A key geometric error tracing method for five-axis nc milling machine

Abstract

A method for tracing the source of key geometric errors in a five-axis CNC milling machine belongs to the field of machine tool accuracy analysis technology. Specifically, it involves a spatial motion error modeling method for multi-axis CNC machine tools based on multibody system theory, a machine tool machining accuracy prediction method based on the side-cut milling principle, and a key geometric error tracing and analysis method. This invention establishes a spatial motion error model, a machining accuracy prediction model, and a key geometric error tracing and analysis model for multi-axis CNC machine tools. By tracing and analyzing the source of key geometric errors in multi-axis CNC machine tools during the machine tool accuracy optimization design phase, machine tool design engineers can accurately identify key geometric errors. This helps to obtain the influence weight of various geometric errors on machine tool machining accuracy before machine tool accuracy optimization design, correctly guiding machine tool accuracy design and laying a theoretical foundation for CNC machine tool accuracy optimization design.

Description

Technical Field

[0001] This invention relates to a method for tracing the source of key geometric errors in multi-axis CNC machine tools, belonging to the field of machine tool accuracy analysis technology. Background Technology

[0002] The overall machining accuracy of CNC machine tools is a crucial indicator of their machining performance and a significant reflection of a nation's overall machinery manufacturing capabilities and development level. Accuracy optimization design is an effective way to improve machine tool machining accuracy. Because different geometric errors have varying degrees of impact on overall machining accuracy, relying solely on past design experience for CNC machine tool optimization can easily lead to subjective influences on accuracy allocation, resulting in excessively high or low machining accuracy. Therefore, sensitivity analysis of various geometric errors is necessary to determine their weighted impact on overall machining accuracy, thereby correctly guiding the machine tool accuracy optimization design.

[0003] The solution to this key problem involves three steps:

[0004] First, based on the kinematics theory of multibody systems, a spatial error model for machine tools is established;

[0005] Currently, scholars both domestically and internationally have conducted numerous studies on machine tool accuracy modeling methods, resulting in methods such as the quadratic relation model method, geometric modeling method, error matrix method, rigid body kinematics method, and multibody system theory method. Based on multibody system kinematics theory, this paper abstracts a five-axis machine tool into a multibody system, using topological structure diagrams and low-order body array tables to describe the machine tool's structure and the relationships between its various bodies. It analyzes the geometric errors of the CNC machine tool, establishes a generalized coordinate system, uses characteristic matrices between adjacent bodies to represent positional relationships, and uses homogeneous transformation matrices to represent the interrelationships between the multibody systems, ultimately establishing a spatial error model for the machine tool.

[0006] Second, based on the side-edge milling principle, a machining error prediction model is established;

[0007] The machine tool spatial motion error model established based on multibody system theory reflects the error at the tool's center point. However, side milling is a machining method where the entire side edge of the tool contacts the machined surface; therefore, the error at the tool's center point needs to be offset accordingly. Based on the principle of edge-measuring milling, the theoretical cutting point can be obtained by offsetting the tool radius by the tool's unit normal vector on the theoretical tool axis trajectory surface. Similarly, the actual cutting point can be obtained for points on the actual tool axis trajectory surface. The surface profile error of the machined workpiece is determined by the normal distance between the ideal cutting surface and the actual cutting surface, ultimately leading to a machining error prediction model.

[0008] Third, establish a sensitivity analysis model for key geometric errors.

[0009] Sensitivity analysis of critical geometric errors reflects the degree of influence of various geometric errors on machining errors in the machining space of a CNC machine tool. To quantify and compare this influence, and to simplify the calculation process, this invention defines a simple sensitivity index that accurately reflects this influence. The peak value of the machining error caused by each geometric error acting alone is used as the sensitivity corresponding to that geometric error. Finally, a sensitivity analysis model for critical geometric errors is established. A larger peak value indicates a greater influence of that geometric error on the machining error, while a smaller peak value indicates a smaller influence.

[0010] The invention patent CN108445839A describes a geometric error identification method based on error increments, which involves relatively large computational loads and complex calculation processes. Therefore, it is necessary to propose a simpler geometric error sensitivity analysis method to facilitate machine tool design engineers in accurately identifying key geometric errors and obtaining the influence weights of various geometric errors on machine tool machining accuracy. Summary of the Invention

[0011] The purpose of this invention is to provide a method for tracing the source of key geometric errors in multi-axis CNC machine tools. By establishing a spatial motion error model for CNC machine tools based on multibody system theory and the principle of side-cut milling, a machine tool machining accuracy prediction model is derived. Based on this model, a simple sensitivity index that accurately reflects the degree of influence is defined. This allows for the accurate identification of key geometric errors in a relatively simple way, laying the foundation for research on machine tool accuracy optimization design and providing practical value and guidance for machine tool design engineers.

