Geometric error measuring method of machine tool rotating shaft

Abstract

The invention relates to a geometric error measuring method for a machine tool rotating shaft, standard balls are mounted on a rotating shaft workbench of a machine tool, a probe is mounted on a machine tool spindle, and the method comprises the following steps: rotating the rotating shaft workbench to obtain sphere center coordinates of a plurality of groups of standard balls; selecting the center coordinates of one group of standard balls, and calculating an optimal fitting plane; according to the optimal fitting plane and the center coordinates of the other groups of standard balls, position-independent errors are obtained; constructing a transformation matrix, and obtaining a coordinate system after the position-independent error is eliminated; obtaining a matrix equation by combining the center coordinates of the plurality of groups of standard balls, the transformation matrix and the coordinate system; and solving the matrix equation to obtain a position correlation error. The measuring method is based on a numerical control machine tool rotating shaft geometric error model, influences of position-independent errors on the center position of a standard ball at the initial position are considered, four position-independent errors and six position-related errors of the rotating shaft are obtained through step-by-step calculation, and comprehensive measurement of ten errors of the rotating shaft is achieved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical control machine tools, and relates to errors of machine tools, in particular to a geometric error measurement method of a rotating shaft of a machine tool. BACKGROUND

[0002] Numerical control machine tools are key technologies in the field of high-end manufacturing, and especially complex curved surfaces such as turbines and blades put forward higher requirements for the machining precision of numerical control machine tools. Compared with three-axis machine tools, five-axis machine tools increase two rotating shafts, which introduces more errors while having stronger flexibility, and has an adverse effect on the machining precision of machine tools.

[0003] The existing geometric error measurement methods of rotating shafts mainly include a laser interferometer, a ball bar instrument and R-TEST, and have the following problems:

[0004] 1. The measurement process of the laser interferometer needs to be operated by aiming the light, and the steps are complex and tedious, and a large amount of time is needed for installation and debugging; and only the positioning error of the rotating shaft of the machine tool can be measured, the measurement result is not comprehensive enough, and the use cost of the instrument is relatively high.

[0005] 2. The ball bar instrument has a high requirement for the space size of the machine tool, and like the R-TEST measurement method, both will introduce installation errors, causing the identification result to be not accurate enough, and the use cost of the instrument is relatively high. SUMMARY

[0006] The application aims to overcome the deficiencies of the prior art, and provide a geometric error measurement method of a rotating shaft of a machine tool, which is simple in method and comprehensive in detection.

[0007] To solve the above problems, the technical scheme of the application is as follows:

[0008] A geometric error measurement method of a rotating shaft of a machine tool, a standard ball is installed on a rotating shaft workbench of the machine tool, and a probe is installed on a main shaft of the machine tool, and the method comprises the following steps:

[0009] Rotating the rotating shaft workbench to obtain the center coordinates of a plurality of groups of standard balls;

[0010] Selecting the center coordinates of a group of standard balls to calculate a best fitting plane;

[0011] Obtaining a position-independent error according to the best fitting plane and the center coordinates of the remaining groups of standard balls;

[0012] Constructing a transformation matrix and obtaining a coordinate system after eliminating the position-independent error;

[0013] Combining the center coordinates of the plurality of groups of standard balls, the transformation matrix and the coordinate system to obtain a matrix equation;

[0014] Solving the matrix equation to obtain a position-dependent error.

[0015] In further embodiments, the rotating-rotation-axis worktable is rotated to obtain the center coordinates of a plurality of sets of standard spheres, specifically including:

[0016] A plurality of rotation angles are set for the rotating-rotation-axis worktable, and the center coordinates of each rotation angle are obtained.

[0017] The installation positions of the standard spheres are changed multiple times, and the center coordinates of each rotation angle are sequentially obtained.

