Geometry-gravity error integrated calibration method for large gantry machine tool

Abstract

The invention provides a geometric-gravity error integrated calibration method of a large gantry machine tool. The method comprises the steps that a geometric error model of the gantry machine tool is established based on the multi-body system kinematics theory and rigid body kinematics analysis, and the geometric error model is used for describing geometric error sources of all motion axes and the transmission relation of the geometric error sources; establishing a gravity deformation error model of the gantry machine tool based on mechanical analysis and a potential energy method; coupling the geometric error model with the gravity deformation error model to obtain a rigid-flexible coupled integrated geometric-gravity error model; measuring static error parameters of each motion axis of the machine tool, and substituting the static error parameters into the integrated geometry-gravity error model to obtain geometric error parameters without influence of gravity error factors; and on the basis of the integrated geometry-gravity error model and the geometric error parameters with the influence of the gravity error factor eliminated, the error compensation amount of each movement position point of the gantry machine tool is calculated, and the gantry machine tool is calibrated on the basis of the error compensation amount of each movement position point.

Description

Technical Field

[0001] This application relates to the field of machine tool manufacturing technology, and in particular to an integrated calibration method for geometric-gravity errors of a large gantry milling machine. Background Technology

[0002] Large gantry milling machines, with their high load-bearing capacity, large-scale machining range and powerful cutting performance, can meet the machining needs of high-speed, high-precision complex parts and are widely used in the manufacturing of key parts in key fields such as aviation, aerospace, aero-engine, and new energy vehicles.

[0003] With the rapid development of the aviation, aerospace, automotive, and machine tool equipment sectors, the market demands increasingly stringent precision in parts processing, posing a more rigorous challenge to the machining accuracy of large gantry milling machines. Therefore, conducting research on improving the precision of large gantry milling machines, breaking through technological bottlenecks, and establishing an independent and controllable precision assurance system have become crucial tasks supporting the development of key areas.

[0004] Strategies for improving machine tool accuracy can be mainly divided into two categories: prior error control before manufacturing and post-manufacturing error calibration. Among them, error calibration, which measures the actual error data at the end of the machine tool and uses parameter identification algorithms to identify unknown parameters in the error model, and then achieves error compensation by modifying the control system, is one of the most direct and effective ways to improve the accuracy of CNC machine tools.

[0005] Compared to ordinary machine tools, large gantry milling machines are characterized by their large structural dimensions, heavy loads, and long working strokes. Their flexibility is also more pronounced, making them prone to significant elastic deformation under their own weight, resulting in gravity-induced deformation errors that severely impact machining quality. Therefore, the influence of gravity-induced deformation cannot be ignored when calibrating the errors of large gantry milling machines.

[0006] In the existing traditional kinematic calibration methods for large gantry milling machines, gravity deformation error and geometric error are coupled with each other, resulting in a decrease in error identification accuracy and making it difficult to accurately predict and compensate for the static error of the machine tool. Summary of the Invention

[0007] The purpose of this application is to provide an integrated geometric-gravity error calibration method for large gantry milling machines, which can solve at least one of the technical problems mentioned in the prior art.

[0008] One aspect of this application provides an integrated geometric-gravity error calibration method for a large gantry milling machine. The method includes: establishing a geometric error model of the gantry milling machine based on multibody system kinematics theory and rigid body kinematics analysis, the geometric error model describing the geometric error sources and their transmission relationships for each motion axis of the gantry milling machine; establishing a gravity deformation error model of the gantry milling machine based on mechanical analysis and potential energy methods; coupling the geometric error model with the gravity deformation error model to obtain a rigid-flexible coupled integrated geometric-gravity error model of the gantry milling machine; measuring the static error parameters of each motion axis of the gantry milling machine and substituting the measured static error parameters into the rigid-flexible coupled integrated geometric-gravity error model to obtain geometric error parameters that eliminate the influence of gravity error factors; calculating the error compensation amount at each motion position point of the gantry milling machine based on the rigid-flexible coupled integrated geometric-gravity error model and the geometric error parameters that eliminate the influence of gravity error factors, and calibrating the gantry milling machine based on the error compensation amount at each motion position point.

[0009] Furthermore, the establishment of the gravity deformation error model of the gantry milling machine based on mechanical analysis and potential energy methods includes: obtaining the stiffness matrix of the machine tool components using finite element software; obtaining the overall stiffness matrix of the gantry milling machine based on the stiffness matrix of the machine tool components using the structural matrix method; considering the internal stress deformation caused by the closed-loop structural constraints of the gantry milling machine, establishing the potential energy equation and deformation compatibility equation of the machine tool system that include the influence of internal stress; and solving for the deformation error at the end under the influence of gravity and internal stress based on the potential energy equation and the deformation compatibility equation of the machine tool system, and based on the principle of minimum potential energy and the Lagrange multiplier method.

[0010] Furthermore, obtaining the stiffness matrix of the machine tool component using finite element software includes: treating the machine tool component as a unit structure, simplifying the gravitational deformation of the machine tool component to the deformation at both ends of the nodes between the component units; and obtaining the stiffness matrix of each node using finite element software.

[0011] Further, the gantry milling machine includes a left column, a right column, a slider, a crossbeam, an apron, a ram, and a CA swing head. The slider is respectively disposed on the left column and the right column, used to realize movement in the X-axis direction; the crossbeam connects the sliders on the left column and the right column; the apron is disposed on the crossbeam, used to realize movement in the Y-axis direction; the ram is disposed on the apron, used to realize movement in the Z-axis direction; the CA swing head is disposed on the ram, used to realize the movement of the rotation axis. Obtaining the stiffness matrix of each node using finite element software includes dividing the machine tool components into 5 component units and 7 nodes. The 5 component units include: the left column (as the first component unit); the crossbeam (as the second component unit); the right column (as the third component unit); the slide... The machine tool is divided into seven parts: a gantry milling machine bed, a 4th component unit; a slide and a CA swing head, a 5th component unit; a crossbeam, a 3rd component unit; a 4th component unit, a 2nd component unit; a 5th component unit, a 6th component unit, a 7th component unit; a 8th component unit, a 9th component unit, a 1st ...

[0012] Furthermore, the expression for the coordinate transformation matrix is: , in, Let be the nodal coordinate transformation matrix of component element j, i.e.: , in, , , These represent the cosines of the X-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Y-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Z-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively.

