Machine tool key error identification method based on geometric error interval and sensitivity analysis

Abstract

The invention discloses a machine tool key error identification method based on geometric error interval and sensitivity analysis, and belongs to the field of numerical control machine tools. The method comprises the steps of defining geometric error terms of motion axes according to a machine tool structure, performing repeated measurement on discrete positions at a plurality of preset time points, and constructing an error interval representing dynamic fluctuation with a maximum value and a minimum value; based on the error interval and the comprehensive error model, calculating the sensitivity coefficient of each geometric error at each position of the working space to the comprehensive error of the tool nose by adopting global sensitivity analysis; and determining a sensitivity coefficient threshold screening geometric error, and determining the geometric error as a key geometric error. According to the method, actually measured data and time-varying characteristics are fused, the influence of an error source on the machining precision is accurately quantified, regionalized and high-pertinence error identification and compensation are achieved, and the machining precision of a machine tool under dynamic working conditions such as thermal deformation is effectively improved.

Description

A Method for Identifying Key Machine Tool Errors Based on Geometric Error Interval and Sensitivity Analysis Technical Field

[0001] This invention relates to the field of CNC machine tool technology, and in particular to a method for identifying key machine tool errors based on geometric error range and sensitivity analysis. Background Technology

[0002] With the increasing demands for machining accuracy in high-end equipment manufacturing, machine tool geometric errors have become one of the main factors affecting machining precision. To improve machine tool machining accuracy, it is usually necessary to measure, model, and compensate for various geometric errors. However, machine tools have a large number of motion axes and complex geometric error terms. Different error sources have significantly different degrees of influence on the overall error. If all errors are treated equally, not only will the measurement and modeling costs be high, but the compensation efficiency will also be low.

[0003] Existing machine tool error analysis methods often employ sensitivity analysis to assess the importance of geometric errors, identifying error terms that significantly impact machining accuracy. However, these methods typically assume that each geometric error has a fixed range of variation throughout the workspace, failing to adequately consider the actual distribution characteristics of geometric errors at different locations. Particularly for position-dependent geometric errors, whose amplitude and distribution vary significantly with the position of the motion axis, using a uniform error range can easily introduce analytical bias, thus affecting the accuracy of critical error identification results.

[0004] Therefore, there is an urgent need for a method that can combine the actual variation range of geometric errors at different locations to conduct a refined sensitivity analysis of machine tool geometric errors, so as to improve the accuracy of key error identification and engineering practicality of machine tools. Summary of the Invention

[0005] To address the problem that existing machine tool geometric error sensitivity analysis methods fail to fully consider the actual variation range of geometric errors at different locations, resulting in insufficient accuracy in identifying critical errors, this invention provides a machine tool critical error identification method based on geometric error range and sensitivity analysis.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a machine tool critical error identification method based on geometric error interval and sensitivity analysis, comprising: analyzing each motion axis according to the machine tool structure and defining geometric error terms for each motion axis; repeatedly measuring the geometric error terms at discrete positions of each motion axis at multiple preset running time points, and establishing an error interval characterizing the dynamic fluctuation range by statistically analyzing the maximum and minimum values ​​of the measured values ​​at each position; establishing a comprehensive error model of the machine tool based on the geometric error terms, and analyzing the comprehensive error of the relative pose of the tool relative to the workpiece; using a global sensitivity analysis method based on the error intervals of each geometric error and the comprehensive error model, uniformly distributing analysis position points within the machine tool workspace according to a preset average sampling interval, and calculating the sensitivity coefficient of each geometric error to the comprehensive error at each analysis position point; determining a sensitivity coefficient threshold, and identifying a critical geometric error when the sensitivity coefficient is greater than the sensitivity coefficient threshold.

[0007] Furthermore, based on the geometric error term, a comprehensive error model of the machine tool is established to analyze the comprehensive error of the relative pose of the tool with respect to the workpiece, including: constructing the motion transformation matrix of each axis based on the geometric error of each axis; obtaining the comprehensive motion transformation matrix based on the motion transformation matrix of each axis to obtain the actual position of the tool tip in the machine tool coordinate system; and determining the comprehensive error of the tool tip point based on the actual position of the tool tip.