[0018] In further embodiments, the center coordinates of one set of standard spheres are selected, and a best fitting plane is calculated, specifically including:

[0019] A least square optimization function is constructed with the center coordinates as input:

[0020]

[0021] In the formula, F j (A j ,B j ,C j ,D j ) is the least square optimization function; i is the number of rotation angles set for the rotating-rotation-axis worktable, and j is the number of installation positions of the standard spheres; A j , B j , C j are the plane normal vectors of the best fitting plane; D j is the vertical distance from the best fitting plane to the coordinate origin; X(i,j), Y(i,j), and Z(i,j) are the X-axis, Y-axis, and Z-axis coordinates of the standard spheres, respectively; λ j is the Lagrange multiplier used to constrain the unitization of the plane normal vector.

[0022] The partial derivatives of the plane normal vector, the vertical distance from the best fitting plane to the coordinate origin, and the Lagrange multiplier are taken and set to zero, and the best fitting plane equation is obtained by combining the least square optimization function:

[0023] A j X+B j Y=C j Z+D j =0.

[0024] In the formula, X, Y, and Z are calculated by respectively inputting X(i,j), Y(i,j), and Z(i,j).

[0025] In further embodiments, the position-independent error is obtained according to the best fitting plane and the center coordinates of the remaining sets of standard spheres, specifically including:

[0026] The center of the standard sphere is projected onto the best fitting plane to construct a rotating-rotation-axis axis equation.

[0027] The position-independent error is obtained based on the equation of the axis of rotation.

[0028] In a further embodiment, the center of the standard sphere is projected onto the best-fit plane to construct the equation of the rotation axis, specifically including:

[0029] By projecting the coordinates of each sphere's center onto the fitting plane using the equation of the best-fit plane, the projection points of the sphere's center coordinates are obtained. The projection formula is as follows:

[0030]

[0031] In the formula, X′ (i，j) 、Y′ (i，j) Z′ (i，j) These are the coordinates of the sphere's center after projection onto the fitted plane;

[0032] During the rotation of the rotary axis worktable (1), the trajectory of the center of the standard ball (4) is a planar circle. An optimization function is constructed to fit the center of the planar circle, and the center is constrained to lie on the best-fit plane:

[0033]

[0034] L j =μ j (A j X 0，j +B j Y 0，j +C j Z 0，j +D j );

[0035] G j (X 0，j Y 0，j Z 0，j r j μ j ) = S j +L j ;

[0036] In the formula, s j The objective function is to minimize the error of a planar circle; X (0，j) Y (0，j) Z (0，j) L represents the coordinates of the center of the planar circle on the best-fit plane. j The constraint condition for the center of the planar circle to lie on the best-fit plane; μ j G is the Lagrange multiplier used to constrain the center of the planar circle to lie on the best-fit plane; j The Lagrangian function for jointly optimizing the objective and constraints; r j Let be the radius of the planar circle.

[0037] X (0，j) , Y (0，j) , Z (0，j) , r j , μ j Partial derivative is obtained and the partial derivative is zero, the coordinates of the center of the plane circle on the best fitting plane are solved;

[0038] The plane normal vector of the best fitting plane is taken as a direction vector, and the coordinates of the center of the plane circle on the best fitting plane are taken as a fixed point to establish a rotation axis axis equation:

[0039]

[0040] In further embodiments, the position-independent error is obtained according to the rotation axis axis equation, specifically comprising:

[0041] The rotation axis error term obtained by the plane normal vector is:

[0042]

[0043]

[0044] In the formula, S xc，j , S yc，j are the perpendicularity errors of the measured rotation axis and the X-axis and the Y-axis at the jth installation position, respectively.

[0045] The condition of the first plane is set as:

[0046] Z = 0;

[0047] According to the rotation axis axis equation, the intersection of the rotation axis axis and the first plane is solved to obtain the position error term:

[0048]

[0049] In the formula, O xc，j , O yc，j are the position errors of the standard sphere and the X-axis and the Y-axis at the jth installation position, respectively.

[0050] According to the center coordinates of a plurality of groups of standard spheres, a plurality of groups of perpendicularity errors and position errors are calculated, and the arithmetic average of a plurality of groups of calculation results is obtained to obtain the position-independent error:

[0051]

[0052] In the formula, S xc , S yc , O xc , O yc are the position-independent errors, and n is the number of center coordinates of the standard sphere.

