Numerical control machine tool key geometric error identification method based on processing track sensitivity index

Abstract

The invention relates to a numerical control machine tool key geometric error identification method based on a processing track sensitivity index. The method comprises the following steps: establishing a space error model of a five-axis machine tool based on a multi-body system theory and a homogeneous coordinate principle; establishing a space error model taking the machine tool position as an independent variable, and establishing an error transfer model of a single geometric error; calculating a sensitivity index of the spatial error based on projection of an error vector generated by any geometric error in the 41 geometric errors in the processing track to the spatial error; and identifying a key geometric error from the 41 geometric errors based on the sensitivity indexes corresponding to the 41 geometric errors. The invention provides a novel sensitivity index. According to the sensitivity analysis method, space error model parameters are simplified, an independent geometric error transfer model is established, and analysis can be directly carried out based on a workpiece machining track. According to the method, the basic condition that space errors serve as vectors is considered, and meanwhile the influence of position changes of all axes and changes of geometric errors in the machining track is reflected.

Description

Technical Field

[0001] The present invention relates to the technical field of geometric error identification, and in particular to a method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity indicators. Background Art

[0002] Machine tools are the "mother machines" of industry. Multi-axis CNC machine tools offer excellent flexibility and high productivity, making them widely used in the machining of complex workpieces. Geometric errors in CNC machine tools arise from machining errors and assembly deviations in their mechanical components and are characterized by repeatability and stability. Therefore, compensating for geometric errors is currently one of the most feasible methods for improving machine tool accuracy. However, due to their complex structure, multi-axis machine tools introduce a greater number of geometric errors, with five-axis CNC machine tools experiencing up to 41 geometric errors. Compensating for all of these errors is labor-intensive and costly, necessitating the identification of critical geometric errors to improve compensation efficiency. Sensitivity analysis is a method that effectively determines the sensitivity of input parameter changes to system outputs in a physical system and effectively identifies the parameters most sensitive to changes in system outputs. This method analyzes the various geometric errors used as input parameters in a machine tool's spatial error model and identifies their impact on spatial error. Therefore, sensitivity analysis has become an effective method for identifying critical machine tool errors. Currently, the main methods for sensitivity analysis of CNC machine tool spatial error models include the Fourier amplitude sensitivity test, the standardized regression coefficient method, the Morris method, the Sobol method, and the extended Fourier amplitude sensitivity test method. Based on the characteristics of machine tool geometric error models, many researchers have proposed sensitivity indices that reflect the impact of various geometric errors on machining accuracy. Existing research on geometric error sensitivity analysis has the following limitations: Sensitivity analysis methods, primarily the Sobol and Morris methods, require a large number of samples and numerical simulations, resulting in a "black-box" error model that is unsolvable. Many sensitivity analysis methods also require presetting each geometric error to a fixed value or specifying specific points during analysis, ignoring the characteristics of geometric errors that vary with axis position, which can affect sensitivity analysis results. Furthermore, existing research primarily focuses on the sensitivity of geometric errors to machine tool spatial errors, with limited research examining error sensitivity in specific workpiece machining. Summary of the Invention

[0003] The purpose of the present invention is to solve at least one of the deficiencies of the prior art and to provide a method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity indicators.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions: Specifically, a method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index is proposed and applied to AC dual-turret five-axis machine tools, including the following: Based on the multi-body system theory and the principle of homogeneous coordinates, a spatial error model of the five-axis machine tool is established; Obtaining measurement results of geometric errors of the five-axis machine tool using a laser interferometer and a ballbar, establishing a spatial error model with the machine tool position as an independent variable based on the measurement results and the spatial error model, and establishing an error transfer model for a single geometric error; Based on the spatial error model with the machine tool position as the independent variable, 41 geometric errors are determined. The sensitivity index is calculated based on the projection of the error vector generated by any geometric error in the machining trajectory on the spatial error, and the sensitivity index corresponding to the 41 geometric errors is obtained. Key geometric errors are identified from the 41 geometric errors based on sensitivity indicators corresponding to the 41 geometric errors, and the key geometric errors are compensated based on the error transfer model.

