A method for calibrating the distance between the center of the turntable and the distance from the axis to the plane of the turntable in a dual-turntable five-axis device.

Abstract

This invention provides a calibration method for the distance between the turntable center and the distance from the axis to the turntable plane in a dual-turntable five-axis device. The method involves repeatedly collecting the coordinates of each positioning point on the turntable at the initial position and under different rotation angle groups, then summing and averaging the data to obtain more accurate positioning point coordinates. Furthermore, based on the changes in the coordinates of the positioning points before and after multiple rotations along the A-axis and C-axis, the relationship between the coordinate changes before and after rotation is obtained. Simultaneously, a set of equations is derived and selected by combining multiple rotation angle groups. Finally, using the obtained set of equations, the x and y coordinates of the turntable center and the z coordinates of the A-axis are obtained through iterative solving. This allows for the calculation of the turntable center coordinates and the distance from the axis to the turntable plane, which are then calibrated. This calibration method improves the calibration of dual-turntable five-axis devices from manual to automatic, reducing measurement errors and improving the accuracy of the turntable center position and the distance from the axis to the turntable plane.

Description

Technical Field

[0001] This invention belongs to the field of measurement and calibration technology, specifically relating to a calibration method for the distance between the center of the turntable and the distance from the axis to the plane of the turntable in a dual-turntable five-axis device. Background Technology

[0002] With the continuous development of manufacturing technology, five-axis machining centers are increasingly widely used in modern industry, especially in the field of high-precision machining. Dual-rotor five-axis machining centers, due to their ability to perform complex surface machining and multi-angle operations, have become key equipment for many high-end manufacturing tasks. As an important component of five-axis machining centers, the precision of the rotary table directly determines the accuracy of the machining results.

[0003] Five-axis equipment typically includes three spatial coordinate axes—X, Y, and Z—as well as an A-axis that rotates around the X-axis and a C-axis that rotates around the Z-axis. Dual-rotor designs offer greater flexibility, but their complex structure also presents new challenges, particularly in calibrating the accuracy of the distance between the rotary table center and the axis of rotation to the rotary table plane.

[0004] Currently, five-axis dual-turntable equipment faces several technical challenges during operation, one key issue being the calibration accuracy of the distance between the turntable center and the axis of rotation to the turntable plane. Due to the complex structure of the turntable, traditional manual calibration methods are prone to significant measurement errors, which in turn affect the overall operational accuracy of the equipment and the processing quality of the products. This is especially true for non-standard customized equipment, where the calibration process is even more complex, further increasing the possibility of errors.

[0005] Therefore, how to calibrate the distance between the turntable center and the axis to the turntable plane of a dual-turntable five-axis device in a more accurate and automated way has become an important research direction in the current development of five-axis device technology. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a calibration method for the distance between the center of the turntable and the distance from the axis to the turntable plane of a dual-turntable five-axis equipment. This method can effectively improve calibration accuracy, reduce measurement errors, and thus improve the overall performance and processing quality of the five-axis equipment.

[0007] A method for calibrating the distance between the center of the turntable and the distance from the axis to the turntable plane in a dual-turntable five-axis device includes the following steps:

[0008] (1) Mark multiple positioning points on the turntable, collect the coordinates of each positioning point at the initial position, and calculate the z-direction coordinates of the turntable center at the initial position based on the coordinates of the multiple positioning points at the initial position;

[0009] (2) Control the A-axis and C-axis of the turntable to rotate multiple times, and collect the coordinates of all positioning points under each rotation angle group;

[0010] (3) Based on the coordinate changes of each positioning point before and after rotation at different angles, obtain the coordinate change relationship before and after rotation;

[0011] (4) Based on the multiple rotation angle sets of the A-axis and C-axis and the coordinate change relationship before and after rotation, multiple sets of three linear equations are derived and multiple sets of solution equations are obtained by screening them.

[0012] (5) Using the obtained multiple sets of equations, the x and y coordinates of the turntable center and the z coordinate of the A-axis center are obtained through iterative solution;

[0013] (6) Based on the x and y coordinates of multiple turntable centers, the z coordinates of the A-axis center, and the z coordinates of the initial turntable center, calculate the turntable center coordinates and the distance from the rotating axis to the turntable plane, and calibrate based on the turntable center coordinates and the distance from the rotating axis to the turntable plane.

