A geometric error parameterization fast modeling method for multi-configuration five-axis machine tool

Abstract

The application discloses a kind of geometric error parameterization fast modeling methods for multi-configuration five-axis machine tool.The method comprises the following steps: constructing the parameterized general transfer vector table of the five-axis machine tool of target type;The parameter set of five-axis machine tool is input into general transfer vector table, and general transfer vector table generates the transfer vector of each geometric error term of five-axis machine tool, to construct geometric error model;Geometric error term and five-axis coordinate are input into model, and model outputs the position deviation and attitude deviation of tool, to be used for the geometric error compensation of tool of five-axis machine tool.The transfer vector table constructed by the application can be reused, and the geometric error model constructed can be suitable for most conventional configuration machine tools;The application can realize the parameterization fast modeling of five-axis machine tool geometric error, can reduce the experience requirement of research and operator, and provides convenience for the accuracy design, error compensation research of various conventional five-axis machine tools and the transverse comparison research between various machine tool configurations and layouts.

Description

Technical Field

[0001] This invention relates to a geometric error modeling method, which relates to the field of machine tool machining accuracy design, and specifically to a rapid parameterized modeling method for geometric errors of multi-configuration five-axis machine tools. Background Technology

[0002] Five-axis machine tools possess unique advantages in the machining and manufacturing of complex curved surfaces and are widely used in aerospace, shipbuilding, automotive, and defense industries. The machining accuracy of five-axis machine tools directly reflects a country's advanced manufacturing technology level. Geometric errors are one of the main factors affecting machine tool machining accuracy, characterized by high systematicity, good repeatability, and long-term stability. Therefore, compensating for geometric errors and rationally designing geometric accuracy have become feasible methods to improve the overall machining accuracy of machine tools.

[0003] Both of the aforementioned methods for reducing the impact of geometric errors rely on a correct geometric error model, namely, the functional relationship between various geometric errors and positioning deviations of a five-axis machine tool. Existing modeling methods are cumbersome, error-prone, lack robustness, and involve massive computational loads, placing significant pressure on subsequent mathematical analyses of the model, such as sensitivity analysis. Furthermore, existing methods struggle to cope with changes in machine tool configuration. During the machine tool design phase, when the machine tool structure, layout, or kinematic chain is reconfigured, or during the error measurement phase when measuring instruments and methods change, the model must be rebuilt from scratch, causing inconvenience to the research. Summary of the Invention

[0004] To address the problems existing in the background art, this invention provides a rapid modeling method for geometric error parameterization of multi-configuration five-axis machine tools. This invention solves the problems of existing methods, such as cumbersome and error-prone modeling processes, low robustness, large computational load, and difficulty in handling changes in machine tool configuration.

[0005] The technical solution adopted in this invention is:

[0006] The present invention provides a rapid modeling method for geometric error parameterization of multi-configuration five-axis machine tools, comprising:

[0007] 1) Based on the machine tool topology parameters of the target type of five-axis machine tool, the transfer vectors of each geometric error term of the five-axis machine tool are obtained using the linear approximation assumption, thereby constructing a parameterized general transfer vector table for the target type of five-axis machine tool; the types of five-axis machine tools include dual rotary table, dual swivel head, hybrid type, etc.

[0008] 2) Based on the configuration of the target type of five-axis machine tool, obtain the parameter set of the five-axis machine tool. The parameter set includes three parameters: motion chain code, offset vector between local coordinate systems, and perpendicularity error reference information. Input the parameter set into the general transfer vector table. The general transfer vector table generates the transfer vector of each geometric error item of the five-axis machine tool. Then, use the linear combination method to construct the geometric error model of the five-axis machine tool, and realize the parameterized rapid modeling of the geometric error of the five-axis machine tool.

[0009] In step 1), the general transfer vector table is constructed based on the local transfer vector, the transfer matrix, the conditional displacement of the motion axis, the cumulative displacement between coordinate systems, the limitation of the motion axis to which the error belongs, and the constraint of the workpiece end motion axis of the five-axis machine tool based on the target type.

[0010] By using linear approximation, the traditional matrix multiplication geometric error model based on homogeneous coordinate transformation is simplified into a transfer vector model expressed by a linear combination of 41 transfer vectors. Based on the general laws in the geometric error modeling process of five-axis machine tools, the definitions of local transfer vector, transfer matrix, conditional displacement of motion axis, cumulative displacement between coordinate systems, and motion axis to which the error belongs are proposed, as well as two special constraints for the motion axis at the workpiece end. Using the proposed definitions and laws, for a specific type of five-axis machine tool, the transfer vectors of the 41 geometric error terms are directly solved using machine tool parameters under the assumption of linear approximation, forming a general transfer vector table with parameters.

[0011] The local transfer vector LV is as follows:

[0012] The i-th geometric error term E for a five-axis machine tool of the target type i In one of the local coordinate systems of a five-axis machine tool, the reference point for the tool tip position of the five-axis machine tool experiences a displacement Δl, where Δl = E. i • LVP, where LVP represents the four-dimensional preset position deviation local transfer vector. The four-row, two-column vector formed by the four-dimensional preset position deviation local transfer vector LVP and the four-dimensional preset attitude deviation local transfer vector LVV is the i-th geometric error term E of the five-axis machine tool of the target type. i The local transfer vector LV in the current local coordinate system, LV = [LVP LVV].

[0013] In a single geometric error E i Under the influence of the motion axis Axis (Axis∈[X,Y,Z,A,B,C,M]), the reference point of the tool tip position undergoes a small displacement E. i • LVP, the tool vector has undergone a small offset E iIf LVV, then the four-row, two-column vector LV = [LVP LVV] composed of vectors LVP and LVV is the geometric error E. i Local transfer vector LV in the local coordinate system AxisCS Axis (E i ), LV Axis (E i ) = [LVP Axis (E i ) LVV Axis (E i )], of which LV Axis (E i () represents the geometric error E i Local transfer vector in the local coordinate system AxisCS, LVP Axis (E i () represents the geometric error E i The local transfer vector of position deviation in the local coordinate system AxisCS, LVV Axis (E i () represents the geometric error E i The local transfer vector of attitude deviation in the local coordinate system AxisCS.

[0014] The specific transition matrix M is as follows:

[0015] After multiplying the local transfer vector LV in the current local coordinate system by a homogeneous transformation matrix, the transfer vector J in the workpiece coordinate system is obtained. Then, the homogeneous transformation matrix is ​​the transfer matrix M of the local transfer vector LV in the current local coordinate system; at this time, the current local coordinate system is transformed into the workpiece coordinate system.