[0005] Furthermore, specifically, based on the multi-body system theory and the principle of homogeneous coordinates, a spatial error model of the five-axis machine tool is established, including: Based on the transfer relationship established by multi-body system theory, the deviation between the actual position of the tool cutting point under the influence of geometric error and its ideal position is the tool's spatial error E, which can be obtained from the following formula: (1) In formula (1), 、 、 are the error components of the spatial error E in the X, Y, and Z directions, respectively; L is the tool length; Pwi is the transfer matrix from the workpiece to the tool cutting point under ideal conditions; Pw represents the transfer matrix from the workpiece to the tool cutting point under the influence of 41 geometric errors.

[0006] Further, specifically, based on the measurement results and the spatial error model, a spatial error model with the machine tool position as the independent variable is established, including: Based on the measurement results, 41 geometric errors were identified. Taking the Y-axis as an example, the Y-axis was fitted using the custom fitting function Fittype in Matlab. The fitted Y-axis geometric error is shown in the following formula: (2) The position-related geometric error of the y-axis is fitted into a fourth-order polynomial, where the y value is the ideal position of the y-axis in machine tool processing. Similarly, the geometric errors on other axes can also be modeled using the same method.

[0007] Furthermore, specifically, an error transfer model of a single geometric error is established, including: Based on formula (1), the expression of the spatial error model can be expressed as: (3) In formula (3), e represents the error vector composed of 41 geometric errors: e = (e1, e2, … e41) T , where ei represents the i-th geometric error, and the value of i is [1,41]; x, y, z, a, c represent the positions of the five axes of the CNC machine tool respectively; Then the error vector caused by a single geometric error can be expressed as: (4) (5) is the machining error caused by the i-th geometric error acting alone, i=1,2,3…41, It is expressed as the error components caused by the geometric error in the X, Y, and Z directions at this position.

[0008] Further, specifically, the sensitivity index of any geometric error is calculated, including, Error transfer model of machine tool spatial error E and single geometric error Can be expressed as: (6) (7) Define the sensitivity index expression Sn: (8) (9) In formula (8) Generates error vectors at data points for individual geometric errors The projection of the total error vector E, N is the number of all data points in the entire machining process; The sensitivity indexes of all geometric errors are normalized, and the normalized sensitivity index Un is defined, which is expressed as: (10).

[0009] Furthermore, specifically, based on the sensitivity indicators corresponding to the 41 geometric errors, key geometric errors are identified from the 41 geometric errors, including: The normalized sensitivity index Un is calculated based on the sensitivity indices corresponding to the 41 geometric errors, and the geometric error items greater than the preset threshold are recorded as key geometric errors.

[0010] Furthermore, specifically, the preset threshold is 0.03.

[0011] The beneficial effects of the present invention are: This paper proposes a method for identifying critical geometric errors in CNC machine tools based on a machining trajectory sensitivity index. This method proposes a new sensitivity index. This sensitivity analysis method simplifies the parameters of the spatial error model and establishes an independent geometric error propagation model, enabling analysis directly based on the workpiece machining trajectory. This method considers the fundamental condition that spatial errors are vectors and simultaneously reflects the influence of position changes on each axis along the machining trajectory and changes in the magnitude of the geometric errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The above and other features of the present disclosure will become more apparent through a detailed description of the embodiments shown in conjunction with the accompanying drawings. The same reference numerals in the drawings of the present disclosure represent the same or similar sampling monitoring points. Obviously, the drawings described below are only some embodiments of the present disclosure. Those skilled in the art can derive other drawings based on these drawings without inventive work. In the drawings: Figure 1 FIG. 1 is a schematic structural diagram of an AC dual-turntable five-axis CNC machine tool according to the present invention; Figure 2 FIG. 1 is a schematic diagram of the topological structure of the AC dual-turntable five-axis CNC machine tool involved in the present invention; Figure 3 The figure shows the transmission relationship between the error vector and spatial error of each geometric error acting alone; Figures 4 (a), (b), (c), (d), and (e) show the ideal positions of the X, Y, Z, A, and C axes during the entire machining process during feasibility verification. Figure 5 Shown is a histogram of geometric error sensitivity during feasibility verification; Figure 6 (a), (b), and (c) show the components of the machining error in the X / Y / Z directions during the entire machining process during feasibility verification; Figure 7 The figure shows the machining error values of the three compensation schemes during the entire machining process during feasibility verification. Figure 8 The figure shows the total machining error of the three compensation schemes during the entire machining process during feasibility verification. DETAILED DESCRIPTION

