Five-axis gantry machine tool position-related geometric error modeling and identification method and system

Abstract

The invention belongs to the technical field of numerical control machine tool geometric error precision measurement and identification, and provides a five-axis gantry machine tool position-related geometric error modeling and identification method and system, and the method comprises the steps: introducing and building a transmission relation between a geometric error and a space error, and constructing a kinematic model; distance information of the tail end position of the machine tool is measured, and actual position coordinates of the measuring points are solved; using a polynomial function to represent the position-related geometric error, and defining a measurement reference at an original point of a coordinate system; and identifying the polynomial function, and identifying and decoupling the error according to the error basic characteristics. According to the method, high identification precision is guaranteed while only the distance information multilateral measurement method is used, all geometric errors of the translation axis and the rotation axis of the five-axis machine tool are identified, error decoupling is achieved in the error identification process, the problem that a Jacobian matrix is singular in the Gauss-Newton method is solved, and the error identification precision and efficiency are improved.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement and identification technology of geometric errors of CNC machine tools, specifically, it relates to a method and system for modeling and identifying position-related geometric errors of a five-axis gantry milling machine. Background Technology

[0002] Spatial positioning error refers to the deviation between the actual and theoretical positions of the tool tip during machining. This error is the result of the combined influence of the geometric errors of each axis of the machine tool on the tool tip, directly reflecting the machining accuracy of the machine tool at various positions within the workspace. To improve the machining accuracy of large five-axis gantry milling machines, it is necessary to measure and compensate for the machine tool's spatial errors. Currently, commonly used instruments for measuring machine tool geometric errors include laser interferometers, ballbars, and R-test measuring instruments. However, these instruments can only measure a portion of the geometric errors at a time, resulting in low measurement efficiency and failing to meet the requirements for efficient and high-precision machine tool measurement.

[0003] The patent document "Method for Detection and Identification of Geometric Errors of Translation Axis of CNC Machine Tool Based on LaserTRACER" (CN106141814A) discloses a method for detecting and identifying geometric errors of translation axes of machine tools. It establishes a mapping model between the end-effector pose error of the machine tool and the coefficients of 21 geometric error polynomials, uses a laser tracker to measure the end-effector pose error of the machine tool, and obtains each geometric error by identifying and solving the polynomial coefficients. However, it only measures and identifies translation axis errors and does not mention the method for measuring and identifying machine tool rotary axis errors. Moreover, the error identification process is relatively complicated.

[0004] The patent document "A Method for Identifying Spatial Errors of CNC Machine Tools" (CN113910001A) discloses a method for identifying spatial errors of a five-axis machine tool. It establishes an error propagation model for spatial and geometric errors, uses Chebyshev polynomials to fit geometric errors, and uses the distance and angle information of a laser tracker to measure the spatial error at the end of the machine tool, thus achieving the identification of geometric errors. However, due to the poor angle measurement accuracy of the tracker and the fact that position-independent geometric errors are regarded as part of position-dependent geometric errors, the decoupling of geometric errors is not achieved, resulting in an incomplete error model and low error measurement accuracy.

[0005] The patent document "A Method and System for Identifying Geometric Errors of a Five-Axis CNC Machine Tool's Swing Head" (CN115415853A) discloses a method that uses a laser tracking interferometer to establish a measurement coordinate system, tracks a reflector on a five-axis CNC machine tool in real time, and determines the geometric error of the rotation axis by solving the homogeneous transformation matrix through distance measurement and the least squares method. It also utilizes rigid body motion constraint theory to reduce random errors and improve measurement accuracy. However, this method does not achieve decoupling of geometric errors; it only measures and identifies the geometric errors of the five-axis machine tool's rotation axes and cannot simultaneously measure and identify the geometric errors of the machine tool's translation axes, resulting in an incomplete error model. Furthermore, the measurement process requires the reflector to be installed in different positions for three measurements, which is also very cumbersome.

[0006] Currently, for the problem of modeling and identifying position-related geometric errors in large five-axis gantry milling machines, there is a need for a method that can clearly represent position-related geometric errors, accurately identify and decouple them, and is easy to operate. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for modeling and identifying position-related geometric errors in a five-axis gantry milling machine.

[0008] A method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine tool, provided by the present invention, includes:

[0009] The model building steps include introducing and establishing the transmission relationship between geometric errors and spatial errors, and constructing the kinematic model of the machine tool.

[0010] The measurement steps involve measuring the distance information at the end of the machine tool, solving for the actual position coordinates of the measuring point, and comparing them with the theoretical coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0011] The transformation steps involve defining the measurement reference at the origin of the machine tool and using a polynomial function to represent the position-related geometric error.

[0012] The identification and decoupling steps include identifying polynomial functions and identifying and decoupling errors based on their fundamental characteristics.

[0013] Preferably, in the model construction step, a machine tool coordinate system X is established at the machine tool's mechanical origin based on the machine tool's topology. M Y M Z M The X-axis is located on the machine tool bed, the Y-axis is located on the X-axis guide rail, the Z-axis is located on the Y-axis guide rail, and the C-axis is located on the Z-axis guide rail, controlling the rotational movement of the tool around the Z-axis. The A-axis is fixed to the C-axis and controls the rotational movement of the tool around the X-axis. X Y X Z X X Y YY Z Y X Z Y Z Z Z X C Y C Z C X A Y A Z A These represent coordinate systems that are fixed to the X, Y, Z, C, and A axes, respectively.

[0014] The position P of the tool tip in the A-axis coordinate system is:

[0015] P = [0 0 -L 1] T

[0016] The ideal position of the blade tip is:

[0017] P i =T(X)T(Y)T(Z)T(C)T(A)P

[0018]

[0019] Where L represents the total length of the tool; T(X), T(Y), and T(Z) represent the homogeneous transformation matrices of the rigid body moving along the X, Y, and Z directions, respectively; T(C) and T(A) represent the homogeneous transformation matrices of the rigid body rotating around the Z and X directions, respectively; and x, y, z, c, and a represent the motion quantities of the machine tool along the X, Y, Z, C, and A axes, respectively.