[0014] In the above calibration method, the coordinates of the positioning points are acquired using the x, y, and z coordinate acquisition system built into the five-axis equipment. The calibration method of this invention automatically acquires the coordinates of the positioning points on the turntable at the initial position and at different angles, and combines this with scientific mathematical calculations and data processing methods to obtain the turntable center position (coordinates) and the distance from the axis to the turntable plane of the dual-turntable five-axis equipment. This transforms manual calibration into automatic calibration, reducing measurement errors in calibrating the turntable center and the distance from the axis to the turntable plane, and improving the calibration accuracy of the dual-turntable five-axis equipment.

[0015] It should be noted that the distance from the pivot to the turntable plane mentioned in this article refers to the distance from axis A (center) to the turntable plane.

[0016] In step (1) above:

[0017] The specific process for this step is as follows:

[0018] Multiple positioning points are marked on the turntable. After obtaining the preset start command, the turntable is initialized. The control equipment coordinate acquisition system moves to each positioning point in sequence and collects data one by one to obtain the initial position coordinates of each positioning point.

[0019] Preferably, the number of marked positioning points is greater than or equal to 3, and any three of these positioning points are not collinear.

[0020] Preferably, the formula for calculating the z-direction coordinates of the turntable center at the initial position, based on the coordinates of multiple positioning points at the initial position, is as follows:

[0021]

[0022] Among them, z c The initial position is the z-coordinate of the turntable center; z i is the z-coordinate of the i-th positioning point at the initial position; n is the number of positioning points.

[0023] In the above technical solution, the coordinates of the initial position positioning point obtained through acquisition are represented as P. i00 (i = 1, ..., n), where n is the number of positioning points; for all initial positions, the z-direction coordinates of the positioning points are... i By summing and averaging the values ​​of (i = 1, ..., n), the z-coordinate of the turntable center can be obtained. This method reduces the impact of random errors on the measurement results and achieves high accuracy.

[0024] In step (2) above:

[0025] As a preferred embodiment, the specific process of controlling the A-axis and C-axis of the turntable to rotate multiple times is as follows:

[0026] The A-axis of the control turntable is randomly rotated multiple times, with rotation angles of [15°, 45°]; and after each rotation of the A-axis, the C-axis is randomly rotated multiple times, with each rotation angle being different, and the rotation angles being [0°, +∞].

[0027] The first rotation angle of the A-axis and the first rotation angle of the C-axis together form a rotation angle group.

[0028] Specifically, if the rotation angle of axis A is θ A The rotation angle of the C-axis is θ C The corresponding rotation angle set is (θ) A θ C ).

[0029] In steps (1) and (2):

[0030] As a preferred method, the coordinates of each positioning point at the initial position and each positioning point under each rotation angle group are collected multiple times to obtain the coordinate set of each positioning point in the corresponding state. The coordinates of each positioning point are then obtained by summing and averaging each coordinate set. The calculation formula is as follows:

[0031]

[0032] in, Rotation angle of axis A is θ A The C-axis rotation angle is θ C When (rotation angle group is (θ) A θ C The coordinates of the i-th positioning point, i∈[1,n], where n is the number of positioning points; Rotation angle of axis A is θ A The C-axis rotation angle is θ C The coordinates of the i-th positioning point acquired in the j-th sampling; m is the rotation angle of the A-axis by θ. A The C-axis rotation angle is θ C The total number of times the i-th location point is collected.

[0033] This technical solution not only ensures that the coordinates of each positioning point are unique under each state, but also reduces the impact of random errors on the measurement results, thereby further improving measurement accuracy.

[0034] Specifically, through multiple data collections, each positioning point can obtain a set of coordinate points in each state (initial position or specific rotation angle group). By summing and averaging each set of coordinate points, the coordinates of each positioning point in each state can be obtained.

[0035] At the initial position, θ A =0, θ C =0; then P i00 P represents the coordinates of the i-th positioning point at the initial position. ij00 is the coordinate of the i-th positioning point in the j-th sampling at the initial position; m is the total number of samplings of the i-th positioning point at the initial position.

[0036] In step (3) above:

[0037] Preferably, the coordinate transformation relationship before and after rotation is as follows:

[0038]

[0039] Where, x i ′、y i ′、z i Let θ' and θ' be the x, y, and z coordinates of the i-th positioning point after rotation, respectively, where i ∈ [1, n] and n is the number of positioning points; C θ A These are the rotation angles along the C-axis and A-axis, respectively; x i y i z i Let x, y, and z be the x, y, and z coordinates of the i-th positioning point before rotation (initial position); x c y c These are the x and y coordinates of the initial position, the center of the turntable; z a Here is the z-coordinate of the center of axis A.

