Three-axis machine tool geometric error identification method based on ball bar measurement

Abstract

The invention discloses a three-axis machine tool geometric error identification method based on ball bar measurement, and the method comprises the following steps: taking a three-axis numerical control machine tool as a research object, and constructing a comprehensive error coefficient model according to an exponential product theory and a three-axis numerical control machine tool kinematic chain in combination with a four-order Chebyshev polynomial pre-fitting model; on the basis of a three-axis linkage detection experiment, pseudo-inverse matrix solution is carried out on the comprehensive error coefficient model, all geometric errors can be identified, and finally the error distribution condition of the machine tool space is obtained through a statistical analysis means. According to the detection steps, 21 geometric errors can be identified only by operating the ball bar instrument for detection once, multiple times of installation, detection, identification and decoupling are not needed, and the identification precision and efficiency are improved.

Description

Technical Field

[0001] The invention relates to the field of precision detection of three-axis CNC machine tools, and in particular to a three-axis machine tool geometric error identification method based on ballbar measurement. Technical Background

[0002] The industry has higher and higher requirements for the precision of CNC machine tools. Geometric error detection has always been a difficult point in the precision detection of machine tools. At present, the research on geometric errors mainly includes devices such as ballbar, laser interferometer and R-test. Among them, due to the low price, high precision and simple operation of ballbar, researchers usually use ballbar for error research.

[0003] At present, the methods for detecting geometric errors have problems such as complex operation, cumbersome detection methods, not fitting the actual processing, unable to reflect the actual error situation of the entire processing space, and low detection efficiency. Therefore, it is very necessary to invent a simple and relatively accurate machine tool error identification method. Summary of the invention

[0004] The purpose of the present invention is to propose a three-axis machine tool geometric error identification method based on ballbar measurement to solve the problems that the detection method is cumbersome, does not fit the actual processing, and cannot reflect the real error situation of the entire processing space. The detection step of the invention only needs to run the ballbar detection once to identify 21 geometric errors, without the need for multiple installations of detection and identification decoupling, improves the identification accuracy and efficiency, and finally obtains the error distribution of the machine tool space through statistical analysis.

[0005] A method for geometric error identification of a three-axis machine tool based on ballbar measurement comprises the following steps:

[0006] Step 1: Based on the exponential product theory, the kinematic chain of three-axis CNC machine tools and the ballbar detection principle, combined with the fourth-order Chebyshev polynomial pre-fitting model, a comprehensive error coefficient model is established.

[0007] Step 2: Conduct a ballbar length comparison experiment to explore the accuracy and validity of the data measured by different bar lengths and select a relatively excellent bar length as the basis for subsequent experiments.

[0008] Step 3: Divide the entire processing space into a series of subspaces according to the selected ballbar length specifications, perform detection in each subspace, and then identify and decouple the detection data to establish the accuracy field of each subspace.

[0009] In step 1, a comprehensive error model is constructed based on the exponential product theory, and a comprehensive error coefficient model is established by combining the fourth-order Chebyshev polynomial pre-fitting model and the ballbar length model, including the following steps:

[0010] Step 1.1. Determine that the geometric errors of the three-axis machine tool are mainly 21 errors.

[0011] Step 1.2: Establish a simple model of the three-axis CNC machine tool based on the X-axis, and establish the machine tool motion chain according to the machine tool topology: worktable W→X→Y→F→Z→spindle tool end T.

[0012] Step 1.3: Establish a unique global coordinate system RCS based on the Product of Exponentials (PoE) theory, and establish the global coordinate system on the workbench.

[0013] Step 1.4: According to the established machine tool kinematic chain and global coordinate system, the three-axis linkage PoE kinematic model is:

[0014]

[0015]

[0016] Step 1.5: The tool tip error of the machine tool is the difference between the actual POE model and the ideal POE model. After considering the small angle approximation assumption and ignoring the second-order and high-order terms, the comprehensive geometric error model of the machine tool is:

[0017]

[0018] Step 1.6: According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials. The second-class Chebyshev polynomials are defined as (-1, 1) on (1-x 2 ) 0.5 The recursive formula of the orthogonal polynomial on is:

[0019]

[0020] According to the characteristics of the 18 error elements, a fourth-order Chebyshev polynomial pre-fitting model is established:

[0021]