[0020] Including geometric errors, the actual motion matrices for each axis are obtained as follows:

[0021]

[0022]

[0023] The actual position of the blade tip is:

[0024] P e =E(X)E(Y)E(Z)E(C)E(A)P

[0025] The spatial error of the machine tool is:

[0026] ΔP=P e -P i

[0027] Where E(X), E(Y), and E(Z) represent the actual motion matrices of the rigid body moving along the X, Y, and Z directions, respectively; E(C) and E(A) represent the actual motion matrices of the rigid body rotating about the Z and X directions, respectively; E AX E BX E CXThese represent the rotational position related errors of the X-axis about the X, Y, and Z axes, respectively; E XX E YX E ZX E represents the translational position correlation error of the X-axis along the X, Y, and Z axes, respectively; AY E BY E CY E represents the rotational position related error of the Y-axis about the X, Y, and Z axes, respectively; XY E YY E ZY E represents the translational position correlation error of the Y-axis along the X, Y, and Z axes, respectively; AZ E BZ E CZ E represents the rotational position related errors of the Z-axis about the X, Y, and Z axes, respectively; XZ E YZ E ZZ E represents the translational position correlation error along the X, Y, and Z axes, respectively; AA E BA E CA These represent the rotational position related errors of axis A about the X, Y, and Z axes, respectively; E XA E YA E ZA These represent the translational positional errors of axis A along the X, Y, and Z axes, respectively; E AC E BC E CC These represent the rotational positional errors of the C-axis around the X, Y, and Z axes, respectively; E XC E YC E ZC E represents the translational position correlation error of the C-axis along the X, Y, and Z axes, respectively; A0Z E B0Z E represents the rotational position-independent error of the Z-axis about the X and Y axes, respectively; C0Y Indicates a position-independent error of the Y-axis rotation about the Z-axis; E A0C E B0C These represent the rotational position-independent errors of the C-axis about the X and Y axes, respectively; E X0C E Y0C E represents the translational position-independent error of the C-axis along the X and Y axes, respectively; B0A E C0A E represents the position-independent error of the A-axis about the Y and Z axes, respectively; Y0A E Z0A These represent translational position-independent errors of axis A along the X and Y axes, respectively.

[0028] Preferably, in the measurement step, the target mirror is installed on the end of the machine tool spindle, and the laser tracker is fixed on the machine tool worktable, with no less than four units. The spindle is controlled to move within the machine tool workspace. When the spindle moves to each measurement point generated according to the kinematic model, it stops for 10 seconds and records the distance information at this time. Then the machine tool continues to move until all measurement points have been measured.

[0029] Laser tracker position T i =(X i ,Y i Z i ) and the location of the measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum of these can be used to establish a minimization problem:

[0030]

[0031] Where s represents the unknowns, there are a total of 3n+4m; m represents the number of trackers; n represents the number of measuring points; X i Y i Z i These represent the X, Y, and Z axis position coordinates of the laser tracker, respectively; x j y j z j F(·) represents the X, Y, and Z axis position coordinates of the measuring point, respectively; F(·) represents the least squares function of ·; f(s) represents the residual function of s.

[0032] Perform a first-order Taylor expansion:

[0033] F(s+Δs)=(f(s)+J(s)Δs) 2

[0034] Where J(s) represents the Jacobian matrix of f(s) with respect to the unknown s; Δs represents the iteration increment.

[0035] Take the partial derivative with respect to Δs and set the derivative to 0:

[0036]

[0037] Δs=-(J(s) T J(s)) -1 J(s) T f(s)

[0038] The actual coordinates of the measuring point are iteratively solved and compared with the coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0039] Preferably, the polynomial function is:

[0040]

[0041] Where, k i represents the coefficient of the i-th order polynomial; n represents the order of the polynomial coefficients; r represents the independent variable of the polynomial.

[0042] In the transformation step, the position-related geometric errors in the geometric errors are represented by polynomials, and the position-independent geometric errors are represented by constants. These are then substituted into the kinematic model to obtain the prediction model for the spatial errors.

[0043] To find the parameters that minimize the deviation between the prediction model and the measured data, iteratively solve for the error vector k:

[0044]

[0045] Δk=-(J(k) T J(k)) -1 J(k) T f(k)

[0046] Where J(k) represents the Jacobian matrix of f(k) with respect to k; Δk represents the iteration increment; k represents the unknown error vector parameters of the model; F(k) represents the least squares function of k; f(k) represents the residual function of k; ΔP predict ΔP represents the spatial error of the measurement points calculated by the prediction model. measure This represents the actual spatial error of the measuring point.

[0047] Preferably, in the identification and decoupling step, the polynomial function is solved based on the Levenberg-Marquardt algorithm, and the error vector is iteratively solved:

[0048] Δk=-(J(k) T J(k)+λI) -1 J(k) T f(k)

[0049] Where Δk represents the iteration increment; J(k) represents the Jacobian matrix of f(k) with respect to k; f(k) represents the residual function of k; λ represents the damping coefficient; and I represents the identity matrix.

[0050] The identification and decoupling steps include:

[0051] Step S4.1: Define the initial value k0 of the error vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size;

[0052] Step S4.2: Calculate the iteration increment Δk;

[0053] Step S4.3: Determine F(k) i +Δk) and F(k) i The size of F(k) i +Δk)≤F(k i Let λ i+1 =λ i / 10,k i+1 =k i +Δk, if F(k) i +Δk)>F(k i Let λ i+1 =10λ i k i+1 =k i ;

[0054] Step S4.4: Determine the size of Δk. If Δk is less than the minimum iteration step size, then output k. i+1 If Δk is greater than or equal to the minimum iteration step size, then proceed to step S4.2.

[0055] Where F(·) represents the least squares function; i represents the ordinal number.

[0056] A system for modeling and identifying position-related geometric errors of a five-axis gantry milling machine tool, according to the present invention, includes:

[0057] The model building module imports and establishes the transmission relationship between geometric and spatial errors to construct the kinematic model of the machine tool.

[0058] The measurement module measures the distance information of the end position of the machine tool, calculates the actual position coordinates of the measuring point, and compares them with the theoretical coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0059] The conversion module defines the measurement reference at the origin of the machine tool and uses a polynomial function to represent the position-related geometric error.

[0060] Identify and decouple modules, identify polynomial functions, and identify and decouple errors based on the basic characteristics of errors.

[0061] Preferably, in the model building module, a machine tool coordinate system X is established at the machine tool's mechanical origin based on the machine tool's topology. M Y M Z M The X-axis is located on the machine tool bed, the Y-axis is located on the X-axis guide rail, the Z-axis is located on the Y-axis guide rail, and the C-axis is located on the Z-axis guide rail, controlling the rotational movement of the tool around the Z-axis. The A-axis is fixed to the C-axis and controls the rotational movement of the tool around the X-axis. X Y X Z X X Y YY Z Y X Z Y Z Z Z X C Y C Z C X A Y A Z A These represent coordinate systems that are fixed to the X, Y, Z, C, and A axes, respectively.

[0062] The position P of the tool tip in the A-axis coordinate system is:

[0063] P = [0 0 -L 1] T

[0064] The ideal position of the blade tip is:

[0065] P i =T(X)T(Y)T(Z)T(C)T(A)P

[0066]

[0067]

[0068] Where L represents the total length of the tool; T(X), T(Y), and T(Z) represent the homogeneous transformation matrices of the rigid body moving along the X, Y, and Z directions, respectively; T(C) and T(A) represent the homogeneous transformation matrices of the rigid body rotating around the Z and X directions, respectively; and x, y, z, c, and a represent the motion quantities of the machine tool along the X, Y, Z, C, and A axes, respectively.