[0016] The relationship between the transition matrix and the local transfer vector is as follows:

[0017] J i =M i ·LV i

[0018] Among them, J i M i and LV i Let represent the transfer vector, transition matrix, and local transfer vector of the i-th geometric error, respectively.

[0019]

[0020] Where R(A), R(B), and R(C) represent the rotation matrices under the nominal angular displacements A, B, and C axes of the machine tool, respectively; M(C) represents the transfer matrix under the nominal angular displacement C of the C axis of the machine tool; M(AC) represents the transfer matrix under the nominal angular displacements A and C axes of the machine tool; and M(BC) represents the transfer matrix under the nominal angular displacements B and C axes of the machine tool.

[0021] Taking a five-axis machine tool with a dual rotary table as an example, the details are as follows:

[0022]

[0023] Where M(Axis) represents the transition matrix of the motion axis Axis, R(Axis) is the rotation matrix of the motion axis Axis, Axis1 and Axis2 represent the first and second motion axes respectively, M(Axis1Axis2) represents the transition matrix of the first and second motion axes, and R(Axis1) and R(Axis2) represent the rotation matrices of the first and second motion axes respectively.

[0024] The specific displacement of the motion axis is as follows:

[0025] Using the three linear axes and two rotary axes of the target type of five-axis machine tool as motion axes, for two of these motion axes, the motion axis closer to the tool end is designated as the high-order body, and the motion axis closer to the workpiece end is designated as the low-order body. The conditional displacement of the motion axis is the nominal displacement of one of the motion axes obtained when the high-order body condition is met. The nominal displacement of the motion axis is the displacement of the motion axis from the initial position to the current position. The selected motion axis has an impact on the form of the transfer vector.

[0026] The cumulative displacement between the coordinate systems is as follows:

[0027] In the initial state where the nominal displacement of each motion axis of the target type of five-axis machine tool is zero, the cumulative displacement vector between the start and end coordinate systems of the target type of five-axis machine tool is taken as the cumulative displacement between coordinate systems.

[0028] The cumulative displacement vector between the local coordinate system Axis1CS of the first motion axis Axis1 and the local coordinate system Axis2CS of the second motion axis Axis2 of the machine tool. Specifically as follows:

[0029]

[0030] in, and These represent the displacements in the X, Y, and Z directions between the local coordinate system Axis1CS of the first motion axis Axis1 and the local coordinate system Axis2CS of the second motion axis Axis2 of the machine tool.

[0031] The specific motion axis to which the error pertains is as follows:

[0032] For the perpendicularity error of two motion axes of a five-axis machine tool of the target type, when the perpendicularity error is based on one motion axis, the other motion axis is taken as the motion axis to which the perpendicularity error belongs.

[0033] A parameterized general transfer vector table specifies the local transfer vectors and transition matrices for 41 geometric errors of a specific type of five-axis machine tool, thus allowing the transfer vector of that geometric error to be obtained. Under the linear approximation assumption, the transfer vectors of the 41 geometric error terms can be directly solved using the machine tool parameters. For a specific type of five-axis machine tool, this solution only needs to be performed once, and the resulting transfer vector table can be reused.

[0034] The motion axis conditional displacement is divided into high-order conditional displacement and low-order conditional displacement. When the high-order body condition is met, the high-order conditional displacement and low-order conditional displacement are obtained as nominal displacements, as detailed below:

[0035]

[0036] in, This represents the high-order conditional displacement of the first motion axis Axis1 relative to the second motion axis Axis2. Let Axis1 be the nominal displacement of the first motion axis, where Axis1∈[X,Y,Z,A,B,C]; This represents the lower-order conditional displacement of the first motion axis Axis1 relative to the second motion axis Axis2.

[0037] The constraints on the workpiece end motion axes of the target-type-based five-axis machine tool are as follows:

[0038] For each linear axis of a five-axis machine tool of the target type, when the linear axis is located at the workpiece end, the nominal displacement of the linear axis is reversed; when the motion axis to which the error belongs is located at the workpiece end, the transmission vector is reversed.

[0039] In step 2), the geometric error model of the five-axis machine tool is as follows:

[0040]

[0041] Where E represents the geometric error model of the five-axis machine tool, E is a 4x2 vector representing the comprehensive deviation of the five-axis machine tool, including positional deviation and attitude deviation; E iThis represents the i-th geometric error term of a five-axis machine tool; and E represents the i-th geometric error term E of the five-axis machine tool. i The projection coefficients of the resulting positional deviation in the X, Y, and Z directions; and E represents the i-th geometric error term E of the five-axis machine tool. i The projection coefficients of the resulting attitude deviation in the X, Y, and Z directions; JP i and JV i E represents the i-th geometric error term E of the five-axis machine tool. i Position deviation transfer vector and attitude deviation transfer vector; J i E represents the i-th geometric error term of a five-axis machine tool. i The transfer vector.

[0042] According to the i-th geometric error term E of the five-axis machine tool i Position deviation transfer vector JP i The tool position deviation is obtained based on the i-th geometric error term E of the five-axis machine tool. i The attitude deviation of the tool is obtained by the attitude deviation transfer vector. The position deviation and attitude deviation caused by each geometric error term acting alone can be obtained directly. The comprehensive deviation requires adding up the deviations caused by each of the 41 geometric error terms.

[0043] The electronic device of the present invention includes a memory and a processor coupled to each other, wherein the memory stores program data and the processor invokes the program data to execute the method described above.

[0044] The present invention provides a computer-readable storage medium having program data stored thereon, which, when executed by a processor, implements the method described above.

[0045] This invention first proposes definitions for local transfer vectors, transition matrices, conditional displacements of motion axes, cumulative displacements between coordinate systems, and the motion axes to which errors belong, along with two special constraints for the workpiece-end motion axis. Then, based on the proposed definitions and constraints, it summarizes parameterized general mathematical formulas for the responses of each geometric error term, forming a transfer vector table. When modeling is required, parameters are simply extracted from the machine tool topology and filled into the transfer vector table to directly generate the geometric error model. Since the transfer vector table is reusable, this modeling method is applicable to most conventional machine tool configurations. This invention enables rapid parameterized modeling of geometric errors in five-axis machine tools, reducing the experience requirements for researchers and operators, and facilitating precision design, error compensation research, and comparative studies between various machine tool configurations and layouts for various conventional five-axis machine tools.

