Positioning error compensation method for coordinate measuring machine based on nonlinear interpolation algorithm

Abstract

The present application relates to three coordinate measuring machine error compensation field, especially in kind based on nonlinear interpolation algorithm three coordinate measuring machine positioning error compensation method. Including in the verification direction according to the preset rule creates multiple verification points;According to the preset scheme, the three coordinate measuring machine is moved to each verification point in turn, and the positioning error value at each verification point is measured by using laser interferometer;The obtained each positioning error value is stored in the error table file;The error space is divided into several error data units;The coordinate value of the actual measurement point is obtained, and the vertex of the error compensation data unit containing the actual measurement point is taken out from the error table file;The positioning error value of the actual measurement point is calculated by nonlinear interpolation algorithm, the calculated positioning error value is added to the coordinate value of the actual measurement point, and the compensated coordinate value of the actual measurement point is obtained, which aims at solving the problems of poor positioning error compensation effect and low error compensation efficiency of three coordinate measuring machine.

Description

Technical Field

[0001] This invention relates to the field of coordinate measuring machine (CMM) error compensation, and more particularly to a CMM positioning error compensation method based on a nonlinear interpolation algorithm. Background Technology

[0002] As a highly efficient precision measurement system, the coordinate measuring machine (CMM) plays an increasingly important role in modern manufacturing and aerospace industries due to its high accuracy, speed, and flexibility. It is a key foundational measurement device in advanced manufacturing and a crucial testing instrument for quality inspection and control in civilian production. It can perform three-dimensional coordinate measurements of the geometric elements, curves, and surfaces of various parts, and can achieve online inspection and automated measurement. With the advancement of science and technology and the development of ultra-precision machining technology, the requirements for the measurement accuracy of CMMs are becoming increasingly stringent. Rapid and accurate calibration of the CMM, detecting its various errors and performing error compensation, is one of the important ways to improve its measurement accuracy. It is an advanced technical means to significantly improve the measurement accuracy of CMMs at a relatively low cost.

[0003] The geometric errors of a coordinate measuring machine mainly include 21 items, namely 3 positioning errors, 6 straightness errors, 9 angle errors and 3 perpendicularity errors. Among them, the positioning errors are mainly caused by the engraving error of the grating ruler and the motion system error of the coordinate measuring machine.

[0004] Currently, the method for verifying positioning accuracy is relatively uniform, namely, using a dual-frequency laser interferometer for measurement. This method offers high measurement accuracy and can be adapted to the error verification of most coordinate measuring machines. However, regarding error compensation methods, especially in the calculation of interpolation algorithms, the use of linear interpolation algorithms, while simple and easy to implement, results in a certain deviation between the calculated error value and the actual engineering situation. This deviation is even more significant when using a smaller measurement step size for error verification, thus affecting the effectiveness of error compensation and ultimately reducing the final accuracy of the coordinate measuring machine.

[0005] Currently, the most common approach to addressing the above problems is to reduce the measurement step size during positioning error verification, so that the measured values ​​can reflect the actual distribution of the coordinate measuring machine's positioning errors as accurately as possible. However, as the step size decreases, the error verification time increases, and the temperature drift of the laser interferometer over time also occurs, leading to inaccurate error verification values, reducing the effectiveness of error compensation, and decreasing compensation efficiency. Summary of the Invention

[0006] (a) Technical problems to be solved

[0007] This invention addresses the above-mentioned problems by proposing a coordinate measuring machine (CMM) positioning error compensation method based on a nonlinear interpolation algorithm. The aim is to solve the problems of poor positioning error compensation effect and low error compensation efficiency in CMMs.

[0008] (II) Technical Solution

[0009] To achieve the above objectives, this invention provides a method for compensating for positioning errors of a coordinate measuring machine based on a nonlinear interpolation algorithm, comprising the following steps:

[0010] Install the laser interferometer and coordinate measuring machine to the target position according to the preset installation plan;

[0011] The calibration direction is determined based on the installation positions of the laser interferometer and the coordinate measuring machine, and multiple calibration points are created within the calibration direction according to preset rules.

[0012] The coordinate measuring machine is moved sequentially to each of the calibration points according to the preset plan, and the positioning error value at each calibration point is measured using the laser interferometer.