[0053] In a further embodiment, the transformation matrix is constructed and the coordinate system after eliminating the position-independent error is obtained, specifically comprising:

[0054] When the rotation angle of the rotation-axis worktable is zero, the coordinate system of the rotation-axis worktable is set as the machine tool coordinate system, and the ideal transformation matrix from the work coordinate system of the standard sphere to the machine tool coordinate system is:

[0055]

[0056] In the formula, is the ideal transformation matrix; C i is the rotation angle of the rotation-axis worktable;

[0057] The actual transformation matrix from the work coordinate system to the machine tool coordinate system is:

[0058]

[0059]

[0060] In the formula, is the actual transformation matrix; T PIGE is the position-independent error transformation matrix; T PDGE is the position-dependent error transformation matrix; δ x (C i ), δ y (C i ), δ z (C i ), ε x (C i ), ε y (C i ), ε z (C i ) is the position-dependent error parameter;

[0061] The initial coordinates of the standard sphere in the machine tool coordinate system are calculated by inverse matrix transformation as:

[0062]

[0063] In the formula, P′ (1，j) is the initial coordinate of the center of the standard sphere after eliminating the error at the jth installation position; P (1，j) is the measured coordinate of the center of the standard sphere at the jth installation position;

[0064] According to the initial coordinates, the coordinates of the center of the standard sphere measured at different angles of the rotation-axis worktable are obtained as:

[0065]

[0066] In the formula, P(i，j) is the rotation angle of the i th rotary axis workbench, and is the measured standard ball center coordinates at the j th installation position.

[0067] In a further embodiment, the matrix equation is obtained by combining the standard ball center coordinates, the transformation matrix, and the coordinate system of several groups of standard balls, and specifically includes:

[0068] The matrix equation is obtained by combining the coordinates of the centers of the several standard balls:

[0069] A 9×1 = B 9×6 ·E 6×1 ;

[0070]

[0071]

[0072] In the formula, A is the difference between the measured center coordinates of the several groups of standard balls and the error-eliminated standard ball center coordinates; B is the error coefficient matrix; and E is the position-related error vector of the to-be-identified position at one of the rotation angles of the rotary axis workbench.

[0073] In a further embodiment, the position-related error is obtained by solving the matrix equation, and specifically includes:

[0074] The matrix equation is solved by the least square method:

[0075] E = (B T B) -1 B T A;

[0076] The position-related error is obtained by calculating the center coordinates of the rotary axis workbench at each rotation angle in combination with the formula of the position-related error vector of the to-be-identified position at one of the rotation angles of the rotary axis workbench.

[0077] In a further embodiment, the standard ball is installed on the rotary axis workbench by a magnetic force seat.

[0078] Compared with the prior art, the present application has the following beneficial effects:

[0079] 1. The measuring method installs the standard ball on the machine tool rotary shaft workbench through the magnetic base, which is convenient to install, move and remove. The probe is installed on the machine tool spindle, and the center position of the standard ball is measured through the probe. Based on the geometric error model of the numerical control machine tool rotary shaft and considering the influence of position-independent error on the initial position of the standard ball center position, the four position-independent errors and six position-dependent errors of the rotary shaft are calculated step by step according to the center positions obtained at different angles, the comprehensive measurement of ten errors of the rotary shaft is realized, the error measurement precision and efficiency are improved, and the cost is low. It can be applied to the measurement of geometric error of five-axis machine tool rotary shaft with double rotary table structure of different sizes.

[0080] 2. The measuring method combines the standard ball measurement point planning and data acquisition method, adopts the automatic measurement strategy driven by numerical control macro program, and constructs the center coordinate data set required for error identification through multi-position and multi-angle data acquisition. This makes the measuring device and method can effectively identify four position-independent errors and six position-dependent errors, and realize the comprehensive measurement of geometric error of numerical control machine tool rotary shaft, which provides complete error data basis for subsequent machine tool precision analysis.