[0013] Furthermore, the structural constraints of the machine tool system potential energy equation and the deformation compatibility equation are as follows: , , Where argmin represents the potential energy equation of the machine tool system. The parameter value that yields the minimum value; The total weight deformation error of the gantry milling machine; Represents the transpose of a matrix; Let be the overall stiffness matrix of the gantry milling machine; The stiffness model of the gantry frame in the gantry machine tool can be derived from the overall machine stiffness matrix. Obtain; The total internal stress deformation error of the gantry frame; This is the equivalent gravity load matrix for all nodes; Let be the equivalent gravity load matrix of the nodes on the gantry frame; This represents the transformation matrix that converts the gravitational deformation of the entire gantry milling machine into displacement in the machine tool coordinate system. This represents the transformation matrix that converts the internal stress deformation of the nodes on the gantry frame into displacement in the machine tool coordinate system; and The coefficients of the deformation compatibility equation for machine tools considering closed-loop structural constraints; , , , These represent the transformation matrices from gravity deformation error to end-point error for nodes 1, 2, 4, and 5, respectively.

[0014] Furthermore, the expression for the deformation error of the end under the influence of gravity and internal stress is as follows: , in, , , , , , These represent the gravitational deformation errors along the X, Y, Z, I, J, and K axes, respectively; the I, J, and K axes represent the directions of rotation around the X, Y, and Z axes, respectively.

[0015] Furthermore, the expression for the rigid-flexible coupled integrated geometric-gravity error model of the gantry milling machine is as follows: , in, The error transfer matrix of the machine tool end under the influence of gravity deformation can be obtained from the gravity deformation error model of the gantry machine tool. This is the geometric error model of the gantry milling machine; This represents the differential error transfer matrix from the component i-coordinate system to the end-effector coordinate system of the gantry milling machine. This indicates the error of component i.

[0016] Furthermore, the gantry milling machine includes three linear motion axes (X, Y, Z) and two rotary axes (C, A). The geometric error model of the gantry milling machine, based on multibody system kinematics theory and rigid body kinematics analysis, includes: defining the five axes X, Y, Z, and C as corresponding to machine tool component numbers 1-5, the tool end-effector coordinate system as corresponding to component number 6, and the local coordinate systems of adjacent components i and j as follows: and Where j>i, and described by a 4×4 DH transformation matrix. arrive The coordinate transfer transformation is performed; starting with any component i, the DH transformation matrices of subsequent components are multiplied sequentially to obtain the homogeneous transformation matrix from component i to the tool end point; based on the homogeneous transformation matrix from component i to the tool end point and the principle of differential transformation, the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point is obtained; based on the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point and combined with the linear and angular errors of each motion axis of the gantry machine tool, the machine end point error caused by component i is obtained, and then superimposed to obtain the total machine end point error caused by all components of the gantry machine tool. The expression for the total machine end point error caused by all components of the gantry machine tool is: , in, , , These represent the components of the tool end space error in the X, Y, and Z axes, respectively. , , These represent the components of the tool attitude error in the I, J, and K axis directions, respectively, where the I, J, and K axis directions are the directions of rotation around the X, Y, and Z axes, respectively. This indicates the machine tool end effector error caused by component i. Let represent the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point. This indicates the error of component i.

[0017] Furthermore, measuring the static error parameters of each motion axis of the gantry machine tool includes: measuring the static error parameters of each motion axis of the gantry machine tool using a laser interferometer; during measurement, the gantry machine tool is treated as a three-axis machine tool for single-axis error measurement; calibrating the gantry machine tool based on the error compensation amount at each motion position point includes: modifying the G-codes related to the four body diagonals within the workspace of the gantry machine tool in the CNC system based on the error compensation amount at each motion position point; and measuring the positioning error of the four body diagonals within the workspace of the gantry machine tool based on the ISO230-6 standard to complete the compensation verification.

[0018] The integrated geometry-gravity error calibration method for large gantry milling machines according to one or more embodiments of this application achieves at least one of the following beneficial technical effects: (1) In view of the problem that geometric error and gravity deformation error are coupled in the traditional kinematic calibration of existing large gantry machine tools and the influence of internal stress deformation of closed-loop structure is ignored, this application proposes an integrated geometric-gravity error modeling idea of ​​rigid-flexible coupling, which realizes accurate comprehensive description of multi-source static error; (2) The rigid-flexible coupling integrated geometric-gravity error model innovatively integrates the geometric error model based on multibody system theory with the gravity deformation model considering structural constraints. For the first time, it systematically incorporates the internal stress deformation caused by the closed-loop structure of the gantry machine tool. It solves the problem by using the minimum potential energy principle and the Lagrange multiplier method, completely getting rid of the limitation of the geometric error identification caused by gravity deformation in traditional calibration. It completely covers the transmission link of geometric error, gravity deformation error and internal stress deformation error from the theoretical level, solving the problem of unsystematic description of error sources and fuzzy transmission relationship in the past, making static error prediction more accurate. (3) In view of the problem that the structure of large machine tool components is complex and the stiffness is difficult to be calculated analytically, this application develops a stiffness characteristic extraction method that combines the structural matrix method and the finite element method, which takes into account both calculation accuracy and efficiency.

[0019] (4) The stiffness matrix of each component unit node in the local coordinate system is obtained by finite element software. After the coordinate transformation is converted into the stiffness matrix of the machine tool coordinate system, the static stiffness model of the entire working space is assembled according to the structural matrix method. At the same time, the machine tool is reasonably disassembled into component units and nodes. Based on the static equivalence principle, the uniformly distributed gravity load is converted into the node concentrated load and moment, which simplifies the calculation complexity and ensures the authenticity of load transmission. It provides accurate key parameter support for the gravity deformation error model and avoids the dilemma of difficulty in balancing accuracy and efficiency in traditional stiffness modeling. (5) In terms of error compensation and practical application, the compensation scheme of this application is accurate and efficient, and significantly improves the positioning accuracy of machine tools; (6) Based on the integrated geometric-gravity error model of rigid-flexible coupling, the error compensation amount of each spatial position point of the computer tool can be directly calculated. The compensation can be achieved by modifying the G code related to the four body diagonals in the working space of the gantry machine tool and inputting it into the CNC system. There is no need to modify the machine tool hardware. When measuring, the XM-60 laser interferometer is used and the machine tool is regarded as a three-axis machine tool to simplify the operation, which is easy to promote in industrial applications. (7) Verified by ISO230-6 standard, by measuring the positioning error of the four body diagonals in the working space of the gantry machine tool, and comparing it with the traditional linear compensation model, it can be seen that after adopting the geometric-gravity error integrated calibration method of the large gantry machine tool of this application, the mean and variance of the positioning error are significantly reduced, the compensation ratio is greatly increased, and the problem of the decrease in accuracy of the large gantry machine tool under load and large stroke conditions is effectively solved. (8) The geometric-gravity error integrated calibration method of the large gantry machine tool in this application is fully adapted to the characteristics of large gantry machine tool with large structural size, heavy load and closed-loop structure. It provides a replicable technical solution for the formation of an independent and controllable precision assurance system for domestic large gantry machine tools, and strongly supports the processing needs of key parts in key fields such as aviation and aerospace. Attached Figure Description

[0020] Figure 1 This is a three-dimensional model of a large gantry milling machine.

