Rotating shaft geometric error identification method based on laser tracking interferometer ranging data

Abstract

This invention discloses a method for identifying the geometrical error of a rotating axis based on ranging data from a laser-tracking interferometer. The method includes the following steps: mounting the laser-tracking interferometer on a machine tool worktable, mounting a reflector on the machine tool tool, and calibrating the center coordinates of the reflector and the dead travel length of the laser-tracking interferometer; obtaining the actual coordinate values ​​of the measurement point in the X, Y, and Z directions in the machine tool coordinate system, which are related to six position-dependent geometrical errors and four position-independent geometrical errors of the C-axis of the machine tool rotating axis, based on the actual position of the workpiece coordinate system in the machine tool coordinate system; constructing an error identification model based on ranging data, and solving it using the Powell algorithm to obtain the six position-dependent geometrical errors and four position-independent geometrical errors of the C-axis of the machine tool rotating axis; the method proposed in this invention significantly improves measurement efficiency while ensuring the accuracy of the measurement data.

Description

Technical Field

[0001] This invention belongs to the field of error identification technology for rotary axes of five-axis machine tools, and in particular, a method for identifying geometric errors of rotary axes based on distance measurement data from a laser tracking interferometer. Background Technology

[0002] The increasing demand for manufacturing precision in fields such as aerospace and automotive manufacturing places higher demands on the machining accuracy of five-axis machine tools. Geometric errors of machine tools have become one of the main factors restricting machining accuracy. These geometric errors include position-independent geometric errors between axes and six position-dependent geometric errors for each motion axis. Position-independent geometric errors cause deviations between the actual and ideal axes of the motion axes, while position-dependent geometric errors result in erroneous motion along the six degrees of freedom of the actual axis. These geometric errors lead to deviations in the relative position and orientation between the machine tool and the workpiece, thereby reducing the machining accuracy of the machine tool.

[0003] For geometric error identification of rotation axes, measuring instruments are mainly used to obtain distance errors, three-dimensional position errors, and six-dimensional pose errors caused by geometric errors, and then construct corresponding identification models to calculate error values. Distance errors are mostly measured using ballbars. Due to their simple installation and ease of use, ballbars are widely used for error identification of rotation axes. However, the installation error of ballbars is difficult to completely eliminate, and the instrument is limited by the fixed rod length, which affects the effectiveness of the identification results and the versatility of the identification method.

[0004] Three-dimensional position error and six-dimensional pose error are often measured using laser tracking interferometers. However, due to limitations in the repeatability of motion axes, the target under test is unlikely to reach the same position in every measurement, which introduces the influence of motion axis repeatability on the measurement results. Therefore, it is necessary to propose a measurement scheme that minimizes the number of measurement base stations while using only distance measurement data, thereby improving measurement efficiency while ensuring the accuracy of the measurement data. Summary of the Invention

[0005] The purpose of this invention is to propose a method for identifying the geometric error of the rotation axis based on the center calibration of the reflector. This method identifies the error based on the distance data obtained by a single-base station laser tracking interferometer, constructs a distance error model between the center of the reflector and the actual position of the measurement point, and finally establishes an error identification model based on the distance measurement data. Through this model, ten geometric errors of the rotation axis can be identified simultaneously.

[0006] To address the problems existing in the background art, the present invention adopts the following technical solution:

[0007] The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data includes the following steps:

[0008] The laser tracking interferometer is installed on the machine tool table, and the reflector is installed at the machine tool tool. The center coordinates of the reflector and the dead travel length of the laser tracking interferometer are calibrated.

[0009] Based on the actual position of the workpiece coordinate system in the machine tool coordinate system, obtain the expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, which are related to the six position-dependent geometric errors and four position-independent geometric errors of the machine tool rotary axis C.

[0010] An error identification model based on ranging data was constructed and solved using the Powell algorithm to obtain six position-dependent geometric errors and four position-independent geometric errors of the machine tool's C-axis rotary axis. The method for constructing the error identification model is as follows:

[0011] The machine tool's C-axis rotates and distance values ​​are measured using an installed laser tracking interferometer to obtain several measurement points. An overdetermined set of equations is constructed between the Euclidean distance between the center of the reflector and the measurement points on the C-axis and the measurement data. This is then further transformed into a least squares problem.

[0012] ;

[0013] in, This represents the maximum number of actual measurements taken at each measurement point. The actual coordinates of the measurement point on the C-axis of rotation. , This represents the calculation of the Euclidean distance between the actual coordinates of the measurement point on the C-axis of rotation and the center of the reflector. The coordinates of the center of the reflector in the machine tool coordinate system are: This is the dead-path length of the laser tracking interferometer. The distance measurement data of the laser tracking interferometer at the i-th measurement point.

