Rotary shaft geometric error self-calibration identification method based on tower-shaped workpiece

Abstract

The invention discloses a rotary shaft geometric error self-calibration identification method based on a tower-shaped workpiece, and the method comprises the following steps: S10, carrying out the design of the tower-shaped workpiece which is formed by neatly stacking five layers of square steps and is of a regular stepped structure; s20, error definition and modeling are carried out, errors comprise workpiece geometric errors, linear axis errors and rotation axis errors, and EG represents workpiece geometric error values at the measuring points, namely, deviation values of actual outlines of the workpieces at the measuring points and theoretical design positions in the normal direction; s30, measuring point distribution setting and measuring mode definition are carried out; and S40, identifying errors by adopting a self-calibration algorithm. By using the method, the geometric errors of the rotating shaft (C shaft), the linear shaft and the workpiece can be synchronously identified.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of numerical control machine tool finishing, and particularly relates to a rotating shaft geometric error self-calibration identification method based on a tower-shaped workpiece. BACKGROUND

[0002] Five-axis machine tools play a key role in the manufacturing of complex parts in the fields of aerospace, automotive, and precision mold, etc. due to their multi-degree-of-freedom machining capability. However, compared with three-axis machine tools, the geometric error sources of five-axis machine tools increase significantly due to the introduction of two rotating axes, and the error coupling phenomenon in the process of multi-axis linkage is more complex. These factors seriously restrict the machining precision and process stability of the machine tool. Under this background, it is particularly important to develop high-precision geometric error identification technology. Only by comprehensively identifying and quantifying the influence of each geometric error can effective precision compensation be achieved.

[0003] From the perspective of geometric error, the precision of five-axis machine tools is mainly affected by two types of errors: linear axis errors and rotating axis errors. Among them, rotating axis errors can be further divided into position-independent geometric errors (PIGE) and position-dependent geometric errors (PDGE) according to their characteristics. The accurate identification and compensation of these errors are the key to improving the machining precision of five-axis machine tools.

[0004] Currently, various measurement methods have been developed for the identification of rotating axis geometric errors of five-axis machine tools, but each method has corresponding technical limitations. In low-cost measurement schemes, the ball-bar test method is the most widely used. Seth et al. established a kinematic model based on homogeneous coordinate transformation, and innovatively used three ball-bar installation modes to successfully identify eight PIGE of rotating axes; Guo et al. further optimized this method, and based on the error characteristics of rotating axes under different motion states, designed four measurement modes to extend the identification capability of PIGE to ten items. Although this method has the advantages of low equipment cost and simple operation, the measurement results are easily affected by the coupling of rotating axis positioning errors and linear axis perpendicularity errors, and need to be decoupled with specific path planning, and is sensitive to installation eccentricity and environmental temperature drift, affecting the measurement accuracy.

[0005] To improve measurement efficiency, the R-test device recommended by ISO 230-1:2012[7] provides a new solution. This device can obtain the coordinates of the center of a three-dimensional sphere through a single sampling, greatly simplifying the measurement process. Pu et al. innovatively integrated the tool tip coordinate error modeling and the kinematic chain transmission error modeling methods, and used the R-test to achieve efficient identification of geometric errors in the three directions of the rotation axis X, Y, and Z. Compared with the traditional ballbar, this method significantly improves measurement efficiency, but its expensive equipment investment cost limits its promotion and application in industrial sites.

[0006] In the field of high-end measurement, laser interferometers hold a prominent position due to their submicron measurement accuracy. Deng et al. introduced the theory of rigid body motion constraints and used laser tracking interferometers to achieve four PIGE and six PDGE measurements of a rotary axis. Ibaraki et al. used open-loop laser tracking interferometers to identify multiple errors in the two-dimensional motion of machine tools. However, this method relies on expensive equipment and has high requirements for the optical path environment, resulting in high measurement costs and complex operations. This significantly reduces measurement efficiency, especially in scenarios requiring rapid or frequent measurements.

[0007] In recent years, visual measurement has also been used to measure errors in rotational axes. Based on visual measurement technology, Yin et al., using a five-axis dispensing machine as a validation object, proposed an error estimation method for identifying all geometric errors of rotational axes within a compact space. Visual measurement offers the advantages of non-contact and real-time dynamic measurement, but it requires precise calibration of the camera and rotation stage positions, places high demands on light source stability and environmental conditions, and is susceptible to interference.

[0008] On-machine measurement has good communication capabilities with the CNC system, which can achieve efficient and automated measurement. The ISO-10791-7:2020 standard lists three types of test workpieces (M1, frustum, and S-shaped workpieces), and evaluates the comprehensive performance indicators of the machining center based on the dimensional deviation of the finished workpiece. Zhang et al. designed a multi-feature workpiece that can simultaneously identify 15 static errors and dynamic errors. Ibaraki et al. proposed a set of multi-mode machining tests, combined with the error identification model derived from the spatial error model, and identified 8 PIGEs of the rotary axis by cutting a pyramid-shaped workpiece. Cheng et al. identified 6 geometric errors of the rotary axis by cutting a misaligned tower-shaped workpiece. Chen et al. also used a similar method to cut a double-feature groove workpiece and identified 5 PIGEs of the rotary axis of a five-axis machine tool. However, these studies usually assume that linear axis errors have been compensated or can be ignored, which leads to the accumulation of uncertainty in the error model. Recently, Cheng et al. proposed a rotation axis error identification method based on a disc-shaped workpiece. This method shielded the influence of the linear axis through a specific processing method, but this method significantly increased time and economic costs, limiting its practicality.