[0021] Figure 2 This is a flowchart of an integrated geometric-gravity error calibration method for a large gantry milling machine according to an embodiment of this application.

[0022] Figure 3 This paper presents a topology analysis and error propagation chain for a gantry milling machine according to an embodiment of this application.

[0023] Figure 4 This is a simplified diagram showing the component division of a gantry milling machine according to one embodiment of this application.

[0024] Figure 5 This is a schematic diagram of the deformation of a gantry milling machine component under a unit force according to an embodiment of this application.

[0025] Figure 6 This is a schematic diagram of the closed-loop structure constraint of a gantry milling machine according to an embodiment of this application.

[0026] Figure 7 This is a simplified schematic diagram of the equivalent gravity of a gantry milling machine component according to an embodiment of this application.

[0027] Figure 8 This is a comparison chart of the double-branch error of a gantry milling machine with and without considering structural constraints.

[0028] Figure 9The image shows a comparison of the compensation effects before and after for the four diagonals of a gantry milling machine under different models.

[0029] Figure 10 The mean error of the gantry milling machine before and after compensation under the linear model and the geometric-gravity model.

[0030] Figure 11 The compensation ratio for the gantry milling machine under the linear model and the geometry-gravity model.

[0031] Figure 12 This is a comparison chart of the variance of the gantry milling machine after compensation under the linear model and the geometric-gravity model. Detailed Implementation

[0032] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses consistent with some aspects of this application as detailed in the appended claims.

[0033] In traditional kinematic calibration methods for large gantry milling machines, gravity deformation errors and geometric errors are coupled, leading to a decrease in error identification accuracy and making it difficult to accurately predict and compensate for the machine's static errors. Furthermore, large gantry milling machines employ a closed-loop structural design; gravity deformation is not simply a matter of nodal stress deformation. The internal stress deformation caused by closed-loop constraints further exacerbates the complexity of error coupling, making it difficult for traditional calibration methods to fully consider the combined effects of geometric and gravity deformation errors, thus limiting the potential for improving machine accuracy.

[0034] Based on the current state of the technology, there is an urgent need for an integrated calibration method that can effectively separate geometric errors from gravity deformation errors and fully consider the influence of closed-loop structural constraints, in order to solve the problem of improving the accuracy of large gantry machine tools caused by the coupling of multiple sources of errors such as manufacturing and assembly errors, structural gravity deformation and internal stress deformation.

[0035] This application provides an integrated geometric-gravity error calibration method for large gantry milling machines. By introducing a gravity error model, the method combines the geometric error model and the gravity error model into a rigid-flexible coupled integrated error model, which effectively improves the calibration accuracy of large gantry milling machines and effectively solves the problem of decreased error identification accuracy caused by the coupling of gravity deformation error into geometric error in the traditional kinematic calibration of large gantry milling machines.

[0036] The integrated geometric-gravity error calibration method for large gantry milling machines provided in this application will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0037] Figure 1 A three-dimensional model of a large gantry milling machine is shown. (For example...) Figure 1 As shown, the large gantry machine tool is a viaduct-type large gantry five-axis machine tool equipped with a CA double-swivel head. The gantry machine tool 100 includes three linear motion axes (X, Y, and Z) and two rotary axes (C and A). The gantry machine tool 100 includes a bed 101 and a gantry frame 102. The gantry frame 102 includes a left column 111, a right column 112, a slide 121, a crossbeam 131, a slide plate 141, a ram 151, and a CA swivel head 161. The sliders 121 are respectively set on the left column 111 and the right column 112 to realize movement in the X-axis direction; the crossbeam 131 connects the sliders 121 on the left column 111 and the right column 112, and the slide plate 141 is set on the crossbeam 131 to realize movement in the Y-axis direction; the slide block 151 is set on the slide plate 141 to realize movement in the Z-axis direction; and the CA swing head 161 is set on the slide block 151 to realize the movement of the rotation axis.

[0038] Figure 2 A flowchart illustrating an embodiment of the geometric-gravity error integrated calibration method for a large gantry milling machine according to this application is provided. Figure 2 As shown, an embodiment of the geometric-gravity error integrated calibration method for a large gantry milling machine may include steps S1 to S5.

[0039] Step S1: Establish the geometric error model of the gantry milling machine 100.

[0040] The geometric error model can be used to describe the geometric error sources and their transmission relationships of each motion axis of the gantry milling machine 100.

[0041] In some embodiments, the geometric error model of the gantry machine tool 100 can be established based on the kinematics theory of multibody systems and rigid body kinematics analysis, using homogeneous coordinate transformation method and motion differential method.

[0042] Figure 3 This application discloses a topology analysis and error propagation chain for a gantry milling machine 100 according to one embodiment. For example... Figure 3As shown, the five axes XYZCA correspond to machine tool component numbers 1-5, and the tool end-effector coordinate system corresponds to number 6. Based on the connection relationships of the moving components of the five-axis machine tool, the motion transformation relationships between them can be modeled. Homogeneous coordinate transformation, as a general coordinate system transformation method, uses a 4×4 matrix to model and describe the transformation relationships between coordinate systems. For two adjacent machine tool components, let their lower-order volume numbers be i and j (where j>i), and their corresponding local coordinate systems are respectively... and The coordinate system corresponding to component i Transform the coordinate values ​​in the coordinate system to the coordinate system corresponding to component j. The coordinate transfer transformation of the coordinate values ​​can be achieved using a 4×4 DH transformation matrix. To describe: (1) Starting with any component i, by successively multiplying the DH transformation matrices of each subsequent lower-order component, we can obtain the homogeneous transformation matrix from any component i to the end of the tool: (2) in, , , This represents the projection component of the X-axis of the end coordinate system onto the machine tool coordinate system; , , This represents the projection component of the Y-axis of the end coordinate system onto the machine coordinate system; , , This represents the projection component of the Z-axis of the end coordinate system onto the machine tool coordinate system; , , This indicates the position of the origin of the end coordinate system in the machine tool coordinate system.

