A spatial error modeling method for CNC machine tools based on time axis compensation

Abstract

The present invention discloses a spatial error modeling method for a numerically controlled machine tool based on time axis compensation, and the steps are as follows: (1) measuring the movement error, angular error and verticality error of three feed axes of the machine tool; (2) establishing an error term fitting function according to the measured error data; (3) selecting a machine tool type mathematical model, establishing a machine tool spatial error simulation model based on a Simulink simulation platform according to the machine tool feed speed and processing time, and obtaining the three-term error calculation expression of the machine tool spatial error; (4) importing the machine tool feed speed and stroke according to the machine tool processing G code, and obtaining the machine tool three-term spatial error change curve based on the time axis change; when the machine tool is processing, the change curve can be used to continuously compensate for the relevant error amount. The method realizes dynamic compensation for the geometric error of the machine tool, makes up for the disadvantage of the discontinuous compensation effect of the existing error modeling method, and further improves the processing accuracy of the machine tool.

Description

Technical Field

[0001] The present invention relates to the field of precision machining and mechanical manufacturing, and more specifically, to a spatial error modeling method for CNC machine tools based on time axis compensation. Background Art

[0002] CNC machine tools are automated machine tools that use digital computing technology and control programs. They have been widely used in modern manufacturing, especially in the processing of complex parts, due to their high degree of automation, good flexibility, and high processing accuracy. However, the manufacturing accuracy of workpieces is limited by the processing errors generated during the use of CNC machine tools. Therefore, research on the processing accuracy of CNC machine tools is beneficial to improving the quality of workpieces and promoting the development and progress of modern manufacturing technology.

[0003] Machine tool error compensation technology can reduce machining errors and improve the machining accuracy of machine tools. It is an important way to improve the machining accuracy of machine tools. The key to machine tool geometric error compensation is to establish a correct machine tool geometric error model. So far, many scholars at home and abroad have proposed a large number of modeling methods. Chinese patent CN 110532667A proposes a method for improving the modeling accuracy of the spatial geometric error model of precision machine tools. The method preprocesses, simplifies, transforms the ideal characteristic matrix of static and motion between bodies and the characteristic matrix of static and motion errors between bodies, discards the high-order infinitesimals of 6Eij, and represents them in the form of a string as a statement to run, and completes the geometric error modeling. Chinese patent CN 114609968A discloses a simple modeling method for the geometric error of CNC machine tools without error high-order terms. The error modeling is completed by establishing a comprehensive motion transformation matrix module for each moving part of the machine tool, and establishing a comprehensive motion transformation matrix module for each moving part of the machine tool without error high-order terms. However, the above two patented methods both use the moving distance of the X, Y, and Z axes to build models. When compensating for the geometric errors of machine tools, they belong to static compensation, which results in discontinuous compensation effects. The machining accuracy of machine tools cannot meet the higher standards of modern advanced manufacturing industries. Summary of the invention

[0004] In view of the above technical problems, the purpose of the present invention is to overcome the defects of static error compensation in the prior art, and propose a CNC machine tool spatial error modeling method based on time axis compensation to achieve dynamic error compensation, reduce processing errors, and improve the processing accuracy of machine tools.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for modeling spatial errors of CNC machine tools based on time axis compensation is as follows:

[0007] (1) Measure the geometric errors of each feed axis of the machine tool and obtain various error data, including the three movement errors and three angular errors of the feed axis X axis, which are represented by the symbol δxx ,δ yx ,δ zx , ε xx , ε yx , ε zx ; The three movement errors and three angular errors of the feed axis Y are represented by the symbol δ xy ,δ yy ,δ zy , ε xy , ε yy , ε zy ; The three movement errors and three angular errors of the feed axis Z are represented by the symbol δ xz ,δ yz ,δ zz , ε xz , ε yz , ε zz ; and three verticality errors, symbolized as S xy , S xz , S yz ;

[0008] (2) According to the measured feed axis movement error and rotation angle error data, error term fitting functions are established respectively;

[0009] (3) Select the machine tool type model, combine the data and functions of steps (1) and (2), and establish a machine tool spatial error simulation model based on the Simulink simulation platform, thereby obtaining the three-term error calculation expression of the machine tool spatial error;

[0010] (4) According to the machine tool processing G code, the machine tool feed speed and stroke, the three spatial error change curves of the machine tool based on the time axis change are calculated and simulated; according to the feed speed and real-time operation time of the machine tool X, Y, and Z axes, the real-time error compensation value is calculated based on the Matlab / Simulink model of the time axis change, and then accumulated with the real-time position of the machine tool and sent to the motor to perform continuous error compensation for the machine tool movement, angle and verticality errors.

