A method for recognizing verticality error of machine tool based on body diagonal

Abstract

The present application belongs to the field of intelligent manufacturing, and specifically relates to a machine tool perpendicularity error identification method based on a body diagonal, which comprises the following steps: defining a body diagonal in a machine tool workspace range, measuring a body diagonal space positioning error based on a laser interferometer; defining a machine tool translational axis perpendicularity error element, constructing a space positioning error model considering the perpendicularity error based on homogeneous coordinate transformation and multi-body system theory; selecting positioning error data of multiple detection points where a specified YZ plane intersects the body diagonal, constructing a perpendicularity error decoupling identification model; and averaging the decoupled perpendicularity errors in different YZ planes to obtain a global average perpendicularity error for machine tool compensation. The present application makes full use of the measurement data of the body diagonal, can not only evaluate the machine tool space accuracy, but also be used for machine tool perpendicularity error identification, and has higher identification accuracy based on the least square method and three-axis linkage measurement data.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing, specifically a method for identifying machine tool perpendicularity error based on body diagonal. Background Technology

[0002] Currently, the main methods for obtaining machine tool perpendicularity error include direct measurement and error decoupling. Direct measurement using a ruler has low accuracy and is insufficient to meet the high-precision machining requirements of machine tools. Error decoupling involves using instruments such as laser interferometers, combined with measurements along a specific path, followed by decoupling. Patent ZL202010746312.2 proposes a method to construct a perpendicularity error identification equation based on the positioning accuracy of two-axis linkage trajectories with different combinations. This method utilizes the displacement errors of multiple measuring points on the two-axis linkage trajectory. However, compared to the accuracy of a three-axis linkage trajectory along the diagonal of a spatial body, the positioning error data of two-axis linkage is insufficient, resulting in inaccurate identification of the perpendicularity error. Ren Yongqiang et al. (Ren Yongqiang, Yang Jianguo, Shen Jinhua et al. Efficient measurement and analysis of machine tool perpendicularity error based on body diagonal[J]. China Mechanical Engineering, 2005, 16(6): 1435-1438) proposed a method for solving the perpendicularity error of a three-axis machine tool by measuring the displacement error of four body diagonals using a laser Doppler displacement measuring instrument. This method only uses the displacement error of the first and last measuring points to participate in the calculation, and its accuracy is easily affected by the data quality.

[0003] For example, Chinese Patent Publication No. CN108115466A, entitled "A Method and System for Detecting Geometric Motion Errors in a Vertical Machining Center," uses a distributed diagonal method to obtain measurement errors on the PPP, NPP, and PNP body diagonals. The actual route involves movement along the X / Y / Z directional components of the body diagonal, thus expanding to nine motion trajectories to reduce the use of the NPP body diagonal. Furthermore, it directly performs least-squares calculations on 18 geometric errors, which is less accurate than identifying perpendicularity errors separately. Chinese Patent Publication No. CN109732402A, entitled "A Method for Measuring and Identifying Spatial Geometric Errors of Multi-line Machine Tools Based on Laser Interferometers," uses 19 detection trajectories to sequentially identify 21 geometric errors in a three-axis machine tool. While its identification accuracy is high, it does not consider the significant impact of perpendicularity errors on machine tool accuracy. Compared to calculating perpendicularity errors using four trajectories, its measurement process is time-consuming and unsuitable for evaluation and identification. Summary of the Invention

[0004] To overcome the limitations of existing technologies, this invention proposes a machine tool perpendicularity error identification method based on the characteristics of the machine tool's spatial diagonal and a kinematic model of perpendicularity error. This method achieves accurate calculation of the perpendicularity error of the machine tool's translational axis and demonstrates good implementation results.

[0005] To achieve the above-mentioned objectives, the technical solution provided in this application is as follows:

[0006] A method for identifying machine tool perpendicularity error based on body diagonal includes the following steps:

[0007] Step S1: Define the body diagonal within the machine tool's workspace and measure the spatial positioning error of the body diagonal based on a laser interferometer;

[0008] Step S2: Define the perpendicularity error elements of the machine tool translation axis, and construct a spatial positioning error model that considers perpendicularity error based on homogeneous coordinate transformation and multibody system theory;

[0009] Step S3: Combining steps S1 and S2, select the positioning error data of multiple detection points where the specified YZ plane intersects with the body diagonal, and construct a verticality error decoupling identification model.

[0010] Step S4: Calculate the average perpendicularity error of the decoupled planes in different YZ planes to obtain the global average perpendicularity error for machine tool compensation.

[0011] Further, step S1 specifically includes:

[0012] S1.1: Based on the working range required for machine tool processing, determine the detection space cube (0,0,0) to (x,y,z), where (0,0,0) is the starting point of the detection space cube, and establish a measurement coordinate system at this point, with the coordinate axis direction consistent with the machine tool coordinate axis direction. (x,y,z) is the farthest point of the detection space cube in the measurement coordinate system, and also represents the X, Y, and Z coordinate values ​​of the farthest point in the measurement coordinate system.

[0013] S1.2: The four diagonals of the spatial cube are denoted as PPP, NPP, PNP, and NNP, respectively. PPP represents the detection trajectory moving along the positive directions of the X, Y, and Z axes; NPP represents the detection trajectory moving along the negative X-axis and the positive Y and Z axes; PNP represents the detection trajectory moving along the positive X-axis, negative Y-axis, and positive Z-axis; and NNP represents the detection trajectory moving along the negative X-axis, negative Y-axis, and positive Z-axis. The starting points of all four volume diagonals are located in the z=0 plane, and each volume diagonal segment is divided into N detection points at equal intervals. To ensure the accuracy of subsequent calculations, according to ISO 230-6, N > 5 points / meter and being an even number is more suitable.

[0014] S1.3: Using a laser interferometer, measure the positioning error of the detection point along each diagonal. For each body diagonal segment, repeat the measurement twice, and take the average of the two measurements as the measurement positioning error value of the current point, denoted as Δl. ij , i∈[PPP, NPP, PNP, NNP], represents the measurement and positioning error value of the j-th detection point on one of the body diagonals of PPP, NPP, PNP, NNP; j=1,2,···,N, represents the j-th detection point on the body diagonal, counted from the starting point.

