A comprehensive error decoupling compensation method for a five-axis numerical control lapping and polishing machine tool

Abstract

This invention discloses a comprehensive error decoupling compensation method for a five-axis CNC polishing machine, comprising: 1. establishing homogeneous transformation matrices for the workpiece kinematic chain and tool kinematic chain of the five-axis polishing machine under ideal and error conditions; 2. establishing a comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the five-axis polishing machine based on the homogeneous transformation matrix; 3. spatially decoupling the comprehensive error transformation matrix of the five-axis polishing machine based on the small error compensation motion assumption, and establishing a comprehensive error compensation model for the five-axis polishing machine to achieve comprehensive error compensation. This invention, through kinematic analysis of a five-axis polishing machine, uses the homogeneous coordinate transformation method to establish a comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the machine tool, spatially decoupling the position and direction error compensation of each motion axis of the five-axis polishing machine, and establishing a comprehensive error compensation model for the five-axis polishing machine, providing a theoretical basis for real-time comprehensive error compensation of a five-axis CNC polishing machine.

Description

Technical Field

[0001] This invention relates to the field of five-axis CNC grinding and polishing machine tool processing, and more specifically to a comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool. Background Technology

[0002] The rapid development of the manufacturing industry and the rapid improvement of processing levels have placed increasingly higher demands on the machining accuracy of CNC machine tools. Five-axis CNC polishing machines can process optical surfaces with complex geometries and high surface finishes, which play a crucial role in aerospace, aviation, and defense. Five-axis CNC polishing machines have not only three translational axes but also two rotary axes, making their error compensation motion complex. The error compensation motion of their kinematic pairs exhibits a coupling effect; a change in one direction of motion can affect changes in other directions. The relative displacement between the tool and the workpiece determines the final machining accuracy, and the overall error between the tool and workpiece affects the machining accuracy of the CNC machine tool. Therefore, it is essential to compensate for the overall machine tool error. Summary of the Invention

[0003] To address the issue of low final machining accuracy in existing five-axis CNC polishing machines, this invention proposes a comprehensive error decoupling compensation method for five-axis CNC polishing machines. This method aims to establish a comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the machine tool through kinematic analysis and homogeneous coordinate transformation. Furthermore, it utilizes differential transformation to decouple and compensate for the comprehensive error spatially, thus providing a theoretical basis for real-time error compensation in five-axis CNC polishing machines.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution: The comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool of the present invention is characterized by the following steps: Step 1: Establish the homogeneous transformation matrices of the workpiece kinematic chain and the tool kinematic chain of the five-axis grinding and polishing machine under ideal and error conditions; Step 2: Based on the homogeneous transformation matrix, establish the comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the five-axis grinding and polishing machine. Step 3: Based on the motion assumption of small error compensation, the comprehensive error transformation matrix of the five-axis grinding and polishing machine is spatially decoupled, and a comprehensive error compensation model of the five-axis grinding and polishing machine is established to achieve compensation for comprehensive error.

