Method for realizing coordinate tracking of five-axis machining center

Abstract

The present application relates to five-axis machining center technical field, a kind of five-axis machining center realization coordinate tracking method, comprising: the rotary center coordinates of the rotary table of measuring machine tool are measured, spare;According to the structure of machine tool rotary table, macro program is written, and the macro program is stored in numerical control machine tool;When the swing axis of machine tool rotary table is at 0 degree, rotary table is at specific position, and is set to 0 degree, find the initial coordinate system zero point, according to the workpiece processed, the macro program is called in NC program, and coordinate tracking is realized.The variable interface value in the calling format of the macro program of the present application can be directly obtained from the workpiece drawing, and can be manually input, solve the technical problem that the variable interface value in the calling format of the macro program can be obtained by computer post-processing and drawing method cooperation in the prior art, greatly facilitate the manual numerical control programming process, improve programming, processing efficiency.

Description

Technical Field

[0001] This invention relates to the field of five-axis machining center technology, and in particular to a method for achieving coordinate tracking in a five-axis machining center. Background Technology

[0002] CNC machine tools, as machining equipment, are indispensable and crucial process equipment for ensuring machining quality, improving production efficiency, and realizing production process automation. Five-axis machining centers, as high-end CNC equipment, play a vital role in the development of the manufacturing industry, especially in aerospace and automotive fields. They possess high flexibility, high precision, high integration, and complete machining capabilities, enabling the machining of multiple surfaces on a workpiece in a single setup. This effectively solves the accuracy and cycle time issues in machining complex parts during new product development, significantly shortening the product development cycle and improving workpiece machining efficiency.

[0003] Due to the high price of high-end five-axis machine tools, the domestic market has a large number of low-end five-axis machine tools that are modified from three-axis machining centers by adding rotary tables. During manual programming of these machine tools, the coordinate system origin needs to be manually readjusted at various angles of the rotary table. This is not only time-consuming and labor-intensive, but also prone to errors and inconvenient for adjusting machining dimensions. This severely restricts the efficiency of manual CNC programming and production processing.

[0004] Currently, Chinese Patent CN108919749B discloses a method for achieving coordinate origin tracking in a toolless five-axis machine tool. This method mainly utilizes computer post-processing (CAM) and drawing methods to achieve the coordinate tracking function of the machining center. However, this method is not convenient to apply (CAM software needs to be reapplied for processing each time an adjustment is made), and it is also inconvenient to adjust dimensions during trial cutting.

[0005] To address this, we provide a more convenient and feature-rich coordinate tracking method for manual programming of five-axis machining centers. Summary of the Invention

[0006] The purpose of this invention is to provide a method for coordinate tracking in a five-axis machining center in order to solve the above-mentioned problems.

[0007] The present invention achieves the above objectives through the following technical solutions:

[0008] A method for coordinate tracking in a five-axis machining center includes the following steps:

[0009] Step 1: Measure the coordinates of the rotation center of the machine tool's rotary table, for later use;

[0010] Step 2: Write a macro program based on the structure of the machine tool's rotary table, and store the macro program in the CNC machine tool;

[0011] Step 3: With the swing axis of the machine tool rotary table at 0 degrees and the rotary table in a specific position and set to 0 degrees, find and set the initial coordinate system zero point.

[0012] Step 4: Based on the workpiece being machined, call the macro program in the NC program to achieve coordinate tracking;

[0013] The macro program's calling format is: G65 P_H_M_S_X_Y_Z_A_B_C_U_V_W_;

[0014] The meanings of the above variable interfaces are as follows: P_ refers to the macro program segment number to be executed, H_ refers to the selected workpiece coordinate system, M_ refers to coordinate tracking, S_ refers to the order of coordinate system rotation around the axis, X_Y_Z_ refers to the movement value in the X, Y, and Z directions of the coordinate system before rotation, respectively, A_B_C_ refers to the angle value of the coordinate system rotation around the X, Y, and Z axes, respectively, and U_V_W_ refers to the movement value in the X, Y, and Z directions of the coordinate system after rotation, respectively.

