Global sensitivity analysis method of geometric errors in five-axis turning-milling machining center

Abstract

The present invention relates to the technical field of geometric error analysis of a five-axis turning-milling compound machining center, and discloses a method for global sensitivity analysis of geometric errors of a five-axis turning-milling compound machining center, comprising the following steps: modeling the machining center as an open multi-rigid body system, determining the relationship between the bodies by adopting a low-order body array; determining the position of each coordinate system; establishing a kinematic model of the five-axis turning-milling compound machining center; determining machine tool error terms; establishing a geometric error model in a milling mode; establishing a geometric error model in a turning mode; and performing a global sensitivity analysis on the geometric errors of the machining center. The present invention improves the efficiency of identifying the sensitivity of error terms in various directions, reduces the computational cost of a global sensitivity metric based on variance, can provide theoretical guidance for engineers to purposefully design and assemble machine tools, reduce geometric errors and improve accuracy, can compensate for highly sensitive geometric errors according to global sensitivity metric coefficients, and provide effective support for error control.

Description

Technical Field

[0001] The invention relates to a method for analyzing geometric errors of a five-axis turning-milling compound machining center, in particular to a horizontal five-axis turning-milling compound machining center, and belongs to the technical field of machine tool processing error analysis (modeling, precision design). Background Art

[0002] The horizontal five-axis milling machining center includes the translation axes X-axis, Y-axis and Z-axis, as well as the rotation axes C-axis and B-axis. It has been popularized in aerospace, automobile manufacturing, mold manufacturing and other fields. The horizontal five-axis milling machining center is widely used in processing that requires high precision, complex surface processing and high efficiency. With the development of technology, high precision has become an inevitable trend in the development of high-end CNC equipment such as horizontal five-axis milling machining centers. The accuracy level of a machine tool is one of the important indicators for evaluating its performance, which directly affects the quality and dimensional accuracy of the processed parts.

[0003] There are many reasons for the deviation of machine tool processing accuracy, mainly including the geometric error of machine tool components, thermal deformation of machine tools caused by temperature changes, mechanical deformation errors generated during cutting, and control errors of servo systems. Among all these factors, geometric error and thermal error are considered to be the main sources of errors in high-end CNC equipment. Geometric error has the characteristics of strong systematicity, good repeatability, long-term stability and easy measurement. Improving machine tool processing accuracy by identifying and compensating geometric errors has become an economical and effective strategy. The horizontal five-axis turning and milling compound machining center is different from traditional machine tools in structure and process implementation. As an important means in the design stage, the analysis of geometric accuracy errors is also difficult to achieve using traditional methods.

[0004] Therefore, it is extremely urgent to find a method that can quickly and accurately detect and identify the geometric errors of horizontal five-axis turning and milling machining centers. Summary of the invention

[0005] Aiming at the deficiencies in geometric error analysis of existing horizontal five-axis turning-milling machining centers, the present invention proposes a global sensitivity analysis method that can quickly and accurately detect and identify the geometric errors of five-axis turning-milling machining centers, which is particularly suitable for horizontal five-axis turning-milling machining centers.

[0006] The geometric error global sensitivity analysis method of the five-axis turning-milling compound machining center of the present invention comprises the following steps.

[0007] Step 1: Model the machining center as an open multi-rigid body system, including tools, five axes and workpieces. The five axes are the translation axes X-axis, Y-axis and Z-axis and the rotation axes C-axis and B-axis. The relationship between the bodies is determined by using a low-order body array.

[0008] The low-order body array is shown in Table 1 below:

[0009] Table 1 Low-order bulk array

[0010]

[0011] Step 2: Determine the position of each coordinate system;

[0012] The directions of each coordinate system are consistent with O-xyz; the machine bed coordinate system is O M , the coordinate system of the Z axis is O Z Distance O along the Z axis M Z Z At, Y-axis coordinate system O Y Distance O along the Y axis Z Y Y At, X axis O X The distance O along the X axis of the coordinate system Y For X X O B is the intersection of the parallel lines of the X-axis and the Y-axis, and the workpiece coordinate system and tool coordinate system are O W and O T .

