Method for calibrating distance between turntable center and rotating shaft of double-turntable five-axis equipment and turntable plane

Abstract

The invention provides a method for calibrating the distance between the center of a rotary table of double-rotary-table five-axis equipment and a rotary table plane and between a rotary shaft and the rotary table plane, and the method comprises the steps: collecting coordinates of each positioning point on the rotary table at an initial position and under different rotation angle groups for multiple times, and then carrying out summation and averaging to obtain more accurate coordinates of the positioning points; obtaining a coordinate change relation before and after rotation according to the coordinate change of the positioning point before and after multiple times of rotation of the A axis and the C axis, and deducing and screening a solving equation set in combination with a plurality of rotation angle groups; and finally, obtaining corresponding x and y direction coordinates of a plurality of groups of rotary table centers and z direction coordinates of an A axis through iterative solution by utilizing the obtained solving equation set, further calculating the coordinates of the rotary table centers and the distance from a rotating shaft to a rotary table plane, and calibrating the coordinates of the rotary table centers and the distance between the rotating shaft and the rotary table plane. According to the calibration method, the calibration of the double-turntable five-axis equipment is changed from manual operation to automatic operation, the measurement error is reduced, and the calibration precision of the central position of the turntable and the distance between the rotating shaft and the plane of the turntable is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of measurement and calibration, and in particular relates to a calibration method for the distance from a turntable center and a rotating shaft to a turntable plane of a double-turntable five-axis device. Background Art

[0002] With the continuous development of manufacturing technology, five-axis equipment is increasingly used in modern industry, especially in the field of high-precision machining. Dual-turntable five-axis equipment has become a key equipment for many high-end manufacturing tasks because it can achieve complex surface machining and multi-angle operation. As an important part of the five-axis equipment, the accuracy of the turntable directly determines the accuracy of the machining results.

[0003] Five-axis equipment usually 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. The dual-turntable design can provide greater flexibility, but its complex structure also brings new challenges, especially the accuracy of calibrating the turntable center and the distance from the axis to the turntable plane.

[0004] At present, dual-turntable five-axis equipment faces some technical problems during use, one of the key issues is the calibration accuracy of the turntable center and the distance from the axis to the turntable plane. Due to the complex structure of the turntable, the traditional manual calibration method is prone to large measurement errors, which in turn affects the operating accuracy of the entire equipment and the processing quality of the product. Especially in non-standard customized equipment, the calibration process is more complicated, further increasing the possibility of errors.

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

[0006] In order to solve the problems existing in the prior art, the present invention provides a calibration method for the turntable center and the distance from the axis to the turntable plane of a dual-turntable five-axis device. This method can effectively improve the calibration accuracy, reduce measurement errors, and thereby improve the overall performance and processing quality of the five-axis device.

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

[0008] (1) marking multiple positioning points on the turntable, collecting the coordinates of each positioning point at the initial position, and calculating the z-direction coordinate of the center of the turntable 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) According to the coordinate changes of each positioning point before and after rotation at different angles, the coordinate change relationship before and after rotation is obtained;

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

[0012] (5) using the obtained multiple sets of equations to be solved, through iterative solutions, the corresponding multiple sets of x- and y-direction coordinates of the center of the turntable and the z-direction coordinates of the center of the A-axis are obtained;

[0013] (6) Based on multiple sets of turntable center x- and y-direction coordinates, the A-axis center z-direction coordinates, and the initial position turntable center z-direction coordinates, the turntable center coordinates and the distance from the rotation axis to the turntable plane are calculated, and calibration is performed based on the turntable center coordinates and the distance from the rotation axis to the turntable plane.

[0014] In the above calibration method, the acquisition of the coordinates of the positioning points is realized by the x, y, and z coordinate acquisition system of the five-axis device. The calibration method of the present invention automatically acquires the coordinates of the positioning points on the turntable at the initial position and different angles, and combines scientific mathematical calculation methods and data processing methods to obtain the turntable center position (coordinates) of the double turntable five-axis device and the distance from the rotation axis to the turntable plane, thereby changing from manual calibration to automatic calibration, reducing the measurement error of calibrating the turntable center of the double turntable five-axis device and the distance from the rotation axis to the turntable plane, and improving the calibration accuracy of the turntable center of the double turntable five-axis device and the distance from the rotation axis to the turntable plane.

