate system j; S12. The homogeneous coordinate transformation matrix from coordinate system i to coordinate system j considering assembly errors is: ; In the formula: represents the increment of the homogeneous coordinate transformation matrix from coordinate system i to coordinate system j considering assembly errors; represents the standard homogeneous coordinate transformation matrix from coordinate system i to coordinate system j without considering assembly errors; wherein, the kinematic equation of the assembly error is transformed into: ; In the formula: and respectively represent the position error parameter and the attitude error parameter in the i coordinate system, represents the translation transformation matrix along the coordinate axes x, y, z, represents three rotation transformation matrices rotating around the coordinate axes x, y, z; S13. Obtain the kinematic matrix considering assembly errors: ; In the formula: and respectively represent the position error parameter and the attitude error parameter in the i coordinate system.

[0008] In S12: The three rotation transformation matrices rotating around the coordinate axes x, y, z are respectively represented as: ; ; .

[0009] In S2, establishing the differential kinematic mapping of assembly errors includes the following steps: S21: Based on the standard link definition and joint coordinates, according to the homogeneous coordinate transformation matrix, the differential motion matrix of assembly errors between coordinate system i and coordinate system j is: ; In the formula: represents the differential motion matrix of assembly errors between coordinate system i and coordinate system j; represents the transpose of the rotation matrix from coordinate system i to coordinate system j; represents the 6x6 dimensional real matrix space; The differential motion matrix is used to describe the transfer relationship of assembly errors between different coordinate systems and is the basis of error mapping. represents the vector The screw-symmetric matrix of, expressed as: ; S22: The differential transformation of the coordinate system includes differential translation transformation and differential rotation transformation. The differential motion vector of coordinate system i is: ; In the formula: and respectively represent the differential translation vector and differential rotation vector in the i coordinate system; The differential motion vectors in different coordinate systems have the following relationship with the differential motion matrices in the corresponding coordinate systems: ; In the formula: represents the differential motion vector in coordinate system j; represents the differential motion vector in coordinate system j; Using transforms the differential motion vector in the i coordinate system to the j coordinate system to obtain .

[0010] In S3, the kinematic modeling of the five-axis measurement workstation includes the following steps: S31. Along the motion chain of the tool, starting from the base coordinate system of the workstation, passing through the X-axis, Y-axis, Z-axis, C-axis, A-axis, and finally reaching the tool, the homogeneous coordinate transformations between adjacent axes are successively: ; ; ; ; ; ; where: represents the homogeneous coordinate transformation matrix from the base coordinate system 0 to the coordinate system X; represents the homogeneous coordinate transformation matrix from the coordinate system X to the coordinate system Y; represents the homogeneous coordinate transformation matrix from the coordinate system Y to the coordinate system Z; represents the homogeneous coordinate transformation matrix from the coordinate system Z to the coordinate system C; represents the homogeneous coordinate transformation matrix from the coordinate system C to the coordinate system A; represents the homogeneous coordinate transformation matrix from the coordinate system A to the tool coordinate system T; , , represents the clamping position of the tool; Along the kinematic chain of the workpiece, starting from the workstation base coordinate system and then reaching the workpiece, the homogeneous coordinate transformations of adjacent axes are successively: ; where: represents the homogeneous coordinate transformation matrix from the workstation base coordinate system to the workpiece coordinate system; , , represents the clamping position of the workpiece; S32. Perform the inverse transformation of the homogeneous coordinate matrix. This continuous coordinate transformation process is expressed as: ; Obtain the tool position and orientation in the workpiece coordinate system: ; where: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T without considering assembly errors; , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems without considering assembly errors. x, y, z represent the tool position in the workpiece coordinate system; I, J, K represent the tool orientation in the workpiece coordinate system; In S32, by multiplying the corresponding local kinematic chain coordinate transformation relationship by the corresponding error term on the left, obtain the forward kinematic transformation relationship considering errors, and thus obtain the tool position and orientation in the workpiece coordinate system. The formula is as follows: ; where: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T considering assembly errors. , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems considering assembly errors. , , , , , represents the increment of the homogeneous coordinate transformation matrix between adjacent coordinate systems considering assembly errors; , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems.

