Five-axis machine tool geometric error identification method based on single-axis and multi-axis measurement

Abstract

The invention discloses a five-axis machine tool geometric error identification method based on single-axis and multi-axis measurement, and belongs to the field of numerical control machine tool precision detection. Error kinematics and multi-axis motion models are established based on a multi-body system theory, and error identification models of a linear axis and a rotating axis are respectively constructed. On the aspect of a linear axis, an identification method based on measurement of a positioning error and a straightness error is provided, two measurement / identification schemes of single-axis motion and two-axis linkage are designed, and 18 linear axis geometric error parameters related to the position and 3 linear axis geometric error parameters irrelevant to the position are obtained through calculation. In the aspect of a rotating shaft, 12 rotating shaft geometric error parameters related to the position and 4 rotating shaft geometric error parameters irrelevant to the position are obtained on the basis of an existing linear shaft result based on a measurement and identification scheme of a double-ball-rod instrument in three directions and six positions. According to the method, positioning and straightness error detection are completed in combination with auxiliary equipment such as a laser interferometer and a double-ball-rod instrument, and the method has good universality.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of precision detection of numerical control machine tools, especially the geometric error identification of five-axis numerical control machine tools, and specifically relates to a five-axis machine tool geometric error identification method based on single-axis and multi-axis measurement. BACKGROUND

[0002] Five-axis numerical control machine tools are widely used in high-end manufacturing fields such as aerospace, automobiles and precision molds due to their multi-axis linkage capability. The geometric error of the machine tool becomes a key factor restricting the processing quality and efficiency. The geometric error includes not only the position-dependent geometric error that changes with the coordinate position, but also the position-independent geometric error that is independent of the position; there is also a significant coupling effect between linear axes and rotary axes, which comprehensively affects the processing results in the working space.

[0003] At present, in engineering practice, single-axis geometric error is mostly measured by laser interferometer. In the multi-axis linkage state, double ball bar is often used for rapid detection. However, such methods are highly sensitive to the installation position and attitude of the detection equipment and tooling, the measurement path and the distribution of measurement points, and the results obtained often only reflect the comprehensive effect of a specific trajectory, making it difficult to distinguish the coupling contribution of linear axes and rotary axes, and unable to comprehensively diagnose the geometric error distribution of geometric error in the three-dimensional machining space.

[0004] Chinese patent CN120447466A proposes a spiral bevel gear tooth surface error compensation method considering machine tool geometric error, which establishes a mapping from geometric error to tooth surface error based on the initial machine tool space error model and the tooth surface equation, first uses the Jacobian matrix to analytically compensate the tool pose error, and then uses the particle swarm optimization (PSO) to optimize the residual error and output the corrected tooth surface, thereby balancing the compensation efficiency and accuracy; but the method relies on model and parameter setting, and it is difficult to make outstanding contributions to the identification of the full-space distribution of geometric error.

[0005] Chinese patent CN120326437A proposes a high-precision geometric error detection method and system for five-axis numerical control machining, which constructs a height error matrix based on the height error data collected by a laser interferometer on the surface of the machine tool workbench, completes error identification and compensation without the need for additional special angle adjustment devices, and weakens the sensitivity to installation position and fixed angle. This method improves the detection accuracy, but still cannot comprehensively identify the spatial distribution of geometric error.

[0006] The Chinese invention patent CN107066721B authorizes a multi-axis numerical control machine tool C-axis geometric error measurement system and parameter identification method. The method is aimed at the structure and characteristics of the multi-axis numerical control machine tool C-axis, and the motion equation with geometric error and the motion equation under ideal state are established according to the working principle of the ball bar in the radial, tangential and axial three linkage modes, the error items of the rotating C-axis are identified, the coupling phenomenon between the geometric error parameters is solved, and the error identification of the remaining rotating shafts of the multi-axis numerical control machine tool has theoretical and practical significance, but the method can accurately identify single-axis geometric error and cannot comprehensively identify the spatial distribution of all geometric errors of the five-axis machine tool. SUMMARY

[0007] The purpose of the present application is to provide a five-axis machine tool geometric error identification method based on single-axis and multi-axis measurement, which can comprehensively identify the geometric error of the five-axis machine tool through error modeling and multiple measurements.

[0008] To achieve the above purpose, the method adopted by the present application is: a five-axis machine tool motion error model is established, including geometric error identification models of linear axes and rotating axes. The positioning error and straightness error measurement is used to design multiple sets of single-axis motion and multi-axis linkage error identification schemes for linear axes. A multi-point measurement identification strategy is proposed by combining the ball bar measurement of rotating axes at different spatial positions. All 21 linear-axis-related geometric errors and 16 rotating-axis-related geometric errors of the five-axis machine tool are successfully identified.