[0013] The positioning error values ​​obtained by the laser interferometer are stored in the coordinate measuring machine error table file;

[0014] The error space of the coordinate measuring machine is divided into several error data units;

[0015] Obtain the coordinate values ​​of the actual measurement point from the coordinate measuring machine, and extract the vertex containing the error compensation data unit of the actual measurement point from the coordinate measuring machine error table file;

[0016] The positioning error value of the actual measurement point is calculated using a nonlinear interpolation algorithm. The calculated positioning error value is then added to the coordinate value of the actual measurement point to obtain the compensated coordinate value of the actual measurement point.

[0017] Furthermore, the nonlinear interpolation algorithms include: Bézier curve interpolation, B-spline curve interpolation, general spline curve interpolation, and parabolic interpolation.

[0018] Furthermore, the steps for calculating the positioning error value of the actual measurement point using the Bézier curve interpolation method include:

[0019] Let each pair of vertices be the starting and ending points of a cubic Bézier curve.

[0020] The two control points are obtained by the collinearity of the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point, wherein the Bézier curves and the two control points are enclosed within the error data unit;

[0021] Draw a cubic Bézier curve passing through the starting point and the ending point based on the starting point, the ending point and the two control points;

[0022] Substituting the coordinates of the actual measurement point into the cubic Bézier curve equation, the positioning error values ​​of the actual measurement point in the three directions are obtained. The calculated positioning error values ​​are added to the coordinate values ​​of the actual measurement point to obtain the compensated coordinate values ​​of the actual measurement point.

[0023] Furthermore, the steps for calculating the positioning error value of the actual measurement point using the cubic spline interpolation method include:

[0024] Create a cubic spline curve equation in each of the error data cells:

[0025] y = ax 3 +bx 2 +cx+d

[0026] Wherein, a, b, c, and d are coefficients in each cubic spline curve equation, and x is a measurement point in a certain error data unit;

[0027] Based on the interpolation conditions, list the equation which is the number of error data units multiplied by the number of four unknowns;

[0028] Calculate the cubic spline curve based on the known positioning error values ​​of the calibration points;

[0029] Find the cubic spline curve equations in the error data units containing the X, Y, and Z axes of each actual measurement point, substitute them with the measured values ​​of the actual measurement points, and calculate the corresponding positioning error values; add the calculated positioning error values ​​to the coordinate values ​​of the actual measurement points to obtain the compensated coordinate values ​​of the actual measurement points.

[0030] Furthermore, the interpolation conditions include: each cubic spline curve passes through its two endpoints, the left and right first derivatives of the interpolation points are equal, the left and right second derivatives of the interpolation points are equal, the third derivative value of the first interpolation point is equal to the third derivative value of the second interpolation point, and finally, the third derivative value of the first interpolation point is equal to the third derivative value of the penultimate interpolation point.

[0031] Further, the steps of sequentially moving the coordinate measuring machine to each of the calibration points according to the preset scheme, and measuring the positioning error value at each calibration point using the laser interferometer include:

[0032] An initial verification point and a final verification point are determined from a plurality of verification points distributed along a first direction;

[0033] Starting from the initial calibration point, the coordinate measuring machine is moved along the first direction 5 times to other calibration points, and the positioning error value is measured at each calibration point using the laser interferometer.

[0034] Starting from the initial calibration point, the coordinate measuring machine is moved along the second direction to the calibration point closest to the initial calibration point, and the above steps are repeated until...

[0035] After the laser interferometer measures the multiple calibration points, it obtains the positioning error difference value of each calibration point.

[0036] Furthermore, it also includes:

[0037] Starting from the termination calibration point, the coordinate measuring machine is moved sequentially along the first direction to other calibration points, and the positioning error value is measured at each calibration point using the laser interferometer.

[0038] 5. Starting from the termination calibration point, move the coordinate measuring machine along the second direction to the calibration point closest to the termination calibration point, and repeat the above steps until the laser interferometer has measured all the calibration points and obtained the positioning error value of each calibration point.

[0039] The arithmetic mean of the positioning error value measured starting from the initial calibration point and the positioning error value measured starting from the termination calibration point is taken as the final positioning error value.

