Machine tool precision improving method based on guide rail morphology design

Abstract

The invention discloses a machine tool precision improving method based on guide rail morphology design, which is characterized in that a mapping relation between the machine tool guide rail morphology and a motion error is determined by analyzing the type and the generation mechanism of the motion error of a machine tool, and a guide rail morphology fitting curve is obtained based on a guide rail processing technology and morphology characteristics. A space error prediction model based on the guide rail morphology is established by adopting a multi-body system theory and a homogeneous coordinate change method, and is compared with space error measured data to obtain a space error correction model meeting the prediction precision. And carrying out guide rail morphology optimization design work to obtain a designed guide rail morphology characterization function, and substituting the designed guide rail morphology characterization function into the corrected space error model to obtain a guide rail morphology scheme beneficial to improving the precision of the machine tool. The shape design of the guide rail is carried out by adopting a digital means, the precision of the machine tool is improved, and the method has the advantages of high operation precision, short development period, low production cost and high universality.

Description

Technical Field

[0001] The invention relates to the field of high-precision numerically controlled machine tools, and in particular to a method for designing the topography of a precision guideway. Background Art

[0002] As a key component of high-precision CNC machine tools, guide rails have a significant impact on the performance of machine tools. During the machining process, guide rails are affected by grinding process, heat treatment, and external loads. Their surfaces are mainly free curves with undulating characteristics. These curves are guide rail geometric errors. Geometric errors are inherent properties of guide rails and cannot be eliminated. Therefore, the surface morphology of guide rails is a key factor limiting the improvement of machine tool accuracy. At present, higher-precision guide rails are usually purchased to meet the performance requirements of machine tools. However, for precision (P) or ultra-precision (UP) guide rails, the guide rail accuracy and price are exponentially related, which greatly increases the manufacturing cost of machine tools. After research, it was found that there is a mapping relationship between the guide rail morphology and the machine tool motion accuracy. Based on the motion error, a machine tool spatial error model can be established. Therefore, mathematical methods can be used to establish the relationship between the guide rail morphology and the machine tool accuracy. By carrying out guide rail morphology design, the machine tool performance can be improved. Summary of the invention

[0003] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, and to propose a method for improving the accuracy of digital machine tools based on the surface morphology of linear guide rails, which is particularly suitable for precision and ultra-precision CNC machine tools.

[0004] The technical solution of the present invention is: a method for improving machine tool accuracy based on guide rail morphology design, characterized in that a mathematical model of guide rail morphology and machine tool error is established based on the machine tool guide rail morphology to guide the improvement of machine tool accuracy, comprising the following steps:

[0005] Step 1: Establish the mapping relationship between the guide rail profile curve and the motion error of the machine tool translation axis. The machine tool has 6 degrees of freedom during the linear motion process, so 6 motion errors will be generated, namely positioning error, horizontal plane straightness error, vertical plane straightness error, pitch angle error, yaw angle error and roll angle error. Except for the positioning error, the other five motion errors are all related to the guide rail profile, and the mapping relationship between these five motion errors and the guide rail profile is established.

[0006]

[0007]

[0008]

[0009]

[0010]

[0011] Where f(z) is the rail morphology, z i-1 、z i 、z i+1 They represent the left, middle and right points of the workbench respectively. L is the length of the workbench, D is the width of the workbench, and T1 is the parallelism tolerance of the guide rail.

[0012] Step 2: Establish a machine tool spatial error prediction model based on guide rail morphology. Based on the multi-body system theory and homogeneous coordinate transformation method, a machine tool spatial error prediction model is established. Combined with the relationship between guide rail morphology and motion error, the error model between machine tool spatial error and guide rail morphology is obtained.

[0013] Table 1 Neighboring body position matrix

[0014]

[0015] Table 2 Adjacent body motion matrix

[0016]

[0017] Where [Sii+1] p 、[Sii+1] pe 、[Sii +1 ] s and [Sii +1 ] se They represent the ideal position matrix, actual position matrix, ideal motion matrix and actual motion matrix between adjacent bodies respectively, i is the adjacent low-order body of i+1, q j =(q jx ,q jy ,q jz ) T Represents the position vector between adjacent body coordinate origins, α ij , β ij and γ ij They are the perpendicularity errors generated around the translation axis and the rotation axis respectively.

