Five-axis machine tool rotating shaft geometric error self-calibration method based on tooth-shaped workpiece

Abstract

The invention discloses a five-axis machine tool rotating shaft geometric error self-calibration method based on a tooth-shaped workpiece. The method comprises the following steps that S1, the workpiece is machined; s2, on-machine measurement; S2.1, measurement point arrangement and fitting; s2.2, a measurement mode: S2.2. 1, positioning a linear shaft of a machine tool at an angular position, measuring a measuring point at the angular position, rotating a shaft C to a position where a next measuring point is located at a measuring head after the measurement is completed, measuring, and so on, rotating the shaft C one by one, and enabling all arc surfaces to sequentially rotate to the position of the measuring head for measurement; s2.2. 2, the linear shaft is adjusted to the next angle position, and other measurement processes are the same as the step S2.2. 1; s2.2. 3, repeating the step S2.2. 2 until the arc surface measurement of the linear shaft at all angle positions is completed; and S3, identifying a workpiece geometric error, a C-axis geometric error, a linear axis error and a total error according to the data measured in the step S2. Therefore, the effects that the workpiece geometric error, the C-axis geometric error and the linear axis error can be identified at the same time, and the identification precision is improved are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical control machine tool machining precision, and particularly relates to a five-axis machine tool rotary axis geometric error self-calibration method based on a tooth-shaped workpiece. BACKGROUND

[0002] Five-axis machine tools play a leading role in manufacturing complex curved surfaces of high-end parts. Compared with three-axis machine tools, the additional two rotary axes can reduce the clamping frequency and reduce the coordinate system conversion error. However, the detection difficulty of the rotary axis geometric error increases. Due to manufacturing defects and assembly errors, the rotary axis geometric error can be generally divided into two categories: position-independent geometric error and position-dependent geometric error, and accurate identification is crucial to ensure the precision of the machine tool.

[0003] The existing rotary axis geometric error measurement methods mainly include direct measurement and indirect measurement. Although the direct measurement method has high accuracy, it is low in efficiency and difficult to realize full error item measurement. The indirect measurement method obtains the comprehensive error through multi-axis linkage, and decouples each error component by combining a mathematical model. For example, ball bar, laser tracking interferometer, R-test, contact trigger probe and cutting feature workpiece. Among them, the contact trigger probe has good communication function with the numerical control system, and this communication capability can significantly improve the automation level of measurement. However, the existing methods have two major limitations: first, the linear axis and rotary axis errors cannot be effectively separated; and second, the calibration efficiency is limited due to the dependence on high-precision reference workpieces. SUMMARY

[0004] In order to overcome the limitations of the existing model, the present application proposes a five-axis machine tool rotary axis geometric error self-calibration method based on a tooth-shaped workpiece, which does not need to rely on external calibration measurement standards, and the geometric errors of the linear axis and the rotary axis can be separated and identified by inversely deducing the machine tool error through multiple measurements of the uncalibrated workpiece. The method has high efficiency and independence, reduces the complexity of parameter solving, and does not require a precision reference workpiece.

[0005] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0006] A five-axis machine tool rotary axis geometric error self-calibration method based on a tooth-shaped workpiece, comprising the following steps:

[0007] S1 workpiece processing

[0008] A tooth-shaped workpiece with n circular grooves and a central position square groove is made;

[0009] S2 in-machine measurement

[0010] S2.1 measurement point arrangement and fitting, a group of measurement points is arranged on the circular arc surface and the upper and lower surfaces of each circular groove, and the ball center position is fitted for each group of measurement points;

[0011] S2.2 measurement method,

[0012] S2.2.1 Position the linear axis of the machine tool at an angular position, measure the measurement point at this position, after the measurement, rotate the C-axis to the next measurement point position at the measurement head, and measure, and so on, rotate the C-axis one by one, so that all the circular arc surfaces are sequentially rotated to the measurement head position for measurement;

[0013] S2.2.2 Adjust the linear axis to the next angular position, the difference between this angular position and the previous angular position is 360 / n, and the remaining measurement process is the same as step S2.2.1;

[0014] S2.2.3 Repeat step S2.2.2 until the circular arc surface measurement at all angular positions of the linear axis is completed;

[0015] S3 Identify the workpiece geometric error, C-axis geometric error, linear axis error and total error according to the data measured in step S2.

[0016] Preferably, the identification equation of the workpiece geometric error is:

[0017]

[0018] Wherein

[0019]

[0020] G X (S j ) is the geometric error of the fitted center of the circular arc surface S j in the X direction, G Y (S j ) is the geometric error of the fitted center of the circular arc surface S j in the Y direction, G Z (S j ) is the geometric error of the fitted center of the circular arc surface S j in the Z direction, and j is the index number of the fitted center of the corresponding circular arc surface (j = 1, 2, …, n).