[0011] Furthermore, the geometric error data is obtained by measuring with a laser interferometer; the travels of the three axes X, Y, and Z are as follows: the X axis is -800 to 0 mm, the Y axis is -500 to 0 mm, and the Z axis is -500 to 0 mm.

[0012] Further, the step (2) comprises the following steps:

[0013] According to the measured data of feed axis movement error and angular error, Matlab platform was used to perform fifth-order polynomial fitting on the six geometric errors of X, Y and Z axes respectively, and the error term fitting function was established.

[0014] Furthermore, the fitting function of step (2) is specifically as follows:

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[0033] Among them, x, y, and z are the moving distances of the machine tool's X, Y, and Z axes respectively.

[0034] Further, the step (3) includes the following sub-steps:

[0035] (3.1) Select the comprehensive mathematical model of XYTZ type machining center;

[0036] (3.2) Coordinate system setting: Assume that the machine tool is in the initial state, create a reference coordinate system O on the machine tool bed, and create local coordinate systems X, Y, and Z on the X, Y, and Z worktables respectively, with the directions consistent with the reference coordinate system O;

[0037] (3.3) Establish the error motion transformation matrix

[0038] Ideally, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix is:

[0039]

[0040] in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z under ideal conditions, is the homogeneous transformation matrix from coordinate system O to coordinate system X under ideal conditions, is the homogeneous transformation matrix from coordinate system X to coordinate system Y under ideal conditions, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z under ideal conditions;

[0041] In actual situations, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, based on the small error assumption and ignoring the second-order and above small quantities, the transformation matrix is:

[0042]

[0043] in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z in actual situations, is the homogeneous transformation matrix from coordinate system O to coordinate system X in actual situations, is the homogeneous transformation matrix from coordinate system X to coordinate system Y in actual situations, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z in actual situations;

[0044] (3.4) According to equations (19) and (20), the comprehensive mathematical model of the XYTZ machining center can be obtained:

[0045]

[0046] Among them, Δx is the comprehensive error in the X-axis direction of the machine tool, Δy is the comprehensive error in the Y-axis direction of the machine tool, and Δz is the comprehensive error in the Z-axis direction of the machine tool;

[0047] When moving in the X, Y, and Z axis directions, the feed speeds are Vx, Vy, and Vz respectively, the operation time is t, and the feed distances in the X, Y, and Z directions are:

[0048]

[0049] A machine tool spatial error simulation model is established based on the Simulink simulation platform, from which the three error calculation expressions of the machine tool spatial error can be obtained.

[0050] Further, the steps of step (4) are as follows:

[0051] (4.1) Select the feed speed and import it into the three-term error calculation expression of the machine tool space error to obtain the change curve of the machine tool three-term space error based on the time axis change;

[0052] (4.2) According to the feed speed and real-time operation time of the X, Y, and Z axes of the machine tool, the real-time error compensation value is obtained based on the change curve of the three spatial errors of the machine tool based on the time axis, and then accumulated with the real-time position of the machine tool and sent to the motor to compensate the machine tool.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] The present invention selects a geometric error mathematical model of a machine tool according to a geometric error term fitting function obtained by fitting geometric error measurement data; based on the mathematical model, a dynamic compensation model of a machine tool geometric error based on time change is established by using a Matlab / Simulink module, and a curve of three spatial errors of the machine tool based on time axis change is simulated; according to the error curve of time axis change, dynamic compensation of the machine tool geometric error is realized, the disadvantage of discontinuous compensation effect of the existing error modeling method is made up, the machining error is reduced, the dynamic compensation effect is better, and the machining accuracy of the machine tool is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of spatial error modeling of CNC machine tools based on time axis compensation;