[0040] Furthermore, the steps of installing the laser interferometer and coordinate measuring machine to the target position according to the preset installation plan also include:

[0041] A shutter sensor is installed at the light output port of the laser interferometer, and a reflector is installed at the lower end of the Z-axis of the coordinate measuring machine.

[0042] Adjust the positions of the laser interferometer and the coordinate measuring machine until the light intensity received by the incident light receiver of the laser interferometer reaches the allowable range when the coordinate measuring machine moves across the full stroke range of all axes to be calibrated.

[0043] (III) Beneficial Effects

[0044] The above-mentioned technical solution of the present invention has the following advantages: the positioning error compensation method of the coordinate measuring machine based on the nonlinear interpolation algorithm has a higher compensation effect than the traditional compensation method based on linear interpolation. The error distribution calculated by the nonlinear interpolation method is closer to the physical error distribution of the machine tool, which can ensure more accurate error compensation under the condition of using fewer calibration steps, thereby effectively improving the overall machine compensation accuracy and compensation efficiency. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the error verification method for a coordinate measuring machine positioning error compensation method based on a nonlinear interpolation algorithm according to the present invention.

[0046] Figure 2 This is a schematic diagram of the error data unit of a coordinate measuring machine positioning error compensation method based on a nonlinear interpolation algorithm according to the present invention.

[0047] Figure 3 This is a diagram illustrating the effect of connecting two collinear Bézier curve segments in adjacent sections.

[0048] Figure 4 This is a schematic diagram of the nonlinear interpolation method for a coordinate measuring machine positioning error compensation method based on a nonlinear interpolation algorithm according to the present invention.

[0049] Figure 5 This is a schematic diagram of cubic Bézier curve interpolation.

[0050] Figure 6 This is a schematic diagram of cubic spline interpolation.

[0051] In the diagram: 1. Coordinate measuring machine; 2. Laser interferometer; 3. Error data unit; 11. Y-axis of the measuring machine; 12. X-axis of the measuring machine; 13. Z-axis of the measuring machine; 21. Main unit of the laser interferometer; 22. Reflector; 23. Tripod. Detailed Implementation

[0052] The technical solutions in the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are also within the scope of protection of this disclosure.

[0053] As indicated in this application and claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include plural forms. Generally speaking, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0054] While this application makes various references to certain modules of the systems according to embodiments of this application, any number of different modules can be used and run on user terminals and / or servers. The modules described are merely illustrative, and different aspects of the systems and methods may use different modules.

[0055] Flowcharts are used in this application to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0056] Figure 1 , Figure 2 , Figure 4 An exemplary flowchart of a coordinate measuring machine positioning error compensation method based on a nonlinear interpolation algorithm according to an embodiment of the present disclosure is shown.

[0057] First, in step S100, the laser interferometer 2 and the coordinate measuring machine 1 are installed at the target position according to the preset installation plan.

[0058] The target location can be determined based on the installation plan, such as... Figure 1 As shown, the dual-frequency laser interferometer host 21 is fixed on the tripod 23, and the whole unit is placed on the ground, or it is fixed to the table of the coordinate measuring machine through special tooling.

[0059] In step S101, the calibration direction is determined according to the installation position of the laser interferometer 2 and the coordinate measuring machine 1, and multiple calibration points are created within the calibration direction according to preset rules.

[0060] The calibration direction is the three sets of axes to be calibrated of the coordinate measuring machine 1. Multiple calibration points are created along the length direction of the three sets of axes to be calibrated according to preset rules. For example, calibration points can be set with the same timing distance or with different timing distances.

[0061] In step S102, the coordinate measuring machine 1 is moved sequentially to each of the calibration points according to the preset scheme, and the positioning error value at each calibration point is measured using the laser interferometer 2.

[0062] Specifically, by setting parameters such as the length of the shaft to be calibrated, the measurement step distance, the expansion coefficient of the grating ruler, and the data acquisition method, the linear measurement program of the laser interferometer 2 is run to measure each calibration point; the laser interferometer 2 records the positioning error value of the calibration point at each preset step position.

[0063] In step S103, the positioning error values ​​obtained by the laser interferometer 2 are stored in the coordinate measuring machine error table file.