[0022] Considering the constant term in the error polynomial modeling will cause the constant term of PIGEs error term and PDGEs error to be redundant, so the constant term of the polynomial is not considered, and the formula is:

[0023]

[0024] Perform coordinate linear normalization on the Chebyshev polynomials:

[0025]

[0026] Step 1.8: According to the ballbar principle, the geometric error of the machine tool can be expressed as:

[0027]

[0028] What the ballbar detects is the error of the three axes coupled together, so the length of the ballbar can be expressed as:

[0029] (R+ΔR) 2 =(x′2-x1) 2 +(y′2-y1) 2 +(z′2-z1) 2 (7)

[0030] The state at the initial installation position is the ideal state, which can be written as:

[0031] R 2 =(x2-x1) 2 +(y2-y1) 2 +(z2-z1) 2 (8)

[0032] Combining the equations, we get the relationship between the ballbar length change and the geometric error, which is expressed as:

[0033]

[0034] Substituting the workpiece end precision spherical coordinates P(x1, y1, z1) into P(0, 0, 0) for optimization, the final ballbar length model can be obtained, as shown in the following formula:

[0035]

[0036] Combining equations (3), (5) and (10), we can get the comprehensive error coefficient model.

[0037] In step 2, a ballbar length comparison experiment is conducted to explore the accuracy and validity of the data measured by different rod lengths and select a relatively excellent rod length as the basis for subsequent experiments, including the following steps:

[0038] Step 2.1: Based on the degree of spatial division of ballbars with different rod lengths, initially select rods with a length of 100 mm and 150 mm for rod length comparison experiments.

[0039] Step 2.2: Randomly select a position in the machine tool space as the detection installation point, and then use a 100mm rod length to perform three three-axis linkage spiral trajectory experiments at this position.

[0040] Step 2.3, wait ten minutes and then use the 150mm rod length for the second experiment, and run three three-axis linkage spiral trajectory experiments at the same position.

[0041] Step 2.4: Based on the method of establishing a comprehensive error coefficient model, models are established and solved for the experimental data of rod lengths of 100 and 150 mm respectively.

[0042] Step 2.5: Substitute the error terms obtained through detection and decoupling into the comprehensive error model to obtain the compensation amounts in the X, Y, and Z directions, and correct the G code.

[0043] Without changing the experimental conditions, compensation is performed, and the experimental test results before compensation and after compensation are compared.

[0044] Then, the two global standards of the residual absolute value sum and residual square sum of the compensated detection results of the 100mm rod length and 150mm rod length are compared respectively.

[0045] Based on the average change rate of the comprehensive rod length and the global standard comparison chart, it is more reasonable to choose a rod length of 150mm for subsequent experiments.

[0046] Step 3: Divide the entire processing space into a series of subspaces according to the selected ballbar length specification, perform detection in each subspace, and then identify and decouple the detection data to establish the accuracy field of each subspace, including the following steps:

[0047] Step 3.1: Divide the entire workspace into four subspaces based on the hemisphere that can accommodate R=150mm. The specification of each subspace is 315*400*25.

[0048] In subsequent experiments, a 150mm long ballbar was used to conduct three-axis linkage experiments in each character space, and the ballbar detection installation point was set to the mechanical coordinate as the origin, namely (157.5, 200, 65), (472.5, 200, 65), (157.5, 200, 330), and (472.5, 2200, 330).

[0049] Step 3.2: Based on the identification results in different subspaces, take the regional error data of subspace No. 1 as an example to draw the accuracy field of the XK714D three-axis machine tool detection area.

[0050] Based on statistical knowledge and using mathematical software MATLAB, the spatial error distribution of the three-axis CNC machine tool within the detection range is obtained.

[0051] The precision field is then sliced ​​and observed along the X-axis, Y-axis, and Z-axis.

[0052] Similarly, the above method is used to establish the accuracy fields of the other three subspaces to obtain their error fluctuation ranges.

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

[0054] The method of the present invention constructs a comprehensive error model based on the Product of Exponentials (PoE) theory, and combines the fourth-order Chebyshev polynomial pre-fitting model and the ballbar length model to establish a comprehensive error coefficient model. The model can simplify the calculation, improve the fitting accuracy, and avoid the matrix ill-conditioned singularity problem. In the experiment, the ballbar test is only run once to obtain the entire identification, and there is no need to install the test identification decoupling multiple times, which improves the identification accuracy and efficiency, and finally obtains the error distribution of the machine tool space through statistical analysis. The experimental results of the method of the present invention and the given error simulation characteristics can be used for the rapid identification of the geometric errors of three-axis machine tools. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Schematic diagram of the XK714D three-axis CNC machine tool structure

[0056] Figure 2 This is the motion chain for the XK714D machine tool.