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

[0016] In the above step (1):

[0017] The specific process of this step is:

[0018] Mark multiple positioning points on the turntable, obtain the preset start command, initialize the turntable, control the device coordinate acquisition system to move to each positioning point in turn, collect data one by one, and 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 positioning points are not collinear.

[0020] Preferably, the calculation formula for obtaining the z-direction coordinate of the center of the turntable at the initial position according to the coordinates of multiple positioning points at the initial position is:

[0021]

[0022] Among them, z c is the z-direction coordinate of the center of the turntable at the initial position; i is the z-coordinate of the ith 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 by acquisition are expressed as P i00 , (i=1,…,n), n is the number of positioning points; for all the initial position positioning point coordinates, the z direction coordinate z i , (i=1,…,n) and average the results to get the z-direction coordinate of the center of the turntable. The z-direction coordinate of the center of the turntable obtained in this way reduces the influence of accidental errors on the measurement results and has high accuracy.

[0024] In the above step (2):

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

[0026] The A axis of the turntable is controlled to rotate randomly multiple times, and the rotation angle is [15°, 45°]. After each rotation of the A axis, the C axis is controlled to rotate randomly multiple times, and each rotation angle is different, and the rotation angle is [0°, +∞].

[0027] Among them, one rotation angle of the A axis and one rotation angle of the C axis together constitute a rotation angle group.

[0028] Specifically, if the rotation angle of the A axis is θ A , the rotation angle of the C axis is θ C , then the corresponding rotation angle group is (θ A ,θ C ).

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

[0030] Preferably, the coordinates of each positioning point in the initial position and each positioning point in each rotation angle group are collected multiple times to obtain a coordinate set of each positioning point in the corresponding state, and each coordinate set is summed and averaged to obtain the coordinates of each positioning point. The calculation formula is:

[0031]

[0032] in, The A-axis rotation angle is θ A , C-axis rotation angle is θ C When (the rotation angle group is (θ A ,θ C ))The coordinates of the i-th positioning point, i∈[1,n], n is the number of positioning points; The A-axis rotation angle is θ A , C axis rotation angle is θ C The coordinates of the i-th positioning point collected for the jth time; m is the rotation angle of the A axis θ A , C axis rotation angle is θ C The total number of times the i-th positioning point is collected.

[0033] Through this technical solution, the coordinates of each positioning point in each state can be determined to be unique, and the influence of accidental errors on the measurement results can be reduced, thereby further improving the measurement accuracy.

[0034] Specifically, through multiple acquisitions, each positioning point can obtain a coordinate point set in each state (initial position or specific rotation angle group), and by summing and averaging each coordinate point set, 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 is the coordinate of the i-th positioning point at the initial position; P ij00 is the point coordinate collected for the jth time at the i-th positioning point at the initial position; m is the total number of times the i-th positioning point is collected at the initial position.

[0036] In the above step (3):

[0037] Preferably, the coordinate change relationship before and after the rotation is:

[0038]

[0039] Among them, x i ′、y i ′、z i ′ are the x, y and z coordinates of the i-th positioning point after rotation, i∈[1,n], n is the number of positioning points; θ C ,θ A are the rotation angles of the C-axis and A-axis respectively; i ,y i 、z i are the x, y and z coordinates of the ith positioning point before rotation (initial position); c ,y c are the x and y coordinates of the center of the turntable at the initial position; z a is the z-coordinate of the center of the A-axis.

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

[0041] The coordinates of the i-th positioning point before rotation (initial position) obtained after collection are P i00 , through (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 the i-th positioning point (θ A ,θ C ) after the coordinates; P i00 is the coordinate of the initial position of the i-th positioning point; T -A is the inverse translation matrix of the center position of the A axis; T A is the translation matrix of the center position of the A axis; T -C is the inverse translation matrix of the center position of the C axis; T C is the translation matrix of the center position of the C axis; R A is the rotation matrix around the A axis; R C is the rotation matrix around the C axis;

[0044]

[0045] According to the change of motion relationship, simplify the solution and let x a =x c ,y a =y c , calculated through mathematical expressions and written in the form of coordinate components;

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

[0047]

[0048] Among them, x i ′、y i ′、z i ′ are the x, y, and z coordinates of the i-th positioning point after rotation, i∈[1,n], n is the number of positioning points; θ C ,θ A are the rotation angles of the C-axis and A-axis respectively; i ,y i 、z i are the x, y, and z coordinates of the ith positioning point before rotation (initial position); c ,y c 、z c are the x, y, and z coordinates of the center of the turntable at the initial position; a ,ya 、z a They are the x, y, and z coordinates of the center of the A-axis respectively.

