A method and application for location-related geometric error identification based on multidimensional measurement data fusion

Abstract

This invention discloses a method and application for identifying position-related geometric errors based on multi-dimensional measurement data fusion. The method includes: constructing an actual motion model of the machine tool rotary axis B-axis under the influence of geometric errors based on dual quaternions, and obtaining the first actual position of the tool end target ball in the machine tool coordinate system; determining the second actual position of the tool end target ball in the machine tool coordinate system based on dual quaternions, and obtaining coordinate value expressions of the X, Y, and Z directions of the measurement points of the rotary axis B-axis in the machine tool coordinate system related to position-related geometric errors and position-independent geometric errors; obtaining the coordinates of the measurement points in the built-in coordinate system of the laser tracker using a laser tracker; constructing a least-squares model of geometric errors and the actual distance between the measurement points of the rotary axis B-axis, and solving it using the Powell algorithm; this invention significantly improves the measurement efficiency of the rotary axis.

Description

Technical Field

[0001] This invention belongs to the field of error identification technology for rotary axes of five-axis machine tools, and particularly relates to a method for identifying position-related geometric errors based on the fusion of multi-dimensional measurement data. Background Technology

[0002] Compared to three-axis machine tools, five-axis machine tools can machine workpieces from any direction, significantly improving machining efficiency. However, the additional rotary axis also introduces additional error sources. Methods for obtaining the geometric error of a rotary axis can be divided into direct measurement and indirect measurement. Direct measurement involves obtaining the geometric error of the rotary axis directly through developed instruments and equipment. However, directly measuring all error terms of a rotary axis is very complex and time-consuming. Therefore, indirect measurement was developed to improve the calibration efficiency of rotary axes. This method obtains actual measurement data under the influence of geometric errors through measuring instruments, constructs an identification model to link unknown error values ​​with the measurement data, and then applies mathematical algorithms to obtain the geometric error value that satisfies the identification model. Therefore, this method is also known as error identification.

[0003] For error identification methods, existing measuring instruments are generally laser trackers. Methods using laser trackers for error identification require measuring the positions of three nonlinear target spheres to obtain sufficient 3D position data or 6D pose data to identify geometric errors. This is mainly because the position-related geometric error values ​​differ at different positions; each additional measurement position adds six position-related geometric error values. A 3D identification model built using only one target sphere is insufficient to calculate these six position-related geometric errors at different positions. Therefore, multiple measurements are needed to construct and solve additional position or attitude identification equations. This method requires each base station to be measured three times, significantly reducing measurement efficiency, and the measurement results are more susceptible to the influence of machine tool repeatability accuracy. Summary of the Invention

[0004] The purpose of this invention is to propose a position-related geometric error identification method based on multi-dimensional measurement data fusion. This method measures the actual coordinates of the target ball in the tracker's coordinate system using a laser tracker, then calculates the Euclidean distance between every two measurement positions, constructs an identification model that includes geometric error and Euclidean distance between measurement positions, transforms it into a least squares problem, and calculates the error value.

[0005] To address the problems existing in the background art, the present invention adopts the following technical solution:

[0006] The location-related geometric error identification method based on multidimensional measurement data fusion includes the following steps:

[0007] Step S1: Construct an actual motion model of the machine tool rotary axis B under the influence of geometric errors based on dual quaternions. Based on the actual motion model, obtain the first actual position of the target ball at the tool in the machine tool coordinate system. ;

[0008] Step S2: Determine the second actual position of the target ball at the tool location in the machine tool coordinate system based on the dual quaternion. Combined with the first actual position of the target ball at the tool location in the machine tool coordinate system obtained in step S1 The coordinate values ​​of the measurement points on the B-axis of the rotary axis in the machine tool coordinate system are obtained, which are related to both position-dependent and position-independent geometric errors.

[0009] S3. Install the laser tracker in front of the machine tool to obtain the coordinate values ​​of each machine tool measurement point in the built-in coordinate system of the laser tracker. Rotate the machine tool's B-axis and measure to obtain several measurement points. Perform multiple measurements on each measurement point and use the laser tracker to obtain the coordinates of the measurement points in the built-in coordinate system of the laser tracker.

[0010] Step S4: Construct a least-squares model for geometric errors and the actual distance between measurement points along the rotation axis B, and solve it using the Powell algorithm to obtain the position-related geometric errors of the measurement points.