[0046] The beneficial effects of this invention are:

[0047] 1) The transfer vector table constructed in this invention is reusable, and the constructed geometric error model is applicable to most conventional machine tools; 2) The method of this invention solves the problems of distortion, poor robustness, and cumbersome and error-prone nature that may occur in traditional modeling methods. It has the characteristics of parameterization and universality and is applicable to most conventional five-axis machine tools; 3) This invention can realize parameterized and rapid modeling of the geometric error of five-axis machine tools. It can respond quickly to changes in the machine tool configuration. It only needs to input the parameter set of the machine tool into the transfer vector table to quickly reconstruct the geometric error model of the machine tool. It is easy to implement by computer programming, and the operation process is simple and fast; 4) This invention can reduce the experience requirements of researchers and operators in the field of geometric accuracy of five-axis machine tools, and provide convenience for the accuracy design, error compensation research of various conventional five-axis machine tools, as well as the horizontal comparison research between various machine tool configurations and layouts. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating a specific embodiment of the method of the present invention;

[0049] Figure 2 For the geometric error term δ xx and ε zx The following diagram illustrates the method for solving the local transfer vector of position-dependent geometric errors (PDGEs) along a linear axis, where... Figure 2 (a) is the geometric error term δ xx A schematic diagram illustrating the method for solving the local transfer vector of PDGEs along a linear axis is provided. Figure 2 (b) is defined by the geometric error term ε zx A schematic diagram illustrating the method for solving the local transfer vector of PDGEs along a linear axis is provided.

[0050] Figure 3 For the geometric error term S xy A schematic diagram illustrating the method for solving the local propagation vector of perpendicularity error is shown below;

[0051] Figure 4 A schematic diagram illustrating the solution of the local transfer vector of attitude deviation using the local transfer vector of position deviation;

[0052] Figure 5 To quickly reconstruct the schematic diagram of the dual rotary table five-axis machine tool structure in Case Study 1;

[0053] Figure 6 This is a schematic diagram illustrating the method for establishing a local coordinate system in Case Study 1, which is used for rapid reconstruction modeling. Figure 6 (a) is a schematic diagram of the method for establishing the local coordinate system of the X-axis in Case 1 of rapid reconstruction modeling. Figure 6 (b) is a schematic diagram of the method for establishing the local coordinate system along the Y-axis in Case 1 of rapid reconstruction modeling. Figure 6 (c) is a schematic diagram of the method for establishing the local coordinate system along the Z-axis in Case 1 of rapid reconstruction modeling. Figure 6 (d) is a schematic diagram of the establishment method of the local coordinate system of the B-axis and C-axis in the case of rapid reconstruction modeling 1;

[0054] Figure 7 This is a schematic diagram illustrating the selection of the rotation axis perpendicularity error benchmark in Case Study 1, which is used for rapid reconstruction modeling. Figure 7 (a) is a schematic diagram of the selection of the B-axis perpendicularity error benchmark in Case 1 of rapid reconstruction modeling. Figure 7 (b) is a schematic diagram of the selection of the C-axis perpendicularity error benchmark in Case 1 of rapid reconstruction modeling;

[0055] Figure 8 To quickly reconstruct the scatter plot for modeling verification in Case Study 1;

[0056] Figure 9 The schematic diagram of the dual rotary table five-axis machine tool structure in Case Study 2 is used for rapid reconstruction modeling;

[0057] Figure 10 This is a schematic diagram illustrating the method for establishing a local coordinate system in Case Study 2 for rapid reconstruction modeling. Figure 10 (a) is a schematic diagram of the method for establishing the local coordinate system of the X-axis in Case 2 of rapid reconstruction modeling. Figure 10 (b) is a schematic diagram of the method for establishing the local coordinate system along the Y-axis in Case 2 of rapid reconstruction modeling. Figure 10 (c) is a schematic diagram of the method for establishing the local coordinate system along the Z-axis in Case 2 of rapid reconstruction modeling. Figure 10 (d) is a schematic diagram of the establishment method of the local coordinate system of the A-axis and C-axis in the case of rapid reconstruction modeling 2;

[0058] Figure 11 A scatter plot for modeling verification in case study 2, used for rapid reconstruction. Detailed Implementation

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] The present invention provides a rapid modeling method for geometric error parameterization of multi-configuration five-axis machine tools, comprising:

[0061] 1) Based on the machine tool topology parameters of the target type of five-axis machine tool, the transfer vectors of each geometric error term of the five-axis machine tool are obtained using the linear approximation assumption, thereby constructing a parameterized general transfer vector table for the target type of five-axis machine tool; the types of five-axis machine tools include dual rotary table, dual swivel head, hybrid type, etc.

[0062] The general transfer vector table is constructed based on local transfer vectors, transfer matrices, motion axis conditional displacement, cumulative displacement between coordinate systems, and the constraints of the motion axis to which the error belongs, as well as the constraints of the workpiece end motion axis of the five-axis machine tool based on the target type.

[0063] By using linear approximation, the traditional matrix multiplication geometric error model based on homogeneous coordinate transformation is simplified into a transfer vector model expressed by a linear combination of 41 transfer vectors. Based on the general laws in the geometric error modeling process of five-axis machine tools, the definitions of local transfer vector, transfer matrix, conditional displacement of motion axis, cumulative displacement between coordinate systems, and motion axis to which the error belongs are proposed, as well as two special constraints for the motion axis at the workpiece end. Using the proposed definitions and laws, for a specific type of five-axis machine tool, the transfer vectors of the 41 geometric error terms are directly solved using machine tool parameters under the assumption of linear approximation, forming a general transfer vector table with parameters.

[0064] The local transfer vector LV is as follows:

[0065] The i-th geometric error term E for a five-axis machine tool of the target type i In one of the local coordinate systems of a five-axis machine tool, the reference point for the tool tip position of the five-axis machine tool experiences a displacement Δl, where Δl = E. i • LVP, where LVP represents the four-dimensional preset position deviation local transfer vector. The four-row, two-column vector formed by the four-dimensional preset position deviation local transfer vector LVP and the four-dimensional preset attitude deviation local transfer vector LVV is the i-th geometric error term E of the five-axis machine tool of the target type. i The local transfer vector LV in the current local coordinate system, LV = [LVP LVV].

[0066] In a single geometric error E i Under the influence of the motion axis Axis (Axis∈[X,Y,Z,A,B,C,M]), the reference point of the tool tip position undergoes a small displacement E. i • LVP, the tool vector has undergone a small offset E i If LVV, then the four-row, two-column vector LV = [LVP LVV] composed of vectors LVP and LVV is the geometric error E. i Local transfer vector LV in the local coordinate system AxisCS Axis (E i ), LV Axis (E i ) = [LVP Axis (E i ) LVV Axis (E i )], of which LV Axis(E i () represents the geometric error E i Local transfer vector in the local coordinate system AxisCS, LVP Axis (E i () represents the geometric error E i The local transfer vector of position deviation in the local coordinate system AxisCS, LVV Axis (E i () represents the geometric error E i The local transfer vector of attitude deviation in the local coordinate system AxisCS.

