Rotation axis position-independent geometric error identification method based on ball bar

Abstract

The invention relates to a rotating shaft position-independent geometric error identification method based on a ball bar, and the method comprises the steps: enabling the center of a tool ball to be installed at an AC axis intersection point, enabling a workpiece ball to be installed in an offset manner in the X and Y directions, and successively controlling the single-axis movement of two axes, thereby achieving the switching of two measurement modes under one-time installation, and 8 position-independent geometric errors of the rotating shaft are identified through three times of installation. The method is simple in installation, does not need an extension rod, does not need to recognize the axis of the rotating shaft, and improves the error measurement efficiency. According to the method, workpiece ball coordinates are inversely solved through an inverse matrix, initial coordinates of a tool ball and a workpiece ball under the RCS are established, a rod length comprehensive model including the installation error of a ball rod instrument is established based on homogeneous coordinate transformation, a preset value and an identification value are compared through analog simulation analysis, and the result shows that residual errors of eight errors are small. The identification method provided by the invention has relatively high precision.

Description

Technical Field

[0001] The present invention relates to the technical field of geometric error identification, and in particular to a method for identifying a rotation axis position-independent geometric error based on a ballbar. Background Art

[0002] Compared with three-axis machine tools, five-axis machine tools have better flexibility and can process complex parts such as turbine blades and engine blocks. However, the addition of two rotating axes introduces more errors, which affects the accuracy of five-axis machine tools. Therefore, the measurement and identification of the geometric errors of the rotating axes are of great significance to improving the machining accuracy of five-axis machine tools. For the measurement of the geometric errors of the rotating axes, the commonly used instruments include laser trackers, contact trigger probes, R-tests, ballbars, etc. Compared with other instruments, ballbars have the advantages of low cost, easy installation, and stable measurement, and are widely used in the measurement of rotating axis errors.

[0003] For the measurement of position-independent geometric errors of rotating axes, the commonly used methods currently include multi-axis linkage measurement and single-axis motion measurement. However, for the multi-axis linkage measurement method, since the geometric error of the translation axis cannot be fully compensated, the measurement result will be affected by the translation axis, resulting in inaccurate final identification results. By controlling the single-axis motion measurement, the influence of the translation axis error on the rotation axis error identification can be eliminated, the coupling problem of the translation axis and the rotation axis geometric error can be solved, and the error identification accuracy can be improved. At the same time, most of the existing identification methods using ballbar measurement require more installation positions, which increases the installation time of the ballbar and the measurement difficulty, affecting the simplicity of error measurement. Summary of the invention

[0004] The object of the present invention is to solve at least one of the deficiencies of the prior art and to provide a method for identifying position-independent geometric errors of a rotating axis based on a ballbar.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: Specifically, a method for identifying the position-independent geometric error of a rotary axis based on a ballbar is proposed and applied to a five-axis machine tool, including the following: The coordinate system is established in sequence according to the kinematic chain of the workpiece end of the five-axis machine tool. The five-axis machine tool consists of three linear axes, X-axis, Y-axis, and Z-axis, and two rotary axes, A-axis and C-axis. The kinematic chain structure of the five-axis machine tool is divided into a tool chain RYXZT and a workpiece chain RACW. Since only the rotary axis is identified, the linear axis is not considered in the process of establishing the coordinate system. The A-axis coordinate system ACS is established at the intersection of the A-axis and C-axis axes, and the C-axis coordinate system CCS is established at the center of the rotary table. To simplify the modeling, the workpiece coordinate system WCS is overlapped with the CCS, and the reference coordinate system RCS is overlapped with the ACS, and the Z-axis axes of the WCS, CCS, RCS, and ACS are collinear. Three installation modes are used for measurement. In the three installation modes, the tool ball B1 is connected to the spindle through the tool cup, and the workpiece ball B2 is fixed to the workbench through the tool cup and the magnetic seat; Specifically, In the first installation mode, the A-axis or C-axis movement is controlled to measure the four position errors respectively to obtain the first ballbar length model; In the second installation mode, the A-axis movement is controlled to measure two perpendicularity errors to obtain the second ballbar length model; In the third installation mode, the C-axis movement is controlled to measure two perpendicularity errors to obtain the third ballbar length model; Based on MATLAB function combined with the first ballbar length model, the second ballbar length model and the third ballbar length model, eight position-independent geometric errors of the rotation axis are fitted and solved.