[0008] Furthermore, based on the geometric errors of each axis, motion transformation matrices for each axis are constructed, including: the motion transformation matrix for the X-axis. The expression is: In the formula, This represents the angular error of the X-axis around the X-axis direction. This represents the angular error of the X-axis around the Y-axis. This represents the angular error of the X-axis around the Z-axis. This refers to the X-axis positioning error. This represents the translation error along the Y direction of the X-axis. The translation error along the Z-axis is the X-axis translation error; the motion transformation matrix along the Z-axis is... The expression is: In the formula, This represents the angular error of the Y-axis around the X-axis. This represents the angular error of the Y-axis around the Y-axis direction. This represents the angular error of the Y-axis around the Z-axis. Y-axis positioning error; This represents the linear error of the Y-axis along the X direction. The straightness error of the Y-axis along the Z-direction; the perpendicularity error between the X-axis and the Z-axis. The motion transformation matrix is ​​expressed as: In the formula, This refers to the verticality error.

[0009] Furthermore, the actual position expression of the tool tip in the machine tool coordinate system is: In the formula, This represents the actual position of the blade tip.

[0010] Furthermore, the comprehensive error expression for the blade tip is: ; In the formula, This is the overall error value; This refers to the actual position of the blade tip; The position coordinates of the tool tip in the X-axis coordinate system; This represents the coordinates of the tool tip in the machine tool coordinate system.

[0011] Furthermore, the sensitivity coefficients of each geometric error to the overall error are calculated, including: establishing a mathematical mapping relationship between the error intervals of the overall error and the geometric errors, expressed as: In the formula, This represents the overall error between the cutting tool and the workpiece. This is the function for the comprehensive error model; Let n be the actual value of the i-th individual geometric error; n is the total number of geometric error terms; based on each geometric error... Error region Generate a matrix by performing uniform random sampling. sum matrix And according to the matrix sum matrix Generate a mixture matrix The expression is: In the formula, For matrix The sampled value in the j-th column and i-th row; For matrix The sampled value in the j-th column and i-th row; To replace the i-th column of matrix A with the i-th column of matrix B, while keeping the other columns unchanged; k is the number of samples; n is the total number of geometric error terms; using Monte Carlo samples, the first-order sensitivity index Si is actually estimated to obtain the sensitivity index of geometric error, expressed as: In the formula, For the i-th geometric error The first-order sensitivity coefficient is used to quantify the proportion of contribution of geometric error alone to the variance of the overall error; This is the function for the comprehensive error model; The sample in the j-th row of matrix B is input into the output value of the comprehensive error model function; To be The j-th row of the matrix contains the output value of the integrated error model function. This is to input the j-th row sample in matrix A into the output value of the comprehensive error model function.

[0012] Furthermore, the global sensitivity analysis method is the Sobol index method.

[0013] Furthermore, the sensitivity coefficient threshold is determined, including setting a fixed threshold based on expert experience as the sensitivity coefficient threshold to screen for key errors.

[0014] Furthermore, determining the sensitivity coefficient threshold includes: dividing the workspace equally according to the machine tool's travel characteristics, calculating the sensitivity coefficient of the geometric error of the analysis position points in each region, and using the average sensitivity coefficient of all analysis position points in each region as the sensitivity coefficient threshold.