[0067] The transition matrix M is as follows:

[0068] After multiplying the local transfer vector LV in the current local coordinate system by a homogeneous transformation matrix, the transfer vector J in the workpiece coordinate system is obtained. Then, the homogeneous transformation matrix is ​​the transfer matrix M of the local transfer vector LV in the current local coordinate system; at this time, the current local coordinate system is transformed into the workpiece coordinate system.

[0069] The relationship between the transition matrix and the local transfer vector is as follows:

[0070] J i =M i ·LV i

[0071] Among them, J i M i and LV i Let represent the transfer vector, transition matrix, and local transfer vector of the i-th geometric error, respectively.

[0072]

[0073] Where R(A), R(B), and R(C) represent the rotation matrices under the nominal angular displacements A, B, and C axes of the machine tool, respectively; M(C) represents the transfer matrix under the nominal angular displacement C of the C axis of the machine tool; M(AC) represents the transfer matrix under the nominal angular displacements A and C axes of the machine tool; and M(BC) represents the transfer matrix under the nominal angular displacements B and C axes of the machine tool.

[0074] Taking a five-axis machine tool with a dual rotary table as an example, the details are as follows:

[0075]

[0076] Where M(Axis) represents the transition matrix of the motion axis Axis, R(Axis) is the rotation matrix of the motion axis Axis, Axis1 and Axis2 represent the first and second motion axes respectively, M(Axis1Axis2) represents the transition matrix of the first and second motion axes, and R(Axis1) and R(Axis2) represent the rotation matrices of the first and second motion axes respectively.

[0077] The specific displacement of the motion axis is as follows:

[0078] Using the three linear axes and two rotary axes of the target type of five-axis machine tool as motion axes, for two of these motion axes, the motion axis closer to the tool end is designated as the high-order body, and the motion axis closer to the workpiece end is designated as the low-order body. The conditional displacement of the motion axis is the nominal displacement of one of the motion axes obtained when the high-order body condition is met. The nominal displacement of the motion axis is the displacement of the motion axis from the initial position to the current position. The selected motion axis has an impact on the form of the transfer vector.

[0079] The cumulative displacement between the coordinate systems is as follows:

[0080] In the initial state where the nominal displacement of each motion axis of the target type of five-axis machine tool is zero, the cumulative displacement vector between the start and end coordinate systems of the target type of five-axis machine tool is taken as the cumulative displacement between coordinate systems.

[0081] The cumulative displacement vector between the local coordinate system Axis1CS of the first motion axis Axis1 and the local coordinate system Axis2CS of the second motion axis Axis2 of the machine tool. Specifically as follows:

[0082]

[0083] in, and These represent the displacements in the X, Y, and Z directions between the local coordinate system Axis1CS of the first motion axis Axis1 and the local coordinate system Axis2CS of the second motion axis Axis2 of the machine tool.

[0084] The specific motion axis to which the error pertains is as follows:

[0085] For the perpendicularity error of two motion axes of a five-axis machine tool of the target type, when the perpendicularity error is based on one motion axis, the other motion axis is taken as the motion axis to which the perpendicularity error belongs.

[0086] A parameterized general transfer vector table specifies the local transfer vectors and transition matrices for 41 geometric errors of a specific type of five-axis machine tool, thus allowing the transfer vector of that geometric error to be obtained. Under the linear approximation assumption, the transfer vectors of the 41 geometric error terms can be directly solved using the machine tool parameters. For a specific type of five-axis machine tool, this solution only needs to be performed once, and the resulting transfer vector table can be reused.

[0087] In the conditional displacement of the motion axis, the conditional displacement is divided into high-order conditional displacement and low-order conditional displacement. When the high-order volume condition is satisfied, the high-order conditional displacement and low-order conditional displacement are obtained as nominal displacements, as detailed below:

[0088]

[0089] in, This represents the high-order conditional displacement of the first motion axis Axis1 relative to the second motion axis Axis2. Let Axis1 be the nominal displacement of the first motion axis, where Axis1∈[X,Y,Z,A,B,C]; This represents the lower-order conditional displacement of the first motion axis Axis1 relative to the second motion axis Axis2. The high-low order is compared using the motion chain code.

[0090] The constraints on the workpiece end motion axes of a five-axis machine tool based on the target type are as follows:

[0091] For each linear axis of a five-axis machine tool of the target type, when the linear axis is located at the workpiece end, the nominal displacement of the linear axis is reversed; when the motion axis to which the error belongs is located at the workpiece end, the transmission vector is reversed.

[0092] The geometric error model for a five-axis machine tool is as follows:

[0093]

[0094] Where E represents the geometric error model of the five-axis machine tool, E is a 4x2 vector representing the comprehensive deviation of the five-axis machine tool, including positional deviation and attitude deviation; E i This represents the i-th geometric error term of a five-axis machine tool; and E represents the i-th geometric error term E of the five-axis machine tool. i The projection coefficients of the resulting positional deviation in the X, Y, and Z directions; and E represents the i-th geometric error term E of the five-axis machine tool. i The projection coefficients of the resulting attitude deviation in the X, Y, and Z directions; JP i and JV i E represents the i-th geometric error term E of the five-axis machine tool.i Position deviation transfer vector and attitude deviation transfer vector; J i E represents the i-th geometric error term of a five-axis machine tool. i The transfer vector.

[0095] According to the i-th geometric error term E of the five-axis machine tool i Position deviation transfer vector JP i The tool position deviation is obtained based on the i-th geometric error term E of the five-axis machine tool. i The attitude deviation of the tool is obtained by the attitude deviation transfer vector. The position deviation and attitude deviation caused by each geometric error term acting alone can be obtained directly. The comprehensive deviation requires adding up the deviations caused by each of the 41 geometric error terms.

[0096] 2) Based on the configuration of the target type of five-axis machine tool, obtain the parameter set of the five-axis machine tool. The parameter set includes three parameters: motion chain code, offset vector between local coordinate systems, and perpendicularity error reference information. Input the parameter set into the general transfer vector table. The general transfer vector table generates the transfer vector of each geometric error item of the five-axis machine tool. Then, use the linear combination method to construct the geometric error model of the five-axis machine tool, and realize the parameterized rapid modeling of the geometric error of the five-axis machine tool.