[0013] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments and features in the embodiments of this application can be combined with each other unless there is a conflict. The same reference numerals used throughout the drawings indicate the same or similar parts.

[0014] In Example 1, the present invention proposes a method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity indicators, which is applied to AC dual-turret five-axis machine tools, including the following: Based on the multi-body system theory and the principle of homogeneous coordinates, a spatial error model of the five-axis machine tool is established; Obtaining measurement results of geometric errors of the five-axis machine tool using a laser interferometer and a ballbar, establishing a spatial error model with the machine tool position as an independent variable based on the measurement results and the spatial error model, and establishing an error transfer model for a single geometric error; Based on the spatial error model with the machine tool position as the independent variable, 41 geometric errors are determined. The sensitivity index is calculated based on the projection of the error vector generated by any geometric error in the machining trajectory on the spatial error, and the sensitivity index corresponding to the 41 geometric errors is obtained. The key geometric errors are identified from the 41 geometric errors based on the sensitivity indicators corresponding to the 41 geometric errors.

[0015] The error vectors caused by each geometric error together form the final tool position error vector. Therefore, the projection of the error vectors caused by each geometric error can be used to describe the impact of each geometric error on the tool position error vector. Therefore, this is used as a basis for defining the sensitivity expression.

[0016] This method takes into account the basic condition that the spatial error is a vector, and at the same time reflects the influence of the position change of each axis in the machining trajectory and the change of the size of the geometric error. After defining the sensitivity index, the previously established geometric error model is substituted into the 41 geometric errors identified. This allows us to determine the spatial error at each point on the machining trajectory and the error vectors caused by the individual effects of the 41 errors. The projection of each error vector on the machining trajectory onto the spatial error is then calculated, along with the sensitivity coefficients for the 41 geometric errors, to identify the key geometric errors.

[0017] The geometric errors with a sensitivity coefficient (i.e., the sensitivity index after normalization) greater than 0.03 are defined as critical geometric errors. In this paper, the S specimen processing is taken as an example. There are 11 geometric errors with a sensitivity coefficient greater than 0.03, so there are 11 critical geometric errors.

[0018] As a preferred embodiment of the present invention, specifically, a spatial error model of the five-axis machine tool is established based on multi-body system theory and homogeneous coordinate principle, including: As one of the current mainstream geometric error modeling methods, multi-body system theory decomposes the machine tool kinematic chain into a rigid body topology structure through abstract processing of the machine tool, and uses homogeneous coordinate transformation to construct the error transfer matrix, which significantly reduces the complexity of multi-axis linkage structure analysis. Figure 1As shown, its motion system consists of translation axes X, Y, Z and rotation axes A, C. Based on the multi-body system theory and the principle of homogeneous coordinate transformation, this paper establishes a spatial error model of the AC double-turntable machine tool. The machine tool is abstracted as a multi-body system consisting of tool branches and workpiece branches. Its motion chain structure is TZXYMACW type. The machine tool topology is as follows: Figure 2 As shown in the figure, WCS is the workpiece coordinate system, ACS and CCS are the rotation axis coordinate systems, XCS, YCS and ZCS are the translation axis coordinate systems, MCS is the machine coordinate system and TCS is the tool coordinate system.