[0015] Through the above technical solution, this invention constructs a dynamic interval model of geometric error through actual measurement, combines a comprehensive error model with global sensitivity analysis, quantifies the influence of each error source on the tool tip pose deviation, and identifies key geometric errors in the workspace partition based on sensitivity coefficient thresholds. This effectively reveals the causal relationship between error and accuracy, avoids blind compensation, and significantly improves the targeting of error compensation and machine tool machining accuracy, making it particularly suitable for high-precision manufacturing scenarios under time-varying conditions such as thermal deformation. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 is a flowchart of the method of the present invention; Figure 2 is a schematic diagram of the machine tool structure configuration in this embodiment; Figure 3 is a schematic diagram of the geometric error definition of the X-axis and Z-axis in this embodiment; Figure 4 is a schematic diagram of the geometric error measurement of each position of each motion axis of the machine tool in this embodiment; Figure 5 is a schematic diagram of the X-axis positioning error measurement result in this embodiment; Figure 6 is a schematic diagram of the error interval at each position of the X-axis positioning error in this embodiment; Figure 7 is a schematic diagram of the trajectory error in the XZ plane in this embodiment; Figure 8 is a schematic diagram of the comparison of the results of identifying key geometric errors in this embodiment; Figure 9 is a schematic diagram of the comparison of the results of key error ratio in this embodiment. Detailed Implementation

[0018] The following detailed description, in conjunction with specific embodiments and accompanying drawings, provides a clear and complete explanation of the machine tool critical error identification method based on geometric error interval and sensitivity analysis proposed in this invention. It should be understood that the following embodiments are merely illustrative of the technical solutions of this invention and are not intended to limit the scope of protection of this invention. Equivalent substitutions or modifications made by those skilled in the art to the technical solutions of this invention without departing from the technical concept of this invention should all fall within the scope of protection of this invention.

[0019] This embodiment takes ultra-precision CNC machine tools as the application object and, considering the characteristic that geometric errors play a dominant role in machining accuracy under stable machining environments, proposes a key error identification method that combines geometric error interval modeling and sensitivity analysis. This method uses the comprehensive error of the relative pose of the tool and the workpiece as the analysis object. Through multiple measurements, it obtains the error intervals of geometric errors at different positions and conducts error sensitivity analysis based on these intervals, thereby identifying the key geometric errors of the machine tool.

[0020] As shown in Figure 1, the machine tool key error identification method based on geometric error interval and sensitivity analysis provided in this embodiment includes the following steps: Step 1, according to the machine tool structure, analyze each motion axis and define the geometric error terms of each motion axis. The geometric error terms include position-related geometric errors and position-independent geometric errors. As shown in Table 1, the X-axis and Z-axis each have 6 position-related geometric errors and 1 position-independent geometric error, namely the perpendicularity error between the X-axis and Z-axis.

[0021] In Table 1, Indicates translation error. This indicates angular error. The second letter of the subscript indicates the target axis to which the error pertains, and the first letter indicates the direction of the error, i.e., translation along a coordinate axis or rotation about a coordinate axis. For example, This represents the translation error of the X-axis along the Y-axis.

[0022] Table 1 Geometric errors of machine tools

[0023] Figure 2 shows a schematic diagram of the machine tool structure. The Z-axis is mounted on the column, and the X-axis is located above the Z-axis. Motion coordinate systems are established for the X-axis and Z-axis respectively, with their initial positions coinciding with the machine tool coordinate system.

[0024] Step 2: At multiple preset running time points, the geometric error term is repeatedly measured at the discrete positions of each motion axis. By statistically analyzing the maximum and minimum values ​​of the measured values ​​at each position, an error interval characterizing the dynamic fluctuation range is established.

[0025] The preset time points include, for example, before powering on, after 1 hour, 2 hours, 3 hours, and 4 hours of continuous operation.

[0026] As shown in Figure 3, when considering the geometric error of the machine tool, the motion transformation matrix needs to be corrected, and the error is introduced as an additional motion.

[0027] Step 3: Based on the geometric error term, establish the comprehensive error model of the machine tool and analyze the comprehensive error of the relative pose of the tool with respect to the workpiece. This includes: the tool is mounted on the X-axis via a tool holder; therefore, the position coordinates of the tool tip in the X-axis coordinate system are: The motion along the X and Z axes can be achieved using coordinate transformation matrices. and This indicates the coordinates of the tool tip in the machine coordinate system after displacement along the X and Z axes. The expression is: The geometric error of the machine tool's motion axis can be regarded as an additional motion superimposed on the nominal axis motion.