[0009] To break through the limitations of traditional methods, self-calibration technology has gradually become the focus of research in the field of precision measurement. In the fields of precision detection such as coordinate measuring machine, spindle detection, roundness measurement, error separation technology and self-calibration method are widely used to distinguish between workpiece error and measurement system error. The core advantage of this technology is that it can achieve high-precision measurement without relying on external calibration workpieces. Self-calibration significantly improves the efficiency and accuracy of machine tool calibration through automated processes, multi-error separation and strong adaptability, especially suitable for complex machining environments with high dynamics and multi-axis linkage. Ibaraki et al. proposed an error modeling and identification method based on a standard disc workpiece. By designing multiple measurement paths, the coupling relationship between 4 PIGE (E AOC , E BOC , E XOC , E YOC ), 3 PDGE (E XC , E YC , E ZC ) and 5 linear axis errors (E radial，XY , E C(OX)Y , E ZX , E ZY , E A(OY)Z ) of the C-axis and the geometric error of the disc-shaped workpiece was successfully separated. The method proposed in this paper can identify the geometric error of the tower-shaped workpiece, 4 PIGE, 6 PDGE and 10 linear axis errors of the C-axis through one measurement process. The complete error term is shown in Table 1, which is superior to the above method in terms of error identification quantity. Subsequent research by Ibaraki et al. proposed an identification method only applicable to two-dimensional planes, which can identify workpiece geometric error, 2 PIGE (E XOC , E YOC ), 3 PDGE (E XC , E YC , E CC ) of the C-axis and 6 linear axis errors (E XX , E YX , E XY , E YY , E CY , E C(OX)Y ).

[0010] Table 1 Error variables that can be identified by self-calibration of tower-shaped workpieces

[0011]

[0012] SUMMARY

[0013] In view of the above problems, the present application provides a self-calibration identification method for geometric errors of rotating shafts based on tower-shaped workpieces, which can simultaneously identify the geometric errors of rotating shafts (C-axis), linear shafts and workpieces.

[0014] To solve the above technical problems, the application adopts the following technical solutions:

[0015] A rotation axis geometric error self-calibration identification method based on a tower-shaped workpiece, comprising the following steps:

[0016] S10, tower-shaped workpiece design: identify the geometric error of the C-axis, the tower-shaped workpiece is neatly stacked by five square steps, showing a regular stepped structure, the bottom step is 100mm in length, and the length of each layer is 10mm in height, and the length decreases in turn: the second layer is 80mm, the third layer is 60mm, the fourth layer is 40mm, and the top layer is 20mm, showing a tower-shaped structure, and the total height of the workpiece is 95mm, as shown in Figure 3 , and the specific size is shown in Figure 4 ;

[0017] S20, error definition and modeling: the error includes workpiece geometric error, linear axis error and rotation axis error, wherein E G represents the workpiece geometric error value at the measuring point, i.e. the deviation of the actual profile of the workpiece at the measuring point from the theoretical design position along the normal direction;

[0018] S30, measurement point distribution setting and measurement mode definition: the measurement coordinate system is set as follows: the X-axis is parallel to one side of the step, the Y-axis is parallel to the other side, and the Z-axis is vertical upward, and the coordinate origin is located 10mm below the first step surface and coincides with the center of the step surface; the measuring points are divided into two parts, the first part is located on the side surface of the workpiece, i.e. the Z=0 plane, and there are 36 measuring points; the second part is located on the top surface of the workpiece, and there are also 36 measuring points; the theoretical position of each measuring point is converted into the position in the machine tool coordinate system, and then the measurement error is obtained according to the position in the machine tool coordinate system;

[0019] S40, error identification using self-calibration algorithm: the position deviation of the measuring point is the result of the combined action of the workpiece geometric error, the linear axis error and the rotation axis error, assuming that the total number of error items to be identified is N i , the number of measuring points at each measuring angle is N p , and the total number of measuring angles is N c , then the total measuring point data amount is N p ·N c , a three-dimensional linear axis volume error model is introduced, the continuous linear axis error is discretized into a finite grid point, the number of error parameters is reduced from N i to a limited value, and by increasing the measuring angle N c , the total number of measuring points satisfies N p ·N c >N iThus, an over-determined equation set is constructed, and finally, the error terms to be identified are solved by least square method to obtain the best estimation of the error terms.

[0020] In one possible implementation, in S20, during the workpiece measurement, the B-axis is fixed at 0° position, and based on this, the volumetric error models of the X, Y and Z axes are established, as shown in equation (1):

[0021]

[0022] When the probe ball is located at the grid point (x line,f ,y line,g ,z line,h ), the positioning errors of the linear axes are modeled by equation (2), E X,total represents the influence of the linear axis at a specific position on the X-axis error, E Y,total represents the influence of the linear axis at a specific position on the Y-axis error, and E Z,total represents the influence of the linear axis at a specific position on the Z-axis error, which reflect the influence of the deviations of the linear axis movement in different directions on the overall positioning accuracy, respectively.

[0023]

[0024] E XX (x line,f )) represents the X-axis linear positioning error, and the error movement of the X-axis is represented by the definition on the discrete X position set x line,f (f = -80, -60, -40, …, 40, 60, 80), and the error value is looked up by the line position, which contains 9 parameters; the error movement of the Y-axis is defined on the y line,g (g = -80, -60, -40, …, 40, 60, 80) position, which also contains 9 parameters; similarly, the error movement of the Z-axis is defined on the z line,h (h = 0, 10, 20, 30, 40, 50) position, which contains 6 parameters; the values in the brackets, including -80, -60, …, 80 in x line,f , represent the discrete positions of the axes, in millimeters (mm), i.e., the error movements of the X, Y and Z axes are represented on the three-dimensional grid point (x line,f ,y line,g ,z line,h ); when the positioning of the X, Y and Z axes is completed, the kinematic model equation (2) is used to describe the positioning errors of the X, Y and Z axes of each grid point (x line,f ,y line,g ,z line,h ); similarly, when the C-axis is rotated to C θθ = 0°, 30°, 60°,..., 300°, 330°, the rotation axis errors are represented by E XC (C θ ), E XOC , E YC (C θ ), E YOC , E CC (C θ ), E AC (C θ ), E AOC , E BC (C θ ) and E BOC , which can be divided into two categories according to their influence range, one mainly affects the motion accuracy in the XY plane, and the other mainly affects the positioning accuracy in the Z-axis direction.