[0011] The expression for the least squares model is as follows:

[0012] ;

[0013] in, , These represent the maximum actual number of measurements for the i-th and j-th measurement points, respectively. ; and These are the coordinates of the i-th and j-th measurement points in the built-in coordinate system of the laser tracker, respectively. Represents the Euclidean distance between the i-th and j-th measurement points: ;in, , and Let X, Y, and Z represent the coordinates of the i-th measurement point in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, respectively. , and These represent the X, Y, and Z coordinates of the j-th measurement point in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, respectively.

[0014] Furthermore, the expressions for the X, Y, and Z coordinate values ​​of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, which are related to both position-dependent and position-independent geometric errors in step S2, are as follows:

[0015]

[0016] in, , , These represent the X, Y, and Z coordinate values ​​of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, respectively. , , , , and These represent the six position-related geometric errors of the rotation axis B, which are expressed as third-order polynomials related to the angle of the B-axis. , , and These represent the four position-independent geometric errors of the rotation axis B; and These represent the initial X and Z positions of the tool in the machine tool coordinate system, respectively. This indicates the rotation angle of the rotation axis B.

[0017] Furthermore, in step S1, the first actual position of the target ball at the tool location in the machine tool coordinate system is obtained. The method is as follows:

[0018] Step S1.1: The ideal motion of the rotation axis B can be represented by dual quaternions:

[0019] ;

[0020] in, The dual quaternion representing the ideal motion of the rotation axis B; Represents the rotation angle of the rotation axis B; The space vector [0,1,0] represents the rotation axis B. For dual symbols, but ; Represents the zero vector;

[0021] Step S1.2: Dual quaternion form of the actual motion of the machine tool rotary axis B under the influence of geometric errors. This can be characterized as a dual quaternion of geometric error independent of the B-axis position of the machine tool rotation axis. Dual quaternions of geometric errors related to the position of the machine tool's B-axis rotation axis The dual quaternion of the ideal motion of the machine tool's B-axis rotation axis The product of:

[0022] ;

[0023] Step S1.3: Install the target ball at the machine tool cutting tool. While the machine tool's B-axis rotates, the X-axis and Y-axis remain stationary. The first actual position of the target ball at the cutting tool end in the machine tool coordinate system. It can be represented as:

[0024] ;

[0025] in, represent The conjugate; This represents the initial position of the tool relative to the machine tool coordinate system, where... and These represent the initial X and Z positions of the tool in the machine tool coordinate system, respectively.

[0026] Furthermore, in step S2, the second actual position of the target ball at the tool position in the machine tool coordinate system is determined based on the dual quaternion. for:

[0027] ;

[0028] in, Represents a unit vector with a magnitude of 1; , , These represent the coordinate values ​​in the X, Y, and Z directions of the machine tool coordinate system, respectively.

[0029] Furthermore, when obtaining the coordinate values ​​of the X, Y, and Z directions of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system related to position-dependent geometric errors and position-independent geometric errors, it is based on the first actual position obtained in step S1. and the second actual position obtained in step S2 The actual positions represented are the same, thus obtaining , and Expressions for position-dependent and position-independent geometric errors of the rotation axis B and the initial position of the tool.

[0030] Furthermore, the dual quaternion of geometric error independent of the machine tool rotary axis B-axis position. Dual quaternions of geometric errors related to the position of the machine tool's B-axis rotation axis The expression is as follows:

[0031] ;

[0032] ;

[0033] in, The dual quaternion representing the four position-independent geometric errors of the machine tool's B-axis rotary axis. ; The dual quaternion representing the six position-related geometric errors of the B-axis of a machine tool. .

[0034] The above-mentioned method for identifying position-related geometric errors based on multidimensional measurement data fusion is used to identify the numerical values ​​of six position-related geometric errors of a five-axis machine tool.