[0013] Step 3: Establish the kinematic model of the five-axis turning and milling machining center; the specific process of this step is:

[0014] The homogeneous transformation matrix of the C-axis motion relative to the machine tool bed is expressed as :

[0015] ,

[0016] ;

[0017] In the formula The angle of rotation of the C axis;

[0018] The homogeneous transformation matrix of the motion of the B axis relative to the X axis is expressed as :

[0019] ;

[0020] In the formula is the rotation angle of the B axis;

[0021] The homogeneous transformation matrix of the workpiece motion relative to the C axis is expressed as :

[0022] ;

[0023] is the identity matrix;

[0024] The homogeneous transformation matrix of the Z-axis motion relative to the bed is expressed as :

[0025] ;

[0026] Where z is the Z-axis moving distance;

[0027] The homogeneous transformation matrix of the Y-axis relative to the Z-axis is expressed as :

[0028] ;

[0029] Where y is the moving distance of Y axis;

[0030] The homogeneous transformation matrix of the X-axis relative to the Y-axis is expressed as :

[0031] ;

[0032] Where x is the moving distance of X axis;

[0033] The homogeneous transformation matrix of the tool motion relative to the B axis is expressed as :

[0034] ;

[0035] The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in milling mode is expressed as:

[0036] ;

[0037] In turning mode, the C axis rotates, and the milling function of the B axis is locked. The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in turning mode is expressed as:

[0038] .

[0039] Step 4: Determine the machine tool error term;

[0040] Each axis of the five-axis milling machining center (translational axis X-axis, Y-axis and Z-axis and rotary axis C-axis and B-axis) has six degrees of freedom in space. Each degree of freedom forms a position-related error in space. The position-related error is divided into position error and angle error, which are respectively expressed as and Indicates that the subscript i represents each axis, and the subscript j represents each direction. There are 41 geometric errors and 30 position-related errors in total;

[0041] The machine tool error terms are shown in Table 2 below:

[0042] Table 2 Machine tool error terms

[0043]

[0044] Step 5: Establish the geometric error model in milling mode; the specific process of this step is:

[0045] Transformation matrix from each coordinate system O to the tool coordinate system Ot It is expressed as:

[0046] ,

[0047] Where: , , , , R is a 3×3 dimensional rotation matrix, P is a 3×1 dimensional position vector;

[0048] The differential motion matrix is ​​established as:

[0049] ,

[0050] Where: DJ represents the rate of change of the Jacobian matrix, and S(P) is the antisymmetric matrix of the position vector P.

[0051] Differential changes occur in each degree of freedom of the axis of each coordinate system, so the differential vector of each axis is expressed as:

[0052] ,

[0053] Then the change of the differential vector of the tool coordinate system T caused by the change of each coordinate system O is calculated as:

[0054] ,

[0055] The verticality error Syz of the Y axis is understood as a constant angle error along the x direction, the verticality error Sxy of the X axis reflects the rotation error of the X axis around the z direction, and Sxz represents the rotation error of the X axis around the y direction;

[0056] ,

[0057] ,

[0058] ,

[0059] It is regarded as a constant linear error in the x-direction of the B axis; for the parts belonging to the workpiece kinematic chain, the geometric error component is negative when the error is modeled; therefore, the error vectors of the B and C axes are expressed as:

[0060] ,

[0061] ,

[0062] The differential motion matrix is ​​used to obtain the influence of the geometric error of each axis on the tool error. The differential motion matrices of the C axis, Z axis, Y axis, X axis and B axis relative to the tool are:

[0063] ,

[0064] ,

[0065] ,

[0066] ,

[0067] ,

[0068] Where: is the rotation angle of the C axis, is the rotation angle of the B axis, x, y, z are the moving distances of the X axis, Y axis and Z axis respectively;

[0069] The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system in milling mode:

[0070] ,

[0071] ,

[0072] ,

[0073] ,

[0074] ,

[0075] ,

[0076] , , , , The tool errors caused by C-axis, Z-axis, Y-axis, X-axis and B-axis in milling mode are respectively: is the total milling error;

[0077] Convert the total error in the tool coordinate system to the workpiece coordinate system:

[0078] ,

[0079] in: represents the error matrix of the milling tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing milling including geometric errors, represents the ideal homogeneous transformation matrix for milling, is the error matrix in the milling tool coordinate system;

[0080] Each It is expressed as:

[0081] ,

[0082] The corresponding tool error matrix is ​​expressed as:

[0083] ,

[0084] Assume the position errors of the milling tool in the workpiece coordinate system are px, py and pz;

[0085] The initial position of the tool position in the tool coordinate system is ;

[0086] .