[0006] Further, specifically, in the first installation mode, the A-axis or C-axis movement is controlled to measure four position errors respectively to obtain a first ballbar length model, including: The initial coordinates of balls B1 and B2 in the reference coordinate system are: (1) (2) In the formula, e x , e y are the installation errors of the center of tool ball B1 in the X and Y directions of the machine tool reference coordinate system, X L , Y L is the offset of the center of the workpiece ball B2 relative to the center of the tool ball B1 in the X and Y directions; When only the A-axis is controlled to move, the workpiece ball B2 moves in a circle around the A-axis. The actual transformation matrix from the A-axis coordinate system to the reference coordinate system is: (3) The initial coordinates of the workpiece ball B2 in the A-axis coordinate system are calculated by inverse matrix transformation: (4) After coordinate matrix transformation, the actual coordinates of B2 in the reference coordinate system are: (5) The tool ball B1 is fixed during the measurement process, so its coordinates remain unchanged in the reference coordinate system. Substituting the coordinates of balls B1 and B2, simplifying the calculation and neglecting small higher-order errors, we get the actual length of the ballbar:L A1 for: (6) When only the C-axis is controlled, the workpiece ball B2 moves in a circle around the C-axis. The actual transformation matrix from the C-axis coordinate system to the A-axis coordinate system is: (7) Calculate the initial coordinates of the workpiece ball B2 in the C-axis coordinate system: (8) Then find the actual coordinates of B2 in the reference coordinate system: (9) Finally, the actual length of the ballbar is obtained according to the coordinates of the two balls. L C1 for: (10).

[0007] Further, specifically, in the second installation mode, the A-axis movement is controlled to measure two verticality errors to obtain a second ballbar length model, including: Only the A-axis motion is controlled. As the installation position of the ballbar changes, the initial coordinates of balls B1 and B2 also change, as shown in equations (11) and (12): (11) (12) In the formula, l is the distance from the center of tool ball B1 to the axis of C axis, L is the nominal length of the ballbar.

[0008] Same as the first installation mode, first calculate the actual coordinates of the workpiece ball B2 in the reference coordinate system, and then get the actual length of the ballbar L A2 for: (13).

[0009] Further, specifically, in the third installation mode, the C-axis movement is controlled to measure two verticality errors to obtain a third ballbar length model, including: Only the C-axis is controlled, and the initial coordinates of balls B1 and B2 are as follows: (14) (15) In the formula, h It is the distance from the center of tool ball B1 to the axis of A axis.

[0010] Similarly, the actual coordinates of B2 can be calculated, and finally the actual length of the ballbar can be obtained. L C3 for: (16).

[0011] The beneficial effects of the present invention are: The present invention proposes a method for identifying the position-independent geometric errors of a rotating axis based on a ballbar. The center of the tool ball is installed at the intersection of the AC axis, the workpiece ball is installed offset in the XY direction, and the single-axis motion of the two axes is controlled successively to achieve the switching of two measurement modes in one installation. Eight position-independent geometric errors of the rotating axis are identified through three installations. The method is easy to install, does not require the use of an extension rod, and does not require the identification of the rotating axis, thereby improving the efficiency of error measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The above and other features of the present disclosure will become more obvious by describing in detail the embodiments shown in the accompanying drawings. The same reference numerals in the accompanying drawings of the present disclosure represent the same or similar sampling monitoring points. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure. For those skilled in the art, other accompanying drawings can be obtained based on these accompanying drawings without creative work. In the accompanying drawings: Figure 1 (a), (b) and (c) are schematic diagrams of three installation modes involved in a method for identifying a rotation axis position-independent geometric error based on a ballbar according to the present invention; Figure 2 (a) and (b) are schematic diagrams of the machine tool structure and coordinate system of a five-axis machine tool to which a method for identifying a rotation axis position-independent geometric error based on a ballbar according to the present invention is applied; Figure 3 (a) and (b) show the principle diagrams of position-independent geometric error definition, respectively. Figure 4 Shown is the schematic diagram of tool ball installation error; Figure 5 (a), (b), and (c) are schematic diagrams of three installation modes at the installation and measurement site in one embodiment; Figure 6 (a) and (b) are respectively graphs of ballbar length data measured twice in one embodiment; Figure 7 (a) and (b) are schematic diagrams of ballbar length prediction errors in three installation modes in one implementation. DETAILED DESCRIPTION

[0013] The following will be combined with the embodiments and drawings to clearly and completely describe the concept, specific structure and technical effects of the present invention, so as to fully understand the purpose, scheme and effect of the present invention. It should be noted that the embodiments in this application and the features in the embodiments can be combined with each other without conflict. The same reference numerals used throughout the drawings indicate the same or similar parts.