[0009] In the same motion branch of the machine tool, the translational motion can be performed in up to three directions. Based on this feature, the corresponding linkage equation is constructed to realize the solution of the motion error parameters. According to the motion error analysis method of multi-body systems, A, B and C represent three motion bodies (such as Figure 1 ) in the same motion branch of the five-axis machine tool. Among them, the coordinate system of the bed body is set as the basic coordinate system and coincides with the absolute coordinate system; the coordinate system origins of the remaining motion components are selected at the center positions of their motion contact surfaces.

[0010] O represents the origin of the basic coordinate system. Q j l and Q j represent the ideal motion reference coordinate system origin and the actual motion reference coordinate system origin of j body respectively; O j l and O j represent the ideal motion position and the actual motion position of the body reference coordinate system origin of j body in the actual motion reference coordinate system, j=A, B, C.[Bmn] p represents the ideal position transformation matrix, [Bmn] pe represents the actual position error transformation matrix, [Bmn] sdenotes the ideal motion transformation matrix, [Bmn] se denotes the actual motion error transformation matrix, m, n = A, B, C.{r C}={r x r y r z 1} T denotes the vector position matrix of a given point P on the C-body relative to the C-body coordinate system.{P T} h ={x h y h z h 1} T denotes the position of a given point P on the C-body when it moves to the hth position relative to the reference coordinate system. At this time, the position equation of the P point on the C-body coordinate system relative to the base coordinate system can be obtained as formula (1).

[0011] (1),

[0012] Let the position parameter h = 0, and at this moment all the geometric error parameters are zero, then the position equation of the given point P on the C-body relative to the base coordinate system when the C-body is in the initial position can be obtained as formula (2).

[0013] (2),

[0014] The ideal transformation matrix and the error transformation matrix between adjacent bodies of the five-axis machine tool are shown in the following table.

[0015]

[0016] According to formula (2) and the above table, the linear axis motion constraint equation of the five-axis machine tool is established, and the result is as formula (3).

[0017] (3),

[0018] The motion constraint equation can be obtained by subtracting two position directions, so the motion constraint equation of the point P moving from the 0 position to the h position is as formula (4).

[0019] (4),

[0020] The positioning accuracy and straightness of each motion axis of the machine tool are comprehensively measured. The measurement route is distributed in the machine tool machining space, and the distribution is as shown in Figure 2 .

[0021] When only the Z1 axis moves linearly, the displacement is z1 h , the X1 axis and the Y axis do not move. There is no position transformation and motion transformation of the X1 axis and the Y axis, so B

[12] p , B

[23] p , B

[12] s , B

[23] s , B

[12] se , B

[23] se is the unit matrix. The movement displacement L izh of the given point P on the tool spindle along the Z1 axis

[0022] (5),

[0023] where i represents the serial number of the measuring point; h represents the movement of the machine tool spindle to the hth given position; r ix , r iy represents the projection of the ith measured point along the X, Y directions in the tool coordinate system.

[0024] When the Z1 axis moves, the displacement L 1zh , L 2zh , L 3zh of the points P1, P2, P3 at three different positions on the tool spindle in the Z axis direction is measured respectively, and three measured displacement equations are obtained, as shown in equation (6).

[0025] (6),

[0026] The positions of the measuring points are appropriately selected to ensure that the matrix in equation 6 is full rank, and the error parameter expression is shown in equation (7).

[0027] (7),

[0028] By measuring the actual displacement L 1zh , L 2zh , L 3zh of the P1, P2, P3 paths, the positioning error δ z (z1 h ), the yaw error ε y (z1 h ), and the roll error ε x (z1 h ) in the Z1 direction are obtained. The measurement results are substituted into the calculation, and the identification results are as follows Figure 3 .

[0029] When only the Y axis moves linearly, the displacement is y h , the X1 axis and the Z1 axis do not move. At this time, there is no position transformation and motion transformation of the X1 axis and the Z1 axis, so B

[01] p , B

[23] p , B

[01] s , B

[23] s , B

[01] se, B

[23] se is the unit matrix. The movement displacement L of the given point P on the tool spindle along the Y axis iyh as shown in equation (8).

[0030] (8),

[0031] where i represents the serial number of the measuring point; h represents the movement of the machine tool spindle to the hth given position; r ix , r iz represents the projection of the ith measured point along the X and Z directions in the tool coordinate system.