[0057] Figure 3 Setup for the experiment.

[0058] Figure 4 The experimental simulation path.

[0059] Figure 5 Identification results of X, Y, Z axis errors and verticality errors for 100mm and 150mm rod lengths

[0060] Figure 6 The figure shows the comparison of compensation results for rod lengths of 100 mm and 150 mm.

[0061] Figure 7 This is a global standard comparison chart of 100mm rod length and 150mm rod length in the same position.

[0062] Figure 8 Schematic diagram of subspace partitioning.

[0063] Fig. 9 It is the total accuracy field error diagram.

[0064] Fig.10 It is the X, Y, and Z axis slice diagram. DETAILED DESCRIPTION

[0065] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0066] Attached Figure 1 The figure shows the structure schematic diagram of the XK714D three-axis CNC machine tool. Taking the three-axis CNC machine tool as an example, the method of the present invention is explained.

[0067] In step 1, a comprehensive error model is constructed based on the exponential product theory, and a comprehensive error coefficient model is established by combining the fourth-order Chebyshev polynomial pre-fitting model and the ballbar length model, including the following steps:

[0068] Step 1.1. Determine that the geometric errors of the three-axis machine tool are mainly 21 errors.

[0069] Step 1.2: Use the X-axis of the three-axis CNC machine tool as the reference to establish a simple model of the machine tool, and establish the machine tool motion chain according to the machine tool topology: worktable W→X→Y→F→Z→spindle tool end T. Figure 2 shown.

[0070] Step 1.3: Establish a unique global coordinate system RCS based on the Product of Exponentials (PoE) theory, and establish the global coordinate system on the workbench.

[0071] Step 1.4: According to the established machine tool kinematic chain and global coordinate system, the three-axis linkage PoE kinematic model is:

[0072]

[0073]

[0074] Step 1.5: The tool tip error of the machine tool is the difference between the actual POE model and the ideal POE model. After considering the small angle approximation assumption and ignoring the second-order and high-order terms, the comprehensive geometric error model of the machine tool is:

[0075]

[0076] Step 1.6: According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials. The second-class Chebyshev polynomials are defined as (-1, 1) on (1-x 2 ) 0.5 The recursive formula of the orthogonal polynomial on is:

[0077]

[0078] According to the characteristics of the 18 error elements, a fourth-order Chebyshev polynomial pre-fitting model is established:

[0079]

[0080] Considering the constant term in the error polynomial modeling will cause the constant term of PIGEs error term and PDGEs error to be redundant, so the constant term of the polynomial is not considered, and the formula is:

[0081]

[0082] Perform coordinate linear normalization on the Chebyshev polynomials:

[0083]

[0084] Step 1.8: According to the ballbar principle, the geometric error of the machine tool can be expressed as:

[0085]

[0086] What the ballbar detects is the error of the three axes coupled together, so the length of the ballbar can be expressed as:

[0087] (R+ΔR) 2 =(x′2-x1) 2 +(y′2-y1) 2 +(z′2-z1) 2 (7)

[0088] The state at the initial installation position is the ideal state, which can be written as:

[0089] R 2 =(x2-x1) 2 +(y2-y1) 2 +(z2-z1) 2 (8)

[0090] Combining the equations, we get the relationship between the ballbar length change and the geometric error, which is expressed as:

[0091]

[0092] Substituting the workpiece end precision spherical coordinates P(x1, y1, z1) into P(0, 0, 0) for optimization, the final ballbar length model can be obtained, as shown in the following formula:

[0093]

[0094] Combining equations (3), (5) and (10), we can get the comprehensive error coefficient model.

[0095] In step 2, a ballbar length comparison experiment is conducted to explore the accuracy and validity of the data measured by different rod lengths and select a relatively excellent rod length as the basis for subsequent experiments, including the following steps:

[0096] Step 2.1: According to the degree of space division of the ballbar with different rod lengths, 100 mm and 150 mm rod lengths are initially selected for rod length comparison experiments. Figure 3 and Figure 4 shown.

