A quantitative evaluation method and system for geometric accuracy robustness of multi-axis CNC machine tools

Abstract

The present invention belongs to the field of precision design of numerical control machine tools, and in particular, relates to a method and system for quantitatively evaluating the robustness of geometric accuracy of multi-axis numerical control machine tools, the method comprising the following steps: providing a multi-axis numerical control machine tool; obtaining the positioning accuracy measurement value of the geometric error of the multi-axis numerical control machine tool; correcting the positioning accuracy measurement value, thereby obtaining the repeat positioning accuracy value; generating a geometric error accuracy curve through the repeat positioning accuracy value; obtaining a first robustness quantitative index using the geometric error accuracy curve; determining the spatial position vector of the multi-axis numerical control machine tool; generating a spatial error accuracy curve using the spatial position vector in combination with the geometric error accuracy curve; obtaining a second robustness quantitative index using the spatial error accuracy curve. The method of the present invention can determine the repeat positioning accuracy of the geometric error uncertainty correction of the multi-axis numerical control machine tool, thereby obtaining a smooth accuracy curve, and accurately quantifying the geometric accuracy robustness in the quasi-static accuracy index of the multi-axis numerical control machine tool.

Description

Technical Field

[0001] The invention belongs to the field of numerical control machine tool precision design, and in particular relates to a method and system for quantitatively evaluating the geometric precision robustness of a multi-axis numerical control machine tool. Background Art

[0002] Geometric accuracy is an important indicator of the quasi-static performance of machine tools and a direct quantitative parameter of machine tool geometric errors. Among the error sources that affect machine tool accuracy, geometric errors account for about 40% of the total machine tool error. Geometric errors mainly come from component design and manufacturing deviations, assembly deviations, and operating wear. Reasonable accuracy distribution and error compensation can effectively ensure that the geometric accuracy of machine tools fluctuates within the allowable range. However, long-term operation of machine tools under variable working conditions and load conditions is bound to cause the geometric error to increase, which in turn brings about geometric accuracy robustness defects. Therefore, it is extremely important to construct a CNC machine tool robustness evaluation method that considers geometric accuracy for CNC machine tool accuracy maintenance and robustness maintenance.

[0003] At present, the geometric accuracy evaluation of machine tools mainly focuses on the accuracy control of assembly structure, as well as the accuracy detection and error compensation during the use of machine tools. Xi'an Jiaotong University disclosed in patent CN108073074B "An assembly quality control method based on the motion characteristics of machine tool feed system", and constructed a machine tool feed system assembly quality control scheme with the transmission error and friction torque motion characteristics of the machine tool feed system as the control criteria. The grating scale signal of the feed system, the rear encoder signal of the motor and the two-phase current signal of the motor were used to comprehensively evaluate the assembly quality control effect. Shanghai Unis Industrial Services Co., Ltd. disclosed in patent CN108873807B "A three-axis CNC machine tool accuracy evaluation method considering processing stability", based on the assumption that each measurement error in adjacent measurement time nodes changes uniformly, and constructed a linear function accuracy evaluation method for the processing stability of three-axis CNC machine tools. Its essence is the same as the research paper "Quantitative evaluation and error sensitivity analysis of CNC machine tool accuracy retention" published by Wang Yongqing, Wu Jiakun, Liu Kuo and others in the Journal of Mechanical Engineering. Beijing University of Technology disclosed in patent CN104965483B "A method for optimizing the machining accuracy retention of multi-axis CNC machine tools based on robust design". Through reliability analysis and sensitivity analysis methods under multiple failure modes, a method for optimizing the machining accuracy retention of machine tools was constructed. The above results have achieved remarkable results in the time domain analysis of precision allocation and geometric accuracy. However, due to the uncertainty of precision fluctuations, the precision curve represented by the Newton interpolation curve has sharp points at the nodes and is not smooth, and the non-differentiable characteristics at the nodes are easily buried in the non-smoothness of geometric precision fluctuations. In order to solve the above constraints, the present invention proposes a method and system for quantitative evaluation of the robustness of geometric accuracy of multi-axis CNC machine tools. Summary of the invention

[0004] In view of the defects in the prior art, on the one hand, the present invention provides a method for quantitatively evaluating the robustness of geometric accuracy of a multi-axis CNC machine tool, comprising the following steps: providing a multi-axis CNC machine tool; obtaining a positioning accuracy measurement value of the geometric error of the multi-axis CNC machine tool; correcting the positioning accuracy measurement value to obtain a repeated positioning accuracy value; generating a geometric error accuracy curve through the repeated positioning accuracy value; using the geometric error accuracy curve to obtain a first robustness quantitative index, the first robustness quantitative index representing a robustness quantitative index of the positioning accuracy of the geometric error; determining the spatial position vector of the multi-axis CNC machine tool; using the spatial position vector and combining the geometric error accuracy curve to generate a spatial error accuracy curve; using the spatial error accuracy curve to obtain a second robustness quantitative index, the second robustness quantitative index representing a robustness quantitative index of the positioning accuracy of the spatial error. The method of the present invention can determine the repeated positioning accuracy of the geometric error uncertainty correction of the multi-axis CNC machine tool, thereby obtaining a smooth accuracy curve, and accurately quantifying the robustness of geometric accuracy in the quasi-static accuracy index of the multi-axis CNC machine tool.

[0005] Optionally, the method of obtaining the positioning accuracy measurement value of the geometric error of the multi-axis CNC machine tool includes the following steps: defining geometric errors in combination with structural characteristics of the multi-axis CNC machine tool, wherein the geometric errors include linear error, straightness error, angular error and inter-axis error; and obtaining the positioning accuracy measurement value of each of the geometric errors.

[0006] Further optionally, the linear error includes δ x (x),δ y (y) and δ z (z); the straightness error includes δ x (y),δ y (x),δ x (z), δ y (z), δ z (y) and δ z (x); the angular error includes ε x (x), ε y (x), ε z (x), ε x (y), ε y (y), ε z (y), ε x (z), ε y (z) and ε z (z); the inter-axial error includes S xy , S yz and S xz .