[0069] Including geometric errors, the actual motion matrices for each axis are obtained as follows:

[0070]

[0071] The actual position of the blade tip is:

[0072] P e =E(X)E(Y)E(Z)E(C)E9A)P

[0073] The spatial error of the machine tool is:

[0074] ΔP=P e -P i

[0075] Where E(X), E(Y), and E(Z) represent the actual motion matrices of the rigid body moving along the X, Y, and Z directions, respectively; E(C) and E(A) represent the actual motion matrices of the rigid body rotating about the Z and X directions, respectively; E AX E BX E CXThese represent the rotational position related errors of the X-axis about the X, Y, and Z axes, respectively; E XX E YX E ZX E represents the translational position correlation error of the X-axis along the X, Y, and Z axes, respectively; AY E BY E CY E represents the rotational position related error of the Y-axis about the X, Y, and Z axes, respectively; XY E YY E ZY E represents the translational position correlation error of the Y-axis along the X, Y, and Z axes, respectively; AZ E BZ E CZ E represents the rotational position related errors of the Z-axis about the X, Y, and Z axes, respectively; XZ E YZ E ZZ E represents the translational position correlation error along the X, Y, and Z axes, respectively; AA E BA E CA These represent the rotational position related errors of axis A about the X, Y, and Z axes, respectively; E XA E YA E ZA These represent the translational positional errors of axis A along the X, Y, and Z axes, respectively; E AC E BC E CC These represent the rotational positional errors of the C-axis around the X, Y, and Z axes, respectively; E XC E YC E ZC E represents the translational position correlation error of the C-axis along the X, Y, and Z axes, respectively; A0Z E B0Z E represents the rotational position-independent error of the Z-axis about the X and Y axes, respectively; C0Y Indicates a position-independent error of the Y-axis rotation about the Z-axis; E A0C E B0C These represent the rotational position-independent errors of the C-axis about the X and Y axes, respectively; E X0C E Y0C E represents the translational position-independent error of the C-axis along the X and Y axes, respectively; B0A E C0A E represents the position-independent error of the A-axis about the Y and Z axes, respectively; Y0A E Z0A These represent translational position-independent errors of axis A along the X and Y axes, respectively.

[0076] Preferably, in the measurement module, the spindle is controlled to move within the machine tool workspace. When the spindle moves to each measurement point generated according to the kinematic model, it pauses for 10 seconds and records the distance information at this time. Then, the machine tool is controlled to continue moving until all measurement points have been measured.

[0077] Laser tracker position T i =(X i ,Y i Z i ) and the location of the measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum of these can be used to establish a minimization problem:

[0078]

[0079] Where s represents the unknowns, there are a total of 3n+4m; m represents the number of trackers; n represents the number of measuring points; X i Y i Z i These represent the X, Y, and Z axis position coordinates of the laser tracker, respectively; x j y j z j F(·) represents the X, Y, and Z axis position coordinates of the measuring point, respectively; F(·) represents the least squares function of ·; f(s) represents the residual function of s.

[0080] Perform a first-order Taylor expansion:

[0081] F(s+Δs)=(f(s)+J(s)Δs) 2

[0082] Where J(s) represents the Jacobian matrix of f(s) with respect to the unknown s; Δs represents the iteration increment.

[0083] Take the partial derivative with respect to Δs and set the derivative to 0:

[0084]

[0085] Δs=-(J(s) T J(s)) -1 J(s) T f(s

[0086] The actual coordinates of the measuring point are iteratively solved and compared with the coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0087] Preferably, the polynomial function is:

[0088]

[0089] Where, k i represents the coefficient of the i-th order polynomial; n represents the order of the polynomial coefficients; r represents the independent variable of the polynomial.

[0090] In the conversion module, position-related geometric errors are represented by polynomials, and position-independent geometric errors are represented by constants. These are then substituted into the kinematic model to obtain a prediction model for spatial errors.

[0091] To find the parameters that minimize the deviation between the prediction model and the measured data, iteratively solve for the error vector k:

[0092]

[0093] Δk=-(J(k) T J(k)) -1 J(k) T f(k)

[0094] Where J(k) represents the Jacobian matrix of f(k) with respect to k; Δk represents the iteration increment; k represents the unknown error vector parameters of the model; F(k) represents the least squares function of k; f(k) represents the residual function of k; ΔP predict ΔP represents the spatial error of the measurement points calculated by the prediction model. measure This represents the actual spatial error of the measuring point.

[0095] Preferably, in the identification and decoupling module, the polynomial function is solved based on the Levenberg-Marquardt algorithm, and the error vector is iteratively solved:

[0096] Δk=-(J(k) T J(k)+λI) -1 J(k) T f(k)

[0097] Where Δk represents the iteration increment; J(k) represents the Jacobian matrix of f(k) with respect to k; f(k) represents the residual function of k; λ represents the damping coefficient; and I represents the identity matrix.

[0098] The identification and decoupling module includes:

[0099] Module M4.1 defines the initial value k0 of the error vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size;

[0100] Module M4.2, calculate the iterative increment Δk;

[0101] Module M4.3, Determine F(k)i +Δk) and F(k) i The size of F(k) i +Δk)≤F(k i Let λ i+1 =λ i / 10,k i+1 =k i +Δk, if F(k) i +Δk)>F(k i Let λ i+1 =10λ i k i+1 =k i ;

[0102] Module M4.4: Determine the size of Δk. If Δk is less than the minimum iteration step size, then output k. i+1 If Δk is greater than or equal to the minimum iteration step size, then module M4.2 is triggered.

[0103] Where F(·) represents the least squares function; i represents the ordinal number.

[0104] Compared with the prior art, the present invention has the following beneficial effects:

[0105] 1. This invention uses a laser interferometer to directly measure the spatial position of the end of the machine tool, and establishes a prediction model for the spatial error of a five-axis gantry machine tool based on the homogeneous coordinate transformation method. It ensures high identification accuracy while using only a polygonal measurement method with distance information, thus shortening the measurement process and time.

[0106] 2. By defining an error measurement benchmark and using a polynomial function to fit the geometric error, this invention can simultaneously identify all geometric errors of the translational and rotary axes of a five-axis machine tool. In the error identification process, error decoupling is achieved, thereby improving the accuracy of error identification.