[0015] Furthermore, the specific steps in step S2 for constructing a spatial positioning error model that considers verticality error are as follows:

[0016] S2.1: Taking a bridge-type gantry machining center as an example, according to the ISO definition, S XY S XZ S YZ This refers to the perpendicularity error between the XY, XZ, and YZ coordinate axes of the machine tool.

[0017] S2.2: Based on its topological structure and the principle of homogeneous coordinate transformation, the theoretical spatial kinematic model is obtained as follows:

[0018] P ideal =trans(X,Y,Z)·P t

[0019] In the formula, P ideal P represents the ideal coordinates of the end-effector tip in the machine tool coordinate system, trans(X,Y,Z) represents the translation matrix of the X, Y, and Z translation axes of the CNC machine tool, and P represents the translation matrix of the end-effector tip in the machine tool coordinate system. t This represents the initial coordinates of the blade tip.

[0020] When considering the perpendicularity error between the translational axes of a bridge-type gantry machining center, the kinematic model of the actual spatial position of the tool tip can be expressed as:

[0021]

[0022] In the formula, P actual This represents the actual coordinates of the end-effector tip in the machine tool coordinate system. Translation matrices representing the error-inducing motion of the X, Y, and Z translation axes of a CNC machine tool;

[0023] S2.3: Spatial positioning error P of the tool tip under the action of perpendicularity error error This can be expressed as:

[0024]

[0025] In the formula, Δx, Δy, and Δz represent the error values ​​of the tool tip in the X, Y, and Z directions of the machine tool coordinate system, respectively; L represents the sum of the machine tool rotation distance and the tool length; and y m This represents the Y-coordinate value of the tool tip in the measurement coordinate system, z. m This represents the Z-axis coordinate of the tool tip in the measurement coordinate system.

[0026] Further, step S3 specifically includes:

[0027] S3.1: Establish the mathematical relationship between the spatial positioning error of the blade tip and the measurement positioning error of the detection point on the body diagonal;

[0028] 1) Since the selected diagonals are all spatial volumes, the measurement direction vectors of the diagonals PPP, NPP, PNP, and NNP in the measurement coordinate system are as follows:

[0029] V PPP =[i V ,j V ,k V ]、V NPP =[-i V ,j V ,k V ]、V PNP =[i V ,-j V ,k V ]、V NNP =[-i V ,-j V ,k V ]

[0030] In the formula x represents the length of the body diagonal in the X direction, y represents the length of the body diagonal in the Y direction, z represents the length of the body diagonal in the Z direction, and D represents the total length of the body diagonal;

[0031] 2) The spatial positioning error of the tool tip is along the three directions in the machine tool coordinate system, and the measurement positioning error of the body diagonal is along the vector direction of the diagonal. The spatial positioning error can be converted into the measurement positioning error:

[0032] Δl ij =P error ·V i

[0033] In the formula, i∈[PPP, NPP, PNP, NNP], j=1,2,···,N,V i It represents one of the measurement direction vectors belonging to the body diagonal PPP, NPP, PNP, and NNP, and j represents the j-th detection point on the body diagonal, counting from the starting point.

[0034] S3.2: 1) In the measurement coordinate system, with the j-th detection point P on the body diagonal PPP, j (x j ,y j ,z j Using ) as a reference, the X-axis coordinate value is defined as x. j The YZ plane will intersect the other three body diagonals at three points. Since the body diagonal segments in step S1.2 have been divided into N equally spaced detection points, the intersections of the YZ plane with the four body diagonals are actually the pre-defined detection points. Therefore:

[0035] The coordinates of the intersection point of the YZ plane and the body diagonal PPP are (x j ,y j ,z j );

[0036] The coordinates of the intersection point of the YZ plane and the body diagonal NPP are (x j ,y N-j+1 ,z N-j+1 );

[0037] The coordinates of the intersection point of the YZ plane and the body diagonal PNP are (x j ,y N-j+1 ,z j );

[0038] The coordinates of the intersection point of the YZ plane and the body diagonal NNP are (x j ,y j ,z N-j+1 );

[0039] The coordinates of the four intersection points in the formula are based on the X, Y, and Z coordinates of the detection points on the diagonal of the reference body. That is, if the y-coordinate value of any intersection point is equal to the y-coordinate value of the intersection point on the diagonal of the PPP, then the coordinates of the four intersection points are equal to the X, Y, and Z coordinates of the detection points on the diagonal of the PPP. j When they are unequal, according to the definition of the four body diagonals, then they are related to y. N-j+1 The coordinate values ​​are equal; if the z-coordinate value of any intersection point is equal to the z-coordinate value of the intersection point on the diagonal of PPP, then... j When they are unequal, according to the definition of four body diagonals, then with z N-j+1 The coordinate values ​​are equal; the subscript N-j+1 refers to the Y-axis or Z-axis coordinate value of the N-j+1th detection point on the diagonal PPP of the reference body.

[0040] 2) Based on the measurement and positioning error transformation model and the body diagonal measurement direction vector from step S3.1, the computer tool detects the measurement and positioning errors of the four body diagonals in the detection space:

[0041] ①The expression for the measurement and positioning error of the diagonal of the PPP body is as follows:

[0042] Δl ppp =P error·V ppp =Δx·i V +Δy·j V +Δz·k V

[0043] Substituting the intersection of the YZ plane and the diagonal of the PPP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0044] Δl PPP,j =(L+z) PPP,j )S XZ,j ·i V -y PPP,j S XY,j ·i V +(Lz PPP,j )S YZ,j ·j V

[0045] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PPP,j z PPP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PPP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0046] ②The expression for the measurement and positioning error of the NPP body diagonal is as follows:

[0047] Δl npp =P error ·V npp =-Δx·i V +Δy·j V +Δz·k V

[0048] Substituting the intersection of the YZ plane and the diagonal of the NPP body as the N-j+1th detection point on the diagonal of the body, the measurement positioning error is:

[0049] Δl NPP,N-j+1 =-(L+z NPP,N-j+1 )S XZ,j ·i V +y NPP,N-j+1 S XY,j ·i V +(Lz NPP,N-j+1 )S YZ,j ·j V

[0050] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NPP,N-j+1 z NPP,N-j+1S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NPP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0051] ③The expression for the measurement and positioning error of the PNP body diagonal is as follows:

[0052] Δl pnp =P error ·V pnp =Δx·i V -Δy·j V +Δz·k V

[0053] Substituting the intersection of the YZ plane and the diagonal of the PNP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0054] Δl PNP,j =(L+z) PNP,j )S XZ,j ·i V -y PNP,j S XY,j ·i V -(Lz PNP,j )S YZ,j ·j V

[0055] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PNP,j z PNP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0056] ④The expression for the measurement and positioning error of the NNP body diagonal is as follows:

[0057] Δl nnp =P error ·V nnp =-Δx·i V -Δy·j V +Δz·k V

[0058] Substituting the intersection of the YZ plane and the diagonal of the NNP body into the value of the (N-j+1)th detection point on the diagonal of the body, the measurement positioning error is:

[0059] Δl NNP,N-j+1 =-(L+z NNP,N-j+1 )SXZ,j ·i V +y NNP,N-j+1 S XY,j ·i V -(Lz NNP,N-j+1 )S YZ,j ·j V

[0060] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NNP,N-j+1 z NNP,N-j+1 S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0061] 3) The measurement and positioning errors of the four body diagonals are summarized as follows:

[0062]

[0063] The above equation can be rewritten in matrix form:

[0064] A j ·T j =B j

[0065] in:

[0066]

[0067]

[0068]

[0069] Substituting the intersection coordinates obtained in step 1) into the matrix, the least squares solution of the system of equations is:

[0070] T j =(A j T A j ) -1 (A j T B j )

[0071] Vector T j It contains all elements of the machine tool verticality error, and at this point, the verticality error at the j-th detection point has been decoupled.

[0072] Furthermore, the calculation formula for step S4 is as follows:

[0073]

[0074] In the formula, Γ XY ,Γ XZ ,Γ YZ This refers to the global average verticality error.

[0075] The beneficial effects of this invention are as follows:

[0076] 1. This invention makes full use of the measurement data of the body diagonal, which can not only evaluate the spatial accuracy of the machine tool, but also be used to identify the perpendicularity error of the machine tool. At the same time, this invention is based on the measurement data of the least squares method and three-axis linkage, which has higher identification accuracy.

[0077] 2. The present invention is more practical. It can quickly obtain the three perpendicularity errors of CNC machine tools using only a laser interferometer, which makes up for the limitations of traditional local measurement with a square ruler. It can be used for machine tool assembly and debugging and machine tool error compensation. Attached Figure Description

[0078] Figure 1 This is the overall flowchart of the present invention.

[0079] Figure 2 This is a schematic diagram of a bridge-type gantry CNC machine tool.

[0080] Figure 3 This is a schematic diagram of the verticality error of a bridge-type gantry CNC machine tool.

[0081] Figure 4 This is a schematic diagram of the detection directions of the four body diagonals of the machine tool workspace involved in the present invention.

[0082] Figure 5 This is a schematic diagram showing the equally spaced detection points along the four body diagonals in this invention.

[0083] Figure 6 This is a schematic diagram of the intersection point of the YZ plane and the volume diagonal selected in this invention.

[0084] Figure 7 This represents the average measurement and positioning error value of the detection points in Example 3.

[0085] Figure 8 The verticality error values ​​are for the 10 detection points in Example 3.

[0086] Figure 9 This refers to the global average verticality error data used for machine tool compensation in Example 3. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are for explaining the invention and not for limiting it. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0088] The specific implementation method of the present invention will be described below with reference to the accompanying drawings and examples. The present invention is not limited to this embodiment.

[0089] Example 1

[0090] like Figure 1 As shown, a machine tool perpendicularity error identification method based on body diagonal includes the following steps:

[0091] Step S1: Define the body diagonal within the machine tool's workspace and measure the spatial positioning error of the body diagonal based on a laser interferometer;

[0092] Step S2: Define the perpendicularity error elements of the machine tool translation axis, and construct a spatial positioning error model that considers perpendicularity error based on homogeneous coordinate transformation and multibody system theory;

[0093] Step S3: Combining steps S1 and S2, select the positioning error data of multiple detection points where the specified YZ plane intersects with the body diagonal, and construct a verticality error decoupling identification model.

[0094] Step S4: Calculate the average perpendicularity error of the decoupled planes in different YZ planes to obtain the global average perpendicularity error for machine tool compensation.

[0095] This invention fully utilizes the measurement data of the body diagonal, which can not only evaluate the spatial accuracy of machine tools but also be used to identify machine tool perpendicularity errors. Furthermore, based on the least squares method and three-axis linkage measurement data, this invention achieves higher identification accuracy. This invention is more practical, requiring only a laser interferometer to quickly obtain the three perpendicularity errors of CNC machine tools, overcoming the limitations of traditional local measurements using a square ruler. It can be used for machine tool assembly and debugging, as well as machine tool error compensation.

[0096] Example 2

[0097] like Figure 1 As shown, a machine tool perpendicularity error identification method based on body diagonal includes the following steps:

[0098] Step S1: Define the body diagonal within the machine tool's workspace and measure the spatial positioning error of the body diagonal based on a laser interferometer;

[0099] Step S2: Define the perpendicularity error elements of the machine tool translation axis, and construct a spatial positioning error model that considers perpendicularity error based on homogeneous coordinate transformation and multibody system theory;

[0100] Step S3: Combining steps S1 and S2, select the positioning error data of multiple detection points where the specified YZ plane intersects with the body diagonal, and construct a verticality error decoupling identification model.

[0101] Step S4: Calculate the average perpendicularity error of the decoupled planes in different YZ planes to obtain the global average perpendicularity error for machine tool compensation.

[0102] Step S1 is as follows:

[0103] S1.1: Based on the working range required for machine tool processing, determine the detection space cube (0,0,0) to (x,y,z), where (0,0,0) is the starting point of the detection space cube, and establish a measurement coordinate system at this point, with the coordinate axis direction consistent with the machine tool coordinate axis direction. (x,y,z) is the farthest point of the detection space cube in the measurement coordinate system, and also represents the X, Y, and Z coordinate values ​​of the farthest point in the measurement coordinate system.