[0021] Preferably, the identification equation of the C-axis geometric error is:

[0022]

[0023] Wherein

[0024]

[0025] E XC,total (C i ) is the linear geometric error component of the C-axis in the X direction when the C-axis is indexed to C i ,

[0026] where E XC,total (C i ) = E X0C + E XC (C i ) ;

[0027] E YC,total (C i ) is the linear geometric error component of the C-axis in the Y-direction when the C-axis is indexed to C i

[0028] where E YC,total (C i ) = E Y0C + E YC (C i ) ;

[0029] E ZC (C i ) is the position error of the C-axis in the Z-direction when the C-axis is indexed to C i

[0030] E AC,total (C i ) is the angular geometric error component of the C-axis in the X-direction when the C-axis is indexed to C i

[0031] where E AC,total (C i ) = E A0C + E AC (C i ) ;

[0032] E BC,total (C i ) is the angular geometric error component of the C-axis in the Y-direction when the C-axis is indexed to C i

[0033] where E BC,total (C i ) = E B0C + E BC (C i ) ;

[0034] E CC (C i ) is the angular positioning error of the C-axis in the Z-direction when the C-axis is indexed to C i

[0035] G(S j ) is the position deviation between the actual measured center position and its nominal center position;

[0036] ​​​​​i is the index number of the rotational axis C axis angle position (i = 1, 2, …, n).

[0037] Preferably, the linear axis error is:

[0038]

[0039] wherein

[0040] θ k is the index of the machine tool linear axis to the angle position;

[0041] E XX (θ k ) is the position error of the linear axis in the X direction when the linear axis is indexed to θ k .

[0042] E YY (θ k ) is the position error of the linear axis in the Y direction when the linear axis is indexed to θ k .

[0043] E YY (θ k ) is the position error of the linear axis in the Z direction when the linear axis is indexed to θ k .

[0044] Preferably, the total error identification equation is:

[0045]

[0046] Preferably, the workpiece and tool body in step S1 are:

[0047] S1.1 The initial position of the workpiece is at the center position of the C axis, and in the case that the rotational axes B and C of the machine tool are both 0°, a layer of surface of the blank is first cut off through the movement of the linear axes X, Y and Z.

[0048] S1.2 The rotational axes B and C are both kept stationary, and a square groove is cut through the movement of the linear axes X, Y and Z.

[0049] S1.3 The rotational axes B and C are both kept stationary, and a circular arc surface S1 is cut through the movement of the linear axes X, Y and Z. Similarly, the rotational axes are kept stationary, and n circular arc surfaces S2, S3…Sn of the same size are continuously cut through the movement of the linear axes X, Y and Z. n .

[0050] Preferably, the measurement point arrangement and fitting in step S2.1 are specifically:

[0051] The arc surface S1 is uniformly divided by three vertical bisectors and three contour lines, nine measuring points are arranged at the intersection of the bisectors and the contour lines, three groups of two-dimensional coordinates (x, y) can be fitted according to the nine measuring points, and the spherical center (x, y) coordinate components of the arc surface are determined by taking the average value; three measuring points are arranged on the upper surface and the lower surface of the arc surface respectively, and the corresponding spherical center z coordinate components are obtained by fitting; the above measurement and fitting method is also applicable to the arc surfaces S2 to S n , so as to obtain the spatial position of the spherical center at all arc surfaces.

[0052] Preferably, the number of the circular grooves in the step S1 is n=12.

[0053] Compared with the prior art, the present application has the following technical effects:

[0054] The self-calibration method of the tooth-shaped workpiece can identify the geometric errors of the rotating shaft, the linear shaft and the workpiece at the same time, and improves the identification accuracy.

[0055] The designed square groove positioning feature combined with the repeatable measurement mechanism can improve the efficiency of periodic accuracy checking and calibration.

[0056] By analyzing the mapping relationship between the spherical center deviation of the arc surface and the error term, an identification model for simultaneously separating the linear shaft error, the rotating shaft error and the workpiece geometric error is established, which eliminates the influence of the linear shaft error on the identification result and reduces the uncertainty caused by the workpiece geometric error.

[0057] By extracting the geometric feature data of the n arc surfaces of the tooth-shaped workpiece, a mapping model of the spherical center deviation and the error term is established, and the synchronous decoupling identification of the 10 geometric errors (4 PI GEs and 6 PD GE) of the C shaft can be realized.

[0058] Twelve measuring steps are designed (for example, n=12), and the linear shaft motion trajectory of the corresponding machined surface in each measuring step remains the same. Therefore, the error of the linear shaft has consistency in the measurement of each group of center points. This makes the solution of the linear shaft error simplified from the original 12x12x3 error parameters at different positions to 12x3 error parameters, thereby reducing the complexity of parameter solving. The present method is based on the measurement of the cutting of the test piece, and the measured feature surface is directly located on the workpiece body, without considering the assembly error between the measured surface and the workpiece, which further reduces the uncertainty of error identification. BRIEF DESCRIPTION OF DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort based on these drawings. Among them:

[0060] Figure 1 The flowchart of the present application;

[0061] Figure 2 The structural diagram of the five-axis machine tool of the present application;

[0062] Figure 3 The structural diagram of the tooth-shaped workpiece of the present application, wherein (a) is a perspective view, (b) is a top view, and (c) is a front view;

[0063] Figure 4 The machining process diagram of the tooth-shaped workpiece of the present application (B=C=0°), wherein (a) is the cutting process of the surface layer of the blank, (b) is the cutting process of the square groove, and (c) is the cutting process of the circular arc surface;

[0064] Figure 5 The fitting diagram of the measuring points of the present application;

[0065] Figure 6 The measurement flowchart of the present application;

[0066] Figure 7 The diagram of the influence of the geometric errors of the workpiece on the detection points of the present application, wherein (a) is the XY plane, and (b) is the XZ plane;