[0087] Step 6: Establish the geometric error model in turning mode; the specific process of this step is:

[0088] The differential motion matrix is ​​as follows:

[0089] , ,

[0090] ,

[0091] ,

[0092] The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system under turning mode:

[0093] ,

[0094] ,

[0095] ,

[0096] ,

[0097] ,

[0098] in: , , , The tool errors caused by C-axis, Z-axis, Y-axis and X-axis in turning mode are respectively: is the total turning error;

[0099] Error matrix converted to workpiece coordinate system:

[0100] ,

[0101] in: represents the error matrix of the turning tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing turning including geometric errors, Represents the ideal homogeneous transformation matrix for turning is the error matrix in the turning tool coordinate system;

[0102] Assume that the position errors of the turning tool in the workpiece coordinate system are px2, py2 and pz2:

[0103] .

[0104] Step 7: Perform global sensitivity analysis on the machining center geometric error; the specific process is as follows:

[0105] (1) Construct two input matrices U and V:

[0106] ,

[0107] U and V are sampling matrices of input variables;

[0108] U is the input sample, with a size of N×n, where N is the number of samples and n is the number of variables. Each row represents a sample, that is, a value in the range of values. V is similar, but for sensitivity analysis, it is generated by randomly replacing some variables.

[0109] (2) represents the complete set of all error terms in the model, is one of the error terms, is to remove the error term The complement of

[0110] according to and The relationship with x is determined by U A and U B , V is determined by V A and V B , U A A new matrix consisting of variables corresponding to the subset A extracted from the input matrix U, U B V is a new matrix composed of variables corresponding to the complement set B extracted from the input matrix U. A and VB Similarly, that is:

[0111] ,

[0112] ,

[0113] ,

[0114] ;

[0115] (3) Synthesize the following two matrices: W A = [U A , V B ] and W B = [V A , U B ],but and for:

[0116] ,

[0117] ,

[0118] In the above formula, V xA is the error term The variance, V xB for The variance of , f is the error function, f0 is the mean of the error function for all error terms;

[0119] (4) The total variance V is calculated using the following formula: is the error term range:

[0120] ,

[0121] ;

[0122] (5) So the error term The variance-based sensitivity coefficient is:

[0123] ,

[0124] ,

[0125] is the error term x A The first-order sensitivity coefficient, For x A Total effect sensitivity coefficient;

[0126] (6) The derivative-based global sensitivity coefficient is calculated using the following equation: :

[0127] ,

[0128] ,

[0129] is the error term x A The partial derivative of the relative error function f, is the error term x A The derivative sensitivity coefficient of x k represents the kth sample point of this item;

[0130] (7) Calculate the derivative-variance mixed global sensitivity metric coefficient using the following equation: :

[0131] ,

[0132] The size of the calculated global sensitivity metric coefficient represents an indicator of the degree of influence of each geometric error term on the spatial error of the machine tool.

[0133] The present invention establishes an error model of a horizontal five-axis turning and milling machining center based on the differential kinematics method, which can solve the problem that the high-order terms of the calculation results are too long and difficult to analyze due to too many error terms. The hybrid global sensitivity analysis improves the sensitivity identification efficiency of error terms in all directions when facing multi-axis and multi-geometric error terms, and reduces the calculation cost of the global sensitivity measurement based on variance. In the machine tool design stage, it can provide engineers with theoretical guidance for the purposeful design and assembly of machine tools, reduce geometric errors and improve accuracy. In terms of machine tool geometric error compensation, high-sensitivity geometric errors can be compensated according to the global sensitivity measurement coefficient, providing effective support for error control. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 It is a flow chart of the sensitivity analysis method of the five-axis turning-milling compound machining center of the present invention.