[0049] In the above step (4):

[0050] Preferably, the specific process of this step is:

[0051] A10. Substituting the coordinates of the corresponding positioning points and the multiple rotation angle groups of the A-axis and the C-axis into the coordinate change relationship before and after the rotation, a three-variable linear equation group of the number of rotation angle groups corresponding to each positioning point is obtained as the original equation group.

[0052] A20, traversing and permuting the component equations in the original equation group of all the positioning points, forming a new three-variable linear equation group with three component equations as a group, and any two component equations in the new three-variable linear equation group do not come from the same original equation group;

[0053] A30. Retain the new three-variable linear equation system whose condition number of all coefficient matrices is less than or equal to the set threshold as the equation system to be solved.

[0054] It is worth noting that in step A10, at least three rotation angle groups of the A-axis and the C-axis are required. Therefore, in step (2), it is required to control the A-axis and the C-axis of the turntable to rotate multiple times so as to obtain at least three different rotation angle groups.

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

[0056] Determine whether the condition number of the coefficient matrix of each new set of three-variable linear equations is less than or equal to the set threshold. If the condition number of the coefficient matrix of a new set of three-variable linear equations is less than or equal to the set threshold, then retain the new set of three-variable linear equations; otherwise, discard it; and finally retain multiple new three-variable linear equations as multiple sets of equations to be solved.

[0057] The technical solution can obtain several sets of ternary linear equations (solvable equations) of non-ill-conditioned coefficient matrices, thereby reducing the number of iterations of subsequent iterative solutions and improving the solution accuracy.

[0058] As a further preferred embodiment, the obtained solution of the equation system is in the form of:

[0059]

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

[0061] In the above step (5):

[0062] Preferably, a fuzzy initial solution is given according to multiple sets of equations to be solved, and an Adam optimizer function is used to perform iterative solution to obtain corresponding multiple sets of solutions in the following form:

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

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

[0065] By using the method of the technical solution, several sets of very accurate coordinates of the center of the turntable in the x and y directions and the coordinate of the center of the A-axis in the z direction can be quickly solved.

[0066] In the above step (6):

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

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

[0069]

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

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

[0072]

[0073] Then the calculation formula for the distance L from the rotation axis (A axis) to the turntable plane is:

[0074] L = z c -z a

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

[0076] The present invention discloses a calibration method for the distance from the turntable center and the rotation axis to the turntable plane of a dual-turntable five-axis device. First, when the dual-turntable five-axis device is in an initial position, a coordinate acquisition system composed of the other three axes (X, Y, and Z) of the device performs a positioning point coordinate acquisition task, and sequentially acquires the coordinates of the positioning points when the turntable is in the initial position; then, the coordinates of the positioning points of the turntable at different angles (rotation angle groups) are acquired multiple times, and average processing is performed based on the coordinates acquired multiple times, so that under a given rotation angle group, the coordinates of a positioning point are unique; then, based on the processed positioning point coordinates, the x, y, and z direction 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 direction coordinates of the turntable center and 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 rotation axis to the turntable plane can be calculated, and calibration is performed based on the coordinates of the turntable center and the distance from the rotation axis to the turntable plane.