[0097] Step 2.2: Randomly select a position in the machine tool space as the detection installation point, and then use a 100mm rod length to perform three three-axis linkage spiral trajectory experiments at this position.

[0098] Step 2.3, wait another ten minutes and then use the 150mm rod length for the second experiment, and run three three-axis linkage spiral trajectory experiments at the same position.

[0099] Step 2.4: According to the method of establishing the comprehensive error coefficient model, the model is established and solved for the experimental data of the 100mm and 150mm rod lengths. The identification results are as follows: Figure 5 shown.

[0100] Step 2.5: Substitute the error terms obtained through detection and decoupling into the comprehensive error model to obtain the compensation amounts in the X, Y, and Z directions, and correct the G code.

[0101] Without changing the experimental conditions, compensation is performed and the test results before and after compensation are compared. Figure 6 Shown

[0102] The two global standards of the residual absolute value and residual square sum of the compensated test results of the 100mm rod length and 150mm rod length are compared respectively. Figure 7 shown.

[0103] Based on the average change rate of the comprehensive rod length and the global standard comparison chart, it is more reasonable to choose a rod length of 150mm for subsequent experiments

[0104] Step 3: Divide the entire processing space into a series of subspaces according to the selected ballbar length specification, perform detection in each subspace, and then identify and decouple the detection data to establish the accuracy field of each subspace, including the following steps:

[0105] Step 3.1: Divide the entire workspace into 4 subspaces based on the hemisphere that can accommodate R = 150 mm. The specifications of each subspace are 315*400*25. Figure 8 shown.

[0106] In subsequent experiments, a 150mm long ballbar was used to conduct three-axis linkage experiments in each character space, and the ballbar detection installation point was set to the mechanical coordinate as the origin, namely (157.5, 200, 65), (472.5, 200, 65), (157.5, 200, 330), and (472.5, 2200, 330).

[0107] Step 3.2: Based on the identification results in different subspaces, take the regional error data of subspace No. 1 as an example to draw the accuracy field of the XK714D three-axis machine tool detection area. Fig. 9 shown.

[0108] Based on statistical knowledge and using mathematical software MATLAB, the spatial error distribution of the three-axis CNC machine tool within the detection range is obtained.

[0109] Then slice and observe the precision field along the X-axis, Y-axis, and Z-axis. Fig.10 shown.

[0110] Similarly, the above method is used to establish the accuracy fields of the other three subspaces to obtain their error fluctuation ranges.

[0111] The present invention finally identifies all geometric errors and finally obtains the error distribution of the machine tool space by means of statistical analysis. The accompanying drawings are only a preferred example. The above embodiments are only for describing the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for geometric error identification of three-axis machine tools based on ballbar measurement, characterized in that: The steps include: Step 1: Based on the exponential product theory, the kinematic chain of three-axis CNC machine tools and the ballbar detection principle, combined with the fourth-order Chebyshev polynomial pre-fitting model, a comprehensive error coefficient model is established; Step 2: Conduct a ballbar length comparison experiment to explore the accuracy and effectiveness of data measured by different bar lengths and select a relatively excellent bar length as the basis for subsequent experiments; Step 3: Divide the entire processing space into a series of subspaces according to the selected ballbar length specifications, perform detection in each subspace, and then identify and decouple the detection data to establish the accuracy field of each subspace.

2. The method for geometric error identification of a three-axis machine tool based on ballbar measurement according to claim 1, characterized in that: In step 1, according to the exponential product theory, the kinematic chain of a three-axis CNC machine tool and the detection principle of a ballbar, combined with a fourth-order Chebyshev polynomial pre-fitting model, a comprehensive error coefficient model is established, including the following steps: Step 1.