[0014] This solution only measures the position-independent geometric error of the rotating axis, controls the movement of a single rotating axis during the measurement process, and reduces the influence of other axes on the error measurement. Embodiment 1, the present invention proposes a method for identifying the position-independent geometric error of a rotating axis based on a ballbar, which is applied to a five-axis machine tool, including the following: The coordinate system is established in sequence according to the kinematic chain of the workpiece end of the five-axis machine tool. The structure of the five-axis machine tool is as follows: Figure 2 As shown in a, the five-axis machine tool consists of three linear axes X-axis, Y-axis, and Z-axis and two rotary axes A-axis and C-axis. The kinematic chain structure of the five-axis machine tool is divided into the tool chain RYXZT and the workpiece chain RACW. Since only the rotary axis is identified, the linear axis is not considered in the process of establishing the coordinate system, such as Figure 2 As shown in b, the A-axis coordinate system ACS is established at the intersection of the A-axis and C-axis axes, and the C-axis coordinate system CCS is established at the center of the rotary table. To simplify the modeling, the workpiece coordinate system WCS is overlapped with CCS, and the reference coordinate system RCS is overlapped with ACS, and the Z-axis axes of WCS, CCS, RCS and ACS are collinear; the capital letter H+CS refers to the coordinate system where the capital letter H is located, and the value of H is RYXZT or RACW; Three installation modes were used for measurement. In the three installation modes, the tool ball B1 was connected to the spindle through the tool cup (installed at the intersection of the AC axis), and the workpiece ball B2 was fixed to the workbench through the tool cup and the magnetic seat; Specifically, In the first installation mode, the A-axis or C-axis movement is controlled to measure the four position errors respectively to obtain the first ballbar length model; Figure 1 As shown in a, the center of the tool ball is installed at the intersection of the AC axes, and the workpiece ball is installed at a distance of 80 mm from the A axis and 60 mm from the C axis.

[0015] In the second installation mode, the A-axis movement is controlled to measure the two verticality errors to obtain the second ballbar length model; Figure 1 As shown in b, the center of the tool ball is installed on the axis of the A-axis, 60mm away from the other axis.

[0016] In the third installation mode, the C-axis movement is controlled to measure the two verticality errors to obtain the third ballbar length model; Figure 1As shown in c, the center of the tool ball is installed on the C-axis axis, 60 mm away from the other axis.

[0017] Based on MATLAB function combined with the first ballbar length model, the second ballbar length model and the third ballbar length model, eight position-independent geometric errors of the rotation axis are fitted and solved.

[0018] According to the ballbar length models under three installation modes and combined with the ballbar length data in the actual measurement process, the ballbar installation error is measured by digital micrometer and ballbar. These data are substituted into the ballbar length model, and the eight position-independent geometric errors of the rotating axis are solved by MATLAB function fitting.

[0019] In this embodiment 1, by installing the center of the tool ball at the intersection of the AC axis, the workpiece ball is offset in the XY direction, and the single-axis motion of the two axes is controlled successively, the switching of the two measurement modes is realized in one installation, and 8 position-independent geometric errors of the rotating axis are identified through three installations. This method is easy to install, does not require the use of an extension rod, and does not require the identification of the rotating axis, which improves the efficiency of error measurement.

[0020] Considering that the position-independent geometric error of the rotary axis is caused by the deviation of the machine tool components during the assembly process, it will cause errors in the position and angle of the axis, affecting the actual processing accuracy of the machine tool. Figure 2 As shown in a, its rotation axis consists of A axis and C axis, with a total of 8 position-independent geometric errors. Each rotation axis has two position errors and two perpendicularity errors, as shown in Figure 3 As shown in (a) and (b). δ ya and δ za The A-axis is along the machine tool reference coordinate system. Y R and Z R Position deviation in direction, S ya and S za The A axis is around Y R and Z R The verticality error of the two axes, δ xc and δ yc The C-axis is along the A-axis coordinate system X A and Y A Position deviation in direction, S xc andS yc The C-axis is around X A and Y A The perpendicularity error between the two axes.