[0097] 3) Input the various geometric error terms and five-axis coordinates of the target type of five-axis machine tool into the geometric error model. The geometric error model outputs the position deviation and attitude deviation of the tool of the five-axis machine tool. Finally, the tool tip can be returned to the desired position according to the geometric error, thus realizing the compensation of geometric error.

[0098] This invention provides a more complete and clear description of its specific implementation using two case studies of rapid reconstruction modeling of geometric errors in two dual-rotary-table five-axis machine tools.

[0099] like Figure 1 As shown, specific embodiments of the present invention are as follows:

[0100] 1) Based on the five-axis machine tool to be modeled, first perform layout analysis to determine the type of the five-axis machine tool to be modeled. Here, we take a dual rotary table machine tool as an example, and then obtain the parameter set of the dual rotary table machine tool.

[0101] 2) Based on the general rules in the geometric error modeling process of five-axis machine tools, we propose local transfer vectors, transfer matrices, conditional displacement of motion axes, cumulative displacement between coordinate systems, and the limitation of the motion axis to which the error belongs, as well as two special constraints for the motion axis at the workpiece end.

[0102] 3) Based on the proposed constraints, for a specified dual-rotary-table five-axis machine tool layout, under the linear approximation assumption, the transfer vectors of 41 geometric error terms are directly solved using the machine tool topology parameters, forming a parameterized general transfer vector table. First, the local transfer vectors LV of the 41 geometric error terms are solved. i (i = 1, 2, ..., 41), and then transfer vector LV to each local vector. i Define the transition matrix M i Finally, a transfer vector table is established.

[0103] When directly solving for the transfer vector, the transfer vectors to be solved can be divided into four main categories: transfer vectors of linear axis PDGEs, transfer vectors of geometric errors of rotary axes excluding perpendicularity errors, transfer vectors of perpendicularity errors, and attitude deviation transfer vectors. Corresponding methods can then be used to quickly solve these categories. The specific steps involve solving for the local transfer vectors of geometric errors and defining their transition matrices. Then, the local transfer vectors and transition matrices are recorded in a table to construct a transfer vector table. Taking one of the geometric error terms ε of a dual-rotor five-axis machine tool as an example... xx For example, the specific construction method of the transfer vector table is as follows:

[0104] Table 1. Examples of Transmission Vector Representation

[0105]

[0106] Where, ε xx This represents the roll angle error of the X-axis around the X-axis. and These represent the conditional displacements between the Z-axis and Y-axis and the X-axis, respectively. and These represent the cumulative displacements between the X-axis local coordinate system XCS and the tool's local coordinate system TCS in the Z and Y directions, respectively, with L representing the tool length.

[0107] Table 1 gives the geometric error term ε xx The local transfer vectors and transfer matrices of the position and attitude deviations can be used to obtain the transfer vectors.

[0108] The parameter set includes three parameters: motion chain code, offset vector between local coordinate systems, and perpendicularity error reference information. Taking a BC dual rotary table five-axis machine tool as an example, the details are as follows:

[0109] Table 2 Examples of Machine Tool Parameter Sets

[0110]

[0111] In the kinematic chain code, W refers to the workpiece, C to the C-axis, B to the B-axis, M to the bed, X to the X-axis, Y to the Y-axis, Z to the Z-axis, and T to the tool; v1, v2, v3, v4, v5, v6, and v7 are the offset vectors between the local coordinate systems W→C, C→B, B→M, M→X, X→Y, Y→Z, and Z→T, respectively; Y0 and Z0 are the X-axis and Z-axis reference positions of the linear axis reference position, respectively.

[0112] Under the linear approximation assumption, the local transfer vectors of all geometric errors are solved by classification, and the transfer matrix of all geometric errors is defined as follows:

[0113] a) Linear axis PDGEs:

[0114] This category contains 18 geometric errors, including δ xx δ yx δ zx δ xy δ yy δ zy δ xz δ yz δ zz ε xx ε yx ε zx ε xy ε yy ε zy ε xz ε yz and ε zz PDGEs refer to position-related geometric errors. In their expression, δ represents straightness error and ε represents angular error. The first subscript indicates the direction of the straightness error or the axis of rotation of the angular error, and the second subscript indicates the axis on which the error is located. For example, δ yx ε represents the straightness error of the X-axis in the Y direction. yx This represents the angular error of the X-axis rotation around the Y-axis. Calculating their local transfer vectors in the machine tool's local coordinate system (MCS) yields transfer matrices of either M(AC) or M(BC). Among the nine straightness errors, the local transfer vectors for the X, Y, and Z directions are [1 0 0 0] respectively. T [0 1 0 0] T [0 0 1 0] T ,like Figure 2 As shown in (a), the geometric error between the ideal tool tip and the actual tool tip is expressed as δ xx For example, its local transfer vector is [1 0 0 0]. TThe transition matrix is ​​M(AC) or M(BC). In solving for the local transfer vectors of the nine angular errors, it is only necessary to know the coordinates of the tool tip in the X-axis local coordinate system XCS, the Y-axis local coordinate system YCS, and the Z-axis local coordinate system ZCS. The local transfer vector of the angle error term can then be obtained, as shown in the figure, XCS. i and XCS r These are the ideal local coordinate system and the actual local coordinate system along the X-axis, respectively. i and Y r The x-axis represents the ideal local coordinate system, and the y-axis represents the actual local coordinate system. i and X r The x-axis represents the ideal local coordinate system and the actual local coordinate system, respectively.

[0115] Coordinates in the local coordinate system XCS (X-axis) Specifically as follows:

[0116]

[0117] Where Δx, Δy, and Δz represent the translations of the local coordinate system in the x, y, and z directions, respectively; These represent the conditional displacements between the X-axis and the bed, the Y-axis and the X-axis, and the Z-axis and the X-axis, respectively. These represent the cumulative displacement between the X-axis local coordinate system XCS and the tool local coordinate system TCS in the X, Y, and Z directions, respectively.

[0118] Coordinates in the local Y-axis coordinate system YCS Specifically as follows:

[0119]

[0120] in, These represent the conditional displacements between the X-axis and Y-axis, the Y-axis and the bed, and the Z-axis and X-axis, respectively. These represent the cumulative displacement between the Y-axis local coordinate system YCS and the tool local coordinate system TCS in the X, Y, and Z directions, respectively.

[0121] Coordinates in the Z-axis local coordinate system ZCS Specifically as follows:

[0122]

[0123]

[0124] in, These represent the conditional displacements between the X-axis and Z-axis, the Y-axis and Z-axis, and the Z-axis and the bed, respectively. These represent the cumulative displacement between the Z-axis local coordinate system ZCS and the tool local coordinate system TCS in the X, Y, and Z directions, respectively.

