CAM post-optimization method and system for geometric error compensation of multi-axis linkage numerical control machine tool

Abstract

The invention relates to the technical field of numerical control machining, in particular to a CAM post-optimization method and system for geometric error compensation of a multi-axis linkage numerical control machine tool. The method comprises the following steps: firstly, carrying out kinematics analysis and geometric error modeling on a target machine tool, and deploying the target machine tool in a CAM post-optimization module; then actual state parameters of the target machine tool in the machining process are collected in real time through a laser interferometer; a motion instruction of a target machine tool and a detection result of a laser interferometer are synchronously obtained through a CAM post-optimization module, and then geometric errors of a linear axis and a rotating axis in the operation process of the target machine tool are calculated in real time through a kinematic model and a geometric error model. According to the method, different linear axis compensation modes are adopted for different instructions; and a cutter shaft attitude vector error and a cutter cutting point position error are calculated in combination with inverse kinematics, and are corrected step by step. The problem that the error compensation precision of a controller in an existing numerical control machine tool is insufficient can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical control machining, and in particular to a CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool, and a corresponding computer program product, a CAM post-optimization module, and a multi-axis linkage numerical control machine tool processing system. Background Art

[0002] Machine tool geometric errors usually include the positioning error and straightness error of linear axes, as well as the deviation of the rotation center of rotary axes, etc. These errors will directly affect the actual position of the tool point, resulting in machining deviation. The core of constructing an error model is to analyze the motion accuracy of the machine tool using measuring devices (such as laser interferometers, laser trackers, etc.) and establish a mathematical model to describe the change of geometric errors with the motion state of the machine tool. In the post-processing stage, the tool path is compensated in combination with the geometric error model. For example, for a five-axis machine tool, the deviation of the swing center of the rotary axis may cause the position deviation of the tool during the machining of complex curved surfaces. The post-processing can correct the motion trajectory of the rotary axis and dynamically adjust the tool path.

[0003] Traditional geometric error compensation mostly relies on internal implementation in the machine tool controller, but the compensation range is limited, and usually only specific errors (such as single-axis positioning error) are corrected. In addition, the real-time compensation in the machine tool controller is limited by the hardware performance and is difficult to handle complex geometric error models, especially in multi-axis linkage or high-speed machining scenarios. The post-processing performs compensation before generating the NC code, can optimize each tool path point according to the global path data, and overcomes the limitations of the controller compensation. The post-processing can flexibly adjust the compensation parameters according to different machining environments (such as the influence of temperature and humidity changes on the machine tool). In ultra-precision machining, the influence of tool path errors on machining quality is significantly amplified. Through pre-compensation, the post-processing can effectively control geometric errors and meet the accuracy requirements of the micron and nanometer levels.

[0004] Machine tool controller compensation is a technology implemented in the control system of CNC machine tools to reduce machining errors and improve machining accuracy. Its basic principle is based on the detection and modeling of machine tool errors. During the operation of the machine tool, the motion commands of each axis are corrected in real time, so as to offset the influence of the machine tool's own geometric errors, thermal errors, dynamic errors, etc. on the machining results. The controllers equipped with modern CNC machine tools (such as FANUC, SIEMENS, HEIDENHAIN, etc.) usually have some automated compensation functions. Through the machine tool's sensors or pre-stored error data tables, error detection and real-time compensation are achieved. The machine tool controller can correct the error by looking up the error table. This implementation method is simple but has limited response ability to the dynamic changes of the error. It can also calculate the compensation value in real time through the mathematical model method to achieve dynamic compensation, but its calculation complexity is relatively high. Or measure the error value through sensors (such as laser interferometers, grating scales) and feedback it to the machine tool controller for compensation. Its compensation accuracy is relatively high, but the compensation cost is also relatively high. In short, for the controllers equipped with CNC machine tools, the computing power and response speed of the controller may not meet the real-time requirements of complex compensation models, and the compensation effect depends on the accuracy of the error model. Summary of the Invention

[0005] To solve the problem that the controller of the existing CNC machine tool is limited by the computing power and response speed, resulting in insufficient error compensation accuracy, the present invention provides a CAM post-optimization method for geometric error compensation of multi-axis linkage CNC machine tools.

[0006] The technical solution provided by the present invention is as follows:

[0007] A CAM post-optimization method for geometric error compensation of multi-axis linkage CNC machine tools, which includes:

[0008] First, perform kinematic analysis and geometric error modeling on the target machine tool and deploy it in a CAM post-optimization module. The modeling process includes:

[0009] Construct the kinematic chain equation of the target machine tool with a five-axis machine tool as the basic model and generate the corresponding kinematic model. Use the double turntable configuration to construct the geometric error characteristic matrix of the target machine tool, integrate the error elements of each linear axis and each rotary axis to deduce the error transfer equation, and establish a geometric error model that represents the error mapping relationship from the machine tool coordinate system to the workpiece coordinate system.

[0010] Second, collect the actual state parameters of the target machine tool during the machining process in real time through a laser interferometer. Synchronously obtain the motion commands of the target machine tool and the detection results of the laser interferometer through a CAM post-optimization module, and then use the kinematic model and geometric error model to calculate the geometric errors of the linear axis and rotary axis during the operation of the target machine tool in real time and perform compensation.

[0011] Among them, the compensation method for the linear axis is as follows: when executing the G00 command each time, calculate the position point error E(P) according to the ideal coordinates of the tool cutting point in the workpiece coordinate system. When E(P) exceeds the preset error tolerance value ξ, perform rapid positioning compensation on the cutting point. When executing the G01 command each time, equally divide the straight line between the starting point and the ending point in the target machine tool movement according to the preset interpolation step Δs, calculate the theoretical coordinates and errors of each interpolation point, and use the point-by-point compensation method to perform linear interpolation compensation on the linear trajectory. When executing the G02 / G03 command each time, determine the starting point, ending point, and radius of the ideal arc in the target machine tool movement, calculate the center coordinates and starting angle according to the interpolation direction of the arc; divide the arc into n segments with equal radian to obtain n + 1 segmentation points; calculate the errors of each segmentation point, and use the point-by-point compensation method to perform circular interpolation error compensation on the arc trajectory.

[0012] The compensation method for the rotary axis is as follows: map the compensation amount in the workpiece coordinate system to the local coordinate systems of each axis of the machine tool through kinematic inverse solution, and calculate the tool axis attitude vector error V p and the tool cutting point position error E p . First, correct the rotation angles of the A-axis and C-axis through the iterative compensation method to eliminate the tool axis attitude error; then, adjust the tool cutting point position through the iterative compensation method to correct the position error of the tool cutting point.

[0013] As a further improvement of the present invention, the kinematic chain equation of the five-axis machine tool can be expressed as:

[0014] T total = T trans ·R axis1 ·R axis2 ·R axis3 ·R axis4 ·R axis5

[0015] In the above formula, T total is the total transformation matrix, T trans is the translation transformation matrix, and R axis1 ~R axis5 are the rotary axis transformation matrices; among them, when there is any missing rotary axis in the five-axis machine tool for the target machine tool first, the corresponding rotary axis transformation matrix is set to the identity matrix I.