[0007] Optionally, the correcting the positioning accuracy measurement value to obtain a repeat positioning accuracy value comprises the following steps: obtaining a volume error of the multi-axis CNC machine tool, wherein the volume error satisfies the following formula:

[0008] V(e)=∑ i V i +∑ i ∑ i<j V ij +V 1,2,…,n ,

[0009] Wherein, V(e) represents the total variance of the geometric error of the multi-axis CNC machine tool; ∑ i V i Represents the sum of the first-order variance of the output due to the influence of a single geometric error, ∑ i ∑ i<j V ij +V 1,2,…,n represents the sum of second-order and higher-order variances due to the interaction between multiple geometric errors;

[0010] The sensitivity of a single geometric error is obtained using the volume error, and the sensitivity satisfies the following formula:

[0011]

[0012] S i represents sensitivity, wherein the sensitivity represents the influence of spatial errors at different positions on geometric errors;

[0013] The standard uncertainty of a single geometric error is obtained using the positioning accuracy measurement value, and the standard uncertainty satisfies the following formula:

[0014]

[0015]

[0016] Among them, x i Represents a single geometric error; X ij Indicates that the single geometric error is x i The jth positioning accuracy measurement value of and represent the average one-way position deviations for positive approach and negative approach, respectively;

[0017] The sensitivity is combined with the standard uncertainty to generate a standard uncertainty component, which satisfies the following formula:

[0018] U i =S i ×U i (x i),

[0019] Among them U i (x i ) indicates that the single geometric error is x i The standard uncertainty, S i Denotes the geometric error as x i Corresponding sensitivity;

[0020] The positioning accuracy measurement value is corrected by the component satisfying the standard uncertainty to obtain the positioning accuracy correction value of the single geometric error, and the positioning accuracy correction value satisfies the following formula:

[0021]

[0022]

[0023] Among them, U i ↑andU i ↓ represents the one-way standard uncertainty component of a certain point approaching in the positive direction and approaching in the negative direction respectively;

[0024] Combined with the positioning accuracy correction value of the single geometric error, the repeat positioning accuracy value of the single geometric error is obtained.

[0025] Optionally, the generating of the geometric error accuracy curve by the repeated positioning accuracy value comprises the following steps: setting a time control node, wherein the time control node comprises t 0 ,t 1 ,t 2 and t 3 ;

[0026] A geometric error accuracy curve is generated in combination with the repeated positioning accuracy value corresponding to the time control node, and the geometric error accuracy curve satisfies the following formula:

[0027]

[0028] Among them, d 0 d 1 d 2 and d 3 Respectively represent t 0 ,t 1 ,t 2 and t 3 The repeat positioning accuracy value at the time;

[0029] Optionally, the obtaining a first robustness quantitative index by using the geometric error accuracy curve comprises the following steps: obtaining a first distance between different data by using the geometric error accuracy curve, wherein the first distance satisfies the following formula:

[0030]

[0031] Where L represents the dimension of the data, i represents the geometric accuracy error of the i-th measurement, and P represents the sequence number of the error item corresponding to the geometric accuracy measurement, where 1≤n≤P, 1≤m≤P, x i (n) represents the measured value of the geometric accuracy error term of the i-th measurement number n, d i (m) Indicates the error value corresponding to the geometric accuracy of the measurement number m when it leaves the factory;

[0032] A first curvature is obtained through the geometric error accuracy curve, and the first curvature satisfies the following equation:

[0033]

[0034] Wherein, k′(t) represents a first curvature, and the first curvature is used to characterize the degree to which the geometric error accuracy curve deviates from the ideal straight line trajectory;

[0035] The first curvature is used to obtain a first curvature change of the geometric error accuracy curve, and the first curvature change satisfies the following equation:

[0036]

[0037] Among them, cu e (t) represents the first curvature change;

[0038] A first robustness quantification index is obtained by combining the first curvature change and the first distance, and the first robustness quantification index satisfies the following formula:

[0039] ARC e =αdist e (x (n) ,d (m) )+βcu e (t),

[0040] Among them, α represents the weight coefficient of the deviation of the repeated positioning accuracy from the ideal value when calculating the geometric error positioning accuracy, and β represents the weight coefficient of the fluctuation curvature of the geometric error accuracy curve.

[0041] Optionally, the determining of the spatial position vector of the multi-axis CNC machine tool comprises the following steps: decomposing the motion joints of the multi-axis CNC machine tool into rotational joints and translational joints;

[0042] The first spin coordinate of the rotational joint and the second spin coordinate of the translational joint are respectively obtained, and the first spin coordinate satisfies the following formula:

[0043]

[0044] Among them, ω i ∈R 3 ,q i ∈R 3 , R 3 represents the rotating three-dimensional spherical space of the multi-axis CNC machine tool, ω i represents the direction of the revolute joint, q i Indicates that the multi-axis CNC machine tool is in the direction ω i At one point, the second spinor coordinates satisfy the following formula:

[0045]

[0046] Among them, ν i ∈R 3 , R 3 represents the rotating three-dimensional spherical space of the multi-axis CNC machine tool, ν i represents the direction of the translation joint, n i represents the screw torque of the multi-axis CNC machine tool model;

[0047] The first screw coordinate is combined with the second screw coordinate to generate a third screw coordinate of the multi-axis CNC machine tool, and the third screw coordinate satisfies the following formula:

[0048]

[0049] The forward motion expression is generated by combining the third screw coordinate with the motion mode of the multi-axis CNC machine tool. The forward motion expression satisfies the following formula:

[0050]

[0051] Where i = 1, 2, ..., n, n represents the degree of freedom, represents the rotation of the motion joint, θ i Indicates the displacement of the moving joint;

[0052] The spatial position vector is obtained using the forward motion expression.

[0053] Optionally, the step of obtaining the spatial position vector by using the forward kinematic expression comprises the following steps: obtaining a first matrix of the workpiece coordinate system relative to the reference coordinate system by using the forward kinematic expression, wherein the first matrix satisfies the following formula:

[0054]

[0055] Among them, T rwT represents the transformation matrix of the workpiece coordinate system relative to the reference coordinate system in the machine tool reference system. bw (0) represents the transformation matrix of the workpiece coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th kinematic joint in the workpiece chain w from the reference coordinate system to the n-th axis, θ iw It represents the displacement of the i-th kinematic joint in the workpiece chain w, counting from the reference coordinate system toward the n-th axis;

[0056] The forward kinematics expression is used to obtain a second matrix of the tool coordinate system relative to the reference coordinate system, and the second matrix satisfies the following formula:

[0057]

[0058] In, T rc T represents the transformation matrix of the tool coordinate system relative to the reference coordinate system in the machine tool reference system. bc (0) represents the transformation matrix of the tool coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th kinematic joint in the tool chain c from the reference coordinate system to the n-th axis, θ ic It represents the displacement of the i-th kinematic joint of the tool chain c from the reference coordinate system in the direction of the n-th axis;

[0059] According to the first matrix and the second matrix, a third matrix of the tool coordinate system relative to the workpiece coordinate system is obtained, and the third matrix satisfies the following formula:

[0060] T w,c =T w,r T r,c =(T r,w ) -1 T r,c ,

[0061] in,

[0062]

[0063] generating a spinor exponential product of the geometric error through the geometric error;