[0021] According to the three installation modes, the initial coordinates of the tool ball B1 and the workpiece ball B2, which contain the ballbar installation error, are established in turn under RCS. During the measurement, only a single rotation axis is controlled, and the coordinates of the tool ball do not change. The actual initial position of the workpiece ball on the measured axis is determined by the inverse transformation matrix. Then, the actual coordinates of the workpiece ball under RCS are determined by the homogeneous transformation matrix, so that the actual coordinates of the balls B1 and B2 are both under RCS, ensuring the consistency of the coordinates of the two balls and improving the recognition accuracy of the model.

[0022] As a preferred embodiment of the present invention, specifically, in the first installation mode, the A-axis or C-axis movement is controlled to measure four position errors respectively to obtain a first ballbar length model, including: The initial coordinates of balls B1 and B2 in the reference coordinate system are: (1) (2) In the formula, e x , e y are the installation errors of the center of tool ball B1 in the X and Y directions of the machine tool reference coordinate system, X L , Y L is the offset of the center of the workpiece ball B2 relative to the center of the tool ball B1 in the X and Y directions; Figure 4 As shown in the figure, the axis of the tool cup and the tool holder deviates from the axis of the reference coordinate system RCS during installation, resulting in errors in the center of the tool ball in the X and Y directions. e x and e y The effect of the workpiece ball installation error on the rod length change is very small, and its effect on the actual measurement test can be ignored.

[0023] When only the A-axis is controlled to move, the workpiece ball B2 moves in a circle around the A-axis. The actual transformation matrix from the A-axis coordinate system to the reference coordinate system is: (3) The initial coordinates of the workpiece ball B2 in the A-axis coordinate system are calculated by inverse matrix transformation: (4) After coordinate matrix transformation, the actual coordinates of B2 in the reference coordinate system are: (5) The tool ball B1 is fixed during the measurement process, so its coordinates remain unchanged in the reference coordinate system. Substituting the coordinates of balls B1 and B2, simplifying the calculation and neglecting small higher-order errors, we get the actual length of the ballbar: L A1 for: (6) When only the C-axis is controlled, the workpiece ball B2 moves in a circle around the C-axis. The actual transformation matrix from the C-axis coordinate system to the A-axis coordinate system is: (7) Calculate the initial coordinates of the workpiece ball B2 in the C-axis coordinate system: (8) Then find the actual coordinates of B2 in the reference coordinate system: (9) Finally, the actual length of the ballbar is obtained according to the coordinates of the two balls. L C1 for: (10).

[0024] As a preferred embodiment of the present invention, specifically, in the second installation mode, the A-axis movement is controlled to measure two verticality errors to obtain a second ballbar length model, including: Only the A-axis motion is controlled. As the installation position of the ballbar changes, the initial coordinates of balls B1 and B2 also change, as shown in equations (11) and (12): (11) (12) In the formula, l is the distance from the center of tool ball B1 to the axis of C axis, L is the nominal length of the ballbar.

[0025] Same as the first installation mode, first calculate the actual coordinates of the workpiece ball B2 in the reference coordinate system, and then get the actual length of the ballbar L A2 for: (13).

[0026] As a preferred embodiment of the present invention, specifically, in the third installation mode, the C-axis movement is controlled to measure two verticality errors to obtain a third ballbar length model, including: Only the C-axis is controlled, and the initial coordinates of balls B1 and B2 are as follows: (14) (15) In the formula, h It is the distance from the center of tool ball B1 to the axis of A axis.

[0027] Similarly, the actual coordinates of B2 can be calculated, and finally the actual length of the ballbar can be obtained. L C3 for: (16).

[0028] In this preferred embodiment, the establishment of the workpiece end coordinate system is simplified. At the same time, the influence of the ballbar installation error on the identification model is taken into account during the model establishment process, and the installation error is eliminated as much as possible through actual measurement, thereby simplifying the error identification model and improving the error identification accuracy.

[0029] In practical applications, 1 Simulation In order to further verify the accuracy of the identification method, this method is simulated and verified. First, eight position-independent geometric errors of the A-axis and C-axis are generated. According to the simulation parameters in Table (1), the ballbar length data including the ballbar installation error are calculated by equations (6), (10), (13), and (16). Then, the actual position-independent geometric errors are identified using the MATLAB fitting function. Finally, the preset values ​​and the identified values ​​are compared to calculate the residuals of each error.