[0016] The kinematic model of the five-axis machine tool is expressed as:

[0017] T base ·T work ·R A ·R B ·R C ·P work = T base ·T tool ·RA ·R B ·R C ·P tool

[0018] In the above formula, T base is the transformation matrix of the reference coordinate system, and T work is the translation transformation matrix of the workpiece coordinate system. R A ~R C respectively represent the rotation transformation matrices about the corresponding axes A~C; P work is the machining point position in the workpiece coordinate system, T tool is the translation transformation matrix of the tool coordinate system, and P tool is the tip point position in the tool coordinate system.

[0019] As a further improvement of the present invention, the geometric error model of the machine tool is expressed as:

[0020]

[0021] In the above formula, P w and V w respectively represent the actual position coordinates and actual vector coordinates of the tool in the workpiece coordinate system; P w' and V w' respectively represent the ideal position coordinates and ideal vector coordinates of the tool in the workpiece coordinate system.

[0022] As a further improvement of the present invention, the process of rapid positioning compensation for the cutting point includes:

[0023] Assume that the ideal coordinates of the tool cutting point in the workpiece coordinate system are P0(P x0 , P y0 , P z0 ). The position error E(P) of the cutting point is calculated through the geometric error model; the actual cutting point P w of the tool is:

[0024] P w = P0 + E(P) = (P x0 + E(P) x , P y0 + E(P) y , P z0 + E(P) z )

[0025] In the above formula, E(P) x , E(P) y and E(P) z are respectively the error components of the cutting point position along the X, Y, and Z directions.

[0026] When E(P) does not exceed the allowable error value ξ, it is considered that the positioning accuracy meets the requirements and no compensation is required; otherwise, error compensation is needed:

[0027] During the compensation process, first calculate the movement amounts of each axis, then calculate the corrected coordinate values after conversion, and finally issue compensation instructions according to the corrected coordinate values until the error value after compensation meets the requirements.

[0028] As a further improvement of the present invention, the cutter axis attitude vector error V p and the tool cutting point position error E p are calculated as follows:

[0029] When the cutter axis vector V is [V x V y V z T at this time, the rotation angles α and β of the A-axis and C-axis are inversely solved through the following formula:

[0030] α = k·arccos(V z ) k = ±1

[0031]

[0032] In the above formula, k represents a sign coefficient, and the sign selection follows the principle of motion continuity to determine the uniqueness of the angle. The swing range of the A-axis is -105° to +120°, and the rotation range of the C-axis is 360°. The angle values need to be reasonably determined according to the actual motion range of the machine tool.

[0033] Calculate the deviation of the rotation angles α and β of the two cutter axes in the actual vector coordinate V w and the ideal vector coordinate V w' to obtain the cutter axis attitude vector error V p .

[0034] When the tool cutting point coordinate P is [P x P y P z T at this time, the translation amounts of the X, Y, and Z axes can be inversely solved through the following formula:

[0035]

[0036] Among them, x ow , y ow , z ow are the position coordinate values in the workpiece coordinate system, and x om , y om , z om are the position coordinate values in the machine tool coordinate system.

[0037] Calculate the actual position coordinate P​​w and the ideal position coordinate P w' Calculate the deviations on the x, y, and z axes to obtain the tool cutting point position error E p .

[0038] As a further improvement of the present invention, the compensation process for the tool axis attitude vector error V p includes:

[0039] Define the rotation angles of the A-axis and C-axis after the i-th compensation as a i and β i , and the actual tool axis attitude vector is V i , then:

[0040] V i = T C (β i )·T A (α i )·V0

[0041] where T C (β i ) and T A (α i ) are the rotation transformation matrices of the C-axis and A-axis respectively, and V0 is the initial tool axis attitude vector.

[0042] Substitute the components of V i ’ into the formula to find the corresponding rotation angles α′ i and β′ i , let Δθ A and Δθ C be the allowable angle error values of the A-axis and C-axis respectively. If both of the following conditions are satisfied:

[0043]

[0044] then the compensation ends. Otherwise, calculate the rotation angles of the A-axis and C-axis in the next round as α i+1 and β i+1 , and continue the iterative compensation;

[0045]

[0046] In the above formula, η is a parameter used to suppress overshoot, and η ∈ (0, 1].

[0047] During the rotation angle adjustment process, when there are multiple sets of feasible solutions, the combination of rotation angles with the minimum Euclidean distance is preferentially selected.

[0048] As a further improvement of the present invention, the compensation method for the tool cutting point position error E p is:

[0049] After determining the cutting point position, reconstruct the motion chain by introducing a displacement correction amount:

[0050]

[0051] Among them, P wj is the actual cutting point position at the j-th iteration, R C , R A is the rotation axis transformation matrix, T m is the translation matrix of the moving axis, l m is the translation amount, Δl m,j is the displacement correction amount of the moving axis m (X / Y / Z) at the j-th iteration, and P0 is the initial tool tip point.

[0052] When the position residual satisfies the threshold ε p , it is determined that the calibration is completed;

[0053]

[0054] Among them, P xj , P yj , c are the measured coordinates of the actual cutting point after the j-th iteration, and P x , P y , P z are the theoretical target position coordinates.

[0055] Otherwise, generate an incremental compensation instruction through the following formula:

[0056] Δl m,j+1 = Δl m,j + λ(P m - P' mj )

[0057] In the above formula, λ is a parameter used to control the convergence speed, and Δl m,j+1 is the new compensation amount of the moving axis m at the (j + 1)-th iteration, and P mj is the actual position component in the direction of axis m after the j-th iteration.

[0058] The present invention also includes a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool as described above. Furthermore, according to the motion instructions of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, the geometric errors of the linear axis and the rotary axis during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

[0059] The present invention further includes a CAM post-optimization module, which includes a memory, a processor, and a computer program stored on the memory and running on the processor. When the computer program is executed by the processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool as described above. Furthermore, according to the motion instructions of the target machine tool and the actual state parameters during the machining process of the target machine tool obtained synchronously, the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

[0060] The present invention further includes a multi-axis linkage numerical control machine tool processing system, which includes: a five-axis machine tool, a laser interferometer, and a CAM post-optimization module. Among them, the laser interferometer is used to collect the actual state parameters during the machining process of the five-axis machine tool in real time. The CAM post-optimization module is communicatively connected to the five-axis machine tool and the laser interferometer, and is used to synchronously obtain the motion instructions of the target machine tool and the detection results of the laser interferometer, and then implement the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool as described above; furthermore, according to the motion instructions of the target machine tool and the actual state parameters during the machining process of the target machine tool obtained synchronously, the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

[0061] The present invention has the following beneficial effects:

[0062] By combining geometric error modeling and compensation strategies, the present invention corrects the tool path of integral blisk parts, reduces the influence of geometric errors on the machining results, thereby improving the machining accuracy of the parts and meeting the requirements for micron-level and even nanometer-level accuracy in high-end manufacturing fields such as aerospace. Among them, the error compensation of the machining process is completed in the post-processing stage. In view of the particularity of the complex curved surface of integral blisk parts, this solution supports dynamic adjustment of CL data to compensate for the trajectory deviation caused by the geometric errors of the machine tool and ensure the smoothness and consistency of the machining path. Finally, by directly embedding the error compensation into the post-processing module, the present invention makes this method adaptable to different types of five-axis machine tools and control systems, especially for the machining environment of machine tools with large errors, and improves the robustness of the process plan.