[0015] The formula for calculating the target coordinate system A1 in the macro program is as follows:

[0016] A1=A0*R1*R(X, a)*R(Y, b)*R(Z, c)*R2,

[0017] A1=A0*R1*R(X, a)*R(Z, c)*R(Y, b)*R2,

[0018] A1=A0*R1*R(Y,b)*R(X,a)*R(Z,c)*R2,

[0019] A1=A0*R1*R(Y,b)*R(Z,c)*R(X,a)*R2,

[0020] A1=A0*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or

[0021] A1=A0*R1*R(Z,c)*R(Y,b)*R(X,a)*R2;

[0022] Where A0 represents the initial coordinate system, R1 represents the motion matrix of the initial coordinate system A0 translating in the X, Y, and Z directions at the forefront of the coordinate system rotation, R(X, a), R(Y, b), and R(Z, c) represent the motion matrices of the coordinate system rotating a degree around the X axis, b degrees around the Y axis, and c degrees around the Z axis, respectively, and R2 represents the motion matrix of the coordinate system translating in the X, Y, and Z directions after the coordinate system rotation;

[0023] The macro program calculates the target coordinate system's Z-axis to move to the same axis as the machine tool spindle based on the target coordinate system's attitude matrix and the machine tool's actual motion structure. The required rotation axis angle c1 and swing axis angle a1 of the machine tool's rotary table are obtained by an ATAN function formula. Simultaneously, it calculates the relative distances ΔX, ΔY, and ΔZ between the zero point of the target coordinate system and the machine tool's rotation center coordinates after the motion, as well as the angle between the target coordinate system's X-axis and the machine tool coordinate system's X-axis after the motion. The program then outputs the initial workpiece coordinate system's offset value and coordinate system rotation value through G52 and G68 commands, thus completing coordinate tracking.

[0024] Preferably, a target coordinate system is described by the variable interface M_S_X_Y_Z_A_B_C_U_V_W_ parameter. This target coordinate system is obtained by changing the initial workpiece coordinate system of the program through one or more "translation-rotation-translation" processes.

[0025] Preferably, the formula for calculating the additional coordinate system A2 in the macro program is as follows:

[0026] A2=A1'*R1*R(X, a)*R(Y, b)*R(Z, c)*R2,

[0027] A2=A1'*R1*R(X, a)*R(Z, c)*R(Y, b)*R2,

[0028] A2=A1'*R1*R(Y, b)*R(X, a)*R(Z, c)*R2,

[0029] A2=A1'*R1*R(Y, b)*R(Z, c)*R(X, a)*R2,

[0030] A2=A1'*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or

[0031] A2=A1'*R1*R(Z, c)*R(Y, b)*R(X, a)*R2;

[0032] Where A1' is the target coordinate system obtained from the previous coordinate tracking.

[0033] Preferably, the calculation formulas for R(X, a), R(Y, b), and R(Z, c) are as follows:

[0034]

[0035]

[0036]

[0037] Preferably, in step four, the macro program G65P_ is called and the H_M_S_X_Y_Z_A_B_C_U_V_W_ parameter is output.

[0038] Preferably, M_ takes the value 0 or 1; where M0 indicates the first coordinate tracking and M1 indicates the additional coordinate tracking.

[0039] Preferably, S takes values ​​from 1 to 6, which represent six possible sequences of rotation of the coordinate system around the axis: XYZ, XZY, YXZ, YZX, ZXY, and ZYX.

[0040] Preferably, the order of steps one and two is interchanged.

[0041] The beneficial effects are:

[0042] 1. The variable interface values ​​in the macro program calling format can be directly obtained from the workpiece drawing and manually entered. This solves the technical problem that existing technologies require computer post-processing and drawing methods to obtain the variable interface values ​​in the macro program calling format, greatly facilitating the manual CNC programming process and improving programming and machining efficiency.

[0043] 2. For five-axis machining centers with different structures, when the workpiece mounting method is the same, the calling format is also the same, which improves the universality of NC programs and avoids waste and occasional errors caused by repeated programming.

