Three-axis machine tool static error identification method based on multi-flexible body system theory

Abstract

The invention discloses a three-axis machine tool static error identification method based on a multi-flexible-body system theory, and the method comprises the steps: building a static error model of a machine tool through the multi-flexible-body system theory and a homogeneous coordinate transformation matrix, building a static error parameterized model through combining with a fourth-order Chebyshev polynomial pre-fitting model, and carrying out the recognition of the static error of the machine tool. The method comprises the following steps: establishing a spatial beam unit, establishing a rigidity model of each subsystem based on the spatial beam unit, carrying out quantitative analysis on an elastic error component, providing a simplified machine tool static error model, establishing a machine tool precision field, analyzing and detecting the distribution condition of a spatial static error, and revealing a coupling relationship between a geometric error and an elastic error. According to the established static error model and experimental results, the influence of geometric errors caused by manufacturing defects and elastic errors caused by gravity of structural components on the static precision of the machine tool is comprehensively considered, and the coupling relation between the geometric errors and the elastic errors is demonstrated, so that the identification precision of the static errors of the machine tool is greatly improved.

Description

Technical Field

[0001] The invention belongs to the field of precision detection of three-axis CNC machine tools, and specifically relates to a static error identification (source tracing analysis) method of three-axis machine tools based on multi-flexible body system theory. Background Art

[0002] The machining accuracy of machine tools is one of the important indicators to measure their performance. The factors affecting machining accuracy can be divided into two categories according to different error sources: dynamic error and static error. At present, the research on static error mainly includes three parts: error modeling, error identification and error compensation.

[0003] Current research mainly considers the geometric errors caused by manufacturing and assembly in the static errors of machine tools, while ignoring the elastic errors caused by external forces, especially gravity. However, as a flexible and efficient automated machine tool, the gravity-induced elastic errors of CNC machine tools cannot be ignored, and there are complex coupling relationships between various errors. Therefore, it is urgent to reasonably establish a static error model of machine tools, and complete experiments, identification and verification on the target machine tools to achieve the purpose of improving the machining accuracy of three-axis CNC machine tools. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a static error identification (source tracing analysis) method for a three-axis machine tool based on the theory of multi-flexible body systems. The method improves the identification accuracy of the static error of the machine tool by comprehensively considering the influence of the geometric errors caused by manufacturing defects and the elastic errors of the structural components caused by gravity on the static accuracy of the machine tool, as well as the coupling relationship between the two.

[0005] In order to solve the above technical problems, the present invention is implemented through the following technical solutions:

[0006] A static error identification method for a three-axis machine tool based on multi-flexible body system theory includes the following steps:

[0007] Step 1) A static error model of a three-axis machine tool is established based on the theory of multi-flexible body systems and homogeneous coordinate transformation matrices, and a geometric error component caused by manufacturing defects and an elastic error component caused by gravity on structural components in the static error are qualitatively analyzed;

[0008] Step 2) using Chebyshev polynomials to establish a static error parameterization model, and quantitatively analyzing the static error based on a ballbar three-axis linkage experiment; and conducting an NC code compensation experiment on a target machine tool;

[0009] Step 3) The machine tool is discretized into three subsystems using the finite element method, and the stiffness model of each subsystem is established through the spatial beam unit, and then the elastic error component in the static error of the machine tool is quantitatively analyzed; then the target machine tool is modeled using three-dimensional modeling software, and the model is imported into the simulation software for simulation, and then the simulation results are compared with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method;

[0010] Step 4) Establish the machine tool accuracy field, analyze and detect the distribution of spatial static errors, and reveal the coupling relationship between geometric errors and elastic errors.

[0011] Furthermore, in step 1, the static error model of the three-axis machine tool is established according to the multi-flexible body system theory and the homogeneous coordinate transformation matrix, and the specific steps are as follows:

[0012] Step 1.1) Determine the number and types of geometric errors and elastic errors in the static errors of the three-axis machine tool;

[0013] Step 1.2) Establish the topological structure of the target machine tool according to the multi-flexible body system theory, and specify the number of main bodies, tool kinematic chains, and workpiece kinematic chains in the constructed topological structure;

[0014] Step 1.3) Based on the theory of multi-flexible body systems, homogeneous coordinate transformation matrices and geometric features between objects, the posture transformation between space points and vectors, the posture transformation process formula under ideal conditions and error is established:

[0015] Ti j =T ijp +T ijs (1);

[0016] T′ ij =T ijp ΔT ijp T ijs ΔT ijs (2);

[0017] In formula (1) and formula (2), T ij Representation B i and B j The ideal pose feature matrix between ijp and T ijs Representation B i and B j The ideal static and ideal motion pose feature matrix between T′ ij Representation B i and B j The actual pose feature matrix containing the error; ΔT ijp and ΔT ijs Indicates the body B i and Bj The actual static and motion pose error matrix between

[0018] According to the coordinates of the tool cutting point and the workpiece being cut point, the coordinate vectors of the tool tip point and the workpiece point in their coordinate system are established:

[0019] P t =[p tx p ty p tz 1] T (3);

[0020] In formula (3), P t p represents the coordinate vector of the tool tip in the tool cutting point coordinates; tx , p ty , p tz are the X, Y, and Z coordinates of the tool cutting point in the tool coordinate system; T represents the transpose of the vector;

[0021] p w =[p wx P wy P wz 1] T (4);

[0022] In formula (4), P w p represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; wx , p wy , p wz are the X, Y, and Z coordinates of the workpiece’s cutting point in the workpiece coordinate system; T represents the transpose of a vector;

[0023] Step 1.4) Due to the influence of static error, the tool cutting point and the workpiece cutting point do not coincide, so the coordinates of the tool tip point and the workpiece point in the reference coordinate system (O-XYZ) are established as:

[0024] P tactual =T′ 15 T′ 56 T′ 67 P t (5)

[0025] In formula (5), P tactual Indicates the coordinates of the tool tip in the reference coordinate system (O-XYZ); t Represents the coordinate vector of the tool tip in the tool cutting point coordinates; T′ 15 Represents the actual pose feature matrix containing errors between bodies B1 and B5; T′ 56 Represents the actual pose feature matrix containing errors between bodies B5 and B6; T′ 67Represents the actual pose feature matrix including errors between bodies B6 and B7;

[0026] P wactual =T′ 12 T′ 23 T′ 34 P w (6);

[0027] In formula (6), P wactual Indicates the coordinates of the workpiece point in the reference coordinate system (O-XYZ); w Represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; T′ 12 Represents the actual pose feature matrix containing errors between bodies B1 and B2; T′ 23 Represents the actual pose feature matrix containing errors between bodies B2 and B3; T′ 34 Represents the actual pose feature matrix including errors between bodies B3 and B4;

[0028] Step 1.5) The static error model of the machine tool is established by subtracting the position coordinates between the actual tool cutting point of the three-axis machine tool and the workpiece being cut; the static error model is as follows:

[0029] E=(E x E y E z 1) T =P tactual -P wactual =E F +E G (7);

[0030] In formula (7), E represents the static error model, P tactual Indicates the coordinates of the tool tip in the reference coordinate system (O-XYZ); wactual Indicates the coordinate E of the workpiece point in the reference coordinate system (O-XYZ) F represents the elastic error model, E G represents the geometric error model;

[0031] Furthermore, in step 2, the static error parameterization model is established by using Chebyshev polynomials, and the static error is quantitatively analyzed based on the three-axis linkage experiment of the ballbar. The specific steps are as follows:

[0032] Step 2.1) According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials; the second-class Chebyshev polynomials are defined as (-1,1) on the The orthogonal polynomials on are expressed as:

[0033]

[0034] Step 2.2) According to the characteristics of all the error elements determined, the fourth-order Chebyshev polynomial is selected to parametrically model the geometric error; the formula for the six static errors of the X-axis is as follows:

[0035]

[0036] In formula (9) is the pre-fitting parameter;

[0037] Step 2.3) According to the ballbar principle, establish the static error and the ideal ballbar length formula at this time:

[0038]

[0039] In formula (10), ΔX, ΔY, ΔZ are the error components of the static error of the tool ball in the X, Y, and Z directions respectively; l is the ideal rod length of the ballbar;

[0040] The actual length of the ballbar is:

[0041]

[0042] In formula (11), l' is the actual length of the ballbar;

[0043] By subtracting the actual length of the ballbar from the ideal length, the relationship between the change in the length of the ballbar and each error component is formed, which can be expressed as:

[0044]

[0045] In formula (12), Δl is the change of the ballbar;

[0046] Step 2.4) Conducting a ballbar test, by randomly selecting a position in the machine tool space as a detection installation point, and conducting a three-axis linkage four-leaf spherical line trajectory test at this position;

[0047] Step 2.5) Substitute the ballbar length change and the Chebyshev polynomial model in the static error model and rewrite it into a matrix form. Then, the static error is solved by the PINV function in MATLAB.

[0048] Furthermore, in step 2, the NC code compensation experiment is performed on the target machine tool to verify the correctness of the three-axis machine tool static error identification method, and the specific steps are:

[0049] Step 2.6) Substitute the decoupling result of the static error back into the geometric error model to obtain the compensation amount in each error direction, and correct the machine tool G code;

[0050] Step 2.7) Under the same experimental conditions, perform point-by-point compensation and compare the experimental test results before compensation with those after compensation.