[0014] Furthermore, the expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, related to the six position-dependent geometric errors and four position-independent geometric errors of the machine tool rotary axis C, are as follows:

[0015] ;

[0016] in, , and These are the actual coordinates of the measurement point along the C-axis of rotation in the X, Y, and Z directions, respectively. , and These represent the initial positions of the workpiece coordinate system relative to the machine tool coordinate system in the X, Y, and Z directions, respectively; , , , , and These represent the six position-related geometric errors of the rotation axis C; , , and These represent the four position-independent geometric errors of the rotation axis C; This indicates the rotation angle of the rotation axis C.

[0017] Furthermore, the method for calibrating the center coordinates of the reflector and the dead path length of the laser tracking interferometer is as follows:

[0018] Define the origin of the machine tool coordinate system and obtain the theoretical initial installation position of the reflector. The distance value measured at the theoretical initial installation position of the reflector using a laser tracking interferometer is [value missing]. ;

[0019] The reflector is moved to different positions by moving the machine tool along the X, Y, and Z axes, and the distance values ​​are measured. For the nth measurement position, the relevant X, Y, and Z axis movements are as follows: , and Then the nth measurement position of the reflector The theoretical coordinates are Distance measurement data was obtained through a tracking interferometer. Move the instrument to at least six positions, and then calibrate the initial installation position of the laser tracking interferometer using a formula. :

[0020] ;

[0021] in, This represents the initial installation position of the laser tracking interferometer in the machine tool coordinate system. Let be the coordinates of the center of the nth measurement position of the reflector in the machine tool coordinate system; This represents the Euclidean distance between two coordinates;

[0022] Solve the system of linear equations to obtain the initial installation position. and dead distance length ;

[0023] The initial coordinates of the laser tracking interferometer obtained from the above solution are... and Using the initial value as the initial value, and through continuous iterative optimization, an optimal set of values ​​is found. The value of minimizes the sum of squares of the difference between the theoretical distance and the actual measured distance, thus bringing the results to convergence.

[0024] Furthermore, the initial coordinates of the laser tracking interferometer are obtained by solving. and Using the initial value as the initial value, and through continuous iterative optimization, an optimal set of values ​​is found. The method to minimize the sum of squares of the differences between the theoretical distance and the actual measured distance, and to bring the results to convergence, is as follows:

[0025] The initial coordinates of the laser tracking interferometer obtained by solving and Using the initial value, substitute it into the following objective function for a second solution. Reduce the residual value using the iterative Gauss-Newton method until convergence is achieved. To obtain more accurate , Coordinate values ​​in the machine tool coordinate system and The value; among which, This is the installation location after the iteration. For convergence accuracy;

[0026] .

[0027] Furthermore, methods for obtaining expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, related to the six position-dependent geometric errors and four position-independent geometric errors of the machine tool rotary axis C, include:

[0028] Obtain the first actual position of the workpiece coordinate system in the machine tool coordinate system. :

[0029] ;

[0030] in, represent conjugate, This indicates the initial position of the workpiece coordinate system relative to the machine tool coordinate system, with coordinates as follows: , The dual quaternion form representing the geometric error of the C-axis of rotation under the influence of geometric error;

[0031] Obtain the second actual position of the workpiece coordinate system corresponding to the measuring point in the machine tool coordinate system. ,in, This represents a unit vector with a magnitude of 1. , and These are the actual coordinates of the measurement point along the C-axis of rotation in the X, Y, and Z directions, respectively.

[0032] The first actual position obtained is the same as the second actual position obtained, thus obtaining the actual coordinate expressions of the X, Y and Z directions of the position-related geometric error and position-independent geometric error of the measurement point about the rotation axis C.

[0033] Furthermore, the dual quaternion form of the geometric error of the C-axis of rotation under the influence of geometric errors. Characterized as dual quaternions of geometrical errors independent of the rotation axis C-axis position. Dual quaternions of geometric errors related to the position of the rotation axis C-axis Ideal motion dual quaternion with rotation axis C-axis The product of:

[0034] .