[0032] When the Y axis moves, the displacement L 4yh , L 5yh , L 6yh of the points P4, P5, and P6 at three different positions on the tool spindle in the Y axis direction are measured respectively, and three actual displacement equations are obtained, as shown in equation (9).

[0033] (9),

[0034] The measuring point positions are appropriately selected to ensure that the matrix in equation (9) is full rank, and the error parameter expression is shown in equation (10).

[0035] (10),

[0036] By measuring the actual displacement L 4yh , L 5yh , L 6yh of P4, P5, and P6, the positioning error δ y (y h ), the yaw error ε z (y h ), and the roll error ε x (y h ) in the Y direction are obtained. The measurement results are also substituted into the calculation, and the geometric error identification results are as shown in Figure 4 .

[0037] When only the X1 axis moves linearly, the displacement is x1 h , and the Y and Z1 axes do not move. At this time, there is no position transformation and motion transformation of the Y and Z1 axes, so B

[01] p , B

[12] p , B

[01] s , B

[12] s and B

[01] se , B

[12] se are unit matrices. The movement displacement L ixh of the given point P on the tool spindle along the X1 axis is shown in equation (11).

[0038] (11),

[0039] where: i represents the serial number of the measuring point; h represents the movement of the machine tool cutter spindle to the hth given position; r iy , r iz represents the projection of the ith measured point in the Y, Z direction of the cutter coordinate system.

[0040] When the X1 axis moves, the displacement L 7zh , L 8zh , L 9zh of the points P7, P8, P9 at three different positions on the cutter axis in the Z axis direction are measured respectively, and three measured displacement equations are obtained, as shown in equation (12).

[0041] (12),

[0042] The measuring point positions are appropriately selected to ensure that the matrix in equation (12) is full rank, and the error parameter expression is as shown in equation (13).

[0043] (13),

[0044] By measuring the actual displacement L 7zh , L 8zh , L 9zh of P7, P8, P9, the positioning error δ x (x1 h ), the runout angle error ε y (x1 h ), and the tilt angle error ε z (x1 h ) of X1 are obtained. The measurement results are also substituted into the calculation, and the geometric error identification result is as shown in Figure 5 .

[0045] When the X1 and Z1 axes are linked, the displacements are x1 h and z1 h , and the Y axis does not move. At this time, there is no position transformation and motion transformation of the Y axis, so B

[12] p , B

[23] p , B

[12] s and B

[12] se are unit matrices. The movement displacement L ixh and L izh of the given point P on the cutter spindle in the X1 and Z1 axis directions are as shown in equation (14).

[0046] (14),

[0047] Where: i represents the serial number of the measuring point; h represents the movement of the machine tool cutter spindle to the hth given position; r ix , r iy , r iz represents the projection of the ith measured point in the X, Y, Z directions along the cutter coordinate system.

[0048] The displacement components of the given point P in three directions cannot be directly measured, and an indirect measurement method needs to be used. Figure 6 In the middle L ih and L l ih respectively represent the actual displacement and ideal displacement of the Pi point, δ ih represents the straightness error of the movement axis in the XOZ plane. According to the geometric position relationship in the figure, the corresponding position relationship equation is established, such as equation (15).

[0049] (15),

[0050] As can be seen from equation (11), there are a total of 5 unknown error parameters δ x (z1 h ), ε z (z1 h ), δ z (x1 h ), ε x1z1 , and ε x (x1 h ) in the equation. The error parameters are only related to the Y coordinate r iy of the measured point Pi. Two points P10 and P11 with different Y coordinates are selected, and their linkage displacements in the XOZ plane are measured, and two sets of displacement measurement equations are constructed. The two sets of displacement measurement equations have four equations, which cannot solve the five error parameters. First, ε x1z1 is regarded as a known quantity, and when the two sets of displacement measurement detection positions are different, i.e., r 10y ≠ r 11y , the expression of the unknown error parameter can be obtained as equation (16).

[0051] (16),

[0052] In equation (16), L 10xh , L 10zh , L 11xh , and L 11zh can be obtained from equation (15). And only the equation related to δ z (x1 h ) contains ε x1z1According to the characteristics of the linear axis straightness error of the CNC machine tool

[36] , the formula (17) is added as a supplementary equation for solving the error parameters when X1-Z1 linkage is used, where m represents the number of discrete points.

[0053] (17),

[0054] According to the P10, P11 path measurement. The results are substituted into the calculation, and the error recognition results are perpendicularity ε x1z1 =0.012 / 300, δ x (z1 h ), ε z (z1 h ), δ z (x1 h ), ε x (x1 h ) as Figure 7 .