[0077] Compared with the prior art, the present invention has the following beneficial effects:

[0078] The calibration method of the turntable center and the distance from the axis to the turntable plane of a dual-turntable five-axis device of the present invention obtains more accurate coordinates of the positioning point by collecting the coordinates of each positioning point on the turntable at the initial position and different rotation angle groups for multiple times, and then summing and averaging them; and according to the change of the coordinates of the positioning point before and after multiple A-axis and C-axis rotations, the coordinate change relationship before and after the rotation is obtained, and at the same time, multiple rotation angle groups and the coordinates of the corresponding positioning points are combined to derive and screen multiple three-variable linear solution equations; finally, the obtained solution equations are used to obtain the corresponding multiple groups of x- and y-direction coordinates of the turntable center and the z-direction coordinates of the A-axis center through iterative solution, and then the turntable center coordinates and the distance from the axis to the turntable plane are calculated, and the two are calibrated. The calibration method of the present invention improves the turntable center position (coordinates) and the distance from the rotation axis to the turntable plane of the dual-turntable five-axis device from manual calibration to automatic calibration, thereby reducing the measurement error generated when calibrating the turntable center and the distance from the rotation axis to the turntable plane of the dual-turntable five-axis device, and improving the accuracy of the calibration of the turntable center position and the distance from the rotation axis to the turntable plane. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 is a flow chart of an embodiment of the present invention;

[0080] Figure 2 is a flow chart of deriving and screening a set of equations for solution in an embodiment of the present invention;

[0081] Figure 3 It is a schematic diagram showing the marking positioning points of the A and C double turntables and the A and C axis coordinate systems of the embodiment of the present invention;

[0082] Figure 4 It is a schematic diagram of the distance between the turntable plane and the rotation axis in an embodiment of the present invention. DETAILED DESCRIPTION

[0083] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below in conjunction with 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, marking multiple positioning points on the turntable, using the x, y, z coordinate acquisition system of the five-axis device to acquire the coordinates of each positioning point at the initial position, and calculating the z direction coordinate of the center of the turntable at the initial position based on the coordinates of the multiple positioning points at the initial position.

[0086] The number of marked positioning points is greater than or equal to 3, and any three of them are not collinear. In specific operations, you can select 4 positioning points for marking (such as Figure 3 shown).

[0087] Each positioning point is collected multiple times, and the number of collections can be determined according to the specific situation. For example, each positioning point can be collected 3 times, and then the coordinates collected multiple times are summed and averaged to obtain a unique coordinate corresponding to each positioning point at the initial position.

[0088] The calculation formula for summing and averaging is:

[0089]

[0090] Among them, P i00 is the coordinate of the i-th positioning point at the initial position, i∈[1,n], n is the number of positioning points; P ij00 is the point coordinate collected for the jth time at the i-th positioning point at the initial position; m is the total number of times the i-th positioning point is collected at the initial position.

[0091] In actual operation, the number of coordinate collection times for each positioning point may be 3, then m=3.

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

[0093]

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

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

[0096] Specifically:

[0097] The A axis of the turntable is controlled to rotate randomly multiple times, and the rotation angle is [15°, 45°]. After each rotation of the A axis, the C axis is controlled to rotate randomly multiple times, and each rotation angle is different, and the rotation angle is [0°, +∞].

[0098] Among them, one rotation angle of the A axis and one rotation angle of the C axis together form a rotation angle group; if the rotation angle of the A axis is θ A , the rotation angle of the C axis is θ C , then the corresponding rotation angle group is (θ A ,θ C ).

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

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

[0101] According to the rotation command, the A-axis and C-axis of the turntable are controlled to rotate at a certain angle, which specifically includes the following steps:

[0102] The A-axis of the turntable is controlled to rotate randomly for multiple times, and the angle range of the A-axis rotation of the turntable is [15°, 45°]; and after each rotation of the A-axis of the turntable is completed, the C-axis of the turntable is controlled to rotate randomly for multiple times, and the angle of each rotation is different, and the angle range of the C-axis rotation of the turntable is [0°, +∞]; after each random rotation of the C-axis, the coordinate acquisition system is controlled to move to each positioning point in turn, and data is collected (coordinate acquisition) one by one to obtain the position coordinates of each positioning point and record the corresponding rotation angles of the A-axis and C-axis, that is, the corresponding rotation angle group;

[0103] Among them, the coordinate set summing and averaging formula is:

[0104]

[0105] in, The A-axis rotation angle is θ A , C-axis rotation angle is θ C When (the rotation angle group is (θ A ,θ C ))The coordinates of the i-th positioning point; The A-axis rotation angle is θ A , C-axis rotation angle is θ C The coordinates of the jth collected at the i-th positioning point at time; m is the rotation angle of the A axis θ A , C-axis rotation angle is θ C The total number of times the i-th positioning point is collected.