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

[0036] The method proposed in this invention aims to significantly improve measurement efficiency while ensuring the accuracy of measurement data. For the measurement of geometric error of the rotating axis, this invention only requires a single-station laser tracking interferometer for measurement, which significantly improves the measurement efficiency. In the identification process, only the distance data of a single base station is used, which avoids the influence of the repeated positioning accuracy of the rotating axis introduced by the sequential polygonal method and improves the accuracy of the measurement results used for identification. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the rotation axis geometric error identification method based on laser tracking interferometer ranging data provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the geometric error related to the position of the rotation axis C-axis provided in an embodiment of the present invention;

[0039] Figure 3 This is a schematic diagram of position-independent geometric errors of the rotation axis C-axis provided in an embodiment of the present invention. Detailed Implementation

[0040] The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data provided by the present invention will be described more clearly and completely below with reference to the accompanying drawings, and will be described in detail with reference to the following specific embodiments:

[0041] The rotation axis geometric error identification method based on laser tracking interferometer ranging data provided in this embodiment includes the following steps:

[0042] S1. Install the laser tracking interferometer on the machine tool worktable and install the reflector on the machine tool tool for measurement; take the center of the reflector as the measurement base station and the position of the laser tracking interferometer as the measurement position, and calibrate the coordinates of the reflector center and the dead travel length of the laser tracking interferometer by moving the three linear axes of the machine tool (X-axis, Y-axis and Z-axis);

[0043] First, the intersection of the two rotary axis axes is defined as the origin of the machine tool coordinate system. The coordinates of the spindle end face center relative to the machine tool coordinate system are determined using machine tool design parameters. Then, the length of the tool holder for mounting the threaded rod is obtained using a tool setter. Figure 1 As shown, the reflector is installed via a threaded connection. Based on the technical parameters of the laser tracking interferometer, the length from the center of the reflector to the threaded rod is determined to be 50mm (this can be a rough value obtained using relevant measuring instruments). The theoretical initial installation position of the reflector is thus obtained using the above method. .

[0044] The distance value is measured using a laser tracking interferometer at the theoretical initial installation position of the reflector. Then, the reflector is moved to different positions by moving the X, Y, and Z axes of the machine tool and the distance values ​​are measured. A total of N positions are measured, where N is greater than 6. For the nth measurement position, the relevant X, Y, and Z axis movements are as follows: , and Then the nth measurement position of the reflector The theoretical coordinates are Distance measurement data was obtained through a tracking interferometer. Move the instrument to at least six positions, and then calibrate the initial installation position of the laser tracking interferometer using a formula. :

[0045] ;

[0046] in, This represents the initial installation position of the laser tracking interferometer in the machine tool coordinate system. Let be the coordinates of the center of the nth measurement position of the reflector in the machine tool coordinate system; The Euclidean distance between two coordinates can be further expressed as: .

[0047] Expanding by squaring both sides of the equation, this equation includes four unknowns. If the number of moves is greater than 4, the equation has a solution. Let The system of equations is transformed into a linear system of equations, which is used to construct a system of equations about the initial installation position of the tracking interferometer. and dead distance length Solving for the least squares function:

[0048] ;

[0049] Solve for the initial installation location and dead distance length Thus concludes the least squares problem. All parameters are known numbers.

[0050] This nonlinear processing introduces computational errors. To further improve accuracy, the initial coordinates of the laser tracking interferometer obtained by the least squares method are... and The value is substituted into the following objective function as the initial value (the purpose of this objective function is to continuously adjust the values ​​of the unknowns using an iterative algorithm based on the initial value to find an optimal set of values). The value of minimizes the sum of squares of the differences between the theoretical distance and the actual measured distance, thus bringing the result to convergence. A second solution is then performed in .

[0051]

[0052] Similarly, the residual value of this problem can be reduced by iterative Gauss-Newton method until convergence accuracy is achieved. ,in This is the installation location after the iteration. For convergence accuracy.

[0053] To obtain more accurate , Coordinate values ​​in the machine tool coordinate system and The value. After optimization. The coordinate values ​​are equivalent to the initial position of the workpiece coordinate system in the error model. At this time After substituting the numerical values ​​into the equation and iterating... coordinates That is, the coordinates of the base station at the center of the reflector.

[0054] S2. Based on the actual position of the workpiece coordinate system in the machine tool coordinate system, obtain the expressions for the actual coordinate values ​​of the measurement points along the C-axis of the rotary axis in the machine tool coordinate system, which are related to the 6 position-dependent geometric errors and 4 position-independent geometric errors of the C-axis. Specifically,

[0055] Dual quaternion form of the geometric error of the C-axis of rotation under the influence of geometric error It can be characterized as a dual quaternion of geometrical error independent of the rotation axis C-axis. Dual quaternions of geometric errors related to the position of the rotation axis C-axis Ideal motion dual quaternion with rotation axis C-axis The product of:

[0056] ;

[0057] Among them, the ideal motion dual quaternion of the rotation axis C-axis. It can be represented as:

[0058] ;

[0059] in, This represents the rotation angle of the C-axis. This method converts the C-axis motion command into the C-axis motion quantity in the right-hand helical coordinate system. The spatial vector [0,0,1] represents the unit vector corresponding to the rotation axis C.