[0081] 3. Compared with other error measurement equipment, the measuring method has lower cost and simple measurement method. At the same time, it is convenient to integrate with numerical control system, and then realize the automation measurement of error items. It not only reduces the investment cost of traditional measurement method on error measurement equipment, but also greatly shortens the period of error measurement and identification, improves the efficiency of machine tool error detection, and is conducive to quickly carrying out machine tool precision calibration work.

[0082] 4. The measuring method fully considers the influence of position-independent error on the initial measurement coordinate, realizes the decoupling of position-independent error and position-dependent error through step-by-step identification, and can efficiently and accurately measure the related error value. It provides a solid theoretical basis and reliable technical support for machine tool precision calibration and error compensation, and helps to improve the machining precision of numerical control machine tool. BRIEF DESCRIPTION OF DRAWINGS

[0083] Fig. 1 Fig. 1 is a schematic diagram of a standard ball for a geometric error measurement method of a machine tool rotary shaft;

[0084] Fig. 2 Fig. 2 is a schematic diagram of a standard ball for a geometric error measurement method of a machine tool rotary shaft;

[0085] Fig. 3 Fig. 3 is a flow chart of a geometric error measurement method of a machine tool rotary shaft.

[0086] In the figure: 1, rotating shaft workbench; 2, magnetic base; 3, support rod; 4, standard ball; 5, probe; 6, trigger device; 7, measuring head handle; 8, machine tool spindle; 9, receiver; 10, machine tool body. DETAILED DESCRIPTION

[0087] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first", "second" and the like can explicitly or implicitly include one or more of the features. In the description of the present application, unless otherwise stated, the meaning of "a plurality of" is two or more.

[0088] Example 1:

[0089] A geometric error measurement method of a machine tool rotating shaft, as shown in the figure, comprising the following steps: Figs. 1-3

[0090] S101, rotate the rotating shaft workbench 1, and obtain the center coordinates of a plurality of standard balls 4:

[0091] A measuring head module is installed on the numerical control machine tool, the measuring head module comprising a magnetic base 2, a support rod 3, a standard ball 4, a probe 5, a trigger device 6, a measuring head handle 7 and a receiver 9. The magnetic base 2, the support rod 3 and the standard ball 4 are sequentially fixed on the rotating shaft workbench 1 of the machine tool, so that the standard ball 4 is conveniently and quickly installed, disassembled and transposed by magnetic attraction. The measuring head handle 7, the trigger device 6 and the probe 5 are sequentially fixed on the machine tool spindle 8, the probe 5 is used to detect the center coordinates of the standard ball 4, the receiver 9 is fixed on the machine tool body 10, the probe 5 serves as a front sensing component of the measurement, and when the probe 5 contacts the standard ball 4, the trigger device 6 generates a trigger signal, the receiver 9 receives the trigger signal and transmits it to the numerical control system, the numerical control system sends an interrupt request after receiving the signal, locks the measured center coordinates of the standard ball 4, records the center coordinates in the storage location in the numerical control system, and performs program jump through G31 instruction, thereby driving the measuring head to move reversely.

[0092] ​The macro program is written using G31 instruction, the rotary shaft workbench 1 is set to 8 rotation angles, which are 0°, 45°, …, 270°, 315° respectively, and the center coordinates of the standard ball 4 are measured at each rotation angle. Fig. 2 As shown in the figure, the measuring points A, B, C, D and E are arranged on the left, right, front, back and top of the surface of the standard ball 4, first, the measuring points A, B, C, D of the standard ball 4 are measured on the XY plane, and the center coordinates of the standard ball 4 on the XY plane are calculated by the average of the coordinates of the measuring points A and B and the average of the coordinates of the measuring points C and D, then the measuring point E at the top of the standard ball 4 is measured in the Z direction based on the center coordinates, and the measured value is subtracted by the radius value of the standard ball 4, to complete the center coordinates measurement of the standard ball 4 at one rotation angle, then the rotary shaft workbench 1 is rotated to the next angle, the machine tool moving shaft is moved to the measurement position at the angle, and the measurement step is repeated to obtain the center coordinates of the standard ball 4 at each rotation angle, and the center coordinates are stored in the public variable.