[0028] Step 31: Based on the geometric errors of each axis, construct the motion transformation matrix for each axis, including: the motion transformation matrix for the six geometric error sources in the X-axis. It can be obtained by superimposing the corresponding error transformation matrix. After linearization approximation based on the small angle assumption, the expression is: In the formula, This represents the angular error of the X-axis around the X-axis direction. This represents the angular error of the X-axis around the Y-axis. This represents the angular error of the X-axis around the Z-axis. This refers to the X-axis positioning error. This represents the translation error along the Y direction of the X-axis. The translation error along the Z-axis is the X-axis translation error; the motion transformation matrices corresponding to the six geometric error sources along the Z-axis are also shown. The expression is: In the formula, This represents the angular error of the Y-axis around the X-axis. This represents the angular error of the Y-axis around the Y-axis direction. This represents the angular error of the Y-axis around the Z-axis. Y-axis positioning error; This represents the linear error of the Y-axis along the X direction. The straightness error of the Y-axis along the Z-direction; the perpendicularity error between the X-axis and the Z-axis. The motion transformation matrix is ​​expressed as: In the formula, For perpendicularity error; Step 32, based on the motion transformation matrices of each axis, obtain the comprehensive motion transformation matrix, and acquire the actual position of the tool tip in the machine tool coordinate system, expressed as: In the formula, This represents the actual position of the blade tip.

[0029] Step 33: Determine the overall error of the tool tip based on its actual position after movement along the X and Z axes. The expression is: In the formula, ΔX is the comprehensive error component of the tool tip in the X direction; ΔY is the comprehensive error component of the tool tip in the Y direction; and ΔZ is the comprehensive error component of the tool tip in the Z direction.

[0030] It should be noted that even if the position-related geometric error is zero at the origin, the perpendicularity error will still occur. Even with the presence of [something], the blade tip may still have an initial pose deviation.

[0031] In this embodiment, the initial error is eliminated through pre-correction, and the corrected comprehensive error component and The expression is shown in the formula: Step 4: Based on the error intervals of each geometric error and the comprehensive error model, a global sensitivity analysis method is used. Analysis points are evenly distributed within the machine tool workspace according to a preset average sampling interval. The sensitivity coefficients of each geometric error to the comprehensive error at each analysis point are calculated, including: The global sensitivity analysis method is the Sobol exponent method; a mathematical mapping relationship between the error intervals of the comprehensive error and the geometric error is established, expressed as: In the formula, This represents the overall error between the cutting tool and the workpiece. This is the function for the comprehensive error model; Let n be the actual value of the i-th individual geometric error; n is the total number of geometric error terms; based on each geometric error... Error region Generate a matrix by performing uniform random sampling. sum matrix And according to the matrix sum matrix Generate a mixture matrix The expression is: In the formula, For matrix The sampled value in the j-th column and i-th row; For matrix The sampled value in the j-th column and i-th row; To replace the i-th column of matrix A with the i-th column of matrix B, while keeping the other columns unchanged; k is the number of samples; n is the total number of geometric error terms; using Monte Carlo samples, the first-order sensitivity index Si is actually estimated to obtain the sensitivity index of geometric error, expressed as: In the formula, For the i-th geometric error The first-order sensitivity coefficient is used to quantify the proportion of contribution of geometric error alone to the variance of the overall error; This is the function for the comprehensive error model; The sample in the j-th row of matrix B is input into the output value of the comprehensive error model function; To be The j-th row of the matrix contains the output value of the integrated error model function. This is to input the j-th row sample in matrix A into the output value of the comprehensive error model function.

[0032] Step 5: Determine the sensitivity coefficient threshold. When the sensitivity coefficient is greater than the sensitivity coefficient threshold, it is determined as a critical geometric error. This includes: In one embodiment, the workspace is divided equally according to the travel characteristics of the machine tool, the sensitivity coefficient of the geometric error of the analysis position point in each region is calculated, and the average sensitivity coefficient of all analysis position points in each region is used as the sensitivity coefficient threshold to screen the critical geometric errors in the current region.