[0018] Based on the position and motion relationship between adjacent bodies and combined with error motion, the ideal and actual positions of the vector intersection point of the workpiece and the tool in the machine tool coordinates are obtained as follows:

[0019]

[0020]

[0021] Where r wi is the ideal position, r wa is the actual position, r t =(-R,0,0,1) TThe position of the tool vector in the tool coordinate system. R is the distance from the machining point to the tool coordinate origin, which is the radius of the grinding wheel in a grinder.

[0022] The difference between the actual position and the ideal position gives the following values ​​of the errors in the coordinate systems of the machine tool space.

[0023]

[0024] The error values ​​of the spatial points during the machine tool movement are as follows.

[0025]

[0026] Step 3: Establish a machine tool spatial error prediction model based on guide rail morphology. Based on the multi-body system theory and the method of homogeneous coordinate transformation, a machine tool spatial error prediction model is established. Combined with the relationship between guide rail morphology and motion error, the error model between machine tool spatial error and guide rail morphology is obtained.

[0027] Step 4: Verify the correctness of the spatial error prediction model based on the guide rail morphology. Carry out a 45° oblique line error test experiment on the machine tool space to obtain the actual measured value of the machine tool space error, and compare it with the error model obtained by the spatial error calculation to verify the prediction accuracy of the spatial error model. If the prediction effect is achieved, carry out the guide rail morphology design to improve the machine tool accuracy; if the prediction effect is not ideal, add a correction coefficient k and re-carry out the spatial error prediction work.

[0028] Step 5: Use digital means to carry out guide rail surface design. Based on the verified prediction model, carry out guide rail morphology design work, and use different characteristic curves to characterize the guide rail morphology instead. Calculate the corrected spatial error model and compare it with the experimental results. If it meets the expected expectations, complete the machine tool accuracy improvement work based on the guide rail morphology design; if it does not meet the expected expectations, change the function type and design range, and re-carry out the guide rail morphology design work until a satisfactory result is obtained.

[0029] The method for improving machine tool accuracy based on guide rail morphology design is characterized by: using a digital design method to sequentially establish mathematical models between guide rail morphology and motion error and spatial error, and using digital means to improve machine tool accuracy; the guide rail surface design can be characterized by arbitrary functions at different positions of the guide rail according to its own needs; the machine tool designer can use the guide rail splicing method to perform morphology design, and verify the machine tool accuracy with the help of the established mathematical model;

[0030] The principle of the above scheme is: the method for improving machine tool precision based on guide rail morphology design proposed in the present invention can realize precision guide rail morphology design based on digital means to improve machine tool precision. Analyze the mechanism and characteristics of the motion error of the linear axis of the machine tool, explore the relationship between the motion error and the guide rail morphology, and establish a mathematical model between the two. Based on the multi-body system theory and the method of homogeneous coordinate transformation, the position error and posture error of adjacent key components are obtained, and the position deviation between the tool tip and the point to be processed is obtained along the machine tool motion chain, and a machine tool spatial error prediction model based on the guide rail morphology is established. Carry out guide rail morphology and machine tool spatial error tests to verify the correctness of the machine tool spatial error prediction model established based on the guide rail morphology. Use different characteristic functions to optimize and characterize the key positions of the machine tool guide rails, compare the effects of the spatial error prediction values ​​before and after optimization and the experimental test values, and achieve machine tool precision improvement based on guide rail morphology design.

[0031] The advantages of the present invention over the prior art are: a method for improving machine tool accuracy based on guide rail morphology design, using a digital modeling method to establish the relationship between guide rails and machine tool accuracy, and can design the guide rail morphology in advance according to the actual processing requirements and characteristics of different machine tools, thus skipping the traditional guide rail processing technology adaptation and exploration stage, reducing costs, shortening the R&D cycle, and achieving autonomous control. In addition, the present method is also universal and applicable to any machine tool guide rail model product.