[0064] After obtaining the positioning error values ​​of each calibration point, the positioning error values ​​need to be entered into the system. Specifically, open the coordinate measuring machine error list file, manually enter the positioning error values ​​measured in step S102 in the corresponding item list, save the file and exit after the input is complete.

[0065] In step S104, the error space of the coordinate measuring machine 1 is divided into several error data units 3.

[0066] Let's illustrate this step with an example, such as... Figure 1 , Figure 2 As shown, assuming the error calibration step of the coordinate measuring machine 1 is S, and the calibration steps of the X-axis 12, Y-axis 11 and Z-axis 13 are Nx, Ny and Nz respectively, then the error space of the coordinate measuring machine 1 is divided into Nx*Ny*Nz cubic error data units 3 with a side length of S. Each cubic error data unit 3 constitutes a compensation space.

[0067] In step S105, the coordinate values ​​of the actual measurement point are obtained by the coordinate measuring machine 1, and the vertex containing the error compensation data unit 3 of the actual measurement point is extracted from the coordinate measuring machine error table file.

[0068] In step S106, the positioning error value of the actual measurement point is calculated using a nonlinear interpolation algorithm. The calculated positioning error value is then added to the coordinate value of the actual measurement point to obtain the compensated coordinate value of the actual measurement point.

[0069] Specifically, the measurement is initiated using a coordinate measuring machine 1, such as... Figure 2 As shown, assuming the measured coordinates of a certain measurement point P in space are (Xp, Yp, Zp), and its coordinates fall into a certain error data unit 3, find the 8 vertices of this cubic error data unit 3, which are named with letters, namely points A to H. The Xp of the measurement point P is between the coordinates of points A and B, the Yp is between the coordinates of points A and D, and the Zp is between the coordinates of points A and E, that is, Xp∈(XA, XB), Yp∈(YA, YD), Zp∈(ZA, ZE). Based on the positional relationship of a certain point in a certain error compensation data unit 3, the error curve of the point is plotted. The positioning error values ​​ΔXp, ΔYp, and ΔZp of the point are calculated using a nonlinear interpolation algorithm. The positioning error values ​​ΔXp, ΔYp, and ΔZp of the measurement point in the X, Y, and Z directions calculated by the nonlinear interpolation algorithm are added to the X, Y, and Z coordinates of the actual measurement point to obtain the compensated coordinate values ​​of the actual measurement point.

[0070] For example, the coordinates of the measurement point P after compensation for positioning error are (Xp+ΔXp, Yp+ΔYp, Zp+ΔZp). This error compensation method can effectively improve the positioning error compensation effect of the coordinate measuring machine 1, further improve the overall accuracy of the coordinate measuring machine 1, and significantly improve the error compensation efficiency.

[0071] Next, please refer to the appendix. Figure 1 The positioning error compensation method of the coordinate measuring machine 1 based on nonlinear interpolation algorithm of the present invention will be further illustrated by specific embodiments.

[0072] Example 1

[0073] Reference Figures 1-5 This invention discloses a method for compensating positioning errors of a coordinate measuring machine based on a nonlinear interpolation algorithm. The detailed steps are as follows:

[0074] Step 1: Collimation of the optical path of the dual-frequency laser interferometer: Fix the dual-frequency laser interferometer main unit 21 on the tripod 23 and place it on the ground, or secure it to the worktable of the coordinate measuring machine 1 using a special fixture; select the linear measurement shutter and install it at the light output port of the dual-frequency laser interferometer main unit 21, and at the same time install the reflector 22 at the lower end of the Z-axis 13 of the coordinate measuring machine using a special fixture; use the operating handle of the coordinate measuring machine 1 to move the coordinate measuring machine 1 to the zero point position of the axis to be calibrated, and adjust the coordinates of the other two axes so that the light emitted from the dual-frequency laser interferometer is reflected back to the incident light receiving port by the reflector, and the light intensity reaches the allowable range.

[0075] Lock the coordinates of the other two axes, use the operating handle to move the coordinate measuring machine 1 to the maximum travel position of the axis to be calibrated, adjust the pitch and yaw angles of the dual-frequency laser interferometer 2 so that the light emitted from the dual-frequency interferometer 2 is reflected back to the incident light receiving port through the reflector and the light intensity reaches the allowable range; repeat the above actions until the coordinate measuring machine 1 moves in the full travel range of the axis to be calibrated and the light intensity received by the incident light receiving port of the coordinate interferometer reaches the allowable range.