[0005] The comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool described in this invention is characterized in that step 1 includes: Step 1.1: Using the machine tool origin as the origin of the coordinate system, and the machine tool transverse feed direction as the coordinate system origin... X The axial direction and longitudinal feed direction areY Axial direction, vertical feed direction is Z Establish a reference coordinate system along the axis. R ; Establish a workpiece coordinate system on the workpiece to be processed. W Establish a tool coordinate system at the tool center. K The established workpiece coordinate system W With the tool coordinate system K Orientation and reference coordinate system R The directions are consistent; Step 1.2: Using equation (1), obtain the workpiece kinematic chain of the five-axis grinding and polishing machine to the reference coordinate system under ideal machine tool conditions. R homogeneous transformation matrix : (1) In equation (1), y For five-axis grinding and polishing machine tools Y The displacement of the translational axis. For five-axis grinding and polishing machine tools B Rotation axis Y The rotation angle of the translation axis. For five-axis grinding and polishing machine tools C Rotation axis Z The rotation angle of the translation axis; Step 1.3: Using equation (2), obtain the tool kinematic chain of the five-axis grinding and polishing machine to the reference coordinate system under ideal machine tool conditions. R homogeneous transformation matrix : (2) In equation (2), x For five-axis grinding and polishing machine tools X The displacement of the translational axis. z For five-axis grinding and polishing machine tools Z The displacement of the translational axis. L The length of the cutting tool; Step 1.4 uses equation (3) to obtain the workpiece motion chain under the error condition of the five-axis polishing machine. X Translation axis to reference coordinate system R homogeneous transformation matrix : (3) In equation (3), , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Directional thermal drift error; Step 1.5: Using equation (4), obtain the workpiece motion chain under the error condition of the five-axis polishing machine. B Rotation axis relative Y Homogeneous transformation matrix of the axial coordinate system : (4) In equation (4), , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Directional thermal drift error; Step 1.6: Using equation (5), obtain the workpiece motion chain under the error condition of the five-axis polishing machine. C Rotating shaft to B Homogeneous transformation matrix of the rotation axis : (5) In equation (5), , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Directional thermal drift error; Step 1.7: Using equation (6), obtain the tool kinematic chain under the error condition of the five-axis polishing machine. X Translation axis to reference coordinate system R homogeneous transformation matrix : (6) In equation (6), , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Directional thermal drift error; Step 1.8: Using equation (7), obtain the Z-axis of the tool motion chain to the tool motion chain under the error condition of the five-axis grinding and polishing machine. X homogeneous transformation matrix of translation axis : (7) In equation (7), , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Directional thermal drift error; Step 1.9: Using equation (8), obtain the tool kinematic chain under the error condition of the five-axis polishing machine. S Spindle-to-tool kinematic chain Z homogeneous transformation matrix of translation axis : (8) In equation (8), , For five-axis grinding and polishing machine tools S On the spindle x, y The angular thermal drift error of the direction. , , For five-axis grinding and polishing machine tools S On the spindle x, y, z Translational thermal drift error in the direction; Step 1.10: Using equation (9), obtain the tool coordinate system of the tool motion chain under the error condition of the five-axis polishing machine. K arrive S Homogeneous transformation matrix of the principal axis : (9).

[0006] Furthermore, step 2 includes: Step 2.1: Using equation (10), obtain the workpiece coordinate system under error-free conditions of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (10) Step 2.2: Using equation (11), obtain the tool coordinate system under error-free conditions of the five-axis polishing machine. K Relative to the workpiece coordinate system W homogeneous transformation matrix : (11) Step 2.3: Using equation (12), obtain the workpiece coordinate system under the error condition of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (12) Step 2.4: Using equation (13), obtain the tool coordinate system under the condition that the five-axis polishing machine has errors. K To the workpiece coordinate system W homogeneous transformation matrix : (13) Step 2.5: Using equation (14), obtain the tool coordinate system under the condition that the five-axis polishing machine tool has errors. K Relative to the workpiece coordinate system W Comprehensive error matrix : (14) In equation (14), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Translational error on the translation axis , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Angular error on the translation axis; Step 2.6: Combining equations (1) and (14), the comprehensive error transformation matrix is ​​obtained. ].

[0007] Furthermore, step 3 includes: Step 3.1: Obtain the tool coordinate system using equation (15) K Relative to workpiece coordinate system W Transform Differential : (15) In equation (15), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Compensating differential motion on the translation axis , For five-axis grinding and polishing machine tools B Rotating shaft C The compensating differential motion of the rotating shaft; Step 3.2: Obtain the tool coordinate system using equation (16). K Relative to the workpiece coordinate system W Error compensation motion matrix : (16) Step 3.3: Combining equations (15) and (16), use equation (17) to obtain the error compensation amount for each axis of the machine tool: (17).

[0008] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in performing the method described therein, and the processor is configured to execute the program stored in the memory.

[0009] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program is executed by a processor to perform the steps of the method described thereon.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention comprehensively considers the complex error compensation motions of five-axis CNC polishing machines during workpiece machining, as these machines have not only three translational axes but also two rotary axes. The error compensation motions of the kinematic pairs exhibit a coupling effect; a change in one direction affects changes in others. Therefore, through kinematic analysis of the five-axis polishing machine, a comprehensive error transformation matrix between the coordinate systems of each kinematic pair is established based on homogeneous coordinate transformation. This yields the error compensation amounts for the machine's translational and rotary axes, providing a theoretical basis for calculating machine tool errors, achieving real-time error compensation, correcting control commands, and improving machining accuracy.