[0107] 3. In the identification process, the present invention uses the Levenberg-Marquardt algorithm for parameter identification, which solves the problem of singularity of the Jacobian matrix in the Gauss-Newton method. Based on the basic characteristics of error, the identification and decoupling of 41 geometric errors can be achieved in a single measurement, thereby improving the identification accuracy and efficiency. Attached Figure Description

[0108] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0109] Figure 1 A schematic diagram of the method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine.

[0110] Figure 2This is a schematic diagram of the topology of a five-axis gantry milling machine.

[0111] Figure 3 This is a schematic diagram illustrating the measurement principle of a laser interferometer tracker.

[0112] Figure 4 This is a schematic diagram showing the distribution of measuring points within the machine tool's workspace. Detailed Implementation

[0113] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0114] The present invention provides a method for modeling and identifying position-related geometric errors in a five-axis gantry milling machine. Figure 1 For example, including:

[0115] Step S1: Establish the kinematic model of the five-axis gantry milling machine based on the topology of the machine tool. Based on the homogeneous coordinate transformation method, use the homogeneous transformation matrix to introduce 41 geometric errors into the kinematic model and establish the transmission relationship with the spatial error of the five-axis gantry milling machine.

[0116] To establish the kinematic model of the machine tool, coordinate systems corresponding to each component are established based on the machine tool's topology. Specifically, a machine tool coordinate system is established at the machine tool's mechanical origin, and the local coordinate systems of each axis coincide with the machine tool coordinate system in their initial positions. For example... Figure 2 As shown, its X-axis is located on the bed and controls the forward and backward movement; the Y-axis is located on the X-axis guide rail and controls the left and right movement relative to the bed; the Z-axis is located on the Y-axis guide rail and controls the vertical movement relative to the bed; the C-axis is located on the Z-axis guide rail and controls the rotation of the tool around the Z-axis; the A-axis is fixed to the C-axis and controls the rotation of the tool around the X-axis.

[0117] Among them, X M Y M Z M X represents the machine tool coordinate system fixed to the machine tool bed. X Y X Z X X Y Y Y Z Y X Z Y Z Z Z X C Y C Z C X A Y A ZA These represent coordinate systems that are fixed to the X, Y, Z, C, and A axes, respectively.

[0118] According to the homogeneous coordinate transformation theory, the position of the tool tip in the A-axis coordinate system can be represented as P = [0 0 -L 1]. T Let L be the total length of the tool. Then the ideal position of the tool tip is:

[0119] P i =T(X)T(Y)T(Z)T(C)T(A)P

[0120] Where T(X), T(Y), and T(Z) represent the homogeneous transformation matrices for the rigid body's translation along the X, Y, and Z directions, respectively, and T(C) and T(A) represent the homogeneous transformation matrices for the rigid body's rotation about the Z and X directions, respectively. When the motion quantities of each axis of the machine tool are x, y, z, c, and a, the matrices are as follows:

[0121]

[0122] The five-axis gantry milling machine has a total of 41 geometric errors, including 30 position-related geometric errors and 11 position-independent geometric errors.

[0123] Geometric errors are represented by the letter E and its following subscript letters. For position-related geometric errors, the first letter of the subscript indicates the error type: X / Y / Z represents translational error along the X / Y / Z axis, and A / B / C represents rotational error about the X / Y / Z axis. The second letter of the subscript indicates the corresponding axis. For example, E CX This represents the rotational error of the X-axis around the Z-axis.

[0124] For position-independent geometric errors, the first letter of the subscript indicates the error type, the second letter is the number 0, and the third letter indicates the corresponding axis. For example, E X0C This represents the translational error of the C-axis along the X-axis.

[0125] Considering the influence of geometric errors on the end-effector position of the machine tool, the actual motion matrices E(X), E(Y), E(Z), E(C), and E(A) of each axis are as follows:

[0126]

[0127] The actual position of the knife tip can then be represented as:

[0128] P e =E(X)E(Y)E(Z)E(C)E(A)P

[0129] Therefore, the spatial error of a five-axis machine tool is expressed as:

[0130] ΔP=P e -Pi

[0131] Step S2: Use a laser interferometer to directly measure the position of the end of the machine tool, measure the distance information from the four trackers to the target mirror, and solve the actual position coordinates of the target mirror based on the principle of polygonal method.

[0132] Specifically, by measuring the distances from multiple laser interferometer trackers (base stations) to the target mirror at the end of the machine tool, the spatial coordinates of the target mirror can be determined. This measurement method is called polygonal measurement. Figure 3 As shown, during the measurement process, the target mirror is installed on the end of the machine tool spindle, and the laser tracker is fixed on the machine tool worktable. The number of trackers is generally no less than four. The spindle is controlled to move within the machine tool workspace. When the spindle moves to each measurement point, it stops for 10 seconds to obtain a stable interferometric distance measurement value. The distance information from the tracker to the measurement point is recorded at this time. Then the machine tool continues to move until all measurement points have been measured.

[0133] During the tracking process, the tracker position T i =(X i ,Y i Z i ) and measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum. Based on the above relationship, a minimization problem can be established:

[0134]

[0135] Where the unknowns s represent the positions of the tracker and the measuring points, as well as the dead path length; F(s) is the least squares function; and f(s) is the residual function. Assuming there are m trackers and n measuring points, there are a total of (3n+4m) unknowns. A first-order Taylor expansion of the function yields:

[0136] F(s+Δs)=(f(s)+J(s)Δs) 2

[0137] Where Δs is the iteration increment, and J(s) is the Jacobian matrix of f(s) with respect to the unknown coefficient vector s.

[0138] Taking the partial derivative of the above equation with respect to Δs and setting the derivative to 0, we get:

[0139]

[0140] Therefore:

[0141] Δs=-(J(s)T J(s)) -1 J(s) T f(s)

[0142] The above formula can be used to calculate the iteration step size of the unknown vector at each step, iteratively solve the actual coordinates of the measuring point position, compare them with the machine tool command coordinates, that is, the theoretical coordinates obtained when the kinematic model is generated, and then obtain the actual spatial error of the measuring point.

[0143] Step S3: Use a polynomial function to represent the position-related geometric error, transform the problem of geometric error identification into the problem of solving the function coefficients, and define the measurement benchmark of the position-related geometric error at the origin of the coordinate system to achieve decoupling of various errors.

[0144] In the error model, position-dependent geometric errors and position-independent geometric errors are coupled together, affecting the error identification results. To address this issue, based on the general procedures for measuring machine tool translational and rotary axes, geometric error measurement is typically defined relative to the measurement starting point, and the error at the starting position is generally set to zero. Therefore, the machine tool origin position is set as the reference for error measurement, and all position-dependent geometric errors are assumed to be zero when X, Y, Z, A, C = 0. This method achieves error decoupling.