[0076] Step 2, Positioning Error Verification: Connect the environmental compensation unit of the dual-frequency laser interferometer 2, and attach the material temperature probe to the vicinity of the grating ruler installation position of the axis to be verified. Run the linear measurement program of the dual-frequency laser interferometer 2; set parameters such as the length of the axis to be verified, the measurement step distance, the grating ruler expansion coefficient, and the data acquisition method; use the control software of the coordinate measuring machine 1 to automatically move the machine tool to the zero position of the axis to be verified, and simultaneously clear the coordinates in the linear measurement software of the dual-frequency laser interferometer 2; click the start measurement button to start the verification process. The coordinate measuring machine 1 performs positioning movement with a fixed step distance, and the dual-frequency laser interferometer 2 records the positioning error value at each preset step position; the measurement adopts a bidirectional positioning method, and the arithmetic mean is taken as the final positioning error verification value.

[0077] It is understandable that the bidirectional positioning method used involves measuring the positioning error values ​​of each verification point from the zero-position verification point to the last-position verification point, and then measuring the positioning error values ​​of each verification point from the last-position verification point to the zero-position verification point. This method can reduce measurement errors and improve measurement accuracy.

[0078] Step 3, Input Positioning Error Verification Value into the System: Open the coordinate measuring machine error list file, manually input the positioning error verification value measured in Step 2 in the corresponding item list, save the file and exit after inputting.

[0079] Step four: Calculate the positioning error compensation data for the actual measurement point based on a nonlinear interpolation algorithm. Based on the coordinates of the actual measurement point, determine its position in the error table and extract the eight vertices of the smallest cubic error data unit 3 enveloping the point. The nonlinear interpolation algorithm that can be used includes, but is not limited to, Bézier curve interpolation, B-spline curve interpolation, general spline curve interpolation, and parabolic interpolation. In this embodiment, a cubic Bézier curve interpolation algorithm is used as an example. The specific method is as follows:

[0080] (1) Assuming the error verification step of the coordinate measuring machine 1 is S, and the verification steps of the coordinate measuring machine X-axis 12, Y-axis 11 and Z-axis 13 are Nx, Ny and Nz respectively, then the error space of the coordinate measuring machine 1 is divided into Nx*Ny*Nz cubic error data units 3 with side length S.

[0081] (2) Assume that the measured coordinates of a certain measurement point P in space are (Xp, Yp, Zp), and its coordinates fall into a certain error data unit. Its 8 vertices are named with letters, namely point A to point H. Then Xp∈(XA, XB), Yp∈(YA, YD), Zp∈(ZA, ZE).

[0082] (3) In the interval (XA, XB), XA and XB are used as the two endpoints of the cubic Bézier curve. Two additional control points are determined. The control points are set to satisfy that the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point are collinear. Thus, the first cubic Bézier curve containing Xp is determined.

[0083] (4) In the interval (YA, YD), YA and YD are used as the two endpoints of the cubic Bézier curve. Two additional control points are determined. The control points are set to satisfy that the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point are collinear. Thus, the second cubic Bézier curve containing Yp is determined.

[0084] (5) In the interval (ZA, ZE), ZA and ZE are used as the two endpoints of the cubic Bézier curve. Two additional control points are determined. The control points are set to satisfy that the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point are collinear. Thus, the third cubic Bézier curve containing Zp is determined.

[0085] (6) Substitute Xp, Yp, and Zp into the three cubic Bézier curve equations respectively to obtain the corresponding positioning error values ​​ΔXp, ΔYp, and ΔZp.

[0086] Step 5, Positioning Error Compensation: The positioning error values ​​of the measurement point in the X, Y, and Z directions, calculated using a nonlinear interpolation algorithm, are added to the actual X, Y, and Z coordinates of the measurement point to obtain the compensated coordinate values ​​of the actual measurement point. That is, the compensated positioning error coordinates of measurement point P in the example from Step 4 are (Xp + ΔXp, Yp + ΔYp, Zp + ΔZp).