[0063] The technical solution provided by the present invention integrates a post - processing algorithm that combines geometric error modeling and screw kinematics solution. By modeling, measuring, and compensating for the geometric errors of a five - axis machine tool, and combining with the post - processing function, the tool path is corrected during the generation of NC code, which can effectively eliminate the influence of geometric errors, thereby improving the accuracy of the five - axis machine tool in complex surface machining. By establishing a fusion model of machine tool kinematics and geometric errors, the collaborative optimization of the computer - aided manufacturing (CAM) system and the computer numerical control (CNC) system at the machining accuracy level is realized, and the manufacturing efficiency of complex surface parts is improved. Description of the Drawings

[0064] Figure 1 It is a flowchart of the steps of the CAM post - optimization method for geometric error compensation of a multi - axis linkage numerical control machine tool provided in Embodiment 1 of the present invention.

[0065] Figure 2 It is a schematic diagram of each axis of the MIKRON UCP 800Duro machine tool used in the verification experiment.

[0066] Figure 3 It is a schematic diagram of the topological structure of the MIKRON UCP 800Duro machine tool used in the verification experiment.

[0067] Figure 4 It is a schematic diagram of the collimation debugging of the mirror group and the moving axis in the laser interferometer in the verification experiment.

[0068] Figure 5 It is the fitting result of some error elements in the verification experiment.

[0069] Figure 6 It is a distribution diagram of the cutting path and measurement points selected on the blisk in the verification experiment.

[0070] Figure 7 It is a comparison of the measurement point errors of the present invention and the control group scheme before and after compensation in the verification experiment. Detailed Embodiment

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0072] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the technical field to which this invention belongs. The terms used in the description of the present invention herein are for the purpose of describing specific embodiments only and are not intended to limit the present invention. The term "or / and" as used herein includes any and all combinations of one or more of the related listed items.

[0073] Embodiment 1

[0074] This embodiment provides a CAM post - optimization method for geometric error compensation of multi - axis linkage numerically controlled machine tools. The purpose of the technical solution provided in this embodiment is to correct the tool path of integral blisk parts by combining geometric error modeling and compensation strategies, reduce the influence of geometric errors on the machining results, thereby improving the machining accuracy of parts and meeting the requirements for micron - level and even nanometer - level accuracy in high - end manufacturing fields such as aerospace.

[0075] In the process of controlling the machining accuracy of numerically controlled machine tools in this embodiment, a post - processing strategy is adopted. Post - processing is one of the core functions of CAM software, and its importance has become increasingly prominent in the modern high - precision manufacturing environment. Its task is to convert the tool path (CL data) into NC codes (such as G codes) that can be executed by specific numerically controlled machine tools, ensuring that the machine tool can machine the designed parts according to the expected accuracy. With the increasing requirements for micron - level and even nanometer - level accuracy in modern manufacturing, post - processing can consider the influence of the machining environment, machine tool characteristics, and physical factors on the machining path. Therefore, this embodiment applies it to processing complex - surface parts and dealing with the geometric errors of machine tools.

[0076] In the post - processing stage, aiming at the particularity of the complex surface of integral blisk parts, the solution provided in this embodiment can dynamically adjust the CL data, compensate for the trajectory deviation caused by the geometric errors of the machine tool, and ensure the smoothness and consistency of the machining path. Finally, by directly embedding the error compensation function into the post - processing module, this method is adapted to different types of five - axis machine tools and control systems, especially for the machining environment of machine tools with large errors, improving the robustness of the process plan.

[0077] Specifically, the solution provided in this embodiment first constructs the function of converting the basic CL file in the post - processing module into NC codes recognizable by the machine tool according to the inverse kinematics solution of screw theory. Then, a Renishaw laser interferometer is used to measure the geometric errors of the machine - tool state measurement axes when machining blisk parts on a Mikron UCP 800 Duro machine tool and perform error modeling. The error amount of each tool - path point is obtained through the error model and compensated into the path points, and then the inverse solution is performed to obtain the compensated NC codes. By directly integrating the error compensation model in post - processing, this method optimizes the delay problem of real - time compensation during machining and is suitable for the machining of high - precision and complex - surface parts.

[0078] Specifically, the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool provided in this embodiment is as follows Figure 1 shown, including the following processes:

[0079] I. Conduct kinematic analysis and geometric error modeling on the target machine tool and deploy it in a CAM post-optimization module.

[0080] Compared with three-axis machine tools, five-axis machine tools have two additional rotary axes. While improving machining diversity, they also introduce more geometric errors, that is, on the basis of linear axis positioning errors and straightness errors, etc., the positioning errors and position errors of the rotary axes are added. Whether it is basic modeling or geometric error modeling, rigid body kinematics or multi-body system dynamics methods are usually used to describe the relationship between the moving parts of the machine tool. Geometric error kinematic modeling adds an error matrix on the basis of coordinate transformation.

[0081] 1.1 Kinematic model of five-axis machine tool

[0082] The transformation from one coordinate system to another can mainly be achieved through three basic forms: translation transformation, rotation transformation, and composite transformation. These transformations can be uniformly described mathematically through homogeneous coordinate transformation matrices, thus providing an efficient and general expression for the mapping between coordinate systems.

[0083] Taking the machine tool base as the reference coordinate system, the position of the machining point in the workpiece coordinate system should be consistent with the position of the tool tip point in the tool coordinate system in the reference coordinate system.

[0084] Therefore, for five-axis machine tools with different configurations, this relationship can be described by establishing a unified equation. The following Table 1 shows the equation expressions of three types of configured machine tools:

[0085] Table 1: Kinematic chain formulas of common five-axis machine tool structures

[0086]

[0087] The transformation from one coordinate system to another can mainly be achieved through three basic forms: translation transformation, rotation transformation, and composite transformation. These transformations can be uniformly described mathematically through homogeneous coordinate transformation matrices, thus providing an efficient and general expression for the mapping between coordinate systems.

[0088] For translation transformation, the direction of the translated coordinate system is the same as that of the initial coordinate system. Assuming that the coordinate system OXYZ moves along the X-axis by a displacement of t x to O'X'Y'Z', the corresponding homogeneous coordinate transformation matrix is:

[0089]

[0090] Assume that the coordinate system OXYZ is displaced by a displacement of t along the Y-axis to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is: y The displacement to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is:

[0091]

[0092] Assume that the coordinate system OXYZ is displaced by a displacement of t along the Z-axis to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is: z The displacement to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is:

[0093]

[0094] Assume that the coordinate system OXYZ is first displaced by a displacement of t along the X-axis x and then by a displacement of t along the Y-axis y and then by a displacement of t along the Z-axis z to O'X'Y'Z', then its translation transformation along the X / Y / Z axes of the Cartesian coordinate system can be expressed as:

[0095]

[0096] For rotational transformation, the coordinate system rotates by a certain angle around a certain reference axis, thereby changing its attitude. Assume that the coordinate system OXYZ rotates by α around the X-axis to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is:

[0097]

[0098] Assume that the coordinate system OXYZ rotates by β around the Y-axis to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is:

[0099]

[0100] Assume that the coordinate system OXYZ rotates by γ around the Z-axis to O'X'Y'Z', then the corresponding homogeneous coordinate transformation matrix is:

[0101]

[0102] Assume that the coordinate system OXYZ rotates successively around multiple different axes. Each rotation is based on the new coordinate system after the previous rotation. Therefore, the order of rotational transformation has an important impact on the final result. The rotation order usually follows the motion chain order of the machine tool. For example, first rotate by an angle of α around the X-axis, then rotate by an angle of β around the Y-axis, and finally rotate by an angle of γ around the Z-axis. The composite rotational transformation matrix R total is:

[0103] R total = R z (γ)·Ry (β)·R x (α)

[0104] To unify the expression of the kinematic model of a five-axis machine tool, the kinematic chain equation can be standardized. Regardless of the number of rotating axes of the actual machine tool, the rotation axis transformation matrix can be added to both sides of the equation. If a certain rotating axis does not exist in reality, its corresponding transformation matrix can be set as the identity matrix, which will not affect the calculation results. In this way, the kinematic chain equation of the five-axis machine tool can be expressed as:

[0105] T total = T trans ·R axis1 ·R axis2 ·R axis3 ·R axis4 ·R axis5

[0106] In the above formula, T total is the total transformation matrix, T trans is the translation transformation matrix, and R axis1 to R axis5 are the rotation axis transformation matrices. If a certain rotating axis does not exist, for example, axes 3 and 5 do not exist, R axis3 and R axis5 can be set as the identity matrix I.

[0107] The unified equation is:

[0108] T base ·T work ·R A ·R B ·R C ·P work = T base ·T tool ·R A ·R B ·R C ·P tool

[0109] In the above formula, T base is the transformation matrix of the reference coordinate system, T work is the translation transformation matrix of the workpiece coordinate system, R A / B / C is the rotation transformation matrix around this axis, P work is the position of the machining point in the workpiece coordinate system, T tool is the translation transformation matrix of the tool coordinate system, and P tool is the position of the tool tip point in the tool coordinate system.

[0110] In this way, it is possible to adapt to five-axis machine tools with different configurations while maintaining the generality and consistency of the expression.

[0111] In the kinematic analysis of five-axis CNC machine tools, the homogeneous coordinate transformation matrix, as the core mathematical tool for describing spatial geometric transformations, can uniformly represent the translation and rotation relationships between coordinate systems. This matrix adopts the form of a 4×4 extended matrix, effectively solving the completeness problem of describing the rigid body motion in three-dimensional space. Its standard mathematical expression T is:

[0112]

[0113] In the above formula: R 3×3 is the rotation matrix, representing the rotational transformation of the coordinate system around the reference axis; P 3×1 is the translation vector, representing the linear displacement of the coordinate system along the coordinate axis; 0 1×3 is the zero vector, ensuring the homogeneity of matrix operations.

[0114] The composite motion synthesis matrix T total is obtained by multiplying the translation and rotation matrices in the order of the kinematic chain. For example, the coordinate system OXYZ first rotates by an angle α around the X-axis, then rotates by an angle β around the Y-axis, and finally translates by the displacement amounts t x 、t y 、t z to O'X'Y'Z':

[0115] T total = T trans ·R y (β)·R x (α)

[0116] After expansion, it is:

[0117]

[0118] If the order is reversed (translation first and then rotation), the calculation process of the composite motion synthesis matrix T' total will become:

[0119] T' total = R y (β)·R x (α)·T trans

[0120] The translation-rotation composite motion is realized through the chain multiplication of the homogeneous coordinate transformation matrix, and the core lies in strictly following the order of the kinematic chain. In five-axis NC machining, the composite transformation model provides a mathematical basis for tool path planning, NC code generation, and error compensation.

[0121] 1.2. Geometric Error Model

[0122] The error motion matrix T erroris a matrix that describes the error transformation of a machine tool during actual movement. If ΔT is the error characteristic matrix, then:

[0123] T error = T total + ΔT

[0124] For example, assume that δ x 、δ y 、δ z represent the linear errors on the X, Y, and Z axes, ∈ x 、∈ y 、∈ z represent the roll and pitch errors on the X, Y, and Z axes, δ a 、δ c represent the axial runout errors of the A and C rotary axes, ∈ a 、∈ c represent the tilt errors of the A and C rotary axes. Then, for a dual-turret type five-axis machine tool, the error characteristic matrix ΔT can be expressed as:

[0125]

[0126] Among them, the first matrix represents the linear axis errors, and the second matrix represents the rotary axis errors.

[0127] For the analysis of the geometric error model, the following defines the symbols of the position-related geometric errors and the position-independent geometric errors to establish the rigid body geometric error pose transfer relationship matrix on the workpiece side.

[0128] Assume that ΔT PIX represents the position-related geometric error of the X axis, ΔT PDX represents the position-independent geometric error of the X axis, ΔT PIY represents the position-related geometric error of the Y axis, ΔT PDY represents the position-independent geometric error of the Y axis, ΔT PIZ represents the position-related geometric error of the Z axis, ΔT PDZ represents the position-independent geometric error of the Z axis, ΔT PIA represents the position-related geometric error of the A axis, ΔT PDA represents the position-independent geometric error of the A axis, ΔT PIC represents the position-related geometric error of the C axis, ΔT PDC represents the position-independent geometric error of the C axis. The position-related geometric errors and the position-independent geometric errors are defined with their corresponding symbols as listed in the following table.

[0129] Table 2: Symbol Definition of Position-Related Geometric Errors

[0130]

[0131] Table 3: Definition of Location-Independent Geometric Error Symbols

[0132]

[0133] On this basis, establish the rigid body geometric error pose transfer relationship matrix T on the workpiece side tw :

[0134] T tw = ΔT PIA ·R x (α)·ΔT PDA ·ΔT PIC ·R z (γ)·ΔT PDC

[0135] Where:

[0136]

[0137] The rigid body geometric error pose transfer relationship matrix T on the tool side tt :

[0138]

[0139] Where:

[0140]

[0141] Calculate the position coordinate P of the tool in the workpiece coordinate system w and the vector coordinate V w , assuming that the position coordinate and direction coordinate of the tool in the tool coordinate system are P t and V t :

[0142] P w = T tw -1 T tt ·P t

[0143] V w = T tw -1 T tt ·V t

[0144] Given the ideal position coordinate and direction coordinate of the tool in the workpiece coordinate system, it can be obtained that:

[0145] P w' = (R x (α)·R z (γ)) -1 T trans(ty) ·T trans(tx) ·Ttrans(tz) ·P t

[0146] V w' = (R x (α)·R z (γ)) -1 T trans(ty) ·T trans(tx) ·T trans(tz) ·V t

[0147] Combining the above derivations, the spatial error formula of the five-axis machine tool is:

[0148]

[0149] Second, the actual state parameters of the target machine tool during the machining process are collected in real time through a laser interferometer. The motion commands of the target machine tool and the detection results of the laser interferometer are synchronously obtained through a CAM post-optimization module, and then the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and geometric error model, and compensated.