[0044] The additional technical features and advantages of the present invention will become more apparent from the following description, or may be learned through practice of the invention. Attached Figure Description

[0045] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof. In the drawings:

[0046] Figure 1 This is a flowchart of the macro program in this invention;

[0047] Figure 2 This is a schematic diagram of the working principle of the present invention;

[0048] Figure 3 This is a schematic diagram of the rotary table structure of an AC-axis five-axis machining center. Detailed Implementation

[0049] like Figure 1 As shown, a method for coordinate tracking in a five-axis machining center includes the following steps:

[0050] Step 1: Measure the coordinates of the rotation center of the machine tool's rotary table for later use; this step only needs to be performed once, and the coordinates of its rotation center remain unchanged if the position of the rotary table does not change.

[0051] Step 2: Write a macro program based on the structure of the machine tool's rotary table, and store the macro program in the CNC machine tool;

[0052] As needed, a macro program can be written first based on the structure of the machine tool's rotary table, then the coordinates of the rotation center of the machine tool's rotary table can be measured, and then the macro program can be stored in the CNC machine tool.

[0053] Step 3: With the swing axis of the machine tool rotary table at 0 degrees and the rotary table in a specific position and set to 0 degrees, find and set the initial coordinate system zero point; the rotation axis of the rotary table can be set to 0 degrees at any position, so the above specific position is set according to the actual workpiece.

[0054] Step 4: Based on the workpiece being machined, call the macro program in the NC program to achieve coordinate tracking;

[0055] The macro program's calling format is: G65 P_H_M_S_X_Y_Z_A_B_C_U_V_W_;

[0056] The meanings of the above variable interfaces are as follows: P_ refers to the macro program segment number to be executed; H_ refers to the selected workpiece coordinate system, with a value of 54 to 59, H54 means that the workpiece coordinate system G54 is selected; M_ refers to coordinate tracking, with a value of 0 or 1, M0 means to perform the first coordinate tracking, M1 means to perform additional coordinate tracking; S_ refers to the order of the coordinate system rotation around the axis, with a value of 1 to 6, representing six possible orders of the coordinate system rotation around the axis: XYZ, XZY, YXZ, YZX, ZXY, and ZYX; X_Y_Z_ refers to the movement value in the X, Y, and Z directions of the coordinate system before rotation, respectively; A_B_C_ refers to the angle value of the coordinate system rotation around the X, Y, and Z axes, respectively; and U_V_W_ refers to the movement value in the X, Y, and Z directions of the coordinate system after rotation, respectively.

[0057] The formula for calculating the target coordinate system A1 in the macro program is as follows:

[0058] A1=A0*R1*R(X, a)*R(Y, b)*R(Z, c)*R2,

[0059] A1=A0*R1*R(X, a)*R(Z, c)*R(Y, b)*R2,

[0060] A1=A0*R1*R(Y,b)*R(X,a)*R(Z,c)*R2,

[0061] A1=A0*R1*R(Y,b)*R(Z,c)*R(X,a)*R2,

[0062] A1=A0*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or

[0063] A1=A0*R1*R(Z,c)*R(Y,b)*R(X,a)*R2;

[0064] Where A0 represents the initial coordinate system, R1 represents the motion matrix of the initial coordinate system A0 translating in the X, Y, and Z directions at the forefront of the coordinate system rotation, R(X, a), R(Y, b), and R(Z, c) represent the motion matrices of the coordinate system rotating a degree around the X axis, b degrees around the Y axis, and c degrees around the Z axis, respectively, and R2 represents the motion matrix of the coordinate system translating in the X, Y, and Z directions after the coordinate system rotation;

[0065] The macro program calculates the target coordinate system's Z-axis to move to the same axis as the machine tool spindle based on the target coordinate system's attitude matrix and the machine tool's actual motion structure. The required rotation axis angle c1 and swing axis angle a1 of the machine tool's rotary table are obtained by an ATAN function formula. Simultaneously, it calculates the relative distances ΔX, ΔY, and ΔZ between the zero point of the target coordinate system and the machine tool's rotation center coordinates after the motion, as well as the angle between the target coordinate system's X-axis and the machine tool coordinate system's X-axis after the motion. The program then outputs the initial workpiece coordinate system's offset value and coordinate system rotation value through G52 and G68 commands, thus completing coordinate tracking.

[0066] As needed, a target coordinate system is described by the variable interface M_S_X_Y_Z_A_B_C_U_V_W_ parameter. This target coordinate system is obtained by changing the initial workpiece coordinate system of the program through one or more "translation-rotation-translation" processes.