[0051] Furthermore, in step 3, the finite element method is used to discretize the machine tool into three subsystems, and the stiffness model of each subsystem is established through the spatial beam unit, and then the elastic error component in the static error of the machine tool is quantitatively analyzed. The specific steps are as follows:

[0052] Step 3.1) Apply the structural mechanics method to the spatial beam element of the subsystem to obtain its stiffness equation, which is as follows:

[0053] F i =K i q i (13);

[0054] In formula (13), F i is the load vector in the local coordinate system; q i is the displacement vector in the local coordinate system; where K i is the stiffness matrix of the node displacement order;

[0055] Step 3.2) According to the topological structure of the machine tool, it is discretized into three subsystems including the workbench system, the slide system, and the spindle system. Taking the workbench system as an example, its equivalent principle formula is as follows:

[0056]

[0057] In formulas (14) and (15), R A , M A is the support force and torque of support point A; R B , M B is the support force and torque of support point B; p0 is the uniform load; L is the length of the workbench support points A and B;

[0058] Step 3.3) Since the reference coordinate system of the model is inconsistent with the local reference system, the local unit stiffness matrix and node load array are transformed into the reference coordinate system through coordinate transformation. The transformation relationship is as follows:

[0059]

[0060] In formulas (16) and (17), is the local stiffness matrix, is the node load array; T i is the coordinate transformation matrix of unit i; T iT T i The transpose of

[0061] Step 3.4) According to the point numbering sequence, the stiffness matrix of each unit and the load matrix of each node in the overall coordinate system are combined to form the overall stiffness matrix and load matrix of the target machine tool. The formulas of the two are as follows:

[0062]

[0063] In equations (18) and (19), k is the stiffness matrix of each unit; is the load array of each node;

[0064] Step 3.5) Substitute the overall stiffness matrix and load matrix into equation (13) to obtain the workbench elastic error analysis model, which is as follows:

[0065]

[0066] In formula (20), q is the displacement vector at any position; K is the overall stiffness matrix; F is the load matrix;

[0067] Step 3.6) The actual motion of the X, Y, and Z axes is simulated by changing the node positions of the model, and then the displacement vector q of the worktable at any position is solved to solve each elastic error;

[0068] Step 3.7) Through the decoupling results, the number of machine tool elastic errors is simplified, and the formula of the corrected static error model is as follows:

[0069]

[0070] Furthermore, in step 3, the target machine tool is modeled using three-dimensional modeling software, and the model is imported into simulation software for simulation, and then the simulation results are compared with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method. The specific steps are as follows:

[0071] Step 3.8) Model the target machine tool by using the 3D modeling software Solidworks, and then modify the positional relationship between each motion axis and the reference coordinate system by applying a specific width constraint to simulate the movement in the X, Y, and Z directions;

[0072] Step 3.9) Import the model into the finite element software ANSYS to analyze the deformation of the machine tool when it is only subjected to gravity in the negative Z direction; finally, compare the ANSYS simulation results with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method.

[0073] Furthermore, in step 4, the establishment of the machine tool accuracy field, the analysis and detection of the distribution of the spatial static error, and the revealing of the coupling relationship between the geometric error and the elastic error are specifically performed as follows:

[0074] Step 4.1) Generate the target machine tool's X, Y, and Z precision fields and superimpose the three-dimensional precision fields to obtain the total precision field of the machine tool detection space based on the statistical and static error models;

[0075] Step 4.2) Analyze the error change through the established precision field model;

[0076] Step 4.3) Then, a comparative analysis of the sensitive error terms is performed to further explore the relationship between elastic error and geometric error.

[0077] A computer device includes: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus, and the memory is used to store at least one executable instruction, and the executable instruction enables the processor to execute the operations corresponding to the static error identification method of a three-axis machine tool based on the multi-flexible system theory.

[0078] A computer-readable storage medium stores at least one executable instruction, wherein the executable instruction enables a processor to execute operations corresponding to the above-mentioned three-axis machine tool static error identification method based on multi-flexible body system theory.

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] The present invention establishes a static error model of a machine tool based on the theory of multi-flexible body systems and homogeneous coordinate transformation matrices, and establishes a static error parameterization model in combination with a fourth-order Chebyshev polynomial pre-fitting model. Then, a stiffness model of each subsystem is established based on a spatial beam unit, and the elastic error component is quantitatively analyzed. A simplified static error model of a machine tool is then proposed. Finally, by establishing a machine tool accuracy field, the distribution of spatial static errors is analyzed and detected, and the coupling relationship between geometric errors and elastic errors is revealed. Based on the established static error model and experimental results, the present invention comprehensively considers the influence of geometric errors caused by manufacturing defects and elastic errors caused by gravity on the static accuracy of machine tools, and demonstrates the coupling relationship between the two, thereby greatly improving the identification accuracy of static errors of machine tools.

[0081] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the invention and implement it according to the contents of the specification, the following is a detailed description of the preferred embodiments of the present invention in conjunction with the accompanying drawings. The specific implementation of the present invention is given in detail by the following embodiments and their accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0083] Figure 1 This is a real photo of the Hanchuan XK714D CNC milling machine, which is the analysis object in the embodiments of the present invention.

[0084] Figure 2 FIG. 4 is a ballbar experiment trajectory diagram in an embodiment of the present invention.

[0085] Figure 3 Schematic diagram of a ballbar experimental device in an embodiment of the present invention.

[0086] Figure 4 Graph showing the static error identification results of the X, Y, and Z axes in an embodiment of the present invention.