[0104] S1.2: The four diagonals of the spatial cube are denoted as PPP, NPP, PNP, and NNP, respectively. PPP represents the detection trajectory moving along the positive directions of the X, Y, and Z axes; NPP represents the detection trajectory moving along the negative X-axis and the positive Y and Z axes; PNP represents the detection trajectory moving along the positive X-axis, negative Y-axis, and positive Z-axis; and NNP represents the detection trajectory moving along the negative X-axis, negative Y-axis, and positive Z-axis. The starting points of all four volume diagonals are located in the z=0 plane, and each volume diagonal segment is divided into N detection points at equal intervals. To ensure the accuracy of subsequent calculations, according to ISO 230-6, N > 5 points / meter and being an even number is more suitable.

[0105] S1.3: Using a laser interferometer, measure the positioning error of the detection point along each diagonal. For each body diagonal segment, repeat the measurement twice, and take the average of the two measurements as the measurement positioning error value of the current point, denoted as Δl. ij , i∈[PPP, NPP, PNP, NNP], represents the measurement and positioning error value of the j-th detection point on one of the body diagonals of PPP, NPP, PNP, NNP; j=1,2,···,N, represents the j-th detection point on the body diagonal, counted from the starting point.

[0106] The specific steps in step S2 for constructing a spatial positioning error model that considers verticality error are as follows:

[0107] S2.1: Taking a bridge-type gantry machining center as an example, according to the ISO definition, S XY S XZ S YZ This refers to the perpendicularity error between the XY, XZ, and YZ coordinate axes of the machine tool.

[0108] S2.2: Based on its topological structure and the principle of homogeneous coordinate transformation, the theoretical spatial kinematic model is obtained as follows:

[0109] P ideal =trans(X,Y,Z)·P t

[0110] In the formula, P ideal P represents the ideal coordinates of the end-effector tip in the machine tool coordinate system, trans(X,Y,Z) represents the translation matrix of the X, Y, and Z translation axes of the CNC machine tool, and P represents the translation matrix of the end-effector tip in the machine tool coordinate system. t This represents the initial coordinates of the blade tip.

[0111] When considering the perpendicularity error between the translational axes of a bridge-type gantry machining center, the kinematic model of the actual spatial position of the tool tip can be expressed as:

[0112]

[0113] In the formula, P actual This represents the actual coordinates of the end-effector tip in the machine tool coordinate system. Translation matrices representing the error-inducing motion of the X, Y, and Z translation axes of a CNC machine tool;

[0114] S2.3: Spatial positioning error P of the tool tip under the action of perpendicularity error error This can be expressed as:

[0115]

[0116] In the formula, Δx, Δy, and Δz represent the error values ​​of the tool tip in the X, Y, and Z directions of the machine tool coordinate system, respectively; L represents the sum of the machine tool rotation distance and the tool length; and y m This represents the Y-coordinate value of the tool tip in the measurement coordinate system, z. m This represents the Z-axis coordinate of the tool tip in the measurement coordinate system.

[0117] Step S3 is as follows:

[0118] S3.1: Establish the mathematical relationship between the spatial positioning error of the blade tip and the measurement positioning error of the detection point on the body diagonal;

[0119] 1) Since the selected diagonals are all spatial volumes, the measurement direction vectors of the diagonals PPP, NPP, PNP, and NNP in the measurement coordinate system are as follows:

[0120] V PPP =[i V ,j V ,k V ]、V NPP =[-i V ,j V ,k V ]、V PNP =[i V ,-j V ,k V ]、V NNP =[-i V ,-j V ,k V ]

[0121] In the formula x represents the length of the body diagonal in the X direction, y represents the length of the body diagonal in the Y direction, z represents the length of the body diagonal in the Z direction, and D represents the total length of the body diagonal;

[0122] 2) The spatial positioning error of the tool tip is along the three directions in the machine tool coordinate system, and the measurement positioning error of the body diagonal is along the vector direction of the diagonal. The spatial positioning error can be converted into the measurement positioning error:

[0123] Δl ij =P error ·V i

[0124] In the formula, i∈[PPP, NPP, PNP, NNP], j=1,2,···,N,V i It represents one of the measurement direction vectors belonging to the body diagonal PPP, NPP, PNP, and NNP, and j represents the j-th detection point on the body diagonal, counting from the starting point.

[0125] S3.2: 1) In the measurement coordinate system, with the j-th detection point P on the body diagonal PPP, j (x j ,y j ,z j Using ) as a reference, the X-axis coordinate value is defined as x. j The YZ plane will intersect the other three body diagonals at three points. Since the body diagonal segments in step S1.2 have been divided into N equally spaced detection points, the intersections of the YZ plane with the four body diagonals are actually the pre-defined detection points. Therefore:

[0126] The coordinates of the intersection point of the YZ plane and the body diagonal PPP are (x j ,y j ,z j );

[0127] The coordinates of the intersection point of the YZ plane and the body diagonal NPP are (x j ,y N-j+1 ,z N-j+1 );

[0128] The coordinates of the intersection point of the YZ plane and the body diagonal PNP are (x j ,y N-j+1 ,z j );

[0129] The coordinates of the intersection point of the YZ plane and the body diagonal NNP are (x j ,y j ,z N-j+1 );

[0130] The coordinates of the four intersection points in the formula are based on the X, Y, and Z coordinates of the detection points on the diagonal of the reference body. That is, if the y-coordinate value of any intersection point is equal to the y-coordinate value of the intersection point on the diagonal of the PPP, then the coordinates of the four intersection points are equal to the X, Y, and Z coordinates of the detection points on the diagonal of the PPP. j When they are unequal, according to the definition of the four body diagonals, then they are related to y. N-j+1 The coordinate values ​​are equal; if the z-coordinate value of any intersection point is equal to the z-coordinate value of the intersection point on the diagonal of PPP, then... j When they are unequal, according to the definition of four body diagonals, then with z N-j+1 The coordinate values ​​are equal; the subscript N-j+1 refers to the Y-axis or Z-axis coordinate value of the N-j+1th detection point on the diagonal PPP of the reference body.