[0025] In one possible implementation, the identification of the errors in the XY plane in S40 includes:

[0026] The measuring points 1-36 are distributed on the plane Z = 0, i.e. the XY plane, and the position error Δ1 total,i,θ is affected by three types of error sources: workpiece geometric error, linear axis error and rotation axis error, and the influence of the workpiece geometric error on the detected displacement at the measuring point position is represented as:

[0027] Δ1 1,i = E G ( w p i * ) (23)

[0028] The influence of the linear axis error on the detected displacement at the measuring point is represented as:

[0029]

[0030] The influence of the rotation axis error on the detected displacement at the measuring point is represented as:

[0031]

[0032] In the formula, n m n * i,θ represents the unit vector perpendicular to the workpiece surface in the MCS at this time;

[0033] The total displacement error is represented as:

[0034]

[0035] Since the linear axis errors are defined on discrete grid points, the total error vector (E X,total ( m x * i,θ , m y * i,θ , m z * i,θ ),E Y,total ( m x * i,θ , m y * i,θ , m z * i,θ )) T is converted into the form expressed by grid point coordinates, considering the characteristics of the measurement plane Z = 0, the Z-axis related terms are ignored, when the actual measurement point ( m x * i,θ , m y * i,θ ) satisfies the grid interval condition:

[0036]

[0037] In this case, the error components are calculated by using the bilinear interpolation method, and the normalized interpolation weight coefficients are defined:

[0038]

[0039] Then, E X,total and E Y,total in equation (2) are converted into the following form by using the linear interpolation method:

[0040]

[0041] Since there is redundancy between the parameters in the model, which can cause the coefficient matrix of the equation set to have a rank deficiency problem, appropriate boundary conditions are introduced to eliminate the rank defect of the coefficient matrix, and at the same time fix the positioning of the origin of the machine coordinate system (MCS), as shown in equation (15):

[0042]

[0043] On the basis of the above boundary conditions, additional boundary conditions are also needed to define the X and Y directions of the MCS and determine the absolute length of the X axis, as shown in equation (14); since the current self-calibration method cannot directly obtain the absolute length, it is necessary to obtain ΔL1 by detecting a standard workpiece with a pre-calibrated length:

[0044]

[0045] After subtracting 11 known boundary conditions, the number of errors to be identified N i = 106, the number of probing points, i.e. the number of equations, is N p · N c = 36 x 11 = 396, since N p · N c > N i , i.e. the number of equations is greater than the number of unknowns, which meets the requirements of the self-calibration algorithm.

[0046] In one possible implementation, in S40, the error identification in the Z-axis direction includes:

[0047] The probing points 37-72 are distributed on the top surface of each step of the workpiece, and the position error Δ2 total,i,θ of the probing points is also affected by three types of error sources, including workpiece geometric error, linear axis error and rotary axis error, and the influence of the workpiece geometric error on the probing displacement at these probing point positions is represented as:

[0048] Δ2 1,i = E G ( w p i * ) (34)

[0049] The influence of the linear axis error on the probing displacement at the probing points is represented as:

[0050]

[0051] The influence of the rotary axis error on the probing displacement at the probing points is represented as:

[0052]

[0053] The total displacement error is represented as:

[0054]

[0055] Boundary conditions are applied for solving, as shown in equation (21), in which ΔL2 is measured by probing a standard workpiece with a pre-calibrated length:

[0056]

[0057] After subtracting 8 known boundary conditions, the number of errors to be identified N i = 60, the number of probing points, i.e. the number of equations, is N p · N c= 36 * 11 = 396; since N p ·N c >N i That is, the number of equations is greater than the number of unknowns, which meets the requirements of the self-calibration algorithm.

[0058] In one possible implementation, in S40, solving the error terms by the least square method comprises:

[0059] When the C-axis rotates to an angle θ (θ = 0°, 30°, 60°, …, 300°, 330°), 36 measuring points distributed in the XY plane and the Z-axis direction are detected, and the position of each measuring point is represented as m p i,θ * = ( m x * i,θ , m y * i,θ , m z * i,θ ), in combination with each measuring position, a total of N p ·N c = 36 * 11 = 396 measuring points, and formula (9) and formula (20) are converted into matrix forms:

[0060]

[0061] In the formula, Δ1 represents a set of workpiece geometric errors, Δ2 represents a set of linear axis errors, and Δ3 represents a set of rotary axis errors, and in the formula, M represents a coefficient matrix composed of coefficients of each error term in the vector (Δ1, Δ2, Δ3) T After a boundary condition is applied, the following minimization problem is solved by the least square method to identify the vector (Δ1, Δ2, Δ3) T containing error parameters on the right side of formula (20):

[0062]

[0063] The two parts of data in the XY plane and the Z-axis direction are substituted into formula (23), and each error term can be identified.

[0064] The present application has the following beneficial effects:

[0065] (1) The error identification model is expanded to three-dimensional space, more rotation axis error terms can be identified in C-axis error identification; in linear axis error identification, the identification ability of Z-axis error term is further introduced, and the coverage range of error terms in XY plane is expanded, so that more comprehensive three-dimensional error modeling is realized, and the integrity and applicability of the model are improved. The three-dimensional volume error model of the linear axis introduced is different from the traditional method which does not consider or directly ignores the linear axis error, or offsets the linear axis error through processing method, the self-calibration algorithm directly solves the linear axis error while identifying the rotation axis error, so as to improve the accuracy of error identification.

[0066] (2) Combined with the designed workpiece, the self-calibration algorithm can keep the error identification result unchanged under repeated clamping, and realize long-term monitoring of the machine tool error. At the same time, the workpiece has universality and can be applied to other types of machine tools without reprocessing, so as to improve the applicability of the method and save the cost.