[0093] After completing the center coordinates measurement of a group of standard balls 4, the initial installation position of the standard ball 4 is changed, and the measurement step of the center coordinates of the standard ball 4 at each rotation angle is performed again; in order to identify the total error of the rotary shaft, at least three different initial installation positions are set, or at least three standard balls 4 with different initial positions are installed on the rotary shaft workbench 1, and the number of initial installation positions cannot be collinear, in this embodiment, three different initial installation positions are set, so that a total of 24 center coordinates (X (i，j) , Y (i，j) , Z (i，j) ) are obtained, where (X (i，j) , Y (i，j) , Z (i，j) ) is the center coordinates of the standard ball 4 at the i-th rotation angle and the j-th installation position.

[0094] S103, select the center coordinates of a group of standard balls 4, and calculate the best fitting plane:

[0095] In the rotation process of the rotary shaft workbench 1, the center trajectory of the standard ball 4 is a planar circle in space, and the best fitting plane of the center coordinates of the standard ball 4 at 8 angles in the jth group is obtained by least square method. Taking the center coordinates (X (i，j) , Y (i，j) , Z (i，j) ) as input, a Lagrange multiplier is introduced to construct a least square optimization function, as shown in formula (1) and formula (2):

[0096]

[0097] wherein F j (A j , B j , C j , D j ) is a least square optimization function; i is the number of rotation angle set by the rotation axis table, j is the number of installation position of the standard sphere; A j , B j , C j is the plane normal vector of the best fitting plane; D j is the vertical distance from the best fitting plane to the coordinate origin; λ j is the Lagrange multiplier used to constrain the unitization of the plane normal vector.

[0098] The partial derivatives of A j , B j , C j , D j , λ j are taken and set to zero, and the best fitting plane equation is obtained as shown in formula (3) by combining the least square optimization function:

[0099] A j X + B j Y + C j Z + D j = 0 (3)

[0100] wherein X, Y, Z are respectively substituted by X(i, j), Y(i, j), Z(i, j) when calculating.

[0101] S105, according to the best fitting plane and the center coordinates of the remaining group of standard spheres 4, the position-independent error is obtained:

[0102] The rotation axis error term is obtained by the plane normal vector as shown in formula (4) and formula (5):

[0103]

[0104] wherein S xc，j , S yc，j are the perpendicularity error of the measured rotation axis and the X axis, Y axis at the jth installation position, respectively.

[0105] Each center coordinate is projected to the best fitting plane by formula (3) to obtain a projection point as shown in formula (6):

[0106]

[0107] wherein X' (i，j) , Y' (i，j) , Z' (i，j) are the center coordinates after projection to the fitting plane.

[0108] The optimization function constructs a plane circle center fitting the trajectory of the standard ball 4, and constrains the circle center to be on the best fitting plane, as shown in equations (7), (8), and (9):

[0109]

[0110]

[0111] In the formula, S j is the error minimization objective function of the plane circle; X (0，j) , Y (0，j) , and Z (0，j) are the coordinates of the circle center of the plane circle on the best fitting plane; L j is the constraint condition of the circle center of the plane circle on the best fitting plane; μ j is the Lagrange multiplier for constraining the circle center of the plane circle on the best fitting plane; G j is the Lagrange function of the joint optimization objective and constraint; and r j is the radius of the plane circle.

[0112] The partial derivatives of X (0，j) , Y (0，j) , Z (0，j) , r j , and μ j are solved and set to zero, and the coordinates of the circle center of the plane circle on the best fitting plane are obtained;

[0113] The plane normal vector of the best fitting plane is taken as the direction vector, and the fitting circle center X (0，j) , Y (0，j) , and Z (0，j) are taken as fixed points, and the axis equation of the machine tool rotating shaft is established, as shown in equation (10):

[0114]

[0115] The intersection of the axis equation and the Z=0 plane is solved by setting Z=0, and the position-independent error term is obtained, as shown in equations (11) and (12):

[0116]

[0117] In the formula, O xc，j and O yc，j are the position errors of the measured rotating shaft and the X-axis and Y-axis at the jth installation position, respectively.