[0135] Figure 2 It is a structural topological diagram of the multi-body system of the five-axis turning-milling compound machining center established in the present invention.

[0136] Figure 3 It is a coordinate system set in the present invention and a position relationship diagram of the coordinate system in space.

[0137] Figure 4 is a histogram of the global sensitivity analysis of milling px.

[0138] Figure 5 is a histogram of the global sensitivity analysis of millingpy.

[0139] Figure 6 is a histogram of the global sensitivity analysis of milling pz.

[0140] Figure 7 It is a histogram of global sensitivity analysis of turning position error px2.

[0141] Figure 8 It is a histogram of global sensitivity analysis of turning position error py2.

[0142] Fig. 9 It is a histogram of global sensitivity analysis of turning position error pz2. DETAILED DESCRIPTION

[0143] The global sensitivity analysis method for geometric errors of a five-axis milling-turning machining center of the present invention identifies key geometric error terms in milling and turning of a horizontal five-axis milling-turning machining center. The specific process steps are as follows: Figure 1 As shown in the figure, according to the multi-body system theory, each rigid body of the horizontal five-axis turning-milling machining center is regarded as a topological structure, and the kinematic models of the horizontal five-axis turning-milling machining center in milling and turning modes are established respectively. After establishing the differential motion matrix of each axis and determining the error vector of each axis, the geometric error model of the horizontal five-axis turning-milling machining center in the workpiece coordinate system is established. On the basis of the variance-based Sobol global sensitivity analysis method, the hybrid global sensitivity measure based on derivative is added to calculate the influence of the geometric error terms of each axis in each direction on the accuracy. Finally, the error terms that have a significant impact on the machining error of the machining center are determined, which provides a theoretical basis for improving the machining accuracy of the machining center.

[0144] The following combination Figure 1 The specific steps of the geometric error global sensitivity analysis method of the five-axis turning-milling compound machining center of the present invention are described in detail.

[0145] Step 1: Model the machining center as an open multi-rigid body system, including tools, machine tool axes, workpieces, etc., and determine the relationship between the bodies by using low-order body arrays.

[0146] Each component of the machining center can be regarded as composed of multiple rigid objects. The machining center is modeled as an open multi-rigid body system, including tools, machine tool axes (X axis, Y axis, Z axis, C axis and B axis) and workpieces. The relationship between the bodies is determined by using the low-order body array given in Table 1. The topological structure of the multi-body system of the machining center is established by the multi-body system theory as follows: Figure 2 shown.

[0147] Table 1 Low-order bulk array

[0148]

[0149] Step 2: Determine the position of each coordinate system, such as Figure 3 shown.

[0150] The directions of the coordinate systems are consistent with O-xyz. The machine bed coordinate system is O M , the coordinate system of the Z axis is O Z Distance O along the Z axis M Z Z At, Y-axis coordinate system O Y Distance O along the Y axis Z Y Y At, X axis O X The distance O along the X axis of the coordinate system Y For X X O B is the intersection of the parallel lines of the X-axis and the Y-axis, and the workpiece coordinate system and tool coordinate system are O W and O T .

[0151] Step 3: Establish the kinematic model of the horizontal five-axis turning-milling machining center.

[0152] For the movement of the C axis relative to the machine bed, the movement of the B axis relative to the X axis, the movement of the workpiece relative to the C axis, the movement of the Z axis relative to the bed, the movement of the Y axis relative to the Z axis, the movement of the X axis relative to the Y axis, and the movement of the tool relative to the B axis, see Figure 2 .

[0153] The homogeneous transformation matrix of the C-axis motion relative to the machine tool bed can be expressed as :

[0154] ,

[0155] ,

[0156] In the formula The angle of rotation of the C axis.

[0157] The homogeneous transformation matrix of the motion of the B axis relative to the X axis can be expressed as :

[0158] ,

[0159] In the formula The rotation angle of the B axis.