[0055] When Y and Z1 axes are linked, the displacement is y h and z1 h , and the X1 axis is not moving. At this time, there is no position transformation and motion transformation of the X1 axis, so B

[23] p , B

[23] pe , B

[23] s and B

[23] se are unit matrices. The movement displacement amount L iyh and L izh of the given point P on the tool spindle along the Y axis and Z1 axis are shown in formula (18).

[0056] (18),

[0057] In the formula, i represents the serial number of the measurement point; h represents the movement of the machine tool tool spindle to the hth given position; r ix , r iy , r iz represent the projection of the ith measured point along the X, Y, Z directions of the tool coordinate system.

[0058] The indirect measurement method of the given point P in the YOZ plane is shown in Figure 8 , L ih and L l ih respectively represent the actual displacement and ideal displacement of the Pi point, and δ ih represents the straightness error of the movement axis in the YOZ plane. According to the geometric position relationship in the figure, the corresponding position relationship equation is established, as shown in formula (19).

[0059] (19),

[0060] From equation (18), it can be seen that there are four unknown error parameters δ y (z1 h ), δ z (y h ), ε y (y h ),ε yz1 in the equation. The error parameters are only related to the X coordinate r ix of the measured point Pi. Two points P12 and P13 with different X coordinates are selected, and the linkage displacement in the YOZ plane is measured, and two groups of displacement measurement equations are constructed, as shown in equation (20).

[0061] (20),

[0062] In equation (20), the first equation and the third equation only contain one unknown parameter, and δ y (z1 h ) can be directly solved. In the second equation and the fourth equation, ε yz1 is regarded as a known quantity, and equation (21) is obtained.

[0063] (21),

[0064] According to equation (21) and equation (22), ε yz1 , δ z (y h ) and ε y (y h ) can be solved. Wherein, m represents the number of discrete points.

[0065] (22),

[0066] According to the measurement of P12 and P13 in Figure 2 , the measurement results are substituted into the calculation, and the error recognition result perpendicularity ε yz1 =0.0021 / 300. δ z (y h ) and ε y (y h ) are as Figure 9 .

[0067] When the X1 and Y axes are linked, the displacement is x1 h and y h , and the Z1 axis does not move. At this time, there is no position transformation and motion transformation of the Z1 axis, so B

[12] p , B

[12] pe , B

[12] s and B

[12] se The identity matrix. The displacement L of a given point P on the tool spindle along the X1 and Y axes. ixh and L iyh As shown in formula (23).

[0068] (twenty three),

[0069] In the formula: i represents the sequence number of the measurement point; h represents the h-th given position reached by the machine tool spindle; r ix , r iy ,r iz This represents the projection of the i-th measured point onto the tool coordinate system along the X, Y, and Z directions.

[0070] Indirect measurement methods for a given point P in the XOY plane, such as... Figure 10 As shown, L ih and L l ih分别 δ represents the actual and ideal displacements of point Pi. ih This represents the straightness error of the motion axis in the XOY plane. Based on the geometric positional relationship in the figure, establish the corresponding positional relationship equation, as shown in formula (24).

[0071] (twenty four),

[0072] Based on equation formula (24) and supplementary equation formula (25), δ can be solved. x (y h ) and δ y (x1 h ), where m represents the number of discrete points.

[0073] (25),

[0074] in accordance with Figure 2 Measurements were taken along path P14. The measurement results were then used in calculations to determine the verticality ε of the error identification result. x1y =0.013 / 300. δ x (y h ), δ y (x1 h )like Figure 11 As shown.

[0075] The ball-bar is used to measure the rotary axis. Take the C1 axis as an example. One end of the ball-bar is fixed on the C1 axis, and the other end is fixed on the tool spindle. In order to realize the trajectory requirement in the measurement process, the linkage of the linear axes is needed. Therefore, in the process of identifying the error parameters of the rotary axis, the coupling problem with the linear axis error is inevitable. Based on the measurement results, the influence of the linear axis error on the motion trajectory is eliminated, and then the geometric error of the rotary axis is accurately calculated.

[0076] In the initial state, the rotation angle of the C1 axis is zero, and the coordinates of the center of the tool tip in the C1 axis are [x0 y0 z0]. When the C1 axis rotates, the coordinates of the tool ball should remain relatively static with the C1 axis. Under ideal conditions, the transformation matrix of the tool relative to the workpiece coordinate system is represented by r w1 , at this time formula (26) is satisfied. During rotation, the linear axis needs to have a corresponding feed amount to cooperate with the movement, and the feed amounts x, y, and z satisfy the relationship of formula (27).

[0077] (26),

[0078] (27),

[0079] After the C1 axis rotates an angle θ C1 , the space error components generated in the X, Y, and Z directions are represented by , , , as shown in formula (28).