[0012] To achieve the above objectives, the technical solution adopted in this invention is a method for tracing the source of key geometric errors in multi-axis CNC machine tools. First, this invention establishes a spatial motion error model for the machine tool based on the kinematics theory of multibody systems. Then, based on the side-edge milling principle and combined with the spatial motion error model, a machine tool machining accuracy prediction model is derived. Next, based on the machining accuracy prediction model, a source-tracing analysis model for key geometric errors in CNC machine tools is established. Finally, simulation analysis and experimental verification of the source-tracing analysis model for key geometric errors in machine tools are conducted, proving the correctness of the model.

[0013] This method specifically includes the following steps:

[0014] Step 1: Spatial motion error modeling based on multibody system theory;

[0015] Based on the kinematics theory of multibody systems, the structure of the machine tool and the relationship between its various bodies are described using a multibody system diagram and a low-order body array table. The geometric error of the CNC machine tool is analyzed, a generalized coordinate system is established, the positional relationship is expressed by the characteristic matrix between adjacent bodies, and the relationship between the multibody systems is represented by the homogeneous transformation matrix.

[0016] Step 1.1 Establish the topology of the CNC machine tool;

[0017] A CNC machine tool is a complex, multi-branched system. It splits into two branches starting at point B1. Besides B1, every object in the system has an adjacent lower-order body. When deriving kinematics and developing computational methods, a table needs to be created for the lower-order bodies of each object in the system, using L... n (j) indicates that it is called the low-order volume array table, as shown in Table 1. j represents the serial number of the object, j = 1, 2, 3...n, and n represents the number of typical bodies contained in the machine tool.

[0018] Table 1: Low-order volume array of CNC machine tools

[0019] <![CDATA[L 0 (j)]]> 1 2 3 4 5 6 <![CDATA[L 1 (j)]]> 0 1 1 3 4 5 <![CDATA[L 2 (j)]]> 0 0 0 1 3 4 <![CDATA[L 3 (j)]]> 0 0 0 0 1 3 <![CDATA[L 4 (j)]]> 0 0 0 0 0 1 <![CDATA[L 5 (j)]]> 0 0 0 0 0 0

[0020] The numbering rules for typical examples are as follows:

[0021] First, select a typical body as B1, and then, along the direction away from B1, label the serial number of each object in the order of natural growth, from one branch of the system to another, until all objects are labeled.

[0022] Step 1.2 Geometric Error Analysis of CNC Machine Tools

[0023] In a spatial coordinate system, any object has 6 degrees of freedom. During the motion, 6 errors will inevitably be generated: 3 linear displacement errors and 3 angular displacement errors. These are all errors related to the position point. There are 3 non-perpendicularity errors between the X, Y, and Z guide rails. There are 4 perpendicularity errors between the C-axis and the X and Y axes, and between the A-axis and the Y and Z axes. Therefore, there are a total of 37 errors as shown in Table 2.

[0024] Table 2: Geometric Error Parameters of CNC Machine Tools

[0025]

[0026]

[0027] Step 1.3: Establish the feature matrix of the CNC machine tool;

[0028] In bed B1 and all components B j A right-handed rectangular Cartesian three-dimensional coordinate system O1-X1Y1Z1 and O are established on each of them and are fixedly connected to them. j -Xj Y j Z j The set of these coordinate systems is called a generalized coordinate system, and each volume coordinate system is called a sub-coordinate system. The three orthogonal bases of each coordinate system are named X, Y, and Z axes according to the right-hand rule. The corresponding coordinate axes of each sub-coordinate system are parallel to each other. The positive direction of the coordinate axis is the same as the positive direction of its corresponding motion axis.

[0029] Based on the motion relationships between the components of the CNC machine tool, the transformation matrix between each adjacent body is established as shown in Table 3.