[0033] In one embodiment, a fixed threshold is set based on expert experience as a sensitivity coefficient threshold to screen critical errors. For example, when the sensitivity coefficient is greater than 0.1, the corresponding error can be regarded as a critical error.

[0034] Through the above technical solution, the present invention can effectively identify key geometric errors of machine tools without relying on additional compensation axes, thereby providing a reliable basis for subsequent error compensation, structural optimization or accuracy maintenance, and has high engineering practical value.

[0035] As shown in Figure 4, the numerical distribution of each geometric error was obtained before conducting the error sensitivity analysis. The position-dependent geometric errors of the linear axes were measured using a multi-beam laser interferometer, measuring six position-dependent geometric errors along the X and Z axes. The position-independent geometric errors, namely the perpendicularity errors, were tested using a ball-bar apparatus (radius R).

[0036] Measurements were taken at five different time points: before power-on, after 1 hour, 2 hours, 3 hours, and 4 hours of continuous operation. At each measurement point, the maximum and minimum values ​​of the measurement results were used as the upper and lower boundaries to obtain the error ranges for each geometric error. Figures 5 and 6 show the five measurement results of the positioning error δxx and the corresponding error ranges.

[0037] As shown in Figure 7, the trajectory error is defined. In contrast to the advantages of the method of this invention in identifying key geometric errors, a two-dimensional trajectory was designed in the XZ plane. This trajectory covers most of the travel distance along the X and Z axes in the XZ plane, thus reducing trajectory errors. This represents the overall error of the machine tool in the XZ plane.

[0038] Figure 8 shows the identification results of key geometric errors involving the combined error components ΔX, ΔZ, and trajectory error ΔL. The XZ plane was divided into 12 regions. During the key geometric error identification process, the average sensitivity coefficient of all points within each region was used as the evaluation index, and the geometric error with the highest sensitivity coefficient was selected as the key geometric error. Key geometric errors identified by the traditional method are marked in blue, while those identified by the method of this invention are marked in red. Figure 8 shows that the key geometric errors identified by the two methods within each region are not the same. These findings clearly demonstrate that the method of this invention can provide more spatially differentiated identification results, highlighting the differences in importance of different geometric errors throughout the workspace.

[0039] To evaluate the effectiveness of this invention in identifying critical geometric errors, the case introduces an index called the critical error ratio, which represents the ratio of the trajectory error caused solely by the identified critical geometric errors to the total trajectory error caused by all geometric errors combined. A higher critical error ratio indicates a higher proportion of the identified critical errors in the total trajectory error.

[0040] The expression for the critical error ratio is: In the formula, The trajectory error is caused by the combined effect of identified key geometric errors. Table 2 and Figure 9 show the key error ratios for different regions. In the 12 regions, the average key error ratio of the traditional method is 0.39, while the average key error ratio of the method of this invention is 0.55. The results show that different methods identify key geometric errors with varying degrees of coverage of the trajectory error. The method of this invention can identify geometric errors that contribute significantly to the trajectory error in most regions, making it particularly suitable for ultra-precision machining scenarios with high efficiency and economic requirements.

[0041] Table 2 shows the numerical distribution of key error ratios based on traditional methods and the method of this invention.

[0042] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for identifying key machine tool errors based on geometric error interval and sensitivity analysis, characterized in that, include: Based on the machine tool structure, each motion axis is analyzed, and the geometric error term for each motion axis is defined; At multiple preset running time points, the geometric error term is repeatedly measured at discrete positions of each motion axis. By statistically analyzing the maximum and minimum values ​​of the measured values ​​at each position, an error interval characterizing the dynamic fluctuation range is established. Based on the geometric error term, a comprehensive error model of the machine tool is established to analyze the comprehensive error of the relative pose of the tool to the workpiece. Based on the error range of each geometric error and the comprehensive error model, a global sensitivity analysis method is adopted. Analysis position points are evenly distributed in the machine tool workspace according to the preset average sampling interval, and the sensitivity coefficient of each geometric error to the comprehensive error at each analysis position point is calculated. Determine the sensitivity coefficient threshold; when the sensitivity coefficient is greater than the sensitivity coefficient threshold, it is identified as a critical geometric error.

2. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 1, characterized in that, The process of establishing a comprehensive error model for the machine tool based on geometric error terms and analyzing the comprehensive error of the relative pose of the tool relative to the workpiece includes: constructing motion transformation matrices for each axis based on the geometric errors of each axis; obtaining a comprehensive motion transformation matrix based on the motion transformation matrices of each axis to obtain the actual position of the tool tip in the machine tool coordinate system; and determining the comprehensive error of the tool tip based on the actual position of the tool tip.

3. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 2, characterized in that, The process of constructing motion transformation matrices for each axis based on their geometric errors includes: the motion transformation matrix for the X-axis. The expression is: In the formula, This represents the angular error of the X-axis around the X-axis direction. This represents the angular error of the X-axis around the Y-axis. This represents the angular error of the X-axis around the Z-axis. This refers to the X-axis positioning error. This represents the translation error along the Y direction of the X-axis. The translation error along the Z-axis is the X-axis translation error; the motion transformation matrix along the Z-axis is... The expression is: In the formula, This represents the angular error of the Y-axis around the X-axis. This represents the angular error of the Y-axis around the Y-axis direction. This represents the angular error of the Y-axis around the Z-axis. Y-axis positioning error; This represents the linear error of the Y-axis along the X direction. The straightness error of the Y-axis along the Z-direction; the perpendicularity error between the X-axis and the Z-axis. The motion transformation matrix is ​​expressed as: In the formula, This refers to the verticality error.

4. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 2, characterized in that, The actual position expression of the tool tip in the machine tool coordinate system is: In the formula, This represents the actual position of the blade tip.

5. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 2, characterized in that, The comprehensive error expression for the blade tip is: ； In the formula, This is the overall error value; This refers to the actual position of the blade tip; The position coordinates of the tool tip in the X-axis coordinate system; This represents the coordinates of the tool tip in the machine tool coordinate system.

6. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 1, characterized in that, The calculation of the sensitivity coefficients of each geometric error to the overall error includes: establishing a mathematical mapping relationship between the error intervals of the overall error and the geometric errors, expressed as: In the formula, This represents the overall error between the cutting tool and the workpiece. This is the function for the comprehensive error model; Let n be the actual value of the i-th individual geometric error; n is the total number of geometric error terms; based on each geometric error... Error region Generate a matrix by performing uniform random sampling. sum matrix And according to the matrix sum matrix Generate a mixing matrix The expression is: In the formula, For matrix The sampled value in the j-th column and i-th row; For matrix The sampled value in the j-th column and i-th row; To replace the i-th column of matrix A with the i-th column of matrix B, while keeping the other columns unchanged; k is the number of samples; n is the total number of geometric error terms; using Monte Carlo samples, the first-order sensitivity index Si is actually estimated to obtain the sensitivity index of geometric error, expressed as: In the formula, For the i-th geometric error The first-order sensitivity coefficient is used to quantify the proportion of contribution of geometric error alone to the variance of the overall error; This is the function for the comprehensive error model; The sample in the j-th row of matrix B is input into the output value of the comprehensive error model function; To be The j-th row of the matrix contains the output value of the integrated error model function. This is to input the j-th row sample in matrix A into the output value of the comprehensive error model function.

7. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 1, characterized in that, The global sensitivity analysis method is the Sobol index method.

8. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 1, characterized in that, The determination of the sensitivity coefficient threshold includes: setting a fixed threshold based on expert experience as the sensitivity coefficient threshold to screen key errors.

9. The method for identifying key machine tool errors based on geometric error interval and sensitivity analysis according to claim 1, characterized in that, The determination of the sensitivity coefficient threshold includes: dividing the workspace equally according to the travel characteristics of the machine tool, calculating the sensitivity coefficient of the geometric error of the analysis position points in each region, and using the average sensitivity coefficient of all analysis position points in each region as the sensitivity coefficient threshold.

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