[0067] As needed, the formula for calculating the additional coordinate system A2 in the macro program is as follows:

[0068] A2=A1'*R1*R(X, a)*R(Y, b)*R(Z, c)*R2,

[0069] A2=A1'*R1*R(X, a)*R(Z, c)*R(Y, b)*R2,

[0070] A2=A1'*R1*R(Y, b)*R(X, a)*R(Z, c)*R2,

[0071] A2=A1'*R1*R(Y, b)*R(Z, c)*R(X, a)*R2,

[0072] A2=A1'*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or

[0073] A2=A1'*R1*R(Z, c)*R(Y, b)*R(X, a)*R2;

[0074] Where A1' is the target coordinate system obtained from the previous coordinate tracking.

[0075] As needed, the calculation formulas for R(X, a), R(Y, b), and R(Z, c) are as follows:

[0076]

[0077]

[0078]

[0079] If necessary, in step four, the macro program G65P_ is called and the parameters H_M_S_X_Y_Z_A_B_C_U_V_W_ are output.

[0080] Example 1

[0081] like Figure 2 As shown, based on the input parameters, a target coordinate system is obtained during the macro program's execution, as detailed below:

[0082] A matrix A0 represents the position and orientation of the initial workpiece coordinate system (such as G54).

[0083]

[0084] In this matrix, the 3×3 matrix in the upper left corner represents the orientation of the workpiece coordinate system; m11, m21, and m31 represent the direction of the X-axis of the workpiece coordinate system, and their values ​​are the cosine values ​​of the angles between the X-axis of the workpiece coordinate system and the X-axis, Y-axis, and Z-axis of the machine coordinate system, respectively; m12, m22, and m32 represent the direction of the Y-axis of the workpiece coordinate system, and their values ​​are the cosine values ​​of the angles between the Y-axis of the workpiece coordinate system and the X-axis, Y-axis, and Z-axis of the machine coordinate system, respectively; m13, m23, and m33 represent the direction of the Z-axis of the workpiece coordinate system, and their values ​​are the cosine values ​​of the angles between the Z-axis of the workpiece coordinate system and the X-axis, Y-axis, and Z-axis of the machine coordinate system, respectively; m14, m24, and m34 represent the position of the origin of the workpiece coordinate system in the machine tool's mechanical coordinate system.

[0085] For example, when creating a new coordinate tracking system, the X, Y, and Z axes of the initial workpiece coordinate system A0 are in the same direction as the X, Y, and Z axes of the five-axis machine tool coordinate system.

[0086]

[0087] When an additional coordinate tracking is added, the initial workpiece coordinate system A0 is equal to the attitude matrix of the target coordinate system obtained after the previous coordinate tracking;

[0088] In other words, when the workpiece coordinate system is translated x, y, and z along the XYZ axes respectively before rotating about the axis, the homogeneous transformation matrix of this motion is R1.

[0089]

[0090] When the workpiece coordinate system rotates by 'a' degrees around the X-axis, the homogeneous transformation matrix of this motion is R(X, a).

[0091]

[0092] When the workpiece coordinate system rotates by b degrees around the Y-axis, the homogeneous transformation matrix of this motion is R(Y, b).

[0093]

[0094] When the workpiece coordinate system rotates by c degrees around the Z-axis, the homogeneous transformation matrix of this motion is R(Z, c).

[0095]

[0096] When the workpiece coordinate system rotates about the axis and then translates along the XYZ axes by u, v, and w respectively, the homogeneous transformation matrix of this motion is R2.

[0097]

[0098] In other words, the workpiece coordinate system is first moved x, y, and z along the X, Y, and Z axes respectively, then rotated b degrees around the Y axis, c degrees around the Z axis, and a degrees around the X axis (the rotation order around the axes is YZX), and then moved u, v, and w along the rotated X, Y, and Z axes respectively, transforming it into the target coordinate system. This target coordinate system is represented by the attitude matrix A1.