[0019] Ideally, the origin of the machine coordinate system (MCS) is defined at the ideal intersection of the A and C axes. The origin of the workpiece coordinate system (WCS) is also defined at the ideal intersection of the A and C axes and is connected to the C-axis coordinate system (CCS). The tool coordinate system is connected to the Z-axis coordinate system (ZCS). The initial coordinate systems of each axis are set to align with the machine coordinate system, and all linear axis coordinate systems are coaxial and share the same origin. When all five axes of the machine tool are at zero, the machine coordinate system (MCS) completely coincides with the workpiece coordinate system (WCS) and the rotational axis coordinate system. The offset of the translational axis coordinate system's origin relative to the machine coordinate system origin in the X, Y, and Z directions has been measured to be [0.417566, 0.405548, 0.624614]T (unit: m). The rotation axes A and C belong to the workpiece motion chain, and the translation axes X, Y, and Z belong to the tool motion chain. According to the motion chain transmission rules, the workpiece motion chain branch follows the W→C→A→M path, and the tool motion chain branch performs posture transformation in the order of M→Y→X→Z→T.

[0020] The five axes X / Y / Z / A / C are the five main moving parts in the kinematic chain of this machine tool. Each kinematic pair has six degrees of freedom in three-dimensional space, which inevitably produces six geometric errors. The five axes produce a total of 30 geometric errors. The magnitude of these 30 errors will change with the position of each axis, so they are called position-dependent geometric errors (PDGEs). In addition, there are three perpendicularity errors between the three translational axes, and the two rotational axes have two position errors and two parallelism errors relative to the ideal axis, totaling eight errors. These 11 errors do not change with the position of each axis, so they are also called position-independent geometric errors (PIGEs). The rotational axis errors are defined according to the technical specifications of the international standard ISO 230-7:2006

[20] . The 41 errors of the AC double-rotary table machine tool are shown in Table 1, where δ is the linear error, ε is the angular error, and S is the perpendicularity error.

[0021] Table 1

[0022] Based on the transfer relationship established by multi-body system theory, the deviation between the actual position of the tool cutting point under the influence of geometric error and its ideal position is the tool's spatial error E, which can be obtained from the following formula: (1) In formula (1), 、 、 are the error components of the spatial error E in the X, Y, and Z directions, respectively; L is the tool length; Pwi is the transfer matrix from the workpiece to the tool cutting point under ideal conditions; Pw represents the transfer matrix from the workpiece to the tool cutting point under the influence of 41 geometric errors.

[0023] As a preferred embodiment of the present invention, specifically, a spatial error model with the machine tool position as an independent variable is established based on the measurement results and the spatial error model, including: Based on the measurement results, 41 geometric errors were identified. Taking the Y-axis as an example, the Y-axis was fitted using the custom fitting function Fittype in Matlab. The fitted Y-axis geometric error is shown in the following formula: (2) The position-related geometric errors of the y-axis are fitted to a fourth-order polynomial. The y-value is the ideal position of the y-axis during machining, expressed in meters. The units of linear error and angular error are μm and μrad, respectively. Similarly, geometric errors on other axes can be modeled using the same method.

[0024] In this preferred embodiment, a Renishaw XL-80 laser interferometer and a Renishaw QC-20W ballbar were used to identify 41 geometric errors. Based on the definition of geometric errors, position-independent errors are constant, while position-dependent geometric errors can be fitted as a function with the axis position as the independent variable.

[0025] Sensitivity analysis begins with defining the sensitivity coefficient. This coefficient measures the degree to which each geometric error in the spatial error model affects the machining error. A larger sensitivity coefficient indicates a more significant impact on workpiece machining. In the spatial error model, errors are vector quantities. During the machining process, each geometric error varies with axis position. This paper defines the sensitivity index as the projection of the error caused by each data point in the machining trajectory, under the influence of each individual geometric error, onto the spatial error. The sensitivity analysis process is detailed below.