[0067] Figure 8 The diagram of the influence of the geometric errors of the C-axis on the detection points of the present application;

[0068] Figure 9 The diagram of the influence of the linear axis errors on the detection points of the present application;

[0069] Figure 10 The identification results of the six PDGEs of the C-axis of the present application, wherein (a) is the linear error EXC, EYC, and EZC, and (b) is the angular error EAC, EBC, and ECC;

[0070] Figure 11 The linear axis errors and the geometric errors of the workpiece of the present application, wherein (a) is the linear axis geometric error, and (b) is the geometric error of the workpiece;

[0071] Figure 12 The comparison between the identification results of the present method and the identification results of the DBB, wherein (a) is the comparison between the identification results of the linear errors EXC, EYC, and EZC, and (b) is the comparison between the identification results of the angular errors EAC, EBC, and ECC;

[0072] Figure 13 For the identification results of the present application and the disc-shaped workpiece identification results, (a) linear error EXC, EYC, EZC identification result comparison. (b) Angle error EAC, EBC, ECC identification result comparison;

[0073] Figure 14 For the extended uncertainty (k = 2) of the C-axis PDGEs estimated by the Monte Carlo method. (a) The extended uncertainty of the linear error EXC, EYC, EZC. (b) The extended uncertainty of the angle error EAC, EBC, ECC;

[0074] Figure 15 For the influence of the angle error EA0C on the probe displacement. (a) XY plane. (b) YZ plane. DETAILED DESCRIPTION

[0075] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific embodiments of the present application will be described in detail below in conjunction with the drawings of the specification. In the following description, a large number of specific details are set forth in order to facilitate a full understanding of the present application, but the present application can also be implemented in other ways different from the description, and those skilled in the art can make similar generalizations without departing from the connotation of the present application, therefore the present application is not limited by the specific embodiments disclosed below.

[0076] Secondly, the "one embodiment" or "embodiment" referred to herein means that the specific features, structures or characteristics can be included in at least one implementation of the present application. "In one embodiment" appearing in different places in the specification does not mean the same embodiment, nor is it an independent or selective embodiment that excludes other embodiments.

[0077] Embodiment 1

[0078] As Figure 1 shown: a five-axis machine tool rotary axis geometric error self-calibration method based on tooth-shaped workpiece, comprising the following steps:

[0079] S1 workpiece machining

[0080] Make a tooth-shaped workpiece with n circular grooves and a square groove at the center position;

[0081] S2 in-machine measurement

[0082] S2.1 Measurement point arrangement and fitting, a group of measurement points are arranged on the circular arc surface of each circular groove and its upper and lower surfaces respectively, and the ball center position is fitted for each group of measurement points;

[0083] S2.2 Measurement

[0084] S2.2.1 Position the linear axis of the machine tool at an angular position, measure the measurement points at this position, after the measurement is completed, rotate the C-axis to the next measurement point position at the measurement head, and measure, and so on, rotate the C-axis one by one, so that all the circular arc surfaces are in turn rotated to the measurement head position for measurement;

[0085] S2.2.2 Adjust the linear axis to the next angular position, and the difference between the angular position and the previous angular position is 360 / n, and the remaining measurement process is the same as step S2.2.1;

[0086] S2.2.3 Repeat step S2.2.2 until the circular arc surface measurement at all angular positions of the linear axis is completed;

[0087] S3 According to the data measured in step S2, the geometric error of the workpiece, the geometric error of the C-axis, the linear axis error and the total error are identified.

[0088] In this embodiment, the five-axis machine tool is an XZRYBC type double-rotary table five-axis machine tool as shown in Figure 2 The structure code of the machine tool is [wC’B’Y’bXZ(C1)t]. During the measurement process, the contact trigger probe is positioned by the X-axis and the Y-axis, and at the same time, based on the multi-height layer measurement requirement, it needs to be layered along the Z-axis direction. This makes the measurement point coordinates affected by the combined effects of multiple error sources: first, the geometric error of the workpiece itself directly affects the measurement accuracy of the feature surface profile; second, the positioning error of the linear axis (X, Y, Z axis) of the machine tool is transmitted to the end of the probe through the motion chain, causing the detection position to deviate; third, the error generated during the rotation of the C-axis will further affect the measurement process.

[0089] The error variables that need to be identified by the method proposed in Table 1

[0090]

[0091] Table 1 defines the error variables based on ISO-230-1

[29] , covering three types of parameter groups: C-axis angular position (Ci), linear axis position (θk) and workpiece machining surface (Sj). This provides a theoretical basis for subsequent decoupling identification of each error.

[0092] S1 Workpiece machining

[0093] As shown in Figure 3 , a tooth-shaped workpiece with 12 circular grooves is designed, including circular arc surfaces and square groove features, wherein the circular arc machining surfaces are named Sj in the counterclockwise direction.

[0094] The specific steps are as follows:

[0095] S1.1 As shown in Figure 3(a) As shown, the initial position of the workpiece is on the center position of C-axis. In the case that the rotary axes B-axis and C-axis are both 0°, a layer of surface of the blank is cut off by the movement of linear axes X, Y and Z.

[0096] S1.2 As shown in Figure 3 (b) As shown, the rotary axes B-axis and C-axis are both kept static, and a square groove is cut by the movement of linear axes X, Y and Z.