[0145] Specifically, since the machine tool position-related geometric error varies with the position of each axis, it can be described as a polynomial function related to the position of each axis:

[0146]

[0147] Where, k i Let represent the coefficients of the i-th order polynomial, and r represent the independent variable of the polynomial, obtained by normalizing the positions of each axis. All 30 position-related geometric errors are represented by polynomials, and the 11 position-independent geometric errors are represented by constants. Substituting these into the machine tool spatial error model (i.e., kinematic model) established in step S1, a spatial error prediction model can be obtained, using an n-th order polynomial. The number of unknown parameters in this model is 30n+41.

[0148] By measuring the actual spatial error data of a five-axis machine tool using a laser interferometer tracker, the geometric error identification problem is transformed into an optimization problem, namely, solving for the optimal parameters to minimize the deviation between the predicted model and the measured data.

[0149]

[0150] Where, the unknown quantity k is the unknown parameter of the model, F(k) is the least squares function, f(k) is the residual function, and ΔP predict The spatial error ΔP is the prediction error calculated for each measuring point using the prediction model.measure The actual spatial error of each measuring point is calculated using the measurement method in step S2. The Gauss-Newton method is used to solve for this error, and the iterative formula for the error vector k is:

[0151] Δk=-(J(k) T J(k)) -1 J(k) T f(k)

[0152] Where Δk is the iteration increment, and J(k) is the Jacobian matrix of f(k) with respect to the unknown coefficient vector k.

[0153] But J(k) T J(k) may be a singular or ill-conditioned matrix, causing the algorithm to fail to converge stably. Therefore, the Levenberg-Marquardt algorithm is used to improve the solution method. By fitting the measurement point data based on the Levenberg-Marquardt algorithm, error parameters can be obtained, thereby enabling the identification of geometric errors.

[0154] Step S4: Identify the polynomial coefficients based on the Levenberg-Marquardt algorithm, identify each geometric error, define the measurement benchmark of position-related geometric errors at the origin of the coordinate system, and realize the identification and decoupling of errors based on the basic characteristics of errors.

[0155] In more preferred examples, in order to identify geometric errors, it is necessary to obtain the spatial errors of a large number of measuring points in the machine tool workspace. After establishing a prediction model, the unknown parameters in the prediction model are obtained by function fitting based on the actual measurement results, thereby identifying the errors.

[0156] If all position-related geometric errors are represented by third-order polynomials, there are a total of 131 unknown parameters. Each measurement point contains error information in three directions, requiring at least 44 measurement points. Furthermore, to identify the geometric errors across the entire machine tool workspace, the distribution of measurement points should be as wide as possible. Random point cloud distributions can cover more information with the same number of points and are more representative of the generality of the data. Therefore, the positions of 100 measurement points are randomly generated within the machine tool workspace, and the distribution of these measurement points within the workspace is as follows: Figure 4 As shown.

[0157] The Levenberg–Marquardt algorithm, based on the Gauss-Newton method, introduces a damping coefficient λ to solve the problem of inverting singular matrices, exhibiting good convergence speed, stability, and applicability. The iterative formula is updated as follows:

[0158] Δk=-(J(k) T J(k)+λI) -1 J(k)T f(k)

[0159] Where I represents the identity matrix.

[0160] The solution process includes:

[0161] Step S4.1: Given the initial value k0 of the unknown coefficient vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size;

[0162] Step S4.2: Calculate the iteration step size Δk;

[0163] Step S4.3, if F(k) i +Δk) <F(k i This indicates that the iteration direction is correct. Increasing the step size accelerates the convergence speed. Let λ i+1 =λ i / 10,k i+1 =k i +Δk;

[0164] Step S4.4, if F(k) i +Δk)>F(k i This indicates that the iteration error has increased. Therefore, the iteration step size should be reduced and the iteration repeated. Let λ... i+1 =10λ i k i+1 =k i ;

[0165] Step S4.5: If Δk is less than the minimum iteration step size, then output k. i+1 Otherwise, return to step two.

[0166] The present invention also provides a system for modeling and identifying position-related geometric errors of a five-axis gantry milling machine. The system can be implemented by executing the process steps of the method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine. That is, those skilled in the art can understand the method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine as a preferred embodiment of the system.

[0167] A system for modeling and identifying position-related geometric errors of a five-axis gantry milling machine tool, according to the present invention, includes:

[0168] The model building module imports and establishes the transmission relationship between geometric and spatial errors to construct the kinematic model of the machine tool.

[0169] The measurement module measures the distance information of the end position of the machine tool, calculates the actual position coordinates of the measuring point, and compares them with the theoretical coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0170] The conversion module defines the measurement reference at the origin of the machine tool and uses a polynomial function to represent the position-related geometric error.

[0171] Identify and decouple modules, identify polynomial functions, and identify and decouple errors based on the basic characteristics of errors.

[0172] In more preferred embodiments, the model building module establishes a machine tool coordinate system X at the machine tool's mechanical origin based on the machine tool's topology. M Y M Z M The X-axis is located on the machine tool bed, the Y-axis is located on the X-axis guide rail, the Z-axis is located on the Y-axis guide rail, and the C-axis is located on the Z-axis guide rail, controlling the rotational movement of the tool around the Z-axis. The A-axis is fixed to the C-axis and controls the rotational movement of the tool around the X-axis. X Y X Z X X Y Y Y Z Y X Z Y Z Z Z X C Y C Z C X A Y A Z A These represent coordinate systems that are fixed to the X, Y, Z, C, and A axes, respectively.

[0173] The position P of the tool tip in the A-axis coordinate system is:

[0174] P = [0 0 -L 1] T

[0175] The ideal position of the blade tip is:

[0176] P i =T(X)T(Y)T(Z)T(C)T(A)P

[0177]

[0178] Where L represents the total length of the tool; T(X), T(Y), and T(Z) represent the homogeneous transformation matrices of the rigid body moving along the X, Y, and Z directions, respectively; T(C) and T(A) represent the homogeneous transformation matrices of the rigid body rotating around the Z and X directions, respectively; and x, y, z, c, and a represent the motion quantities of the machine tool along the X, Y, Z, C, and A axes, respectively.