[0043] The end-effector pose error of a machine tool is obtained by the error propagation of various machine tool components. Since the actual measurement involves measuring the end-effector pose, it is necessary to map the geometric errors of each machine tool component to the end-effector. Based on the homogeneous transformation matrix from component i to the end-effector and the principle of differential transformation, the differential error propagation matrix from the coordinate system of component i to the end-effector coordinate system is obtained, as shown below: (3) From the perspective of rigid body kinematics, a rigid body has six degrees of freedom in three-dimensional space. Therefore, errors will occur in the corresponding directions of these degrees of freedom during actual motion. Specifically, for the large gantry milling machine 100, each linear motion axis has three linear errors (one positioning error and two straightness errors) and three angular errors (pitch error, yaw error, and roll error); each rotational motion axis also has three linear errors (one axial linear error and two radial linear errors) and three angular errors (one angular positioning error and two tilt errors), as shown in the following formula: (4) Where T represents the transpose of the matrix; Indicates the error of component i; , 、. , respectively, represent the linear errors of component i in the X, Y, and Z directions; , , These are the angular errors of component i in the X, Y, and Z directions (i.e., I, J, and K directions), respectively.

[0044] Therefore, based on the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point, and combined with the linear and angular errors of each motion axis of the gantry milling machine 100, the end point error caused by component i can be obtained, as shown below: (5) The total error at the end of the machine tool caused by all components of the gantry milling machine 100 is then summed up, as shown below: (6) in, , , These represent the components of the tool end space error in the X, Y, and Z axes, respectively. , , These represent the components of the tool attitude error in the I, J, and K axis directions, respectively, where the I, J, and K axis directions are the directions of rotation around the X, Y, and Z axes, respectively. This indicates the machine tool end effector error caused by component i. Let represent the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point. This indicates the error of component i.

[0045] Thus, a geometric error model for the large gantry milling machine 100 was established. This geometric error model shows that by inputting the dimensional parameters of the homogeneous coordinate transformation matrix, the motion coordinates of each axis, and the geometric error data, the spatial end-effector positioning error at different positions in the motion space, the deviation of the tool posture, and ultimately, the accuracy level of the actual machine tool can be evaluated.

[0046] Step S2: Establish the gravity deformation error model of the gantry milling machine 100.

[0047] In some embodiments, step S2 may further include steps S21 to S23.

[0048] Step S21: Obtain the stiffness matrix of the machine tool components using finite element software.

[0049] To solve the gravity deformation error of the gantry machine tool 100 under various positions, a gravity deformation error model of the gantry machine tool 100 is first established. The gravity error of the machine tool is due to the flexible deformation of the machine tool components caused by gravity. The machine tool components can be considered as unit structures, and the gravity deformation of the machine tool components can be simplified to the deformation at the ends of the nodes between the unit components. Since the machine tool bed 101 and the worktable are directly fixed to the ground and have high rigidity, they can be considered as rigid bodies. The remaining components are considered as flexible bodies. The rotational position of the CA oscillating head 161 has little impact on the gravity of the machine tool and can be considered as a component integrated with the slide ram 151. The large gantry machine tool 100 is simplified to a structure of 5 unit components and 7 nodes.

[0050] Figure 4 A simplified component division diagram of a gantry milling machine 100 according to an embodiment of this application is disclosed. Figure 4 In the diagram, circled numbers represent component units, while uncircled numbers represent nodes. For example... Figure 4 As shown, the five component units include: left column 111 as the first component unit; crossbeam 131 as the second component unit; right column 112 as the third component unit; slider 121 as the fourth component unit; and ram 151 and CA swing head 161 as the fifth component unit. Among them, crossbeam 131 is a three-node component unit, and the other component units are two-node component units. The seven nodes include the first node between the left side of the bed 101 of the gantry machine tool 100 and the ground, the second node between crossbeam 131 and slider 121 on the left column 111, the third node between crossbeam 131 and slide 141, the fourth node between crossbeam 131 and slider 121 on the right column 112, the fifth node between the right side of the bed 101 of the gantry machine tool 100 and the ground, the sixth node between slide 141 and ram 151, and the seventh node at the end.

[0051] The coordinate system of each node is set with the node as the origin, and the X, Y, and Z directions of the coordinate system are consistent with the machine tool coordinate system. The gravitational deformation of machine tool node i is defined as follows: : (7) The homogeneous transformation matrix from machine node i to the end of the tool can be expressed as: (8) It is necessary to transform the errors of each node to the end-effector coordinate system to establish the mapping relationship between the deformation errors of each node and the pose error of the machine tool end-effector. According to the principle of differential transformation, the transformation matrix from the deformation error of machine tool node i to the end-effector error can be obtained: (9) Solving for the gravitational deformation of a machine tool requires establishing a static stiffness model of the machine tool in various positions. For components with uniform cross-sections and regular shapes, the element stiffness matrix can be directly calculated using theoretical formulas. However, the components of a large gantry milling machine (model 100) have complex structures and irregular dimensions, making it difficult to obtain the stiffness matrix analytically. Therefore, this application uses finite element method (FEM) technology to extract the stiffness of the complex variable cross-section structure of the machine tool.

[0052] Figure 5 A schematic diagram illustrating the deformation of a component of a gantry milling machine 100 under a unit force, according to an embodiment of this application, is shown. Figure 5 As shown, component 100 of the gantry milling machine will deform under a unit force. In the force analysis of the nodes, it is assumed that the linear and angular displacements of node i under external load can be considered as linear, small deformations. The stiffness matrix of node i is... It can be defined as: (10) (11) (12) in, Represents the nodal unit load matrix; , , , , , These represent the linear and angular displacements of node i in three orthogonal directions under a unit force or torque, respectively. , , , , , Let be the unit force and unit moment of node i in the three orthogonal directions, respectively; and let be the stiffness matrix of node i. for The symmetric, positive semi-definite matrix has elements with clear physical meanings: the main diagonal elements represent the stiffness coefficients between internal forces / torques and linear / angular displacements in the same direction, reflecting the direct stiffness characteristics of that degree of freedom; the off-diagonal elements characterize the stiffness coupling effect between different degrees of freedom, that is, the stiffness of the displacement caused by a force or torque in one direction in another direction. The stiffness of each component node of the machine tool is obtained by using the equivalent force method.

[0053] Therefore, the stiffness matrix of each node in the local coordinate system is obtained using finite element software.

[0054] The stiffness matrix of component element j is the coordinate transformation matrix from the local coordinate system to the machine tool coordinate system, and its expression is as follows: (13) in, Let be the nodal coordinate transformation matrix of component element j, i.e.: (14) in, , , These represent the cosines of the X-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Y-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Z-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively.

[0055] Assume that the stiffness matrix of component element j in its local coordinate system is Then the stiffness matrix of component element j in the machine tool coordinate system is: (15) Therefore, the stiffness matrix of each node in the local coordinate system is transformed into the stiffness matrix of each node in the machine tool coordinate system through the coordinate transformation matrix.