[0150] 2.1 Compensation method for geometric errors of linear axes

[0151] In this embodiment, the compensation method for the linear axis is as follows: When the G00 command is executed each time, the position point error E(P) is calculated according to the ideal coordinates of the tool cutting point in the workpiece coordinate system. When E(P) exceeds the preset error tolerance ξ, rapid positioning compensation is performed on the cutting point. When the G01 command is executed each time, the straight line between the starting point and the ending point in the target machine tool movement is equally divided according to the preset interpolation step Δs, the theoretical coordinates and errors of each interpolation point are calculated, and the linear trajectory is linearly interpolated and compensated using the point-by-point compensation method. When the G02 / G03 command is executed each time, the starting point, ending point and radius of the ideal arc in the target machine tool movement are determined, and the center coordinates and starting angle are calculated according to the interpolation direction of the arc; the arc is equally divided into n segments to obtain n + 1 segmentation points; the errors of each segmentation point are calculated, and the arc interpolation error of the arc trajectory is compensated using the point-by-point compensation method.

[0152] (I) G00 rapid positioning compensation

[0153] Assume that the ideal coordinates of the tool cutting point in the workpiece coordinate system are P0(P x0 , P y0 , P z0 ), calculate the position point error E(P), and the error components in the X, Y, and Z directions are E(P) x , E(P) y , E(P) z . The actual tool cutting point P s is:

[0154] P s = P0 + E(P) = (P x0 + E(P) x ,P y0 + E(P) y ,P z0 + E(P) z )

[0155] where E(P) is calculated from the geometric error model:

[0156]

[0157] Set the error tolerance ξ and determine whether the error value E(P) satisfies:

[0158]

[0159] If it is satisfied, it is considered that the positioning accuracy meets the requirements and no compensation is required; otherwise, error compensation is needed.

[0160] When performing the first compensation, use E(P) as the compensation amount and correct the tool cutting point P c1 to:

[0161] P c1 = P0 - E(P)

[0162] According to P c1 correct the G00 command value, and the correction process is divided into the following two steps:

[0163] (1) Calculate the movement amount of each axis:

[0164]

[0165] where x ow 、y ow 、z ow are the position coordinate values in the workpiece coordinate system, and x om 、y om 、z om are the position coordinate values in the machine tool coordinate system.

[0166] (2) Calculate the corrected coordinate values after conversion:

[0167] Convert the coordinate value P m,comp in each local coordinate system to the corrected coordinate value P w,comp in the workpiece coordinate system:

[0168] P w,comp = T m→w ·P m,comp

[0169] where Tm→w It is the homogeneous transformation matrix from the workpiece coordinate system to the machine tool base coordinate system.

[0170] Since there will still be errors when the machine tool moves according to the corrected instructions, it is necessary to calculate and compensate for the errors of each corrected instruction until the compensated error value satisfies ‖E(P)‖≤ξ.

[0171] Then, at the nth compensation, the cutting point P of the tool cn is corrected to:

[0172] P cn = P c(n-1) - E(P c(n-1) )

[0173] The actual arrival point P of the tool cutting sn is:

[0174] P sn = P c(n-1) - E(P c(n-1) ) + E(P cn )

[0175] The error E(P n ) after the nth compensation is:

[0176] E(P n ) = E(P c(n+1) ) - E(P cn )

[0177] The compensation ends until the compensated error value satisfies ‖E(P)‖≤ξ; otherwise, continue recursive compensation.

[0178] (2) G01 Linear Interpolation Compensation

[0179] The error compensation method for linear interpolation is to locate the errors during the movement and use the point-by-point compensation method for compensation. The process is as follows:

[0180] Set the ideal interpolation line L i , and set the starting point and the ending point as P1(P x1 , P y1 , P z1 ) and P2(P x2 , P y2 , P z2 ), respectively. Divide the line equally according to the interpolation step Δs, and calculate the theoretical coordinates of each interpolation point P i (P xi , P yi , P zi ). Then calculate the error at each interpolation point P i :

[0181] E(Pi ) = P si -P i

[0182] Determine whether the judgment error meets the accuracy requirement ξ. If ‖E(P i )‖≥ξ, then the corrected interpolation point is P ci :

[0183] P ci = P i -E(P i )

[0184] Calculate the actual arrival position P of the corrected interpolation point si :

[0185] P si = P ci +E(P i+1 )

[0186] Continue to iterate until all interpolation points meet the error requirements.

[0187] (III) G02 / G03 Circular Interpolation Compensation

[0188] The compensation method for circular interpolation is similar to that for linear interpolation. When performing circular interpolation in the XY plane, the CAM generates G02 / G03 instructions to determine the starting point, ending point, and radius of the ideal circle, which are set as P1(P x1 , P y1 , P z1 ), P2(P x2 , P y2 , P z2 ), and r respectively. According to the interpolation direction of the circle, the center coordinates O(x0, y0, z0) and the starting angles θ1, θ2 can be calculated. For the convenience of compensation, the circle is divided into n segments according to equal radian, and the corresponding n + 1 segmentation points P i can be expressed as:

[0189]

[0190] Among them, θ i represents the angle corresponding to the i-th equal division point and satisfies the linear relationship:

[0191]

[0192] For the compensation of circular interpolation error, the point-by-point compensation method is also adopted.

[0193] 2.1. Compensation Method for Geometric Error of Rotating Axis

[0194] In this embodiment, the compensation method for the rotation axis is as follows: the compensation amount in the workpiece coordinate system is mapped to the local coordinate systems of each axis of the machine tool through kinematic inverse solution, and the tool axis attitude vector error V p and the tool cutting point position error E p are calculated. First, the rotation angles of the A-axis and C-axis are corrected by the iterative compensation method to eliminate the tool axis attitude error; then, the tool cutting point position is adjusted by the iterative compensation method to correct the position error of the tool cutting point.

[0195] In a five-axis CNC machine tool, the geometric errors of the rotation axes (A-axis and C-axis) will cause deviations in the tool axis attitude vector and the tool cutting point position. To effectively suppress the influence of such errors on the machining accuracy, a phased compensation strategy needs to be adopted: first, the tool axis direction is corrected cyclically, and then the trajectory of the tool contact point is calibrated. From the derivation results of error modeling, the position coordinates P w of the tool in the workpiece coordinate system and the vector coordinates V w can be expressed as:

[0196]

[0197] where x w , y w , z w are the position coordinate values in the workpiece coordinate system, x p , y p , z p are the tool axis attitude coordinate values in the workpiece coordinate system, and α and β are the rotation angles of the A-axis and C-axis.

[0198]

[0199] When the tool axis vector V is [V x V y V z T , the rotation angles α and β of the A-axis and C-axis can be inversely solved as follows:

[0200] α = k·arccos(V z ) k = ±1

[0201]

[0202] where k represents the sign coefficient, which is used to determine the uniqueness of the angle. The swing range of the A-axis is -105° to +120°, and the rotation range of the C-axis is 360°. The angle values need to be reasonably determined according to the actual motion range of the machine tool.

[0203] When the tool cutting point coordinates P are [P x P y P z T ​​When, the translation amounts of the X, Y, and Z axes can be inversely solved by the following formula:

[0204]

[0205] where, x ow , y ow , z ow are the position coordinate values in the workpiece coordinate system, and x om , y om , z om are the position coordinate values in the machine tool coordinate system.