[0099]

[0100] The formula for calculating A1 is as follows:

[0101] A1=A0*R1*R(X,a)*R(Y,b)*R(Z,c)*R2

[0102] When the order of rotation of the coordinate system around the axes is XZY,

[0103] A1=A0*R1*R(X, a)*R(Z, c)*R(Y, b)*R2

[0104] When the order of rotation of the coordinate system around the axes is YXZ,

[0105] A1=A0*R1*R(Y,b)*R(X,a)*R(Z,c)*R2

[0106] When the order of rotation of the coordinate system around the axes is YZX,

[0107] A1=A0*R1*R(Y,b)*R(Z,c)*R(X,a)*R2

[0108] When the order of rotation of the coordinate system around the axes is ZXY,

[0109] A1=A0*R1*R(Z,c)*R(X,a)*R(Y,b)*R2

[0110] When the order of rotation of the coordinate system around the axes is ZYX,

[0111] A1=A0*R1*R(Z,c)*R(Y,b)*R(X,a)*R2

[0112] Taking the rotation sequence XYZ around the axis as an example, the values ​​of each element of the target coordinate system attitude matrix A1 are obtained, as shown in the table below:

[0113]

[0114] In a specific implementation, a virtual target attitude matrix register can be established to store the attitude matrix of the target coordinate system after one coordinate tracking operation. During the initial coordinate tracking, the target attitude matrix register is A1. During subsequent coordinate tracking, the value of the target attitude matrix register is assigned to the initial workpiece coordinate system A0, i.e., A0 = A1; simultaneously, the value of the target attitude matrix register is updated to the recalculated A1.

[0115] During the macro program's execution, inverse calculations are performed on the target coordinate system A1 to obtain the mechanical angle of the five-axis machining center's rotary table. This causes the target coordinate system on the workpiece to move along the Z-axis to a position coaxial with the machine tool's Z-axis, and the rotary table is then instructed to move. Simultaneously, the relative position between the origin of the target coordinate system and the origin of the original coordinate system after the movement, as well as the angle between the target coordinate system's X-axis and the machine coordinate system's X-axis, are calculated. Coordinate tracking is then achieved using the G52 and G68 commands.

[0116] Example 2

[0117] like Figure 3 As shown, the calculation process is illustrated using the rotary table of a five-axis machining center with AC axis as an example. For instance, the rotary table of this five-axis machining center can rotate 360 ​​degrees around the Z axis, and the swing table can rotate a certain angle around the X axis.

[0118] Assuming the target coordinate system A1 is rotated c1 degrees around the Z-axis and a1 degrees around the X-axis, a new attitude matrix A2 is obtained, representing the target coordinate system after the motion.

[0119] A2 = RG_X * RG_Z * A1

[0120] in,

[0121]

[0122]

[0123]

[0124] The values ​​of each element in A2 are shown in the table below:

[0125]

[0126]

[0127] Let p13 = 0, then we get c1 = atan(n13 / n23);

[0128] Let p23 = 0, then a1 = atan((n23*cos(c1)+n13*sin(c1)) / n33);

[0129] Substituting the calculated a1 and c1 into p33 should make p33 = 1. Since the range of the ATAN function is (-90°, 90°), there may be a situation where p33 ≠ 1. In this case, the calculated a1 and c1 should be corrected.

[0130] Based on a1 and c1, p14, p24, and p34 can be further calculated.

[0131] △X=p14-m14,

[0132] △Y=p14-m14,

[0133] △Z=p14-m14;

[0134] △X, △Y, and △Z represent the relative positions between the origin of the target coordinate system and the origin of the original coordinate system after the motion.

[0135] The X-direction vector of the mechanical coordinate system is a = (1, 0, 0);

[0136] The X-direction vector of the coordinate system represented by the A2 attitude matrix is ​​b = (p11, p21, p31);

[0137] <a,b> =arcos[(a, b)]

[0138] <a,b>This is the angle between the X-axis of the target coordinate system and the X-axis of the machine coordinate system after the motion.

[0139] Based on △X, △Y, △Z and<a,b> This enables coordinate tracking.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be covered within the protection scope of the present invention.