[0179] Including geometric errors, the actual motion matrices for each axis are obtained as follows:

[0180]

[0181]

[0182] The actual position of the blade tip is:

[0183] P e =E(X)E(Y)E(Z)E(C)E(A)P

[0184] The spatial error of the machine tool is:

[0185] ΔP=P e -P i

[0186] Where E(X), E(Y), and E(Z) represent the actual motion matrices of the rigid body moving along the X, Y, and Z directions, respectively; E(C) and E(A) represent the actual motion matrices of the rigid body rotating about the Z and X directions, respectively; E AX E BX E CX These represent the rotational position related errors of the X-axis about the X, Y, and Z axes, respectively; E XX E YX E ZX E represents the translational position correlation error of the X-axis along the X, Y, and Z axes, respectively; AY E BY E CY E represents the rotational position related error of the Y-axis about the X, Y, and Z axes, respectively; XY E YY E ZY E represents the translational position correlation error of the Y-axis along the X, Y, and Z axes, respectively; AZ E BZ E CZ E represents the rotational position related errors of the Z-axis about the X, Y, and Z axes, respectively; XZ E YZ E ZZ E represents the translational position correlation error along the X, Y, and Z axes, respectively; AA E BA E CA These represent the rotational position related errors of axis A about the X, Y, and Z axes, respectively; E XA E YA E ZA These represent the translational positional errors of axis A along the X, Y, and Z axes, respectively; E AC E BC E CC These represent the rotational positional errors of the C-axis around the X, Y, and Z axes, respectively; E XC E YC E ZC E represents the translational position correlation error of the C-axis along the X, Y, and Z axes, respectively; A0Z EB0Z E represents the rotational position-independent error of the Z-axis about the X and Y axes, respectively; C0Y Indicates a position-independent error of the Y-axis rotation about the Z-axis; E A0C E B0C These represent the rotational position-independent errors of the C-axis about the X and Y axes, respectively; E X0C E Y0C E represents the translational position-independent error of the C-axis along the X and Y axes, respectively; B0A E C0A E represents the position-independent error of the A-axis about the Y and Z axes, respectively; Y0A E Z0A These represent translational position-independent errors of axis A along the X and Y axes, respectively.

[0187] In more preferred embodiments, the measurement module controls the spindle to move within the machine tool workspace. When the spindle moves to each measurement point generated according to the kinematic model, it pauses for 10 seconds and records the distance information at this time. Then, the machine tool is controlled to continue moving until all measurement points have been measured.

[0188] Laser tracker position T i =(X i ,Y i Z i ) and the location of the measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum of these can be used to establish a minimization problem:

[0189]

[0190] Where s represents the unknowns, there are a total of 3n+4m; m represents the number of trackers; n represents the number of measuring points; X i Y i Z i These represent the X, Y, and Z axis position coordinates of the laser tracker, respectively; x j y j z j F(·) represents the X, Y, and Z axis position coordinates of the measuring point, respectively; F(·) represents the least squares function of ·; f(s) represents the residual function of s.

[0191] Perform a first-order Taylor expansion:

[0192] F(s+Δs)=(f(s)+J(s)Δs) 2

[0193] Where J(s) represents the Jacobian matrix of f(s) with respect to the unknown s; Δs represents the iteration increment.

[0194] Take the partial derivative with respect to Δs and set the derivative to 0:

[0195]

[0196] Δs=-(J(s) T J(s)) -1 J(s) T f(s)

[0197] The actual coordinates of the measuring point are iteratively solved and compared with the coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

[0198] In more preferred embodiments, the polynomial function is:

[0199]

[0200] Where, k i represents the coefficient of the i-th order polynomial; n represents the order of the polynomial coefficients; r represents the independent variable of the polynomial.

[0201] In the conversion module, position-related geometric errors are represented by polynomials, and position-independent geometric errors are represented by constants. These are then substituted into the kinematic model to obtain a prediction model for spatial errors.

[0202] To find the parameters that minimize the deviation between the prediction model and the measured data, iteratively solve for the error vector k:

[0203]

[0204] Δk=-(J(k) T J(k)) -1 J(k) T f(k)

[0205] Where J(k) represents the Jacobian matrix of f(k) with respect to k; Δk represents the iteration increment; k represents the unknown error vector parameters of the model; F(k) represents the least squares function of k; f(k) represents the residual function of k; ΔP predict ΔP represents the spatial error of the measurement points calculated by the prediction model. measure This represents the actual spatial error of the measuring point.

[0206] In more preferred embodiments, the identification and decoupling module solves for the polynomial function based on the Levenberg-Marquardt algorithm, and iteratively solves for the error vector:

[0207] Δk=-(J(k) TJ(k)+λI) -1 J(k) T f(k)

[0208] Where Δk represents the iteration increment; J(k) represents the Jacobian matrix of f(k) with respect to k; f(k) represents the residual function of k; λ represents the damping coefficient; and I represents the identity matrix.

[0209] The identification and decoupling module includes:

[0210] Module M4.1 defines the initial value k0 of the error vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size;

[0211] Module M4.2, calculate the iterative increment Δk;

[0212] Module M4.3, Determine F(k) i +Δk) and F(k) i The size of F(k) i +Δk)≤F(k i Let λ i+1 =λ i / 10,k i+1 =k i +Δk, if F(k) i +Δk)>F(k i Let λ i+1 =10λ i k i+1 =k i ;

[0213] Module M4.4: Determine the size of Δk. If Δk is less than the minimum iteration step size, then output k. i+1 If Δk is greater than or equal to the minimum iteration step size, then module M4.2 is triggered.

[0214] Where F(·) represents the least squares function; i represents the ordinal number.

[0215] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function as logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0216] In the description of this application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0217] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for modeling and identifying position-related geometric errors in a five-axis gantry milling machine, characterized in that, include: The model building steps include introducing and establishing the transmission relationship between geometric errors and spatial errors, and constructing the kinematic model of the machine tool. The measurement steps involve measuring the distance information at the end of the machine tool, solving for the actual position coordinates of the measuring point, and comparing them with the theoretical coordinates of the measuring point in the kinematic model to obtain the actual spatial error. The transformation steps involve defining the measurement reference at the origin of the machine tool and using a polynomial function to represent the position-related geometric error. The identification and decoupling steps include identifying polynomial functions and identifying and decoupling errors based on their fundamental characteristics.