[0206] In this embodiment, the rotary axis error compensation is divided into two parts: the tool axis attitude vector compensation and the tool cutting point position compensation. The tool axis attitude vector compensation needs to correct the rotation angles of the A axis and the C axis to eliminate the tool axis attitude error. Since new errors will still be generated after the corrected movement, iterative compensation is required to gradually approach the target accuracy. The tool cutting point position compensation further corrects the position error of the tool cutting point after the tool axis attitude vector compensation.

[0207] Specifically, the compensation process of the tool axis attitude vector error V p includes:

[0208] Define the rotation angles of the A axis and the C axis after the i-th compensation as α i and β i , the actual tool axis attitude vector is V i , then:

[0209] V i = T C (β i )·T A (α i )·V0

[0210] where, T C (β i ) and T A (α i ) are the rotation transformation matrices of the C axis and the A axis respectively, and V0 is the initial tool axis attitude vector.

[0211] Substitute the components of V i into the formula to find the corresponding rotation angles α′ i and β′ i of the A axis and the C axis. Let Δθ A and Δθ C be the allowable angle error values of the A axis and the C axis respectively. If both of the following conditions are satisfied:

[0212]

[0213] Then the compensation ends. Otherwise, calculate the rotation angles of the A-axis and C-axis in the next round as α i+1 and β i+1 , and continue iterative compensation;

[0214]

[0215] In the above formula, η is a parameter used to suppress overshoot, and η ∈ (0, 1].

[0216] In addition, during the adjustment process of the rotation angles of the two axes, when there are multiple sets of feasible solutions, the rotation angle combination with the smallest Euclidean distance is preferentially selected.

[0217] Among them, the compensation method for the position error E p of the tool cutting point includes the following process:

[0218] After completing the attitude correction, the actual cutting point position P w is determined by the following formula:

[0219]

[0220] Among them, R C (β), R A (α) are rotation axis transformation matrices, l m is the translation amount, T m is the translation matrix of the moving axis, and P0 is the initial tool tip point.

[0221] After determining the cutting point position, by introducing the displacement correction amount (Δx j , Δy j , Δz j ) to reconstruct the motion chain:

[0222] P wj = R C R A T base ∏ m T m (l m + Δl m,j )P0,

[0223] Among them, P wj is the actual cutting point position of the j-th iteration, R C , R A are rotation axis transformation matrices, and Δl m,j is the displacement correction amount of the moving axis m (X / Y / Z) during the j-th iteration.

[0224] When the position residual satisfies the threshold ε p :

[0225]

[0226] Among them, P xj , P yj , and c are the measured coordinates of the actual cutting point after the j-th iteration, and P x , P y , P z are the theoretical target position coordinates.

[0227] Then it is determined that the calibration is completed; otherwise, an incremental compensation instruction is generated through the following formula:

[0228] Δl m,j+1 = Δl m,j + λ(P m - P mj )

[0229] In the above formula, λ is a parameter used to control the convergence speed, and Δl m,j+1 is the new compensation amount of the moving axis m at the (j + 1)-th iteration, and P mj is the actual position component in the direction of axis m after the j-th iteration.

[0230] Among them, when mapping the compensation amount in the workpiece coordinate system to the local coordinate systems of each axis of the machine tool, the kinematic inverse solution is required to obtain the displacement correction amount (Δx, Δy, Δz):

[0231]

[0232] Among them, (x ref , y ref , z ref ) is the origin of the reference system, θ is the plane projection angle, and ρ is the rotational axis coupling compensation function. Finally, each coordinate is corrected to obtain the required movement amount, that is, the error compensation amount for the rotational axis.

[0233] Finally, for the linear axis, after the above compensation and correction, the actual motion coordinate parameters (q x , q y , q z ) of the linear axis are recalculated:

[0234]

[0235] Among them, is the inverse kinematic transformation matrix of the linear axis of the machine tool, is the compensated theoretical target position (coordinates in the workpiece coordinate system), and P offset is the initial offset of the tool or workpiece (such as tool length compensation, workpiece installation deviation).

[0236] For the rotational axis, taking the A axis as an example, considering the radial runout, the actual screw coordinate is:

[0237]

[0238] In the above formula, δ rA is the radial runout of the A-axis, θ A is the rotation angle parameter, and ε A is the theoretical screw coordinate.

[0239] When calculating θ1 (assuming the A-axis corresponds to θ1), recalculate the rotation axis parameters:

[0240]

[0241] In the above formula, Δθ A0 is the zero-position error of the A-axis, ω1 is the rotation direction vector of the A-axis, ν is the linear velocity vector in the screw coordinate, z1 is the reference axis direction of the rotation center of the A-axis, and λ1 is the sign factor (taking ±1, used to determine the rotation direction).

[0242] Embodiment 2

[0243] Based on the solution of Embodiment 1, this embodiment further provides products that can implement the foregoing method, including computer program products, CAM post-optimization modules, and a multi-axis linkage numerical control machine tool processing system.

[0244] Among them, the computer program product provided in this embodiment includes a computer program. When the computer program is executed by a processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool as in Embodiment 1, and then, according to the motion instructions of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, uses the kinematic model and geometric error model to calculate the geometric errors of the linear axis and rotation axis during the operation of the target machine tool in real time, and generates correction instructions for compensating the corresponding errors.

[0245] The CAM post-optimization module provided in this embodiment includes a memory, a processor, and a computer program stored on the memory and running on the processor. When the computer program is executed by the processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool as in Embodiment 1, and then, according to the motion instructions of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, uses the kinematic model and geometric error model to calculate the geometric errors of the linear axis and rotation axis during the operation of the target machine tool in real time, and generates correction instructions for compensating the corresponding errors.

[0246] This embodiment further provides a multi-axis linkage numerical control machine tool processing system, which includes: a five-axis machine tool, a laser interferometer, and a CAM post-optimization module. Among them, the laser interferometer is used to collect the actual state parameters of the five-axis machine tool during the machining process in real time. The CAM post-optimization module is communicatively connected to the five-axis machine tool and the laser interferometer, and is used to synchronously obtain the motion instructions of the target machine tool and the detection results of the laser interferometer, and then implement the CAM post-optimization method for geometric error compensation of the multi-axis linkage numerical control machine tool as in Embodiment 1; furthermore, according to the motion instructions of the target machine tool and the actual state parameters of the target machine tool during the machining process obtained synchronously, the geometric errors of the linear axis and the rotary axis during the operation of the target machine tool are calculated in real time by using the kinematic model and the geometric error model, and a correction instruction for compensating the corresponding errors is generated.

[0247] In the actual application process, the CAM post-optimization module is essentially a computer device, and this computer device can be a notebook computer, a tablet computer, a desktop computer, or a medium and large computer device such as a rack-mounted server, a blade server, a tower server, or a cabinet server (including an independent server, or a server cluster composed of multiple servers) that can execute computer programs.