1. Determine that the geometric errors of the three-axis machine tool are mainly 21 errors. Step 1.2: Establish a simple model of the three-axis CNC machine tool based on the X-axis, and establish the machine tool motion chain according to the machine tool topology: worktable W→X→Y→F→Z→spindle tool end T. Step 1.3: Establish a unique global coordinate system RCS based on the Product of Exponentials (PoE) theory, and establish the global coordinate system on the workbench. Step 1.4: According to the established machine tool kinematic chain and global coordinate system, the three-axis linkage PoE kinematic model is: Step 1.5: The tool tip error of the machine tool is the difference between the actual POE model and the ideal POE model. After considering the small angle approximation assumption and ignoring the second-order and high-order terms, the comprehensive geometric error model of the machine tool is: Step 1.6: According to the characteristics of Chebyshev polynomials, choose to build a pre-fitting model based on the second-class Chebyshev polynomials. The second-class Chebyshev polynomials are defined as (-1, 1) on (1-x 2 ) 0.5 The recursive formula of the orthogonal polynomial on is: According to the characteristics of the 18 error elements, a fourth-order Chebyshev polynomial pre-fitting model is established: Considering the constant term in the error polynomial modeling will cause the constant term of PIGEs error term and PDGEs error to be redundant, so the constant term of the polynomial is not considered, and the formula is: Perform coordinate linear normalization on the Chebyshev polynomials: Step 1.8: According to the ballbar principle, the geometric error of the machine tool can be expressed as: What the ballbar detects is the coupled value of the three-axis errors, so the ballbar length can be expressed as: (R+ΔR) 2 (x′2-x1) 2 +(y′2-y1) 2 +(z′2-z1) 2 (7) The state at the initial installation position is the ideal state, which can be written as: <h2 style=";text-align:left;direction:ltr">R<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> (x2-x1)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +(y2-y1)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +(z2-z1)<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> (8) Combining the equations, we get the relationship between the ballbar length change and the geometric error, which is expressed as: Substituting the workpiece end precision spherical coordinates P(x1, y1, z1) into P(0, 0, 0) for optimization, the final ballbar length model can be obtained, as shown in the following formula: Combining equations (3), (5) and (10), we can get the comprehensive error coefficient model.

3. The method for geometric error identification of a three-axis machine tool based on ballbar measurement according to claim 1, characterized in that: In step 2, a ballbar length comparison experiment is conducted to explore the accuracy and effectiveness of data measured by different rod lengths and select a relatively excellent rod length as the basis for subsequent experiments, including the following steps: Step 2.1: Based on the degree of spatial division of ballbars with different rod lengths, initially select rods with a length of 100 mm and 150 mm for rod length comparison experiments. Step 2.2: Randomly select a position in the machine tool space as the detection installation point, and then perform three three-axis linkage spiral trajectory experiments at this position with a rod length of 100 mm. Step 2.3, wait ten minutes and then use the 150mm rod length for the second experiment, and run three three-axis linkage spiral trajectory experiments at the same position. Step 2.4: Based on the method of establishing a comprehensive error coefficient model, models are established and solved for the experimental data of rod lengths of 100 mm and 150 mm respectively. Step 2.5: Substitute the error terms obtained through detection and decoupling into the comprehensive error model to obtain the compensation amounts in the X, Y, and Z directions, and correct the G code. Without changing the experimental conditions, compensation is performed, and the experimental test results before compensation and after compensation are compared. Then, the two global standards of the residual absolute value sum and residual square sum of the compensated detection results of the 100mm rod length and 150mm rod length are compared respectively. Based on the average change rate of the comprehensive rod length and the global standard comparison chart, it is more reasonable to choose a rod length of 150mm for subsequent experiments.

4. The method for geometric error identification of a three-axis machine tool based on ballbar measurement according to claim 1, characterized in that: In step 3, the entire processing space is divided into a series of subspaces according to the selected ballbar length specification, and detection is performed in each subspace, and then the detection data is identified and decoupled to establish the accuracy field of each subspace, including the steps of: Step 3.1: Divide the entire workspace into four subspaces based on the hemisphere that can accommodate R=150mm. The specification of each subspace is 315*400*25. In subsequent experiments, a 150mm long ballbar was used to conduct three-axis linkage experiments in each character space, and the ballbar detection installation point was set to the mechanical coordinate as the origin, namely (157.5, 200, 65), (472.5, 200, 65), (157.5, 200, 330), and (472.5, 2200, 330). Step 3.2: Based on the identification results in different subspaces, take the regional error data of subspace No. 1 as an example to draw the accuracy field of the XK714D three-axis machine tool detection area. Based on statistical knowledge and using mathematical software MATLAB, the spatial error distribution of the three-axis CNC machine tool within the detection range is obtained. The precision field is then sliced ​​and observed along the X-axis, Y-axis, and Z-axis. Similarly, the above method is used to establish the accuracy fields of the other three subspaces to obtain their error fluctuation ranges.

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