[0056] Figure 2 It is a schematic diagram of 21 geometric errors of the machine tool feed axis;

[0057] Figure 3 It is a schematic diagram of the six geometric error fitting functions of the X-axis;

[0058] Figure 4 It is a schematic diagram of the six geometric error fitting functions of the Y axis;

[0059] Figure 5 It is a schematic diagram of the six geometric error fitting functions of the Z axis;

[0060] Figure 6 It is a schematic diagram of the structure of the XYTZ type machining center;

[0061] Figure 7 It is the Simulink error calculation expression in the X direction of the XYTZ type machining center;

[0062] Figure 8 It is the Simulink error calculation expression in the Y direction of the XYTZ type machining center;

[0063] Fig. 9 It is the Simulink error calculation expression in the Z direction of the XYTZ type machining center;

[0064] Fig.10 It is the Simulink error variation curve in the X direction of the XYTZ type machining center;

[0065] Fig.11 It is the Simulink error variation curve in the Y direction of the XYTZ type machining center;

[0066] Fig.12 It is the Simulink error variation curve in the Z direction of the XYTZ type machining center. DETAILED DESCRIPTION

[0067] The present invention is further described below in conjunction with specific embodiments, but the content of the present invention is not limited thereto at all.

[0068] Example

[0069] This embodiment takes the XHK715 three-axis vertical machining center as an example. Figure 2 The working stroke of the machine tool is: the machine tool stroke in the X-axis movement direction is 1800mm, the machine tool stroke in the Y-axis movement direction is 1500mm, and the machine tool stroke in the Z-axis movement direction is 1200mm.

[0070] like Figure 1 As shown in the figure, the steps of the CNC machine tool spatial error modeling method based on time axis compensation are as follows:

[0071] 1. Measure the geometric errors of each feed axis of the machine tool and obtain various error data, including three movement errors and three angular errors of the feed axis X axis, which are represented by the symbol δ xx ,δ yx ,δ zx , ε xx , ε yx , ε zx ; The three movement errors and three angular errors of the feed axis Y are represented by the symbol δ xy ,δ yy ,δ zy , ε xy , ε yy , ε zy ; The three movement errors and three angular errors of the feed axis Z are represented by the symbol δ xz ,δ yz ,δ zz , ε xz , ε yz , ε zz ; and three verticality errors, symbolized as Sxy , S xz , S yz .

[0072] In the case of no collision, considering the rationality of the experiment, the travel of the three axes of X, Y, and Z is selected as follows: X axis is -800~0mm; Y axis is -500~0mm; Z axis is -500~0mm. In the case of meeting the relevant national measurement requirements, the measurement spacing is selected as 50mm, 50mm, and 50mm. The X axis is divided into 17 sections, and the Y axis and Z axis are divided into 11 sections. The 21 geometric error data of the feed axis are measured in sequence by laser interferometer. Among them, S is measured by laser interferometer. xy , S xz , S yz The three verticality errors are: 0.00148mm / m, 0.00182mm / m, 0.00132mm / m. Compensation is performed based on the verticality error data obtained by direct measurement.

[0073] 2. Based on the 18 measured feed axis movement errors and angular error data, the Matlab platform was used to perform fifth-order polynomial fitting on the six geometric errors of the X, Y, and Z axes, and the error term fitting function was established.

[0074] Specifically:

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[0093] Among them, x, y, and z are the moving distances of the machine tool's X, Y, and Z axes respectively.

[0094] 3. Select the comprehensive mathematical model of the XYTZ machining center, combine the relevant data and functions of steps 1 and 2, and establish a machine tool spatial error simulation model based on the Simulink simulation platform, thereby obtaining the three error calculation expressions of the machine tool spatial error.

[0095] The details are as follows:

[0096] (3.1) Select the comprehensive mathematical model of XYTZ type machining center;

[0097] (3.2) Coordinate system setting

[0098] Assume that the machine tool is in the initial state, create a reference coordinate system O on the machine tool bed, and create local coordinate systems X, Y, and Z on the X, Y, and Z worktables respectively, and their directions are consistent with the reference coordinate system O.