[0032] In order to more clearly describe the principles, methods and advantages of the present invention, a detailed description is given below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of the technical solution of the present invention;

[0034] Figure 2 This is a mapping relationship diagram between the YOZ plane guide rail morphology, straightness and pitch angle of the technical solution of the present invention;

[0035] Figure 3 This is a mapping relationship diagram between the XOZ plane guide rail morphology and the straightness and the deflection angle of the technical solution of the present invention;

[0036] Figure 4 A mapping relationship diagram between the guide rail morphology and the roll angle of the technical solution of the present invention;

[0036] Figure 5 It is a spatial error modeling diagram of the technical solution of the present invention;

[0037] Figure 6 This is a design diagram of the guide rail morphology of the technical solution of the present invention;

[0038] Figure 7 This is a diagram showing the effect of improving the machine tool accuracy of the technical solution of the present invention; DETAILED DESCRIPTION

[0039] like Figure 1 The flowchart of the technical solution of the present invention is shown, which is characterized in that a mathematical model of the guide rail morphology and the machine tool error is established based on the machine tool guide rail morphology to guide the improvement of the machine tool accuracy, including the following steps:

[0040] Step 1: Establish the mapping relationship between the guide rail profile curve and the motion error of the machine tool translation axis. The machine tool has 6 degrees of freedom during the linear motion process, so 6 motion errors will be generated, namely positioning error, horizontal plane straightness error, vertical plane straightness error, pitch angle error, yaw angle error and roll angle error. Except for the positioning error, the other five motion errors are all related to the guide rail profile, and the mapping relationship between these five motion errors and the guide rail profile is established.

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] Where f(z) is the rail morphology, z i-1 、z i 、z i+1 They represent the left, middle and right points of the workbench respectively. L is the length of the workbench, D is the width of the workbench, and T is the parallelism of the guide rail.

[0047] Step 2: Establish a machine tool spatial error prediction model based on guide rail morphology. Based on the multi-body system theory and homogeneous coordinate transformation method, a machine tool spatial error prediction model is established. Combined with the relationship between guide rail morphology and motion error, the error model between machine tool spatial error and guide rail morphology is obtained.

[0048] Table 1 Neighboring body position matrix

[0049]

[0050] Table 2 Adjacent body motion matrix

[0051]

[0052] Where [Sii+1] p 、[Sii+1] pe 、[Sii +1 ] s and [Sii +1] se They represent the ideal position matrix, actual position matrix, ideal motion matrix and actual motion matrix between adjacent bodies respectively, i is the adjacent low-order body of i+1, q j =(q jx ,q jy ,q jz ) T Represents the position vector between adjacent body coordinate origins, α ij , β ij and γ ij They are the perpendicularity errors generated around the translation axis and the rotation axis respectively.

[0053] Based on the position and motion relationship between adjacent bodies and combined with error motion, the ideal and actual positions of the vector intersection point of the workpiece and the tool in the machine tool coordinates are obtained as follows:

[0054]

[0055]

[0056] Where r wi is the ideal position, r wa is the actual position, r t =(-R,0,0,1) T The position of the tool vector in the tool coordinate system. R is the distance from the machining point to the tool coordinate origin, which is the radius of the grinding wheel in a grinder.

[0057] The difference between the actual position and the ideal position is used to obtain the error value of each coordinate system in the machine tool space.

[0058]

[0059] The error value of the space point during the machine tool movement is

[0060]

[0061] Step 3: Establish a machine tool spatial error prediction model based on guide rail morphology. Based on the multi-body system theory and the method of homogeneous coordinate transformation, a machine tool spatial error prediction model is established. Combined with the relationship between guide rail morphology and motion error, the error model between machine tool spatial error and guide rail morphology is obtained.

[0062] Step 4: Verify the correctness of the spatial error prediction model based on the guide rail morphology. Carry out a 45° oblique line error test experiment on the machine tool space to obtain the actual measurement value of the machine tool space error, and compare it with the error model obtained by the spatial error calculation to verify the influence of the guide rail morphology on the machine tool space error. If the prediction effect is achieved, carry out the guide rail morphology design to improve the machine tool accuracy; if the prediction effect is not ideal, add a correction coefficient k and re-carry out the spatial error prediction work.

[0063] Step 5: Use digital means to carry out guide rail surface design. Based on the verified prediction model, carry out guide rail morphology design work, and use different characteristic curves to characterize the guide rail morphology instead. Calculate the corrected spatial error model and compare it with the experimental results. If it meets the expected expectations, complete the machine tool accuracy improvement work based on the guide rail morphology design; if it does not meet the expected expectations, change the function type and design range, and re-carry out the guide rail morphology design work until a satisfactory result is obtained.