[0106] S30, according to 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] Among them, x i ′、y i ′、z i′ are the x, y and z coordinates of the i-th positioning point after rotation; θ C ,θ A are the rotation angles of the C-axis and A-axis respectively; i ,y i 、z i are the x, y and z coordinates of the ith positioning point before rotation (initial position); c ,y c are the x and y coordinates of the center of the turntable at the initial position; z a is the z-coordinate of the center of the A-axis.

[0109] The specific derivation process is:

[0110] The coordinates of the i-th positioning point before rotation (initial position) obtained after collection are P i00 , through (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 the i-th positioning point (θ A ,θ C ) after the coordinates; P i00 is the coordinate of the initial position of the i-th positioning point; T -A is the inverse translation matrix of the center position of the A axis; T A is the translation matrix of the center position of the A axis; T -C is the inverse translation matrix of the center position of the C axis; T C is the translation matrix of the center position of the C axis; R A is the rotation matrix around the A axis; R C is the rotation matrix around the C axis;

[0113]

[0114] According to the change of motion relationship, simplify the solution and let x a =x c ,y a =y c , calculated through mathematical expressions and written in the form of coordinate components;

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

[0116]

[0117] Among them, xi ′、y i ′、z i ′ are the x, y, and z coordinates of the i-th positioning point after rotation; θ C ,θ A are the rotation angles of the C-axis and A-axis respectively; i ,y i 、z i are the x, y, and z coordinates of the ith positioning point before rotation (initial position); c ,y c and zc are the x, y, and z coordinates of the center of the turntable at the initial position, respectively; a ,y a 、z a They are the x, y, and z coordinates of the center of the A-axis respectively.

[0118] It should be noted that, because the coefficient matrix of the three-variable linear equation group formed by the collinear points is not full rank, the corresponding three-variable linear equation group has no solution, so the division requirement includes that the final spatial coordinates divided into a group cannot be collinear, so 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, deriving a plurality of three-variable linear equation groups according to a plurality of rotation angle groups of the A axis and the C axis and the coordinate change relationship before and after the rotation, and screening out a plurality of equation groups to be solved.

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

[0121] A10. Substituting the coordinates of the corresponding positioning points and the multiple rotation angle groups of the A-axis and the C-axis into the coordinate change relationship before and after the rotation, a three-variable linear equation group of the number of rotation angle groups corresponding to each positioning point is obtained as the original equation group.

[0122] In this step, at least three rotation angle groups of the A-axis and the C-axis are required, so it is required that in step S20, when the A-axis and the C-axis of the turntable are controlled to rotate multiple times, at least three different rotation angle groups can be obtained.

[0123] A20, traversing and permuting the component equations in the original equation group of all the positioning points, forming a new three-variable linear equation group with three component equations as a group, and any two component equations in the new three-variable linear equation group do not come from the same original equation group;

[0124] A30, retaining a new set of three-variable linear equations whose condition numbers of all coefficient matrices are less than or equal to a set threshold as the set of equations to be solved;

[0125] The specific process of this step is:

[0126] Determine whether the condition number of the coefficient matrix of each new set of three-variable linear equations is less than or equal to the set threshold. If the condition number of the coefficient matrix of a new set of three-variable linear equations is less than or equal to the set threshold, then retain the new set of three-variable linear equations; otherwise, discard it; and finally retain multiple new three-variable linear equations as multiple sets of equations to be solved.

[0127] The resulting solution system is in the form of:

[0128]

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

[0130] To simplify the operation process and calculation, in actual operation, the A axis can be rotated once (θ A2 =θ A3 =θ A ), corresponding to three different rotation angles of the C axis (θ C1 ,θ C2 ,θ C3 ), and three different rotation angle groups are obtained; for example, the turntable randomly rotates around the A axis by 30°, and the turntable randomly rotates around the C axis by 3 times. The turntable first rotates around the C axis by 30° for the first time, and then the turntable rotates around the C axis by 45° for the second time, and finally the turntable rotates around the C axis by 60°, and then the turntable ends its random rotation around the AC axis.