[0099] (3.3) Establish the error motion transformation matrix

[0100] Ideally, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix is:

[0101]

[0102] in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z under ideal conditions, is the homogeneous transformation matrix from coordinate system O to coordinate system X under ideal conditions, is the homogeneous transformation matrix from coordinate system X to coordinate system Y under ideal conditions, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z under ideal conditions. This transformation matrix uses the principle of homogeneous coordinate transformation to describe the error dynamic characteristics of each kinematic pair and the chain transformation between each kinematic pair.

[0103] In actual situations, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, based on the small error assumption and ignoring the second-order and above small quantities, the transformation matrix is:

[0104]

[0105] in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z in actual situations, is the homogeneous transformation matrix from coordinate system O to coordinate system X in actual situations, is the homogeneous transformation matrix from coordinate system X to coordinate system Y in actual situations, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z in actual situations;

[0106] (3.4) Comprehensive mathematical model of XYTZ type machining center

[0107] According to formula (19) and formula (20), the comprehensive mathematical model of XYTZ type machining center can be obtained:

[0108]

[0109] Among them, Δx is the comprehensive error in the X-axis direction of the machine tool, Δy is the comprehensive error in the Y-axis direction of the machine tool, and Δz is the comprehensive error in the Z-axis direction of the machine tool;

[0110] When moving in the X, Y, and Z axis directions, the feed speeds are Vx, Vy, and Vz respectively, the operation time is t, and the feed distances in the X, Y, and Z directions are:

[0111]

[0112] Based on the Simulink simulation platform, a machine tool spatial error simulation model is established, from which the three error calculation expressions of the machine tool spatial error can be obtained, such as Figure 7 , Figure 8 , Fig. 9 shown. Figure 7 In the example, Lxx, Lxy, Lxz, Axx, Ayx, and Ayy are used to represent δ xx ,δ xy ,δ xz , ε xx , ε yx , ε yy . Figure 8 In the equation, Lyx, Lyy, Lyz, Axx, and Axy are used to represent δ yx ,δ yy ,δ yz , ε xx , ε xy . Fig. 9 In the example, Lzx, Lzy, Lzz, and Axx are used to represent δ zx ,δ zy ,δ zz, ε xx .

[0113] 4. According to the machine tool processing G code, the machine tool feed speed and stroke, calculate and simulate the three spatial error change curves of the machine tool based on the time axis change.

[0114] In order to achieve high quality, high yield, low cost and safe operation, taking into account the machine tool potential and tool cutting performance, the feed speeds of X, Y and Z axes are selected as Vx = -0.035mm / s, Vy = -0.02mm / s, Vz = -0.02mm / s, respectively, and the negative sign indicates the direction of movement.

[0115] By importing all parameters including time, feed speed of each axis, etc. into the three-term error calculation expression of machine tool space error, the change curve of machine tool three-term space error based on the change of time axis can be obtained, such as Figures 10-12 shown.

[0116] According to the feed speed and real-time operation time of the X, Y, and Z axes of the machine tool, the real-time error compensation value is calculated based on the Matlab / Simulink model of the time axis change, and then it is calculated and accumulated with the real-time position of the machine tool and sent to the motor to compensate the machine tool. Continuous compensation of the machine tool can be achieved, thereby improving the machining accuracy of the machine tool.

[0117] The above description is only a preferred specific implementation manner of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the scope of protection of the invention.