[0067] (3) The experimental results show that compared with the disc-shaped workpiece, the error identification result consistency of the proposed method reaches 89.8%, which verifies the feasibility and effectiveness of the method. At the same time, the experimental data further prove that the method can stably identify C-axis error under different measurement angles, which provides valuable reference and guidance for error compensation and precision improvement of five-axis machine tools. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 A step flow chart of a rotation axis geometric error self-calibration identification method based on a tower-shaped workpiece according to an embodiment of the present application;

[0069] Figure 2 A structure schematic diagram of a five-axis machine tool configured in an embodiment of the present application;

[0070] Figure 3 A tower-shaped workpiece schematic diagram in an embodiment of the present application;

[0071] Figure 4 A tower-shaped workpiece size schematic diagram in an embodiment of the present application;

[0072] Figure 5 A workpiece geometric error definition schematic diagram in an embodiment of the present application;

[0073] Figure 6 A linear axis error definition schematic diagram on a three-dimensional grid point in an embodiment of the present application;

[0074] Figure 7 A schematic diagram of the influence of the rotation axis error on the tower-shaped workpiece in an embodiment of the present application;

[0075] Figure 8Figure 2 is a schematic diagram of the distribution of side measurement points in an embodiment of the present application;

[0076] Figure 9 Figure 3 is a schematic diagram of the distribution of top measurement points in an embodiment of the present application;

[0077] Figure 10 Figure 4 is a schematic diagram of the influence of error terms on the detected displacement in the XY plane in an embodiment of the present application;

[0078] Figure 11 Figure 5 is a schematic diagram of the influence of error terms on the detected displacement in the Z axis direction in an embodiment of the present application;

[0079] Figure 12 Figure 6 is a schematic diagram of a workpiece being machined in an embodiment of the present application;

[0080] Figure 13 Figure 7 is a schematic diagram of a workpiece being measured in an embodiment of the present application;

[0081] Figure 14 Figure 8 is a schematic diagram of the workpiece geometric error of side measurement points in an embodiment of the present application;

[0082] Figure 15 Figure 9 is a schematic diagram of the workpiece geometric error of top measurement points in an embodiment of the present application;

[0083] Figure 16 Figure 10 is a schematic diagram of the X axis displacement error in an embodiment of the present application;

[0084] Figure 17 Figure 11 is a schematic diagram of the Y axis displacement error in an embodiment of the present application;

[0085] Figure 18 Figure 12 is a schematic diagram of the Z axis displacement error in an embodiment of the present application;

[0086] Figure 19 Figure 13 is a schematic diagram of the X axis angle error in an embodiment of the present application;

[0087] Figure 20 Figure 14 is a schematic diagram of the C axis linear error in an embodiment of the present application;

[0088] Figure 21 Figure 15 is a schematic diagram of the C axis angle error in an embodiment of the present application. DETAILED DESCRIPTION

[0089] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0090] Reference Figure 1, as shown in a kind of based on the rotating shaft geometric error self-calibration identification method of tower-shaped workpiece, comprising the following steps:

[0091] S10, tower type workpiece design is carried out: as shown in the figure Figure 3 And Figure 4 Tower type workpiece is neatly stacked by five square steps, showing regular ladder structure, the bottom step side length is 100mm, the height of each layer is 10mm, the side length decreases in turn: the second layer is 80mm, the third layer is 60mm, the fourth layer is 40mm, the top layer is 20mm, the overall tower structure, the total height of workpiece is 95mm;

[0092] S20, error definition and modeling is carried out: trigger probe realizes positioning through the linear drive of X, Y and Z axis, and its detection position is not only affected by workpiece geometric error, but also interfered by X, Y and Z axis linear error. These errors may cause the probe positioning deviation, and then affect the measurement accuracy. In addition, in order to complete the complete measurement process, the workpiece needs to be rotated through C axis, and the error motion of C axis will also affect the position of the probe. Error identification work is mainly aimed at various error variables listed in table 1, in order to analyze its influence on measurement accuracy. The error includes workpiece geometric error, linear axis error, rotary axis error, wherein E G Indicates the workpiece geometric error value at the measuring point, that is, the deviation amount of the actual profile of the workpiece at the measuring point from the theoretical design position along the normal direction;

[0093] S30, measurement point distribution setting and measurement mode definition are carried out: Figure 8 And Figure 9 The measurement point distribution diagram on the tower-shaped workpiece in the experiment is shown. The measurement coordinate system is set as follows: X axis is parallel to one side of the step, Y axis is parallel to the other side, Z axis is vertical upward, and the coordinate origin is located 10mm below the first step surface and coincides with the step surface center; the measuring points are divided into two parts, the first part is located on the side surface of the workpiece, that is, Z=0 plane, and there are 36 measuring points; the second part is located on the top surface of the workpiece, and there are also 36 measuring points; the theoretical position of each measuring point is converted into the position in the machine tool coordinate system, and then the measurement error is obtained according to the position in the machine tool coordinate system;

[0094] S40, error is identified by using self-calibration algorithm: the core of self-calibration algorithm is to construct overdetermined equation set through multi-angle measurement data, and to realize optimal estimation of error parameters by using least square method. The position deviation of measuring point is the result of the joint action of workpiece geometric error, linear axis error and rotary axis error, assuming that the total number of error items to be identified is N i , the number of measuring points under each measuring angle is N p , and the total number of measuring angles is N c , then the total measuring point data amount is Np ·N c Since the linear axis error changes with the position of the bed coordinate system, if all error terms are directly modeled globally, the number of parameters to be identified, Ni, will exceed the amount of valid measurement point data (i.e., Ni>Np·Nc), thus forming an underdetermined problem. To solve this problem, a three-dimensional linear axis volume error model is introduced to discretize the continuous linear axis error into a finite grid point, reducing the number of error parameters from N to N. i Infinite reduction to finite value by increasing the measurement angle N c , so that the total number of measurement points satisfies N p ·N c >N i , thereby constructing an overdetermined set of equations. Finally, the error term to be identified is solved by solving the minimization problem using the least squares method, thereby obtaining the best estimate of the error term.

[0095] The above-mentioned self-calibration and identification method of the geometric error of the rotating axis based on the tower-shaped workpiece is applicable to any five-axis machine tool with three orthogonal linear axes and the C-axis, provided that the workpiece must be mounted on the rotary table (C-axis). In order to express the method more intuitively, this paper chooses the following example: Figure 2 The five-axis machine tool with a double turntable mechanism shown has a structure code of [wC'B'Y'BXZ(C1)t].