[0097] S1.3 As shown in Figure 3 (c) As shown, the rotary axes B-axis and C-axis are both kept static, and a circular arc surface S1 is cut by the movement of linear axes X, Y and Z. Similarly, the rotary axes are kept static, and 11 circular arc surfaces S2, S3…S12 of the same size are continuously cut by the movement of linear axes X, Y and Z.

[0098] In the machining process as described above, the circular arc surfaces machined in steps S1.1 and S1.3, the upper surface and the lower surface serve as the measurement surface for subsequent measurement of point data, and the square groove machined in step S1.2 provides a basis for subsequent calibration using the workpiece. This design allows the machine tool to be reclamped and aligned when calibration is required, thereby facilitating regular precision inspection and calibration of the machine tool.

[0099] To improve machining efficiency, the machining process is rough machining, only the approximate geometric shape can be obtained, and the precise geometric shape of the machined surface is not calibrated, but the cut surface is smooth enough not to affect subsequent measurement.

[0100] S2 In-machine measurement

[0101] The measurement target is to accurately measure the circular arc feature surface and the upper and lower surfaces of the tooth-shaped workpiece using the machine tool probe, and to fit the corresponding spherical center position based on the measurement data. In the measurement process, the pre-travel of the probe has been pre-calibrated, and the uncertainty of the probe itself is not considered in the present application. The research focus is on the measurement deviation caused by the related errors of the machine tool linear axes and C-axis.

[0102] S2.1 Measurement point arrangement and fitting

[0103] As shown in Figure 5As shown in the figure, a total of 180 measuring points are arranged on the processing surface. Taking the arc surface S1 as an example, the arc surface is evenly divided by three vertical bisectors (arc spacing p) and three contour lines (contour distance h), and the measuring points are set at the intersection of the bisectors and the contour lines, so that 9 measuring points are obtained on each arc surface. According to these 9 measuring points, 3 sets of two-dimensional coordinates (x, y) can be fitted to obtain the spherical center (x, y) coordinate components of the arc surface. For the z coordinate component of the spherical center, 3 measuring points are arranged on the upper cutting surface and the lower cutting surface of the workpiece respectively, and the corresponding spherical center z is obtained by fitting. The above measurement and fitting method is also applicable to arc surfaces S2 to S12 to obtain the spatial position of the spherical center of each feature surface.

[0104] S2.2 Measurement method

[0105] like Figure 6 As shown,

[0106] S2.2.1: First, position the machine tool's linear axis at the first angular position θ1, keeping the C-axis stationary. At this point, measure the positions of the measuring points on the arc surface S1 and its upper and lower surfaces. After the measurement is completed, while maintaining the linear axis angular position θ1 unchanged, rotate the C-axis to move the arc surface S2 to the position of the probe and perform the corresponding measurement. Similarly, rotate the C-axis one by one so that all 12 arc surfaces are moved to the probe position for measurement. After completing the measurement of the 12 arc surfaces, rotate the C-axis to return it to its initial angular position (i.e., return the C-axis to 0).

[0107] S2.2.2 Adjust the linear axis to the second angle position θ2. The measurement process is the same as step 1. Measure 12 arc surfaces in sequence by rotating the C axis. After the measurement is completed, return the C axis to 0.

[0108] S2.2.3 Position the linear axis at θ3 to θ 12 Repeat the measurement operation in the same way as the previous steps for each angle position until the arc surface measurement at all angle positions is completed.

[0109] During the measurement process described above, the linear axis motion trajectory remains consistent across the machined surface for each measurement step. Therefore, the linear axis-related errors consistently affect the acquired center point data across all measurement steps. Specifically, if n sets of center point position data are collected, each set containing m center points, then there are n corresponding linear axis-related error terms. Each error term consistently affects the measurement results for all m center points within that set during the measurement step to which it belongs.

[0110] The machine coordinate system (MCS) is defined as a fixed coordinate system with its origin set at the intersection of the nominal B-axis and C-axis. When a vector is expressed in the MCS, it is identified by a superscript "M". When the C-axis is indexed to an angular position C M , the center point of the jth circular surface S i on the workpiece in the workpiece coordinate system (WCS) is denoted as j . This point can be transformed into the MCS by equation (1), and the corresponding representation is . In this paper, the superscript "*" is used to represent the nominal value.

[0111]

[0112] wherein

[0113]

[0114] According to the aforementioned measurement procedure, the indexing operation of the machine linear axes will be involved in the subsequent analysis. The relationship between the indexing variables i, j and k can be represented by equation (2), where "mod" represents the modulo operation (i.e. the remainder). In particular, when the condition (i+k-1) mod 12 = 0 is satisfied, j = 12 is defined.

[0115] j = (i+k-1) mod 12 (2)

[0116] In addition, during the measurement process, when the machine linear axes are indexed to an angular position θ k and the C-axis is indexed to an angular position C i , the corresponding actual measurement point in the MCS is denoted as In this chapter, variables with a tilde symbol (~) represent actual measurement values. Thus, in the MCS, the three-dimensional displacement caused by geometric errors during the measurement process can be represented by the three-dimensional vector , and its specific expression is shown in equation (3).