[0040] The derivation of the coordinate transformation relationship before and after rotation is as follows:

[0041] The coordinates of the i-th positioning point before rotation (initial position) obtained after acquisition are P. i00 via (θ) A ,θ C The coordinates after rotation are The coordinates of the same positioning point before and after rotation produce the following motion relationship:

[0042]

[0043] in: Rotate (θ) for the i-th positioning point A θ C The coordinates after ); P i00 T represents the initial coordinates of the i-th positioning point; -A T is the inverse translation matrix at the center position of axis A; A T is the translation matrix for the center position of axis A; -C T is the inverse translation matrix at the center position of the C-axis; C R is the translation matrix for the center position of the C-axis; A R is the rotation matrix about axis A; C Let be the rotation matrix about the C-axis;

[0044]

[0045] To simplify the solution by adapting to the changing motion relationship, let x a =x c ,y a =y c The calculation is performed using mathematical expressions and written in coordinate component form.

[0046] Therefore, the mathematical coordinate component expression of the motion relationship (the coordinate transformation relationship before and after rotation) is:

[0047]

[0048] Where, x i ′、y i ′、z i Let θ' and y' be the x, y, and z coordinates of the i-th positioning point after rotation, where i ∈ [1, n] and n is the number of positioning points; C θ A These are the rotation angles along the C-axis and A-axis, respectively; x i y i z i Let x, y, and z be the x, y, and z coordinates of the i-th positioning point before rotation (initial position); x c y c z c These are the x, y, and z coordinates of the initial position, the center of the turntable; x a ya z a These are the x, y, and z coordinates of the center of axis A, respectively.

[0049] In step (4) above:

[0050] As a preferred option, the specific process of this step is as follows:

[0051] A10. Based on the multiple rotation angle sets of the A-axis and C-axis and the coordinates of the corresponding positioning points, substitute them into the coordinate change relationship before and after rotation to obtain a set of three linear equations with respect to the number of rotation angle sets corresponding to each positioning point, which serves as the original set of equations.

[0052] A20. Traverse and combine the component equations in the original equation set of all the obtained positioning points, and form a new three-element linear equation set by taking three component equations as a group, and any two component equations in the new three-element linear equation set do not come from the same original equation set.

[0053] A30. Retain a new system of three linear equations in all coefficient matrices whose condition number is less than or equal to a set threshold, and use it as the system of equations to be solved.

[0054] It is worth noting that in step A10, at least three rotation angle groups of the A-axis and C-axis are required. Therefore, in step (2), when controlling the A-axis and C-axis of the turntable to rotate multiple times, at least three different rotation angle groups must be obtained.

[0055] The specific process of step A30 above is as follows:

[0056] Determine whether the condition number of the coefficient matrix of each new system of three linear equations is less than or equal to a set threshold. If the condition number of the coefficient matrix of a new system of three linear equations is less than or equal to the set threshold, then retain the new system of three linear equations; otherwise, discard it. Finally, the multiple retained new systems of three linear equations are used as multiple systems of equations to be solved.

[0057] This technical solution can obtain several sets of three linear equations with non-ill-conditioned coefficient matrices (solving the equations), thereby reducing the number of iterations in subsequent iterations and improving the solution accuracy.

[0058] As a further optimization, the resulting system of equations takes the following form:

[0059]

[0060] Where: x i ′、y i ′、z i Let θ' and y' be the x, y, and z coordinates of the i-th positioning point after rotation, respectively, where i ∈ [1, n] and n is the number of positioning points; C1 θC2 θ C3 Let θ be the three rotation angles along the C-axis, and let θ be the rotation angles along the C-axis. C1 ≠θ C2 ≠θ C3 ;θ A2 θ A3 These represent the two rotation angles along axis A; x i y i z i Let x, y, and z be the x, y, and z coordinates of the i-th positioning point before rotation (initial position); x c y c These are the x and y coordinates of the initial position, the center of the turntable; z a Here is the z-coordinate of the center of axis A.

[0061] In step (5) above:

[0062] As a preferred approach, given a fuzzy initial solution based on multiple systems of equations, the Adam optimizer function is used for iterative solving to obtain multiple sets of solutions in the following form:

[0063] N k =[x ck y ck z ak ]

[0064] Where, x ck and y ck These are the x and y coordinates of the turntable center, respectively, for the solution to the k-th system of equations; z ak Let be the z-coordinate of the center of the A-axis of the k-th solution to the system of equations, k∈[1,w], where w is the number of equations to be solved.