[0087] In Example 1, a crucial property of Bézier curves is that their starting (ending) point is tangent to the first (last) segment of the Bézier polygon. Therefore, if a curve is composed of multiple Bézier curve segments, and in two adjacent Bézier curves, the last segment of the preceding segment and the first segment of the following segment are collinear, then the junction of the two segments will not have jagged edges. Figure 3 The diagram shows the effect of connecting two collinear Bézier curve segments: O is the midpoint of line segment O2O3, the curve between point O1 and point O represents one Bézier curve segment, and line segment O2O is the node of this Bézier curve segment; the curve between point O and point O4 represents another Bézier curve segment, OO3 is the node of this Bézier curve segment, and point O4 is the connection point of the two Bézier curve segments. As can be seen from the diagram, the two Bézier curve segments can be regarded as a smooth curve, that is, the control point setting satisfies that the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point are collinear.

[0088] Example 2:

[0089] Reference Figure 1 , Figure 2 , Figure 4 and Figure 6 This invention discloses a method for compensating positioning errors of a coordinate measuring machine based on a nonlinear interpolation algorithm. The detailed steps are as follows:

[0090] Step 1: Collimation of the dual-frequency laser interferometer's optical path: Fix the dual-frequency laser interferometer main unit 21 on the tripod 23 and place it on the ground, or secure it to the table of the coordinate measuring machine (CMM) using a special fixture; select the linear measurement shutter and install it at the output port of the laser interferometer main unit 21, and simultaneously install the reflector 22 to the lower end of the CMM's Z-axis 13 using a special fixture; use the CMM 1 operating handle to move the CMM 1 to the zero point position of the axis to be calibrated, and adjust the coordinates of the other two axes so that the light emitted from the dual-frequency laser interferometer 2 passes through... The reflector reflects the light back to the incident light receiver, ensuring the light intensity is within the allowable range. The remaining two axes are locked. The coordinate measuring machine 1 is moved to the maximum travel position of the axis to be calibrated using the operating handle. The pitch and yaw angles of the dual-frequency laser interferometer 2 are adjusted so that the light emitted from the dual-frequency laser interferometer 2 is reflected back to the incident light receiver through the reflector, ensuring the light intensity is within the allowable range. This process is repeated until the light intensity received by the incident light receiver of the dual-frequency laser interferometer 2 reaches the allowable range when the coordinate measuring machine 1 moves across the full travel range of the axis to be calibrated.

[0091] Step 2, Positioning Error Verification: Connect the environmental compensation unit of the dual-frequency laser interferometer 2, and attach the material temperature probe to the vicinity of the grating ruler installation position of the axis to be verified. Run the linear measurement program of the laser interferometer 2; set parameters such as the length of the axis to be verified, the measurement step distance, the grating ruler expansion coefficient, and the data acquisition method; use the control software of the coordinate measuring machine 1 to automatically move the machine tool to the zero position of the axis to be verified, and simultaneously clear the coordinates in the linear measurement software of the dual-frequency laser interferometer 2; click the start measurement button to start the verification process. The coordinate measuring machine 1 performs positioning movement with a fixed step distance, and the dual-frequency laser interferometer 2 records the positioning error value at each preset step position; the measurement adopts a bidirectional positioning method, and the arithmetic mean is taken as the final positioning error verification value.

[0092] Step 3, Input Positioning Error Verification Value into the System: Open the error list file of the coordinate measuring machine 1, manually input the positioning error verification value measured in Step 2 in the corresponding item list, save the file and exit after inputting.

[0093] Step four: Calculate the positioning error compensation data for the actual measurement point based on a nonlinear interpolation algorithm. Based on the coordinates of the actual measurement point, determine its position in the error table and extract the eight vertices of the smallest cubic error data unit 3 enveloping the point. The nonlinear interpolation algorithm that can be used includes, but is not limited to, Bézier curve interpolation, B-spline curve interpolation, general spline curve interpolation, and parabolic interpolation. In this embodiment, a cubic spline curve interpolation algorithm is used as an example. The specific method is as follows:

[0094] (1) Assuming the error verification step of the coordinate measuring machine 1 is S, and the verification steps of the X-axis, Y-axis and Z-axis of the measuring machine are Nx, Ny and Nz respectively, then the error space of the coordinate measuring machine 1 is divided into Nx*Ny*Nz cubic error data units 3 with a side length of S.