[0035] The beneficial technical effects of this invention are as follows:

[0036] The method proposed in this invention is applicable to the rotary axes of any five-axis machine tool. The position-related geometric error of any rotary axis can be obtained by fusing measurement data. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a five-axis machining center provided in an embodiment of the present invention; Detailed Implementation

[0038] The location-related geometric error identification method and its application based on multidimensional measurement data fusion provided by the present invention will be further described clearly and completely below with reference to the accompanying drawings, and detailed in conjunction with the following specific embodiments:

[0039] The location-related geometric error identification method based on multidimensional measurement data fusion provided in this embodiment includes the following steps:

[0040] Step S1: Construct an actual motion model of the machine tool rotary axis B under the influence of geometric errors based on dual quaternions; based on the actual motion model, obtain the first actual position of the target ball at the tool in the machine tool coordinate system; specifically including the following steps:

[0041] Step S1.1: The ideal motion of the rotation axis B can be represented by dual quaternions:

[0042] ;

[0043] in, The dual quaternion representing the ideal motion of the rotation axis B; Represents the rotation angle of the rotation axis B; The space vector [0,1,0] represents the rotation axis B. For dual symbols, but ; Represents the zero vector;

[0044] Step S1.2: According to ISO 230-1, the dual quaternion form of the actual motion of the machine tool rotary axis B under the influence of geometric errors. This can be characterized as a dual quaternion of geometric error independent of the B-axis position of the machine tool rotation axis. Dual quaternions of geometric errors related to the position of the machine tool's B-axis rotation axis The dual quaternion of the ideal motion of the machine tool's B-axis rotation axis The product of:

[0045] ;

[0046] ;

[0047] ;

[0048] in, The dual quaternion representing the four position-independent geometric errors of the machine tool's B-axis rotary axis. The dual quaternion representing the six position-related geometric errors of the B-axis of a machine tool;

[0049] It should be noted that the relevant provisions in ISO 230-1 can be referenced in standard BS ISO 230-1:2012 Testcode for machine tools Part 1: Geometric accuracy of machines operating under no-load or quasi-static conditions;

[0050] Step S1.3: Install the target ball at the machine tool cutting tool. When the machine tool's rotary axis B rotates, the X-axis and Y-axis (here, the X-axis and Y-axis are related to...) Figure 1 (With the X and Y directions aligned) the target ball remains stationary, and the first actual position of the target ball at the tool location in the machine tool coordinate system is... It can be represented as:

[0051] ;

[0052] in, represent The conjugate; This represents the initial position of the tool relative to the machine tool coordinate system, where... and These represent the initial X and Z positions of the tool in the machine tool coordinate system, respectively.

[0053] Step S2: Determine the second actual position of the target ball at the tool location in the machine tool coordinate system based on the dual quaternion. :

[0054] ;

[0055] in, Represents a unit vector with a magnitude of 1; , , These represent the coordinate values ​​in the X, Y, and Z directions of the machine tool coordinate system, respectively.

[0056] It should be noted that the second actual position of the target ball at the tool location in the machine tool coordinate system is based on the dual quaternion. The method for obtaining the error can be found in the paper Yao S, Dai Y, Tian W, et al. Rapid error identification for rotary axis based on distance errors[J]. Journal of Manufacturing Processes, 2026, 158: 65-73. The process can be considered a publicly available technology.

[0057] Based on the first actual position obtained in step S1 and the second actual position obtained in step S2 The coordinate values ​​of the measurement points on the B-axis of the machine tool in the machine tool coordinate system are obtained, relating to the six position-dependent geometric errors and four position-independent geometric errors of the B-axis:

[0058]

[0059] in, , , These represent the X, Y, and Z coordinate values ​​of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, respectively. , , , , and These represent the six position-related geometric errors of the rotation axis B, which are expressed as third-order polynomials related to the angle of the B-axis. , , and These represent the four position-independent geometric errors of the rotation axis B; and These represent the initial X and Z positions of the tool in the machine tool coordinate system, respectively. This indicates the rotation angle of the rotation axis B;

[0060] It should be explained that when obtaining the coordinate values ​​of the measurement points of the B-axis in the machine tool coordinate system related to the six position-dependent geometric errors and four position-independent geometric errors of the B-axis, the first actual position obtained in step S1 is used. and the second actual position obtained in step S2 The actual positions are the same, so the coordinate values ​​of the measurement points on the rotation axis B are obtained from the X, Y, and Z directions, thus yielding... , and The expressions for the six position-dependent geometric errors and four position-independent geometric errors of the B-axis rotary axis, as well as the initial position of the tool, can be obtained by referring to the paper (Yao S, Dai Y, Tian W, et al. Rapid error identification for rotary axis based on distance errors[J]. Journal of Manufacturing Processes, 2026, 158: 65-73.).