[0064] like Figure 2 The figure shows the mapping relationship between the YOZ plane rail morphology and the straightness and pitch angle of the technical solution of the present invention. f1(z) is the rail profile curve in the YOZ plane. Since f1(z) is a random curve, it is very difficult and complicated to obtain the accurate mathematical function of the rail morphology. Therefore, g(z) is used to fit and characterize the rail morphology based on the rail morphology profile characteristics. y (z) and ε x (z) are the straightness error and pitch angle error of the Z-guide rail in the Y direction, respectively. The worktable with a length of L is supported by two balls A and B regarded as rigid bodies. The coordinates of the two balls are z i-1 and z i+1 , P is the midpoint of the workbench, and its coordinate value is z i Based on the geometric physical model, the value at the midpoint P of the worktable represents the straightness error δ y (z). Because points A and B are in contact with the guide rail plane, the guide rail topography curve value can be obtained based on the coordinate values ​​of the two points, and the average value of the guide rail topography curve value at these two points is used to represent the δ at point P. y (z), which is: Angle error ε x (z) is mainly expressed as a ratio relationship. The ratio of the difference between the A and B rail morphology values ​​to the workbench length L is ε x The sine angle value of (z) is calculated by using the inverse sine function to obtain ε x (z) is: Based on the method of determining the direction of the rotation vector, the positive direction of the X axis in the spatial coordinate system where the YOZ plane is located faces inward, so ε x (z) is a negative value.

[0065] like Figure 3 The figure shows the mapping relationship between the XOZ plane guide rail morphology and the straightness and the deflection angle of the technical solution of the present invention. f2(z) is the guide rail profile curve in the XOZ plane, δ x (z) and ε y (z) are the straightness error and runout angle error of the Z guide rail in the X direction, and Figure 2 Medium Delta y (z) and ε xThe calculation method of (z) is similar, δ x (z) and ε y (z) is also calculated using the mean and ratio of the rail morphology, respectively: In the spatial coordinate system where the XOZ plane is located, the positive direction of the Y axis points outward, so ε y (z) is a positive value.

[0066] like Figure 4 The figure shows the mapping relationship between the guide rail morphology and the roll angle of the technical solution of the present invention. The roll angle ε z (z) Parallelism error T1 between the two guide rails (1 and 2), guide rail topography straightness δ y (z) and the table width D. Among them, T1 is mainly manifested in the form of angular error and is oriented in one direction within the entire length of the guide rail. Based on ε z (z), the error expression is obtained as follows:

[0067] like Figure 5 The figure shows the spatial error modeling diagram of the technical solution of the present invention, where O0, O t , and O w They are the basic coordinate system, tool coordinate system and workpiece coordinate system, O i is the coordinate system of the key moving parts in the workpiece motion chain, O j is the coordinate system of the key moving parts in the tool motion chain, S is the motion matrix, and P is the position matrix. Based on the multi-degree-of-freedom machine tool position and posture transmission process under the workpiece motion chain and the tool motion chain, the two motion branches intersect at the processing point M. The machine tool spatial error model is established using the multi-body system theory and homogeneous coordinate transformation method, and the spatial error calculation result based on the guide rail topography curve is obtained. Carry out a spatial 45° oblique line error test, compare the spatial error calculation results, and modify the calculation model if necessary to meet the prediction effect.

[0068] like Figure 6 The figure shows the design scheme of the guide rail morphology of the technical solution of the present invention, where (a) is the overall guide rail morphology design scheme, (b) is the two-segment guide rail morphology design scheme, (c) is the multi-segment guide rail design scheme, and (d) is the guide rail splicing scheme. Scheme (a) shows that the guide rail morphology can be designed based on the arch function g2(z), the linear function g3(z), the broken line function g4(z) and the multivariate multiple function. On the basis of the broken line function g4(z), the segmented function g 41 (z) and g 42 (z) Design the rail morphology. Further, based on the small range of the rail's common working area, the constant equation g is used 43Finally, based on the stress deformation and processing technology in the guide rail processing process, that is, the characteristics of the arch function g2(z), multiple small arch guide rails can be spliced ​​in the form of g 21 (z) Design the guide rail morphology. Based on the above method, the spatial motion accuracy and processing accuracy of the machine tool can be improved.

[0069] like Figure 7 This is a diagram of the machine tool precision improvement effect of the technical solution of the present invention. A guide rail morphology design scheme is adopted, combined with a spatial error prediction model based on the guide rail morphology, to obtain an optimized spatial error calculation curve. By comparing the precision improvement effects before and after optimization, a guide rail morphology optimization design scheme that is beneficial to improving machine tool precision is obtained.