[0065] Using the method of this technical solution, several sets of very accurate x and y coordinates of the turntable center and z coordinates of the A-axis center can be quickly obtained.

[0066] In step (6) above:

[0067] Preferably, based on the multiple sets of x and y coordinates of the turntable center obtained in step (5), the z coordinates of the A-axis, and the z coordinates of the initial position turntable center, the coordinates of the turntable center and the distance from the rotation axis to the turntable plane are calculated using the following formulas:

[0068] The formulas for calculating the x and y coordinates of the turntable center are as follows:

[0069]

[0070] The coordinates of the turntable center are N. c =[x c yc z c ];

[0071] The formula for calculating the z-coordinate of the center of axis A is:

[0072]

[0073] The formula for calculating the distance L from the axis of rotation (A-axis) to the turntable plane is:

[0074] L = z c -z a

[0075] Where, x ck and y ck These are the x and y coordinates of the turntable center, respectively, for the solution to the k-th system of equations; N c z represents the coordinates of the turntable center; ak Let x be the z-coordinate of the center of the A-axis of the solution to the k-th system of equations; c y c These are the x and y coordinates of the initial position, the center of the turntable; z a is the z-coordinate of the center of axis A; w represents the number of equations to be solved.

[0076] The present invention discloses a method for calibrating the distance between the turntable center and the axis of rotation to the turntable plane in a dual-turntable five-axis device. First, when the dual-turntable five-axis device is in its initial position, the coordinate acquisition system consisting of the other three axes (X, Y, Z) performs a positioning point coordinate acquisition task, sequentially acquiring the coordinates of the positioning points at the initial position of the turntable. Then, the coordinates of the positioning points at different angles (rotation angle groups) are acquired multiple times, and the coordinates are averaged to ensure that the coordinates of a positioning point are unique within a given rotation angle group. Next, based on the processed positioning point coordinates, the x, y, and z coordinates of the turntable center and the z-direction coordinate of the A-axis center are calculated. Then, based on the x, y, and z coordinates of the turntable center, the z-direction coordinate of the A-axis center, and the z-direction coordinate of the turntable center at the initial position, the coordinates of the turntable center and the distance from the axis of rotation to the turntable plane can be calculated, and calibration is performed based on these coordinates.

[0077] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0078] The present invention provides a method for calibrating the distance between the turntable center and the axis of rotation to the turntable plane in a dual-turntable five-axis device. This method involves repeatedly collecting the coordinates of each positioning point on the turntable at the initial position and under different rotation angle groups, then summing and averaging the data to obtain more accurate positioning point coordinates. Furthermore, based on the changes in the coordinates of the positioning points before and after multiple rotations along the A-axis and C-axis, the relationship between the coordinate changes before and after rotation is obtained. Simultaneously, by combining multiple rotation angle groups and the coordinates of the corresponding positioning points, multiple sets of ternary linear equations are derived and selected. Finally, using the obtained equations, the x and y coordinates of the turntable center and the z coordinates of the A-axis center are obtained through iterative solving. This allows for the calculation of the turntable center coordinates and the distance from the axis of rotation to the turntable plane, which are then calibrated. The calibration method of the present invention improves the calibration of the turntable center position (coordinates) and the distance from the axis to the turntable plane of the dual-turntable five-axis equipment from manual calibration to automatic calibration, reducing the measurement error generated when calibrating the turntable center and the distance from the axis to the turntable plane of the dual-turntable five-axis equipment, and improving the accuracy of the calibration of the turntable center position and the distance from the axis to the turntable plane. Attached Figure Description

[0079] Figure 1 This is a flowchart of an embodiment of the present invention;

[0080] Figure 2 This is a flowchart illustrating the derivation and selection of the solution system of equations in an embodiment of the present invention;

[0081] Figure 3 This is a schematic diagram of the marking and positioning points of the dual turntables A and C and the coordinate system of the A and C axes in an embodiment of the present invention.

[0082] Figure 4 This is a schematic diagram showing the distance between the turntable plane and the rotation axis in an embodiment of the present invention. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0084] like Figure 1 As shown, a method for calibrating the turntable center and the distance from the axis to the turntable plane of a dual-turntable five-axis device specifically includes the following steps:

[0085] S10. Mark multiple positioning points on the turntable, use the x, y, z coordinate acquisition system of the five-axis equipment to acquire the coordinates of each positioning point at the initial position, and calculate the z-direction coordinate of the turntable center at the initial position based on the coordinates of the multiple positioning points at the initial position.