[0125] like Figure 2 As shown in (b), with ε zx For example, its transition matrix is ​​M(AC) or M(BC), and the local transfer vector is as follows:

[0126] b) Geometric errors of the rotation axis other than perpendicularity error:

[0127] This category includes 12 PDGEs for two rotary axes and 4 PIGEs excluding perpendicularity error. Among these, the 12 PDGEs, taking the AC type dual rotary table machine tool as an example, include δ... xa δ ya δ za δ xc δ yc δ zc ε xa ε ya ε za ε xc ε yc ε zc Its definition is consistent with that of linear axis PDGEs, and its local transfer vector calculation method is also similar to that of linear axis PDGEs, but it requires matrix transformation to obtain the tool tip reference point coordinates in the local coordinate system of the rotary axis. Taking the AC type double rotary table machine tool as an example, let the local coordinate system of the A axis be ACS0 in the initial state.

[0128] Coordinates in the local coordinate system ACS of axis A Specifically as follows:

[0129]

[0130] in, The coordinates of the A-axis in the local coordinate system ACS. In the initial state, the local coordinate system of axis A is the coordinate system in ACS0; and These represent the cumulative displacement between the A-axis local coordinate system ACS and the tool local coordinate system TCS in the X, Y, and Z directions, respectively.

[0131] Depend on The local transfer vector of PDGEs along the A-axis in the ACS can be obtained, and the transfer matrix is ​​M(C).

[0132] Coordinates in the local coordinate system CCS (C-axis) Specifically as follows:

[0133]

[0134] in, The coordinates are in the local coordinate system CCS for the C-axis. and These represent the cumulative displacements between the local coordinate system CCS (C-axis) and the local coordinate system ACS (A-axis) in the X, Y, and Z directions, respectively.

[0135] Depend on The local transfer vector of C-axis PDGEs in the CCS can be obtained, and the transfer matrix is ​​the identity matrix E. 4×4 .

[0136] The four PIGEs other than perpendicularity error include o ay o az o cx o cy These are the deviations of the A-axis axis in the Y and Z directions, and the deviations of the C-axis axis in the X and Y directions, respectively.

[0137] Geometric error term o ay and o az The local transfer vector of the positional deviation is as follows:

[0138]

[0139] Among them, LVP M (o ay ) and LVP M (o az ) represent the geometric error terms o ay and o az The local transfer vectors of the positional deviation; their transfer matrices are all M(AC).

[0140] Geometric error term o cx and O cy The local transfer vector of the positional deviation is as follows:

[0141]

[0142] Among them, LVP A (o cx ) and LVP A (o cy ) represent the geometric error terms o cx and o cy The local transfer vectors of the positional deviation; their transfer matrices are all M(C).

[0143] c) Verticality error:

[0144] This category contains 7 geometric errors. Taking the AC type machine tool as an example, these include S... xyS yz S xz S at S az S cx S cy The subscript for perpendicularity error indicates the two axes of motion involved. When the angle between the two axes is greater than 90°, the perpendicularity error is positive. The effect of perpendicularity error is equivalent to a translation and a rotation. Figure 3 As shown, the verticality error S xy The following example illustrates the method for calculating the local transfer vector of perpendicularity error. When the X-axis is the reference axis, the perpendicularity error S... xy Under the influence of this, on the one hand, the Y-axis undergoes a translation in the X direction Δx = -S xy ·Δy=-S xy ·(Y-Y0), where Y represents the nominal displacement along the Y-axis and Y0 represents the perpendicularity error S. xy The reference position; on the other hand, the Y-axis rotated in the Z direction, with a rotation angle of S. xy Therefore, the verticality error S xy The local transfer vector of the positional deviation is as follows:

[0145] LVP M (S xy =LVP M (ε zy )-(Y-Y0)LVP M (δ xy )

[0146] Among them, LVP M (S xy ), LVP M (ε zy ) and LVP M (δ xy ) represent the geometric error term S respectively xy ε zy and δ xy The local transfer vector of the positional deviation.

[0147] like Figure 4 The diagram illustrates how a geometric error causes changes in tool position and orientation. Orientation deviation and position deviation are correlated; the local transfer vector of the orientation deviation can be cleverly and directly derived from the local transfer vector of the position deviation, where V... i and V r Let L1 and L2 represent the ideal and actual tool vectors, respectively, and LVV represent the local propagation vector of the attitude deviation to be determined. If we consider the local propagation vector LVP of this geometric error as a function of the tool length L, then, assuming all other parameters are known, the LVV of this geometric error in the same local coordinate system is as follows:

[0148] LVV = LVP | L＝-1 -LVP| L＝0

[0149] Among them, LVP| L＝-1 and LVP| L＝0 These are the local transfer vectors of position deviation when the tool length is -1 and 0, respectively. That is, by setting L to -1 and all other parameters to 0 in the LVP expression for this geometric error, we can obtain the LVV for this geometric error.

[0150] These four types cover all 41 undetermined local transfer vectors and transition matrices. Using the above solution method, the transfer vector table of the dual rotary table five-axis machine tool can be determined, as follows:

[0151] Table 3. Transfer Vector Table for Five-Axis Machine Tools with Dual Rotary Tables

[0152]

[0153]

[0154]

[0155] Where X0, Y0, and Z0 represent the reference positions for perpendicularity error of the X-axis, Y-axis, and Z-axis, respectively, and X0′, Y0′, and Z0′ represent the reference positions for perpendicularity error of the A-axis, B-axis, and C-axis, respectively. and These represent the cumulative displacements between the local coordinate systems Ax1 and Ax2 in the X, Y, and Z directions, respectively.

[0156] 4) When modeling is required, extract the parameter set from the specific configuration of the target machine tool, including three parameters: kinematic chain code, offset vector between local coordinate systems, and perpendicularity error reference information. Substitute the parameter set into the transfer vector table to determine the transfer vector J. i =M i ·LV i (i = 1, 2, ..., 41), and finally construct the geometric error model F.

[0157] The kinematics code involves substituting parameters into the pass vector table, such as ε. zc Whether the input is of type AC or BC, and the values ​​of all conditional displacements, all need to be compared in the motion chain code to determine the order of the two letters. Offset vectors between local coordinate systems are used extensively in the transfer vector table, so all such... Such quantities all need to be obtained from this. Perpendicularity error reference information involves substituting parameters into the transfer vector representation, such as S. xyIs the reference axis X-axis or Y-axis used for substitution?