2. The method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine according to claim 1, characterized in that, In the model construction step, a machine tool coordinate system X is established at the machine tool mechanical origin based on the machine tool's topology. M Y M Z M The X-axis is located on the machine tool bed, the Y-axis is located on the X-axis guide rail, the Z-axis is located on the Y-axis guide rail, and the C-axis is located on the Z-axis guide rail, controlling the rotational movement of the tool around the Z-axis. The A-axis is fixed to the C-axis and controls the rotational movement of the tool around the X-axis. X Y X Z X X Y Y Y Z Y X Z Y Z Z Z X C Y C Z C X A Y A Z A These represent coordinate systems fixed to the X, Y, Z, C, and A axes, respectively. The position P of the tool tip in the A-axis coordinate system is: P=[0 0 -L 1] T The ideal position of the blade tip is: P i =T(X)T(Y)T(Z)T(C)T(A)P Where L represents the total length of the tool; T(X), T(Y), and T(Z) represent the homogeneous transformation matrices of the rigid body as it moves along the X, Y, and Z directions, respectively. T(C) and T(A) represent the homogeneous transformation matrices of the rigid body rotating about the Z and X directions, respectively; x, y, z, c, and a represent the motion quantities of the X, Y, Z, C, and A axes of the machine tool, respectively; Including geometric errors, the actual motion matrices for each axis are obtained as follows: The actual position of the blade tip is: P e =E(X)E(Y)E(Z)E(C)E(A)P The spatial error of the machine tool is: ΔP=P e -P i Where E(X), E(Y), and E(Z) represent the actual motion matrices of the rigid body moving along the X, Y, and Z directions, respectively; and E(C) and E(A) represent the actual motion matrices of the rigid body rotating around the Z and X directions, respectively. E AX E BX E CX These represent the rotational positional errors of the X-axis around the X, Y, and Z axes, respectively. E XX E YX E ZX These represent the translational positional errors of the X-axis along the X, Y, and Z axes, respectively. E AY E BY E CY These represent the rotational positional errors of the Y-axis around the X, Y, and Z axes, respectively. E XY E YY E ZY These represent the translational positional errors of the Y-axis along the X, Y, and Z axes, respectively. E AZ E BZ E CZ These represent the rotational positional errors of the Z-axis around the X, Y, and Z axes, respectively. E XZ E YZ E ZZ These represent the translational positional errors of the Z-axis along the X, Y, and Z axes, respectively. E AA E BA E CA These represent the rotational positional errors of axis A around the X, Y, and Z axes, respectively. E XA E YA E ZA These represent the translational positional errors of axis A along the X, Y, and Z axes, respectively. E AC E BC E CC These represent the rotational positional errors of the C-axis around the X, Y, and Z axes, respectively. E XC E YC E ZC These represent the translational positional errors of the C-axis along the X, Y, and Z axes, respectively. E A0Z E B0Z These represent rotational position-independent errors of the Z-axis about the X and Y axes, respectively. E C0Y This indicates that the rotational position error of the Y-axis about the Z-axis is independent; E A0C E B0C These represent position-independent errors of the C-axis around the X and Y axes, respectively. E X0C E Y0C These represent translational position-independent errors of the C-axis along the X and Y axes, respectively. E B0A E C0A These represent the position-independent errors of the A-axis around the Y and Z axes, respectively. E Y0A E Z0A These represent translational position-independent errors of axis A along the X and Y axes, respectively.

3. The method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine according to claim 1, characterized in that, In the measurement steps, the target mirror is installed on the end of the machine tool spindle, and the laser tracker is fixed on the machine tool worktable. There are no fewer than four laser trackers. The spindle is controlled to move within the machine tool workspace. When the spindle moves to each measurement point generated according to the kinematic model, it stops for 10 seconds and records the distance information at this time. Then the machine tool continues to move until all measurement points have been measured. Laser tracker position T i =(X i ,Y i Z i ) and the location of the measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum of these can be used to establish a minimization problem: Where s represents the unknowns, there are a total of 3n+4m; m represents the number of trackers; n represents the number of measurement points; X i Y i Z i These represent the X, Y, and Z axis position coordinates of the laser tracker, respectively. x j y j z j These represent the X, Y, and Z axis position coordinates of the measuring point, respectively. F(·) denotes the least squares function of ·; f(s) represents the residual function of s; Perform a first-order Taylor expansion: F(s+Δs)=(f(s)+J(s)Δs) 2 Where J(s) represents the Jacobian matrix of f(s) with respect to the unknown s; Δs represents the iteration increment; Take the partial derivative with respect to Δs and set the derivative to 0: Δs=-(J(s) T J(s)) -1 J(s) T f(s) The actual coordinates of the measuring point are iteratively solved and compared with the coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

4. The method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine according to claim 1, characterized in that, The polynomial function is: Where, k i Denotes the coefficients of the i-th order polynomial; n represents the order of the polynomial coefficients; r represents the independent variable of the polynomial; In the transformation step, the position-related geometric errors in the geometric errors are represented by polynomials, and the position-independent geometric errors are represented by constants. These are then substituted into the kinematic model to obtain the prediction model for the spatial errors. To find the parameters that minimize the deviation between the prediction model and the measured data, iteratively solve for the error vector k: Δk=-(J(k) T J(k) -1 J(k) T f(k Where J(k) represents the Jacobian matrix of f(k) with respect to k; Δk represents the iteration increment; k represents the unknown error vector parameters of the model; F(k) represents the least squares function of k; f(k) represents the residual function of k; ΔP predict This represents the spatial error of the measurement points calculated by the prediction model; ΔP measure This represents the actual spatial error of the measuring point.

5. The method for modeling and identifying position-related geometric errors of a five-axis gantry milling machine according to claim 1, characterized in that, In the identification and decoupling step, the polynomial function is solved based on the Levenberg-Marquardt algorithm, and the error vector is iteratively solved: Δk=-(J(k) T J(k)+λI) -1 J(k) T f(k) Where Δk represents the iteration increment; J(k) represents the Jacobian matrix of f(k) with respect to k; f(k) represents the residual function of k; λ represents the damping coefficient; I represents the identity matrix; The identification and decoupling steps include: Step S4.1: Define the initial value k0 of the error vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size; Step S4.2: Calculate the iteration increment Δk; Step S4.3: Determine F(k) i +Δk) and F(k) i The size of F(k) i +Δk)≤F(k i Let λ i+1 =λ i / 10,k i+1 =k i +Δk, if F(k) i +Δk)>F(k i Let λ i+1 =10λ i k i+1 =k i ; Step S4.4: Determine the size of Δk. If Δk is less than the minimum iteration step size, then output k. i+1 If Δk is greater than or equal to the minimum iteration step size, then proceed to step S4.

2. Where F(·) denotes the least squares function; i represents the ordinal number.

6. A system for modeling and identifying position-related geometric errors of a five-axis gantry milling machine, characterized in that, include: The model building module imports and establishes the transmission relationship between geometric and spatial errors to construct the kinematic model of the machine tool. The measurement module measures the distance information of the end position of the machine tool, calculates the actual position coordinates of the measuring point, and compares them with the theoretical coordinates of the measuring point in the kinematic model to obtain the actual spatial error. The conversion module defines the measurement reference at the origin of the machine tool and uses a polynomial function to represent the position-related geometric error. Identify and decouple modules, identify polynomial functions, and identify and decouple errors based on the basic characteristics of errors.