[0011] 2. Because there is a certain coupling relationship between the compensation motion values ​​of each kinematic pair of the machine tool and the error values ​​between the tool and the workpiece, it is necessary to decouple them based on the comprehensive error to obtain the position or direction error compensation motion amount of each kinematic pair. Therefore, based on the assumption of small error compensation motion, the relationship between machine tool error motion and compensation motion is analyzed. The position and direction error compensation motions of each motion axis of the five-axis grinding and polishing machine are decoupled, and a comprehensive error compensation model and algorithm for the five-axis grinding and polishing machine is established, providing a theoretical basis for real-time comprehensive error compensation of the five-axis CNC grinding and polishing machine. Attached Figure Description

[0012] Figure 1 This is a flowchart of the comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool according to the present invention; Figure 2 This is a schematic diagram of a five-axis CNC polishing machine. Figure 3 This is a schematic diagram of the motion relationship of a five-axis grinding and polishing machine. Detailed Implementation

[0013] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0014] Referring to the attached diagram, a comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine is presented. Based on the small-error compensation motion assumption, it analyzes the relationship between error motion and compensation motion, spatially decouples the position and direction error compensations of each motion axis of the five-axis grinding and polishing machine, and establishes a comprehensive error compensation model and algorithm for the five-axis grinding and polishing machine. This provides a theoretical basis for real-time comprehensive error compensation of the five-axis CNC grinding and polishing machine. Specifically, its flowchart is as follows: Figure 1 As shown, the method includes the following steps: Step 1: Establish the homogeneous transformation matrices of the workpiece kinematic chain and the tool kinematic chain under ideal and error conditions: Step 1.1: Using the machine tool origin as the origin of the coordinate system, such as... Figure 2 As shown, the transverse feed direction of the machine tool is taken as... X The axial direction and longitudinal feed direction are Y Axial direction, vertical feed direction is Z Establish a reference coordinate system along the axis. R ; Establish a workpiece coordinate system on the workpiece to be processed. W Establish a tool coordinate system at the tool center. K The established workpiece coordinate system W With the tool coordinate system K Orientation and reference coordinate system R They are in the same direction.

[0015] Step 1.2: Based on the structural characteristics of the five-axis grinding and polishing machine, such as... Figure 3 As shown, a five-axis CNC grinding and polishing machine tool can be divided into two motion chains, one of which is the machine tool workpiece motion chain: "bed" H — Y axis- B axis- C Shaft—Workpiece W When the machine tool workpiece kinematic chain moves, equation (1) is used to obtain the ideal state of the machine tool workpiece kinematic chain to the reference coordinate system. R Transformation matrix : (1) In equation (1), y For five-axis grinding and polishing machine tools Y The displacement of the translational axis. For five-axis grinding and polishing machine tools B Rotation axis Y The rotation angle of the translation axis. For five-axis grinding and polishing machine tools C Rotation axis Z The rotation angle of the translation axis.

[0016] Step 1.3, Tool Kinematic Chain of a Five-Axis CNC Grinding and Polishing Machine: Bed H — X axis- Z Axis—Spindle S — knives R When the machine tool tool kinematic chain moves, equation (2) is used to obtain the ideal state of the machine tool tool kinematic chain to the reference coordinate system. R Transformation matrix : (2) In equation (2), x For five-axis grinding and polishing machine tools X The displacement of the translational axis. z For five-axis grinding and polishing machine tools Z The displacement of the translational axis. L This represents the length of the cutting tool.

[0017] Step 1.4: During actual machining and production, machine tools will generate a series of errors, including geometric errors and thermal errors, due to factors such as assembly defects, component manufacturing, tool wear, component thermal deformation, and cutting forces. Y The translational shaft moves nominal displacement on the bed y At that time, due to the error of the machine tool, Y Translation axis relative to reference coordinate system R There are 6 motion errors and 3 thermal drift errors. Using equation (3), the workpiece motion chain under the error conditions of the five-axis polishing machine is obtained. X Translation axis to reference coordinate system R homogeneous transformation matrix : (3) In equation (3), , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Directional thermal drift error.