[0096] In another embodiment of the present invention, a self-calibration and identification method for a rotating axis geometric error based on a tower-shaped workpiece is provided. In S20, E G Indicates the geometric error value of the workpiece at the measuring point, such as Figure 5 As shown in , that is, the deviation of the actual contour of the workpiece at the measurement point from the theoretical design position along the normal direction. This error term directly reflects the degree of deviation of the machined surface from the ideal geometric model and is one of the core factors affecting the accuracy of on-machine measurement. Assuming that the volume error model associates the error motion of each axis with the position of the tool center point, during the workpiece measurement process, the B axis is fixed at the 0° position, and based on this, the volume error models of the X, Y, and Z axes are established, as shown in formula (1):

[0097]

[0098] Where, The volume expression of the machine tool coordinate system relative to the workpiece coordinate system, The volume expression of the machine tool coordinate system relative to the Y axis is: It represents the volume expression of the workpiece coordinate system relative to the tool coordinate system. The subscript e represents the actual state, and the subscript i represents the ideal state. ΔP represents the position error, (0001) T It represents a vector, which is multiplied by the previous position matrix to obtain the position error.

[0099] When the probe ball is located at the grid point (x line,f ,y line,g ,z line,h ), the positioning error of the linear axis is modeled by equation (2), E Xtotal represents the influence of the linear axis at a specific position on the X-axis error, E Ytotal represents the influence of the linear axis at a specific position on the Y-axis error, and E Z,total represents the influence of the linear axis at a specific position on the Z-axis error, which respectively reflects the influence of the deviation of linear axis movement in different directions on the overall positioning accuracy.

[0100]

[0101] In the equation, E X，total (x line,f ,y line,g ,x line,h ) represents the total displacement error in the X direction at the position (x line,f ,y line,g ,x line,h ). E Y，total (x line,f ,y line,g ,x line,h ) and E Z，total (x line,f ,y line,g ,x line,h ) are the same; yz represents the y and z coordinates at that point.

[0102] The symbol E (such as E XX (x line,f )) represents the error movement of the X, Y or Z axis, which is defined as shown in Table 1. The naming of the above symbols follows the ISO 230-1 standard, and the error movement of each axis is related to the current position (X, Y, Z). The naming of the above symbols follows the ISO 230-1 standard, and the error movement of each axis is related to the current position (X, Y, Z); the error movement of the X axis is represented by definition on a discrete set of X positions x line,f (f = -80, -60, -40,..., 40, 60, 80), and the error value is found by linear position lookup, which contains 9 parameters; the error movement of the Y axis is defined at y line,g (g = -80, -60, -40,..., 40, 60, 80) positions, which also contains 9 parameters; similarly, the error movement of the Z axis is defined at z line,h (h = 0, 10, 20, 30, 40, 50) positions, which contains 6 parameters, and the values in the brackets include x line,fThe -80, -60, ..., 80) in the figure represent the discrete positions of each axis in millimeters (mm), that is, the error motion of the X, Y and Z axes at the three-dimensional grid point (x line,f ,y line,g ,z line,h ) is indicated on Figure 6 The geometric errors of the linear axes defined on the grid points are shown. When the positioning of the X, Y and Z axes is completed, the kinematic model (2) is used to describe each grid point (x line,f ,y line,g ,z line,h ) of the X, Y, and Z axes; similarly, when the C axis rotates to C θ At each angular position (θ=0°, 30°,60°,…,300°,330°), the rotation axis error is respectively given by E XC (C θ ), E XOC 、E YC (C θ ), E YOC 、E CC (C θ ), E AC (C θ ), E AOC 、E BC (C θ ) and E BOC These error terms can be divided into two categories according to their influence range. One category mainly affects the motion accuracy in the XY plane, and the other category mainly affects the positioning accuracy in the Z axis direction. The geometric relationship of the specific error terms is as follows: Figure 7 As shown in Figure 2, the figure clearly shows the influence mechanism of each error component on the pyramidal workpiece.

[0103] In S30, each measuring point is marked with a unique serial number i (i = 1, 2, 3 ... 72), and its theoretical position is recorded as w p i * =( w x i * , w y i * , w z i * ), where the superscript w indicates that the coordinate is defined in the workpiece coordinate system (WCS), and the superscript * indicates a theoretical value. When installing the workpiece, ensure that one side of the workpiece is parallel to the X axis of the machine coordinate system (MCS) and fixed to the C axis. θ (θ=0°, 30°, 60°, ..., 300°, 330°) are measured in sequence according to the measuring point number, and the subscript θ represents the position when the C-axis angle is θ. According to the kinematic convention of machine tool axes, Cθ Theoretical position in workpiece coordinate system w p i * Can be converted into the position in the machine tool coordinate system by the following transformation m p i,θ * :

[0104] m p i,θ * = R(-C θ )· w p i * (43)

[0105]

[0106] Where R(-C θ ) represents a rotation matrix rotating θ degrees counterclockwise around the Z axis (because the C-axis rotates clockwise, which is equivalent to the coordinate system rotating counterclockwise).

[0107] Assuming that when the C-axis rotation angle is θ, the unit normal vector perpendicular to the workpiece surface at the i-th measuring point is represented in the machine tool coordinate system (MCS) as m n * i,θ , the measurement error can be represented as:

[0108] E total = m n * i,θ ·( m p i,θ e - m p i,θ * ) (45)

[0109] Where, m p i,θ e is the actual position of the i-th measuring point in the machine tool coordinate system at θ angle measured by the measuring head; the superscript e indicates the actual value; E total represents the total measurement error.

[0110] Another embodiment of the present application is a method for self-calibrating and identifying the geometric error of the rotating shaft based on a tower-shaped workpiece, wherein the identification of the error in the XY plane in S40 includes:

[0111] The measuring points 1-36 are distributed on the plane Z=0, i.e. the XY plane, and the position error Δ1 total,i,θ of the detection points is affected by three types of error sources: workpiece geometric error, linear axis error and rotating shaft error,Figure 10 The influence of the above errors on the probe displacement is shown intuitively. At these measuring point positions, the influence of the workpiece geometric error on the probe displacement is represented as:

[0112] Δ1 1,i = E G w p i * (46)

[0113] where Δ1 1,i represents the influence of the workpiece geometric error on the probe displacement; E G represents the workpiece geometric error.

[0114] The influence of the linear axis error at the measuring point on the probe displacement is represented as:

[0115]

[0116] where Δ1 2,i,θ represents the influence of the linear axis error at the measuring point on the probe displacement.