[0087] Figure 5 Graph showing compensation results in an embodiment of the present invention.

[0088] Figure 6 Schematic diagram of a spatial beam unit in an embodiment of the present invention.

[0089] Figure 7 1 is a spatial beam unit model diagram of each subsystem in an embodiment of the present invention; wherein (a) is the workbench system, (b) is the sliding system, and (c) is the main axis system.

[0090] Figure 8 It is an equivalent principle diagram in an embodiment of the present invention.

[0091] Fig. 9 1 is a diagram of elastic error identification results of each axis in an embodiment of the present invention; wherein (a) is the X-axis, (b) is the Y-axis, and (c) is the Z-axis.

[0092] Fig.10 ANSYS simulation result diagram of the deformation of the machine tool in various directions in the embodiment of the present invention; (a) is the X direction, (b) is the Y direction, and (c) is the Z direction.

[0093] Fig.11 : It is the spatial error distribution diagram in the embodiment of the present invention; wherein (a) is the X-axis slice, (b) is the Y-axis slice, (c) is the Z-axis slice, and (d) is the total accuracy field.

[0094] Fig.12 is a comparison result diagram of the elastic error and the static error in an embodiment of the present invention. DETAILED DESCRIPTION

[0095] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings so that the purpose, features and advantages of the invention can be more clearly understood. It should be understood that the embodiments shown in the accompanying drawings are not intended to limit the scope of the present invention, but are only intended to illustrate the essential spirit of the technical solution of the present invention.

[0096] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the relevant art will recognize that the embodiments may be practiced without one or more of these specific details. In other cases, well-known devices, structures, and techniques associated with the present application may not be shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0097] Unless the context requires otherwise, throughout the specification and claims, the word "comprise" and variations such as "include" and "have" should be construed in an open, inclusive sense, ie, should be interpreted as "including, but not limited to."

[0098] References throughout the specification to "one embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of "in one embodiment" or "in an embodiment" in various places throughout the specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any manner in one or more embodiments.

[0099] As used in this specification and the appended claims, the singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. It should be noted that the term "or" is generally employed in its sense including "and / or" unless the context clearly dictates otherwise.

[0100] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0101] See also Figure 1 As shown, Figure 1 A Hanchuan XK714D CNC milling machine is demonstrated, and the method of the present invention is described below by taking a three-axis CNC machine tool as an example.

[0102] A static error identification method for a three-axis machine tool based on multi-flexible body system theory, the specific steps are as follows:

[0103] Step 1) Based on the theory of multi-flexible body system and homogeneous coordinate transformation matrix, a static error model of the three-axis machine tool is established to qualitatively analyze the geometric error component caused by manufacturing defects and the elastic error component caused by gravity on the structural components in the static error. The steps include:

[0104] Step 1.1) Determine that the static errors of the three-axis machine tool mainly include 18 geometric errors and 18 elastic errors;

[0105] Step 1.2) Establish the topological structure of the target machine tool according to the multi-flexible body system theory. The constructed topological structure has 7 main bodies, a tool kinematic chain, and a workpiece kinematic chain;

[0106] Step 1.3) Based on the theory of multi-flexible body systems, homogeneous coordinate transformation matrices and geometric features between objects, the posture transformation between space points and vectors, the posture transformation process formula under ideal conditions and error is established:

[0107] Ti j =T ijp +T ijs (1);

[0108] T′ ij =T ijp ΔT ijp T ijs ΔT ijs (2);

[0109] In formula (1) and formula (2), T ij Representation B i and B j The ideal pose feature matrix between ijp and T ijs Representation B i and B j The ideal static and ideal motion pose feature matrix between T′ ij Representation B i and B j The actual pose feature matrix containing the error; ΔT ijp and ΔT ijs Indicates the body B i and B j The actual static and motion pose error matrix between

[0110] According to the coordinates of the tool cutting point and the workpiece being cut point, the coordinate vectors of the tool tip point and the workpiece point in their coordinate system are established:

[0111] P t =[p tx p ty p tz 1] T (3);

[0112] In formula (3), P t p represents the coordinate vector of the tool tip in the tool cutting point coordinates; tx , p ty , ptz are the X, Y, and Z coordinates of the tool cutting point in the tool coordinate system; T represents the transpose of the vector;

[0113] P w =[p wx p wy p wz 1] T (4);

[0114] In formula (4), P w p represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; wx , p wy , p wz are the X, Y, and Z coordinates of the workpiece’s cutting point in the workpiece coordinate system; T represents the transpose of a vector;

[0115] Step 1.4) Due to the influence of static error, the tool cutting point and the workpiece cutting point do not coincide, so the coordinates of the tool tip point and the workpiece point in the reference coordinate system (O-XYZ) are established as:

[0116] P tactual =T′ 15 T′ 56 T′ 67 P t (5)