[0026] As a preferred embodiment of the present invention, specifically, an error transfer model of a single geometric error is established, including: According to the definition of the machine tool spatial error model formula (1), the parameters in the model include the working position of the five axes of the CNC machine tool, 41 geometric errors and the tool length L. Therefore, the expression of the spatial error model can be expressed as: (3) In formula (3), e represents the error vector composed of 41 geometric errors: e = (e1, e2, … e41) T , where ei represents the i-th geometric error, and the value of i is [1,41]; x, y, z, a, c represent the positions of the five axes of the CNC machine tool respectively; During modeling, the geometric error can be defined as a small amount of motion, and the mutual influence of geometric errors can be ignored. At this time, the spatial error vector E can be regarded as the sum of the error vectors generated by the separate effects of the 41 geometric errors. Figure 3 The error vector caused by each geometric error acting alone and the spatial error vector are expressed as follows: (4) (5) is the machining error caused by the i-th geometric error acting alone, i=1,2,3…41, It is expressed as the error components caused by the geometric error in the X, Y, and Z directions at this position.

[0027] As a preferred embodiment of the present invention, specifically, calculating the sensitivity index of any geometric error includes: From the geometric error modeling mentioned above, we know that the position-independent error is a constant, and the position-dependent error is a function of the axis position as the independent variable. The spatial error model can be simplified to a function with only the five-axis position of the machine tool as a parameter. Before actual processing, engineering software is usually used to generate the machine tool processing program for the workpiece. The motion data of each axis of the machine tool can be obtained through post-processing of the processing program. The position of each axis corresponds to the data point one by one. Therefore, the error transmission model of the machine tool spatial error E and the single geometric error is Can be expressed as: (6) (7) The error vector caused by each geometric error is considered to form the final tool position error vector. Figure 3 middle Is E and The projection on E shows The projection size on E can be used to describe the impact of each geometric error on the tool position error vector. Therefore, this can be used as a basis to define the sensitivity expression Sn: (8) (9) In formula (8) Generates error vectors at data points for individual geometric errors The projection of the total error vector E, N is the number of all data points in the entire machining process. The sensitivity Sn of the nth geometric error in formula (9) is defined as: the sum of the absolute values of the projection Pi of the error vector Ei caused by the geometric error at all data points (the total number of data points is N) on the spatial error E; In order to facilitate the evaluation of the relative influence of each geometric error on the spatial error, the sensitivity index of all geometric errors is normalized, and the normalized sensitivity index Un is defined, which is expressed as follows: (10).

[0028] In this preferred embodiment, based on the position-dependent error polynomial obtained by fitting above, the spatial error model is simplified into a function E with the ideal position as a parameter, and on this basis, a transfer model with each geometric error acting alone is obtained. . The size of the projection on E represents the degree of influence of each geometric error on the spatial error and can therefore be defined as a sensitivity index. This sensitivity analysis method simplifies the parameters of the spatial error model and establishes an independent geometric error transfer model, enabling analysis directly based on the workpiece machining trajectory. This method considers the fundamental condition that spatial errors are vectors and simultaneously reflects the influence of position changes of each axis along the machining trajectory and changes in the magnitude of the geometric errors.

[0029] The feasibility verification process of the present invention is as follows: This paper selects the S specimen as the analysis object. The S specimen is an international standard specimen for precision testing and performance evaluation of five-axis CNC machine tools. It was proposed by China Chengfei in 2013 and later adopted by ISO as a recommended specimen for dynamic precision testing of five-axis machine tools (ISO 10791-7:2020)

[24] . It has been widely used in the machining precision testing and inspection of multi-axis CNC machine tools at home and abroad.

[0030] The UG NX CAM module imports the 3D digital model of the sample, completes the configuration of process parameters such as tool type selection and feed rate setting, and calls the post-processor to generate the NC program for machining the S-shaped specimen surface. This allows the theoretical position data of each motion axis during the five-axis linkage process to be analyzed. Figures 4(a)-(e) respectively show the ideal positions of each axis of the AC dual-turret machine tool when machining the S-shaped specimen surface. The units of translational axis displacement are meters, and the units of rotational axis angle are degrees.