[0061] Step S3: Install the laser tracker in front of the machine tool to obtain the coordinate values ​​of each machine tool measurement point in the built-in coordinate system of the laser tracker. Rotate the machine tool's B-axis and measure to obtain several measurement points. Perform multiple measurements on each measurement point and use the laser tracker to obtain the coordinates of the measurement points in the built-in coordinate system of the laser tracker.

[0062] It should be noted that the coordinates of the measurement point on the B-axis of the rotation are within the built-in coordinate system of the laser tracker. The coordinates of the i-th and j-th measurement points in the laser tracker's built-in coordinate system can be directly measured using a laser tracker. and The coordinate values ​​of the measurement points will change due to coordinate system transformation, but the Euclidean distance between the measurement points is not affected by coordinate system transformation of the same scale. Therefore, the Euclidean distance between the i-th and j-th measurement points in the built-in coordinate system of the laser tracker is equal to the Euclidean distance between the i-th and j-th measurement points in the machine tool coordinate system.

[0063] Step S4: Construct a least-squares model for geometric errors and the actual distance between measurement points along the rotation axis B, and solve it using the Powell algorithm to obtain the position-related geometric errors of the measurement points.

[0064] Specifically, the expression for the least squares model is as follows:

[0065] ;

[0066] in, , These represent the maximum actual number of measurements for the i-th and j-th measurement points, respectively. ; and These are the coordinates of the i-th and j-th measurement points in the built-in coordinate system of the laser tracker, respectively. This represents the Euclidean distance between the i-th and j-th measurement points in the machine tool coordinate system. ;in, , and Let X, Y, and Z represent the coordinates of the i-th measurement point in the machine tool coordinate system, respectively. , and These represent the coordinates of the j-th measurement point in the X, Y, and Z directions of the machine tool coordinate system, respectively.

[0067] When solving the above least squares model, the coordinate values ​​of the X, Y and Z directions of the measurement point of the rotation axis B need to be replaced with the coordinate expressions related to the 6 position-related geometric errors and 4 position-independent geometric errors of the machine tool rotation axis B obtained in step S2, and then the solution is performed. This nonlinear least squares problem can be solved by the Powell algorithm.

[0068] As an example, in this embodiment, when identifying the position-related geometric errors of the five-axis machine tool's rotary axis using the above method, a target ball needs to be installed at the machine tool's cutting tool, and a laser tracker needs to be installed in front of the machine tool to obtain the coordinate values ​​of each machine tool measurement point in the laser tracker's built-in coordinate system. When the machine tool's rotary axis B rotates, it can be considered that a measurement is performed every 5° of rotation, with a rotation range of -90° to 0°, thereby obtaining several measurement points and obtaining the coordinates of the measurement points in the laser tracker's built-in coordinate system. The Euclidean distance expression between two points related to the position-related geometric errors and position-independent geometric errors of the machine tool's rotary axis B is obtained, thereby constructing a least squares model and solving the least squares problem using the Powell algorithm.

[0069] The method proposed in this invention is applicable to the rotary axes of any five-axis machine tool. By fusing measurement data, six position-related geometric errors of any rotary axis can be obtained.

[0070] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for identifying location-related geometric errors based on multidimensional measurement data fusion, characterized in that, Includes the following steps: Step S1: Construct an actual motion model of the machine tool rotary axis B under the influence of geometric errors based on dual quaternions. Based on the actual motion model, obtain the first actual position of the target ball at the tool in the machine tool coordinate system. ; Step S2: Determine the second actual position of the target ball at the tool location in the machine tool coordinate system based on the dual quaternion. Combined with the first actual position of the target ball at the tool location in the machine tool coordinate system obtained in step S1 The coordinate values ​​of the measurement points of the B-axis of the rotary axis in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, are expressed as follows: S3. Install the laser tracker in front of the machine tool to obtain the coordinate values ​​of each machine tool measurement point in the built-in coordinate system of the laser tracker. Rotate the machine tool's B-axis and measure to obtain several measurement points. Perform multiple measurements on each measurement point and use the laser tracker to obtain the coordinates of the measurement points in the built-in coordinate system of the laser tracker. Step S4: Construct a least-squares model for geometric errors and the actual distance between measurement points along the rotation axis B, and solve it using the Powell algorithm to obtain the position-related geometric errors of the measurement points. The expression for the least squares model is as follows: ； in, , These represent the maximum actual number of measurements for the i-th and j-th measurement points, respectively. ; and These are the coordinates of the i-th and j-th measurement points in the built-in coordinate system of the laser tracker, respectively. Represents the Euclidean distance between the i-th and j-th measurement points: ;in, , and Let X, Y, and Z represent the coordinates of the i-th measurement point in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, respectively. , and These represent the X, Y, and Z coordinates of the j-th measurement point in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, respectively.