[0056] Step S22: Based on the stiffness matrix of the machine tool components, obtain the overall stiffness matrix (i.e., the static stiffness model of the entire workspace) K of the large gantry machine tool 100 through the structural matrix method.

[0057] Step S23: Considering the closed-loop structural constraints and internal stress deformation of the gantry machine tool 100, a gravity deformation error model of the gantry machine tool 100 is established based on the principle of minimum potential energy and the Lagrange multiplier method.

[0058] In some embodiments, step S23 may further include steps S231 and S232.

[0059] Step S231: Consider the internal stress deformation caused by the closed-loop structure constraint of the gantry machine tool 100, and establish the potential energy equation and deformation compatibility equation of the machine tool system that include the influence of internal stress.

[0060] Figure 6 A schematic diagram illustrating the closed-loop structural constraints of a gantry milling machine 100 according to an embodiment of this application is shown. Figure 6 As shown, the large gantry milling machine 100 has two gravity error transmission chains, which are transmitted from the bed 101 along the left and right columns 112. The two chains coincide at the middle node of the crossbeam 131. The node set of the left chain is as follows: The set of nodes in the right-hand branch is The constraints that the deformation error must satisfy are called the deformation compatibility equations, which are essentially kinematic constraint equations that take into account the deformation error. Therefore, determining the deformation compatibility equations means adding a deformation error term to the error propagation. The machine tool kinematics can be viewed as a combination of two branches: the left branch runs from the bed 101 from the left support column to the end of the tool, and the right branch runs from the bed 101 from the right branch to the end of the tool.

[0061] By adding deformation error to the kinematic gravity error model of the machine tool's branches, a gravity error model of the machine tool considering internal stress deformation is obtained: (16) In the above formula, To account for machine tool gravity error in the case of internal stress deformation; Let be the internal stress deformation of node i; The node where branch 1 coincides with gantry frame 102, For the node where branch 2 coincides with gantry frame 102, the deformation compatibility equation that the deformation error needs to satisfy can be obtained from the above formula: (17) in, and The coefficients of the deformation compatibility equations for the machine tool considering closed-loop structural constraints are expressed as follows: (18) in, , , , These represent the transformation matrices from gravity deformation error to end-point error for nodes 1, 2, 4, and 5, respectively.

[0062] Thus, we obtained the deformation compatibility equations considering the constraints of the closed-loop structure.

[0063] According to mechanics of materials, the total potential energy of the gantry milling machine 100 can be expressed as the difference between strain potential energy and external force work. Strain potential energy is determined by the deformation and stiffness matrix of each component of the machine tool, while external force work is determined by the internal stress and corresponding displacement of each component. Considering the machine tool components as unit components, in a two-node unit component, from the perspective of the machine tool end-effector pose, only the deformation of the two end nodes of the unit needs to be considered, without needing to concern ourselves with the displacement field function inside the component.

[0064] For the large gantry machine tool 100, its gantry frame 102 is a closed-loop mechanical structure. When the gravity error on the left and right sides is different, the gantry structure will be forced to generate corresponding internal stress as the state of the machine tool changes, resulting in internal stress deformation, thereby keeping the structure closed-loop. Since the magnitude of internal stress is different under different postures, the deformation error caused by internal stress will be determined by both gravity error and machine tool posture.

[0065] Because assembly and movement are impossible when the internal stress in a machine tool is high, the deformation caused by internal stress is usually small. Let's assume that the deformation is within the linear elastic range of the material and can be considered a first-order small quantity, whose relationship with the internal stress obeys Hooke's theorem. Therefore, the overall strain potential energy of the machine tool can be expressed as: (19) The above formula, The stiffness matrix of the gantry frame 102 can be obtained from the overall stiffness matrix K. The internal stress deformation of node i on the gantry frame 102 is: The overall internal stress deformation vector of gantry frame 102 is .

[0066] The following will explain that under the action of internal stress, the total external force work done by the internal stress of the machine tool is zero. Let the internal stress at node i of the machine tool be... The internal stress deformation is The work done by the internal stress at this node is For a machine tool, the internal stress at a node is the sum of the internal stresses of the two component units at that node: j and j+1 represent two adjacent component elements at node i, and the stress change within the node is: At this point, the work done by the internal stress at node i can be expressed as: (20) According to Newton's third law, the internal stresses at the nodes of the two component units are opposite forces, i.e. At this time The sum of the external forces is 0. In a machine tool, the internal stress at each node can be determined as a pair of external forces that sum to zero. Therefore, the total external force work of the internal stress of the entire machine tool can be divided into a pair of external force work sums, and the sum of these external forces is also 0.

[0067] Therefore, the overall potential energy equation for the internal stress of the machine tool can be obtained: (twenty one) The gravity deformation error at each node i of the machine tool is defined as... The overall gravity deformation error is The overall gravity variation energy of the machine tool It can be represented as: (twenty two) In the analysis of machine tool gravity deformation, in order to introduce the distributed gravity load into the discretized structural model, it is necessary to convert the uniformly distributed gravity load on each component unit into concentrated loads and moments on the corresponding nodes based on the small deformation assumption and the static equivalence principle.

[0068] For any component element j, it is stipulated that its nodal forces are positive when under tension and its nodal bending moments are positive when in the counterclockwise direction. Figure 7 A simplified equivalent gravity diagram of a gantry milling machine 100 component according to an embodiment of this application is shown. Figure 7 As shown in the diagram on the left, the direction of gravity is perpendicular to the lines connecting the nodes of the component elements, such as component 131 and component 141 on component 131. The direction of gravity is parallel to the lines connecting the nodes of the component elements, such as component 112 on the left and right and component 151 on the ram. The equivalent nodal load distribution under the action of gravity for these two types of component elements is shown in the left and right diagrams, respectively. This represents the equivalent gravitational load of component element j at node i; This represents the equivalent gravitational load of component element j at node i+1; , These are the corresponding equivalent moments of component element j at node i and node i+1, respectively.

[0069] The structural deformation of a machine tool under gravity includes the self-weight deformation caused by the gravity of the machine tool components themselves and the stress deformation caused by the gravity of related components. The equivalent gravity load and equivalent moment at each node can be given by the following formula: (twenty three) Finally, the equivalent gravity loads at all nodes are obtained: (twenty four) in, , , , , , These are the equivalent gravity loads at nodes 1, 2, 3, 4, 6, and 7, respectively. , , , , , These are the equivalent moments for nodes 1, 2, 3, 4, 6, and 7, respectively. , , , , These represent the masses of component units 1, 2, 3, 4, and 5, respectively. It is the acceleration due to gravity; This represents the distance between the second and third nodes, which changes as the Y-axis moves. This represents the distance between the second and fourth nodes; This represents the distance between the 3rd and 4th nodes, which changes as the Y-axis moves. This represents the distance between the 3rd and 6th nodes, which changes as the Z-axis moves.