[0141] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for coordinate tracking in a five-axis machining center, characterized in that: Includes the following steps: Step 1: Measure the coordinates of the rotation center of the machine tool's rotary table, for later use; Step 2: Write a macro program based on the structure of the machine tool's rotary table, and store the macro program in the CNC machine tool; Step 3: With the swing axis of the machine tool rotary table at 0 degrees and the rotary table in a specific position and set to 0 degrees, find and set the initial coordinate system zero point. Step 4: Based on the workpiece being machined, call the macro program in the NC program to achieve coordinate tracking; The macro program's calling format is: G65 P_H_M_S_X_Y_Z_A_B_C_U_V_W_; The meanings of the above variable interfaces are as follows: P_ refers to the macro program segment number to be executed, H_ refers to the selected workpiece coordinate system, M_ refers to coordinate tracking, S_ refers to the order of coordinate system rotation around the axis, X_Y_Z_ refers to the movement value in the X, Y, and Z directions of the coordinate system before rotation, respectively, A_B_C_ refers to the angle value of the coordinate system rotation around the X, Y, and Z axes, respectively, and U_V_W_ refers to the movement value in the X, Y, and Z directions of the coordinate system after rotation, respectively. The formula for calculating the target coordinate system A1 in the macro program is as follows: A1=A0*R1*R(X, a)*R(Y, b)*R(Z, c)*R2, A1=A0*R1*R(X, a)*R(Z, c)*R(Y, b)*R2, A1=A0*R1*R(Y,b)*R(X,a)*R(Z,c)*R2, A1=A0*R1*R(Y,b)*R(Z,c)*R(X,a)*R2, A1=A0*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or A1=A0*R1*R(Z,c)*R(Y,b)*R(X,a)*R2; Where A0 represents the initial coordinate system, R1 represents the motion matrix of the initial coordinate system A0 translating in the X, Y, and Z directions at the forefront of the coordinate system rotation, R(X, a), R(Y, b), and R(Z, c) represent the motion matrices of the coordinate system rotating a degree around the X axis, b degrees around the Y axis, and c degrees around the Z axis, respectively, and R2 represents the motion matrix of the coordinate system translating in the X, Y, and Z directions after the coordinate system rotation; The macro program calculates the target coordinate system's Z-axis to move to the same axis as the machine tool spindle based on the target coordinate system's attitude matrix and the machine tool's actual motion structure. The required rotation axis angle c1 and swing axis angle a1 of the machine tool's rotary table are obtained by an ATAN function formula. Simultaneously, it calculates the relative distances ΔX, ΔY, and ΔZ between the zero point of the target coordinate system and the machine tool's rotation center coordinates after the motion, as well as the angle between the target coordinate system's X-axis and the machine tool coordinate system's X-axis after the motion. The program then outputs the initial workpiece coordinate system's offset value and coordinate system rotation value through G52 and G68 commands, thus completing coordinate tracking.

2. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: A target coordinate system is described by the variable interface M_S_X_Y_Z_A_B_C_U_V_W_ parameter. This target coordinate system is obtained by changing the initial workpiece coordinate system of the program through one or more "translation-rotation-translation" processes.

3. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: The formula for calculating the additional coordinate system A2 in the macro program is as follows: A2=A1'*R1*R(X, a)*R(Y, b)*R(Z, c)*R2, A2=A1'*R1*R(X, a)*R(Z, c)*R(Y, b)*R2, A2=A1'*R1*R(Y, b)*R(X, a)*R(Z, c)*R2, A2=A1'*R1*R(Y, b)*R(Z, c)*R(X, a)*R2, A2=A1'*R1*R(Z,c)*R(X,a)*R(Y,b)*R2 or A2=A1'*R1*R(Z, c)*R(Y, b)*R(X, a)*R2; Where A1' is the target coordinate system obtained from the previous coordinate tracking.

4. A method for coordinate tracking in a five-axis machining center according to claim 1 or 3, characterized in that: The calculation formulas for R(X, a), R(Y, b), and R(Z, c) are as follows:

5. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: In step four, the macro program G65P_ is called, and the parameters H_M_S_X_Y_Z_A_B_C_U_V_W_ are output.

6. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: The value of M_ is 0 or 1; where M0 indicates the initial coordinate tracking and M1 indicates the additional coordinate tracking.

7. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: The value of S ranges from 1 to 6, representing six possible sequences of rotation around the coordinate system: XYZ, XZY, YXZ, YZX, ZXY, and ZYX.

8. The method for coordinate tracking in a five-axis machining center according to claim 1, characterized in that: The order of steps one and two is reversed.

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