[0131] 2) Based on the measurement and positioning error transformation model and the body diagonal measurement direction vector from step S3.1, the computer tool detects the measurement and positioning errors of the four body diagonals in the detection space:

[0132] ①The expression for the measurement and positioning error of the diagonal of the PPP body is as follows:

[0133] Δl ppp =P error ·V ppp =Δx·i V +Δy·j V +Δz·k V

[0134] Substituting the intersection of the YZ plane and the diagonal of the PPP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0135] Δl PPP,j =(L+z) PPP,j )S XZ,j ·i V -y PPP,j S XY,j ·i V +(Lz PPP,j )S YZ,j ·jV

[0136] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PPP,j z PPP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PPP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0137] ②The expression for the measurement and positioning error of the NPP body diagonal is as follows:

[0138] Δl npp =P error ·V npp =-Δx·i V +Δy·j V +Δz·k V

[0139] Substituting the intersection of the YZ plane and the diagonal of the NPP body as the N-j+1th detection point on the diagonal of the body, the measurement positioning error is:

[0140] Δl NPP,N-j+1 =-(L+z NPP,N-j+1 )S XZ,j ·i V +y NPP,N-j+1 S XY,j ·i V +(Lz NPP,N-j+1 )S YZ,j ·j V

[0141] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NPP,N-j+1 z NPP,N-j+1 S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NPP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0142] ③The expression for the measurement and positioning error of the PNP body diagonal is as follows:

[0143] Δl pnp =P error ·V pnp =Δx·i V -Δy·j V +Δz·k V

[0144] Substituting the intersection of the YZ plane and the diagonal of the PNP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0145] Δl PNP,j =(L+z) PNP,j )S XZ,j ·i V -y PNP,j S XY,j ·i V -(Lz PNP,j )S YZ,j ·j V

[0146] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PNP,j z PNP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0147] ④The expression for the measurement and positioning error of the NNP body diagonal is as follows:

[0148] Δl nnp =P error ·V nnp =-Δx·i V -Δy·j V +Δz·k V

[0149] Substituting the intersection of the YZ plane and the diagonal of the NNP body into the value of the (N-j+1)th detection point on the diagonal of the body, the measurement positioning error is:

[0150] Δl NNP,N-j+1 =-(L+z NNP,N-j+1 )S XZ,j ·i V +y NNP,N-j+1 S XY,j ·i V -(Lz NNP,N-j+1 )S YZ,j ·j V

[0151] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NNP,N-j+1 z NNP,N-j+1 S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0152] 3) The measurement and positioning errors of the four body diagonals are summarized as follows:

[0153]

[0154] The above equation can be rewritten in matrix form:

[0155] A j ·T j =B j

[0156] in:

[0157]

[0158]

[0159]

[0160] Substituting the intersection coordinates obtained in step 1) into the matrix, the least squares solution of the system of equations is:

[0161] T j =(A j T A j ) -1 (A j T B j )

[0162] Vector T j It contains all elements of the machine tool verticality error, and at this point, the verticality error at the j-th detection point has been decoupled.

[0163] The calculation formula for step S4 is:

[0164]

[0165] In the formula, Γ XY ,Γ XZ ,Γ YZ This refers to the global average verticality error.

[0166] Example 3

[0167] Based on Examples 1 and 2, such as Figure 1 The flowchart shown is for identifying machine tool perpendicularity error according to this patent. Based on the flowchart, the specific implementation of this invention is as follows:

[0168] Step S1: Define the body diagonal within the machine tool's workspace, and measure the spatial positioning error of the body diagonal using a laser interferometer. The specific implementation steps are as follows:

[0169] S1.1: As Figure 2 The diagram shows a typical bridge-type gantry CNC machine tool. Based on the working range required for machining by this machine tool, the detection space cube is defined as (0,0,0) to (x,y,z), where (0,0,0) is the starting point of the detection space cube, and a measurement coordinate system is established at this point. The coordinate axes are aligned with the machine tool coordinate axes, and (x,y,z) is the farthest point of the detection space cube in the measurement coordinate system.

[0170] S1.2: The four diagonals of the detection space cube are denoted as PPP, NPP, PNP, and NNP, respectively. Figure 4 As shown, the starting points of the four diagonals are all located in the z=0 plane. PPP represents the detection trajectory moving along the positive directions of the X, Y, and Z axes; NPP represents the detection trajectory moving along the negative X-axis and the positive Y and Z axes; PNP represents the detection trajectory moving along the positive X-axis, negative Y-axis, and positive Z-axis; and NNP represents the detection trajectory moving along the negative X-axis, negative Y-axis, and positive Z-axis. The diagonal segments are divided into N detection points at equal intervals. To ensure the accuracy of subsequent calculations, according to ISO 230-6 recommendations, N > 5 points / meter and being an even number is more suitable. Figure 5 As shown, taking NPP as an example, the starting point is a and the ending point is b. The two points are divided into 5 segments with equal intervals, for a total of 6 detection points.

[0171] S1.3: Use a laser interferometer to measure the positioning error of the detection point along each diagonal. Repeat the measurement twice for each body diagonal segment, and take the average of the two measurements as the measurement positioning error value of the current point, denoted as Δl. ij , i∈[PPP, NPP, PNP, NNP], j=1,2,···,N.

[0172] Spatial error assessment is performed on all measured positioning error values, and assessment thresholds are set, which can be comprehensively set according to the processing objects and processing methods involved by the machine tool. Machine tool error identification and compensation are only considered when the assessment fails.

[0173] Step S2: Define the perpendicularity error elements of the machine tool translation axis, and construct a spatial positioning error model considering perpendicularity error based on homogeneous coordinate transformation and multibody system theory. The specific implementation steps are as follows:

[0174] S2.1: Taking a bridge-type gantry machining center as an example, as follows... Figure 3 As shown, S XY S XZ S YZ This refers to the perpendicularity error between the XY, XZ, and YZ coordinate axes of the machine tool.

[0175] S2.2: Based on its topological structure and the principle of homogeneous coordinate transformation, the theoretical spatial kinematic model is obtained as follows:

[0176] P ideal =trans(X,Y,Z)·P t

[0177] In the formula, P ideal This represents the ideal coordinates of the end-effector tip in the machine tool coordinate system.

[0178] The translation matrix representing the X, Y, and Z translational coordinate axes of the machine tool;

[0179] P t =[0,0,-L,1] represents the initial coordinates of the blade tip.