[0070] After gravity is equivalently applied to the nodes of the machine tool component, the external force work done by the machine tool component i under gravity is divided into a gravity displacement component and an internal stress displacement component of the nodes on the gantry frame. The deformation of the nodes needs to be converted into the displacement in the machine tool coordinate system, which can be expressed as: (25) in, The nodal deformation of the gravity displacement portion of the external force work done by machine tool component i under gravity is converted into the displacement in the machine tool coordinate system. The nodal deformation of the internal stress displacement portion of the external force work done by machine tool component i under gravity is converted into the displacement in the machine tool coordinate system. This represents the equivalent gravitational load at node i; , Let A and B represent the error differential transfer matrices from node a and node b to node i, respectively. The displacement of node i in the machine tool coordinate system can be calculated from the deformation amount. This represents the gravitational deformation of node a; This represents the internal stress deformation at node b; This represents the index i and its lower-order node numbers within the set of branches to which node i belongs. For example, when node i = 2, it belongs to branch 1, and the index i and its lower-order node numbers are 1 and 2, so a ∈ {1, 2}; similarly, when node i = 6, it is also considered to belong to branch 1, and the index i and its lower-order nodes are 1, 2, 3, and 6, so a ∈ {1, 2, 3, 6}.

[0071] The total external work done by the overall gravity of the machine tool is the sum of the external work done at the 7 nodes, expressed as: (26) in, This represents the equivalent gravity load matrix of the nodes on the gantry frame. and These represent the transformation matrices that convert the gravity deformation of the machine tool nodes and the internal stress deformation of the gantry frame nodes into displacements, respectively.

[0072] From equations (22) and (26), the overall potential energy equation of the machine tool considering gravitational deformation can be obtained as follows: (27) Therefore, based on equations (21) and (27), the potential energy equation of the machine tool system can be obtained.

[0073] Step S232: Based on the machine tool system potential energy equation and deformation compatibility equation, and based on the minimum potential energy principle and the Lagrange multiplier method, the deformation error of the end under the influence of gravity and internal stress is obtained.

[0074] According to the principle of minimum potential energy, the actual gravitational deformation always minimizes the potential energy equation. Therefore, the gravitational deformation error is the optimal solution to the following problem: (28) Where argmin represents the potential energy equation of the machine tool system. The parameter value that yields the minimum value; The total gravity deformation error of the gantry machine tool 100 (i.e., the gravity deformation error from node 1 to node 7). Represents the transpose of a matrix; The overall stiffness matrix of the gantry milling machine 100; The stiffness model of the gantry frame 102 in the gantry machine tool 100 can be derived from the overall machine stiffness matrix. Obtain; The equivalent gravity load matrix of the entire node of the gantry milling machine 100; This is the node equivalent gravity load matrix of the gantry frame 102 in the gantry machine tool 100. This refers to the total internal stress deformation error of the gantry frame 102 (i.e., the stress deformation error of nodes 1 to 5 on the gantry frame 102).

[0075] According to the Lagrange multiplier method, the above equation-constrained optimization problem can be transformed into an unconstrained optimization problem: (29) The optimized function is: (30) in, It is a Lagrange multiplier.

[0076] Based on the KKT conditions for unconstrained optimization, the actual satisfy: (31) Substituting the KKT conditions, we get: (32) (33) (34) Therefore, the solutions for the gravitational deformation and passive deformation error under internal stress at each node can be obtained as follows: (35) in, and They are respectively and The pseudo-inverse matrix.

[0077] To verify the correctness of the obtained deformation compatibility equations, multiple pose points were selected in the machine tool workspace, and the error outputs of the two branches of the machine tool were calculated under the conditions of considering and ignoring structural constraints. Figure 8 A comparison chart showing the double-branch error of the gantry milling machine 100 with and without structural constraints is presented. (See figure.) Figure 8 As shown, without considering structural constraints, the mapping results of the left and right branches to their ends differ, which does not conform to the actual situation; after considering structural errors, the mapping results of the left and right branches to their ends tend to be consistent, indicating the correctness of the structural constraints.

[0078] At this point, the machine tool gravity error considering internal stress deformation is obtained according to formula (16). Furthermore, the deformation error at the end under the influence of gravity and internal stress can be obtained as follows: (36) in, The deformation error at the end under the influence of gravity and internal stress is in matrix form. , , , , , These represent the gravity deformation errors along the X, Y, Z, I, J, and K axes, respectively.

[0079] Step S3: Couple the geometric error model established in step S1 with the gravity deformation error model established in step S2 to obtain the rigid-flexible coupled integrated geometric-gravity error model of the gantry machine tool 100.

[0080] Gravity deformation error model of gantry milling machine 100 based on equation (36) The error propagation matrix of the machine tool end under the influence of gravity deformation can be derived using the methods of formulas (3) and (4) above.

[0081] The expression for the rigid-flexible coupled integrated geometry-gravity error model of the gantry milling machine 100 is as follows: (37) in, This is the error propagation matrix of the machine tool end effector under the influence of gravitational deformation. Geometric error model for gantry milling machine 100; Let represent the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point. This indicates the error of component i.

[0082] Step S4: Measure the geometric error parameters of each motion axis of the gantry milling machine 100, and substitute the measured static error parameters into the rigid-flexible coupling integrated geometric-gravity error model to obtain the geometric error parameters after eliminating the influence of gravity error factors.

[0083] The static error parameters of each motion axis of the gantry milling machine 100 can be measured using a laser interferometer. Optionally, an XM-60 laser interferometer can be used. For the large gantry milling machine 100 under study, since the verified rigid-flexible coupled integrated geometry-gravity error model is independent of the rotation axis pose, the gantry milling machine 100 can be considered as a three-axis machine tool for measurement. Single-axis error measurements are performed using the XM-60 laser interferometer, and the measured static error parameters are substituted into the rigid-flexible coupled integrated geometry-gravity error model to obtain the geometric error parameters free from the influence of gravity.

[0084] Step S5: After completing the error measurement, the error compensation amount of each motion position point of the gantry machine tool 100 can be calculated based on the integrated geometric-gravity error model of rigid-flexible coupling and the geometric error parameters that eliminate the influence of gravity error factors. The gantry machine tool 100 can then be calibrated based on the error compensation amount of each motion position point.