[0117]

[0118] S3 Identifying the workpiece geometric error, C-axis geometric error, linear axis error and total error according to the data measured in step S2;

[0119] ​During the measurement process, geometric deviations in the machine tool's C-axis, linear axes, and the workpiece itself all affect the on-machine measurement results. By uniformly mapping the effects of all error sources to the coordinates of the sphere center reconstructed from the arc surface, and based on the deviation between the theoretical and actual sphere centers, we can gradually analyze the mechanisms by which these various errors affect the measurement results.

[0120] S3.1 Identification of workpiece geometric errors

[0121] Since the workpiece machining process belongs to the rough machining stage, there are certain geometric errors in the workpiece cutting surface itself. Figure 7 As shown, when the machine tool probe is used to measure the jth arc surface S j When measuring, the geometric error of the workpiece will cause a three-dimensional position deviation between the actual measured center position and its nominal center position, which is recorded as G(S j ). Therefore, when only affected by the geometric error of the workpiece itself, the resulting measurement displacement deviation can be described by equation (4). The meanings of the relevant symbols are detailed in Table 1.

[0122]

[0123] Where:

[0124]

[0125] S3.2 Influence of C-axis geometric error

[0126] When the rotation axis C axis is indexed to the angle position C i When the measurement is performed on-machine, there are three displacement errors and three rotation errors that affect the on-machine measurement process. This type of error is further divided into four PIGEs and six PDGEs, with detailed definitions and descriptions in Table 1. These errors originate from the on-machine measurement process. To facilitate subsequent analysis and presentation, we combine these errors into two three-dimensional vectors:

[0127]

[0128] Among them, C i =0°, 30°...330°, a total of 12 division angles.

[0129] like Figure 8 As shown, due to the influence of the C-axis geometric error, when the C-axis is at the i-th index angle, combined with the above-mentioned workpiece geometric error, the arc surface S is measured under the action of the C-axis geometric error. j When , the three-dimensional displacement deviation of the machine tool probe can be given by formula (5):

[0130]

[0131] in:

[0132]

[0133] S3.3 Effect of Linear Axis Error

[0134] When the machine tool linear axis indexes to the angle position θ k When , there are three displacement errors in the X, Y and Z directions respectively. The details are shown in Table 1. For ease of description, these errors are combined into a three-dimensional vector:

[0135]

[0136] Among them, θ k =0°, 30°...330°, a total of 12 division angles.

[0137] like Figure 9 As shown in the figure, when the machine tool performs on-machine measurement on the cutting surface of the workpiece, the linear axis error will directly affect the measurement accuracy of the detection point, causing the center point of the target detection surface received by the machine tool system to be displaced in the X, Y and Z directions.

[0138] S3.4 Overall formula under the influence of various errors

[0139] In summary, considering the influence of various error sources shown in Table 1, when the C axis index is C i and the linear axis is indexed at θ k When the arc surface S j During measurement, the workpiece geometric error, C-axis geometric error and linear axis error will jointly affect the measurement results of the machine tool probe, resulting in the measured arc surface S j The total three-dimensional displacement deviation corresponding to the center point is given by formula (6).

[0140]

[0141] Identification algorithm

[0142] When the C axis index is C i and the linear axis is indexed at θ k When the measured arc surface S j The three-dimensional displacement deviation of the actual measurement result can be expressed as Specifically, see formula (3). Combined with all detection points, all model parameters in Table 1 involved in formula (7) are estimated by least squares fitting, that is, solving the following minimization problem by the least squares method:

[0143]

[0144] In addition, in order to ensure the solvability of the mathematical model, the following boundary conditions must be added:

[0145] (1) Since all errors of the C-axis are defined with respect to the initial angle C i = 0°. Therefore, the following boundary conditions must be defined.

[0146]

[0147] (2) For linear axis errors, the following boundary conditions must be applied to define the X and Y directions of the MCS.

[0148]

[0149] (3) By definition, the XY plane of the MCS is parallel to the XY plane of the machine tool. Therefore, the following boundary conditions must also be added.

[0150]

[0151] Experimental verification

[0152] Experimental conditions, machining verification experiments were carried out on a five-axis machine tool equipped with a BC dual-rotary table structure, and the machine tool structure configuration is shown in Figure 1 . The experiment was carried out in a constant temperature laboratory with a temperature control accuracy of ±0.5°C (reference temperature 20°C), and the spindle and the whole machine were preheated before machining to reduce the influence of thermal effects. 6061 aluminum alloy was selected as the workpiece material. First, the surface of the blank was milled, and then a rectangular groove and 12 circular arc surfaces were machined according to the size requirements shown in Figure 2 . The characteristic workpiece after milling is shown in Figure 3 (a). To ensure the thermal stability of the measurement system, the workpiece was left to stand for 4h after machining to restore the thermal equilibrium state of the machine tool, and then the characteristic workpiece was measured based on the above in-machine measurement strategy.

[0153] Table 2 Process parameters for workpiece cutting

[0154]

[0155] Identification results

[0156] Based on the geometric feature data obtained by the in-machine measurement system, combined with the error identification model constructed above, the deviation between the actual measured position and the target position is used to calculate the defined error variables.

[0157] Table 3 shows the identification results of the four PIGEs of the C-axis. As shown in Table 3, the linear deviation of the C-axis axis in the X direction E X0C is larger, which is 15.6μm, and the linear deviation in the Y direction E Y0C is smaller, which is -8.8μm; the angular deviation of the C-axis axis around the X axis E A0CThe angular deviation around the Y axis is -13.5″, E B0C It’s relatively small at -9.7″.