[0064] The spinor exponential product is combined with the spatial topological relationship of the multi-axis CNC machine tool to obtain a spatial position vector, which satisfies the following expression:

[0065] P=[P X ,P Y ,P Z ,1] T =(T bw( 0)) -1 TZ T Y T X T bc (0)[0 0 0 1] T ,

[0066] in,

[0067]

[0068] Optionally, the generating of the spatial error accuracy curve by using the spatial position vector in combination with the geometric error accuracy curve comprises the following steps: introducing an installation error;

[0069] The installation error is combined with the geometric error to obtain a unified spatial position error, which satisfies the following expression:

[0070]

[0071] Among them, (Δx, Δy, Δz) represents the spatial error vector in the X, Y, and Z directions, (x, y, z) represents the motion instructions received by the three linear axes X, Y, and Z, including position parameters; (x T ,y T ,z T ) represents the installation error; a spatial error accuracy curve is generated by combining the position error with the geometric error accuracy curve, and the spatial error accuracy curve satisfies the following expression:

[0072]

[0073] Among them, d 0 d 1 d 2 and d 3 Respectively represent t 0 ,t 1 ,t 2 and t 3 The repeat positioning accuracy value at the time;

[0074] Optionally, the obtaining a second robustness quantitative index by using the spatial error precision curve comprises the following steps: obtaining a second distance between different data by using the spatial error precision curve, wherein the second distance satisfies the following formula:

[0075]

[0076] Where L represents the dimension of the data, i represents the spatial accuracy error of the i-th measurement, and P represents the sequence number of the error item corresponding to the spatial accuracy measurement, where 1≤n≤P, 1≤m≤P, x i(n) represents the measured value of the spatial accuracy error term of the i-th measurement number n, d i (m) Indicates that the measurement serial number is the error value corresponding to the spatial accuracy when it leaves the factory;

[0077] A second curvature is obtained by the spatial error accuracy curve, and the second curvature satisfies the following equation:

[0078]

[0079] Among them, k′ νe (t) represents a second curvature, wherein the second curvature is used to characterize the degree to which the spatial error accuracy curve deviates from the ideal straight line trajectory;

[0080] The second curvature is used to obtain a second curvature change of the spatial error accuracy curve, and the second curvature change satisfies the following equation:

[0081]

[0082] Among them, cu νe (t) represents the second curvature change;

[0083] A second robustness quantification index is obtained by combining the second curvature change and the second distance, and the second robustness quantification index satisfies the following formula:

[0084] ARC νe =χdist νe (x (n) ,d (m) )+ψcu νe (t),

[0085] Among them, χ represents the weight coefficient of the deviation of the repeated positioning accuracy from the ideal value when calculating the spatial error positioning accuracy, and ψ represents the weight coefficient of the fluctuation curvature of the spatial error accuracy curve.

[0086] On the other hand, the present invention also provides a multi-axis CNC machine tool geometric accuracy robustness quantitative evaluation system, the system includes an input device, a processor, a memory and an output device, the input device, the processor, the memory and the output device are interconnected, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is configured to call the program instructions to execute the method according to any one of claims 1 to 9. The present invention provides a physical system for executing a multi-axis CNC machine tool geometric accuracy robustness quantitative evaluation method, and at the same time, the system has a compact structure, stable operation, easy installation, and can be well combined with the method of the present invention, which makes the present invention more practical and commercially valuable. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 A flow chart of a method for quantitatively evaluating the robustness of geometric accuracy of a multi-axis CNC machine tool according to the present invention;

[0088] Figure 2 It is a schematic diagram of the structure of the multi-axis CNC machine tool of the present invention;

[0089] Figure 3 The present invention is a schematic diagram of the structure of a multi-axis CNC machine tool geometric accuracy robustness quantitative evaluation system. DETAILED DESCRIPTION

[0090] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0091] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0092] In an alternative embodiment, see Figure 1 The present invention provides a method for quantitatively evaluating the robustness of geometric accuracy of a multi-axis CNC machine tool, comprising the following steps:

[0093] S1. Provide multi-axis CNC machine tools.

[0094] See also Figure 2 The multi-axis CNC machine tool includes a workpiece chain and a tool chain. The workpiece chain includes a workpiece linear axis, a worktable and a workpiece. The tool chain consists of a tool A, a spindle B, a tool linear axis and a machine bed C. A coordinate system is established according to the structural characteristics of the multi-axis CNC machine tool. In detail, the reference coordinate system 02(0 r -XYZ) is established on the spindle B, and the local coordinate system includes the workpiece coordinate system 04 (O w -XYZ), spindle coordinate system 02 (O s-XYZ) and tool coordinate system 03 (O t -XYZ), X-axis coordinate system 05(O x -XYZ), Y axis coordinate system 06 (O y -XYZ) and Z-axis coordinate system 01(O z -XYZ) local coordinate system and the reference coordinate system 02 (O r -XYZ) direction, specifically, the workpiece coordinate system, the spindle coordinate system, and the tool coordinate system are connected to the workbench, the Z axis, and the spindle B respectively.

[0095] S2. Obtaining a positioning accuracy measurement value of a geometric error of the multi-axis CNC machine tool.

[0096] In a specific embodiment, the step of obtaining the positioning accuracy measurement value of the geometric error of the multi-axis CNC machine tool comprises the following steps: defining the geometric error in combination with the structural characteristics of the multi-axis CNC machine tool. The geometric error includes: linear error, straightness error, angular error and inter-axis error; the linear error includes δ x (x),δ y (y) and δ z (z); the straightness error includes δ x (y),δ y (x),δ x (z), δ y (z), δ z (y) and δ z (x); the angular error includes ε x (x), ε y (x), ε z (x), ε x (y), ε y (y), ε z (y), ε x (z), ε y (z) and ε z (z); the inter-axial error includes S xy , S yz and S xz The geometric error is defined for the motion axes (i.e., X-axis, Y-axis, and Z-axis) of a multi-axis CNC machine tool. Each motion axis includes three linear errors and three angular errors. Specifically, the three motion axes correspond to three linear errors of δ x (x),δ y (y) and δ z (z), the straightness error δ between the three motion axes x (y),δ y (x),δ x (z), δ y (z), δz (y) and δ z (x), the angular error ε between the motion axes x (x), ε y (x), ε z (x), ε x (y), ε y (y), ε z (y), ε x (z), ε y (z) and ε z (z), the inter-axis error S of the three motion axes xy , S yz and S xz .