[0080] (28),

[0081] Substitute the displacement amounts x, y, and z of the linear axis into formula (3) to solve the error components caused by the movement of the linear axis, and eliminate the high-order infinitesimal in the calculation process. The calculation result is formula (29).

[0082] (29),

[0083] The perpendicularity error is regarded as a part of the corresponding rotation angle error. The parameter terms related to the perpendicularity are represented by A1, B1, and C1. The calculation result in formula (29) can be simplified to formula (30).

[0084] (30),

[0085] In the process of identifying rotation axis error parameters using a ballbar, the ballbar readings reflect its positioning error information in the sensitive direction. Six different positions are preset on the worktable for placing the ballbar. By collecting data sets of ballbar readings at different points, all error parameters, including six geometric errors, are identified. For example... Figure 12 As shown, at measurement positions 1 and 4, the ballbar is along the Z direction; at measurement positions 2, 5, and 6, the ballbar is along the Y direction. At measurement position 3, the ballbar is along the X direction. Formula (30) can be expressed in matrix form as formula (31).

[0086] (31),

[0087] In the formula This represents the spatial error component of the machine tool in the j direction at measurement position k on axis C1, where j = x, y, z. (x k , y k , z k ) represents the initial coordinates at the measurement location k, k = 1, 2, ..., 6.

[0088] Let P denote the error identification matrix of the C1 axis, as shown in formula (32).

[0089] (32),

[0090] To ensure that the identification matrix can completely identify all geometric error parameters and obtain a unique solution, it is necessary to select appropriate coordinate values ​​to ensure that the error identification P matrix is ​​full rank. Point selection can be referenced in formula (32). Based on the matrix calculation relationship, the geometric error identification equation related to the position of the C1 axis is obtained as shown in formula (33).

[0091] (33),

[0092] At the zero position, the position-related geometric error is 0. When the rotation axis is at the 0 position, the reading of the ball bar is the value of the perpendicularity error, and the perpendicularity error identification equation of the C1 axis is as shown in formula (34).

[0093] (34),

[0094] A ballbar is used to measure a five-axis machine tool. During measurement, the magnetic chuck is fixed at a set position on the C1 axis, and the tool ball on the magnetic chuck contacts the ballbar. The other end of the ballbar contacts the spindle tool cup clamped on the spindle. According to the measurement requirements for each measurement, the linkage path is set to ensure the linkage between the two ends of the ballbar, as shown in formula (33).

[0095] The identification results of the geometric error related to the position of axis C1 are as follows:Figure 13 and Figure 14 The perpendicularity error calculation result ε x1C1 =0.011 / 300, ε yC1 =0.013 / 300.

[0096] The error identification model of the B axis is referenced to the C1 axis method. The position-related geometric error identification result is as follows Figure 13 and Figure 14 The perpendicularity error identification result ε x1B =0.024 / 300, ε Bz1 =0.020 / 300.

[0097] The five-axis machine tool geometric error identification method based on single-axis and multi-axis measurement uses the multi-body system theory to establish a multi-axis motion model, and further proposes a linear axis error identification model and a rotary axis error identification model.

[0098] The beneficial effects of the present application are as follows:

[0099] The linear axis geometric error identification method based on positioning error and straightness error measurement designs a single-axis and two-axis linkage measurement and error identification scheme. According to the measurement results, 18 position-related geometric error parameters and 3 position-independent error parameters related to the linear axis can be calculated. On the basis of the linear axis error identification result, an error identification scheme of a ball bar in three directions and six different positions is designed. Through experimental measurement and calculation, 12 position-related geometric error parameters and 4 position-independent error parameters related to the rotary axis can be identified.

[0100] The above is only one of the specific embodiments of the present application, and the protection scope of the present application is not limited thereto. Any technical transformation or substitution made by a professional in the technical field within the technical scope of the present application should be covered within the inclusive scope of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0101] Figure 1 Topological structure diagram of linear axis motion body.

[0102] Figure 2 Linear axis error measurement route diagram.

[0103] Figure 3 Error identification result diagram along the Z1 axis motion.

[0104] Figure 4 Error identification result diagram along the Y axis motion.

[0105] Figure 5 Error identification result diagram along the X1 axis motion.

[0106] Figure 6 Displacement curve of Pi in XOZ plane.

[0107] Figure 7 X1-Z1 axis linkage error identification result graph.

[0108] Figure 8 Displacement curve of Pi in YOZ plane.

[0109] Figure 9 Y-Z1 axis linkage error identification result graph.

[0110] Figure 10 Displacement curve of Pi in XOY plane.