[0018] Step 1.5, when the machine tool B Rotation axis Ynominal angle of axis rotation At an angle, due to machine tool errors, B Rotation axis relative Y The translational axis has 6 motion errors and 3 thermal drift errors. Using equation (4), the workpiece motion chain under the error conditions of the five-axis polishing machine is obtained. B Rotation axis relative Y homogeneous transformation matrix of axis : (4) In equation (4), , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Directional thermal drift error.

[0019] Step 1.6, when the machine tool C Turntable Z nominal angle of axis rotation At an angle, due to machine tool errors, the C-turntable has 6 motion errors and 3 thermal drift errors. Using equation (5), the workpiece motion chain under the error conditions of the five-axis polishing machine is obtained. C Rotating shaft to B Homogeneous transformation matrix of the rotation axis : (5) In equation (5), , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Directional thermal drift error.

[0020] Step 1.7, when X The axis moves nominal displacement on the bed x At that time, due to the existence of machine tool errors, X Axis coordinate system relative to reference coordinate system R There are 6 motion errors and 3 thermal drift errors. Using equation (6), the tool kinematic chain under the error conditions of the five-axis grinding and polishing machine is obtained. X Translation axis to reference coordinate system R homogeneous transformation matrix : (6) In equation (6), , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Directional thermal drift error.

[0021] Step 1.8, when Z The axis moves nominal displacement on the bed z At that time, due to the error of the machine tool, Z relative axes coordinate system X The five-axis coordinate system has six motion errors and three thermal drift errors. Using equation (7), the tool kinematic chain under the error conditions of the five-axis polishing machine is obtained. Z Translational axis to tool kinematic chain X homogeneous transformation matrix of translation axis : (7) In equation (7), , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Directional thermal drift error.

[0022] Step 1.9: When the machine tool spindle rotates, due to the machine tool's inherent error and the spindle's lack of geometric error, the machine tool spindle only has 5 thermal drift errors. Using equation (8), the tool motion chain under the error condition of the five-axis grinding and polishing machine is obtained. S Spindle-to-tool kinematic chain Z homogeneous transformation matrix of translation axis : (8) In equation (8), , For five-axis grinding and polishing machine tools S On the spindle x, y The angular thermal drift error of the direction. , , For five-axis grinding and polishing machine tools S On the spindle x, y, z Translational thermal drift error in direction.

[0023] Step 1.10: Considering the frequent tool changes required by CNC machine tools, the tool length is determined during modeling. L Separate modeling, assuming the tool is completely fixed on the spindle, with no motion or rotational errors, and no thermal errors, the tool coordinate system of the tool motion chain under the error condition of the five-axis grinding and polishing machine is obtained using equation (9). K arrive S Homogeneous transformation matrix of the principal axis : (9) Step 2: Based on the homogeneous transformation matrix, establish the comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the five-axis grinding and polishing machine.

[0024] Step 2.1: Under ideal conditions, the tool tip coincides with the theoretical cutting point on the workpiece, such as... Figure 2 As shown, using equation (10), the workpiece coordinate system under error-free conditions of a five-axis polishing machine is obtained. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (10) Step 2.2: Using equation (10), obtain the workpiece coordinate system under error-free conditions of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines CHomogeneous transformation matrix of the rotation axis : (11) Step 2.3: Using equation (12), obtain the workpiece coordinate system under the error condition of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (12) Step 2.4: Using equation (13), obtain the tool coordinate system under the condition that the five-axis polishing machine has errors. K To the workpiece coordinate system W homogeneous transformation matrix : (13) Step 2.5, Tool Coordinate System K Relative to the workpiece coordinate system W The transformation matrix can be regarded as a superposition of a comprehensive error matrix under ideal conditions. Using equation (14), the tool coordinate system under the condition that the five-axis polishing machine tool has errors can be obtained. K Relative to the workpiece coordinate system W Comprehensive error matrix : (14) In equation (14), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Translational error on the translation axis , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z The angular error on the translation axis.