[0085] Specifically, based on the calculated error compensation amount at each moving position point of the gantry machine tool 100, the G-code related to the four body diagonals in the workspace of the gantry machine tool 100 in the CNC system is modified. The error compensation amount is written into the CNC system by modifying the G-code program. Then, the positioning error of the four body diagonals in the workspace of the gantry machine tool 100 is measured according to the ISO230-6 standard to verify the positioning accuracy of the four body diagonals in the workspace of the gantry machine tool 100, thereby completing the compensation verification.

[0086] Figure 9 The image shows a comparison of the compensation effects of the four body diagonals of the 100-type gantry milling machine under different models before and after the compensation. Figure 10 The mean error of the gantry milling machine 100 before and after compensation was revealed under the linear model and the geometry-gravity model; Figure 11 The compensation ratio of the gantry milling machine 100 under linear and geometry-gravity models was revealed. From Figures 9 to 11 It can be seen that after using the integrated geometric-gravity error model in the geometric-gravity error integrated calibration method for large gantry machine tools of this application, the positioning error of the four body diagonals of the gantry machine tool 100 has decreased significantly, and the compensation effect has increased substantially, thus proving the effectiveness of the geometric-gravity error integrated calibration method for large gantry machine tools proposed in this application.

[0087] Figure 12 The diagram shows a comparison of the variance of the gantry milling machine 100 after compensation under linear and geometric-gravity models. (See diagram for example.) Figure 12 As shown, the integrated geometry-gravity error compensation proposed in this application has a lower variance compared to traditional linear compensation, thus demonstrating the stability of the integrated geometry-gravity error model in this application.

[0088] Compared with the prior art, the integrated geometric-gravity error calibration method for large gantry milling machines of this application has at least the following beneficial technical effects: (1) In view of the problem that geometric error and gravity deformation error are coupled in the traditional kinematic calibration of existing large gantry machine tool 100 and the influence of internal stress deformation of closed-loop structure is ignored, this application proposes the idea of ​​rigid-flexible coupling integrated geometric-gravity error modeling, which realizes accurate comprehensive description of multi-source static error; (2) The rigid-flexible coupling integrated geometry-gravity error model innovatively integrates the geometric error model based on multibody system theory with the gravity deformation model considering structural constraints. For the first time, it systematically incorporates the internal stress deformation caused by the 100 closed-loop structure of the gantry machine tool. It solves the problem by using the minimum potential energy principle and the Lagrange multiplier method, completely getting rid of the limitation of the geometric error identification caused by gravity deformation interference in the traditional calibration. It completely covers the transmission link of geometric error, gravity deformation error and internal stress deformation error from the theoretical level, and solves the problem of unsystematic description of error sources and fuzzy transmission relationship in the past, making the static error prediction more accurate. (3) In view of the problem that the structure of large machine tool components is complex and the stiffness is difficult to be calculated analytically, this application develops a stiffness characteristic extraction method that combines the structural matrix method and the finite element method, which takes into account both calculation accuracy and efficiency.

[0089] (4) The stiffness matrix of each component unit node in the local coordinate system is obtained by finite element software. After the coordinate transformation is converted into the stiffness matrix of the machine tool coordinate system, the static stiffness model of the entire working space is assembled according to the structural matrix method. At the same time, the machine tool is reasonably disassembled into component units and nodes. Based on the static equivalence principle, the uniformly distributed gravity load is converted into the node concentrated load and moment, which simplifies the calculation complexity and ensures the authenticity of load transmission. It provides accurate key parameter support for the gravity deformation error model and avoids the dilemma of difficulty in balancing accuracy and efficiency in traditional stiffness modeling. (5) In terms of error compensation and practical application, the compensation scheme of this application is accurate and efficient, and significantly improves the positioning accuracy of machine tools; (6) Based on the integrated geometric-gravity error model of rigid-flexible coupling, the error compensation amount of each spatial position point of the computer tool can be directly calculated. The compensation can be achieved by modifying the G code related to the four body diagonals in the 100 working space of the gantry machine tool and inputting it into the CNC system. There is no need to modify the machine tool hardware. When measuring, the XM-60 laser interferometer is used and the machine tool is regarded as a three-axis machine tool to simplify the operation, which is easy to promote in industrial applications. (7) Verified by ISO230-6 standard, by measuring the positioning error of the four body diagonals in the working space of the gantry machine tool 100, and comparing it with the traditional linear compensation model, it can be seen that after adopting the geometric-gravity error integrated calibration method of the large gantry machine tool of this application, the mean and variance of the positioning error are significantly reduced, the compensation ratio is greatly increased, and the problem of the decrease in accuracy of the large gantry machine tool 100 under load and large stroke conditions is effectively solved. (8) The geometric-gravity error integrated calibration method of the large gantry machine tool in this application is fully adapted to the characteristics of the large gantry machine tool 100, such as large structural size, heavy load and closed-loop structure. It provides a replicable technical solution for the formation of an independent and controllable precision assurance system for the domestic large gantry machine tool 100, and strongly supports the processing needs of key parts in key fields such as aviation and aerospace.

[0090] The integrated geometric-gravity error calibration method for large gantry milling machines provided in this application has been described in detail above. Specific examples have been used to illustrate the integrated geometric-gravity error calibration method for large gantry milling machines in this application. The descriptions of the above embodiments are only for helping to understand the core ideas of this application and are not intended to limit this application. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the spirit and principles of this application, and these improvements and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for integrated geometric-gravity error calibration of a large gantry milling machine, characterized in that, include: Based on the kinematics theory of multibody systems and the kinematics analysis of rigid bodies, a geometric error model of a gantry milling machine is established. The geometric error model is used to describe the geometric error sources of each motion axis of the gantry milling machine and their transmission relationships. A gravity deformation error model for the gantry milling machine is established based on mechanical analysis and potential energy methods. By coupling the geometric error model with the gravity deformation error model, a rigid-flexible coupled integrated geometric-gravity error model of the gantry milling machine is obtained. The static error parameters of each motion axis of the gantry machine tool are measured, and the measured static error parameters are substituted into the rigid-flexible coupled integrated geometric-gravity error model to obtain the geometric error parameters that eliminate the influence of gravity error factors. Based on the integrated geometric-gravity error model of rigid-flexible coupling and the geometric error parameters that eliminate the influence of gravity error factors, the error compensation amount of each motion position point of the gantry machine tool is calculated, and the gantry machine tool is calibrated based on the error compensation amount of each motion position point.