[0031] There are 1935 data points in the machining program of the S specimen surface. By substituting the motion axis position information of each data point into the established spatial error mathematical model (6), the geometric error component of each cutting position in the tool path can be solved. Similarly, by substituting the error transfer model (7) of the 41 geometric errors acting alone, the machining error caused by each geometric error can be calculated. Substituting equations (6)-(10) into the machining trajectory of the S specimen surface, the sensitivity coefficients of the 41 geometric errors after normalization can be obtained. In order to better count the geometric errors, the 41 errors are numbered, and the results are shown in Table 2: Table 2

[0032] Sort the obtained sensitivity values by size, the results are as follows Figure 5 As shown in the figure, it is obvious that the geometric errors of item 30 (εz(c)), 26 (δy(c)), 13 (δx(z)), and 29 (εy(c)) account for a large proportion. In this paper, the geometric error is defined as a critical geometric error if the sensitivity coefficient after normalization is greater than 0.03. Figure 5 From Table 2, we can see that there are 11 key errors in machining the surface of the S specimen, including 4 geometric errors of the translation axis and 7 geometric errors of the rotation axis. It can be seen that the geometric error of the rotation axis has an important influence on the machining accuracy of the S specimen surface.

[0033] Based on Table 2 and Figure 5 The presented geometric error sensitivity coefficients provide key parameters for developing subsequent machine tool precision compensation strategies by evaluating the weight of each geometric error in the overall machining process. Specifically, the weight factor is positively correlated with error sensitivity, and its numerical characteristics directly determine the resource allocation priority for error correction, providing a theoretical basis for critical geometric error compensation.

[0034] 2 Experimental verification To verify the reliability of the proposed geometric error sensitivity analysis method, this paper simulated milling using the surface machining program for the S specimen obtained through post-processing. A φ20 rod milling cutter was used on a V545III AC double-turret machine tool. The 11 identified key errors were compensated for by substituting them into the machine tool's spatial error model (Equation (3)). This compensated for the key geometric errors and determined the tool's error components in the X, Y, and Z directions throughout the machining process. Figure 4 shows the error components in each direction before and after compensation for the key errors, in μm.

[0035] As shown in Figures 6(a)-(c), after compensating for the 11 key errors, the error components in the Y and Z directions are significantly reduced, and the error extremes in the X direction are significantly improved. These results demonstrate that compensating for key geometric errors can significantly improve machining accuracy, validating the effectiveness of this method. Therefore, this method can be used to identify and specifically compensate for key errors in actual machining processes.

[0036] In order to prove that the identified key error has a greater impact on machining than the residual geometric error and to demonstrate its high efficiency in compensating workpiece machining errors, this paper designed three different machine tool accuracy compensation schemes (Table 3) and compared the machining errors of the S specimen surface.

[0037] Table 3

[0038] Figure 7 is the spatial error value of each data point in the entire processing process, in μm. Figure 8 The figure shows the change in the total amount of error during the entire surface machining process of the S specimen under different compensation schemes. Taking the total amount of error without compensating for any errors as a benchmark, after compensating for 11 key errors, the error values of each data point were significantly reduced throughout the entire machining process, and the total error value improved to 26.37% of the pre-compensation value. After compensating for the remaining 30 geometric errors, the error values of each data point did not change significantly, and the total error value reached 88.72% of the pre-compensation value, proving that compensating for key geometric errors can greatly improve machine tool machining accuracy. Compared with compensating for other errors, compensating for key geometric errors has fewer error items and a more significant effect. This shows that compensating for the key geometric errors identified by the sensitivity analysis method in this paper is more effective in improving workpiece machining accuracy. Similarly, this method can also be applied to the sensitivity analysis of error components in the X, Y, and Z directions in any interval during the machining process.

[0039] Although the present invention has been described in considerable detail and with particularity with respect to several described embodiments, it is not intended to be limited to any of these details or embodiments or any particular embodiment, but rather should be construed as providing a broad possible interpretation of these claims in view of the prior art by reference to the appended claims, thereby effectively encompassing the intended scope of the invention. In addition, the invention has been described above in terms of embodiments foreseen by the inventors for the purpose of providing a useful description, and those insubstantial modifications of the invention that are not currently foreseen may still represent equivalent modifications of the invention.