[0160] The homogeneous transformation matrix of the workpiece motion relative to the C axis is expressed as :

[0161] ;

[0162] is the identity matrix.

[0163] The homogeneous transformation matrix of the Z-axis motion relative to the bed is expressed as :

[0164] ;

[0165] Where z is the Z-axis moving distance.

[0166] The homogeneous transformation matrix of the Y-axis relative to the Z-axis is expressed as :

[0167] ;

[0168] Where y is the moving distance on the Y axis.

[0169] The homogeneous transformation matrix of the X-axis relative to the Y-axis is expressed as :

[0170] ;

[0171] Where x is the moving distance of the X-axis.

[0172] The homogeneous transformation matrix of the tool motion relative to the B axis is expressed as :

[0173] ;

[0174] is the identity matrix.

[0175] The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in milling mode can be expressed as:

[0176] .

[0177] In turning mode, the C axis rotates, and the milling function of the spindle B axis is locked. The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in turning mode can be expressed as:

[0178] .

[0179] Step 4: Determine the machine tool error term.

[0180] The horizontal five-axis milling and turning machining center includes the translation axes X, Y, and Z, and the rotation axes C and B. Each axis has six degrees of freedom in space, and each degree of freedom forms position-related errors in space. Position-related errors are divided into position errors and angle errors, which are respectively expressed as and The subscript i represents each axis, and the subscript j represents each direction. The machining center has 41 geometric errors and 30 position-related errors. The determined machine tool error items are shown in Table 2.

[0181] Table 2 Machine tool error terms

[0182]

[0183] Step 5: Establish the geometric error model in the milling mode of the machining center.

[0184] Step 5: Establish the geometric error model in milling mode;

[0185] Transformation matrix from each coordinate system O to the tool coordinate system Ot It is expressed as:

[0186] ,

[0187] In the formula , , , , R is a 3×3 dimensional rotation matrix, and P is a 3×1 dimensional position vector.

[0188] The differential motion matrix is ​​established as:

[0189] ,

[0190] DJ represents the rate of change of the Jacobian matrix, and S(P) is the antisymmetric matrix of the position vector P.

[0191] Differential changes occur in each degree of freedom of the axis of each coordinate system, so the differential vector of each axis is expressed as:

[0192] ,

[0193] Then the change of the differential vector of the tool coordinate system T caused by the change of each coordinate system O is calculated as:

[0194] ,

[0195] The verticality error Syz of the Y axis is understood as a constant angle error along the x direction, the verticality error Sxy of the X axis reflects the rotation error of the X axis around the z direction, and Sxz represents the rotation error of the X axis around the y direction;

[0196] ,

[0197] ,

[0198] .

[0199] It can be regarded as a constant linear error in the x-direction of the B axis. For parts belonging to the workpiece kinematic chain, the geometric error component is negative when the error is modeled. Therefore, the error vectors of the B and C axes are expressed as:

[0200] ,

[0201] .

[0202] The differential motion matrix can be used to find the influence of the geometric error of each axis on the tool error. The differential motion matrix of each axis relative to the tool is:

[0203] ,

[0204] ,

[0205] ,

[0206] ,

[0207] .

[0208] In the formula is the rotation angle of the C axis, is the rotation angle of the B axis, and x, y, and z are the moving distances of the X axis, Y axis, and Z axis respectively.

[0209] The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system in milling mode:

[0210] ,

[0211] ,

[0212] ,

[0213] ,

[0214] ,

[0215] .

[0216] , , , , The tool errors caused by C-axis, Z-axis, Y-axis, X-axis and B-axis in milling mode are respectively: is the total milling error.

[0217] Convert the total error in the tool coordinate system to the workpiece coordinate system:

[0218] ,

[0219] in: represents the error matrix of the milling tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing milling including geometric errors, represents the ideal homogeneous transformation matrix for milling, is the error matrix in the milling tool coordinate system.

[0220] Each It can be expressed as:

[0221] ,

[0222] The corresponding tool error matrix can be expressed as:

[0223] .

[0224] Assume the position errors of the milling tool in the workpiece coordinate system are px, py and pz;

[0225] The initial position of the tool position in the tool coordinate system is ;

[0226] .