[0030] Table 3: Transformation Matrix Between Adjacent Volumes

[0031]

[0032]

[0033] Among them: [Sij] p B j Body relative to B i The relative position transformation matrix of the body;

[0034] [Sij] pe B j Body relative to B i The relative position error transformation matrix of the body;

[0035] [Sij] s B j Body relative to B i The relative motion transformation matrix of the body;

[0036] [Sij] se B j Body relative to B i The relative motion error transformation matrix of the body;

[0037] x represents the distance translated along the X-axis;

[0038] y represents the distance translated along the Y-axis;

[0039] z represents the distance translated along the Z-axis;

[0040] 'a' represents the angle of rotation of axis A;

[0041] c represents the angle of rotation of the C-axis;

[0042] Step 1.4 Establish the spatial error model of the machine tool

[0043] Establishment of an ideal model of the motion relationship between adjacent bodies;

[0044] Let point P be B jFor any point on the body, P lies at point B. i body coordinate system O i -X i Y i Z i The position matrix expression in the middle is:

[0045] P ji =[Sij] p [Sij] s r j (1)

[0046] In the formula: P ji Point P in coordinate system O i -X i Y i Z i The position matrix expression in the text;

[0047] r j Point P in coordinate system O j -X j Y j Z j The position matrix expression in the text;

[0048] [Sij] p B j Body relative to B i The relative position transformation matrix of the body;

[0049] [Sij] s B j Body relative to B i The relative motion transformation matrix of the body;

[0050] Establishment of a model of the motion relationship between adjacent bodies under the condition of error;

[0051] Let point P be B j For any point on the body, P lies at point B. i body coordinate system O i -X i Y i Z i The position matrix expression in the middle is:

[0052] P ji =[Sij] p [Sij] pe [Sij] s [Sij] se r j (2)

[0053] In the formula: P ji Point P in coordinate system O i -X i Yi Z i The position matrix expression in the text;

[0054] r j Point P in coordinate system O j -X j Y j Z j The position matrix expression in the text;

[0055] [Sij] p B j Body relative to B i The relative position transformation matrix of the body;

[0056] [Sij] pe B j Body relative to B i The relative position error transformation matrix of the body;

[0057] [Sij] s B j Body relative to B i The relative motion transformation matrix of the body;

[0058] [Sij] se B j Body relative to B i The relative motion error transformation matrix of the body;

[0059] The coordinates of the tool center point in the tool coordinate system are:

[0060] r t =[0,0,l,1] T (3)

[0061] In the formula: l represents the tool length;

[0062] The subscript t indicates the cutting tool.

[0063] Ideally, the position matrix expression of the tool center point P in the inertial coordinate system according to the "CNC machine tool-workpiece" branch is as follows:

[0064]

[0065] Ideally, the position matrix expression of the tool center point P in the inertial coordinate system according to the "CNC machine tool - tool" branch is as follows:

[0066]

[0067] Precision machining equations for CNC commands:

[0068] P w I =P tI (6)

[0069] Ideally, the position matrix expression of CNC commands in the workpiece coordinate system is:

[0070]

[0071] In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-workpiece" branch is as follows:

[0072]

[0073] In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-tool" branch is as follows:

[0074]

[0075] In practice, the expression for the position matrix of CNC commands in the workpiece coordinate system is as follows:

[0076]

[0077] The spatial error model of a CNC machine tool is then expressed as:

[0078] E = r w -r w I (11)

[0079] Step 2: Construction of the machining accuracy prediction model;

[0080] The machine tool spatial motion error model reflects the error on the tool axis trajectory surface, while side milling is a machining method in which the entire side edge of the tool contacts the machined surface. Therefore, it is necessary to offset the points on the tool axis trajectory surface according to the normal vector at those points in order to obtain the error at the cutting point.

[0081] The ideal position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position:

[0082]

[0083] The actual position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position:

[0084]

[0085] In the formula: r tjk Let r be the position vector of the tool center point corresponding to the k-th cutting point in the tool coordinate system, and r tjk =(0 0 -l k1).

[0086] By offsetting the tool radius d by the tool offset normal vector at a point on the actual tool axis trajectory surface, the actual cutting point corresponding to that point can be obtained.

[0087] u jk =r wjk (dn pjk (14)

[0088] In the formula: u jk This represents the actual position vector of the k-th cutting point at the j-th tool position point in the workpiece coordinate system;

[0089] d is the tool radius;

[0090] n pjk Let be the tool offset normal vector at the k-th cutting point of the j-th tool position.

[0091] By offsetting the tool radius d by the tool offset normal vector at that point on the theoretical tool axis trajectory surface, the theoretical cutting point corresponding to that point can be obtained.