[0070] The contents not described in detail in the specification of the present invention belong to the prior art known to the professional and technical personnel in this field.

Claims

1. A method for improving machine tool accuracy based on guide rail profile design, characterized in that: Based on the machine tool guide rail morphology, a mathematical model of guide rail morphology and machine tool error is established to guide the improvement of machine tool accuracy, including the following steps: Step 1: Establish the mapping relationship between the guide rail profile curve and the motion error of the machine tool translation axis; the machine tool has 6 degrees of freedom during the linear motion process, so 6 motion errors will be generated, namely the positioning error δ z (z), horizontal plane straightness error δ x (z), vertical surface straightness error δ y (z), pitch angle error ε x (x), yaw angle error ε y (x) and roll angle error ε z (z); Except for the positioning error, the other five motion errors are related to the guide rail morphology, and the mapping relationship between the five motion errors and the guide rail morphology is established; Where f(z) is the rail morphology, z i-1 、z i 、z i+1 They represent the left, middle and right points of the workbench respectively; L is the length of the workbench, D is the width of the workbench, and T1 is the parallelism tolerance of the guide rail; Step 2: Establish a machine tool spatial error prediction model based on the guide rail morphology; Based on the multi-body system theory and the method of homogeneous coordinate transformation, establish a machine tool spatial error prediction model; Combined with the relationship between the guide rail morphology and the motion error, obtain the error model between the machine tool spatial error and the guide rail morphology; Table 1 Neighboring body position matrix Table 2 Adjacent body motion matrix Where [Sii+1] p 、[Sii+1] pe 、[Sii +1 ] s and [Sii +1 ] se They represent the ideal position matrix, actual position matrix, ideal motion matrix and actual motion matrix between adjacent bodies respectively, i is the adjacent low-order body of i+1, q j =(q jx ,q jy ,q jz ) T Represents the position vector between adjacent body coordinate origins, α ij , β ij and γ ij are the perpendicularity errors generated around the translation axis and the rotation axis respectively; Based on the position and motion relationship between adjacent bodies and combined with error motion, the ideal and actual positions of the vector intersection point of the workpiece and the tool in the machine tool coordinates are obtained as follows: Where r wi is the ideal position, r wa is the actual position, r t =(-R,0,0,1) T The position of the tool vector in the tool coordinates, R is the distance from the processing point to the tool coordinate origin, which is the radius of the grinding wheel in the grinder; The difference between the actual position and the ideal position gives the error value of each coordinate system in the machine tool space; The error value of the space point during the machine tool movement is: Step 3: Establish a machine tool spatial error prediction model based on the guide rail morphology; Based on the multi-body system theory and the method of homogeneous coordinate transformation, establish a machine tool spatial error prediction model; Combined with the relationship between the guide rail morphology and the motion error, obtain the error model between the machine tool spatial error and the guide rail morphology; Step 4: Verify the correctness of the spatial error prediction model based on the guide rail morphology; conduct a 45° oblique line error test experiment on the machine tool space to obtain the actual measured value of the machine tool space error, and compare it with the error model obtained by the spatial error calculation to verify the prediction accuracy of the spatial error model; if the prediction effect is achieved, carry out the guide rail morphology design to improve the machine tool accuracy; if the prediction effect is not ideal, add a correction coefficient k and re-carry out the spatial error prediction work; Step 5: Use digital means to carry out guide rail surface design; based on the verified prediction model, carry out guide rail morphology design work, and use different characteristic curves to characterize the guide rail morphology instead; calculate the corrected spatial error model and compare it with the experimental results; if it meets the expected expectations, complete the machine tool accuracy improvement work based on the guide rail morphology design; if it does not meet the expected expectations, change the function type and design range, and re-carry out the guide rail morphology design work until satisfactory results are obtained.

2. The method for improving machine tool accuracy based on guide rail profile design according to claim 1, characterized in that: A digital design method is adopted to establish mathematical models between guide rail morphology and motion error and spatial error in sequence, and digital means are used to improve the accuracy of machine tools.

3. The method for improving machine tool accuracy based on guide rail profile design according to claim 1, characterized in that: The guide rail surface design is characterized by arbitrary functions at different positions of the guide rail according to its own needs.

4. The method for improving machine tool accuracy based on guide rail profile design according to claim 1, characterized in that: The machine tool designer uses the guide rail splicing method to design the topography and verifies the machine tool accuracy with the help of the established mathematical model.

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