[0158] Table 3 PIGEs identification results

[0159]

[0160] The identification results of the six PDGEs on the C axis are as follows Figure 10 As shown. Figure 10 (a) It can be seen that the linear error of the C axis is generally within [-18.2μm, 19.2μm]. When the C axis is at 120°, the linear error E ZC The maximum is -9.9μm; when the C axis is at 210°, the linear error E XC The maximum is 17.9μm; when the C axis is at 270°, the linear error E YC Reaching a maximum of 19.2μm. Figure 10 (b) It can be seen that the angle error E AC The range is [-13.3″, 20.7″], and the angle error E BC With E CC The ranges are [-23.9″,20.1″] and [-18.1″,21.6″] respectively.

[0161] The linear axis error and the geometric error of the 12 arc surfaces of the toothed workpiece are as follows: Figure 11 As shown. Figure 11 (a) shows that the overall linear axis error is within [-4.7μm, 7.4μm], which is smaller than the C-axis error. Figure 11 (b) It can be seen that the maximum value of the measured workpiece geometric error is 72.9μm, which is 53.7μm higher than the maximum value of the C-axis linear error.

[0162] The identification results of the rotational axis geometric error, linear axis error, and workpiece geometric error show that the workpiece geometric error is of comparable magnitude to the machine tool geometric error. Therefore, if the workpiece geometric error is not effectively decoupled and separated, the uncertainty of the machine tool geometric error identification results will increase.

[0163] Results comparison and verification

[0164] (1) Comparison and verification with DBB identification method

[0165] To verify the accuracy of the C-axis geometric error identification results, this paper compares and verifies the DBB identification method proposed by Tsutsumi. Using the DBB identification method, the four PIGEs and six PDGEs of the C-axis can be identified simultaneously.

[0166] Table 4 shows the difference in PIGEs identification results between this method and the DBB measurement method. It can be seen from the differences that the identification results of the two methods are highly similar. X0C Compared with the DBB identification result, the difference is 2.5μm; and the linear error E Y0C The difference is only 0.9μm; the angle error E A0C With E B0C The difference is -1.9" and -1.4", respectively. The matching rate of the recognition results reaches 87.6%, which verifies the accuracy of this method.

[0167] Table 4 Comparison of PIGEs identification results and DBB experiments

[0168]

[0169] Using the DBB measurement method, six PDGEs of the C axis were also identified. Figure 12 The results of DBB identification of PDGEs are presented, and a bar graph is drawn in the figure to show the deviation between the PDGEs identified by this method and the DBB measurement method. Figure 12 From the histogram of (a), we can see that the linear error E XC The identification result deviation is between [-1.1μm, 1.9μm], and the linear error E YC With E ZC The identification result deviations are between [-2.5μm, 1.8μm] and [-0.9μm, 0.8μm]. Figure 12 From the histogram of (b), we can see that the angle error E AC The identification result deviation is between [-1.5″, 1.3″], and the angle error E BC With E CC The identification result deviations are between [-1.6", 2.7"] and [-1.6", 2.8"] respectively. The matching rate of the identification results reaches 88.3%, which verifies the effectiveness of this method.

[0170] (2) Comparison and verification with feature artifact identification method

[0171] To fully verify the effectiveness of the proposed method, a comparison is also conducted with the identification method based on a disc-shaped workpiece proposed by Cheng

[30] . A disc-shaped workpiece with 12 rectangular slots was cut, and the identification equations of the geometric errors were derived based on the spatial error model to identify the four PIGEs and six PDGEs of the C-axis.

[0172] Table 5 shows the difference in PIGEs identification results between this method and the disc-type workpiece measurement method. X0C Compared with the disc-shaped workpiece identification result, the difference is 3.6μm; and the linear error EY0C The difference is only 1.1μm; the angular error E A0C With E B0C The difference is 1.6" and -0.9", respectively. The matching rate of the recognition results reaches 86.3%, which verifies the accuracy of this method.

[0173] Table 5 Comparison of PIGEs identification results and disc-shaped workpiece experiments

[0174]

[0175] Figure 13 The PDGEs identification results of this method and the disk-type workpiece measurement method are given. The bar graph in the figure shows the deviation between the PDGEs results identified by this method and the disk-type workpiece experiment. Figure 13 From the histogram of (a), we can see that the linear error E XC The identification result deviation is between [-2.4μm, 1.6μm], and the linear error E YC With E ZC The identification result deviations are between [-2.8μm, 1.9μm] and [-1.2μm, 0.9μm]. Figure 13 From the histogram of (b), we can see that the angle error E AC The identification result deviation is between [-2.1″, 1.7″], and the angle error E BC With E CC The identification result deviations are between [-2.3″, 1.9″] and [-2.5″, 1.8″] respectively. The matching rate of the identification results reaches 87.9%, which verifies the effectiveness of this method.

[0176] Uncertainty analysis

[0177] The uncertainty of the output parameters in the self-calibration measurement method for toothed workpieces. Since the self-calibration method is built on the basis of a multi-input and multi-output model, it is necessary to analyze the uncertainty propagation in the model. According to the uncertainty evaluation framework proposed in the Guide to the expression of uncertainty in measurement (GUM)

[31] , the uncertainty of the output parameters is estimated using the Monte Carlo method. In addition, the linear axis error of the machine tool is taken into account during the modeling process of the self-calibration method. The uncertainty analysis focuses on the repeatability of the overall measurement system of the machine tool and the error propagation in the self-calibration model.