[0030] Table 1 Basic simulation parameters

[0031] Table 2 Simulation results

[0032] The simulation results are shown in Table (2). It can be seen that the residuals of each error are very small. The simulation results show that the identification method has high accuracy and can accurately identify the eight position-independent geometric errors of the rotating axis.

[0033] 2 Identification experiment In the measurement experiment, the nominal length of the ballbar is 100mm, the A-axis motion range is -15° to 70°, and the C-axis motion range is 0° to 360°. Figure 1The ballbar is installed in the three installation modes shown. After installation, the A-axis or C-axis is controlled to move in each mode, and the length data of the ballbar is recorded every 5°. Each set of measurements is repeated twice to avoid accidental measurement results. Figure 5 As shown in (a), (b), and (c), the A-axis movement is controlled in mode 1 and mode 2, and the C-axis movement is controlled in mode 1 and mode 3.

[0034] After the measurement is completed, the two results of each set of measurements are fitted by curve fitting, such as Figure 6 As shown in (a) and (b), it can be seen that the curves of the two measurements basically overlap, and the four sets of data results are highly repeatable.

[0035] The average of the two ballbar measurement data is taken, and the angle and length data are substituted into the MATLAB function to identify the eight position-independent geometric errors. Based on the error identification results, the predicted values ​​of the ballbar length under the three installation modes are obtained, and then the predicted values ​​are subtracted from the actual measured values ​​to obtain the predicted errors of the length. The predicted error can indirectly reflect the accuracy of the error identification results. The smaller its value, the closer the error value obtained by identification is to the true value. The predicted errors under the three installation modes are as follows: Figure 7 As shown in (a) and (b). The results show that the maximum value of the rod length prediction error of the four measurement experiments does not exceed 1μm. Therefore, the proposed identification method has high accuracy and can effectively identify the position-independent geometric error of the rotation axis.

[0036] Summarize: (1) In order to quickly and accurately identify the geometric errors of the rotating axis, a method for measuring and identifying the position-independent geometric errors of the rotating axis based on three installations of the ballbar was proposed. The center of the tool ball was installed at the intersection of the AC axis, the workpiece ball was offset in the XY direction, and the single-axis motion of the two axes was controlled successively to achieve the switching of two measurement modes in one installation. Through three installations, eight position-independent geometric errors of the rotating axis were identified. This method is easy to install, does not require the use of an extension rod, and does not require the identification of the rotating axis, which improves the efficiency of error measurement.

[0037] (2) The coordinates of the workpiece ball are inverted by inverting the matrix, and the initial coordinates of the tool ball and the workpiece ball under RCS are established. A comprehensive model of the ballbar length including the ballbar installation error is established based on the homogeneous coordinate transformation. The preset values ​​are compared with the identified values ​​through simulation analysis. The results show that the residuals of the eight errors are very small, and the proposed identification method has high accuracy.

[0038] (3) In the identification experiment, the installation error was measured by a digital micrometer and a ballbar, which basically eliminated the influence of the tool end installation error. The effectiveness of the identification method was verified by comparing the length prediction error of the ballbar. The maximum value of the ballbar length prediction error in the four measurement experiments did not exceed 1μm. The proposed identification method can effectively identify the position-independent geometric error of the rotating axis.

[0039] Although the description of the present invention has been quite detailed and specifically describes several described embodiments, it is not intended to be limited to any of these details or embodiments or any particular embodiment, but should be regarded as providing a broad possible interpretation of these claims in view of the prior art by reference to the appended claims, thereby effectively covering the intended scope of the present invention. In addition, the above description of the present invention is based on the embodiments foreseeable by the inventor, and its purpose is to provide a useful description, and those non-substantial changes to the present invention that have not yet been foreseen may still represent equivalent changes to the present invention.

[0040] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, it should belong to the protection scope of the present invention. Within the protection scope of the present invention, its technical scheme and / or implementation method can have various modifications and changes.