[0092]

[0093] Therefore, the surface profile error of the workpiece is:

[0094]

[0095] Where: n sjk This represents the unit normal vector of the specimen at the k-th cutting point at the j-th tool position.

[0096] Substituting equations (14) and (15) into equation (16), we can obtain the machining accuracy prediction model for a gantry-type five-axis CNC milling machine.

[0097] e = (e x e y e z 0) T (17)

[0098] In the formula: e x This represents the component of the machining error in the X direction.

[0099] e y This represents the component of the machining error in the Y direction.

[0100] e z This represents the component of the machining error in the Z direction.

[0101] Step 3: Construction of the source analysis model for key geometric errors of CNC machine tools;

[0102] Geometric error sensitivity analysis reflects the degree of influence of various geometric errors on machining errors in the machining space of a CNC machine tool. To quantify and compare this influence, and to simplify the calculation process, a simple sensitivity index that accurately reflects this influence is needed. This invention uses the peak value of the machining error caused by each geometric error acting alone as the sensitivity corresponding to that geometric error. A larger peak value indicates a greater influence of that geometric error on the machining error, while a smaller peak value indicates a smaller influence.

[0103] According to equation (17), the machining error generated when each geometric error acts alone can be obtained:

[0104] e i =(e ix e iy e iz 0) T (18)

[0105] In the formula, i represents the geometric error of the i-th term, i = 1, 2, 3, ..., n; e i This refers to the machining error generated when the i-th geometric error acts alone.

[0106] Therefore, the sensitivity expressions for each geometric error can be obtained from equation (18):

[0107]

[0108] To more intuitively identify key geometric errors and assign weights to each geometric error, the sensitivity of each geometric error is normalized, resulting in sensitivity coefficients for each geometric error:

[0109]

[0110] Based on the source analysis model for key geometric errors of machine tools established according to this invention, the source analysis of key geometric errors of machine tools is performed using MATLAB R2016b. This facilitates machine tool design engineers to accurately identify key geometric errors, thereby helping to obtain the influence weight of various geometric errors on the machining accuracy of machine tools before the precision optimization design of machine tools, and correctly guiding the precision design of machine tools.

[0111] Compared with the prior art, the present invention has the following beneficial effects.

[0112] Existing methods for sensitivity analysis of geometric errors in CNC machine tools are computationally intensive, complex, and lack feasibility and practicality. To facilitate the calculation of sensitivity coefficients for various geometric errors, some researchers assume all geometric errors are constant values. This leads to sensitivity analysis results that fail to reflect the crucial factor of how CNC machine tool geometric errors change with the machining position. Furthermore, the units of angular error parameters and linear error parameters differ, requiring separate sensitivity calculations. To accurately identify key geometric errors and simplify the calculation process, this invention defines a simple sensitivity index that accurately reflects the impact of various geometric errors on machine tool machining accuracy. This invention first establishes a predictive model for the overall machining accuracy of the machine tool; then, based on this model, it establishes a sensitivity analysis model for each geometric error, while defining a new sensitivity index to determine the influence weight of each geometric error on the overall machining accuracy, thereby correctly guiding machine tool accuracy design. Attached Figure Description

[0113] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0114] Figure 2 This is a structural schematic diagram of a five-axis machine tool;

[0115] Figure 3 This is a topology diagram of a five-axis machine tool;

[0116] Figure 4 This is a schematic diagram of side milling.

[0117] Figure 5 Define the side milling machining error;

[0118] Figure 6 Sort by geometric error sensitivity coefficients;

[0119] Figure 7 This is a flowchart for experimental verification.

[0120] Figure 8 The location of the error detection point for the "S"-shaped test piece;

[0121] Figure 9a The profile error on the first inspection line of the "S"-shaped test piece;

[0122] Figure 9b The profile error on the first inspection line of the "S"-shaped test piece;

[0123] Figure 9c The profile error on the first inspection line of the “S” shaped test piece. Detailed Implementation

[0124] This invention takes a five-axis overhead beam moving gantry CNC milling machine as an example to verify the above-mentioned method for predicting the machining accuracy of a five-axis CNC milling machine.