[0158] 5) When the machine tool layout is updated, you can directly return to step 1) for quick reconstruction; if it is not updated, the process ends and subsequent analysis and compensation are performed.

[0159] like Figure 5 The image shows a BC dual-rotary-table five-axis machine tool, which is used as Case 1 for rapid reconstruction modeling. It is assumed that geometric error modeling is performed for error measurement and compensation purposes. The kinematic chain code for this machine tool is WCBMXYZT, which is also the first parameter in the parameter set, representing the machine tool's kinematic chain.

[0160] Assuming a laser interferometer is used to measure the geometric error of the linear axis and a ball bar is used to measure the geometric error of the rotational axis, then the local coordinate systems for each axis established for the measurement mode are as follows: Figure 6 As shown. Figure 6 of (a), Figure 6 (b) Figure 6 (c) and Figure 6 As shown in (d), the five local coordinate systems fixed to the X-axis, Y-axis, Z-axis, B-axis, and C-axis are established respectively. The workpiece coordinate system (WCS) is established at the center of the C-axis rotary table surface, and the tool coordinate system (TCS) is established at the tool root. At this time, the second parameter in the parameter set, the local coordinate system offset vector, is determined. In Case 1, the three linear axes of the machine tool are all distributed at the tool tip, so the reference for the perpendicularity error of the linear axes can be directly obtained from the kinematic chain code, that is, the X-axis is the first reference and the Y-axis is the second reference. In the initial state, the Y-axis is located at the middle of the stroke and the Z-axis is located at the top of the stroke. Therefore, the perpendicularity reference positions of the Y-axis and Z-axis are selected as Y=0 and Z=0, respectively.

[0161] As shown in 7(a), considering the cradle structure of the B-axis rotation, the pivot point closest to the bed is selected as the reference for the B-axis perpendicularity error. This reference position is Y = 43°. Figure 7 As shown in (b), the perpendicularity error reference position of the C-axis is selected near the interface where the B-axis cradle is installed, rather than at the origin of the local coordinate system CCS, at a position of Z = -200. At this point, the perpendicularity error reference information for the third parameter in the parameter set is determined.

[0162] All three types of parameters have been determined, and the parameter set of the machine tool can be determined, as shown in Table 4. A complete Hierarchical Temporal Memory (HTM) model can be established.

[0163] Table 4. Parameter Set for BC Dual Rotary Table Five-Axis Machine Tool

[0164]

[0165] First, based on the information in Table 4, a traditional HTM method model is performed to obtain a matrix chain multiplication model, as follows:

[0166]

[0167]

[0168] In the above formula, setting all 41 geometric error terms to zero yields T. ideal The matrix chain multiplication model obtained by the traditional HTM method is:

[0169]

[0170] Among them, T real and T ideal Let ΔP represent the actual transformation matrix and the ideal transformation matrix between the two local coordinate systems, respectively. x ΔP y and ΔP z ΔV represents the positional deviation of the tool in the x, y, and z directions, respectively. x ΔV y and ΔV z These represent the orientation deviations of the tool in the x, y, and z directions, respectively.

[0171] Then, based on the parameterized geometric error model E of the fast production cost method in the table... rapid 10,000 sets of five-axis coordinate points and geometric error values ​​are randomly generated within the five-axis travel range of the machine tool in a uniform distribution, and then substituted into the matrix multiplication model and the parametric geometric error model E, respectively. rapid The statistical difference rate and model computation time are as follows: The difference rate Δ is as follows:

[0172]

[0173] Where t and t rapid These represent the computation time of the matrix chain multiplication model and the parameterized geometric error model, respectively.

[0174] The statistical results are finally presented in the form of a scatter plot, such as... Figure 8 As shown. From Figure 8 It can be seen that in most cases, E rapid The difference rates between E and E are both within 1 / 10000, indicating that E rapid Discarding second-order and higher-order minterms is entirely acceptable. Furthermore, after discarding second-order and higher-order minterms, E... rapid The computation time of E is almost only 1 / 5 of that of E, indicating that E rapid Its performance is far superior to E.

[0175] Taking a Sobol sensitivity analysis with an N value of 1024 performed on 720 sampling points in the workspace of a five-axis machine tool as an example, according to Saltelli's improved Sobol algorithm, 720 × (41 + 2) × 1024 = 31,703,040 model calculations are required. In this scenario, E rapid It can save approximately 4.45 hours per Sobol analysis.

[0176] like Figure 9 The image shows an AC dual-rotary-table five-axis machine tool, which is used as Case 2 for rapid reconstruction modeling. We assume that geometric error modeling is performed for the purpose of forward design. The kinematic chain code for this machine tool is WCAYMXZT. For forward design purposes, the local coordinate system is established near the moving parts of each axis, such as... Figure 10 As shown.

[0177] like Figure 10 of (a), Figure 10 (b) Figure 10 (c) and Figure 10 As shown in (d), these are the methods for establishing five local coordinate systems fixed to the X-axis, Y-axis, Z-axis, A-axis, and C-axis, respectively. The workpiece coordinate system (WCS) is established at the center of the C-axis rotary table surface, and the tool coordinate system (TCS) is established at the tool root.

[0178] For the perpendicularity error of the linear axes, the Y-axis is selected as the first reference and the X-axis as the second reference. In the initial state of the machine tool, the X-axis is located at the middle of the stroke and the Z-axis is located at the top of the stroke. Therefore, the perpendicularity reference positions of the X and Z axes are selected as X=0 and Z=0.

[0179] The rotating shaft structure shown in Case 2 is exactly the same as that in Case 1, therefore the parameters related to the perpendicularity error of the rotating shaft can also be calculated similarly. Figure 7 As shown, the values ​​are A-axis: X = -430 and C-axis: Z = -60.

[0180] The parameter set is now determined, as shown in Table 5.

[0181] Table 5 AC Dual Rotary Table Five-Axis Machine Tool Parameter Set

[0182]

[0183] First, based on the information in Table 5, a traditional HTM method model is performed to obtain the matrix chain multiplication model, as follows:

[0184]

[0185]

[0186] In the above formula, setting all 41 geometric error terms to zero yields T. ideal The matrix chain multiplication model obtained by the traditional HTM method is:

[0187]

[0188] Then, according to the parameterized geometric error model E of the rapid production cost method in Table 5. rapid 10,000 sets of five-axis coordinate points and geometric error values ​​were randomly generated within the five-axis travel range of the machine tool in a uniform distribution. These values ​​were then substituted into both a matrix multiplication model and a parametric geometric error model. The difference rate Δ and model computation time were statistically analyzed, and the results were presented as a scatter plot. Figure 11 As shown.