[0097] In another specific embodiment, the step of obtaining the positioning accuracy measurement value of the geometric error of the multi-axis CNC machine tool further includes the following steps: obtaining the positioning accuracy measurement value of each of the geometric errors. 0 = 1 day, t 2 =11 days, t 3 =21 days, t 4 =31 days and other time nodes to detect the multi-axis CNC machine tool. Specifically, the interval of the detection time can be defined as the following expression: n =a 1 +(n-1)d, where d is the time interval between two measurements, d=10 days; n∈N*; the positioning accuracy measurement values ​​of the geometric error are shown in Table 1:

[0098] Table 1

[0099]

[0100] S3. Correct the positioning accuracy measurement value to obtain a repeatable positioning accuracy value.

[0101] In another specific embodiment, the correction of the positioning accuracy measurement value to obtain a repeat positioning accuracy value includes the following steps: obtaining a volume error of the multi-axis CNC machine tool, wherein the volume error satisfies the following formula:

[0102] V(e)=∑ i V i +∑ i ∑ i < j V ij +V 1,2,…,n ,

[0103] Wherein, V(e) represents the total variance of the geometric error of the multi-axis CNC machine tool; ∑ i V iRepresents the sum of the first-order variance of the output due to the influence of a single geometric error, ∑ i ∑ i<j V ij +V 1,2,…,n It represents the sum of the second-order and higher-order variances caused by the interaction between multiple geometric errors. However, the second-order or higher-order error terms have little effect on the volume error, so these terms can be ignored. Specifically, in this embodiment, n×k samples are created to calculate the output variance, where n=21 is the total number of geometric errors; k=100 is the number of sample points in each geometric error.

[0104] The sensitivity of a single geometric error is obtained using the volume error, and the sensitivity satisfies the following formula:

[0105]

[0106] S i It represents sensitivity, and the sensitivity characterizes the influence of spatial error at different positions on geometric error. In this embodiment, the sensitivity of a single geometric error is obtained for the data in Table 1 as shown in Table 2:

[0107] Table 2

[0108]

[0109] The standard uncertainty of the single geometric error is obtained by using the positioning accuracy measurement value, and the standard uncertainty satisfies the following formula:

[0110]

[0111]

[0112] Among them, x i Represents geometric error; X ij Denotes the geometric error as x i The jth positioning accuracy measurement value of and They represent the average one-way position deviations of positive approach and negative approach, respectively.

[0113] The sensitivity is combined with the standard uncertainty to generate a standard uncertainty component, which satisfies the following formula:

[0114] U i =S i ×U i (x i ),

[0115] Among them U i (x i ) indicates that the input quantity is xi The standard uncertainty of x i represents the geometric error, S i Denotes the geometric error as x i The corresponding sensitivity.

[0116] The positioning accuracy measurement value is corrected by the component satisfying the standard uncertainty to obtain the positioning accuracy correction value of the single geometric error, and the positioning accuracy correction value satisfies the following formula:

[0117]

[0118]

[0119] Among them, U i ↑andU i ↓ respectively represent the unidirectional standard uncertainty components of a certain position approaching in the positive direction and approaching in the negative direction. Combining the data in Table 1 and Table 2, the positioning accuracy correction values ​​are obtained after correction as shown in Table 3:

[0120] Table 3

[0121]

[0122] Combined with the positioning accuracy correction value of the single geometric error, the repeat positioning accuracy value of the single geometric error is obtained.

[0123] S4. Generate a geometric error accuracy curve using the repeated positioning accuracy value.

[0124] In a specific embodiment, the generating of the geometric error accuracy curve by the repeated positioning accuracy value comprises the following steps: setting a time control node, wherein the time control node comprises t 0 ,t 1 ,t 2 and t 3 ; Generate a geometric error accuracy curve in combination with the repeated positioning accuracy value corresponding to the time control node, and the geometric error accuracy curve satisfies the following formula:

[0125]

[0126] Among them, d 0 d 1 d 2 and d 3 Respectively represent t 0 ,t 1 ,t 2 and t 3 The repeat positioning accuracy value at the time;

[0127] In order to facilitate calculation, the geometric error accuracy curve is converted into a matrix form, and the matrix form satisfies the following formula:

[0128]

[0129] S5. Obtain a first robustness quantitative index using the geometric error accuracy curve.

[0130] In a specific embodiment, the method of obtaining a quantitative index of geometric error positioning accuracy robustness by using the geometric error accuracy curve comprises the following steps: obtaining a first distance between different data through the geometric error accuracy curve, wherein the first distance can be determined by the logarithm of the ratio of the arithmetic mean to the geometric mean between the data, and the first distance satisfies the following formula:

[0131]

[0132] Where L represents the dimension of the data, i represents the geometric accuracy error of the i-th measurement, and P represents the sequence number of the error item corresponding to the geometric accuracy measurement, where 1≤n≤P, 1≤m≤P, x i (n) represents the measured value of the geometric accuracy error term of the i-th measurement number n, d i (m) Indicates the error value corresponding to the geometric accuracy of the measurement number m when it leaves the factory; for example, x 1 (2) is the ε with sequence number 2 y (x) the positioning accuracy value determined by the first measurement, and d 1 (2) Represents ε with sequence number 2 y (x) Positioning accuracy value determined at the factory.

[0133] A first curvature is obtained through the geometric error accuracy curve, and the first curvature satisfies the following equation:

[0134]

[0135] Among them, k′ e(t) represents the first curvature, e′(t) represents one derivation of the geometric error accuracy curve, and e″(t) represents two derivations of the geometric error accuracy curve. The first curvature is used to characterize the degree to which the geometric error accuracy curve deviates from the ideal straight line trajectory. The first curvature expresses the rotation rate of the tangent direction angle to the arc length at any point on the geometric error accuracy curve. The first curvature of the geometric error accuracy curve can characterize the degree of curvature of any point on the geometric error accuracy curve, that is, the greater the curvature of the geometric error accuracy curve, the greater the curvature of the geometric error accuracy curve. When the geometric error accuracy curve approaches a straight line, the absolute curvature of the geometric error accuracy curve is small, but it cannot guarantee that the curvature of the geometric error accuracy curve changes uniformly, that is, when the geometric error accuracy value suddenly changes, the curvature of the geometric error accuracy curve fluctuates greatly. At this time, the deviation between the data points before and after the actual geometric error accuracy curve changes is too large, which does not meet the requirements.

[0136] The first curvature is used to obtain a first curvature change of the geometric error accuracy curve, and the first curvature change satisfies the following equation:

[0137]

[0138] Among them, cu e (t) represents the first curvature change, k e ″(t) represents the first curvature k′ e (t) The expression obtained after taking a derivative.