[0118] The above calculation is performed on the ball center coordinate data of the three groups of standard balls 4, and the three independent results obtained are arithmetically averaged to obtain the final position-independent error parameters, as shown in equation (13):

[0119]

[0120] wherein S xc , S yc , O xc , O yc is the position-independent error, and n is the number of coordinate sets of the center of the standard sphere.

[0121] S107, construct a transformation matrix, and obtain a coordinate system after eliminating the position-independent error:

[0122] The homogeneous coordinate transformation theory is used to establish a geometric error kinematics model of the rotary shaft. When the rotary angle of the rotary shaft worktable 1 is 0, the coordinate system of the rotary shaft worktable 1 is set as the machine tool coordinate system. When the rotary shaft worktable 1 is at other rotary angles, the ideal transformation matrix of the work coordinate system to the machine tool coordinate system based on the standard sphere 4 is shown in formula (14):

[0123]

[0124] wherein, is the ideal transformation matrix; C i is the rotary angle of the rotary shaft worktable;

[0125] Under the influence of the geometric error, the actual transformation matrix of the work coordinate system to the machine tool coordinate system is shown in formula (15), (16) and (17):

[0126]

[0127] wherein, is the actual transformation matrix; T PIGE is the position-independent error transformation matrix; T PDGE is the position-dependent error transformation matrix; δ x (C i ), δ y (C i ), δ z (C i ), ε x (C i ), ε y (C i ), ε z (C i ) is the position-dependent error parameter.

[0128] In the actual measurement process, the center point of the standard sphere 4 measured at the initial position of the standard sphere 4 is affected by the position-independent error. The initial coordinates of the standard sphere 4 under the reference coordinate system are calculated by inverse matrix transformation, as shown in formula (18):

[0129]

[0130] P' = P - e (1,j) is the initial coordinate of the ball center of the standard ball after eliminating the error at the jth mounting position; P (1，j) is the measured coordinate of the ball center of the standard ball at the jth mounting position;

[0131] Therefore, the measured coordinates of the ball center of the standard ball 4 at different rotation angles of the rotation axis workbench 1 are as shown in formula (19):

[0132]

[0133] P = P' + e (i，j) is the measured coordinate of the ball center of the standard ball at the jth mounting position of the i th rotation axis workbench.

[0134] S109, combine the ball center coordinates of several groups of standard balls 4, the transformation matrix, and the coordinate system to obtain a matrix equation:

[0135] The three groups of ball center coordinates are calculated through the above steps, and the obtained three groups of data are solved together, and formula (19) is arranged in a matrix form, as shown in formulas (20), (21), (22), and (23):

[0136] A 9×1 = B 9×6 · E 6×1 (20)

[0137]

[0138] In the formula, A is the difference between the measured ball center coordinates in the steps of obtaining the ball center coordinates of several groups of standard balls and the ball center coordinates of the standard ball after eliminating the error; B is an error coefficient matrix; and E is an error vector related to the to-be-identified position at one of the rotation angles of the rotation axis workbench.

[0139] S111, solve the matrix equation to obtain the position-related error:

[0140] Formulas (20), (21), (22), and (23) are solved by the least square method, and formula (24) is obtained:

[0141] E = (B T B) -1 B T A (24)

[0142] Combined with formula (24), the ball center coordinates at each rotation angle of the rotation axis workbench 1 are calculated, the position-related error is obtained, and the decoupling identification of the position-related error is realized.

[0143] Furthermore, it should be understood that although the specification is described in terms of embodiments, not every embodiment includes every feature described. The specification can include implicit combinations of explicitly mentioned features and / or explicit combinations of implicitely mentioned features. Each embodiment depends on the explicit combinations of features and / or the implicit combinations of features made specifically within that embodiment, and each such embodiment can be combined with every other such embodiment to create further embodiments.