[0060] The first actual position of the workpiece coordinate system in the machine tool coordinate system It can be represented as:

[0061] ;

[0062] in, represent conjugate, This indicates the initial position of the workpiece coordinate system relative to the machine tool coordinate system, with coordinates as follows: .

[0063] In addition, the second actual position of the workpiece coordinate system corresponding to the measuring point in the machine tool coordinate system ,in, This represents a unit vector with a magnitude of 1. , and These are the actual coordinates of the measurement points along the C-axis of the rotation axis in the X, Y, and Z directions, respectively. They are affected by 6 position-dependent geometric errors and 4 position-independent geometric errors along the C-axis of the rotation axis.

[0064] Based on the first actual position of the workpiece coordinate system in the machine tool coordinate system and the second actual position Because of the first actual position and the second actual position Representing the same position, we obtain the actual coordinate values ​​of the measurement point on the C-axis of the machine tool coordinate system in the X, Y, and Z directions, which are related to the 6 position-dependent geometric errors and 4 position-independent geometric errors of the C-axis of the machine tool:

[0065] ;

[0066] in, , and These represent the initial positions of the workpiece coordinate system relative to the machine tool coordinate system in the X, Y, and Z directions, respectively; , , , , and These represent the six position-related geometric errors of the rotation axis C; , , and These represent the four position-independent geometric errors of the rotation axis C;

[0067] S3. Construct an error identification model based on ranging data to obtain 6 position-related geometric errors and 4 position-independent geometric errors of the machine tool's C-axis; specifically,

[0068] The machine tool's C-axis rotates and measures distance values ​​using an installed laser tracking interferometer to obtain several measurement points. The coordinates of the reflector center are defined in the machine tool coordinate system. The Euclidean distance between the reflector center and the measurement points on the C-axis is constructed. This distance is the sum of the distance measurement data from the laser tracking interferometer and the dead travel length.

[0069] Specifically, an overdetermined system of equations is constructed between the Euclidean distance between the center of the mirror and the measurement point on the C-axis of rotation, and the measurement data, and then further transformed into a least squares problem:

[0070] ;

[0071] in, This represents the maximum number of actual measurements taken at the i-th measurement point; The actual coordinates of the measurement point on the C-axis of rotation. , This represents the calculation of the Euclidean distance between the actual coordinates of the measurement point on the C-axis of rotation and the center of the reflector.

[0072] When solving the above least squares problem, the coordinate values ​​of the X, Y and Z directions of the measurement point of the C-axis of the rotary axis need to be replaced with the coordinate expressions related to the 6 position-dependent geometric errors and 4 position-independent geometric errors of the C-axis of the machine tool obtained in step S2, and then the problem is solved. This nonlinear least squares problem can be solved by the Powell algorithm, and finally the 10 geometric errors of the C-axis of the rotary axis can be obtained at the same time.

[0073] In summary, the method of the present invention can be used to identify the numerical values ​​of six position-related geometric errors and four position-independent geometric errors of the C-axis of a five-axis machine tool.

[0074] 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 the geometrical error of a rotation axis based on ranging data from a laser tracking interferometer, characterized in that, Includes the following steps: The laser tracking interferometer is installed on the machine tool table, and the reflector is installed at the machine tool tool. The center coordinates of the reflector and the dead travel length of the laser tracking interferometer are calibrated. Based on the actual position of the workpiece coordinate system in the machine tool coordinate system, obtain the expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, which are related to the six position-dependent geometric errors and four position-independent geometric errors of the machine tool rotary axis C. An error identification model based on ranging data was constructed and solved using the Powell algorithm to obtain six position-dependent geometric errors and four position-independent geometric errors of the machine tool's C-axis rotary axis. The method for constructing the error identification model is as follows: The machine tool's C-axis rotates and distance values ​​are measured using an installed laser tracking interferometer to obtain several measurement points. An overdetermined set of equations is constructed between the Euclidean distance between the center of the reflector and the measurement points on the C-axis and the measurement data. This is then further transformed into a least squares problem. ； in, This represents the maximum number of actual measurements taken at each measurement point. The actual coordinates of the measurement point on the C-axis of rotation. , This represents the calculation of the Euclidean distance between the actual coordinates of the measurement point on the C-axis of rotation and the center of the reflector. The coordinates of the center of the reflector in the machine tool coordinate system are: This is the dead-path length of the laser tracking interferometer. The distance measurement data of the laser tracking interferometer at the i-th measurement point.