[0125] Specifically, the steps include the following:

[0126] Step 1: Taking a five-axis CNC machine tool as an example, establish the spatial error model of the machine tool;

[0127] Based on the kinematics theory of multibody systems, the structure of the machine tool and the relationship between its various bodies are described using topological structure diagrams and low-order body array tables. The geometric errors of the CNC machine tool are analyzed, a generalized coordinate system is established, the positional relationship is expressed by the characteristic matrix between adjacent bodies, and the mutual relationship between the multibody systems is represented by the homogeneous transformation matrix.

[0128] Step 1.1 Establish the topology of the five-axis CNC machine tool;

[0129] The structure of the machine tool is as follows Figure 2 As shown. Includes the bed, worktable, cutting tool, workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis, and spindle;

[0130] A five-axis CNC machine tool is a complex system with multiple branches. Its topology is as follows: Figure 3 As shown, the system splits into two branches from point B1. Each object, except for one at B1, has an adjacent lower-order body. When deriving the kinematics and developing the computational method, a table needs to be created for the lower-order bodies of each object in the system, using L... n (j) indicates that it is called the low-order volume array table, as shown in Table 1. j represents the index of the object (j = 1, 2, 3...n), and n represents the number of typical bodies contained in the machine tool.

[0131] Table 1: Low-order volume array of CNC machine tools

[0132]

[0133]

[0134] The numbering rules for typical examples are as follows:

[0135] First, select a typical body as B1, and then, along the direction away from B1, label the serial number of each object in the order of natural growth, from one branch of the system to another, until all objects are labeled.

[0136] Step 1.2 Analyze the geometric errors of the five-axis CNC machine tool;

[0137] In a spatial coordinate system, any object has 6 degrees of freedom. During the motion, 6 errors will inevitably be generated: 3 linear displacement errors and 3 angular displacement errors. These are all errors related to the position point. There are 3 non-perpendicularity errors between the X, Y, and Z guide rails. There are 4 perpendicularity errors between the C-axis and the X and Y axes, and between the A-axis and the Y and Z axes. Therefore, there are a total of 37 errors as shown in Table 2.

[0138] Table 2: Geometric Error Parameters of Five-Axis CNC Machine Tools

[0139]

[0140] Step 1.3: Establish the feature matrix of the five-axis CNC machine tool;

[0141] In bed B1 and all components B j A right-handed rectangular Cartesian three-dimensional coordinate system O1-X1Y1Z1 and O are established on each of them and are fixedly connected to them. j -X j Y j Z j The set of these coordinate systems is called a generalized coordinate system, and each volume coordinate system is called a sub-coordinate system. The three orthogonal bases of each coordinate system are named X, Y, and Z axes according to the right-hand rule. The corresponding coordinate axes of each sub-coordinate system are parallel to each other. The positive direction of the coordinate axis is the same as the positive direction of its corresponding motion axis.

[0142] Based on the motion relationships between the components of a CNC machine tool, the transformation matrix between adjacent bodies can be established as shown in Table 3.

[0143] Table 3: Transformation Matrix Between Adjacent Volumes

[0144]

[0145]

[0146] Step 1.4 Establish the spatial error model of the machine tool;

[0147] The coordinates of the tool center point in the tool coordinate system are:

[0148] r t =[0,0,l,1] T (1)

[0149] l represents the tool length;

[0150] The subscript t indicates the cutting tool

[0151] The ideal expression for the position matrix of the tool center point P in the inertial coordinate system according to the "machine-workpiece" branch is as follows:

[0152] P wI =[S12] p [S12] s r w (2)

[0153] The ideal expression for the position matrix of the tool center point P in the inertial coordinate system according to the "machine-tool" branch is as follows:

[0154] P t I =[S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r t (3)

[0155] Precision machining equations for CNC commands:

[0156] P w I =P t I (4)

[0157] Ideally, the position matrix expression of CNC commands in the workpiece coordinate system is:

[0158] r w I =([S12]) p [S12] s ) -1 [S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r t (5)

[0159] In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-workpiece" branch is as follows:

[0160] P w =[S12] p [S12] pe [S12] s [S12] se r w (6)

[0161] In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-tool" branch is as follows:

[0162]

[0163] In practice, the expression for the position matrix of CNC commands in the workpiece coordinate system is as follows:

[0164]

[0165] The spatial error model of the machine tool is then expressed as:

[0166] E = r w -r w I (9)

[0167] Step 2: Construction of the machining accuracy prediction model;

[0168] The machine tool spatial motion error model reflects the error on the tool axis trajectory surface, while side milling is a machining method in which the entire side edge of the tool contacts the machined surface, such as... Figure 4 As shown, it is therefore necessary to offset the points on the tool axis trajectory surface according to the normal vector at those points in order to obtain the error at the cutting point. The surface profile error of the machined workpiece is determined by the normal distance between the ideal cutting surface and the actual cutting surface, such as... Figure 5 As shown.