2. The method as described in claim 1, characterized in that, The gravity deformation error model of the gantry milling machine established based on mechanical analysis and potential energy methods includes: The stiffness matrix of the machine tool components is obtained using finite element method software; The overall stiffness matrix of the gantry milling machine is obtained from the stiffness matrix of the machine tool components using the structural matrix method. Considering the internal stress deformation caused by the closed-loop structural constraints of the gantry milling machine, establish the potential energy equation and deformation compatibility equation of the machine tool system that include the influence of internal stress. Based on the potential energy equation of the machine tool system and the deformation compatibility equation, and based on the principle of minimum potential energy and the Lagrange multiplier method, the deformation error of the end under the influence of gravity and internal stress is obtained.

3. The method as described in claim 2, characterized in that, The process of obtaining the stiffness matrix of the machine tool components using finite element software includes: The machine tool components are considered as unit structures, and the gravitational deformation of the machine tool components is simplified to the deformation at both ends of the nodes between the component units; The stiffness matrix of each node was obtained using finite element method software.

4. The method as described in claim 3, characterized in that, The gantry milling machine includes a left column, a right column, a slider, a crossbeam, an apron, a ram, and a CA swing head. The slider is mounted on both the left and right columns and is used for movement along the X-axis. The crossbeam connects the sliders on the left and right columns. The apron is mounted on the crossbeam and is used for movement along the Y-axis. The ram is mounted on the apron and is used for movement along the Z-axis. The CA swing head is mounted on the ram and is used for movement along the rotary axis. The process of obtaining the stiffness matrix of each node using finite element software includes: The machine tool components are divided into 5 component units and 7 nodes. The 5 component units include: a left column as the first component unit; a crossbeam as the second component unit; a right column as the third component unit; a slider as the fourth component unit; and a ram and CA swing head as the fifth component unit. The crossbeam is a three-node component unit, and the other component units are two-node component units. The 7 nodes include the first node between the left side of the gantry machine bed and the ground, the second node between the crossbeam and the slider on the left column, the third node between the crossbeam and the slide, the fourth node between the crossbeam and the slider on the right column, the fifth node between the right side of the gantry machine bed and the ground, the sixth node between the slide and the ram, and the seventh node at the end. The stiffness matrix of each node in the local coordinate system was obtained using finite element software. The stiffness matrix of each node in the local coordinate system is transformed into the stiffness matrix of each node in the machine tool coordinate system through the coordinate transformation matrix.

5. The method as described in claim 4, characterized in that, The expression for the coordinate transformation matrix is: , in, Let be the nodal coordinate transformation matrix of component element j, i.e.: , in, , , These represent the cosines of the X-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Y-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively. , , These represent the cosines of the Z-axis coordinate of the local coordinate system of component unit j with respect to the coordinate axes of the machine tool coordinate system in the X, Y, and Z directions, respectively.

6. The method as described in claim 4, characterized in that, The structural constraints of the potential energy equation and the deformation compatibility equation of the machine tool system are: , , Where argmin represents the potential energy equation of the machine tool system. The parameter value that yields the minimum value; The total weight deformation error of the gantry milling machine; Represents the transpose of a matrix; Let be the overall stiffness matrix of the gantry milling machine; The stiffness model of the gantry frame in the gantry machine tool can be derived from the overall machine stiffness matrix. Obtain; The total internal stress deformation error of the gantry frame; This is the equivalent gravity load matrix for all nodes; Let be the equivalent gravity load matrix of the nodes on the gantry frame; This represents the transformation matrix that converts the gravitational deformation of the entire gantry milling machine into displacement in the machine tool coordinate system. This represents the transformation matrix that converts the internal stress deformation of the nodes on the gantry frame into displacement in the machine tool coordinate system; and The coefficients of the deformation compatibility equation for machine tools considering closed-loop structural constraints; , , , These represent the transformation matrices from gravity deformation error to end-point error for nodes 1, 2, 4, and 5, respectively.

7. The method as described in claim 2, characterized in that, The expression for the deformation error matrix of the end under the influence of gravity and internal stress is: , in, , , , , , These represent the gravitational deformation errors along the X, Y, Z, I, J, and K axes, respectively; the I, J, and K axes represent the directions of rotation around the X, Y, and Z axes, respectively.

8. The method as described in claim 1, characterized in that, The expression for the rigid-flexible coupled integrated geometry-gravity error model of the gantry milling machine is as follows: , in, The error transfer matrix of the machine tool end under the influence of gravity deformation can be obtained from the gravity deformation error model of the gantry machine tool. This is the geometric error model of the gantry milling machine; This represents the differential error transfer matrix from the component i-coordinate system to the end-effector coordinate system of the gantry milling machine. This indicates the error of component i.

9. The method as described in claim 1, characterized in that, The gantry milling machine includes three linear motion axes (X, Y, Z) and two rotary axes (C, A). The geometric error model of the gantry milling machine, based on multibody system kinematics theory and rigid body kinematics analysis, includes: Define the five axes XYZCA as machine tool component numbers 1-5, the tool end coordinate system as number 6, and the local coordinate systems of adjacent components i and j as follows: and Where j>i, and described by a 4×4 DH transformation matrix. arrive Coordinate transfer transformation; Starting with any component i, the DH transformation matrices of each subsequent component are multiplied together to obtain the homogeneous transformation matrix from any component i to the end of the tool. Based on the homogeneous transformation matrix from part i to the end of the tool and the principle of differential transformation, the differential error transfer matrix from the coordinate system of part i to the coordinate system of the end is obtained. Based on the differential error transfer matrix from component i's coordinate system to the end-effector coordinate system, and combined with the linear and angular errors of each motion axis of the gantry milling machine, the end-effector error caused by component i is obtained. This error is then summed to obtain the total end-effector error caused by all components of the gantry milling machine. The expression for the total end-effector error caused by all components of the gantry milling machine is as follows: , in, , , These represent the components of the tool end space error in the X, Y, and Z axes, respectively. , , These represent the components of the tool attitude error in the I, J, and K axis directions, respectively, where the I, J, and K axis directions are the directions of rotation around the X, Y, and Z axes, respectively. This indicates the machine tool end effector error caused by component i. Let represent the differential error transfer matrix from the coordinate system of component i to the coordinate system of the end point. This indicates the error of component i.

10. The method as described in claim 1, characterized in that, The static error parameters of each motion axis of the gantry milling machine are measured as follows: The static error parameters of each motion axis of the gantry milling machine were measured using a laser interferometer. During the measurement, the gantry milling machine was treated as a three-axis machine tool for single-axis error measurement. The calibration of the gantry milling machine based on the error compensation amount at each motion position point includes: Based on the error compensation amount at each motion position point, modify the G-code related to the four body diagonals in the workspace of the gantry machine tool in the CNC system; The positioning error of the four body diagonals within the workspace of the gantry milling machine was measured based on the ISO230-6 standard to complete the compensation verification.

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