[0086] The number of marked positioning points must be greater than or equal to 3, and no three of these positioning points must be collinear. In practice, 4 positioning points can be selected for marking (e.g., ...). Figure 3 (As shown).

[0087] Coordinates are collected multiple times for each location point. The number of collections can be determined based on specific circumstances. For example, each location point can be collected three times. The coordinates collected from multiple collections are then summed and averaged to obtain a unique coordinate for each location point at its initial position.

[0088] The formula for calculating the average is:

[0089]

[0090] Among them, P i00 P represents the coordinates of the i-th positioning point at the initial position, where i ∈ [1, n] and n is the number of positioning points; ij00 is the coordinate of the i-th positioning point in the j-th sampling at the initial position; m is the total number of samplings of the i-th positioning point at the initial position.

[0091] In practice, the coordinates of each positioning point can be collected 3 times, so m = 3.

[0092] The formula for calculating the z-coordinate of the initial position turntable center is:

[0093]

[0094] Among them, z c The initial position is the z-coordinate of the turntable center; z i is the z-coordinate of the i-th positioning point at the initial position; n is the number of positioning points.

[0095] S20. Control the A-axis and C-axis of the turntable to rotate multiple times, and collect the coordinates of all positioning points under each rotation angle group.

[0096] Specifically:

[0097] The A-axis of the control turntable is randomly rotated multiple times, with rotation angles of [15°, 45°]; and after each rotation of the A-axis, the C-axis is randomly rotated multiple times, with each rotation angle being different, and the rotation angles being [0°, +∞].

[0098] The first rotation angle of the A-axis and the first rotation angle of the C-axis together form a set of rotation angles; if the rotation angle of the A-axis is θ A The rotation angle of the C-axis is θ C The corresponding rotation angle set is (θ) A θ C ).

[0099] For each rotation angle group, the coordinates of each positioning point are collected multiple times to obtain the coordinate set corresponding to each positioning point; then, the coordinate sets are summed and averaged to obtain the coordinates of each positioning point for each rotation angle group.

[0100] This invention relates to a dual-turntable AC-axis five-axis device, wherein the five axes of the dual-turntable AC-axis five-axis device are the x-axis for horizontal movement, the y-axis for forward and backward movement, the z-axis for vertical movement, the A-axis for rotation around the x-axis, and the C-axis for rotation around the z-axis.

[0101] The rotation of the turntable's A and C axes is controlled according to rotation commands, rotating by several angles. This includes the following steps:

[0102] The A-axis of the control turntable is randomly rotated multiple times, with the rotation angle range being [15°, 45°]. After each rotation of the A-axis, the C-axis of the control turntable is randomly rotated multiple times, with each rotation angle being different, and the rotation angle range being [0°, +∞]. After each random rotation of the C-axis, the coordinate acquisition system is moved sequentially to each positioning point to collect data (coordinate acquisition) one by one, obtaining the position coordinates of each positioning point and recording the corresponding rotation angles of the A-axis and C-axis, i.e., the corresponding rotation angle group.

[0103] The formula for summing and averaging coordinate sets is:

[0104]

[0105] in, Rotation angle of axis A is θ A The C-axis rotation angle is θ C When (rotation angle group is (θ) A θ C The coordinates of the i-th positioning point; Rotation angle of axis A is θ A The C-axis rotation angle is θ C The coordinates of the i-th positioning point acquired in the j-th sampling; m is the rotation angle of the A-axis by θ. A The C-axis rotation angle is θ C The total number of times the i-th location point is collected.

[0106] S30. Based on the coordinate changes of each positioning point before and after rotation at different angles, the following coordinate change relationship before and after rotation is obtained:

[0107]

[0108] Where, x i ′、y i ′、z iθ' represents the x, y, and z coordinates of the i-th positioning point after rotation; C θ A These are the rotation angles along the C-axis and A-axis, respectively; x i y i z i Let x, y, and z be the x, y, and z coordinates of the i-th positioning point before rotation (initial position); x c y c These are the x and y coordinates of the initial position, the center of the turntable; z a Here is the z-coordinate of the center of axis A.

[0109] The specific derivation process is as follows:

[0110] The coordinates of the i-th positioning point before rotation (initial position) obtained after acquisition are P. i00 via (θ) A ,θ C The coordinates after rotation are The coordinates of the same positioning point before and after rotation produce the following motion relationship:

[0111]

[0112] in: Rotate (θ) for the i-th positioning point A θ C The coordinates after ); P i00 T represents the initial coordinates of the i-th positioning point; -A T is the inverse translation matrix at the center position of axis A; A T is the translation matrix for the center position of axis A; -C T is the inverse translation matrix at the center position of the C-axis; C R is the translation matrix for the center position of the C-axis; A R is the rotation matrix about axis A; C Let be the rotation matrix about the C-axis;

[0113]

[0114] To simplify the solution by adapting to the changing motion relationship, let x a =x c ,y a =y c The calculation is performed using mathematical expressions and written in coordinate component form.