[0227] Step 6: Establish the geometric error model in turning mode.

[0228] The differential motion matrix is ​​as follows:

[0229] , ,

[0230] ,

[0231] .

[0232] The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system under turning mode:

[0233] ,

[0234] ,

[0235] ,

[0236] ,

[0237] .

[0238] , , , The tool errors caused by C-axis, Z-axis, Y-axis and X-axis in turning mode are respectively: is the total turning error.

[0239] Error matrix converted to workpiece coordinate system:

[0240] .

[0241] in: represents the error matrix of the turning tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing turning including geometric errors, Represents the ideal homogeneous transformation matrix for turning is the error matrix in the turning tool coordinate system.

[0242] Assume that the position errors of the turning tool in the workpiece coordinate system are px2, py2 and pz2, and the error matrix is ​​the machine tool geometric error:

[0243] .

[0244] Step 7: Perform global sensitivity analysis on the machining center geometric error.

[0245] The specific process is as follows:

[0246] (1) Construct two input matrices U and V:

[0247] ,

[0248] U and V are the sampling matrices of the input variables.

[0249] U is the input sample, with a size of N×n, where N is the number of samples and n is the number of variables. Each row represents a sample, that is, a value within the range of values. V is similar, but for sensitivity analysis, it is generated by randomly replacing some variables.

[0250] (2) represents the complete set of all error terms in the model, is one of the error terms, is to remove the error term The complement of

[0251] according to and The relationship with x is determined by U A and U B, V is determined by V A and V B , U A A new matrix consisting of variables corresponding to the subset A extracted from the input matrix U, U B V is a new matrix composed of variables corresponding to the complement set B extracted from the input matrix U. A and V B Similarly, that is:

[0252] ,

[0253] ,

[0254] ,

[0255] ;

[0256] (3) Synthesize the following two matrices: W A = [U A , V B ] and W B = [V A , U B ],but and for:

[0257] ,

[0258] ,

[0259] In the above formula, V xA is the error term The variance, V xB for The variance of , f is the error function, f0 is the mean of the error function for all error terms;

[0260] (4) The total variance V can be calculated using the following formula: is the error term range, which corresponds to the error term range. The present invention takes ±0.015 for linear error, ±0.02 for angular error, and ±0.01 for nonlinear error:

[0261] ,

[0262] .

[0263] (5) So the error term The variance-based sensitivity coefficient is:

[0264] ,

[0265] ,

[0266] is the error term x A The first-order sensitivity coefficient, For x A Total effect sensitivity coefficient.

[0267] (6) The derivative-based global sensitivity coefficient is calculated using the following equation: :

[0268] ,

[0269] ,

[0270] is the error term x A The partial derivative of the relative error function f, is the error term x A The derivative sensitivity coefficient of x k represents the kth sample point of this item;

[0271] (7) Calculate the derivative-variance mixed global sensitivity metric coefficient using the following equation: :

[0272] .

[0273] The error terms that have a greater impact on the geometric error of the machine tool are determined based on the global sensitivity measurement coefficient. Figure 4 , Figure 5 and Figure 6 Global sensitivity analysis was performed for milling px, py and pz respectively. Figure 7 , Figure 8 and Fig. 9 The global sensitivity analysis is performed on turning px2, py2, and pz2 respectively, and the histogram is more intuitive. It is generally believed that several items whose global sensitivity measurement coefficient accounts for ≥ 90% of the total coefficient can be considered as sensitive items.

[0274] In the case of milling, for the X direction, error terms 4, 7, 8, 12, 13, 15, 19, 27, 28, 29, 30, 31, 37, 38, 40, 41 are sensitive items; for the Y direction, error terms 4, 7, 8, 12, 13, 15, 19, 31, 37, 38, 40, 41 are sensitive items; for the Z direction, error terms 7, 8, 15, 19, 27, 28, 31, 40, 41 are sensitive items.

[0275] In the case of turning, for the X direction, error terms 19, 27, and 28 are sensitive items; for the Y direction, error terms 14, 19, 20, 27, and 28 are sensitive items; for the Z direction, error terms 7, 8, 15, 21, and 31 are sensitive items.