[0025] Step 2.6: Combining equations (1)-(14), the comprehensive error transformation matrix is ​​obtained. ].

[0026] Step 3: Based on the small error compensation motion assumption, spatially decouple the comprehensive error transformation matrix of the five-axis grinding and polishing machine, and establish a comprehensive error compensation model for the five-axis grinding and polishing machine to achieve compensation for the comprehensive error. Step 3.1: Error compensation of a five-axis CNC polishing machine tool must be achieved through the differential motion of each kinematic joint of the machine tool, so that the workpiece coordinate system and the tool coordinate system coincide in space. Since there is a certain coupling relationship between the compensation kinematic chain of each kinematic joint of the machine tool and the error values ​​between the tool and the workpiece, it is necessary to decouple according to the comprehensive error of the machine tool to obtain the compensation motion amount on the position or direction error of each kinematic joint. Based on the small error compensation assumption, according to the kinematic differential transformation principle of the machine tool, the machine tool coordinate system is obtained by using equation (15). K Relative to workpiece coordinate system W Transform Differential : (15) In equation (15), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Compensating differential motion on the translation axis , For five-axis grinding and polishing machine tools B Rotating shaft C The compensating differential motion of the rotating shaft.

[0027] Step 3.2: Based on the small error assumption, the tool coordinate system is obtained using equation (16). K Relative to the workpiece coordinate system W Error-compensated motion matrix: (16) Step 3.3: Combining equations (15) and (16), use equation (17) to obtain the error compensation amount for each axis of the machine tool: (17) In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0028] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0029] In summary, through motion error analysis of a five-axis CNC grinding and polishing machine, a comprehensive error model was established using homogeneous coordinate transformation, and the relationship between error motion and compensation motion was further analyzed. Based on the assumption of small error compensation motion, the interrelationship between error motion and compensation motion was analyzed, and the position and direction error compensation motions of each motion axis of the five-axis grinding and polishing machine were decoupled. The error compensation amounts of each kinematic pair of the five-axis CNC grinding and polishing machine were obtained, providing a theoretical basis for real-time compensation of the five-axis CNC grinding and polishing machine.

Claims

1. A comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine, characterized in that, Includes the following steps: Step 1: Establish the homogeneous transformation matrices of the workpiece kinematic chain and the tool kinematic chain of the five-axis grinding and polishing machine under ideal and error conditions; Step 2: Based on the homogeneous transformation matrix, establish the comprehensive error transformation matrix between the coordinate systems of each kinematic pair of the five-axis grinding and polishing machine. Step 3: Based on the motion assumption of small error compensation, the comprehensive error transformation matrix of the five-axis grinding and polishing machine is spatially decoupled, and a comprehensive error compensation model of the five-axis grinding and polishing machine is established to achieve compensation for comprehensive error.