[0115] Therefore, the mathematical coordinate component expression of the motion relationship (the coordinate transformation relationship before and after rotation) is:

[0116]

[0117] Where, xi ′、y i ′、z i θ' represents the x, y, and z coordinates of the i-th positioning point after rotation; C θ A These are the rotation angles along the C-axis and A-axis, respectively; x i y i z i Let x, y, and z be the x, y, and z coordinates of the i-th positioning point before rotation (initial position); x c y c z and zc are the x, y, and z coordinates of the initial position of the turntable center, respectively; x a y a z a These are the x, y, and z coordinates of the center of axis A, respectively.

[0118] It should be noted that because the coefficient matrix of the system of three linear equations formed by collinear points is not full rank, the corresponding system of three linear equations has no solution. Therefore, the partitioning requirement includes that the final spatial coordinates of the partitioned group cannot be collinear. Thus, it is required that every three positioning points among the multiple positioning points marked in step S10 are not collinear with each other.

[0119] S40. Based on multiple rotation angle sets of the A-axis and C-axis and the coordinate change relationship before and after rotation, derive multiple sets of three-variable linear equations and select multiple sets of solution equations from them.

[0120] like Figure 2 As shown, the specific process of step S40 is as follows:

[0121] A10. Based on the multiple rotation angle sets of the A-axis and C-axis and the coordinates of the corresponding positioning points, substitute them into the coordinate change relationship before and after rotation to obtain a set of three linear equations with respect to the number of rotation angle sets corresponding to each positioning point, which serves as the original set of equations.

[0122] In this step, at least three rotation angle groups are required for the A-axis and C-axis. Therefore, in step S20, when controlling the A-axis and C-axis of the turntable to rotate multiple times, at least three different rotation angle groups must be obtained.

[0123] A20. Traverse and combine the component equations in the original equation set of all the obtained positioning points, and form a new three-element linear equation set by taking three component equations as a group, and any two component equations in the new three-element linear equation set do not come from the same original equation set.

[0124] A30. Retain a new system of three linear equations with all coefficient matrices having a condition number less than or equal to a set threshold, and use it as the system of equations to be solved.

[0125] The specific process for this step is as follows:

[0126] Determine whether the condition number of the coefficient matrix of each new system of three linear equations is less than or equal to a set threshold. If the condition number of the coefficient matrix of a new system of three linear equations is less than or equal to the set threshold, then retain the new system of three linear equations; otherwise, discard it. Finally, the multiple retained new systems of three linear equations are used as multiple systems of equations to be solved.

[0127] The resulting system of equations takes the following form:

[0128]

[0129] Where: x i ′、y i ′、z i θ' represents the x, y, and z coordinates of the i-th positioning point after rotation; θ' represents the x, y, and z coordinates of the i-th positioning point after rotation. C1 θ C2 θ C3 Let θ be the three rotation angles along the C-axis, and let θ be the rotation angles along the C-axis. C1 ≠θ C2 ≠θ C3 ;θ A2 θ A3 These represent the two rotation angles along axis A; x i y i z i These are the x, y, and z coordinates of the i-th positioning point before rotation; x c y c These are the x and y coordinates of the initial position, the center of the turntable; z a Here is the z-coordinate of the center of axis A.

[0130] To simplify the operation process and calculations, in actual operation, the A-axis can be rotated once (θ). A2 =θ A3 =θ A This corresponds to three different angles (θ) rotating along the C-axis. C1 θ C2 θ C3 This yields three different rotation angle groups; for example, the turntable rotates randomly around axis A by 30°, and the turntable rotates randomly around axis C three times. The first time, the turntable rotates around axis C by 30°, then the second time it rotates around axis C by 45°, and finally the turntable rotates around axis C by 60°, after which the turntable stops rotating randomly around axis AC.

[0131] The above system of equations can then be simplified to the following form:

[0132]

[0133] S50. Using the obtained multiple sets of equations, through iterative solutions, we obtain the corresponding x and y coordinates of the turntable center and the z coordinate of the A-axis center.