[0248] Specifically, the computer device of this embodiment at least includes, but is not limited to: a memory and a processor that can communicate with each other through a system bus. In this embodiment, the memory (i.e., the readable storage medium) includes flash memory, a hard disk, a multimedia card, a card-type memory (for example, an SD or DX memory, etc.), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the memory can be an internal storage unit of the computer device, such as the hard disk or memory of the computer device. In other embodiments, the memory can also be an external storage device of the computer device, such as a plug-in hard disk equipped on the computer device, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. Of course, the memory can also include both the internal storage unit and the external storage device of the computer device. In this embodiment, the memory is usually used to store the operating system and various application software installed on the computer device. In addition, the memory can also be used to temporarily store various data that have been output or will be output.

[0249] In some embodiments, the processor may be a Central Processing Unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chips. The processor is generally used to control the overall operation of the computer device.

[0250] Performance Test

[0251] In order to verify the performance of the solution of the present invention, technicians formulated an experimental plan to verify the CAM post-optimization method for geometric error compensation of multi-axis linkage numerically controlled machine tools provided by the present invention in a five-axis machine tool processing system.

[0252] The processing equipment used in this experiment is a five-axis machining center of the MIKRON UCP 800 Duro model, and the machine tool structure is as Figure 2 shown. The following table shows the main parameters of the MIKRON UCP 800 Duro machine tool:

[0253] Table 4: Main parameters of the MIKRON UCP 800 Duro machine tool

[0254]

[0255] The schematic diagram of the topological structure of the five-axis machining center of the MIKRON UCP 800 Duro model used in this experiment is as Figure 3 shown. For the double-turret configuration of the target machine tool (Mikron UCP 800 Duro), its geometric error characteristic matrix is constructed, and the error elements of the linear axes (X / Y / Z) and the rotary axes (A / C) are integrated. The error transfer equation is derived to establish the error mapping relationship from the machine tool coordinate system to the workpiece coordinate system.

[0256] For the linear axis measurement, the measuring instrument used in this example is a Renishaw XL 80 laser interferometer. The linear measurement accuracy of this laser interferometer is ±0.5 ppm (parts per million), the laser frequency stabilization accuracy is ±0.05 ppm, and the linear resolution reaches 1 nm.

[0257] During the linear axis geometric error measurement experiment, after installing and connecting the software, the required mirror group is correctly installed on the machine tool to be measured, and the operations are carried out as Figure 4Collimation of the mirror group and the moving axis as shown. By adjusting the position and angle of the mirror group, the laser beam can be reflected back to the receiver of the laser interferometer. At this time, the software interface of the laser interferometer will display the intensity of the laser signal. Then use the fine-tuning device (adjusting screw or knob) on the mirror group to gradually adjust the angle and position of the mirror group until the laser signal intensity reaches the maximum value. Move the linear axis of the machine tool to move slowly within the measurement range. If the laser beam deviates from the center, the angle of the mirror group needs to be readjusted until the laser beam remains stable throughout the moving range. After the adjustment is completed, move the linear axis of the machine tool again to check whether the laser signal intensity remains consistent throughout the measurement range.

[0258] During the experiment, by substituting the collected linear axis positioning error and straightness error data into the corresponding error model formula, the geometric error elements of each axis were successfully identified. However, since discrete coordinate points were used to collect data during the measurement, the obtained error elements were also discrete values. To obtain a continuous and smooth error curve, the least squares method was used to fit the discrete data in this paper. Some fitting results are as Figure 5 shown.

[0259] In the compensation part, for the three basic modes of the linear axis: rapid positioning command (G00), linear interpolation command (G01), and circular interpolation command (G02 / G03), point-by-point compensation was carried out respectively. For the rotary axis, the point-by-point compensation method for the rotary axis was used, and the error of the rotary axis was corrected by multiple iterative compensations. The implementation method of the compensation function in this experiment was mainly to replace the theoretical kinematic model of the AC double turntable type machine tool with the geometric error model of this machine tool, and then correct the NC code according to the compensation scheme provided above. The output file was the NC code format considering the geometric error of the machine tool.

[0260] Finally, in the Vericut software, two different error thresholds were set in this experiment and compared with the uncompensated ideal machining simulation effect. The following table shows the specific settings of these two error thresholds.

[0261] Table 5: Error Thresholds Set for Machine Tool Simulation

[0262]

[0263] Analysis of the data in the above table shows that: compared with the control group scheme, the compensation accuracy of the present invention is higher, and the overcut phenomenon in the simulation result after compensation is effectively reduced.

[0264] Further, four cutting paths were taken on the side of a single blade of the blisk for error measurement during the experiment. A total of 32 measurement points were selected. The selected cutting paths and measurement points are as Figure 6 shown. Comparing the errors of the blade measurement points before and after compensation, the measurement results are as Figure 7 shown.

[0265] Combined with Figure 6 and Figure 7 the data, it can be clearly seen that the compensation effects of both groups are relatively significant. The error value range of Group 1 before compensation was -0.1758 mm to -0.0043 mm, while the error value range after compensation was reduced to -0.1233 mm to -0.0013 mm; the error value range of Group 2 before compensation was -0.1343 mm to -0.0012 mm, while the error value range after compensation was reduced to -0.1126 mm to -0.0002 mm.

[0266] According to the above simulation effects and measurement result analysis, the accuracy of Group 1 increased by approximately 19.45% after compensation, and the accuracy of Group 2 increased by approximately 15.55% after compensation, proving that the geometric error compensation function in the post-processing of the invention has an ideal compensation effect on the target machine tool, can effectively reduce errors, and improve the machining accuracy.

[0267] The above-described embodiments only represent one implementation manner of the present invention, and its description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool, characterized in that It includes:

1. Conduct kinematic analysis and geometric error modeling on the target machine tool and deploy it in a CAM post-optimization module; The modeling process includes: Construct the kinematic chain equation of the target machine tool with a five-axis machine tool as the basic model and generate the corresponding kinematic model; adopt a double rotary table configuration to construct the geometric error characteristic matrix of the target machine tool, integrate the error elements of each linear axis and each rotary axis to derive the error transfer equation, and establish a geometric error model representing the error mapping relationship from the machine tool coordinate system to the workpiece coordinate system; 2. Real-time collect the actual state parameters of the target machine tool during the machining process through a laser interferometer; synchronously obtain the motion instructions of the target machine tool and the detection results of the laser interferometer through a CAM post-optimization module, and then use the kinematic model and geometric error model to calculate the geometric errors of the linear axis and rotary axis during the operation of the target machine tool in real time and perform compensation: Among them, the compensation method for the linear axis is as follows: when each G00 instruction is executed, calculate the position point error E(P) according to the ideal coordinates of the tool cutting point in the workpiece coordinate system. When E(P) exceeds the preset error tolerance ξ, perform rapid positioning compensation on the cutting point; when each G01 instruction is executed, equally divide the straight line between the starting point and the ending point in the action of the target machine tool according to the preset interpolation step Δs, calculate the theoretical coordinates and errors of each interpolation point, and perform linear interpolation compensation on the linear trajectory by the point-by-point compensation method; when each G02 / G03 instruction is executed, determine the starting point, ending point and radius of the ideal arc in the action of the target machine tool, and calculate the center coordinates and starting angle according to the interpolation direction of the arc; divide the arc into n segments with equal radian to obtain n + 1 segmentation points; calculate the errors of each segmentation point, and perform circular interpolation error compensation on the arc trajectory by the point-by-point compensation method; The compensation method of the rotating axis is to map the compensation amount in the workpiece coordinate system to the local coordinate system of each axis of the machine tool through kinematic inverse solution, and calculate the tool axis posture vector error V p and tool cutting point position error E p ; First, the A-axis and C-axis rotation angles are corrected by the iterative compensation method to eliminate the tool axis posture error; then the tool cutting point position is adjusted by the iterative compensation method to correct the position error of the tool cutting point.

2. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool according to claim 1, characterized in that: The kinematic chain equation of the five-axis machine tool can be expressed as: T total = T trans ·R axis1 ·R axis2 ·R axis3 ·R axis4 ·R axis5 In the above formula, T total is the total transformation matrix, T trans is the translation transformation matrix, and R axis1 ~R axis5 respectively represent the transformation matrices of five rotation axes; among them, when there is any missing rotation axis in the target machine tool relative to the five-axis machine tool, the corresponding rotation axis transformation matrix is set to the identity matrix I; The kinematic model of the five-axis machine tool is expressed as: T base ·T work ·R A ·R B ·R C ·P work =T base ·T tool ·R A ·R B ·R C ·P tool In the above formula, T base is the transformation matrix of the reference coordinate system, T work is the translation transformation matrix of the workpiece coordinate system, and R A to R C respectively represent the rotation transformation matrices about the corresponding axes A to C; P work is the position of the machining point in the workpiece coordinate system, T tool is the translation transformation matrix of the tool coordinate system, and P tool is the position of the tip point in the tool coordinate system.

3. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool according to claim 2, wherein The geometric error model of the machine tool is expressed as: In the above formula, P w and V w respectively represent the actual position coordinates and the actual vector coordinates of the cutting tool in the workpiece coordinate system; P w ' and V w ' respectively represent the ideal position coordinates and the ideal vector coordinates of the cutting tool in the workpiece coordinate system.

4. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerical control machine tool according to claim 3, wherein The process of rapid positioning compensation of the cutting point includes: Suppose the ideal coordinates of the cutting point of the tool in the workpiece coordinate system are P0(P x0 , P y0 , P z0 ). The position error E(P) of the cutting point is calculated through the geometric error model; the actual cutting point P of the tool w is: P w = P0 + E(P) = (P x0 + E(P) x ,P y0 + E(P) y ,P z0 + E(P) z ) In the above formula, E(P) x , E(P) y and E(P) z are the error components of the cutting point position along the X, Y, and Z directions, respectively; When E(P) does not exceed the error tolerance ξ, it is considered that the positioning accuracy meets the requirements and no compensation is required; otherwise, error compensation is required: During the compensation process, first calculate the movement amounts of each axis, then calculate the converted corrected coordinate values, and finally issue a compensation instruction according to the corrected coordinate values until the compensated error value meets the requirements.

5. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool according to claim 4, wherein: The calculation method of the cutter shaft attitude vector error V p and the cutter tip position error E p is as follows: When the cutter axis vector V is [V x V y V z T , the rotation angles α and β of the A-axis and C-axis are inversely solved by the following formula:​ In the above formula, k represents the sign coefficient; Calculate the actual vector coordinate V w and the ideal vector coordinate V w ' to obtain the deviation of the rotation angles α and β of the two tool axes, and get the tool axis attitude vector error V p ; When the coordinate of the cutting point P of the tool is [P x P y P z T at this time, the translation amounts of the X, Y, and Z axes can be inversely solved by the following formula:​ Among them, x ow , y ow , z ow are the position coordinate values in the workpiece coordinate system, and x om , y om , z om are the position coordinate values in the machine tool coordinate system; Calculate the actual position coordinate P w and the ideal position coordinate P w 's deviations on the x, y, and z axes to obtain the tool cutting point position error E p .

6. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool according to claim 1, wherein Tool axis attitude vector error V p The compensation process includes: Define that after the i-th compensation, the rotation angles of the A-axis and the C-axis are α i and β i , and the actual tool axis attitude vector is V i , then: V i = T C (β i )·T A (α i )·V0 Among them, T C (β i ) and T A (α i ) are the rotation transformation matrices of the C-axis and the A-axis respectively, and V0 is the initial tool axis attitude vector; Substitute the components of V i into the formula to obtain the corresponding rotation angles α′ i and β′ i of the A-axis and C-axis. Let Δθ A and Δθ C be the allowable angular error values of the A-axis and C-axis respectively. If the following conditions are simultaneously satisfied: Then the compensation ends. Otherwise, calculate the rotation angles of the A-axis and C-axis in the next round as α i+1 and β i+1 , and continue iterative compensation; In the above formula, η is a parameter used to suppress overshoot, η ∈ (0, 1]; During the rotation angle adjustment process, when there are multiple sets of feasible solutions, the rotation angle combination with the minimum Euclidean distance is preferentially selected.

7. The CAM post-optimization method for geometric error compensation of a multi-axis linkage numerically controlled machine tool according to claim 4, wherein: Tool cutting point position error E p The compensation method is as follows: After determining the cutting point position, reconstruct the kinematic chain by introducing a displacement correction amount: Among them, P wj is the actual cutting point position at the j-th iteration, R C , R A is the rotation axis transformation matrix, T m is the translation matrix of the moving axis, l m is the translation amount, Δl m,j is the displacement correction amount of the moving axis m (X / Y / Z) at the j-th iteration, and P0 is the initial tool tip point; When the position residual meets the threshold ε p , it is determined that the calibration is completed; Among which P xj , P yj , c are the measured coordinates of the actual cutting point after the j-th iteration; P x , P y , P z are the theoretical target position coordinates; Otherwise, generate an incremental compensation instruction through the following formula: Δl m,j+1 = Δl m,j + λ(P m - P' mj ) In the above formula, λ is a parameter used to control the convergence rate, and Δl m,j+1 is the new compensation amount of the moving axis m at the (j + 1)-th iteration, and P mj is the actual position component in the direction of axis m after the j-th iteration.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis CNC machine tool as described in any one of claims 1-7. Furthermore, based on the motion commands of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

9. A CAM post-optimization module, characterized in that It includes a memory, a processor, and a computer program stored on the memory and running on the processor. When the computer program is executed by the processor, it implements the CAM post-optimization method for geometric error compensation of a multi-axis CNC machine tool as described in any one of claims 1-7. Furthermore, based on the motion commands of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

10. A multi-axis CNC machine tool processing system, which comprises: A five-axis machine tool, A laser interferometer, which is used to collect the actual state parameters during the machining process of the five-axis machine tool in real time; A CAM post-optimization module, which is communicatively connected to the five-axis machine tool and the laser interferometer, and is used to synchronously obtain the motion commands of the target machine tool and the detection results of the laser interferometer, and then implement the CAM post-optimization method for geometric error compensation of a multi-axis CNC machine tool as described in any one of claims 1-7. Furthermore, based on the motion commands of the target machine tool obtained synchronously and the actual state parameters during the machining process of the target machine tool, the geometric errors of the linear axes and rotary axes during the operation of the target machine tool are calculated in real time using the kinematic model and the geometric error model, and correction instructions for compensating the corresponding errors are generated.

Images