[0139] A first robustness quantification index is obtained by combining the first curvature change and the first distance, wherein the first robustness quantification index represents a robustness quantification index of the positioning accuracy of the geometric error, and the robustness quantification index of the positioning accuracy of the geometric error satisfies the following formula:

[0140] ARC e =αdist e (x (n) ,d (m) )+βcu e (t),

[0141] Among them, α represents the weight coefficient of the deviation of the repeatability positioning accuracy from the ideal value when calculating the geometric error accuracy, and β represents the weight coefficient of the fluctuation curvature of the geometric error accuracy curve; in detail, ARC e It represents the curvature of the entire geometric error accuracy curve and the sum of the deviations between the data points before and after the accuracy change; the order of magnitude of the accuracy deviation from the ideal value is equivalent to 10 of the change in the curvature of the geometric error accuracy curve. 2times, when conducting quantitative analysis of the robustness of geometric error accuracy, the stability of the four arithmetic operations will appear, which may easily cause the curvature change of the geometric error accuracy curve to be ignored. To solve the above problems, it is necessary to ensure that the weight of the deviation degree of repeated positioning accuracy and the curvature of the geometric accuracy error curve fluctuation are at the same order of magnitude; therefore, the weight coefficients are introduced into the fitness function α and β to introduce the quantitative index ARC of the robustness of geometric error positioning accuracy e In the formula, when the weight coefficient of the geometric error accuracy robustness quantitative index is set to α = γβ, γ≈100, the weight coefficient of the deviation of the repeat positioning accuracy from the ideal value and the fluctuation curvature of the geometric error accuracy curve can be made to have the same order of magnitude. In order to improve the calculation efficiency, the weight coefficients are defined as α = 1, β = 0.01, respectively. Combining the data in Tables 1 to 3, the corresponding geometric error positioning accuracy robustness quantitative index is obtained as shown in Table 4:

[0142] Table 4

[0143] Serial number Error term Moment 1 Moment 2 Moment 3 Moment 4 Moment 5 Moment 6 1 εxx 0.912 0.893 0.886 0.873 0.846 0.835 2 εyx 0.867 0.957 0.942 0.837 0.803 0.709 3 εzx 0.900 0.899 0.869 0.857 0.829 0.800 4 δxx 0.927 0.887 0.875 0.864 0.814 0.810 5 δyx 1.010 0.957 0.940 0.934 0.867 0.833 6 δzx 0.935 0.920 0.915 0.878 0.850 0.812 7 εxy 0.949 0.893 0.885 0.872 0.804 0.780 8 εyy 0.999 0.947 0.914 0.879 0.848 0.787 9 εzy 0.912 0.868 0.862 0.858 0.841 0.838 10 δxy 0.913 0.911 0.895 0.876 0.860 0.819 11 δyy 0.918 0.918 0.913 0.910 0.839 0.802 12 δzy 1.046 0.951 0.927 0.913 0.910 0.863 13 εxz 0.944 0.931 0.870 0.849 0.849 0.815 14 εyz 0.920 0.908 0.892 0.858 0.856 0.847 15 εzz 0.945 0.938 0.937 0.935 0.861 0.857 16 δxz 0.938 0.913 0.900 0.881 0.840 0.827 17 δyz 0.906 0.862 0.851 0.823 0.810 0.786 18 δzz 0.948 0.930 0.926 0.878 0.823 0.799 19 Sx 0.972 0.926 0.905 0.886 0.846 0.843 20 Sx 1.005 0.920 0.908 0.880 0.870 0.853 21 Syz 0.969 0.917 0.897 0.893 0.822 0.819

[0144] (Since four consecutive time nodes can determine a set of geometric error positioning accuracy robustness quantitative indicators, the nine time nodes in Tables 1 to 3 can determine six geometric error positioning accuracy robustness quantitative indicators) In the same time domain, the smaller the value of the geometric error positioning accuracy robustness quantitative indicator, the better the corresponding geometric error positioning accuracy robustness.

[0145] S6. Determine the spatial position vector of the multi-axis CNC machine tool.

[0146] In a specific embodiment, determining the spatial position vector of the multi-axis CNC machine tool includes the following steps: decomposing the motion joints of the multi-axis CNC machine tool into rotational joints and translational joints; and respectively acquiring the first rotational coordinates of the rotational joints and the second rotational coordinates of the translational joints.

[0147] In detail, in this embodiment, the first spinor coordinate satisfies the following formula:

[0148]

[0149] Among them, ω i ∈R 3 ,q i ∈R 3 , R 3 represents the rotating three-dimensional spherical space of the multi-axis CNC machine tool, ω i represents the direction of the revolute joint, q i Indicates that the multi-axis CNC machine tool is in the direction ω i In more detail, the first rotation quantity of the revolute joint is obtained by using the first rotation quantity coordinate, and the first rotation quantity satisfies the following expression:

[0150]

[0151] Among them, ‖ω i ‖=1,ω i ·ν i =0,ω i and ν i Used to characterize the screw unit; using the first screw, the motion instruction of the rotating joint is the instruction θ i When the first motion quantity η′ is obtained i , the first motion quantity η′ i Satisfies the following formula:

[0152]

[0153] in, I 3×3 Represents the identity matrix.

[0154] In detail, in this embodiment, the second spinor coordinate satisfies the following formula:

[0155]

[0156] Among them, ν i ∈R 3 , R 3 represents the rotating three-dimensional spherical space of the multi-axis CNC machine tool, ν i represents the direction of the translation joint, n i The screw torque representing the motion of the multi-axis CNC machine tool model; in more detail, the second screw coordinate is used to obtain the second screw of the translation joint, and the second screw satisfies the following expression:

[0157]

[0158] Among them, ‖ν i ‖=1,ν i Used to characterize the screw unit; using the second screw, the movement instruction of the translation joint is the instruction m i When the second motion quantity η is obtained li , the second movement amount η li Satisfies the following formula:

[0159]

[0160] In a specific embodiment, the determining of the spatial position vector of the multi-axis CNC machine tool further includes the following step: using the first screw coordinate in combination with the second screw coordinate to generate a third screw coordinate of the multi-axis CNC machine tool, wherein the third screw coordinate satisfies the following formula:

[0161]

[0162] In a specific embodiment, the determining of the spatial position vector of the multi-axis CNC machine tool further includes the following steps: generating a forward motion expression by combining the third screw coordinate with the motion mode of the multi-axis CNC machine tool, wherein the forward motion expression satisfies the following formula:

[0163]

[0164] i=1,2,…,n, n represents the degree of freedom, represents the rotation of the motion joint, θ i represents the displacement of the moving joint, that is The rotation of the motion joint generated by the third rotation coordinate.