[0169] The ideal position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position:

[0170] r wjk I =([S12]) p [S12] s ) -1 [S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r tjk (10)

[0171] The actual position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position:

[0172]

[0173] In the formula: rtjk Let r be the position vector of the tool center point corresponding to the k-th cutting point in the tool coordinate system, and r tjk =(0 0 -l k 1).

[0174] By offsetting the tool radius d by the tool offset normal vector at a point on the actual tool axis trajectory surface, the actual cutting point corresponding to that point can be obtained.

[0175] u jk =r wjk (dn pjk (12)

[0176] In the formula: u jk This represents the actual position vector of the k-th cutting point at the j-th tool position point in the workpiece coordinate system;

[0177] d is the tool radius;

[0178] n pjk Let be the tool offset normal vector at the k-th cutting point of the j-th tool position.

[0179] By offsetting the tool radius d by the tool offset normal vector at that point on the theoretical tool axis trajectory surface, the theoretical cutting point corresponding to that point can be obtained.

[0180]

[0181] Therefore, the surface profile error of the workpiece is:

[0182]

[0183] Where: n sjk This represents the unit normal vector of the specimen at the k-th cutting point at the j-th tool position.

[0184] Substituting equations (12) and (13) into equation (14), we can obtain the machining accuracy prediction model for a gantry-type five-axis CNC milling machine.

[0185] e = (e x e y e z 0) T (15)

[0186] In the formula: e x This represents the component of the machining error in the X direction.

[0187] e y This represents the component of the machining error in the Y direction.

[0188] e z This represents the component of the machining error in the Z direction.

[0189] Step 3: Construction of the source analysis model for key geometric errors of CNC machine tools;

[0190] Geometric error sensitivity analysis reflects the degree of influence of various geometric errors on machining errors in the machining space of a CNC machine tool. To quantify and compare this influence, and to simplify the calculation process, a simple sensitivity index that accurately reflects this influence is needed. This invention uses the peak value of the machining error caused by each geometric error acting alone as the sensitivity corresponding to that geometric error. A larger peak value indicates a greater influence of that geometric error on the machining error, while a smaller peak value indicates a smaller influence.

[0191] According to equation (15), the machining error generated when each geometric error acts alone can be obtained:

[0192] e i =(e ix e iy e iz 0) T (16)

[0193] In the formula, i represents the geometric error of the i-th term, i = 1, 2, 3, ..., 37; e i This refers to the machining error generated when the i-th geometric error acts alone.

[0194] Therefore, the sensitivity expressions for each geometric error can be obtained from equation (16):

[0195]

[0196] To more intuitively identify key geometric errors and assign weights to each geometric error, the sensitivity of each geometric error is normalized, resulting in sensitivity coefficients for each geometric error:

[0197]

[0198] In order to more intuitively characterize the influence of each geometric error on the machining error of the machine tool when acting alone, this invention selects the “S”-shaped test piece, which is suitable for the inspection and acceptance of machining accuracy of five-axis CNC machine tools, as the research object. According to formula (16), the surface contour error of the “S”-shaped test piece is simulated and analyzed using MATLAB R2016b.

[0199] To better illustrate the various geometric errors, they are numbered as shown in Table 4. Based on the simulation analysis results of the surface contour error of the "S"-shaped test piece, the sensitivity values ​​of each geometric error can be obtained. Based on equation (18) and the sensitivity values ​​of each geometric error, the sensitivity coefficients of each geometric error can be obtained and sorted, as shown in Table 4. Figure 6 As shown, a sensitivity coefficient greater than 0.05 is defined as a critical geometric error. The figure clearly shows that geometric errors 10, 17, 22, 24, and 37 are the critical geometric errors of this machine tool. Furthermore, according to... Figure 6 We can obtain the weighting factors for each geometric error, and assign weights to each geometric error based on the weighting factors, laying the foundation for the subsequent research on machine tool accuracy optimization.