[0111] Figure 11 X1-Y axis linkage error identification result graph.

[0112] Figure 12 Rotary axis error identification ball bar position distribution graph.

[0113] Figure 13 C1 axis linear deviation identification result graph.

[0114] Figure 14 C1 axis angle deviation identification result graph.

[0115] Figure 15 B axis linear deviation identification result graph.

[0116] Figure 16 B axis angle deviation identification result graph.

[0117] Figure 17 Is the method flowchart of the application. DETAILED DESCRIPTION

[0118] The positioning accuracy and straightness of each motion axis of the measuring machine are comprehensively measured. The measurement route is distributed in the machining space of the machine tool, and the distribution is as shown in Figure 2 .

[0119] When the Z1 axis moves, the displacement amounts L 1zh , L 2zh , L 3zh of the points P1, P2, P3 at three different positions on the tool shaft in the Z axis direction are measured respectively, and three measured displacement equations are obtained, as shown in equation (6).

[0120] (6),

[0121] The measurement point positions are appropriately selected to ensure that the matrix in equation 6 is full rank, and the error parameter expression is as shown in equation (7).

[0122] (7),

[0123] By measuring the actual displacement L 1zh , L 2zh , L 3zh of the points P1, P2, P3, the positioning error δ z (z1 h ), the yaw error ε y (z1 h ) and the pitch error ε x (z1 h ) in the direction of Z1 are obtained. The measurement results are substituted into the calculation at the same time.

[0124] When the Y-axis moves, the displacement L 4yh , L 5yh , L 6yh of the points P4, P5, P6 at three different positions on the tool axis in the direction of Y-axis is measured respectively, and three measured displacement equations are obtained, as shown in equation (9).

[0125] (9),

[0126] The measurement point positions are appropriately selected to ensure that the matrix in equation (9) is full rank, and the error parameter expression is shown in equation (10).

[0127] (10),

[0128] By measuring the actual displacement L 4yh , L 5yh , L 6yh of the points P4, P5, P6, the positioning error δ y (y h ), the yaw error ε z (y h ) and the pitch error ε x (y h ) in the direction of Y are obtained. The measurement results are substituted into the calculation at the same time.

[0129] When the X1-axis moves, the displacement L 7zh , L 8zh , L 9zh of the points P7, P8, P9 at three different positions on the tool axis in the direction of Z-axis is measured respectively, and three measured displacement equations are obtained, as shown in equation (12).

[0130] (12),

[0131] The measurement point positions are appropriately selected to ensure that the matrix in equation (12) is full rank, and the error parameter expression is shown in equation (13).

[0132] (13),

[0133] By measuring the actual displacement L 7zh , L 8zh , L 9zh of P7, P8, P9, the positioning error δ x (x1 h ), the yaw error ε y (x1 h ) and the pitch error ε z (x1 h ) of X1 are obtained. The measurement results are substituted into the calculation at the same time.

[0134] When X1 and Z1 axes are linked, the displacements are x1 h and z1 h respectively, and Y axis is not moved. At this time, there is no position transformation and motion transformation of Y axis, so B

[12] p , B

[23] p , B

[12] s and B

[12] se are unit matrices. The motion displacement L ixh and L izh of the given point P on the tool spindle along the X1 and Z1 axes are as shown in formula (14).

[0135] (14),

[0136] The displacement components of the given point P in three directions cannot be directly measured, and an indirect measurement method needs to be used. Figure 6 L ih and L l ih in formula (15) respectively represent the actual displacement and ideal displacement of Pi, and δ ih represents the straightness error of the motion axis in the XOZ plane. According to the geometric position relationship in the figure, the corresponding position relationship equation is established, as shown in formula (15).

[0137] (15),

[0138] Two points P10 and P11 with different Y coordinates are selected, and the linked displacements of P10 and P11 in the XOZ plane are measured respectively, so that two sets of displacement measurement equations can be constructed. There are four equations in the two sets of displacement measurement equations, which cannot solve five error parameters. First, ε x1z1 is regarded as a known quantity, when the measurement positions of the two sets of displacement measurement are different, i.e. r 10y ≠ r 11y , the expression of the unknown error parameter can be obtained as shown in formula (16).

[0139] (16),

[0140] L 10xh , L 10zh , L 11xh , L 11zh can be obtained from equation (15). And only δ z (x1 h ) related equation contains ε x1z1 . According to the characteristics of linear error of linear axis of CNC machine tools

[36] , equation (17) is added as a supplementary equation to solve the error parameters when X1-Z1 linkage. Where, m represents the number of discrete points.