[0117] The influence of the rotary axis error at the measuring point on the probe displacement is represented as:

[0118]

[0119] where m n * i,θ represents the unit vector in the MCS perpendicular to the workpiece surface at this time;

[0120] The total displacement error is represented as:

[0121]

[0122] where Δ1 total,i,θ represents the total displacement error.

[0123] As shown in Figure 7 , since the linear axis error is defined at discrete grid points, the total error vector (E X,total ( m x * i,θ , m y * i,θ , m z * i,θ ), E Y,total ( m x * i,θ , m ​y * i,θ , m z * i,θ )) T Transforming into the form expressed by grid point coordinates, considering the characteristics of the measurement plane Z = 0, the Z-axis related terms are ignored, and the actual measurement point ( m x * i,θ , m y * i,θ ) satisfies the grid interval condition:

[0124]

[0125] In this case, the bilinear interpolation method is used to calculate the error component, and the normalized interpolation weight coefficient is defined:

[0126]

[0127] Then, the E X,total and E Y,total in equation (2) are converted into the following form by the linear interpolation method:

[0128]

[0129] In the formula, E X,total ( m x * i,θ , m y * i,θ , m z * i,θ ) represents the total displacement error in the X direction at point ( m x * i,θ , m y * i,θ , m z * i,θ ).

[0130] Because there is redundancy between parameters in the model, which may cause the coefficient matrix of the equation system to have a rank deficiency problem, appropriate boundary conditions need to be introduced to eliminate the rank defect of the coefficient matrix and fix the positioning of the machine coordinate system (MCS) origin, as shown in equation (15).

[0131]

[0132] On the basis of the above boundary conditions, additional boundary conditions are needed to define the X and Y directions of the MCS and determine the absolute length of the X axis, as shown in equation (14); since the current self-calibration method cannot directly obtain the absolute length, it is necessary to obtain AL1 by detecting a standard workpiece with a pre-calibration length:

[0133]

[0134] After subtracting 11 known boundary conditions, the number of errors to be identified N i = 106, the number of detection points, i.e. the number of equations, is N p · N c = 36 x 11 = 396, since N p · N c > N i , i.e. the number of equations is greater than the number of unknowns, meeting the requirements of the self-calibration algorithm.

[0135] Further, in S40, the error identification of the Z axis direction includes:

[0136] The measurement points 37-72 are all distributed on the top surface of each step of the workpiece, and the position error of the detection points is Δ2 total,i,θ affected by three types of error sources, including workpiece geometric error, linear axis error and rotary axis error, Figure 11 which intuitively shows the influence characteristics of the above errors on the detection displacement. At these measurement point positions, the influence of the workpiece geometric error on the detection displacement is represented as:

[0137] Δ2 1,i = E G ( w p i * ) (57)

[0138] The influence of the linear axis error on the detection displacement at the measurement point is represented as:

[0139]

[0140] The influence of the rotary axis error on the detection displacement at the measurement point is represented as:

[0141]

[0142] The total displacement error is represented as:

[0143]

[0144] In the formula, xy represents the x-axis position and y-axis position at the point.

[0145] The boundary conditions are applied to solve the equation, as shown in equation (21), where ΔL2 is the pre-calibration length of the standard workpiece measured by the probe:

[0146]

[0147] After subtracting the 8 known boundary conditions, the number of errors to be identified N i = 60, the number of probing points, i.e., the number of equations, is N p · N c = 36 x 11 = 396; since N p · N c > N i , i.e., the number of equations is greater than the number of unknowns, which meets the requirements of the self-calibration algorithm.

[0148] Further, in S40, the error terms are solved by the least square method, including:

[0149] When the C-axis is rotated to an angle θ (θ = 0°, 30°, 60°, …, 300°, 330°), 36 measuring points distributed in the XY plane and the Z-axis direction are probed, and the position of each measuring point is represented as m p i,θ * = ( m x * i,θ , m y * i,θ , m z * i,θ ), combined with each measuring position, a total of N p · N c = 36 x 11 = 396 measuring points, and equations (9) and (20) are converted into matrix form:

[0150]

[0151] In equation (23), Δ1 represents a set of workpiece geometric errors, Δ2 represents a set of linear axis errors, and Δ3 represents a set of rotary axis errors, where M represents a coefficient matrix composed of the coefficient of each error term in the vector (Δ1, Δ2, Δ3) T After applying the boundary conditions, the following minimization problem is solved by the least square method to identify the vector (Δ1, Δ2, Δ3) containing error parameters on the right side of equation (20): T :

[0152]

[0153] The two parts of data in the XY plane and the Z-axis direction are substituted into equation (23) to identify each error term.

[0154] To verify the effectiveness of the method, experiments were conducted. The experiments were carried out on a five-axis machine tool as shown in Figure 2 To ensure the accuracy of the measurement, the experimental environment temperature was strictly controlled at a constant temperature of (20±0.5)℃. Before the experiment, the machine tool was preheated to eliminate the influence of thermal deformation. The 6061 aluminum alloy was selected as the workpiece material, and the hard alloy flat-bottom milling cutter with a diameter of 10mm was used for processing. The processing was divided into two stages: first, the workpiece was rough machined to form, focusing on controlling the surface quality to ensure that the surface roughness meets the measurement requirements, and the completed workpiece is as shown in Figure 12 The whole process takes about 30 minutes; after processing, the machine tool is left for 4 hours to ensure complete cooling. Then the on-machine measurement method described in section 3.1 is used for detection, as shown in Figure 13 The measurement process only takes 6 minutes, and the influence of thermal error can be ignored.

[0155] Compared with the traditional method, the method has significant advantages. The traditional workpiece error identification method usually requires immediate measurement after processing to prevent the alignment accuracy from decreasing after the workpiece is removed. However, the workpiece and method designed in this paper allow the workpiece to be removed and reinstalled at any time after processing. As long as it is clamped in the specified way, the rotational axis error can still be accurately identified. In addition, the error of re-clamping is integrated into the geometric error of the workpiece and does not affect the identification of the rotational axis error, thereby realizing long-term monitoring of the machine tool error. The workpiece can be directly installed on other qualified machine tools without the need for reprocessing, and the error identification method can be used to greatly save time and cost.