Claims

1. A method for identifying position-independent geometric errors of a rotating axis based on a ballbar, characterized in that: Applicable to five-axis machine tools, including the following: The coordinate system is established in sequence according to the kinematic chain of the workpiece end of the five-axis machine tool. The five-axis machine tool consists of three linear axes, X-axis, Y-axis, and Z-axis, and two rotary axes, A-axis and C-axis. The kinematic chain structure of the five-axis machine tool is divided into a tool chain RYXZT and a workpiece chain RACW. Since only the rotary axis is identified, the linear axis is not considered in the process of establishing the coordinate system. The A-axis coordinate system ACS is established at the intersection of the A-axis and C-axis axes, and the C-axis coordinate system CCS is established at the center of the rotary table. To simplify the modeling, the workpiece coordinate system WCS is overlapped with the CCS, and the reference coordinate system RCS is overlapped with the ACS, and the Z-axis axes of the WCS, CCS, RCS, and ACS are collinear. Three installation modes are used for measurement. In the three installation modes, the tool ball B1 is connected to the spindle through the tool cup, and the workpiece ball B2 is fixed to the workbench through the tool cup and the magnetic seat; Specifically, In the first installation mode, the A-axis or C-axis movement is controlled to measure the four position errors respectively to obtain the first ballbar length model; In the second installation mode, the A-axis movement is controlled to measure two perpendicularity errors to obtain the second ballbar length model; In the third installation mode, the C-axis movement is controlled to measure two perpendicularity errors to obtain the third ballbar length model; Based on MATLAB function combined with the first ballbar length model, the second ballbar length model and the third ballbar length model, eight position-independent geometric errors of the rotation axis are fitted and solved.

2. The method for identifying position-independent geometric errors of a rotating axis based on a ballbar according to claim 1, characterized in that: Specifically, in the first installation mode, the A-axis or C-axis movement is controlled to measure four position errors respectively to obtain a first ballbar length model, including: The initial coordinates of balls B1 and B2 in the reference coordinate system are: (1) (2)， In the formula, e x , e y are the installation errors of the center of tool ball B1 in the X and Y directions of the machine tool reference coordinate system, X L , Y L is the offset of the center of the workpiece ball B2 relative to the center of the tool ball B1 in the X and Y directions; When only the A-axis is controlled to move, the workpiece ball B2 moves in a circle around the A-axis. The actual transformation matrix from the A-axis coordinate system to the reference coordinate system is: (3) The initial coordinates of the workpiece ball B2 in the A-axis coordinate system are calculated by inverse matrix transformation: (4) After coordinate matrix transformation, the actual coordinates of B2 in the reference coordinate system are: (5) The tool ball B1 is fixed during the measurement process, so its coordinates remain unchanged in the reference coordinate system. Substituting the coordinates of balls B1 and B2, simplifying the calculation and neglecting small higher-order errors, we get the actual length of the ballbar: L A1 for: (6) When only the C-axis is controlled, the workpiece ball B2 moves in a circle around the C-axis. The actual transformation matrix from the C-axis coordinate system to the A-axis coordinate system is: (7) in Z AC Indicates the distance between ACS and CCS; Calculate the initial coordinates of the workpiece ball B2 in the C-axis coordinate system: (8) Then find the actual coordinates of B2 in the reference coordinate system: (9) Finally, the actual length of the ballbar is obtained according to the coordinates of the two balls. L C1 for: (10)。 3. The method for identifying position-independent geometric errors of a rotating axis based on a ballbar according to claim 2, characterized in that: Specifically, in the second installation mode, the A-axis movement is controlled to measure two verticality errors to obtain a second ballbar length model, including: Only the A-axis motion is controlled. As the installation position of the ballbar changes, the initial coordinates of balls B1 and B2 also change, as shown in equations (11) and (12): (11) (12) In the formula, l is the distance from the center of tool ball B1 to the axis of C axis, L is the nominal length of the ballbar, Same as the first installation mode, first calculate the actual coordinates of the workpiece ball B2 in the reference coordinate system, and then get the actual length of the ballbar L A2 for: (13)。 4. The method for identifying position-independent geometric errors of a rotating axis based on a ballbar according to claim 3, characterized in that: Specifically, in the third installation mode, the C-axis movement is controlled to measure two verticality errors to obtain a third ballbar length model, including: Only the C-axis is controlled, and the initial coordinates of balls B1 and B2 are as follows: (14) (15) In the formula, h is the distance from the center of tool ball B1 to the axis of A axis, Similarly, the actual coordinates of B2 can be calculated, and finally the actual length of the ballbar can be obtained. L C3 for: (16)。

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