[0200] Table 4. Numbers corresponding to each geometric error

[0201]

[0202] To verify the accuracy of the proposed tolerance parameter sensitivity analysis method, an "S"-shaped test piece was milled using a gantry-type five-axis CNC milling machine. The experimental verification flowchart is as follows: Figure 7 As shown, compensation strategy 1 uses an iterative compensation method to compensate for the key geometric errors identified and obtain the compensated NC instruction code, while compensation strategy 2 uses an iterative compensation method to compensate for all geometric errors and obtain the compensated NC instruction code.

[0203] To facilitate the detection of contour error in "S"-shaped test pieces, such as Figure 8 As shown, three test lines, S1, S2, and S3, are taken along the height direction of the S-shaped test piece's flange. S3 is 5mm from the top of the S-shaped flange, and the distances between S2 and S3, and between S1 and S2, are both 12.5mm. Twenty-five test points are equidistantly selected along each of the three test lines, resulting in a total of 75 test points. The distribution of these 75 test points is shown below. Figure 8 As shown in Figure 9, the measurement results are presented. To more intuitively reflect the effectiveness of the proposed key geometric error identification method, the average profile error of the "S"-shaped test piece obtained based on the two compensation strategies is compared, as shown in Table 5.

[0204] Table 5 Comparison of Average Contour Error of “S” Shaped Test Specimens

[0205]

[0206] Table 5 shows that the average profile error on S1, S2, and S3 decreased from 0.041 mm to 0.036 mm, from 0.036 mm to 0.032 mm, and from 0.044 mm to 0.038 mm, respectively. This means that the average profile error of the "S"-shaped test piece obtained based on compensation strategy 2 decreased by 0.005 mm, 0.004 mm, and 0.006 mm on S1, S2, and S3, respectively. The comparison results indicate that the profile error obtained by the key geometric error identified through compensation is not significantly different from the final profile error obtained by all geometric errors. Therefore, the key geometric error source analysis method proposed in this invention can effectively identify key geometric errors of machine tools and reasonably allocate weights to each geometric error, thereby correctly guiding the precision optimization design of five-axis CNC machine tools.

