CN110837246A - Method for analyzing geometric error sensitivity of double rotating shafts of five-axis numerical control machine tool - Google Patents
Method for analyzing geometric error sensitivity of double rotating shafts of five-axis numerical control machine tool Download PDFInfo
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Abstract
The invention provides a method for analyzing geometric error sensitivity of double rotating shafts of a five-axis numerical control machine tool, which comprises the following steps of: firstly, a mathematical model of the geometric errors of the double rotating shafts is constructed based on a multi-body system theory and a homogeneous transformation matrix, then, a Monte Carlo method is utilized to sample error parameters, and sensitivity analysis is carried out on the geometric errors of the double rotating shafts of the numerical control machine tool; finally, sensitivity analysis is carried out on the error parameters based on the positions of the specific corners of the double rotating shafts, and the first-order sensitivity and the global sensitivity of each geometric error of the double rotating shafts at the positions are calculated by setting the positions of five groups of specific corners; the method can identify the key geometric errors in the 20 geometric errors of the double rotating shafts by a Sobol sensitivity analysis method, and completes the identification of the geometric errors of the double rotating shafts of the five-axis numerical control machine. The invention has the advantages of simple detection steps, convenient measurement and high identification precision.
Description
Technical Field
The invention belongs to the technical field of numerical control machine tool error detection, and particularly relates to a five-axis numerical control machine tool double-rotating-shaft geometric error identification method based on sensitivity analysis.
Technical Field
Five-axis numerically-controlled machine tools have the ability to process complex parts relative to three-axis numerically-controlled machine tools because five-axis numerically-controlled machine tools have two additional axes of rotation compared to three-axis numerically-controlled machine tools. When the five-axis numerical control machine tool is used for machining, the generated cutter path has higher flexibility than that of the traditional three-axis machine tool. However, the rotating shaft introduces self-error elements during machining, wherein the geometric errors have great influence on the total errors, and the machining precision of the machine tool is greatly influenced.
The geometric errors are generally regarded as quasi-static errors generated due to the characteristics of the geometric errors, account for more than half of the total errors of the machine tool, and therefore, the study on the geometric errors of the rotating shaft is important for improving the precision of the five-axis numerical control machine tool. All geometric errors of the rotating shafts are mutually coupled, and the common method is difficult to quickly identify the geometric errors of the double rotating shafts, so that the method capable of quickly and simply identifying the geometric errors of the double rotating shafts of the five-axis numerical control machine tool is very important for improving the machining precision of the machine tool.
Disclosure of Invention
In order to solve the problems, the invention provides a method for identifying the geometric errors of double rotating shafts of a five-axis numerical control machine tool based on sensitivity analysis. The method can simply, conveniently and accurately identify the geometric errors, obtain the influence degree of each error element on the total errors, and further improve the processing quality by controlling the key geometric errors. The method comprises the following specific steps:
step 1, performing geometric error modeling by using a multi-body system theory and a homogeneous transformation matrix, and specifically comprising the following steps:
step 1.1, setting a reference coordinate system and a local coordinate system for the numerical control machine tool based on the topological structure relation of the numerical control machine tool parts, and setting the Y-axis local coordinate system to be coincident with the reference coordinate system.
And step 1.2, identifying Geometric Errors of double rotating shafts of the numerical control machine tool, wherein the Geometric Errors comprise 12 Position-Dependent Geometric Errors (PDGEs) and 8 Position-Independent Geometric Errors (PIGEs).
And 1.3, constructing an error transformation matrix by using the homogeneous transformation matrix.
Position error E of actual revolution center line of A axis in Y axis directionYOAIs the deviation of the axis of the A-axis in the Y direction, DYOAIs the error transformation matrix:
position error E of actual rotation center line of A axis in Z axis directionZOAIs the deviation of the axis of the A-axis in the Z direction, DZOAIs the error transformation matrix:
the projection of the actual revolution center line of the A axis on the XOZ plane forms an included angle E with the X axisBOAIs the parallelism error of the axis of the A-axis around the Y-axis, TB0AIs the error transformation matrix:
the projection of the actual revolution center line of the A axis on the XOY plane forms an included angle E with the X axisCOAIs the parallelism error of the axis of the A-axis around the Z-axis, TC0AIs the error transformation matrix:
wherein D isYOA、DZOA、TB0A、TC0AIs the 4-term PIGEs error transformation matrix for the A-axis.
Position error E of C-axis actual rotation center line in X-axis directionXOCIs the deviation of the C-axis in the X direction, DXOCIs the error transformation matrix:
the position error of the C-axis actual rotation center line in the Y-axis direction is EYOCIs the deviation of the C-axis in the Y-direction, DYOCIs the error transformation matrix:
the projection of the C-axis actual rotation center line on the YOZ plane and the included angle E of the Z axisAOCIs the parallelism error of the C-axis around the X-axis, TAOCIs the error transformation matrix:
step C, forming an included angle E between the projection of the actual rotation center line of the axis C on the XOZ plane and the axis ZBOCIs the parallelism error of the C-axis around the Y-axis, TBOCIs the error transformation matrix:
wherein D isXOC、DYOC、TAOC、TBOCIs a 4-term PIGEs error transformation matrix for the C-axis.
wherein,
the method is a dual-rotation-axis PDGEs error transformation matrix based on a small-angle approximation principle.