[0095] (2) Assume that the measured coordinates of a certain measurement point P in space are (Xp, Yp, Zp), and its coordinates fall into a certain error data unit 3. Its 8 vertices are named with letters, namely point A to point H. Then Xp∈(XA, XB), Yp∈(YA, YD), Zp∈(ZA, ZE).

[0096] (3) A cubic spline curve can be represented as:

[0097] y = ax 3 +bx 2 +cx+d

[0098] Wherein, a, b, c, and d are coefficients in each of the cubic spline curve equations, and x is a measurement point in a certain error data unit;

[0099] Then, a cubic spline curve is inserted between every two shape points, that is, Nx cubic splines can be inserted along the X-axis, Ny cubic splines along the Y-axis, and Nz cubic splines along the Z-axis.

[0100] (4) Taking the X-axis direction as an example, in order to solve Nx cubic splines, 4*Nx unknowns need to be determined, that is, 4*Nx equations need to be solved.

[0101] (5) Based on the following constraints, all 4*Nx equations can be listed:

[0102] Each of the cubic spline curves passes through the two endpoints of its curve.

[0103] The left and right first derivatives at the interpolation point are equal.

[0104] The second derivatives on the left and right sides of the interpolation point are equal.

[0105] The third derivative value of the first interpolation point is equal to the third derivative value of the second interpolation point, and finally the third derivative value of the first interpolation point is equal to the third derivative value of the penultimate interpolation point.

[0106] (6) Based on the known X-axis positioning error value, all Nx cubic spline curves can be calculated.

[0107] (7) Find the cubic spline curve equation of the cubic error data cell where the X coordinate of the measurement point P is located, substitute the Xp value, and the corresponding positioning error value ΔXp can be calculated.

[0108] (8) The cubic spline solution method in the Y-axis and Z-axis directions is similar to that in the X-axis. The positioning errors ΔYp and ΔZp corresponding to the Y and Z coordinates of the measurement point P can also be calculated.

[0109] Step 5, Positioning Error Compensation: The positioning error values ​​of the measurement point in the X, Y, and Z directions, calculated using a nonlinear interpolation algorithm, are added to the actual X, Y, and Z coordinates of the measurement point to obtain the compensated coordinate values ​​of the actual measurement point. That is, the compensated positioning error coordinates of measurement point P in the example from Step 4 are (Xp + ΔXp, Yp + ΔYp, Zp + ΔZp).

[0110] The above embodiments employ two different nonlinear interpolation algorithms: cubic Bézier curve interpolation and cubic spline curve interpolation. Analysis of the results shows that... Figure 5 , Figure 6 As shown, the error curve obtained by cubic spline interpolation is smoother and the estimation of positioning error is more accurate.

[0111] When using other nonlinear interpolation methods (including but not limited to B-spline interpolation, parabolic interpolation, etc.) to compensate for the positioning error of the coordinate measuring machine 1, the operation steps are the same as those in the above case.