7. The five-axis gantry milling machine tool position-related geometric error modeling and identification system according to claim 6, characterized in that, In the model construction module, a machine tool coordinate system X is established at the machine tool's mechanical origin based on the machine tool's topology. M Y M Z M The X-axis is located on the machine tool bed, the Y-axis is located on the X-axis guide rail, the Z-axis is located on the Y-axis guide rail, and the C-axis is located on the Z-axis guide rail, controlling the rotational movement of the tool around the Z-axis. The A-axis is fixed to the C-axis and controls the rotational movement of the tool around the X-axis. X Y X Z X X Y Y Y Z Y X Z Y Z Z Z X C Y C Z C X A Y A Z A These represent coordinate systems fixed to the X, Y, Z, C, and A axes, respectively. The position P of the tool tip in the A-axis coordinate system is: P=[0 0 -L 1] T The ideal position of the blade tip is: P i =T(X)T(Y)T(Z)T(C)T(A)P Where L represents the total length of the tool; T(X), T(Y), and T9Z) represent the homogeneous transformation matrices of the rigid body as it moves along the X, Y, and Z directions, respectively. T(C) and T(A) represent the homogeneous transformation matrices of the rigid body rotating about the Z and X directions, respectively; x, y, z, c, and a represent the motion quantities of the X, Y, Z, C, and A axes of the machine tool, respectively; Including geometric errors, the actual motion matrices for each axis are obtained as follows: The actual position of the blade tip is: P e =E(X)E(Y)E(Z)E(C)E(A)P The spatial error of the machine tool is: ΔP=P e -P i Where E(X), E(Y), and E(Z) represent the actual motion matrices of the rigid body moving along the X, Y, and Z directions, respectively; and E(C) and E(A) represent the actual motion matrices of the rigid body rotating around the Z and X directions, respectively. E AX E BX E CX These represent the rotational positional errors of the X-axis around the X, Y, and Z axes, respectively. E XX E YX E ZX These represent the translational positional errors of the X-axis along the X, Y, and Z axes, respectively. E AY E BY E CY These represent the rotational positional errors of the Y-axis around the X, Y, and Z axes, respectively. E XY E YY E ZY These represent the translational positional errors of the Y-axis along the X, Y, and Z axes, respectively. E AZ E BZ E CZ These represent the rotational positional errors of the Z-axis around the X, Y, and Z axes, respectively. E XZ E YZ E ZZ These represent the translational positional errors of the Z-axis along the X, Y, and Z axes, respectively. E AA E BA E CA These represent the rotational positional errors of axis A around the X, Y, and Z axes, respectively. E XA E YA E ZA These represent the translational positional errors of axis A along the X, Y, and Z axes, respectively. E AC E BC E CC These represent the rotational positional errors of the C-axis around the X, Y, and Z axes, respectively. E XC E YC E ZC These represent the translational positional errors of the C-axis along the X, Y, and Z axes, respectively. E A0Z E B0Z These represent rotational position-independent errors of the Z-axis about the X and Y axes, respectively. E C0Y This indicates that the rotational position error of the Y-axis about the Z-axis is independent; E A0C E B0C These represent position-independent errors of the C-axis around the X and Y axes, respectively. E X0C E Y0C These represent translational position-independent errors of the C-axis along the X and Y axes, respectively. E B0A E C0A These represent the position-independent errors of the A-axis around the Y and Z axes, respectively. E Y0A E Z0A These represent translational position-independent errors of axis A along the X and Y axes, respectively.

8. The five-axis gantry milling machine tool position-related geometric error modeling and identification system according to claim 6, characterized in that, In the measurement module, the spindle is controlled to move within the machine tool workspace. When the spindle moves to each measurement point generated according to the kinematic model, it stops for 10 seconds and records the distance information at this time. Then, the machine tool is controlled to continue moving until all measurement points have been measured. Laser tracker position T i =(X i ,Y i Z i ) and the location of the measuring point P j =(x j ,y j ,z j The distance between them is the relative ranging value ΔL of the laser tracker. ij Dead diameter length L of interferometry 0i The sum of these can be used to establish a minimization problem: Where s represents the unknowns, there are a total of 3n+4m; m represents the number of trackers; n represents the number of measurement points; X i Y i Z i These represent the X, Y, and Z axis position coordinates of the laser tracker, respectively. x j y j z j These represent the X, Y, and Z axis position coordinates of the measuring point, respectively. F(·) denotes the least squares function of ·; f(s) represents the residual function of s; Perform a first-order Taylor expansion: F(s+Δs)=(f(s)+J(s)Δs) 2 Where J(s) represents the Jacobian matrix of f(s) with respect to the unknown s; Δs represents the iteration increment; Take the partial derivative with respect to Δs and set the derivative to 0: Δs=-(J(s) T J(s)) -1 J(s) T f(s) The actual coordinates of the measuring point are iteratively solved and compared with the coordinates of the measuring point in the kinematic model to obtain the actual spatial error.

9. The five-axis gantry milling machine tool position-related geometric error modeling and identification system according to claim 6, characterized in that, The polynomial function is: Where, k i Denotes the coefficients of the i-th order polynomial; n represents the order of the polynomial coefficients; r represents the independent variable of the polynomial; In the conversion module, position-related geometric errors are represented by polynomials, and position-independent geometric errors are represented by constants. These are then substituted into the kinematic model to obtain a prediction model for spatial errors. To find the parameters that minimize the deviation between the prediction model and the measured data, iteratively solve for the error vector k: Δk=-(J(k) T J(k)) -1 J(k) T f(k) Where J(k) represents the Jacobian matrix of f(k) with respect to k; Δk represents the iteration increment; k represents the unknown error vector parameters of the model; F(k) represents the least squares function of k; f(k) represents the residual function of k; ΔP predict This represents the spatial error of the measurement points calculated by the prediction model; ΔP measure This represents the actual spatial error of the measuring point.

10. The five-axis gantry milling machine tool position-related geometric error modeling and identification system according to claim 6, characterized in that, In the identification and decoupling module, the polynomial function is solved based on the Levenberg-Marquardt algorithm, and the error vector is iteratively solved. Δk=-(J(k) T J(k)+λI) -1 J(k) T f(k) Where Δk represents the iteration increment; J(k) represents the Jacobian matrix of f(k) with respect to k; f(k) represents the residual function of k; λ represents the damping coefficient; I represents the identity matrix; The identification and decoupling module includes: Module M4.1 defines the initial value k0 of the error vector, the initial damping factor, the maximum number of iterations λ0, and the minimum iteration step size; Module M4.2, calculate the iterative increment Δk; Module M4.3, Determine F(k) i +Δk) and F(k) i The size of F(k) i +Δk)≤F(k i Let λ i+1 =λ i / 10,k i+1 =k i +Δk, if F(k) i +Δk)>F(k i Let λ i+1 =10λ i k i+1 =k i ; Module M4.4: Determine the size of Δk. If Δk is less than the minimum iteration step size, then output k. i+1 If Δk is greater than or equal to the minimum iteration step size, then module M4.2 is triggered. Where F(·) denotes the least squares function; i represents the ordinal number.

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