2. The comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool according to claim 1, characterized in that, Step 1 includes: Step 1.1: Using the machine tool origin as the origin of the coordinate system, and the machine tool transverse feed direction as the coordinate system origin... X Axial direction and longitudinal feed direction are Y Axial direction, vertical feed direction are Z Establish a reference coordinate system along the axis. R ; Establish a workpiece coordinate system on the workpiece to be processed. W Establish a tool coordinate system at the tool center. K The established workpiece coordinate system W With the tool coordinate system K Direction and reference coordinate system R The directions are consistent; Step 1.2: Using equation (1), obtain the workpiece kinematic chain of the five-axis grinding and polishing machine to the reference coordinate system under ideal machine tool conditions. R homogeneous transformation matrix : (1) In equation (1), y For five-axis grinding and polishing machine tools Y The displacement of the translational axis. For five-axis grinding and polishing machine tools B Rotation axis Y The rotation angle of the translation axis. For five-axis grinding and polishing machine tools C Rotation axis Z The rotation angle of the translation axis; Step 1.3: Using equation (2), obtain the tool kinematic chain of the five-axis grinding and polishing machine to the reference coordinate system under ideal machine tool conditions. R homogeneous transformation matrix : (2) In equation (2), x For five-axis grinding and polishing machine tools X The displacement of the translational axis. z For five-axis grinding and polishing machine tools Z The displacement of the translational axis. L The length of the cutting tool; Step 1.4 uses equation (3) to obtain the workpiece motion chain under the error condition of the five-axis polishing machine. X Translation axis to reference coordinate system R homogeneous transformation matrix : (3) In equation (3), , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Y On the translation axis x, y, z Directional thermal drift error; Step 1.5: Using equation (4), obtain the workpiece motion chain under the error condition of the five-axis polishing machine. B Rotation axis relative Y Homogeneous transformation matrix of the axial coordinate system : (4) In equation (4), , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools B On the rotating shaft x, y, z Directional thermal drift error; Step 1.6: Using equation (5), obtain the workpiece motion chain under the error condition of the five-axis polishing machine. C Rotating axis to B Homogeneous transformation matrix of the rotation axis : (5) In equation (5), , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools C On the rotating shaft x, y, z Directional thermal drift error; Step 1.7: Using equation (6), obtain the tool kinematic chain under the error condition of the five-axis polishing machine. X Translation axis to reference coordinate system R homogeneous transformation matrix : (6) In equation (6), , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools X On the translation axis x, y, z Directional thermal drift error; Step 1.8: Using equation (7), obtain the Z-axis of the tool motion chain to the tool motion chain under the error condition of the five-axis grinding and polishing machine. X homogeneous transformation matrix of translation axis : (7) In equation (7), , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z The angular error of the direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Displacement error in direction. , , For five-axis grinding and polishing machine tools Z On the translation axis x, y, z Directional thermal drift error; Step 1.9: Using equation (8), obtain the tool kinematic chain under the error condition of the five-axis polishing machine. S Spindle-to-tool kinematic chain Z homogeneous transformation matrix of translation axis : (8) In equation (8), , For five-axis grinding and polishing machine tools S On the spindle x, y The angular thermal drift error of the direction. , , For five-axis grinding and polishing machine tools S On the spindle x, y, z Translational thermal drift error in the direction; Step 1.10: Using equation (9), obtain the tool coordinate system of the tool motion chain under the error condition of the five-axis polishing machine. K arrive S Homogeneous transformation matrix of the principal axis : (9)。 3. The comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool according to claim 2, characterized in that, Step 2 includes: Step 2.1: Using equation (10), obtain the workpiece coordinate system under error-free conditions of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (10) Step 2.2: Using equation (11), obtain the tool coordinate system under error-free conditions of the five-axis polishing machine. K Relative to the workpiece coordinate system W homogeneous transformation matrix : (11) Step 2.3: Using equation (12), obtain the workpiece coordinate system under the error condition of the five-axis polishing machine. W Compared to five-axis grinding and polishing machines C Homogeneous transformation matrix of the rotation axis : (12) Step 2.4: Using equation (13), obtain the tool coordinate system under the condition that the five-axis polishing machine has errors. K To the workpiece coordinate system W homogeneous transformation matrix : (13) Step 2.5: Using equation (14), obtain the tool coordinate system under the condition that the five-axis polishing machine tool has errors. K Relative to the workpiece coordinate system W Comprehensive error matrix : (14) In equation (14), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Translational error on the translation axis , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Angular error on the translation axis; Step 2.6: Combining equations (1) to (14), the comprehensive error transformation matrix is ​​obtained. ].

4. The comprehensive error decoupling compensation method for a five-axis CNC grinding and polishing machine tool as described in claim 3, characterized in that, Step 3 includes: Step 3.1: Obtain the tool coordinate system using equation (15) K Relative to workpiece coordinate system W Transformation Differential : (15) In equation (15), , , For five-axis grinding and polishing machine tools X Translation axis Y Translation axis Z Compensating differential motion on the translation axis , For five-axis grinding and polishing machine tools B Rotating shaft C The compensating differential motion of the rotating shaft; Step 3.2: Obtain the tool coordinate system using equation (16). K Relative to the workpiece coordinate system W Error compensation motion matrix : (16) Step 3.3: Combining equations (15) and (16), use equation (17) to obtain the error compensation amount for each axis of the machine tool: (17)。 5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-4, the processor being configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the method according to any one of claims 1-4.

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