[0134] Specifically:

[0135] Given a fuzzy initial solution based on multiple systems of equations, the Adam optimizer function is used for iterative solving, yielding multiple sets of solutions in the following form:

[0136] N k =[x ck y ck z ak ]

[0137] Where, x ck and y ck These are the x and y coordinates of the turntable center, respectively, for the solution to the k-th system of equations; z ak Let be the z-coordinate of the center of the A-axis of the k-th solution to the system of equations, k∈[1,w], where w is the number of equations to be solved.

[0138] Each system of equations can be solved iteratively to obtain a set of corresponding solutions.

[0139] S60. Based on the x and y coordinates of multiple turntable centers, the z coordinates of the A-axis center, and the z coordinates of the initial turntable center, calculate the turntable center coordinates and the distance from the rotating axis to the turntable plane, and calibrate based on the turntable center coordinates and the distance from the rotating axis to the turntable plane.

[0140] Specifically, this step includes the following steps:

[0141] Based on the obtained solutions, the exact solution is obtained by summing and averaging the results.

[0142] Formula for calculating the x-coordinate of the turntable center:

[0143]

[0144] Formula for calculating the y-coordinate of the turntable center:

[0145]

[0146] Therefore, the coordinates of the turntable center are N. c =[x c y c z c ];

[0147] Formula for calculating the z-coordinate of the center of axis A:

[0148]

[0149] Then, such as Figure 4 The formula for calculating the distance L from the central axis (A-axis) to the turntable plane is:

[0150] L = z c -z a

[0151] Where: x ck and y ck These are the x and y coordinates of the solution to the k-th system of equations; z ak Let z be the z-coordinate of the center of the A-axis of the solution to the k-th system of equations; refer to Figure 3 x c y c The initial positions are O. c The x and y coordinates of the origin of the coordinate system in the base coordinate system, i.e., the x and y coordinates of the initial position of the turntable center; z a Initial position O A The coordinates of the origin of the coordinate system in the z-direction of the base coordinate system, i.e., the z-direction coordinates of the center of the A-axis; w represents the number of equations to be solved.

[0152] It should be noted that the present invention calculates several turntable center coordinates and axis center coordinates based on the coordinates of multiple positioning points before and after each group of three different rotation angles. The average value is then used to calculate the final turntable center coordinates and the distance from the rotation axis to the turntable plane.

[0153] The above embodiments are only used to describe the technical solutions of this application in detail and to help understand its core ideas, and should not be regarded as a limitation of this application. Any changes or substitutions made by those skilled in the art within the scope of the technology disclosed in this application should be covered by the protection scope of this application.

Claims

1. A method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a dual-turntable five-axis device, characterized in that, Includes the following steps: (1) Mark multiple positioning points on the turntable, collect the coordinates of each positioning point at the initial position, and calculate the z-direction coordinates of the turntable center at the initial position based on the coordinates of the multiple positioning points at the initial position; (2) Control the A-axis and C-axis of the turntable to rotate multiple times, and collect the coordinates of all positioning points under each rotation angle group; (3) Based on the coordinate changes of each positioning point before and after rotation at different angles, obtain the coordinate change relationship before and after rotation; (4) Based on the multiple rotation angles of the A-axis and C-axis and the coordinate changes before and after the rotation, multiple sets of three linear equations are derived and multiple sets of solution equations are obtained from them. (5) Using the obtained multiple sets of equations, through iterative solution, the corresponding x and y coordinates of the turntable center and the z coordinate of the A-axis center are obtained; (6) Based on the x and y coordinates of multiple turntable centers, the z coordinates of the A-axis center, and the z coordinates of the initial turntable center, calculate the turntable center coordinates and the distance from the rotating axis to the turntable plane, and calibrate based on the turntable center coordinates and the distance from the rotating axis to the turntable plane; The specific process of step (4) is as follows: A10. Based on the multiple rotation angle sets of the A-axis and C-axis and the coordinates of the corresponding positioning points, substitute them into the coordinate change relationship before and after rotation to obtain a set of three linear equations with respect to the number of rotation angle sets corresponding to each positioning point, which serves as the original set of equations. A20. Traverse and combine the component equations in the original equation set of all the obtained positioning points, and form a new three-element linear equation set by taking three component equations as a group, and any two component equations in the new three-element linear equation set do not come from the same original equation set. A30. Retain a new system of three linear equations in all coefficient matrices whose condition number is less than or equal to a set threshold, and use it as the system of equations to be solved.

2. The method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a dual-turntable five-axis device according to claim 1, characterized in that, In step (1), the number of marked positioning points is greater than or equal to 3, and any three of them are not collinear.