[0165] In a specific embodiment, the determining of the spatial position vector of the multi-axis CNC machine tool further includes the following steps: obtaining the spatial position using the forward kinematic expression. In detail, in this embodiment, obtaining the spatial position using the forward kinematic expression includes the following steps: obtaining a first matrix of the workpiece coordinate system relative to the reference coordinate system using the forward kinematic expression, the first matrix satisfying the following formula:

[0166]

[0167] Among them, T rw T represents the transformation matrix of the workpiece coordinate system in the machine tool reference system relative to the base coordinate system. bw (0) represents the transformation matrix of the workpiece coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th motion joint in the workpiece chain w from the base coordinate system to the n-th axis, θ iw It represents the displacement of the i-th motion joint in the workpiece chain w, counting from the base coordinate system toward the n-th axis.

[0168] The forward kinematics expression is used to obtain a second matrix of the tool coordinate system relative to the reference coordinate system, and the second matrix satisfies the following formula:

[0169]

[0170] Among them, T rc It represents the transformation matrix of the tool coordinate system in the machine tool reference system relative to the base coordinate system, T bc (0) represents the transformation matrix of the tool coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th motion joint in the tool chain c from the base coordinate system to the n-th axis, θ ic It represents the displacement of the i-th motion joint of the tool chain c from the base coordinate system in the direction of the n-th axis.

[0171] According to the first matrix and the second matrix, a third matrix of the tool coordinate system relative to the workpiece coordinate system is obtained, and the third matrix satisfies the following formula:

[0172] T w,c =T w,r T r,c =(T r,w ) -1 T r,c ,

[0173] in,

[0174]

[0175] The spin exponential product of the geometric error is generated by the geometric error. Specifically, in this embodiment, for the convenience of calculation, the spin exponential product of the geometric error is converted into a homogeneous coordinate expression matrix. The expression matrices HTMs of the geometric errors are shown in Table 5:

[0176]

[0177]

[0178] The spinor exponential product is combined with the spatial topological relationship of the multi-axis CNC machine tool to obtain a spatial position vector, which satisfies the following expression:

[0179] P=[P X ,P Y ,P Z ,1] T =(T bw (0)) -1 T Z T Y T X T bc (0)[0 0 0 1] T ,

[0180] in,

[0181]

[0182] S7. Generate a spatial error accuracy curve by using the spatial position vector and combining it with the geometric error accuracy curve.

[0183] In a specific embodiment, the generating of the spatial error accuracy curve by using the spatial position vector in combination with the geometric error accuracy curve comprises the following steps:

[0184] Introducing installation error (x T ,y T ,z T ). By combining the installation error with the geometric error, a unified spatial position error is obtained, and the spatial position error satisfies the following expression:

[0185]

[0186] Among them, (Δx, Δy, Δz) represents the spatial error vector in the X, Y, and Z directions, (x, y, z) represents the motion instructions received by the three linear axes X, Y, and Z, including position parameters; (x T ,y T ,z T ) indicates installation error.

[0187] The spatial error accuracy curve is generated by combining the position error with the geometric error accuracy curve, and the spatial error accuracy curve satisfies the following expression:

[0188]

[0189] Among them, d 0 d 1 d 2 and d 3 Respectively represent t 0 ,t 1 ,t 2 and t 3 The repeat positioning accuracy value at the time;

[0190] In order to facilitate calculation, the spatial error accuracy curve is converted into a matrix form, and the matrix form satisfies the following formula:

[0191]

[0192] S8. Obtain a second robustness quantitative index using the spatial error accuracy curve.

[0193] In a specific embodiment, the method of obtaining a quantitative index of spatial error positioning accuracy robustness by using the spatial error accuracy curve comprises the following steps:

[0194] The second distance between different data is obtained through the spatial error accuracy curve, and the second distance satisfies the following formula:

[0195]

[0196] Where L represents the dimension of the data, i represents the spatial accuracy error of the i-th measurement, and P represents the sequence number of the error item corresponding to the spatial accuracy measurement, where 1≤n≤P, 1≤m≤P, x i (n) represents the measured value of the spatial accuracy error term of the i-th measurement number n, d i (m) Indicates the error value corresponding to the geometric accuracy of measurement number m when it leaves the factory.

[0197] A second curvature is obtained by the spatial error accuracy curve, and the second curvature satisfies the following equation:

[0198]

[0199] Among them, k′ νe (t) represents the second curvature, Δτ e ′(t) represents the spatial error accuracy curve Δτ e (t) is differentiated once, Δτ e ″(t) represents the spatial error accuracy curve Δτ e (t) is derivatized twice, and the second curvature is used to characterize the degree to which the spatial error accuracy curve deviates from the ideal straight line trajectory; the second curvature expresses the rotation rate of the tangent direction angle to the arc length at any point on the spatial error accuracy curve; the second curvature of the spatial error accuracy curve can characterize the degree of curvature of any point on the spatial error accuracy curve, that is, the greater the curvature of the spatial error accuracy curve, the greater the curvature of the spatial error accuracy curve. When the spatial error accuracy curve approaches a straight line, the absolute curvature of the spatial error accuracy curve is small, but it cannot guarantee that the curvature of the spatial error accuracy curve changes uniformly, that is, when the spatial error accuracy value suddenly changes, the curvature of the spatial error accuracy curve fluctuates greatly. At this time, the deviation between the data points before and after the actual spatial error accuracy curve changes is too large, which does not meet the requirements.

[0200] The second curvature is used to obtain a second curvature change of the spatial error accuracy curve, and the second curvature change satisfies the following equation:

[0201]

[0202] Among them, cu νe (t) represents the second curvature change, k″ νe (t) represents the second curvature k′ νe (t) perform a derivative;

[0203] A second robustness quantification index is obtained by combining the second curvature change and the second distance, wherein the second robustness quantification index represents a robustness quantification index of the positioning accuracy of the spatial error, and the robustness quantification index of the positioning accuracy of the spatial error satisfies the following formula:

[0204] ARC νe =χdist νe (x (n) ,d (m) )+ψcu νe (t),

[0205] Among them, χ represents the weight coefficient of the deviation of the repeatability positioning accuracy from the ideal value when calculating the spatial error accuracy, and ψ represents the weight coefficient of the fluctuation curvature of the spatial error accuracy curve. In detail, ARC νe The curvature of the geometric accuracy curve that represents the error vector is the sum of the deviations between the data points before and after the accuracy change; the order of magnitude of the accuracy deviation from the ideal value is equivalent to 10 of the curvature change of the spatial error accuracy curve. 3 times, when conducting quantitative analysis of spatial error accuracy robustness, the stability problem of the four arithmetic operations will appear, which may easily cause the curvature change of the spatial error accuracy curve to be ignored. To solve the above problems, it is necessary to ensure that the weight of the deviation degree of repeated positioning accuracy and the fluctuation curvature of the spatial accuracy error curve are at the same order of magnitude; therefore, the weight coefficients are introduced into the fitness function χ and ψ to introduce the quantitative index ARC of spatial error positioning accuracy robustness ve In the above, when the weight coefficient of the spatial error accuracy robustness quantitative index is set to χ = ρψ, ρ ≈ 1000, the weight coefficient of the deviation of the repeat positioning accuracy from the ideal value and the fluctuation curvature of the spatial error accuracy curve can be made to have the same order of magnitude. In order to improve the calculation efficiency, the weight coefficients are defined as χ = 1, ψ = 0.001, respectively. Combining the data in Tables 1 to 3, the corresponding spatial error positioning accuracy robustness quantitative index is obtained as shown in Table 6:

[0206] Table 6

[0207] Moment 1 Moment 2 Moment 3 Moment 4 Moment 5 Moment 6 Δx 0.9706 0.9585 0.9566 0.9319 0.9207 0.8815 Δy 0.9305 0.8968 0.8854 0.8495 0.8480 0.8276 Δz 0.9229 0.8899 0.8628 0.8347 0.8067 0.7433

[0208] (Since four consecutive time nodes can determine a set of spatial error positioning accuracy robustness quantitative indicators, the nine time nodes in Tables 1 to 3 can determine six spatial error positioning accuracy robustness quantitative indicators) In the same time domain, the smaller the value of the spatial error positioning accuracy robustness quantitative indicator, the better the corresponding geometric error positioning accuracy robustness.

[0209] In summary, the method of the present invention can determine the repeatability of the geometric error uncertainty correction of the multi-axis CNC machine tool, thereby obtaining a smooth accuracy curve and accurately quantifying the geometric accuracy robustness in the quasi-static accuracy index of the multi-axis CNC machine tool.

[0210] On the other hand, the present invention also provides a system for quantitatively evaluating the robustness of geometric accuracy of multi-axis CNC machine tools, the system comprising an input device, a processor, a memory and an output device, wherein the input device, the processor, the memory and the output device are interconnected, wherein the memory is used to store a computer program, the computer program comprises program instructions, and the processor is configured to call the program instructions to execute a method for quantitatively evaluating the robustness of geometric accuracy of multi-axis CNC machine tools.

[0211] In summary, the present invention provides a physical system for executing a quantitative evaluation method for the robustness of the geometric accuracy of multi-axis CNC machine tools. At the same time, the system has a compact structure, stable operation, and is easy to install. It can also be well combined with the method of the present invention, which makes the present invention more practical and commercially valuable.

[0212] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. A quantitative evaluation method for the robustness of geometric accuracy of multi-axis CNC machine tools, characterized in that: The steps include: Provide multi-axis CNC machine tools; In combination with the structural characteristics of the multi-axis CNC machine tool, a geometric error is defined, wherein the geometric error includes: linear error, straightness error, angular error and inter-axis error; Obtaining positioning accuracy measurement values ​​of each of the geometric errors; The volume error of the multi-axis CNC machine tool is obtained, and the volume error satisfies the following formula: V(e)=∑ i V i +∑ i ∑ i<j V ij +V 1,2,…,n , Wherein, V(e) represents the total variance of the geometric error of the multi-axis CNC machine tool; Σ i V i Represents the sum of the first-order variance of the output due to the influence of single geometric errors, Σ i Σ i<j V ij +V 1,2,…,n represents the sum of second-order and higher-order variances due to the interaction between multiple geometric errors; The sensitivity of a single geometric error is obtained using the volume error, and the sensitivity satisfies the following formula: S i represents sensitivity, wherein the sensitivity represents the influence of spatial errors at different positions on geometric errors; The standard uncertainty of a single geometric error is obtained using the positioning accuracy measurement value, and the standard uncertainty satisfies the following formula: Among them, x i Represents a single geometric error; X ij Indicates that the single geometric error is x i The jth positioning accuracy measurement value of and represent the average one-way position deviations for positive approach and negative approach, respectively; The sensitivity is combined with the standard uncertainty to generate a standard uncertainty component, which satisfies the following formula: U i =S i ×U i (x i ), Among them U i (x i ) indicates that the single geometric error is x i The standard uncertainty, S i Denotes the geometric error as x i Corresponding sensitivity; The positioning accuracy measurement value is corrected by the component satisfying the standard uncertainty to obtain the positioning accuracy correction value of the single geometric error, and the positioning accuracy correction value satisfies the following formula: Among them, U i ↑andU i ↓ represents the one-way standard uncertainty component of a certain point approaching in the positive direction and approaching in the negative direction respectively; Combined with the positioning accuracy correction value of the single geometric error, the repeat positioning accuracy value of the single geometric error is obtained; Generate a geometric error accuracy curve through the repeated positioning accuracy value; Obtaining a first robustness quantification index using the geometric error accuracy curve, wherein the first robustness quantification index represents a robustness quantification index of positioning accuracy of the geometric error; Determining the spatial position vector of the multi-axis CNC machine tool; Generate a spatial error accuracy curve by using the spatial position vector in combination with the geometric error accuracy curve; A second robustness quantification index is obtained by using the spatial error accuracy curve, where the second robustness quantification index represents a robustness quantification index of the positioning accuracy of the spatial error.

2. A method for quantitatively evaluating the robustness of geometric accuracy of a multi-axis CNC machine tool according to claim 1, characterized in that: The step of generating a geometric error accuracy curve by using the repeated positioning accuracy value comprises the following steps: Setting time control nodes, the time control nodes include t0, t1, t2 and t3; A geometric error accuracy curve is generated in combination with the repeated positioning accuracy value corresponding to the time control node, and the geometric error accuracy curve satisfies the following formula: Wherein, d0, d1, d2 and d3 represent the repeatability accuracy values ​​at time t0, t1, t2 and t3 respectively.

3. The method for quantitatively evaluating the geometric accuracy robustness of a multi-axis CNC machine tool according to claim 1, characterized in that: The method of obtaining a first robustness quantitative index by using the geometric error accuracy curve comprises the following steps: The first distance between different data is obtained through the geometric error accuracy curve, and the first distance satisfies the following formula: Among them, x (n) It represents the measured value of the geometric accuracy error term with measurement number n, d (m) Indicates the error value corresponding to the geometric accuracy of the measurement number m when it leaves the factory, dist e (x (n) ,d (m) ) represents x (n) and d (m) The first distance between, L represents the dimension of the data, P represents the sequence number of the error term corresponding to the geometric accuracy measurement, where 1≤n≤P, 1≤m≤P, x i (n) represents the measured value of the geometric accuracy error term of the i-th measurement number n, d i (m) It indicates the error value corresponding to the geometric accuracy of the i-th measurement number m when it leaves the factory; A first curvature is obtained through the geometric error accuracy curve, and the first curvature satisfies the following equation: Among them, k′ e (t) represents a first curvature, which is used to characterize the degree to which the geometric error accuracy curve deviates from the ideal straight line trajectory; The first curvature is used to obtain a first curvature change of the geometric error accuracy curve, and the first curvature change satisfies the following equation: Among them, cu e (t) represents the first curvature change; A first robustness quantification index is obtained by combining the first curvature change and the first distance, and the first robustness quantification index satisfies the following formula: ARC e =αdist e (x (n) ,d (m) )+βcu e (t), Among them, α represents the weight coefficient of the deviation of the repeated positioning accuracy from the ideal value when calculating the geometric error positioning accuracy, and β represents the weight coefficient of the fluctuation curvature of the geometric error accuracy curve.