[0117] In formula (5), P tactual Indicates the coordinates of the tool tip in the reference coordinate system (O-XYZ); t Represents the coordinate vector of the tool tip in the tool cutting point coordinates; T′ 15 Represents the actual pose feature matrix containing errors between bodies B1 and B5; T′ 56 Represents the actual pose feature matrix containing errors between bodies B5 and B6; T′ 67 Represents the actual pose feature matrix including errors between bodies B6 and B7;

[0118] P wactual =T′ 12 T′ 23 T′ 34 P w (6);

[0119] In formula (6), P wactual Indicates the coordinates of the workpiece point in the reference coordinate system (O-XYZ); w Represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; T′ 12 Represents the actual pose feature matrix containing errors between bodies B1 and B2; T′ 23 Represents the actual pose feature matrix containing errors between bodies B2 and B3; T′34 Represents the actual pose feature matrix including errors between bodies B3 and B4;

[0120] Step 1.5) The static error model of the machine tool is established by subtracting the position coordinates between the actual tool cutting point of the three-axis machine tool and the workpiece being cut; the static error model is as follows:

[0121] E=(E x E y E z 1) T =P tactual -P wactual =E F +E G (7);

[0122] In formula (7), E represents the static error model, P tactual Indicates the coordinates of the tool tip in the reference coordinate system (O-XYZ); wactual Indicates the coordinate E of the workpiece point in the reference coordinate system (O-XYZ) F represents the elastic error model, E G represents the geometric error model;

[0123] Combining equations (1), (2), (3), (4), (5), (6) and (7) we can get the static error model of the machine tool.

[0124] Step 2) Use Chebyshev polynomials to establish a static error parameterization model, and quantitatively analyze the static error based on the ballbar three-axis linkage experiment; and perform NC code compensation experiments on the target machine tool to verify the correctness of the method proposed in the present invention. It includes the following steps:

[0125] Step 2.1) According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials; the second-class Chebyshev polynomials are defined as (-1,1) on the The orthogonal polynomials on are expressed as:

[0126]

[0127] Step 2.2) According to the characteristics of the 18 error elements, the fourth-order Chebyshev polynomial is used to parametrically model the geometric error; taking the six static errors of the X-axis as an example, the formula is as follows:

[0128]

[0129] In formula (9) is the pre-fitting parameter;

[0130] Step 2.3) According to the ballbar principle, establish the static error and the ideal ballbar length formula at this time:

[0131]

[0132] In formula (10), ΔX, ΔY, ΔZ are the error components of the static error of the tool ball in the X, Y, and Z directions respectively; l is the ideal rod length of the ballbar;

[0133] The actual length of the ballbar is:

[0134]

[0135] In formula (11), l' is the actual length of the ballbar;

[0136] By subtracting the actual length of the ballbar from the ideal length, the relationship between the change in the length of the ballbar and each error component is formed, which can be expressed as:

[0137]

[0138] In formula (12), Δl is the change of the ballbar;

[0139] Step 2.4) See Figure 3 As shown in the figure, a ballbar test is conducted by randomly selecting a position in the machine tool space as the detection installation point and conducting a three-axis linkage four-leaf spherical line trajectory test at this position, as shown in the figure. Figure 2 As shown;

[0140] Step 2.5) Substitute the ballbar length variation and Chebyshev polynomial model in the static error model and rewrite it into a matrix form. Then, use the PINV function in MATLAB to solve the static error and obtain the following: Figure 4 The static error identification results of X, Y and Z axes are shown;

[0141] Step 2.6) Substitute the decoupling result of the static error back into the geometric error model to obtain the compensation amount in each error direction, and correct the machine tool G code;

[0142] Step 2.7) Under the same experimental conditions, compensation is performed point by point, and the experimental test results before compensation are compared with the test results after compensation. The compensation results are as follows: Figure 5 As shown;

[0143] Step 3) The machine tool is discretized into three subsystems using the finite element method, and the stiffness model of each subsystem is established through the spatial beam unit, and then the elastic error component in the static error of the machine tool is quantitatively analyzed; then the target machine tool is modeled using three-dimensional modeling software, and the model is imported into the simulation software for simulation, and then the simulation results are compared with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method. It includes the following steps:

[0144] Step 3.1) By using the spatial beam element of the subsystem, such as Figure 6 As shown, the stiffness equation is obtained by using the method of structural mechanics, and the formula is as follows:

[0145] F i =K i q i (13);

[0146] In formula (13), F i is the load vector in the local coordinate system; q i is the displacement vector in the local coordinate system; where K i is the stiffness matrix of the node displacement order;

[0147] Step 3.2) According to the topological structure of the machine tool, it is discretized into Figure 7 The three subsystems shown ( Figure 7 a represents the workbench system, Figure 7 b represents the slide system, Figure 7 c represents the spindle system). Taking the workbench system as an example, due to the elastic error caused by the influence of gravity on the workbench, the deadweight of each component needs to be converted into a node load. The equivalent principle is as follows: Figure 8 As shown, the formula is as follows:

[0148]

[0149] In formulas (14) and (15), R A , M A is the support force and torque of support point A; R B , M B is the support force and torque of support point B; p0 is the uniform load; L is the length of the workbench support points A and B;