[0178] Before the Monte Carlo simulation, the uncertainty of input parameters should be determined. The probability density function of input parameters can be estimated by using the program of uncertainty type A, which is based on multiple repeated experiments and can analyze the repeatability of the entire measuring system of the machine tool. By measuring the target point multiple times, the maximum standard uncertainty of 0.83 μm is calculated, which is less than the measurement repeatability of the machine tool of 1 μm. Therefore, the measurement repeatability of the machine tool of 1 μm is taken as the input uncertainty of the Monte Carlo simulation this time. Subsequently, based on the above input uncertainty, 500,000 times of Monte Carlo simulation are carried out to estimate the standard uncertainty of the output parameters. Table 6 summarizes the uncertainty evaluation results of the C-axis 4 PIGEs with a confidence level of 95% (k = 2). In addition, the evaluation results of the expanded uncertainty (k = 2) of the C-axis 6 PDGEs are shown in Table 7. Figure 14

[0179] Table 6 Expanded uncertainty (k = 2) of C-axis PIGEs estimated by Monte Carlo method

[0180]

[0181] Comparison with classical cutting tests

[0182] Ibaraki proposed a tower-shaped feature workpiece to map the rotational axis error by cutting multiple layers of rectangular feature surfaces. However, this method has the following limitations: First, due to the difference in the layered structure of the tower-shaped workpiece, linear axis errors will interfere with rotational axis errors, but the identification model does not consider linear axis errors, which limits the accuracy of error identification. Second, this method can only obtain data at 0°, 90°, 180°, and 270° discrete angle positions, making it difficult to fully characterize the error characteristics in the continuous motion of the rotational axis; more importantly, each calibration requires re-cutting the workpiece and measuring the machined surface, which reduces the calibration efficiency.

[0183] In contrast, the self-calibration method of the tooth-shaped workpiece proposed in the present application can identify rotational axis geometric errors, linear axis errors, and workpiece geometric errors simultaneously, improving the identification accuracy. Second, the 0° to 330° interval of the rotational axis is sampled by a 30° indexing strategy, making the error identification interval more compact. In addition, the designed square slot positioning feature combined with the repeatable measurement mechanism can improve the efficiency of regular accuracy checking and calibration.

[0184] Comparison with other self-calibration methods

[0185] Ibaraki proposed an error separation method based on a contact trigger probe and an uncalibrated cylindrical workpiece. This method designs four measurement modes and establishes an error and probe displacement mapping model based on geometric projection principles, as shown in equations (11)-(12), where Δr is the total probe displacement, Δr1…Δr n ​The probe displacement caused by each error. The angle error E A0C For example, the influence of the axial probe displacement is shown in Fig. Figure 15 (a), in the XY plane, the radius of the cylindrical workpiece is R, and the probe indexing angle is θ. By geometric transformation to the YZ plane, as shown in Fig. Figure 15 (b), the expression of the axial displacement influence of E A0C can be derived as shown in equation (12). Similarly, other error terms (Δr2…Δr n ) can also be decoupled by geometric modeling, so as to realize the synchronous identification of linear axes, rotary axes and workpiece errors. However, this method does not consider the other 2 PDGEs (E AC and E BC ) of the C-axis, resulting in insufficient error identification integrity.

[0186] Δr = Δr1+…+Δr n (11)

[0187] Δr1= E A0C ·R·sinθ (12)

[0188] In contrast, the method proposed in the present application can realize the synchronous decoupling identification of 10 geometric errors (4 PIGEs and 6 PDGEs) of the C-axis by extracting the geometric feature data of 12 circular arc surfaces of the tooth-shaped workpiece and establishing a mapping model of the spherical center deviation and error terms.

[0189] Keller based on the principle of "three-rosette method", proposed a new type of self-calibration method, which can be used to identify the geometric error of coordinate measuring machine (CMM) and machine tool rotary table. This method measures a plurality of balls on an uncalibrated spherical plate at a plurality of angle positions, establishes a mathematical model using the deviation between the actual position and the ideal position of the balls, and uses the least squares method for fitting, so as to separate the error components of the rotary table in 6 degrees of freedom, the manufacturing error of the ball, and the measurement error of the CMM. However, this method involves many parameters, resulting in a complex solving process. For the identification of rotary axis error, this method can only identify the overall error component of the rotary axis in 6 degrees of freedom, and cannot further separate and identify the PIGEs and PDGEs of the rotary axis. In addition, this method has high requirements for the manufacturing accuracy of the precision ball and the installation accuracy of the ball on the spherical plate, and the matching error between the spherical plate and the spherical plate also significantly increases the uncertainty of the error identification.

[0190] In contrast, the self-calibration measurement method based on the tooth-shaped workpiece proposed in this paper designs 12 measurement steps, and the linear axis motion trajectory of the corresponding machined surface in each measurement step remains consistent. Therefore, the error of the linear axis has consistency in the measurement of each group of center points. This makes the solution of the linear axis error simplified from the original 12x12x3 error parameters at different positions to 12x3 error parameters, thereby reducing the complexity of parameter solving. For the geometric error of the rotary axis, the method proposed in this paper can identify 4 PIGEs and 6 PDGEs of the rotary axis at the same time. In addition, the method measures based on the cutting of the test piece, and the measured feature surface is directly located on the workpiece body, without considering the assembly error between the measured surface and the workpiece, further reducing the uncertainty of error identification.