[0040] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. As long as the technical effects of the present invention are achieved by the same means, they shall fall within the scope of protection of the present invention. Within the scope of protection of the present invention, various modifications and variations of the technical solutions and / or implementation methods may be made.

Claims

1. A method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index, characterized in that: Applicable to AC dual-turret five-axis machine tools, including the following: Based on the multi-body system theory and the principle of homogeneous coordinates, a spatial error model of the five-axis machine tool is established; Obtaining measurement results of geometric errors of the five-axis machine tool using a laser interferometer and a ballbar, establishing a spatial error model with the machine tool position as an independent variable based on the measurement results and the spatial error model, and establishing an error transfer model for a single geometric error; Based on the spatial error model with the machine tool position as the independent variable, 41 geometric errors are determined. The sensitivity index is calculated based on the projection of the error vector generated by any geometric error in the machining trajectory on the spatial error, and the sensitivity index corresponding to the 41 geometric errors is obtained. The key geometric errors are identified from the 41 geometric errors based on the sensitivity indicators corresponding to the 41 geometric errors.

2. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 1, characterized in that: Specifically, based on the multi-body system theory and the principle of homogeneous coordinates, the spatial error model of the five-axis machine tool is established, including: Based on the transfer relationship established by multi-body system theory, the deviation between the actual position of the tool cutting point under the influence of geometric error and its ideal position is the tool's spatial error E, which can be obtained from the following formula: (1) In formula (1), 、 、 are the error components of the spatial error E in the X, Y, and Z directions, respectively; L is the tool length; Pwi is the transfer matrix from the workpiece to the tool cutting point under ideal conditions; Pw represents the transfer matrix from the workpiece to the tool cutting point under the influence of 41 geometric errors.

3. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 2, characterized in that: Specifically, based on the measurement results and the spatial error model, a spatial error model with the machine tool position as the independent variable is established, including: Based on the measurement results, 41 geometric errors were identified. Taking the Y-axis as an example, the Y-axis was fitted using the custom fitting function Fittype in Matlab. The fitted Y-axis geometric error is shown in the following formula: (2) The position-related geometric error of the y-axis is fitted into a fourth-order polynomial, where the y value is the ideal position of the y-axis in machine tool processing. Similarly, the geometric errors on other axes can also be modeled using the same method.

4. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 3, characterized in that: Specifically, an error transmission model of single geometric error is established, including: Based on formula (1), the expression of the spatial error model can be expressed as: (3) In formula (3), e represents the error vector composed of 41 geometric errors: e = (e1, e2, … e41) T , where ei represents the i-th geometric error, and the value of i is [1,41]; x, y, z, a, c represent the positions of the five axes of the CNC machine tool respectively; Then the error vector caused by a single geometric error can be expressed as: (4) (5) is the machining error caused by the i-th geometric error acting alone, i=1,2,3…41, It is expressed as the error components caused by the geometric error in the X, Y, and Z directions at this position.

5. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 4, characterized in that: Specifically, the sensitivity index of arbitrary geometric errors is calculated, including, Error transfer model of machine tool spatial error E and single geometric error Can be expressed as: (6) (7) Define the sensitivity index expression Sn: (8) (9) In formula (8) Generates error vectors at data points for individual geometric errors The projection of the total error vector E, N is the number of all data points in the entire machining process; The sensitivity indexes of all geometric errors are normalized, and the normalized sensitivity index Un is defined, which is expressed as: (10)。 6. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 5, characterized in that: Specifically, based on the sensitivity indicators corresponding to the 41 geometric errors, key geometric errors are identified from the 41 geometric errors, including: The normalized sensitivity index Un is calculated based on the sensitivity indices corresponding to the 41 geometric errors, and the geometric error items greater than the preset threshold are recorded as key geometric errors.

7. The method for identifying key geometric errors of CNC machine tools based on machining trajectory sensitivity index according to claim 6, characterized in that: Specifically, the preset threshold is 0.03.

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