[0011] In S4, the assembly error mapping of the five-axis measurement workstation includes the following steps: S41: According to the homogeneous coordinate transformation matrices between the various motion axes obtained from the kinematic model of the five-axis measurement workstation, combine to obtain the homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system; S42: Transform the local assembly errors of the workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis, and the tool from the local coordinate system to the tool coordinate system to obtain the assembly errors at the local position in the tool coordinate system; S43: Obtain the total tool tip position error caused by the assembly errors of each axis in the tool coordinate system.

[0012] The homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system is: ; In the formula: represents the 4×4 identity matrix; , , , , , , represents the homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system; , , , , , represents the homogeneous coordinate transformation matrix between adjacent motion axes.

[0013] The assembly error at the local position in the tool coordinate system is: ; In the formula: ; represents the assembly error at the local position i in the coordinate system of the corresponding local position i; represents the assembly error at the local position i in the tool coordinate system T; represents the differential motion matrix from the coordinate system of the local position i to the tool coordinate system T; The assembly error at the local position in the tool coordinate system is: The relationship between the position-independent spatial error at the tool position and the local assembly error is: ; Expand the cumulative form into a matrix form: ; In the formula, the local axes All relevant features or parameters are arranged in a specific form; is the total tool tip position error caused by the assembly error of each axis in the tool coordinate system; and the attitude error , is the Jacobian matrix that maps the assembly error of each axis to the spatial profile error at the tool end; is the assembly error of each axis in the local position coordinate system of each axis.

[0014] The present invention has the following beneficial effects: 1. The present invention maps the assembly error through the method of differential kinematics, and constructs an error mapping between the assembly error of the five-axis measurement workstation and the end profile error, so as to solve the problems such as profile error caused by factors such as manufacturing precision, assembly precision and use wear of each component in the manufacturing process of the five-axis measurement workstation, and improve the operation precision of the five-axis measurement workstation.

[0015] 2. In order to better analyze the mapping relationship between the assembly precision of each moving axis of the five-axis measurement workstation and the end profile error, the present invention constructs a differential motion matrix based on the Newton-Euler method, and combines the transmission relationship of the motion chain of the five-axis measurement workstation to construct an error mapping Jacobian matrix between the assembly error of the five-axis measurement workstation and the end profile error, providing a scientific basis for the precision improvement and error compensation of the five-axis measurement workstation.

[0016] 3. The process of establishing the position-independent contour error model for the five-axis measurement workstation in the present invention is clear, the formula calculation is simple, and the model accuracy is relatively good. Through the homogeneous coordinate transformation principle, the DH matrix of the linear axis and the rotary axis of the five-axis measurement workstation and the forward kinematics model are constructed. Based on the differential motion principle of error mapping, the corresponding error transfer matrix is constructed. Combining the transfer relationship of the motion chain, the error mapping Jacobian of the five-axis measurement workstation is constructed, thereby obtaining the influence model of the assembly error term on the position-independent contour error. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0018] Figure 1 It is a schematic diagram of the establishment steps of a method for establishing a position-independent contour error model for a five-axis measurement workstation provided by the present invention. Figure 2 It is a certain five-axis measurement workstation involved in the present invention.

[0019] Figure 3 It is the assembly process entity model and motion chain of a certain five-axis measurement workstation involved in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS The following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0020] See Figure 1 , a method for establishing a position-independent contour error model for a five-axis measurement workstation, including the following steps: S1. Assembly error modeling; S2. Differential kinematic mapping of assembly errors; S3. Kinematic modeling of the five-axis measurement workstation; S4. Assembly error mapping of the five-axis measurement workstation.

[0021] Through the above steps, the position-independent contour error modeling of the five-axis measurement workstation is achieved. The relationship between the assembly error and the end error is established through the error model to solve the problems such as contour error caused by factors such as manufacturing precision, assembly precision, and use wear of each component during the manufacturing process of the five-axis measurement workstation, so as to improve the operation precision of the five-axis measurement workstation.