Claims

1. A global sensitivity analysis method for geometric errors of a five-axis turning-milling machining center, characterized in that: The following steps are involved: Step 1: Model the machining center as an open multi-rigid body system, including tools, five axes and workpieces. The five axes are the translation axes X-axis, Y-axis and Z-axis and the rotation axes C-axis and B-axis. The relationship between the bodies is determined by using a low-order body array. Step 2: Determine the position of each coordinate system; The directions of each coordinate system are consistent with O-xyz; the machine bed coordinate system is O M , the coordinate system of the Z axis is O Z Distance O along the Z axis M Z Z At, Y-axis coordinate system O Y Distance O along the Y axis Z Y Y At, X axis O X The distance O along the X axis of the coordinate system Y For X X O B is the intersection of the parallel lines of the X-axis and the Y-axis, and the workpiece coordinate system and tool coordinate system are O W and O T ; Step 3: Establish the kinematic model of the five-axis turning and milling machining center; Step 4: Determine the machine tool error term; Each axis of the five-axis milling machining center has six degrees of freedom in space. Each degree of freedom forms a position-related error in space. The position-related error is divided into position error and angle error, which are expressed by δ ij and ε ij Indicates that the subscript i represents each axis, and the subscript j represents each direction. There are 41 geometric errors and 30 position-related errors in total; Step 5: Establish the geometric error model in milling mode; Step 6: Establish the geometric error model in turning mode; Step 7: Perform global sensitivity analysis on the machining center geometric error; The specific process of establishing the kinematic model of the five-axis turning-milling machining center in step 3 is: The homogeneous transformation matrix of the C-axis motion relative to the machine tool bed is expressed as T1 2 : Where γ is the rotation angle of the C axis; The homogeneous transformation matrix of the motion of the B axis relative to the X axis is expressed as Where β is the rotation angle of the B axis; The homogeneous transformation matrix of the workpiece motion relative to the C axis is expressed as I is the identity matrix; The homogeneous transformation matrix of the Z-axis motion relative to the bed is expressed as Where z is the Z-axis moving distance; The homogeneous transformation matrix of the Y-axis relative to the Z-axis is expressed as Where y is the moving distance of Y axis; The homogeneous transformation matrix of the X-axis relative to the Y-axis is expressed as Where x is the moving distance of X axis; The homogeneous transformation matrix of the tool motion relative to the B axis is expressed as The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in milling mode is expressed as: In turning mode, the C axis rotates, and the milling function of the B axis is locked. The homogeneous transformation matrix from the workpiece coordinate system to the tool coordinate system in turning mode is expressed as: The specific process of establishing the geometric error model in the milling mode in step 5 is: Transformation matrix from each coordinate system O to the tool coordinate system Ot It is expressed as: Where: n = [n x ,n y ,n z ] T , o=[o x ,o y ,o z ] T , a=[a x ,a y ,a z ] T , p=[p x ,p y ,p z ] T , R is a 3×3 dimensional rotation matrix, P is a 3×1 dimensional position vector; The differential motion matrix is ​​established as: Where: DJ represents the rate of change of the Jacobian matrix, S(P) is the antisymmetric matrix of the position vector P; Differential changes occur in each degree of freedom of the axis of each coordinate system, so the differential vector of each axis is expressed as: DE O =[δ xo d yo d zo e xo e yo e zo ] T , Then the change of the differential vector of the tool coordinate system T caused by the change of each coordinate system O is calculated as: The verticality error Syz of the Y axis is understood as a constant angle error along the x direction, the verticality error Sxy of the X axis reflects the rotation error of the X axis around the z direction, and Sxz represents the rotation error of the X axis around the y direction; DE X =[δ xx d yx d zx e xx (e yx +S xz (e) zx +S xy )] T , DE Y =[δ xy d yy d zy (e xy +S yz )e yy e zy ] T , DE Z =[δ xz d yz d zz e xz e yz e zz ] T , o bx is regarded as a constant linear error in the x-direction of the B axis; for parts belonging to the workpiece kinematic chain, the geometric error component is negative when the error is modeled; therefore, the error vectors of the B and C axes are expressed as: DE C =[-(δ xc +o cx )-(d yc +o cy )-d zc -(e xc +S cy )-(e yc +S cx )-e zc ] T , DE B =[(δ xb +o bx )d yb (d zb +o bz (e) xb +S bx )e yb (e zb +S bz )] T , The differential motion matrix is ​​used to obtain the influence of the geometric error of each axis on the tool error. The differential motion matrices of the C axis, Z axis, Y axis, X axis and B axis relative to the tool are: Where: γ is the rotation angle of the C axis, β is the rotation angle of the B axis; x, y, and z are the moving distances of the X-axis, Y-axis, and Z-axis respectively; The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system in milling mode: The tool errors caused by C-axis, Z-axis, Y-axis, X-axis and B-axis in milling mode are respectively: is the total milling error; Convert the total error in the tool coordinate system to the workpiece coordinate system: in: represents the error matrix of the milling tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing milling including geometric errors, represents the ideal homogeneous transformation matrix for milling, ΔT T is the error matrix in the milling tool coordinate system; Each It is expressed as: The corresponding tool error matrix is ​​expressed as: Assume the position errors of the milling tool in the workpiece coordinate system are px, py and pz; The initial position of the tool position in the tool coordinate system is P t =(0,0,0,1) T ; 2. The geometric error global sensitivity analysis method of the five-axis turning-milling machining center according to claim 1 is characterized in that: The specific process of step 6 to establish the geometric error model in turning mode is: The differential motion matrix is ​​as follows: The error vector of each axis is used to calculate the geometric error and total error of each axis in the tool coordinate system under turning mode: in: The tool errors caused by C-axis, Z-axis, Y-axis and X-axis in turning mode are respectively: is the total turning error; Error matrix converted to workpiece coordinate system: in: represents the error matrix of the turning tool relative to the workpiece coordinate system, The true homogeneous transformation matrix representing turning including geometric errors, Denotes the ideal homogeneous transformation matrix ΔT for turning T(2) is the error matrix in the turning tool coordinate system; Assume that the position errors of the turning tool in the workpiece coordinate system are px2, py2 and pz2:

3. The geometric error global sensitivity analysis method of the five-axis turning-milling machining center according to claim 1 is characterized in that: The specific process of the step 7 for global sensitivity analysis of the machining center geometric error is as follows: (1) Construct two input matrices U and V: U and V are sampling matrices of input variables; U is the input sample, with a size of N×n, where N is the number of samples and n is the number of variables. Each row represents a sample, that is, a value in the range of values. V is similar, but for sensitivity analysis, it is generated by randomly replacing some variables. (2) x = {x1, x2, x3, ···x n } represents the full set of all error terms in the model, x A is one of the error terms, x B is to remove the error term x A The complement of According to x A and x B The relationship with x is determined by U A and U B , V is determined by V A and V B , U A A new matrix consisting of variables corresponding to the subset A extracted from the input matrix U, U B V is a new matrix composed of variables corresponding to the complement set B extracted from the input matrix U. A and V B Similarly, that is: (3) Synthesize the following two matrices: W A =[U A , V B ] and W B =[V A , U B ],but and for: In the above formula, V xA is the error term x A The variance, V xB For x B The variance of ; f is the error function, f0 is the mean of the error function for all error terms; (4) The total variance V is calculated using the following formula: n is the error term range: (5) So the error term x A The variance-based sensitivity coefficient is: S xA is the error term x A The first-order sensitivity coefficient, For x A Total effect sensitivity coefficient; (6) Calculate the derivative-based global sensitivity coefficient using the following equation: is the error term x A The partial derivative of the relative error function f, is the error term x A The derivative sensitivity coefficient, x k Represents the error term x A The kth sample point; (7) Calculate the derivative-variance mixed global sensitivity metric coefficient using the following equation The size of the calculated global sensitivity metric coefficient represents an indicator of the degree of influence of each geometric error term on the spatial error of the machine tool.

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