2. The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data according to claim 1, characterized in that, The expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, related to the six position-dependent geometric errors and four position-independent geometric errors of the C-axis of the machine tool, are as follows: ； in, , and These are the actual coordinates of the measurement point along the C-axis of rotation in the X, Y, and Z directions, respectively. , and These represent the initial positions of the workpiece coordinate system relative to the machine tool coordinate system in the X, Y, and Z directions, respectively; , , , , and These represent the six position-related geometric errors of the rotation axis C; , , and These represent the four position-independent geometric errors of the rotation axis C; This indicates the rotation angle of the rotation axis C.

3. The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data according to claim 1, characterized in that, The method for calibrating the center coordinates of the reflector and the dead path length of the laser tracking interferometer is as follows: Define the origin of the machine tool coordinate system and obtain the theoretical initial installation position of the reflector. The distance value measured at the theoretical initial installation position of the reflector using a laser tracking interferometer is [value missing]. ; The reflector is moved to different positions by moving the machine tool along the X, Y, and Z axes, and the distance values ​​are measured. For the nth measurement position, the relevant X, Y, and Z axis movements are as follows: , and Then the nth measurement position of the reflector The theoretical coordinates are Distance measurement data was obtained through a tracking interferometer. Move the instrument to at least six positions, and then calibrate the initial installation position of the laser tracking interferometer using a formula. : ； in, This represents the initial installation position of the laser tracking interferometer in the machine tool coordinate system. Let be the coordinates of the center of the nth measurement position of the reflector in the machine tool coordinate system; This represents the Euclidean distance between two coordinates; Solve the system of linear equations to obtain the initial installation position. and dead distance length ; The initial coordinates of the laser tracking interferometer obtained from the above solution are... and Using the initial value as the initial value, and through continuous iterative optimization, an optimal set of values ​​is found. The value of minimizes the sum of squares of the difference between the theoretical distance and the actual measured distance, thus bringing the results to convergence.

4. The method for identifying rotation axis geometric errors based on laser tracking interferometer ranging data according to claim 3, characterized in that, The initial coordinates of the laser tracking interferometer obtained by solving and Using the initial value as the initial value, and through continuous iterative optimization, an optimal set of values ​​is found. The method to minimize the sum of squares of the differences between the theoretical distance and the actual measured distance, and to bring the results to convergence, is as follows: The initial coordinates of the laser tracking interferometer obtained by solving and Using the initial value, substitute it into the following objective function for a second solution. Reduce the residual value using the iterative Gauss-Newton method until convergence is achieved. To obtain more accurate , Coordinate values ​​in the machine tool coordinate system and The value; among which, This is the installation location after the iteration. For convergence accuracy; 。 5. The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data according to claim 1, characterized in that, Methods for obtaining the expressions for the actual coordinate values ​​of the measurement points in the X, Y, and Z directions in the machine tool coordinate system, which are related to the six position-dependent geometric errors and four position-independent geometric errors of the machine tool rotary axis C, include: Obtain the first actual position of the workpiece coordinate system in the machine tool coordinate system. : ； in, represent conjugate, This indicates the initial position of the workpiece coordinate system relative to the machine tool coordinate system, with coordinates as follows: , The dual quaternion form representing the geometric error of the C-axis of rotation under the influence of geometric error; Obtain the second actual position of the workpiece coordinate system corresponding to the measuring point in the machine tool coordinate system. ,in, This represents a unit vector with a magnitude of 1. , and These are the actual coordinates of the measurement point along the C-axis of rotation in the X, Y, and Z directions, respectively. The first actual position obtained is the same as the second actual position obtained, thus obtaining the actual coordinate expressions of the X, Y and Z directions of the position-related geometric error and position-independent geometric error of the measurement point about the rotation axis C.

6. The method for identifying the geometric error of the rotation axis based on laser tracking interferometer ranging data according to claim 1, characterized in that, Dual quaternion form of the geometric error of the C-axis of rotation under the influence of geometric error Characterized as dual quaternions of geometrical errors independent of the rotation axis C-axis position. Dual quaternions of geometric errors related to the position of the rotation axis C-axis Ideal motion dual quaternion with rotation axis C-axis The product of: 。

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