[0131] Then the above solution equations can be simplified to the following form:

[0132]

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

[0134] Specifically:

[0135] According to multiple sets of equations, given a fuzzy initial solution, the Adam optimizer function is used for iterative solution to obtain the corresponding multiple sets of solutions in the following form:

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

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

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

[0139] S60. Calculate the turntable center coordinates and the distance from the axis to the turntable plane based on multiple sets of turntable center x- and y-direction coordinates, the A-axis center z-direction coordinates, and the initial position turntable center z-direction coordinates, and perform calibration based on the turntable center coordinates and the distance from the axis to the turntable plane.

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

[0141] According to the obtained several groups of solutions, the exact solution is obtained through summing and averaging.

[0142] The calculation formula for the x-direction coordinate of the turntable center is:

[0143]

[0144] The calculation formula for the y-direction coordinate of the turntable center is:

[0145]

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

[0147] The calculation formula for the z-direction coordinate of the center of the A-axis is:

[0148]

[0149] Then, if Figure 4 The calculation formula for 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 ck are the x and y coordinates of the solution of the kth set of equations; z ak is the z-direction coordinate of the center of the A axis of the k-th solution of the equation system; refer to Figure 3 , x c ,y c The initial positions O c The x and y coordinates of the origin of the coordinate system in the base coordinate system, that is, the x and y coordinates of the center of the turntable at the initial position; z a is the initial position O A The z-coordinate of the origin of the coordinate system in the base coordinate system, that is, the z-coordinate 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 a number of turntable center coordinates and axis center coordinates based on the coordinates of multiple positioning points before and after rotation for each of three different rotation angle groups, and uses the average value method to calculate a number of turntable center coordinates and a number of axis center coordinates to obtain the final turntable center coordinates and the distance from the axis to the turntable plane.

[0153] The above embodiments are only used to describe the technical solution of the present application in detail to help understand its core idea and should not be regarded as limiting the present application. Any changes or substitutions made by technicians in the technical field within the technical scope disclosed in the present application should be included in the protection scope of the present application.

Claims

1. A method for calibrating the distance between the center of a turntable and the axis of rotation to the turntable plane of a dual turntable five-axis device, characterized in that: The following steps are involved: (1) marking multiple positioning points on the turntable, collecting the coordinates of each positioning point at the initial position, and calculating the z-direction coordinate of the center of the turntable 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) According to the coordinate changes of each positioning point before and after rotation at different angles, the coordinate change relationship before and after rotation is obtained; (4) Based on multiple rotation angles of the A-axis and the C-axis and the coordinate change relationship before and after the rotation, multiple three-variable linear equations are derived and multiple solution equations are obtained by screening; (5) using the obtained multiple sets of equations to be solved, through iterative solutions, the corresponding multiple sets of x- and y-direction coordinates of the center of the turntable and the z-direction coordinates of the center of the A-axis are obtained; (6) Based on multiple sets of turntable center x- and y-direction coordinates, the A-axis center z-direction coordinates, and the initial position turntable center z-direction coordinates, the turntable center coordinates and the distance from the rotation axis to the turntable plane are calculated, and calibration is performed based on the turntable center coordinates and the distance from the rotation axis to the turntable plane.

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

3. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 1 is characterized in that: In step (1), the calculation formula for obtaining the z-direction coordinate of the center of the turntable at the initial position according to the coordinates of multiple positioning points at the initial position is: Among them, z c is the z-direction coordinate of the center of the turntable at the initial position; i is the z-coordinate of the ith positioning point at the initial position; n is the number of positioning points.

4. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 1 is 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 turntable is controlled to rotate randomly multiple times, and the rotation angle is [15°, 45°]. After each rotation of the A axis, the C axis is controlled to rotate randomly multiple times, and each rotation angle is different, and the rotation angle is [0°, +∞]. Among them, one rotation angle of the A axis and one rotation angle of the C axis together constitute a rotation angle group.

5. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 1 is characterized in that: In steps (1) and (2), the coordinates of each positioning point in the initial position and each positioning point in each rotation angle group are collected multiple times to obtain a coordinate set of each positioning point in the corresponding state. Each coordinate set is summed and averaged to obtain the coordinates of each positioning point. The calculation formula is: in, The A-axis rotation angle is θ A , C axis rotation angle is θ C The coordinates of the i-th positioning point at time, i∈[1,n], n is the number of positioning points; The A-axis rotation angle is θ A , C axis rotation angle is θ C The coordinates of the jth collected at the i-th positioning point at time; m is the rotation angle of the A axis θ A , C axis rotation angle is θ C The total number of times the i-th positioning point is collected.

6. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 1 is characterized in that: In step (3), the coordinate change relationship before and after rotation is: Among them, x i ′、y i ′、z i ′ are the x, y, and z coordinates of the i-th positioning point after rotation, i∈[1,n], n is the number of positioning points; θ C ,θ A are the rotation angles of the C-axis and A-axis respectively; i ,y i 、z i are the x, y, and z coordinates of the i-th positioning point before rotation; x c ,y c are the x and y coordinates of the center of the turntable at the initial position; z a is the z-coordinate of the center of the A-axis.

7. The calibration method for the distance between the turntable center and the rotation axis to the turntable plane of the dual turntable five-axis equipment according to claim 1 is characterized in that: The specific process of step (4) is as follows: A10. Substituting the coordinates of the corresponding positioning points and the multiple rotation angle groups of the A-axis and the C-axis into the coordinate change relationship before and after the rotation, a three-variable linear equation group of the number of rotation angle groups corresponding to each positioning point is obtained as the original equation group. A20, traversing and permuting the component equations in the original equation group of all the positioning points, forming a new three-variable linear equation group with three component equations as a group, and any two component equations in the new three-variable linear equation group do not come from the same original equation group; A30. Retain the new three-variable linear equation system whose condition number of all coefficient matrices is less than or equal to the set threshold as the equation system to be solved.

8. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 7 is characterized in that: The resulting solution system is in the form of: Among them, x i ′、y i ′、z i ′ are the x, y and z coordinates of the i-th positioning point after rotation, i∈[1,n], n is the number of positioning points; θ C1 ,θ C2 ,θ C3 are the three rotation angles of the C axis, and θ C1 ≠θ C2 ≠θ C3 θ A2 ,θ A3 They are the two rotation angles of the A axis; x i ,y i 、z i are the x, y and z coordinates of the i-th positioning point before rotation; c ,y c are the x and y coordinates of the center of the turntable at the initial position; z a is the z-coordinate of the center of the A-axis.

9. The calibration method for the distance between the turntable center and the axis of rotation to the turntable plane of the dual turntable five-axis equipment according to claim 1 is characterized in that: In step (5), a fuzzy initial solution is given according to multiple sets of equations to be solved, and the Adam optimizer function is used to iteratively solve the problem, and the corresponding multiple sets of solutions in the following form are obtained: N k [x ck y ck z ak ] Among them, x ck and ck are the x and y coordinates of the center of the turntable for the kth solution of the system of equations; ak is the z-coordinate of the center of the A-axis of the k-th solution of the system of equations; k∈[1,w], w is the number of the system of equations to be solved.

10. The calibration method for the distance between the turntable center and the rotation axis to the turntable plane of the dual turntable five-axis equipment according to claim 1, characterized in that: In step (6), based on the multiple sets of x- and y-direction coordinates of the turntable center obtained in step (5), the z-direction coordinates of the A-axis center, and the z-direction coordinates of the turntable center at the initial position, the following formulas are used to calculate the turntable center coordinates and the distance from the axis to the turntable plane: The calculation formulas for the x and y coordinates of the turntable center are: Then the coordinates of the center of the turntable are N c =[x c y c z c ]; The calculation formula for the z-direction coordinate of the center of the A-axis is: The calculation formula for the distance L from the rotating axis to the turntable plane is: L=z c -With a Among them, x ck and ck are the x and y coordinates of the center of the turntable for the kth solution of the equation system; N c is the center coordinate of the turntable; z ak is the z-direction coordinate of the center of the A axis of the k-th solution of the system of equations; c ,y c are the x and y coordinates of the center of the turntable at the initial position; z a is the z-coordinate of the center of the A-axis; w represents the number of equations to be solved.

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