Claims

1. A spatial error modeling method for CNC machine tools based on time axis compensation, characterized in that: Here are the steps: (1) Measure the geometric errors of each feed axis of the machine tool and obtain various error data, including the three movement errors and three angular errors of the feed axis X axis, which are expressed as , , , , , ; The three movement errors and three angular errors of the feed axis Y are expressed as , , , , , ; The three movement errors and three angular errors of the feed axis Z are expressed as , , , , , ; and three verticality errors, expressed as , , ; (2) Based on the measured feed axis movement error and angular error data, the error term fitting functions are established respectively; (3) Select the machine tool type model, combine the data and functions in steps (1) and (2), and establish a machine tool spatial error simulation model based on the Simulink simulation platform, thereby obtaining the three-term error calculation expressions of the machine tool spatial error; The step (3) includes the following sub-steps: (3.1) Select the comprehensive mathematical model of XYTZ type machining center; (3.2) Coordinate system setting: Assume that the machine tool is in the initial state, create a reference coordinate system O on the machine tool bed, and create local coordinate systems X, Y, and Z on the X, Y, and Z axes of the worktable, respectively, with the directions consistent with the reference coordinate system O; (3.3) Establish the error motion transformation matrix Ideally, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, the transformation matrix is: （19） in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z under ideal conditions, is the homogeneous transformation matrix from coordinate system O to coordinate system X under ideal conditions, is the homogeneous transformation matrix from coordinate system X to coordinate system Y under ideal conditions, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z under ideal conditions; In actual situations, when the machine tool moves x, y, and z distances along the X, Y, and Z directions respectively, based on the small error assumption and ignoring the second-order and above small quantities, the transformation matrix is: in, is the homogeneous transformation matrix from the reference coordinate system O to the coordinate system Z in actual situations, is the homogeneous transformation matrix from coordinate system O to coordinate system X in actual situations, is the homogeneous transformation matrix from coordinate system X to coordinate system Y in actual situations, is the homogeneous transformation matrix from coordinate system Y to coordinate system Z in actual situations; (3.4) According to equations (19) and (20), the comprehensive mathematical model of the XYTZ machining center can be obtained: （21） in, is the comprehensive error in the X-axis direction of the machine tool, is the comprehensive error in the Y-axis direction of the machine tool, is the comprehensive error in the Z-axis direction of the machine tool; When moving in the X, Y, and Z axis directions, the feed speeds are Vx, Vy, and Vz respectively, the operation time is t, and the feed distances in the X, Y, and Z directions are: （22） Based on the Simulink simulation platform, a machine tool spatial error simulation model is established, from which the three error calculation expressions of the machine tool spatial error can be obtained. (4) According to the machine tool processing G code, the machine tool feed speed and stroke, the three spatial error change curves of the machine tool based on the time axis change are calculated and simulated; according to the feed speed and real-time operation time of the machine tool X, Y, and Z axes, the real-time error compensation value is calculated based on the Matlab / Simulink model of the time axis change, and then it is accumulated with the real-time position of the machine tool and sent to the motor to perform continuous error compensation for the machine tool movement, angle and verticality errors.

2. The method for modeling spatial errors of CNC machine tools according to claim 1, characterized in that: The geometric error data is obtained by measuring with a laser interferometer; the travels of the X, Y, and Z axes are as follows: the X axis is -800 to 0 mm, the Y axis is -500 to 0 mm, and the Z axis is -500 to 0 mm.

3. The method for modeling spatial errors of CNC machine tools according to claim 1, characterized in that: The step (2) comprises the following steps: According to the measured data of feed axis movement error and angular error, Matlab platform was used to perform fifth-order polynomial fitting on the six geometric errors of X, Y and Z axes respectively, and the error term fitting function was established.

4. The method for modeling spatial errors of CNC machine tools according to claim 3, characterized in that: The fitting function of step (2) is specifically as follows: （1） （2） （3） （4） （5） （6） （7） （8） （9） （10） （11） （12） （13） （14） （15） （16） （17） （18） Among them, x, y, z are the moving distances of the machine tool's X, Y, and Z axes respectively.

5. The method for modeling spatial errors of CNC machine tools according to claim 1, characterized in that: The steps of step (4) are as follows: (4.1) Select the feed speed and import it into the three-term error calculation expression of the machine tool spatial error to obtain the change curve of the machine tool three-term spatial error based on the time axis change; (4.2) According to the feed speed and real-time operation time of the X, Y, and Z axes of the machine tool, the real-time error compensation value is obtained based on the change curve of the three spatial errors of the machine tool based on the time axis, and then it is accumulated with the real-time position of the machine tool and sent to the motor to compensate the machine tool.

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