Claims

1. A method for measuring geometric errors of a rotary axis of a machine tool, wherein a standard ball (4) is mounted on a rotary axis table (1) of the machine tool, and a probe (5) is mounted on a main shaft (8) of the machine tool, characterized in that, The method comprises the following steps: rotating the rotation axis workbench (1) to obtain the coordinates of the centers of a plurality of groups of standard balls (4); selecting the coordinates of the centers of one group of standard balls (4) to calculate the best fitting plane; obtaining the position-independent error according to the best fitting plane and the coordinates of the centers of the remaining groups of standard balls (4); constructing a transformation matrix and obtaining a coordinate system after eliminating the position-independent error; combining the coordinates of the centers of a plurality of groups of standard balls (4), the transformation matrix, and the coordinate system to obtain a matrix equation; solving the matrix equation to obtain the position-dependent error.

2. The method of geometric error measurement of a rotary axis of a machine tool according to claim 1, characterized in that, rotating the rotation axis workbench (1) to obtain the coordinates of the centers of a plurality of groups of standard balls (4), specifically comprising: setting a plurality of rotation angles for the rotation axis workbench (1) to obtain the coordinates of the centers of the standard balls (4) at each rotation angle; changing the installation positions of the standard balls (4) multiple times to obtain the coordinates of the centers of the standard balls (4) at each rotation angle in turn.

3. The method of geometric error measurement of a rotary axis of a machine tool according to claim 2, characterized in that, selecting the coordinates of the centers of one group of standard balls (4) to calculate the best fitting plane, specifically comprising: inputting the coordinates of the centers into a least squares optimization function: wherein F j (A j , B j , C j , D j ) is a least square optimization function; i is the number of rotation angles set for the rotation axis table, j is the number of installation positions of the standard sphere; A j , B j , C j are the plane normal vectors of the best fitting plane; D j is the vertical distance from the best fitting plane to the coordinate origin; X(i, j), Y(i, j), Z(i, j) are respectively the X-axis, Y-axis, Z-axis coordinates of the standard sphere; λ j is the Lagrange multiplier used to constrain the plane normal vector to be unitized. taking the partial derivatives of the plane normal vector, the perpendicular distance from the best fitting plane to the coordinate origin, and the Lagrange multiplier and setting the partial derivatives to zero, and combining the least squares optimization function to obtain the best fitting plane equation as: A j X+B j Y+C j Z+D j = 0; wherein X, Y, and Z are respectively substituted with X(i, j), Y(i, j), and Z(i, j) when calculating.

4. The method of geometric error measurement of a rotary axis of a machine tool according to claim 3, characterized in that, obtaining the position-independent error according to the best fitting plane and the coordinates of the centers of the remaining groups of standard balls (4), specifically comprising: projecting the centers of the standard balls (4) onto the best fitting plane to construct a rotation axis equation; obtaining the position-independent error according to the rotation axis equation.

5. The method of geometric error measurement of a rotary axis of a machine tool according to claim 4, characterized in that, projecting the centers of the standard balls (4) onto the best fitting plane to construct a rotation axis equation, specifically comprising: projecting each of the coordinates of the centers onto the fitting plane through the best fitting plane equation to obtain the projection points of the coordinates of the centers, and the projection formula is: In the formula, X′ (i，j) 、Y′ (i，j) Z′ (i，j) These are the coordinates of the sphere's center after projection onto the fitted plane; in the rotation process of the rotation axis workbench (1), the motion trajectory of the center of the standard ball (4) is a planar circle, an optimization function is constructed to fit the center of the planar circle, and the center is constrained to be located on the best fitting plane: L j = μ j (A j X 0，j + B j Y 0，j + C j Z 0，j + D j ); G j (X 0，j , Y 0，j , Z 0，j , r j , μ j ) = S j + L j ; where S j is the error minimization objective function for a planar circle; X (0，j) , Y (0，j) , Z (0，j) are the coordinates of the center of the planar circle on the best fit plane; L j is the constraint condition for the center of the planar circle on the best fit plane; μ j is the Lagrange multiplier for constraining the center of the planar circle on the best fit plane; G j is the Lagrange function for jointly optimizing the objective and the constraint; r j is the radius of the planar circle. X (0，j) , Y (0，j) , Z (0，j) , r j , μ j Taking partial derivatives and setting them to zero, the coordinates of the center of the circle on the best fitting plane are obtained. taking the plane normal vector of the best fitting plane as a direction vector and taking the coordinates of the center of the planar circle on the best fitting plane as a fixed point to establish the rotation axis equation:

6. The method of geometric error measurement of a rotary axis of a machine tool according to claim 5, characterized in that, obtaining the position-independent error according to the rotation axis equation, specifically comprising: obtaining the rotation axis error term through the plane normal vector as: In the formula, S xc,j , S yc,j are the perpendicularity errors of the rotation axis and the X-axis and Y-axis respectively at the jth mounting position. setting the condition of the first plane as: Z＝0； solving the intersection of the rotation axis and the first plane according to the rotation axis equation to obtain the position error term: In the formula, O xc，j , O yc，j are the position errors of the rotation axis and the X-axis and Y-axis respectively under the jth installation position. calculating a plurality of groups of perpendicularity errors and position errors according to the coordinates of the centers of the plurality of groups of standard balls, respectively, and performing arithmetic averaging on the calculation results of the plurality of groups to obtain the position-independent error: where S xc , S yc , O xc , O yc are position-independent errors, and n is the number of coordinate sets of the center of the standard sphere.

7. The method of geometric error measurement of a rotary axis of a machine tool according to claim 6, characterized in that, constructing a transformation matrix and obtaining a coordinate system after eliminating the position-independent error, specifically comprising: When the rotation angle of the rotary axis worktable (1) is zero, the coordinate system of the rotary axis worktable (1) is set as a machine tool coordinate system, and an ideal transformation matrix of the work coordinate system of the standard sphere (4) to the machine tool coordinate system is: In the formula, is an ideal transformation matrix; C i is the rotation angle of the rotation axis table; An actual transformation matrix of the work coordinate system to the machine tool coordinate system is: wherein is the actual transformation matrix; T PIGE is the position independent error transformation matrix; T PDGE is the position dependent error transformation matrix; δ x (C i ), δ y (C i ), δ z (C i , ε x (C i ), ε y (C i ), ε z (C i ) is the position dependent error parameter; An initial coordinate of the standard sphere (4) in the machine tool coordinate system is calculated through inverse matrix transformation: wherein P' (1，j) is the initial coordinates of the center of the standard ball after eliminating errors at the jth mounting position; P (1，j) is the measured coordinates of the center of the standard ball at the jth mounting position; According to the initial coordinate, the coordinates of the center of the standard sphere (4) measured at different angles of the rotary axis worktable (1) are obtained: In the formula, P (i，j) is the rotation angle of the i-th rotary table, and is the measured standard sphere center coordinates at the j-th mounting position.

8. The method of geometric error measurement of a rotary axis of a machine tool according to claim 7, characterized in that, In combination with the center coordinates of a plurality of sets of the standard sphere (4), the transformation matrix, and the coordinate system, a matrix equation is obtained, specifically including: The center coordinates of a plurality of sets of the standard sphere (4) are combined to obtain a matrix equation: A 9×1 = B 9×6 • E 6×1 ; E 6×1 = [δ x (C i ) δ y (C i ) δ z (C i ) ε x (C i ) ε y (C i ) ε z (C i )] T ; In the formula, A is a rotary rotary axis worktable, and the difference between the center coordinates measured in the steps of obtaining the center coordinates of a plurality of sets of standard spheres and the center coordinates of the standard sphere after error elimination; B is an error coefficient matrix; and E is a position-related error vector to be identified at one of the rotation angles of the rotary axis worktable.

9. The method of geometric error measurement of a rotary axis of a machine tool according to claim 8, characterized in that, The matrix equation is solved to obtain a position-related error, specifically including: The matrix equation is solved by the least square method: E = (B T B) -1 B T A; In combination with the formula of the position-related error vector to be identified at one of the rotation angles of the rotary axis worktable, the center coordinates of the standard sphere (4) at each rotation angle of the rotary axis worktable (1) are calculated to obtain the position-related error.

10. The method of geometric error measurement of a rotary axis of a machine tool according to claim 9, characterized in that, The standard sphere (4) is installed on the rotary axis worktable (1) through the magnetic base (2).

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