[0156] The workpiece geometric error identification results of the workpiece measuring points are shown in Figure 14 and Figure 15 For measuring points No. 1-36, i.e., the side measuring points of the tower-shaped workpiece, the workpiece geometric error E G ranges from [-11μm, 18.6μm]. While the workpiece geometric error of measuring points No. 37-72, i.e., the top measuring points of the tower-shaped workpiece, ranges from [-7.8μm, 21.6μm], the overall change range is relatively small.

[0157] The identification results of the linear axis related error are shown in Figure 16 to Figure 19 The geometric error of the linear axis changes little, among which the geometric error of the X-axis ranges from [-5.2μm, 6.4μm], the yaw error E CX and the roll error E AX range from [-3μm, 2.3μm] and [-2.5μm, 3.6μm] respectively; the geometric error of the Y-axis ranges from [-4.6μm, 4.6μm], and the geometric error identified by the Z-axis ranges from [0μm, 2.8μm]. The perpendicularity error EC(OX)Y The value is 8.6".

[0158] Table 2 shows the identification results of the four PIGEs in the C-axis. XOC 14.5 μm, which is larger than the linear offset E in the Y direction. YOC (9.1μm). The perpendicularity error between the C-axis and the Y-axis is E AOC The vertical error between the C-axis and the X-axis is 13.5". BOC It is relatively small, only 6.8". The uncertainty of the results is analyzed and explained in Section 4.3.

[0159] Table 2 PIGE identification results

[0160]

[0161] The identification results of the 6 PDGE items on the C axis are as follows Figure 20 and Figure 21 As shown. The linear error is generally within ±30μm; when C=240°, E XC The maximum value reaches 23.5μm when C=150°, E YC The maximum value reaches 12.5μm when C=120°, E ZC The maximum value reaches 13.5μm. Angle error E AC With E BC The range is [-5.3″, 12.5″] and [-19.8″, 13.5″], and the angular positioning error E CC The range is [-4.5″,7.4″], and the change is relatively stable.

[0162] In order to verify the accuracy of the identification results, a disc-shaped workpiece was used to compare the error differences. The disc-shaped workpiece was identified and the identification results of the method were compared and analyzed. The results show that the linear error E XC , E YC With E ZC The identification result deviations are between [-3.1″, 1.6″], [-1.9″, 0.9″] and [-1.1″, 0.8″] respectively; the angle error E AC , E BC With E CC The deviations of the recognition results are between [-1.2", 1.3"], [-0.7", 0.6"] and [-1.8", 1.6"] respectively. The average agreement between the two recognition results is 89.8%, which confirms the accuracy of the proposed method.

[0163] It is to be understood that the example embodiments described herein are illustrative rather than limiting. Although one or more embodiments of the application are described in connection with the accompanying drawings, it will be understood that various modifications in form and detail can be made without departing from the spirit and scope of the application as defined by the appended claims.

Claims

1. A self-calibration and identification method for the geometric error of a rotating axis based on a tower-shaped workpiece, characterized in that: The following steps are involved: S10, designing a tower-shaped workpiece: The tower-shaped workpiece is formed by neatly stacking five layers of square steps in a regular stepped structure. The bottom step has a side length of 100 mm, and each layer above it is 10 mm high. The side lengths decrease in sequence: the second layer is 80 mm, the third layer is 60 mm, the fourth layer is 40 mm, and the top layer is 20 mm. The overall tower-shaped structure has a total height of 95 mm. S20, perform error definition and modeling: the error includes workpiece geometric error, linear axis error, and rotation axis error, where E G Indicates the geometric error value of the workpiece at the measuring point, that is, the deviation between the actual contour of the workpiece at the measuring point and the theoretical design position along the normal direction; S30, setting the measurement point distribution and defining the measurement mode: The measurement coordinate system is set as follows: the X-axis is parallel to one side of the step, the Y-axis is parallel to the other side, and the Z-axis is vertically upward. The coordinate origin is located 10 mm below the first step surface and coincides with the center of the step surface. The measurement points are divided into two parts. The first part is located on the side of the workpiece, that is, the Z=0 plane, and has a total of 36 measurement points. The second part is located on the top surface of the workpiece and also has 36 measurement points. The theoretical position of each measurement point is transformed into a position in the machine tool coordinate system, and then the measurement error is expressed based on the position in the machine tool coordinate system. S40, using the self-calibration algorithm to identify the error: the position deviation of the measuring point is the result of the combined effect of the workpiece geometric error, linear axis error and rotation axis error. Assume that the total number of error items to be identified is N i , the number of measuring points at each measuring angle is N p , the total number of measured angles is N c , then the total amount of measurement point data is N p ·N c , introduce the three-dimensional linear axis volume error model, discretize the continuous linear axis error into a finite grid point, and reduce the number of error parameters from N i Infinite reduction to finite value by increasing the measurement angle N c , so that the total number of measurement points satisfies N p ·N c >N i , thereby constructing an overdetermined set of equations. Finally, the error term to be identified is solved by solving the minimization problem using the least squares method, thereby obtaining the best estimate of the error term.