[0141] (17),

[0142] According to P10, P11 path measurement. The results are substituted into the calculation.

[0143] When Y and Z1 axis linkage, displacement is y h and z1 h , X1 axis does not move. At this time there is no position transformation and motion transformation of X1 axis, so B

[23] p , B

[23] pe , B

[23] s and B

[23] se are unit matrix. The given point P on the tool spindle in the direction of Y axis and Z1 axis movement displacement L iyh and L izh , as shown in equation (18).

[0144] (18),

[0145] The indirect measurement method of given point P in YOZ plane is shown in Figure 8 L ih and L l ih respectively represent the actual displacement and ideal displacement of Pi point, δ ih represents the straightness error of the movement axis in the YOZ plane. According to the geometric position relationship in the figure, the corresponding position relationship equation is established, as shown in equation (19).

[0146] (19),

[0147] As can be seen from equation (18), there are 4 unknown error parameters δ y (z1 h ), δ z (y h ), ε y (y h ),ε yz1The error parameters are only related to the X coordinate r ix Two points P12 and P13 with different X coordinates are selected, and their linkage displacements in the YOZ plane are measured to construct two sets of displacement measurement equations as shown in equation (20).

[0148] (20)

[0149] The first and third equations of the above formulae only contain one unknown parameter, and can be directly solved for δ y (z1 h ). In the second and fourth equations, ε yz1 is regarded as a known quantity, and equation (21) is obtained.

[0150] (21)

[0151] According to equation (21) and equation (22), ε yz1 , δ z (y h ) and ε y (y h ) can be solved. Wherein, m represents the number of discrete points.

[0152] (22)

[0153] According to the measurement of P12 and P13 in Figure 2 , the measurement results are substituted into the calculation.

[0154] When the X1 and Y axes are linked, the displacement is x1 h and y h , and the Z1 axis does not move. At this time, there is no position transformation and motion transformation of the Z1 axis, so B

[12] p , B

[12] pe , B

[12] s and B

[12] se are unit matrices. The movement displacement amount L ixh and L iyh of the given point P on the tool spindle along the X1 axis and the Y axis are shown in equation (23).

[0155] (23)

[0156] The indirect measurement method of the given point P in the XOY plane is shown in Figure 10 , L ih and L l ih分别 represent the actual displacement and ideal displacement of the Pi point, and δ ihThe straightness error of the motion axis in the XOY plane is represented. According to the geometric position relationship in the figure, a corresponding position relationship equation is established, as formula (24).

[0157] (24),

[0158] According to formula (24) and supplementary equation formula (25), δ x (y h ) and δ y (x1 h ) can be solved.

[0159] (25),

[0160] According to the P14 path, the measurement is performed. Meanwhile, the measurement results are substituted into the calculation.

[0161] The ball bar is used to measure the rotating shaft. Taking the C1 shaft as an example, one end of the ball bar is fixed on the C1 shaft, and the other end is fixed on the tool spindle. In order to realize the trajectory requirement in the measurement process, the linkage of the linear shafts is required. Therefore, in the process of identifying the error parameters of the rotating shaft, the coupling problem with the linear shaft error is inevitable. Based on the measurement results, the influence of the linear shaft error on the motion trajectory is eliminated, and then the geometric error of the rotating shaft is accurately calculated.

[0162] In the initial state, the rotation angle of the C1 shaft is zero, and the coordinates of the center of the tool tip in the C1 shaft are [x0 y0 z0]. When the C1 shaft rotates, the coordinates of the tool ball should remain relatively stationary with the C1 shaft. Under ideal conditions, the transformation matrix of the tool relative to the workpiece coordinate system is represented by r w1 , at this time, formula (26) is satisfied. During rotation, the linear shaft needs to have a corresponding feed amount to cooperate with the movement, and the feed amounts x, y and z satisfy the relationship of formula (27).

[0163] (26),

[0164] (27),

[0165] After the C1 shaft rotates by an angle θ C1 , the space error components generated in the X, Y and Z directions are represented by , , , as formula (28).

[0166] (28),

[0167] Substituting the displacements x, y, and z of the linear axis into formula (3) allows us to solve for the error components caused by the linear axis motion and eliminate higher-order infinitesimals during the calculation process. The calculation results are shown in formula (29).

[0168] (29)

[0169] The verticality error is considered as part of the corresponding angle error. The parameters related to verticality are represented by A1, B1, and C1, and the calculation result in formula (29) can be simplified to formula (30).