[0150] Step 3.3) Since (O”-X'Y'Z') is the reference coordinate system of the model, it is different from the local reference system (O” i -X' i Y' i Z' i )(i=1,2...n) are inconsistent, so the local unit stiffness matrix and node load array are transformed into the reference coordinate system through coordinate transformation. The transformation relationship is as follows:

[0151]

[0152] In formulas (16) and (17), is the local stiffness matrix, is the node load array; T i is the coordinate transformation matrix of unit i; T iT T i The transpose of

[0153] Step 3.4) According to the point numbering sequence, the stiffness matrix of each unit and the load matrix of each node in the overall coordinate system are combined to form the overall stiffness matrix and load matrix of the target machine tool. The formulas of the two are as follows:

[0154]

[0155] In equations (18) and (19), k is the stiffness matrix of each unit; is the load array of each node;

[0156] Step 3.5) Substitute the overall stiffness matrix and load matrix into equation (13) to obtain the workbench elastic error analysis model, which is as follows:

[0157]

[0158] In formula (20), q is the displacement vector at any position; K is the overall stiffness matrix; and F is the load matrix.

[0159] Step 3.6) By changing the node position of the model to simulate the actual movement of the X, Y, and Z axes, the displacement vector q of the workbench at any position is solved to solve the 18 elastic errors; the elastic error identification results of each axis are as follows: Fig. 9 As shown, Fig. 9 a represents the X-axis elastic error identification result, Fig. 9 b represents the Y-axis elastic error identification result, Fig. 9 c represents the Z-axis elastic error identification result.

[0160] Step 3.7) Through the decoupling results, the machine tool elastic error is simplified to 7 items, and the formula of the corrected static error model is as follows:

[0161]

[0162] Step 3.8) Model the target machine tool by using the 3D modeling software Solidworks, and then modify the positional relationship between each motion axis and the reference coordinate system by applying a specific width constraint to simulate the movement in the X, Y, and Z directions;

[0163] Step 3.9) Import the model into the finite element software ANSYS to analyze the deformation of the machine tool when it is only subjected to gravity in the negative Z direction. The deformation simulation results are Fig.10 As shown, Fig.10 a represents the ANSYS simulation result of deformation in the X direction, Fig.10 b represents the ANSYS simulation result of deformation in the Y direction, Fig.10 c represents the ANSYS simulation results of deformation in the Z direction; finally, the accuracy of the decoupling method is evaluated by comparing the ANSYS simulation results with the stiffness model solution results at multiple positions.

[0164] Step 4) Establish the machine tool accuracy field, analyze the distribution of the static error in the detection space, and reveal the coupling relationship between the geometric error and the elastic error. It includes the following steps:

[0165] Step 4.1) Based on the statistical and static error models, the X, Y, and Z precision fields of the target machine tool are generated and the three-dimensional precision fields are superimposed to obtain the total precision field of the machine tool detection space. The resulting precision field is as follows: Fig.11 As shown;

[0166] Step 4.2) Analyze the error change through the established precision field model;

[0167] Step 4.3) In order to further explore the relationship between elastic error and geometric error, the sensitive error terms are then compared and analyzed. The comparison results are as follows: Fig.12 shown.

[0168] The present invention proposes a new method for tracing the static error of a three-axis machine tool based on the theory of multi-flexible body systems, which comprehensively considers the influence of the geometric error caused by manufacturing defects and the elastic error caused by gravity on the static accuracy of the machine tool, as well as the coupling relationship between the two. This method quantitatively and qualitatively analyzes the rigidity and elastic error parts of the static error of the machine tool, and then demonstrates the coupling relationship between the two by using the finite element analysis method, and establishes a simplified static error model of the machine tool, thereby improving the identification accuracy of the static error of the machine tool.

[0169] The present invention also provides a computer device, comprising: a processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus, and the memory is used to store at least one executable instruction, and the executable instruction enables the processor to execute the operations corresponding to the above-mentioned three-axis machine tool static error identification method based on multi-flexible body system theory.

[0170] The present invention also provides a computer-readable storage medium, in which at least one executable instruction is stored, and the executable instruction enables a processor to execute operations corresponding to the above-mentioned three-axis machine tool static error identification method based on multi-flexible body system theory.

[0171] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A static error identification method for a three-axis machine tool based on multi-flexible body system theory, characterized in that: The following steps are involved: Step 1) A static error model of a three-axis machine tool is established based on the theory of multi-flexible body systems and homogeneous coordinate transformation matrices, and a geometric error component caused by manufacturing defects and an elastic error component caused by gravity on structural components in the static error are qualitatively analyzed; Step 2) using Chebyshev polynomials to establish a static error parameterization model, and quantitatively analyzing the static error based on a ballbar three-axis linkage experiment; and conducting an NC code compensation experiment on a target machine tool; Step 3) The machine tool is discretized into three subsystems using the finite element method, and the stiffness model of each subsystem is established through the spatial beam unit, and then the elastic error component in the static error of the machine tool is quantitatively analyzed; Then, the target machine tool is modeled using 3D modeling software, and the model is imported into simulation software for simulation. The simulation results are then compared with the results of the stiffness model solution at multiple positions to evaluate the accuracy of the decoupling method. Step 4) Establish the machine tool accuracy field, analyze and detect the distribution of spatial static errors, and reveal the coupling relationship between geometric errors and elastic errors.

2. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1 is characterized in that: In step 1, the static error model of the three-axis machine tool is established according to the multi-flexible body system theory and the homogeneous coordinate transformation matrix, and the specific steps are as follows: Step 1.1) Determine the number and types of geometric errors and elastic errors in the static errors of the three-axis machine tool; Step 1.2) Establish the topological structure of the target machine tool according to the multi-flexible body system theory, and specify the number of main bodies, tool kinematic chains, and workpiece kinematic chains in the constructed topological structure; Step 1.3) Based on the theory of multi-flexible body systems, homogeneous coordinate transformation matrices and geometric features between objects, the posture transformation between space points and vectors is established to establish the posture transformation process formula under ideal conditions and errors: T ij =T ijp +T ijs (1); T′ ij =T ijp ΔT ijp T ijs ΔT ijs (2); In formula (1) and formula (2), Ti j Representation B i and B j The ideal pose feature matrix between T ijp and T ijs Represents the ideal static and ideal motion pose feature matrix between bodies Bi and Bj; T ij ' indicates body B i and B j The actual pose feature matrix containing the error; Δ T ijp and ΔT ijs Representation B i and B j The actual static and motion pose error matrix between According to the coordinates of the tool cutting point and the workpiece being cut point, the coordinate vectors of the tool tip point and the workpiece point in their coordinate system are established: P t =[p tx p ty p tz 1] T (3); In formula (3), P t p represents the coordinate vector of the tool tip in the tool cutting point coordinates; tx , p ty , p tz are the X, Y, and Z coordinates of the tool cutting point in the tool coordinate system; T represents the transpose of the vector; P w =[p wx p wy p wz 1] T (4); In formula (4), P w p represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; wx , p wy , p wz are the X, Y, and Z coordinates of the workpiece’s cutting point in the workpiece coordinate system, and T represents the transpose of a vector; Step 1.4) Due to the influence of static error, the tool cutting point and the workpiece cutting point do not coincide, so the coordinates of the tool tip point and the workpiece point in the reference coordinate system (O-XYZ) are established as: P tactal =T′ 15 T′ 56 T′ 67 P t (5); In formula (5), P tactual represents the coordinates of the tool tip in the reference coordinate system (O-XYZ); Pt represents the coordinate vector of the tool tip in the tool cutting point coordinates; T′ 15 Represents the actual pose feature matrix including errors between bodies B1 and B5; T′ 56 Represents the actual pose feature matrix containing errors between bodies B5 and B6; T′ 67 Represents the actual pose feature matrix including errors between bodies B6 and B7; P wactual =T′ 12 T′ 23 T 34 P w (6); In formula (6), P wactual Indicates the coordinates of the workpiece point in the reference coordinate system (O-XYZ); w Represents the coordinate vector of the workpiece point in the coordinate system of the workpiece cutting point; T′ 12 Represents the actual pose feature matrix containing errors between bodies B1 and B2; T′ 23 Represents the actual pose feature matrix containing errors between bodies B2 and B3; T′ 34 Represents the actual pose feature matrix including errors between bodies B3 and B4; Step 1.5) The static error model of the machine tool is established by subtracting the position coordinates between the actual tool cutting point of the three-axis machine tool and the workpiece being cut; the static error model is as follows: And=(And x AND y AND z 1) T =P tactual -P wactal =And F +E G (7); In formula (7), E represents the static error model, P tactual Indicates the coordinates of the tool tip in the reference coordinate system (O-XYZ); wactual Indicates the coordinate E of the workpiece point in the reference coordinate system (O-XYZ) F represents the elastic error model, E G Represents the geometric error model.

3. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1 is characterized in that: In step 2, the static error parameterization model is established by using Chebyshev polynomials, and the static error is quantitatively analyzed based on the three-axis linkage experiment of the ballbar. The specific steps are as follows: Step 2.1) According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials; the second-class Chebyshev polynomials are defined as (-1,1) on the The orthogonal polynomials on are expressed as: Step 2.2) According to the characteristics of all the error elements determined, the fourth-order Chebyshev polynomial is used to parametrically model the geometric error; the formula for the six static errors of the X-axis is as follows: In formula (9) is the pre-fitting parameter; Step 2.3) According to the ballbar principle, establish the static error and the ideal ballbar length formula at this time: In formula (10), ΔX, ΔY, ΔZ are the error components of the static error of the tool ball in the X, Y, and Z directions respectively; l is the ideal rod length of the ballbar; The actual length of the ballbar is: In formula (11), l' is the actual length of the ballbar; By subtracting the actual length of the ballbar from the ideal length, the relationship between the change in the length of the ballbar and each error component is formed, which can be expressed as: In formula (12), Δl is the change of the ballbar; Step 2.4) Conducting a ballbar test, by randomly selecting a position in the machine tool space as a detection installation point, and conducting a three-axis linkage four-leaf spherical line trajectory test at this position; Step 2.5) Substitute the ballbar length change and the Chebyshev polynomial model in the static error model and rewrite it into a matrix form. Then, the static error is solved by the PINV function in MATLAB.

4. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1 is characterized in that: In step 2, the NC code compensation experiment is performed on the target machine tool to verify the correctness of the three-axis machine tool static error identification method, and the specific steps are: Step 2.6) Substitute the decoupling result of the static error back into the geometric error model to obtain the compensation amount in each error direction, and correct the machine tool G code; Step 2.7) Under the same experimental conditions, perform point-by-point compensation and compare the experimental test results before compensation with those after compensation.

5. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1 is characterized in that: In step 3, the machine tool is discretized into three subsystems by using the finite element method, and the stiffness model of each subsystem is established by using the spatial beam unit, and then the elastic error component in the static error of the machine tool is quantitatively analyzed. The specific steps are as follows: Step 3.1) Apply the structural mechanics method to the spatial beam element of the subsystem to obtain its stiffness equation, which is as follows: F i =K i q i (13); In formula (13), F i is the load vector in the local coordinate system; q i is the displacement vector in the local coordinate system; where K i is the stiffness matrix of the node displacement order; Step 3.2) According to the topological structure of the machine tool, it is discretized into three subsystems including the workbench system, the slide system, and the spindle system. Taking the workbench system as an example, its equivalent principle formula is as follows: In formulas (14) and (15), R A is the support force of support point A; M A is the torque at support point A; R B is the support force of support point B; M B is the torque of the support point B; p0 is the uniform load; L is the length of the support points A and B of the workbench; Step 3.3) Since the reference coordinate system of the model is inconsistent with the local reference system, the local unit stiffness matrix and node load array are transformed into the reference coordinate system through coordinate transformation. The transformation relationship is as follows: In formulas (16) and (17), is the local stiffness matrix, is the node load array; T i is the coordinate transformation matrix of unit i; T iT T i The transpose of Step 3.4) According to the point numbering sequence, the stiffness matrix of each unit and the load matrix of each node in the overall coordinate system are combined to form the overall stiffness matrix and load matrix of the target machine tool. The formulas of the two are as follows: In equations (18) and (19), k is the stiffness matrix of each unit; is the load array of each node; Step 3.5) Substitute the overall stiffness matrix and load matrix into equation (13) to obtain the workbench elastic error analysis model, which is as follows: In formula (20), q is the displacement vector at any position; K is the overall stiffness matrix; F is the load matrix; Step 3.6) The actual motion of the X, Y, and Z axes is simulated by changing the node positions of the model, and then the displacement vector q of the worktable at any position is solved to solve each elastic error; Step 3.7) Through the decoupling results, the number of machine tool elastic errors is simplified, and the formula of the corrected static error model is as follows:

6. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1 is characterized in that: In step 3, the target machine tool is modeled using 3D modeling software, and the model is imported into simulation software for simulation, and then the simulation results are compared with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method. The specific steps are as follows: Step 3.8) Model the target machine tool by using the 3D modeling software Solidworks, and then modify the positional relationship between each motion axis and the reference coordinate system by applying a specific width constraint to simulate the movement in the X, Y, and Z directions; Step 3.9) Import the model into the finite element software ANSYS to analyze the deformation of the machine tool when it is only subjected to gravity in the negative Z direction; finally, compare the ANSYS simulation results with the stiffness model solution results at multiple positions to evaluate the accuracy of the decoupling method.

7. The static error identification method of a three-axis machine tool based on multi-flexible body system theory according to claim 1, characterized in that: In step 4, the machine tool accuracy field is established, the distribution of the static error in the detection space is analyzed, and the coupling relationship between the geometric error and the elastic error is revealed. The specific steps are as follows: Step 4.1) Generate the target machine tool's X, Y, and Z precision fields and superimpose the three-dimensional precision fields to obtain the total precision field of the machine tool detection space based on the statistical and static error models; Step 4.2) Analyze the error change through the established precision field model; Step 4.3) Then, a comparative analysis of the sensitive error terms is performed to further explore the relationship between elastic error and geometric error.

8. A computer device, characterized in that: include: A processor, a memory, a communication interface and a communication bus, wherein the processor, the memory and the communication interface communicate with each other through the communication bus, and the memory is used to store at least one executable instruction, and the executable instruction enables the processor to perform operations corresponding to the static error identification method of a three-axis machine tool based on multi-flexible body system theory as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The computer storage medium stores at least one executable instruction, and the executable instruction enables the processor to perform operations corresponding to the static error identification method of a three-axis machine tool based on multi-flexible body system theory as described in any one of claims 1 to 7.

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