[0022] In S1, the assembly error modeling includes the following steps: S11. The homogeneous coordinate transformation is the basis of the kinematic transformation of the five-axis measurement workstation and also the basis of differential kinematics. The homogeneous coordinate transformation matrix from coordinate system i to coordinate system j is: ; In the formula: and respectively represent the rotation transformation matrix and the translation vector from coordinate system i to coordinate system j; , , represent the elements of the first row of the rotation matrix from coordinate system i to coordinate system j; , , represent the elements of the second row of the rotation matrix from coordinate system i to coordinate system j; , , represent the elements of the third row of the rotation matrix from coordinate system i to coordinate system j; S12. The homogeneous coordinate transformation matrix from coordinate system i to coordinate system j considering the assembly error is: ; In the formula: represents the increment of the homogeneous coordinate transformation matrix from coordinate system i to coordinate system j considering the assembly error; represents the standard homogeneous coordinate transformation matrix from coordinate system i to coordinate system j without considering the assembly error; In the actual assembly process, due to the limitations of manufacturing precision and assembly precision, the actual coordinate transformation matrix will deviate from the theoretical value. Therefore, it is necessary to introduce the assembly error increment to correct the theoretical homogeneous coordinate transformation matrix , Among them, the kinematic equation transformation of the assembly error is: ; In the formula: and respectively represent the position error parameter and the attitude error parameter in the i coordinate system, Represents the translation transformation matrix along the coordinate axes x, y, and z. Represents three rotation transformation matrices for rotation about the coordinate axes x, y, and z.

[0023] Specifically, in S12: The three rotation transformation matrices for rotation about the coordinate axes x, y, and z Are respectively represented as: ; ; .

[0024] S13. Since each error is a small quantity, it can be simplified into the following two forms: ; Furthermore, the kinematic matrix considering assembly errors is obtained: ; In the formula: and Respectively represent the position error parameter and the attitude error parameter in the i coordinate system.

[0025] In S2, establishing the differential kinematic mapping of assembly errors includes the following steps: S21: Based on the standard link definition and joint coordinates, according to the homogeneous coordinate transformation matrix, the differential motion matrix of assembly errors between coordinate system i and coordinate system j is: ; In the formula: Represents the differential motion matrix of assembly errors between coordinate system i and coordinate system j; Represents the transpose of the rotation matrix from coordinate system i to coordinate system j; Represents the 6x6 dimensional real matrix space; Represents the vector The screw-symmetric matrix of, is represented as: .

[0026] S22: The differential transformation of the coordinate system includes differential translation transformation and differential rotation transformation, which can be represented by a 6-dimensional differential vector. Assuming the differential motion vector of coordinate system i is: ; In the formula: and Respectively represent the differential translation vector and the differential rotation vector in the i coordinate system; The differential motion vectors in different coordinate systems have the following relationship with the differential motion matrices in the corresponding coordinate systems: ; In the formula: represents the differential motion vector in coordinate system j; represents the differential motion vector in coordinate system j; In this way, can be used to transform the differential motion vector in coordinate system i to coordinate system j and obtain

[0027] In S3, the kinematic modeling of the five-axis measurement workstation includes the following steps: S31. Taking the assembly process of a certain five-axis measurement workstation as an example for analysis, the workstation solid model and kinematic chain are as Figure 2 , 3 shown. It can be found that the only component in the kinematic chain at the workpiece end is the workpiece W. At the tool end, the layout of the kinematic chain starts from the tool T and successively passes through the A-axis, C-axis, Z-axis, Y-axis, and X-axis. Among them, the X-axis is connected through the workstation body. According to the kinematic chain of the five-axis measuring machine, the ideal kinematic relationship between the tool and the workpiece is established.