2. The self-calibration and identification method of the geometric error of the rotating axis based on the pyramid-shaped workpiece according to claim 1, characterized in that: In S20, during the workpiece measurement process, the B axis is fixed at the 0° position, and based on this, the volume error models of the X, Y, and Z axes are established, as shown in formula (1): When the probe sphere is located at the grid point (x line,f ,y line,g ,z line,h ), the positioning error of the linear axis is modeled by formula (2), E X,total It represents the influence of the linear axis on the X-axis error at a specific position, E Y,total Indicates the influence of the linear axis at a specific position on the Y-axis error, E Z,total Indicates the influence of the linear axis at a specific position on the Z-axis error. These errors reflect the influence of the deviation of the linear axis movement in different directions on the overall positioning accuracy. E XX (x line,f )) represents the linear positioning error of the X axis; the error motion of the X axis is expressed by the discrete X position set x line,f (f=-80,-60,-40,…,40,60,80), the error value is found by line position, which contains 9 parameters, and the error motion of the Y axis is in y line,g (g=-80,-60,-40,…,40,60,80) position, which also contains 9 parameters; similarly, the error motion of the Z axis is defined in z line,h (h=0,10,20,30,40,50) position definition, which contains 6 parameters, the values ​​in brackets, including x line,f The -80, -60, ..., 80) in the figure represent the discrete positions of each axis in millimeters (mm), that is, the error motion of the X, Y and Z axes at the three-dimensional grid point (x line,f ,y line,g ,z line,h ) is represented on the grid; when the positioning of the X, Y and Z axes is completed, the kinematic model (2) is used to describe each grid point (x line,f ,y line,g ,z line,h ) of the X, Y, and Z axes; similarly, when the C axis rotates to C θ At each angular position (θ=0°, 30°,60°,…,300°,330°), the rotation axis error is respectively given by E XC (C θ ), E XOC 、E YC (C θ ), E YOC 、E CC (C θ ), E AC (C θ ), E AOC 、E BC (C θ ) and E BOC These error terms can be divided into two categories according to their influence range. One category mainly affects the motion accuracy in the XY plane, and the other category mainly affects the positioning accuracy in the Z axis direction.

3. The self-calibration and identification method of the geometric error of the rotating axis based on the pyramid-shaped workpiece according to claim 1, characterized in that: In S40, the identification of the error in the XY plane includes: The measuring points 1-36 are all distributed on the plane of Z=0, that is, the XY plane, and the position error of the detection points is Δ1 total,i,θ Affected by three types of error sources: workpiece geometric error, linear axis error and rotational axis error, at these measuring points, the influence of workpiece geometric error on the detection displacement is expressed as: Δ1 1,i =And G ( w p i * ) (3) The effect of linear axis error on the detection displacement at the measuring point is expressed as: The effect of the rotation axis error on the detection displacement at the measuring point is expressed as: In the formula m n * i,θ It represents the unit vector perpendicular to the workpiece surface in the MCS at this time; Considering the influence of the above error components on the detected displacement, the total displacement error is expressed as: Since the linear axis error is defined at discrete grid points, the total error vector (E X,total ( m x * i,θ , m y * i,θ , m z * i,θ ),E Y,total ( m x * i,θ , m y * i,θ , m z * i,θ )) T Converted into the form of grid point coordinates, considering the characteristic of measuring plane Z=0, Z axis related items are ignored, when the actual measuring point ( m x * i,θ , m y * i,θ ) satisfies the grid interval conditions: x line,f ≤ m x * i,θ ≤x line,f+20 and line,g ≤ m and * i,θ ≤y line,g+20 (7) In this case, the bilinear interpolation method is used to calculate the error component, and the normalized interpolation weight coefficient is defined as: Then, the linear interpolation method is used to convert E in formula (2) into X,total and E Y,total Converts to the following form: Due to the redundancy between parameters in the model, the coefficient matrix of the equation group may have a rank deficiency problem. Therefore, appropriate boundary conditions are introduced to eliminate the rank defect of the coefficient matrix, and the location of the origin of the machine coordinate system (MCS) is fixed, as shown in Equation (15): In addition to the above boundary conditions, additional boundary conditions are required to define the X and Y directions of the MCS and determine the absolute length of the X axis, as shown in Equation (14). Since the current self-calibration method cannot directly obtain the absolute length, it is necessary to obtain ΔL1 by probing a standard workpiece with a pre-calibrated length: After subtracting the 11 known boundary conditions, the number of errors that need to be identified is N i =106, the number of detection points, that is, the number of equations, is N p ·N c =36×11=396, because N p ·N c >N i , that is, the number of equations is greater than the number of unknowns, which meets the requirements of the self-calibration algorithm.

4. The self-calibration and identification method of the geometric error of the rotating axis based on the pyramid-shaped workpiece according to claim 3 is characterized in that: In S40, the error identification in the Z-axis direction includes: Measuring points 37-72 are distributed on the top surface of each step of the workpiece, and the position error of the detection points is Δ2 total,i,θ It is also affected by three types of error sources, including workpiece geometric error, linear axis error, and rotational axis error. At these measuring points, the influence of workpiece geometric error on the detection displacement is expressed as: Δ2 1,i =E G ( w p i * ) (14) The effect of linear axis error on the detection displacement at the measuring point is expressed as: The effect of the rotation axis error on the detection displacement at the measuring point is expressed as: Δ2 3,i,θ =E ZC (C θ )+y·(E AC (C θ )+E AOC ) -x·(E BC (C θ )+E BOC )(16) Considering the influence of the above error components on the detected displacement, the total displacement error is expressed as: The boundary conditions are applied to solve the problem, as shown in Equation (21), where ΔL2 is measured by probing a standard workpiece with a pre-calibrated length: After subtracting the 8 known boundary conditions, the number of errors that need to be identified is N i =60, the number of detection points, that is, the number of equations, is N p ·N c =36×11=396; due to N p ·N c >N i , that is, the number of equations is greater than the number of unknowns, which meets the requirements of the self-calibration algorithm.

5. The self-calibration and identification method of the rotation axis geometric error based on the pyramidal workpiece according to claim 4, characterized in that: In S40, the error term solved by the least squares method includes: When the C-axis rotates to an angle of θ (θ = 0°, 30°, 60°, ..., 300°, 330°), the position of each measuring point is expressed as follows: m p i,θ * =( m x * i,θ , m y * i,θ , m z * i,θ ), combined with each measurement position, a total of N p ·N c =36×11=396 measuring points, equations (9) and (20) are converted into matrix form: Where Δ1 represents the set of workpiece geometric errors, Δ2 represents the set of linear axis errors, Δ3 represents the set of rotational axis errors, and M represents the vector (Δ1, Δ2, Δ3) T The coefficient matrix composed of the coefficients of the various error terms in , after applying the boundary conditions, is solved by the least squares method to solve the following minimization problem, thereby identifying the vector (Δ1, Δ2, Δ3) containing the error parameters on the right side of Equation (20) T : Substituting the two parts of data in the XY plane and Z axis direction into formula (23), the various error terms can be identified.

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