[0180] When considering the perpendicularity error between the translational axes of a bridge-type gantry machining center, the kinematic model of the actual spatial position of the tool tip can be expressed as:

[0181]

[0182] In the formula, P actual This indicates the actual coordinates of the end-effector tip in the machine tool coordinate system;

[0183]

[0184] This represents the translation matrix of the X, Y, and Z translation axes of a CNC machine tool, including the motion with errors.

[0185] S2.3: Spatial positioning error P of the tool tip under the action of perpendicularity error error This can be expressed as:

[0186]

[0187] In the formula, Δx, Δy, and Δz represent the error values ​​of the tool tip in the X, Y, and Z directions of the machine tool coordinate system, respectively; L represents the sum of the machine tool rotation distance and the tool length; and y m This represents the Y-coordinate value of the tool tip in the measurement coordinate system, z. m This represents the Z-axis coordinate of the tool tip in the measurement coordinate system.

[0188] Step S3: Combining steps S1 and S2, select the positioning error data of multiple detection points where the specified YZ plane intersects with the body diagonal, and construct a verticality error decoupling identification model. The specific implementation steps are as follows:

[0189] S3.1: Establish the mathematical relationship between the spatial positioning error of the blade tip and the measurement positioning error of the detection point on the body diagonal.

[0190] 1) Since the selected diagonals are all spatial volumes, the measurement direction vectors of the diagonals PPP, NPP, PNP, and NNP in the measurement coordinate system are as follows:

[0191] V PPP =[i V ,j V ,k V ]、V NPP =[-i V ,j V ,k V ]、V PNP =[i V ,-j V ,k V ]、V NNP =[-i V ,-j V ,k V ]

[0192] In the formula x represents the length of the body diagonal in the X direction, y represents the length of the body diagonal in the Y direction, z represents the length of the body diagonal in the Z direction, and D represents the total length of the body diagonal.

[0193] 2) The spatial positioning error of the tool tip is in three directions along the machine tool coordinate system, while the measurement positioning error of the body diagonal is in the vector direction along the diagonal. The spatial positioning error can be converted into the measurement positioning error:

[0194] Δl ij =P error ·V i

[0195] In the formula, i∈[PPP, NPP, PNP, NNP], j=1,2,···,N,V i It represents one of the measurement direction vectors belonging to the body diagonal PPP, NPP, PNP, and NNP, and j represents the j-th detection point on the body diagonal, counting from the starting point.

[0196] S3.2: Since there are three machine tool verticality error parameters, at least three detection points at different measurement heights are needed to construct the identification equation. Therefore, four detection points are selected in the space cube to construct the equation system. The selected scheme is as follows:

[0197] 1) such as Figure 6 As shown, in the measurement coordinate system, a certain detection point P along the body diagonal PPP is... j (x j ,y j ,z j Using ) as a reference, select the X-axis coordinate value as x jThe YZ plane will intersect the other three body diagonals at three points: point 2 is the intersection of the YZ plane and the body diagonal NNP, point 3 is the intersection of the YZ plane and the body diagonal PNP, and point 4 is the intersection of the YZ plane and the body diagonal NPP.

[0198] Since the body diagonal segments in step S1.2 have been divided into N detection points at equal intervals, the intersections of the YZ plane with the four body diagonals are actually the pre-divided detection points. Therefore:

[0199] Appendix Figure 6 The coordinates of the intersection point 1 are (x j ,y j ,z j );

[0200] Appendix Figure 6 The coordinates of the intersection point 4 are (x j ,y N-j+1 ,z N-j+1 );

[0201] Appendix Figure 6 The coordinates of the intersection point 3 are (x j ,y N-j+1 ,z j );

[0202] Appendix Figure 6 The coordinates of the intersection point 2 are (x j ,y j ,z N-j+1 );

[0203] The coordinates of the four intersection points in the formula are based on the X, Y, and Z coordinates of the detection points on the diagonal of the reference body. That is, if the y-coordinate value of any intersection point is equal to the y-coordinate value of the intersection point on the diagonal of the PPP, then the coordinates of the four intersection points are equal to the X, Y, and Z coordinates of the detection points on the diagonal of the PPP. j When they are unequal, according to the definition of the four body diagonals, then they are related to y. N-j+1 The coordinate values ​​are equal; if the z-coordinate value of any intersection point is equal to the z-coordinate value of the intersection point on the diagonal of PPP, then... j When they are unequal, according to the definition of four body diagonals, then with z N-j+1 The coordinate values ​​are equal; the subscript N-j+1 refers to the Y-axis or Z-axis coordinate value of the N-j+1th detection point on the diagonal PPP of the reference body.

[0204] 2) Based on the measurement and positioning error transformation model and the body diagonal measurement direction vector from step S3.1, the computer tool detects the measurement and positioning errors of the four body diagonals in the detection space:

[0205] ①The expression for the measurement and positioning error of the diagonal of the PPP body is as follows:

[0206] Δl ppp =P error ·V ppp=Δx·i V +Δy·j V +Δz·k V

[0207] Substituting the intersection of the YZ plane and the diagonal of the PPP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0208] Δl PPP,j =(L+z) PPP,j )S XZ,j ·i V -y PPP,j S XY,j ·i V +(Lz PPP,j )S YZ,j ·j V

[0209] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PPP,j z PPP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PPP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0210] ②The expression for the measurement and positioning error of the NPP body diagonal is as follows:

[0211] Δl npp =P error ·V npp =-Δx·i V +Δy·j V +Δz·k V

[0212] Substituting the intersection of the YZ plane and the diagonal of the NPP body as the N-j+1th detection point on the diagonal of the body, the measurement positioning error is:

[0213] Δl NPP,N-j+1 =-(L+z NPP,N-j+1 )S XZ,j ·i V +y NPP,N-j+1 S XY,j ·i V +(Lz NPP,N-j+1 )S YZ,j ·j V

[0214] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NPP,N-j+1 z NPP,N-j+1 S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NPP body, respectively.XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0215] ③The expression for the measurement and positioning error of the PNP body diagonal is as follows:

[0216] Δl pnp =P error ·V pnp =Δx·i V -Δy·j V +Δz·k V

[0217] Substituting the intersection of the YZ plane and the diagonal of the PNP body as the j-th detection point on the diagonal of the body, the measurement positioning error is:

[0218] Δl PNP,j =(L+z) PNP,j )S XZ,j ·i V -y PNP,j S XY,j ·i V -(Lz PNP,j )S YZ,j ·j V

[0219] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y PNP,j z PNP,j S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonals of the PNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0220] ④The expression for the measurement and positioning error of the NNP body diagonal is as follows:

[0221] Δl nnp =P error ·V nnp =-Δx·i V -Δy·j V +Δz·k V

[0222] Substituting the intersection of the YZ plane and the diagonal of the NNP body into the value of the (N-j+1)th detection point on the diagonal of the body, the measurement positioning error is:

[0223] Δl NNP,N-j+1 =-(L+z NNP,N-j+1 )S XZ,j ·i V +yNNP,N-j+1 S XY,j ·i V -(Lz NNP,N-j+1 )S YZ,j ·j V

[0224] In the formula, L represents the sum of the machine tool rotary distance and the tool length, y NNP,N-j+1 z NNP,N-j+1 S represents the Y-coordinate and Z-coordinate of the intersection point on the diagonal of the NNP body, respectively. XZ,j S XY,j S YZ,j This represents the perpendicularity error of the j-th detection point with reference to the diagonal of the PPP body.

[0225] 3) The measurement and positioning errors of the four body diagonals are summarized as follows:

[0226]

[0227] The above equation can be rewritten in matrix form:

[0228] A j ·T j =B j

[0229] in:

[0230]

[0231]

[0232]

[0233] Substituting the intersection coordinates obtained in step 1) into the matrix, the least squares solution of the system of equations is:

[0234] T j =(A j T A j ) -1 (A j T B j )

[0235] Vector T j It contains all elements of the machine tool verticality error, and at this point, the verticality error at the j-th detection point has been decoupled.

[0236] Step S4: Average the perpendicularity errors of decoupling in different YZ planes to obtain the global average perpendicularity error used for machine tool compensation:

[0237]

[0238] In the formula, Γ XY ,Γ XZ ,Γ YZ This refers to the global average verticality error.

[0239] Example 4

[0240] exist Figure 2 and Figure 3 The perpendicularity error was tested and verified on the machine tool shown. A laser interferometer was installed on the side of the worktable, and a pyramidal reflector was installed at the spindle end. A 5400mm*1800mm*900mm area of ​​the machine tool's working space was taken as the detection space cube. Four diagonals (PPP, NPP, PNP, NNP) were set with an interval of 9 segments, resulting in a total of N=10 detection points. A detection program was developed to drive the pyramidal reflector at the spindle end to move along the diagonals. The average measurement and positioning error value of the detection points was further obtained as follows: Figure 7 As shown.

[0241] At this point, using the scheme of this embodiment, the verticality error values ​​of the 10 detection points are obtained as follows: Figure 8 As shown.

[0242] The perpendicularity error is averaged to obtain the global average perpendicularity error used for machine tool compensation, as shown below. Figure 9 As shown.

[0243] The obtained perpendicularity error compensation is updated in the CNC system, thereby improving the machining accuracy of the machine tool.

[0244] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for identifying machine tool perpendicularity error based on body diagonal, characterized in that, Includes the following steps: Step S1: Define the body diagonal within the machine tool's workspace and measure the spatial positioning error of the body diagonal based on a laser interferometer; Step S2: Define the perpendicularity error elements of the machine tool translation axis, and construct a spatial positioning error model that considers perpendicularity error based on homogeneous coordinate transformation and multibody system theory; Step S3: Combining steps S1 and S2, select the positioning error data of multiple detection points where the specified YZ plane intersects with the body diagonal, and construct a verticality error decoupling identification model. Step S4: Calculate the average perpendicularity error of the decoupled planes in different YZ planes to obtain the global average perpendicularity error for machine tool compensation; Step S3 specifically involves: S3.1: Establish the mathematical relationship between the spatial positioning error of the blade tip and the measurement positioning error of the detection point on the body diagonal; S3.2:1) In the measurement coordinate system, with the body diagonal PPP as the first... j Each testing site For reference, the X-axis coordinate value is defined as follows: The YZ plane will intersect the other three body diagonals at three points. Since the body diagonal segments in step S1.2 have been equally divided into N detection points, the intersections of the YZ plane with the four body diagonals are actually the pre-defined detection points. Therefore: The coordinates of the intersection point of the YZ plane and the body diagonal PPP are: ; The coordinates of the intersection point of the YZ plane and the body diagonal NPP are: ; The coordinates of the intersection point of the YZ plane and the body diagonal PNP are: ; The coordinates of the intersection point of the YZ plane and the body diagonal NNP are: ; The coordinates of the four intersection points in the formula are based on the X, Y, and Z coordinates of the detection point on the diagonal of the reference body, that is, the coordinates of any intersection point are... y If the coordinate values ​​intersect the coordinate values ​​of the point on the diagonal of PPP When they are unequal, according to the definition of four body diagonals, then... The coordinate values ​​are equal; the coordinates of any intersection point are equal. z If the coordinate values ​​intersect the coordinate values ​​of the point on the diagonal of PPP When they are unequal, according to the definition of four body diagonals, then they are equal to... Equal coordinate values; subscript N-j+ 1 refers to the diagonal of the reference body PPP. N-j+ The Y-coordinate or Z-coordinate value of a single detection point; 2) Based on the measurement and positioning error transformation model and the body diagonal measurement direction vector, the computer tool detects the measurement and positioning errors of the four body diagonals in the detection space: 3) Combine the measurement and positioning errors of the four body diagonals; The measurement and positioning errors of the four body diagonals in step S3.2, 2) are specifically as follows: ①The expression for the measurement and positioning error of the diagonal of the PPP body is as follows: Substituting the intersection of the YZ plane and the diagonal of the PPP body, we get the nth point on the diagonal of the body. j If there are 1 detection point, the measurement and positioning error is: In the formula, L This represents the sum of the machine tool's rotational distance and the tool length. , These represent the Y-coordinates and Z-coordinates of the intersection point on the diagonals of the PPP body, respectively. , , Indicates the first reference to the diagonal of the PPP body. j Verticality error of each detection point; ②The expression for the measurement and positioning error of the NPP body diagonal is as follows: Substituting the intersection of the YZ plane and the diagonal of the NPP body, we get the nth point on the diagonal of the body. N - j+ With one detection point, the measurement and positioning error is: In the formula, L This represents the sum of the machine tool's rotational distance and the tool length. , These represent the Y-coordinates and Z-coordinates of the intersection point on the diagonals of the NPP body, respectively. , , Indicates the first reference to the diagonal of the PPP body. j Verticality error of each detection point; ③The expression for the measurement and positioning error of the PNP body diagonal is as follows: Substituting the intersection of the YZ plane and the diagonal of the PNP body, we get the nth point on the diagonal of the body. j If there are 1 detection point, the measurement and positioning error is: In the formula, L This represents the sum of the machine tool's rotational distance and the tool length. , These represent the Y-coordinates and Z-coordinates of the intersection point on the diagonals of the PNP body, respectively. , , Indicates the first reference to the diagonal of the PPP body. j Verticality error of each detection point; ④The expression for the measurement and positioning error of the NNP body diagonal is as follows: Substituting the intersection of the YZ plane and the diagonal of the NNP body, we get the nth point on the diagonal of the body. N - j+ With one detection point, the measurement and positioning error is: In the formula, L This represents the sum of the machine tool's rotational distance and the tool length. , These represent the Y-coordinates and Z-coordinates of the intersection point on the diagonals of the NNP body, respectively. , , Indicates the first reference to the diagonal of the PPP body. j Verticality error of each detection point; In section 3) of S3.2, the measurement and positioning errors of the four body diagonals are specifically summarized as follows: The above equation can be rewritten in matrix form: in: Substituting the intersection coordinates obtained in step 1) into the matrix, the least squares solution to the system of equations is: vector T j This includes elements related to the machine tool perpendicularity error; at this point, the... j The verticality error at each detection point has been decoupled. The calculation formula for step S4 is as follows: 、 、 In the formula, , , This refers to the global average verticality error.