[0028] Along the kinematic chain of the tool, starting from the base coordinate system of the workstation, passing through the X-axis, Y-axis, Z-axis, C-axis, and A-axis, and finally reaching the tool. The homogeneous coordinate transformations between adjacent axes are successively: ; ; ; ; ; ; In the formula: represents the homogeneous coordinate transformation matrix from the base coordinate system 0 to coordinate system X; represents the homogeneous coordinate transformation matrix from coordinate system X to coordinate system Y; represents the homogeneous coordinate transformation matrix from coordinate system Y to coordinate system Z; represents the homogeneous coordinate transformation matrix from coordinate system Z to coordinate system C; represents the homogeneous coordinate transformation matrix from coordinate system C to coordinate system A; represents the homogeneous coordinate transformation matrix from coordinate system A to the tool coordinate system T; , , represents the clamping position of the tool; Along the kinematic chain of the workpiece, starting from the workstation base coordinate system and then reaching the workpiece. The homogeneous coordinate transformations between adjacent axes are successively: ; In the formula: represents the homogeneous coordinate transformation matrix from the workstation base coordinate system to the workpiece coordinate system; , , represents the clamping position of the workpiece; S32. In the overall motion chain, starting from the workpiece coordinate system W, followed by the machine tool's base coordinate system, and then passing through the X-axis, Y-axis, Z-axis, C-axis, and A-axis, finally reaching the tool coordinate system T. Since the overall motion chain is opposite to the workpiece motion chain, the inverse transformation of the homogeneous coordinate matrix is performed. This continuous coordinate transformation process is expressed as: ; In S32, according to the method of left-multiplying the corresponding local motion chain coordinate transformation relationship by the corresponding error term, the forward kinematic transformation relationship considering errors is obtained, thereby obtaining the tool position and attitude in the workpiece coordinate system. The formula is as follows: ; In the formula: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T considering assembly errors. , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems considering assembly errors. , , , , , represents the increment of the homogeneous coordinate transformation matrix between adjacent coordinate systems considering assembly errors; , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems.

[0029] Thus, the tool position and attitude in the workpiece coordinate system are obtained: ; In the formula: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T considering assembly errors.

[0030] In S4, the mapping of the assembly errors of the five-axis measurement workstation includes the following steps: S41: Obtain the homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system by combining the homogeneous coordinate transformation matrices between the respective motion axes obtained from the kinematic model of the five-axis measurement workstation.

[0031] The homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system is: ; Where: represents the 4×4 identity matrix; , , , , , , represents the homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis, and the local position coordinate system of the tool to the tool coordinate system; , , , , , represents the homogeneous coordinate transformation matrix between adjacent motion axes.

[0032] S42: Transform the local assembly errors of the workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis, and the tool from the local coordinate system to the tool coordinate system to obtain the assembly errors at the local position in the tool coordinate system.

[0033] The differential motion matrix can map the local assembly error from one coordinate system to another. The local assembly errors of the workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis, and the tool, etc., are transformed from the local coordinate system to the tool coordinate system to obtain: ; Where: ; represents the assembly error at the local position i in the corresponding local position i coordinate system; represents the assembly error at the local position i in the tool coordinate system T; represents the differential motion matrix from the local position i coordinate system to the tool coordinate system T; S43: Obtain the total tool tip position error caused by the assembly errors of each axis in the tool coordinate system.

[0034] The relationship between the position-independent spatial error and the local assembly error at the tool position is: ; Expand the cumulative form into a matrix form: ; In the formula, local axes are adopted All relevant features or parameters are arranged in a specific form; is the total tool tip position error caused by the assembly errors of each axis in the tool coordinate system; and attitude error , is the Jacobian matrix that maps the assembly errors of each axis to the spatial profile error at the tool end; are the assembly errors of each axis of the local position coordinate system of each axis.

[0035] Through the Jacobian matrix , we can map these local assembly errors to the tool coordinate system, so as to obtain the total assembly error at the tool end . This helps us evaluate the influence of assembly errors on the position and attitude of the tool end, and provides a basis for error compensation.

[0036] The process of establishing the position-independent profile error model of the five-axis measurement workstation in the present invention is clear, the formula calculation is simple, and the model accuracy is good. Through the homogeneous coordinate transformation principle, the DH matrix of the linear axis and the rotary axis of the five-axis measurement workstation, as well as the forward kinematics model, are constructed. Based on the differential motion principle of error mapping, the corresponding error transfer matrix is constructed. Combining the transfer relationship of the motion chain, the error mapping Jacobian of the five-axis measurement workstation is constructed, and the influence model of 42 assembly error items on the position-independent profile error is obtained.