4. A method for quantitatively evaluating the geometric accuracy robustness of a multi-axis CNC machine tool according to claim 1, characterized in that: Determining the spatial position vector of the multi-axis CNC machine tool comprises the following steps: Decomposing the motion joints of the multi-axis CNC machine tool into rotational joints and translational joints; The first spin coordinate of the rotational joint and the second spin coordinate of the translational joint are respectively obtained, and the first spin coordinate satisfies the following formula: Among them, ω i ∈R 3 ,q i ∈R 3 , R 3 represents the rotating three-dimensional spherical space of the multi-axis CNC machine tool, ω i represents the direction of the revolute joint, q i Indicates that the multi-axis CNC machine tool is in the direction ω i At one point, the second spinor coordinates satisfy the following formula: Among them, n i represents the screw torque of the multi-axis CNC machine tool model; The first screw coordinate is combined with the second screw coordinate to generate a third screw coordinate of the multi-axis CNC machine tool, and the third screw coordinate satisfies the following formula: The forward motion expression is generated by combining the third screw coordinate with the motion mode of the multi-axis CNC machine tool. The forward motion expression satisfies the following formula: Where i = 1, 2, ..., n, n represents the degree of freedom, represents the rotation of the motion joint, θ i Indicates the displacement of the moving joint; The spatial position vector is obtained using the forward motion expression.

5. A method for quantitatively evaluating the geometric accuracy robustness of a multi-axis CNC machine tool according to claim 4, characterized in that: The method of obtaining a spatial position vector by using the forward motion expression comprises the following steps: The forward kinematics expression is used to obtain a first matrix of the workpiece coordinate system relative to the reference coordinate system, and the first matrix satisfies the following formula: Among them, T rw It represents the transformation matrix of the workpiece coordinate system relative to the reference coordinate system in the machine tool reference system, T bw (0) represents the transformation matrix of the workpiece coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th kinematic joint in the workpiece chain w from the reference coordinate system to the n-th axis, θ iw It represents the displacement of the i-th kinematic joint in the workpiece chain w, counting from the reference coordinate system toward the n-th axis; The forward kinematics expression is used to obtain a second matrix of the tool coordinate system relative to the reference coordinate system, and the second matrix satisfies the following formula: Among them, T rc It represents the transformation matrix of the tool coordinate system relative to the reference coordinate system in the machine tool reference system, T bc (0) represents the transformation matrix of the tool coordinate system relative to the base coordinate system in the machine tool reference system, represents the rotation of the i-th kinematic joint in the tool chain c from the reference coordinate system to the n-th axis, θ ic It represents the displacement of the i-th kinematic joint of the tool chain c from the reference coordinate system in the direction of the n-th axis; According to the first matrix and the second matrix, a third matrix of the tool coordinate system relative to the workpiece coordinate system is obtained, and the third matrix satisfies the following formula: T w,c =T w,r T r,c =(T r,w ) -1 T r,c , generating a spinor exponential product of the geometric error through the geometric error; The spinor exponential product is combined with the spatial topological relationship of the multi-axis CNC machine tool to obtain a spatial position vector, which satisfies the following expression: P=[P X ,P Y ,P Z ,1] T =(T bw (0)) -1 T Z T Y T X T bc (0)[0 0 0 1] T , in, 6. A method for quantitatively evaluating the robustness of geometric accuracy of a multi-axis CNC machine tool according to claim 5, characterized in that: The step of generating a spatial error accuracy curve by using the spatial position vector in combination with the geometric error accuracy curve comprises the following steps: Introducing installation error (x T ,y T ,z T ); The installation error is combined with the geometric error to obtain a unified spatial position error, which satisfies the following expression: Among them, (Δx, Δy, Δz) represents the spatial error vector in the X, Y, and Z directions; (x, y, z) represents the motion instructions received by the X, Y, and Z motion axes, including position parameters; T ,y T ,z T ) indicates installation error; The spatial error accuracy curve is generated by combining the position error with the geometric error accuracy curve, and the spatial error accuracy curve satisfies the following expression: Wherein, d0, d1, d2 and d3 represent the repeatability values ​​at times t0, t1, t2 and t3 respectively; 7. A method for quantitatively evaluating the geometric accuracy robustness of a multi-axis CNC machine tool according to claim 6, characterized in that: The step of obtaining a second robustness quantitative index by using the spatial error accuracy curve comprises the following steps: The second distance between different data is obtained through the spatial error accuracy curve, and the second distance satisfies the following formula: Where L represents the dimension of the data, i represents the spatial accuracy error of the i-th measurement, and P represents the sequence number of the error item corresponding to the spatial accuracy measurement, where 1≤n≤P, 1≤m≤P, x i (n) represents the measured value of the spatial accuracy error term of the i-th measurement number n, d i (m) It indicates the error value corresponding to the geometric accuracy of the measurement number m when it leaves the factory; A second curvature is obtained by the spatial error accuracy curve, and the second curvature satisfies the following equation: Among them, k′ νe (t) represents a second curvature, wherein the second curvature is used to characterize the degree to which the spatial error accuracy curve deviates from the ideal straight line trajectory; The second curvature is used to obtain a second curvature change of the spatial error accuracy curve, and the second curvature change satisfies the following equation: Among them, cu νe (t) represents the second curvature change; A second robustness quantification index is obtained by combining the second curvature change and the second distance, and the second robustness quantification index satisfies the following formula: ARC νe =χdist νe (x (n) ,d (m) )+ψcu νe (t), Among them, χ represents the weight coefficient of the deviation of the repeated positioning accuracy from the ideal value when calculating the spatial error positioning accuracy, and ψ represents the weight coefficient of the fluctuation curvature of the spatial error accuracy curve.

8. A quantitative evaluation system for the robustness of geometric accuracy of multi-axis CNC machine tools, characterized in that: The invention comprises an input device, a processor, a memory and an output device, wherein the input device, the processor, the memory and the output device are connected to each other, wherein the memory is used to store a computer program, the computer program comprises program instructions, and the processor is configured to call the program instructions to execute the method as claimed in any one of claims 1 to 7.

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