[0189] from Figure 11 It can be seen that in most cases, E rapid The difference rates between E and E are both within 1 / 10000, indicating that E rapid Discarding second-order and higher-order minterms is entirely acceptable. Furthermore, after discarding second-order and higher-order minterms, E... rapid The computation time of E is almost only 1 / 5 of that of E, indicating that E rapid Its performance is far superior to E.

[0190] Taking a Sobol sensitivity analysis with an N value of 1024 performed on 720 sampling points within the workspace of a five-axis machine tool as an example, according to Saltelli's improved Sobol algorithm, 720 × (41 + 2) × 1024 = 31,703,040 model calculations are required. In this scenario, E rapid It can save approximately 4.64 hours per Sobol analysis.

[0191] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A geometric error parameterization fast modeling method for multi-configuration five-axis machine tools, characterized in that, The method comprises the following steps: 1) obtaining the transfer vector of each geometric error term of the five-axis machine tool according to the machine tool topology parameters of the target type of five-axis machine tool using linear approximation assumption, thereby constructing the parameterized general transfer vector table of the target type of five-axis machine tool; 2) obtaining the parameter set of the five-axis machine tool according to the configuration of the target type of five-axis machine tool, the parameter set comprising three parameters of kinematic chain code, offset vector between local coordinate systems, and perpendicularity error reference information; inputting the parameter set into the general transfer vector table, and the general transfer vector table generating the transfer vector of each geometric error term of the five-axis machine tool, thereby constructing the geometric error model of the five-axis machine tool using linear combination method, and realizing the parameterized rapid modeling of the geometric error of the five-axis machine tool.

2. The geometric error parameterization fast modeling method for multi-configuration five-axis machine tools according to claim 1, characterized in that: In the step 1), the general transfer vector table is constructed based on the local transfer vector, the transfer matrix, the conditional displacement of the motion axis, the cumulative displacement between coordinate systems, the limitation of the error belonging to the motion axis, and the constraint of the workpiece end motion axis of the target type of five-axis machine tool.

3. The geometric error parameterization fast modeling method for multi-configuration five-axis machine tools according to claim 2, characterized in that: The local transfer vector LV is specifically as follows: The i-th geometric error term E of the target type five-axis machine tool i In one of the local coordinate systems of the five-axis machine tool, the reference point of the tool tip position of the tool of the five-axis machine tool generates displacement Δl, Δl = E i · LVP, wherein LVP represents a four-dimensional preset position deviation local transfer vector, and at this time, the four rows and two columns of vectors composed of the four-dimensional preset position deviation local transfer vector LVP and the four-dimensional preset attitude deviation local transfer vector LVV are the i-th geometric error term E of the target type five-axis machine tool i The local transfer vector LV under the current local coordinate system, LV = [LVP LVP] The transfer matrix M is specifically as follows: After the local transfer vector LV in the current local coordinate system is multiplied by a homogeneous transformation matrix, the transfer vector J in the workpiece coordinate system is obtained by conversion, and the homogeneous transformation matrix is the transfer matrix M of the local transfer vector LV in the current local coordinate system. The conditional displacement of the motion axis is specifically as follows: Taking the three linear axes and the two rotary axes of the target type of five-axis machine tool as the motion axes, for two of the motion axes, the motion axis closer to the tool end is taken as the high-order body, and the motion axis closer to the workpiece end is taken as the low-order body, and the conditional displacement of the motion axis is the nominal displacement of one of the motion axes obtained when the high-order body condition is met. The cumulative displacement between coordinate systems is specifically as follows: In the initial state that the nominal displacements of all the motion axes of the target type of five-axis machine tool are zero, the cumulative displacement vector between the start and end coordinate systems of the target type of five-axis machine tool is taken as the cumulative displacement between coordinate systems. The error belonging to the motion axis is specifically as follows: For the perpendicularity error of two motion axes of the target type of five-axis machine tool, when the perpendicularity error takes one of the motion axes as the reference, the other motion axis is taken as the motion axis belonging to the perpendicularity error.

4. The geometric error parameterization fast modeling method for multi-configuration five-axis machine tools according to claim 3, characterized in that: In the conditional displacement of the motion axis, the conditional displacement of the motion axis is divided into high-order conditional displacement and low-order conditional displacement, the high-order conditional displacement and the low-order conditional displacement are taken as the nominal displacement when the high-order body condition is met, and the high-order conditional displacement and the low-order conditional displacement are specifically as follows: wherein, represents a high-order conditional displacement amount of the first motion axis Axis1 with respect to the second motion axis Axis2, is a nominal displacement of the first motion axis Axis1 ; represents a low-order conditional displacement amount of the first motion axis Axis1 with respect to the second motion axis Axis2.

5. The geometric error parameterization fast modeling method for multi-configuration five-axis machine tools according to claim 2, characterized in that: The constraint of the workpiece end motion axis of the target type of five-axis machine tool is specifically as follows: For each linear axis of the target type of five-axis machine tool, when the linear axis is located at the workpiece end, the linear axis nominal displacement of the linear axis is taken as negative; when the error belongs to the motion axis located at the workpiece end, the transfer vector is taken as negative.

6. The geometric error parameterization fast modeling method for multi-configuration five-axis machine tools according to claim 2, characterized in that: In the step 2), the geometric error model of the five-axis machine tool is specifically as follows: wherein E represents a geometric error model of the five-axis machine tool; E i represents the i-th geometric error term of the five-axis machine tool; and respectively represent the i-th geometric error term E i of the five-axis machine tool, and the projection coefficients of the position deviation caused by the i-th geometric error term E and respectively represent the i-th geometric error term E i of the five-axis machine tool, and the projection coefficients of the attitude deviation caused by the i-th geometric error term E i and JV i respectively represent the i-th geometric error term E i of the five-axis machine tool, and the position deviation transmission vector and the attitude deviation transmission vector of the i-th geometric error term E i of the five-axis machine tool; and i represents the transmission vector of the i-th geometric error term E a position deviation propagation vector JP of the i-th geometric error term E i of the five-axis machine tool i a position deviation of the tool is obtained, a pose deviation propagation vector JP of the i-th geometric error term E i of the five-axis machine tool is obtained, a pose deviation of the tool is obtained.

7. An electronic device, comprising: The method comprises the following steps: The memory and the processor are coupled with each other, the memory stores program data, and the processor calls the program data to execute the method in any one of claims 1-6.

8. A computer readable storage medium having stored thereon program data, wherein, The program data, when executed by the processor, implement the method of any of claims 1-6.

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