[0037] The above embodiments are only used to illustrate the present invention. The structures, connection methods, manufacturing processes, etc. of each component can be changed. Any equivalent transformation and improvement based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.​​

Claims

1. A position-independent contour error modeling method for a five-axis measurement workstation, characterized in that: The following steps are involved: S1, assembly error modeling; S2, differential kinematic mapping of assembly errors; S3, kinematic modeling of five-axis measurement workstation; S4. Assembly error mapping of five-axis measurement workstation.

2. A position-independent contour error modeling method for a five-axis measurement workstation according to claim 1, characterized in that: In S1, assembly error modeling includes the following steps: S11. Homogeneous coordinate transformation. The homogeneous coordinate transformation matrix between coordinate system i and coordinate system j is: ； Where: and They represent the rotation transformation matrix and translation vector from coordinate system i to coordinate system j respectively; Represents the component of the translation vector from coordinate system i to coordinate system j on the x-axis; Represents the component of the translation vector from coordinate system i to coordinate system j on the y-axis; Represents the component of the translation vector from coordinate system i to coordinate system j on the z-axis; , , Represents the elements of the first row of the rotation matrix from coordinate system i to coordinate system j; , , Represents the elements of the second row of the rotation matrix from coordinate system i to coordinate system j; , , Represents the elements of the third row of the rotation matrix from coordinate system i to coordinate system j; S12. The homogeneous coordinate transformation matrix between coordinate system i and coordinate system j considering assembly error is: ; Where: It represents the increment of the homogeneous coordinate transformation matrix between coordinate system i and coordinate system j after considering the assembly error; Represents the standard homogeneous coordinate transformation matrix between coordinate system i and coordinate system j without considering assembly error; Among them, the kinematic equation of assembly error is transformed into: ； Where: and They represent the position error parameter and attitude error parameter in the i coordinate system respectively, Represents the translation transformation matrix along the coordinate axes x, y, and z. Represents three rotation transformation matrices rotating around coordinate axes x, y, and z; S13. Get the kinematic matrix considering assembly error: ； Where: and They represent the position error parameters and attitude error parameters in the i coordinate system respectively.

3. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 2, characterized in that: In S12: Three rotation transformation matrices for rotation around coordinate axes x, y, and z Respectively expressed as: ； ； 。 4. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 1, characterized in that: In S2, establishing the differential kinematics mapping of assembly errors includes the following steps: S21: Based on the standard link definition and joint coordinates, according to the homogeneous coordinate transformation matrix, the differential motion matrix of the assembly error between coordinate system i and coordinate system j is: ； Where: The differential motion matrix representing the assembly error between coordinate system i and coordinate system j; Represents the transpose of the rotation matrix from coordinate system i to coordinate system j; Represents a 6x6 dimensional real matrix space; Differential Motion Matrix Used to describe the transfer relationship between assembly errors in different coordinate systems. Represents vector The spinor-symmetric matrix of is expressed as: ； S22: The differential transformation of the coordinate system includes differential translation transformation and differential rotation transformation. The differential motion vector of coordinate system i is: ； Where: and They represent the differential translation vector and differential rotation vector in the i coordinate system respectively; The relationship between the differential motion vector in different coordinate systems and the differential motion matrix in the corresponding coordinate system is as follows: ； Where: represents the differential motion vector in coordinate system j; represents the differential motion vector in coordinate system j; use The differential motion vector in the i coordinate system Transform to the j coordinate system and obtain .

5. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 1, characterized in that: In S3, the kinematic modeling of the five-axis measurement workstation includes the following steps: S31, along the kinematic chain of the tool, starting from the basic coordinate system of the workstation, passing through the X-axis, Y-axis, Z-axis, C-axis, A-axis, and finally reaching the tool, the homogeneous coordinate transformation matrices between adjacent axes are: ； ； ； ； ； ； Where: Represents the homogeneous coordinate transformation matrix from base coordinate system 0 to coordinate system X; Represents the homogeneous coordinate transformation matrix from coordinate system X to coordinate system Y; Represents the homogeneous coordinate transformation matrix from coordinate system Y to coordinate system Z; Represents the homogeneous coordinate transformation matrix from coordinate system Z to coordinate system C; Represents the homogeneous coordinate transformation matrix from coordinate system C to coordinate system A; Represents the homogeneous coordinate transformation matrix from coordinate system A to tool coordinate system T; , , Indicates the clamping position of the tool; Along the kinematic chain of the workpiece, starting from the workstation base coordinate system and then reaching the workpiece, the homogeneous coordinate transformations of adjacent axes are: ； Where: Represents the homogeneous coordinate transformation matrix from the workstation base coordinate system to the workpiece coordinate system; , , Indicates the clamping position of the workpiece; S32, perform inverse transformation of the homogeneous coordinate matrix. This continuous coordinate transformation process is expressed as: ； Get the tool position and posture in the workpiece coordinate system: ； Where: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T without considering the assembly error; , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems without considering assembly errors; x, y, z represent the tool position in the workpiece coordinate system; I, J, K represent the tool posture in the workpiece coordinate system.

6. A position-independent contour error modeling method for a five-axis measurement workstation according to claim 5, characterized in that: In S32, the corresponding error term is multiplied by the corresponding local kinematic chain coordinate transformation relationship to obtain the forward kinematic transformation relationship considering the error, so as to obtain the tool position and posture in the workpiece coordinate system, and the formula is as follows: ； Where: represents the homogeneous coordinate transformation matrix from the workpiece coordinate system W to the tool coordinate system T considering the assembly error; , , , , , represents the homogeneous coordinate transformation matrix between adjacent coordinate systems considering assembly errors; , , , , , It represents the increment of the homogeneous coordinate transformation matrix between adjacent coordinate systems after considering the assembly error; , , , , , Represents the homogeneous coordinate transformation matrix between adjacent coordinate systems.

7. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 1, characterized in that: In S4, the five-axis measurement workstation assembly error mapping includes the following steps: S41: according to the homogeneous coordinate transformation matrix between each motion axis obtained in the kinematic model of the five-axis measurement workstation, a homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis and tool local position coordinate system to the tool coordinate system is obtained by combination; S42: transforming local assembly errors of the workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis and tool from the local coordinate system to the tool coordinate system to obtain assembly errors at local positions in the tool coordinate system; S43: Obtain the total tool tip position error caused by the assembly errors of each axis in the tool coordinate system.

8. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 7, characterized in that: The homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis and tool local position coordinate system to the tool coordinate system is: ； Where: represents a 4×4 identity matrix; , , , , , , Represents the homogeneous coordinate transformation matrix from the workpiece, X-axis, Y-axis, Z-axis, C-axis, A-axis and tool local position coordinate system to the tool coordinate system; , , , , , Represents the homogeneous coordinate transformation matrix between adjacent motion axes.

9. A position-independent contour error modeling method for a five-axis measurement workstation according to claim 8, characterized in that: The assembly error at the local position in the tool coordinate system is: ； Where: ; represents the assembly error at the local position i in the coordinate system of the corresponding local position i; represents the assembly error at the local position i in the tool coordinate system T; Represents the differential motion matrix from the local position i coordinate system to the tool coordinate system T.

10. The position-independent contour error modeling method for a five-axis measurement workstation according to claim 9, characterized in that: The assembly error at the local position in the tool coordinate system is: The relationship between the position-independent spatial error at the tool position and the local assembly error is: ； Expand the cumulative form into matrix form: ; Among them, the local axis is used The relevant features or parameters are all arranged in a specific form; It is the total tool tip position error caused by the assembly errors of each axis in the tool coordinate system; and attitude error , The Jacobian matrix that maps the assembly errors of each axis to the spatial profile error of the tool end; It is the assembly error of each axis in the local position coordinate system of each axis.

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