3. The method for calibrating the distance between the center of the turntable and the distance from the axis to the turntable plane of a dual-turntable five-axis device according to claim 1, characterized in that, In step (1), the formula for calculating the z-direction coordinates of the turntable center at the initial position, based on the coordinates of multiple positioning points at the initial position, is as follows: ； in, The initial position is the z-coordinate of the turntable center. is the z-coordinate of the i-th positioning point at the initial position; n is the number of positioning points.

4. The method for calibrating the distance between the center of the turntable and the distance from the axis to the turntable plane of a dual-turntable five-axis device according to claim 1, characterized in that, In step (2), the specific process of controlling the A-axis and C-axis of the turntable to rotate multiple times is as follows: The A-axis of the control turntable is randomly rotated multiple times, with rotation angles of [15°, 45°]; and after each rotation of the A-axis, the C-axis is randomly rotated multiple times, with each rotation angle being different, and the rotation angles being [0°, +∞]. The first rotation angle of the A-axis and the first rotation angle of the C-axis together form a rotation angle group.

5. The method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a dual-turntable five-axis device according to claim 1, characterized in that, In steps (1) and (2), the coordinates of each positioning point at the initial position and each positioning point under each rotation angle group are collected multiple times to obtain the coordinate set of each positioning point in the corresponding state. The coordinates of each positioning point are obtained by summing and averaging each coordinate set. The calculation formula is as follows: ； in, The rotation angle of axis A is The C-axis rotation angle is Let i be the coordinates of the i-th positioning point, i∈[1,n], and n be the number of positioning points; The rotation angle of axis A is The C-axis rotation angle is The coordinates of the i-th positioning point acquired in the j-th iteration; m is the rotation angle of the A-axis. The C-axis rotation angle is The total number of times the i-th location point is collected.

6. The method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a five-axis dual-turntable equipment according to claim 1, characterized in that, In step (3), the coordinate transformation relationship before and after rotation is as follows: ； in, , , Let x, y, and z be the x, y, and z coordinates of the i-th positioning point after rotation, i ∈ [1, n], and n be the number of positioning points; , These are the rotation angles along the C-axis and A-axis, respectively. , , These are the x, y, and z coordinates of the i-th positioning point before rotation; , These are the x and y coordinates of the initial position, the center of the turntable; Here is the z-coordinate of the center of axis A.

7. The method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a dual-turntable five-axis device according to claim 1, characterized in that, The resulting system of equations takes the following form: ； in, , , Let x, y and z be the x, y and z coordinates of the i-th positioning point after rotation, i∈[1,n], and n is the number of positioning points; , , These are the three rotation angles along the C-axis, and ; , These represent the two rotation angles along axis A; , , These are the x, y, and z coordinates of the i-th positioning point before rotation; , These are the x and y coordinates of the initial position, the center of the turntable; Here is the z-coordinate of the center of axis A.

8. The method for calibrating the distance between the center of the turntable and the distance from the axis to the plane of the turntable in a dual-turntable five-axis device according to claim 1, characterized in that, In step (5), based on multiple systems of equations, a fuzzy initial solution is given, and the Adam optimizer function is used for iterative solving to obtain multiple sets of solutions in the following form: ； in, and These are the x and y coordinates of the turntable center, respectively, for the solution to the k-th system of equations. Let be the z-coordinate of the center of the A-axis of the solution to the k-th system of equations; k∈[1,w], where w is the number of equations to be solved.

9. The method for calibrating the distance between the center of the turntable and the distance from the axis of rotation to the plane of the turntable in a dual-turntable five-axis device according to claim 1, characterized in that, In step (6), based on the multiple sets of x and y coordinates of the turntable center obtained in step (5), the z coordinates of the A-axis center, and the z coordinates of the initial position turntable center, the coordinates of the turntable center and the distance from the rotation axis to the turntable plane are calculated using the following formulas: The formulas for calculating the x and y coordinates of the turntable center are as follows: 、 ； The coordinates of the turntable center are: ; The formula for calculating the z-coordinate of the center of axis A is: ； The formula for calculating the distance L from the pivot to the turntable plane is: ； in, and These are the x and y coordinates of the turntable center, respectively, for the solution to the k-th system of equations. The coordinates of the turntable center; Let z be the z-coordinate of the center of the A-axis of the solution to the k-th system of equations. , These are the x and y coordinates of the initial position, the center of the turntable; is the z-coordinate of the center of axis A; w represents the number of equations to be solved.

Images