2. The location-related geometric error identification method based on multi-dimensional measurement data fusion according to claim 1, characterized in that, The coordinate values ​​of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, which are related to both position-dependent and position-independent geometric errors in step S2, are expressed as follows: ； in, , , These represent the X, Y, and Z coordinate values ​​of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, respectively. , , , , and These represent the six position-related geometric errors of the rotation axis B, which are expressed as third-order polynomials related to the angle of the B-axis. , , and These represent the four position-independent geometric errors of the rotation axis B. and These represent the initial X and Z positions of the tool in the machine tool coordinate system, respectively. This indicates the rotation angle of the rotation axis B.

3. The location-related geometric error identification method based on multi-dimensional measurement data fusion according to claim 1, characterized in that, In step S1, the first actual position of the target ball at the tool location in the machine tool coordinate system is obtained. The method is as follows: Step S1.1: The ideal motion of the rotation axis B can be represented by dual quaternions: ； in, The dual quaternion representing the ideal motion of the rotation axis B; Represents the rotation angle of the rotation axis B; The space vector [0,1,0] represents the rotation axis B. For dual symbols, but ; Represents the zero vector; Step S1.2: Dual quaternion form of the actual motion of the machine tool rotary axis B under the influence of geometric errors. This can be characterized as a dual quaternion of geometric error independent of the B-axis position of the machine tool rotation axis. Dual quaternions of geometric errors related to the position of the machine tool's B-axis rotation axis The dual quaternion of the ideal motion of the machine tool's B-axis rotation axis The product of: ； Step S1.3: Install the target ball at the machine tool cutting tool. While the machine tool's B-axis rotates, the X-axis and Y-axis remain stationary. The first actual position of the target ball at the cutting tool end in the machine tool coordinate system. It can be represented as: ； in, represent The conjugate; This represents the initial position of the tool relative to the machine tool coordinate system, where... and These represent the initial X-axis and Z-axis positions of the tool in the machine tool coordinate system, respectively.

4. The location-related geometric error identification method based on multi-dimensional measurement data fusion according to claim 3, characterized in that, In step S2, the second actual position of the target ball at the tool location in the machine coordinate system based on dual quaternions. for: ； in, Represents a unit vector with a magnitude of 1; , , These represent the coordinate values ​​in the X, Y, and Z directions of the machine tool coordinate system, respectively.

5. The location-related geometric error identification method based on multi-dimensional measurement data fusion according to claim 4, characterized in that, When obtaining the coordinate values ​​of the X, Y, and Z directions of the measurement point on the B-axis of the rotary axis in the machine tool coordinate system, which are related to position-dependent geometric errors and position-independent geometric errors, the first actual position obtained in step S1 is used. and the second actual position obtained in step S2 The actual positions represented are the same, thus obtaining , and Expressions for position-dependent and position-independent geometric errors of the rotation axis B and the initial position of the tool.

6. The location-related geometric error identification method based on multi-dimensional measurement data fusion according to claim 3, characterized in that, Machine tool rotary axis B-axis position-independent geometric error dual quaternion Dual quaternions of geometric errors related to the position of the machine tool's B-axis rotation axis The expression is as follows: ； ； in, The dual quaternion representing the four position-independent geometric errors of the machine tool's B-axis rotary axis. ; The dual quaternion representing the six position-related geometric errors of the B-axis of a machine tool. .

7. The application of the location-related geometric error identification method based on multidimensional measurement data fusion as described in any one of claims 1-6, characterized in that, The method is used to identify six position-related geometric errors of a five-axis machine tool.

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