[0112] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for compensating positioning errors of a coordinate measuring machine based on a nonlinear interpolation algorithm, characterized in that, The geometric errors of the coordinate measuring machine include 3 positioning errors, 6 straightness errors, 9 angular errors, and 3 perpendicularity errors; the method includes the following steps: Install the laser interferometer and coordinate measuring machine to the target position according to the preset installation plan; The calibration direction is determined based on the installation positions of the laser interferometer and the coordinate measuring machine, and multiple calibration points are created within the calibration direction according to preset rules. The coordinate measuring machine is moved sequentially to each of the calibration points according to the preset plan, and the positioning error value at each calibration point is measured using the laser interferometer. The positioning error values ​​obtained by the laser interferometer are stored in the coordinate measuring machine error table file; The error space of the coordinate measuring machine is divided into several error data units; Obtain the coordinate values ​​of the actual measurement point from the coordinate measuring machine, and extract the vertex containing the error compensation data unit of the actual measurement point from the coordinate measuring machine error table file; The positioning error value of the actual measurement point is calculated using a nonlinear interpolation algorithm. The calculated positioning error value is then added to the coordinate value of the actual measurement point to obtain the compensated coordinate value of the actual measurement point. The nonlinear interpolation algorithm includes the Bézier curve interpolation method. The steps for calculating the positioning error value of the actual measurement point using the Bézier curve interpolation method include: Let each pair of vertices be the starting and ending points of a cubic Bézier curve. The two control points are obtained by the collinearity of the connection point of two adjacent Bézier curves and the control points on the left and right sides of the connection point, wherein the Bézier curves and the two control points are enclosed within the error data unit; Draw a cubic Bézier curve passing through the starting point and the ending point based on the starting point, the ending point and the two control points; Substituting the coordinates of the actual measurement point into the cubic Bézier curve equation, the positioning error values ​​of the actual measurement point in the three directions are obtained. The calculated positioning error values ​​are added to the coordinate values ​​of the actual measurement point to obtain the compensated coordinate values ​​of the actual measurement point. The steps for calculating the positioning error of actual measurement points using cubic spline interpolation include: Create a cubic spline curve equation in each of the error data cells: y=ax 3 +bx 2 +cx+d Wherein, a, b, c, and d are coefficients in each cubic spline curve equation, and x is a measurement point in a certain error data unit; Based on the interpolation conditions, list the equation which is the number of error data units multiplied by the number of four unknowns; Calculate the cubic spline curve based on the known positioning error values ​​of the calibration points; Find the cubic spline curve equations in the error data units containing the X, Y, and Z axes of each actual measurement point, substitute them with the measured values ​​of the actual measurement points, and calculate the corresponding positioning error values; add the calculated positioning error values ​​to the coordinate values ​​of the actual measurement points to obtain the compensated coordinate values ​​of the actual measurement points; The interpolation conditions include: each cubic spline curve passes through its two endpoints, the left and right first derivatives of the interpolation points are equal, the left and right second derivatives of the interpolation points are equal, the third derivative value of the first interpolation point is equal to the third derivative value of the second interpolation point, and finally, the third derivative value of the first interpolation point is equal to the third derivative value of the penultimate interpolation point.

2. The coordinate measuring machine positioning error compensation method based on nonlinear interpolation algorithm as described in claim 1, characterized in that, The nonlinear interpolation algorithms also include B-spline curve interpolation, general spline curve interpolation, and parabolic interpolation.

3. The coordinate measuring machine positioning error compensation method based on nonlinear interpolation algorithm as described in claim 1, characterized in that, The steps of moving the coordinate measuring machine sequentially to each calibration point according to a preset plan, and measuring the positioning error value at each calibration point using the laser interferometer include: An initial verification point and a final verification point are determined from a plurality of verification points distributed along a first direction; Starting from the initial calibration point, the coordinate measuring machine is moved sequentially along the first direction to other calibration points, and the positioning error value is measured at each calibration point using the laser interferometer. Starting from the initial calibration point, the coordinate measuring machine is moved along the second direction to the calibration point closest to the initial calibration point, and the above steps are repeated until the laser interferometer has measured all the calibration points and obtained the positioning error value of each calibration point.

4. The coordinate measuring machine positioning error compensation method based on nonlinear interpolation algorithm as described in claim 3, characterized in that, Also includes: Starting from the termination calibration point, the coordinate measuring machine is moved sequentially along the first direction to other calibration points, and the positioning error value is measured at each calibration point using the laser interferometer. Starting from the termination calibration point, the coordinate measuring machine is moved along the second direction to the calibration point closest to the termination calibration point, and the above steps are repeated until the laser interferometer has measured all the calibration points and obtained the positioning error value of each calibration point. The arithmetic mean of the positioning error value measured starting from the initial calibration point and the positioning error value measured starting from the final calibration point is taken as the final positioning error value.

5. The coordinate measuring machine positioning error compensation method based on nonlinear interpolation algorithm as described in claim 1, characterized in that, The steps for installing the laser interferometer and coordinate measuring machine to the target location according to the preset installation plan also include: A shutter sensor is installed at the light output port of the laser interferometer, and a reflector is installed at the lower end of the Z-axis of the coordinate measuring machine. Adjust the positions of the laser interferometer and the coordinate measuring machine until the light intensity received by the incident light receiver of the laser interferometer reaches the allowable range when the coordinate measuring machine moves across the full stroke range of all axes to be calibrated.

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