[0170] (30)

[0171] In the process of identifying rotation axis error parameters using a ballbar, the ballbar readings reflect its positioning error information in the sensitive direction. Six different positions are preset on the worktable for placing the ballbar. By collecting data sets of ballbar readings at different points, all error parameters, including six geometric errors, are identified. For example... Figure 12 As shown, at measurement positions 1 and 4, the ballbar is along the Z direction; at measurement positions 2, 5, and 6, the ballbar is along the Y direction. At measurement position 3, the ballbar is along the X direction. Formula (30) can be expressed in matrix form as formula (31).

[0172] (31),

[0173] In the formula This represents the spatial error component of the machine tool in the j direction at measurement position k on axis C1, where j = x, y, z. (x k , y k , z k ) represents the initial coordinates at the measurement location k, k = 1, 2, ..., 6.

[0174] Let P denote the error identification matrix of the C1 axis, as shown in formula (32).

[0175] (32),

[0176] To ensure that the identification matrix can completely identify all geometric error parameters and obtain a unique solution, it is necessary to select appropriate coordinate values ​​to ensure that the error identification P matrix is ​​full rank. Point selection can be referenced in formula (32). Based on the matrix calculation relationship, the geometric error identification equation related to the position of the C1 axis is obtained as shown in formula (33).

[0177] (33),

[0178] When the zero position, the position related geometric error is 0. When the rotation axis is in the 0 position, the reading of the ball bar is the value of the verticality error, and the verticality error identification equation of the C1 axis is as formula (34).

[0179] (34),

[0180] The ball bar is used to measure the five-axis machine tool. During the measurement, the magnetic seat is fixed at the set position on the C1 axis, and the tool ball on the magnetic seat is in contact with the ball bar. The other end of the ball bar is in contact with the spindle tool cup clamped on the spindle. According to the measurement requirement each time, the linkage path is set respectively to ensure the linkage of the two ends of the ball bar, as shown in formula (33).

[0181] The error identification model of the B axis is referred to the method of the C1 axis.

Claims

1. A method for identifying geometric error of a five-axis machine tool based on single-axis and multi-axis measurement, characterized in that: A multi-axis motion model is established, and a linear axis error identification model and a rotating axis error identification model are proposed, which can identify the distribution of all geometric errors of a five-axis machine tool in three-dimensional space. The method comprises the following detection steps: (1) A multi-body system motion error model of the five-axis machine tool is established, ideal and actual reference coordinate systems of each motion component are defined, ideal position and motion transformation matrices and corresponding position and motion error transformation matrices are established, and a motion constraint equation for error solving is derived; (2) Single-axis measurement is performed on the linear axis: in the Z1, Y, X1 single-axis motion process, three different position measuring points on the tool axis are selected, and the positioning error parameters of each axis are measured; (3) Two-axis linkage measurement is performed: X1-Z1 linkage, at least two measuring lines are selected at different Y coordinates to obtain displacement data, and a constraint equation is introduced to supplement the equation solving; Y-Z1 linkage, at least two measuring lines are selected at different X coordinates, and a supplementary constraint is introduced to identify the Y-Z1 perpendicularity and position-related error parameters; X1-Y linkage, displacement data are obtained along the preset path, and a supplementary constraint is introduced to identify the X-Y perpendicularity and position-related error parameters; (4) Multi-point and multi-direction measurement is performed on the rotating axis, the ball bar is measured at six positions on the workbench, the rotating axis error identification matrix is constructed in the X, Y, Z three directions according to the ball bar measurement results, and the full rank is ensured through point coordinate design; in the rotating axis identification process, the perpendicularity error is introduced into the corresponding rotation angle error term, and the coupling effect of the linear axis error on the trajectory is eliminated.

2. The method according to claim 1, wherein the method is a method for identifying geometric error of a five-axis machine tool based on single-axis and multi-axis measurement. The X1-Z1 linkage measurement constructs multiple displacement equations through two measuring lines at different Y coordinates, and introduces a supplementary constraint based on straightness characteristics, so that the equation set is solvable, thereby jointly solving the X1-Z1 perpendicularity and position-related error parameters; the Y-Z1 linkage measurement constructs multiple displacement equations through two measuring lines at different X coordinates.

3. The method of claim 1, wherein the method is a method of identifying geometric error of a five-axis machine tool based on single-axis and multi-axis measurements. During the rotating axis measurement, the ball bar is arranged at at least six measurement positions, so that sensitive readings are obtained along the Z direction at positions 1 and 4, along the Y direction at positions 2, 5 and 6, and along the X direction at position 3, and an error identification matrix P is constructed accordingly, and the full rank of the matrix is ensured through point coordinate design; in the rotating axis error identification process, the coupling effect of the linear axis error on the ball bar readings is eliminated through path linkage and model substitution.

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