2. The machine tool perpendicularity error identification method based on body diagonal according to claim 1, characterized in that, Step S1 specifically involves: S1.1: Based on the working range required for machine tool processing, determine the detection space cube from (0,0,0) to ( x , y , z ), where (0,0,0) is the starting point of the detection space cube, and a measurement coordinate system is established at this point, with the coordinate axes aligned with the machine tool coordinate axes. x , y , z This is used to detect the farthest point of the spatial cube in the measurement coordinate system, and also to represent the X, Y, and Z coordinates of the farthest point in the measurement coordinate system.

3. The machine tool perpendicularity error identification method based on body diagonal according to claim 2, characterized in that, Step S1 further includes: S1.2: The four diagonals of the spatial cube are denoted as PPP, NPP, PNP, and NNP, respectively. PPP represents the detection trajectory moving along the positive directions of the X-axis, Y-axis, and Z-axis; NPP represents the detection trajectory moving along the negative direction of the X-axis and the positive directions of the Y-axis and Z-axis; PNP represents the detection trajectory moving along the positive direction of the X-axis, the negative direction of the Y-axis, and the positive direction of the Z-axis; and NNP represents the detection trajectory moving along the negative direction of the X-axis, the negative direction of the Y-axis, and the positive direction of the Z-axis. The starting points of the four volume diagonals are all located in the z=0 plane, and the volume diagonal segments are divided into N detection points at equal intervals.

4. The machine tool perpendicularity error identification method based on body diagonal according to claim 3, characterized in that, Step S1 further includes: S1.3: Using a laser interferometer, measure the positioning error of the detection point along each diagonal. Repeat the measurement twice for each body diagonal segment, and take the average of the two measurements as the positioning error value of the current point, denoted as... , , indicating the first position on the diagonal of one of PPP, NPP, PNP, and NNP. j The measurement and positioning error value of each detection point; , indicating the number of the diagonal line counting from the starting point. j There are several testing sites.

5. The machine tool perpendicularity error identification method based on body diagonal according to claim 3, characterized in that, N >5 points / meter and is an even number.

6. The machine tool perpendicularity error identification method based on body diagonal according to claim 1, characterized in that, The specific steps in step S2 for constructing a spatial positioning error model that considers verticality error are as follows: S2.1: , , This refers to the perpendicularity error between the XY, XZ, and YZ coordinate axes of the machine tool. S2.2: Based on its topological structure and the principle of homogeneous coordinate transformation, the theoretical spatial kinematic model is obtained as follows: In the formula, This represents the ideal coordinates of the end-effector tip in the machine tool coordinate system. This represents the translation matrix of the X, Y, and Z translation axes of a CNC machine tool. This represents the initial coordinates of the blade tip. The kinematic model of the actual spatial position of the blade tip can be expressed as: In the formula, This represents the actual coordinates of the end-effector tip in the machine tool coordinate system. Translation matrices representing the error-inducing motion of the X, Y, and Z translation axes of a CNC machine tool; S2.3: Spatial positioning error of the tool tip under the influence of perpendicularity error This can be expressed as: In the formula, These represent the error values ​​of the tool tip in the X, Y, and Z directions of the machine tool coordinate system, respectively. L This represents the sum of the machine tool's rotational distance and the tool length. y m This represents the Y-coordinate value of the tool tip in the measurement coordinate system. z m This represents the Z-axis coordinate of the tool tip in the measurement coordinate system.

7. The machine tool perpendicularity error identification method based on body diagonal according to claim 1, characterized in that, Step S3.1 specifically includes: 1) Since the selected diagonals are all spatial volumes, the measurement direction vectors of the diagonals PPP, NPP, PNP, and NNP in the measurement coordinate system are as follows: 、 、 、 In the formula , , , , x This represents the length of the body diagonal in the X direction. y This represents the length of the body diagonal in the Y direction. z The length of the body diagonal in the Z direction is represented by , and D represents the total length of the body diagonal. 2) The spatial positioning error of the tool tip is along the three directions in the machine tool coordinate system, and the measurement positioning error of the body diagonal is along the vector direction of the diagonal. The spatial positioning error can be converted into the measurement positioning error: In the formula, , , V i This indicates that it belongs to one of the measurement direction vectors of the body diagonal PPP, NPP, PNP, and NNP. j This indicates the number of the diagonal line counting from the starting point. j There are several testing sites.

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