[0191] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit it. Although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solutions of the present application can be modified or replaced equivalently without departing from the spirit and scope of the technical solutions of the present application, which should be covered in the scope of the claims of the present application.

Claims

1. A self-calibration method for the geometric error of the rotating axis of a five-axis machine tool based on a tooth-shaped workpiece, characterized in that: The following steps are involved: S1 workpiece processing Make a toothed workpiece with n circular grooves and a square groove in the center; S2 on-machine measurement S2.1 Measurement point arrangement and fitting: Set up groups of measurement points on the arc surface and upper and lower surfaces of each circular groove, and fit the sphere center position for each group of measurement points; S2.2 Measurement method, S2.2.1 Position the linear axis of the machine tool at an angular position and measure the measuring point at that position. After the measurement is completed, rotate the C-axis to the next measuring point at the probe and measure it again. Repeat this process by rotating the C-axis one by one until all arc surfaces are in the probe position for measurement. S2.2.2 Adjust the linear axis to the next angular position. The difference between this angle and the previous angle is 360 / n. The rest of the measurement process is the same as step S2.2.

1. S2.2.3 Repeat step S2.2.2 until the arc surface measurement at all angular positions of the linear axis is completed; S3 identifies the workpiece geometric error, C-axis geometric error, linear axis error and total error based on the data measured in step S2.

2. The method for self-calibration of geometric errors of a five-axis machine tool rotating axis based on a tooth-shaped workpiece according to claim 1, characterized in that: The identification equation of the workpiece geometric error is: in G X (S j ) is the arc surface S j The geometric error of the fitted circle center in the X direction, G Y (S j ) is the arc surface S j The geometric error of the fitted circle center in the Y direction, G Z (S j ) is the arc surface S j The geometric error of the fitted circle center in the Z direction, j is the index number of the corresponding arc surface fitting circle center (j = 1, 2, ..., n).

3. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 1, characterized in that: The identification equation of the C-axis geometric error is: in E XC,total (C i ) is the C axis index in C i When the linear geometric error component of the C axis in the X direction is Among them, E XC,total (C i )=E X0C +E XC (C i ); E YC,total (C i ) is the C axis index in C i When the linear geometric error component of the C axis in the Y direction is Among them, E YC,total (C i )=E Y0C +E YC (C i ); E ZC (C i ) is the C axis index in C i When , the position error of C axis in Z direction; E AC,total (C i ) is the C axis index in C i When , the angular geometric error component of the C axis in the X direction is, Among them, E AC,total (C i )=E A0C +E AC (C i ); E BC,total (C i ) is the C axis index in C i When , the angular geometric error component of the C axis in the Y direction; Among them, E BC,total (C i )=E B0C +E BC (C i ); E CC (C i ) is the C axis index in C i Angular positioning error of the C-axis in the Z direction; G(S j ) is the positional deviation between the actual measured center position and its nominal center position; i is the index number of the angular position of the rotation axis C (i=1, 2, ..., n).

4. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 1, characterized in that: The identification equation of the linear axis error is: in θ k Index the machine tool linear axis to the angular position; E XX (θ k ) is the linear axis index at θ k When the linear axis is in the X direction, the position error is E YY (θ k ) linear axis indexed at θ k When the linear axis is in the Y direction, the position error is E YY (θ k ) is the linear axis index at θ k The position error of the linear axis in the Z direction when .

5. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 1, characterized in that: The identification equation of the total error is:

6. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 1, characterized in that: Step S1: Workpiece processing is specifically as follows: S1.1 The initial position of the workpiece is at the center of the C axis. When the machine tool's rotary axes B and C are both at 0°, the linear axes X, Y, and Z are used to cut away a layer of the blank surface. S1.2 The rotary axes B and C remain stationary, and a square groove is cut by moving the linear axes X, Y, and Z. S1.3 The rotation axis B and C axes remain stationary, and the arc surface S1 is cut by the movement of the linear axes X, Y and Z. Similarly, the rotation axis remains stationary, and the linear axes X, Y and Z axes continue to cut n arc surfaces of the same size S2, S3...S n .

7. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 6, characterized in that: Step S2.1: Measurement point arrangement and fitting are as follows: The arc surface S1 is evenly divided by three vertical bisectors and three contour lines. Nine measuring points are set at the intersection of the bisectors and the contour lines. Three sets of two-dimensional coordinates (x, y) can be fitted based on these nine measuring points. The (x, y) coordinate components of the center of the arc surface are determined by taking their averages. Three measuring points are arranged on the upper and lower surfaces of the arc surface respectively, and the corresponding z coordinate components of the center of the arc surface are obtained by fitting. The above measurement and fitting methods are also applicable to the arc surfaces S2 to S n , to obtain the spatial position of the sphere center at all arc surfaces.

8. The method for self-calibration of geometric errors of a five-axis machine tool rotation axis based on a tooth-shaped workpiece according to claim 1, characterized in that: In step S1 , the number of circular grooves n=12.

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