Claims

1. A method for tracing key geometric errors of a five-axis NC milling machine, characterized in that, The method specifically includes the following steps: Step 1: Establish the spatial error model of the machine tool; Based on the kinematics theory of multibody systems, the structure of the machine tool and the relationship between its various bodies are described using topological structure diagrams and low-order body array tables. The geometric errors of the CNC machine tool are analyzed, a generalized coordinate system is established, the positional relationship is expressed by the characteristic matrix between adjacent bodies, and the mutual relationship between the multibody systems is represented by the homogeneous transformation matrix. Step 1.1 Establish the topology of the five-axis CNC machine tool; Includes bed, worktable, cutting tool, workpiece, X-axis, Y-axis, Z-axis, A-axis, C-axis, and spindle; A five-axis CNC machine tool is a complex, multi-branched system. It splits into two branches starting at point B1. Besides B1, each object has an adjacent lower-order body. When deriving kinematics and developing computational methods, a table needs to be created for the lower-order bodies of each object in the system, using L... n (j) indicates that it is called the low-order volume array table, as shown in Table 1. j represents the index of the object (j = 1, 2, 3...n), and n represents the number of typical bodies contained in the machine tool. Table 1: Low-order volume array of CNC machine tools The numbering rules for typical examples are as follows: First, select a typical body as B1, and then, along the direction away from B1, label the serial number of each object in the order of natural growth, from one branch of the system to another, until all objects are labeled. Step 1.2 Analyze the geometric errors of the five-axis CNC machine tool; In a spatial coordinate system, any object has 6 degrees of freedom. During the motion, 6 errors will inevitably be generated: 3 linear displacement errors and 3 angular displacement errors. These are all errors related to the position point. There are 3 non-perpendicularity errors between the X, Y, and Z guide rails. There are 4 perpendicularity errors between the C-axis and the X and Y axes, and between the A-axis and the Y and Z axes. Therefore, there are a total of 37 errors as shown in Table 2. Table 2: Geometric Error Parameters of Five-Axis CNC Machine Tools Step 1.3: Establish the feature matrix of the five-axis CNC machine tool; In bed B1 and all components B j A right-handed rectangular Cartesian three-dimensional coordinate system O1-X1Y1Z1 and O are established on each of them and are fixedly connected to them. j -X j Y j Z j The set of these coordinate systems is called a generalized coordinate system, and each volume coordinate system is called a sub-coordinate system. The three orthogonal bases of each coordinate system are named X, Y, and Z axes according to the right-hand rule. The corresponding coordinate axes of each sub-coordinate system are parallel to each other. The positive direction of the coordinate axis is the same as the positive direction of its corresponding motion axis. Based on the motion relationships between the components of a CNC machine tool, the transformation matrix between adjacent bodies can be established as shown in Table 3. Table 3: Transformation Matrix Between Adjacent Volumes Step 1.4 Establish the spatial error model of the machine tool; The coordinates of the tool center point in the tool coordinate system are: r t ＝[0,0,l,1] T (1) l represents the tool length; The subscript t indicates the cutting tool The ideal expression for the position matrix of the tool center point P in the inertial coordinate system according to the "machine-workpiece" branch is as follows: P w I = [S12] p [S12] s r w (2) The ideal expression for the position matrix of the tool center point P in the inertial coordinate system according to the "machine tool-tool" branch is as follows: P t I = [S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r t (3) Precision machining equations for CNC commands: P w I = P t I (4) Ideally, the position matrix expression of CNC commands in the workpiece coordinate system is: r w I =([S12] p [S12] s ) -1 [S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r t (5) In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-workpiece" branch is as follows: P w = [S12] p [S12] pe [S12] s [S12] se r w (6) In practice, the position matrix expression of the tool center point P in the inertial coordinate system according to the "machine tool-tool" branch is as follows: In practice, the expression for the position matrix of CNC commands in the workpiece coordinate system is as follows: The spatial error model of the machine tool is then expressed as: E＝r w -r w I (9) Step 2: Construction of the machining accuracy prediction model; The machine tool spatial motion error model reflects the error on the tool axis trajectory surface. Side milling is a machining method in which the entire side edge of the tool contacts the machined surface. Therefore, it is necessary to offset the points on the tool axis trajectory surface according to the normal vector at that point in order to obtain the error at the cutting point. The surface profile error of the machined workpiece is determined by the normal distance between the ideal cutting surface and the actual cutting surface. The ideal position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position: r wjk I =([S12] p [S12] s ) -1 [S13] p [S13] s [S34] p [S34] s [S45] p [S45] s [S56] p [S56] s r tjk (10) The actual position vector of the tool center point in the workpiece coordinate system corresponding to the k-th cutting point at the j-th tool position: In the formula: r tjk Let r be the position vector of the tool center point corresponding to the k-th cutting point in the tool coordinate system, and r tjk =(00-l k 1); By offsetting the tool radius d by the tool offset normal vector at that point on the actual tool axis trajectory surface, the actual cutting point corresponding to that point can be obtained. u jk = r wjk (dn pjk ) (12) In the formula: u jk This represents the actual position vector of the k-th cutting point at the j-th tool position point in the workpiece coordinate system; d is the tool radius; n pjk is the tool offset normal vector at the kth cutting point of the jth tool position; By offsetting the tool radius d by the tool offset normal vector at that point on the theoretical tool axis trajectory surface, the theoretical cutting point corresponding to that point can be obtained. Therefore, the surface profile error of the workpiece is: wherein: n sjk nj k represents the unit normal vector of the test piece on the kth cutting point at the jth tool position; Substituting equations (12) and (13) into equation (14), we can obtain the machining accuracy prediction model for a gantry-type five-axis CNC milling machine. e = (e x e y e z 0) T (15) wherein: e x is the component of the machining error in the X direction; e y is the component of the processing error in the Y direction; e z is the component of the machining error in the Z direction; Step 3: Construction of the source analysis model for key geometric errors of CNC machine tools; Geometric error sensitivity analysis reflects the degree of influence of various geometric errors on machining errors in the machining space of a CNC machine tool. In order to quantify and compare this degree of influence and simplify the calculation process, it is necessary to define a simple sensitivity index that can truly reflect this degree of influence. This invention uses the peak value of the machining error caused by each geometric error acting alone as the sensitivity corresponding to each geometric error; the larger the peak value of the machining error, the greater the influence of the geometric error on the machining error, and the smaller the peak value, the smaller the influence. According to equation (15), the machining error generated when each geometric error acts alone can be obtained: e i = (e ix e iy e iz 0) T (16) where i is the i-th geometric error, i = 1, 2, 3,..., 37; e i is the machining error produced by the i-th geometric error acting alone; Therefore, the sensitivity expressions for each geometric error can be obtained from equation (16): To more intuitively identify key geometric errors and assign weights to each geometric error, the sensitivity of each geometric error is normalized, resulting in sensitivity coefficients for each geometric error:

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