And integrating the error matrixes, wherein the geometric error of the workpiece relative to the cutter is as follows:
and 2.1, sampling the error parameters by adopting a Monte Carlo method, and generating a Sobol sequence to determine the influence of each error on the space error of the machine tool.
Step 2.2, variance-based Sobol sensitivity analysis requires the determination of the number of errors, k, with 20 error terms in both axes of rotation, so k is set to 20.
Step 2.3, generating two parameter sample matrixes of the Sobol sequence A, B, and recording as follows:
wherein xijAn ith (j ═ 1, 2, 3.. n) sample representing the jth (i ═ 1, 2, 3.. k) error element.
Step 2.4, the ith column of the matrix B is changed to the ith column of the matrix A, and the rest columns of the matrix A are unchanged, so that the matrix AB is obtainediAs follows:
the matrix A, B, AB is constructed by the method described aboveiThe total (k +2) N sets of rotation axis error parameters are obtained, thus obtaining (k +2) N sets
The value is obtained. For each group
There is a unique matrix A, B, ABiCorresponding to f (A), f (B), f (AB)i)。
Step 2.5, calculating the first-order sensitivity and the global sensitivity of each error element by a variance calculation formula of system response, wherein the calculation formula is as follows:
Var(Y)＝Var(YA+YB) (3)
Y＝(ya1ya2... yanyb1yb2... ybn)T(6)
wherein y isj1Var (Y) is the standard deviation of Y for the corresponding output values of the input matrix.
Step 2.6, calculating a formula of the first-order sensitivity and the global sensitivity of the error element:
Sirepresenting an error element xiFirst order sensitivity of STiRepresenting an error element xiGlobal sensitivity of (c). Error element xiThe first order sensitivity of (a) represents the direct effect of the error on the machine space error, and the global sensitivity represents the coupled effect of the error on the machine space error.
The sampling ratio of PDGEs and PIGEs of the target five-axis numerical control machine tool is 3: 7, wherein the sampling ranges of the position error and the angle error are (0, 1) mu m and (0, 1)', respectively.
And 3, carrying out sensitivity analysis on the error parameters based on the specific rotation angle position of the rotating shaft. Because the rotating angles of the rotating shafts are different, the influence of various errors of the rotating shafts on the precision of the machine tool is changed. Aiming at the problem of sensitivity of the rotating shaft of the five-axis numerical control machine tool at different corner positions, five groups of specific corner positions and one group of random change of the corner positions in the machining range are set to carry out sensitivity analysis on double rotating shafts of the five-axis numerical control machine tool.
And 3.1, setting the rotation angle of the shaft A to be 0 degrees and the rotation angle of the shaft C to be 0 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.2, setting the rotation angle of the shaft A to be 45 degrees and the rotation angle of the shaft C to be 45 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.3, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.4, setting the rotation angle of the shaft A to be 0 degree and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.5, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 0 degree, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.6, setting the rotation angle of the shaft A to randomly change within 0-90 degrees and the rotation angle of the shaft C to randomly change within 0-360 degrees, carrying out sensitivity analysis on the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
The Sobol sensitivity analysis result in the step 3 shows that the errors influencing the processing precision are mainly distributed in PIGEs. The PIGEs have a large influence on the space errors of the five-axis numerical control machine tool, the PDGEs have a small influence on the space errors of the five-axis numerical control machine tool, and the key geometric errors in the 20 geometric errors can be identified through a Sobol sensitivity analysis method. Influencing the accuracy of the machine in geometric errorsThe critical geometric error comes from E in PIGEsY0A、EY0C、EA0CThe first-order sensitivity affecting the machining precision accounts for 67.42% of the 20 geometric errors, and the global sensitivity affecting the machining precision accounts for 26.97% of the 20 geometric errors under the condition of interaction.
Through the Sobol sensitivity analysis result, geometric errors of the five-axis numerical control machine tool are identified, and the accuracy of the numerical control machine tool can be improved by controlling key errors.
The sensitivity analysis of the geometric errors of the double rotating shafts of the five-axis numerical control machine tool is completed, and the sensitivity analysis comprises 8 items of geometric errors independent of the position and 12 items of geometric errors related to the position.
The method effectively solves the problem of identification and detection of the geometric errors of the double rotating shafts in the five-axis numerical control machine tool, and provides effective analysis of the geometric error sensitivity of the double rotating shafts of the five-axis numerical control machine tool.
Drawings
FIG. 1 is a diagram of a reference coordinate system of a five-axis NC machine tool according to an embodiment of the method of the invention.
FIG. 2 is a schematic diagram of PIGEs for axis A in an embodiment of the method of the present invention.
FIG. 3 is a schematic view of PIGEs for the C axis in an embodiment of the method of the present invention.
FIG. 4 is a graph showing the first order sensitivity results of the method of the present invention. In this case, reference numeral 1 indicates the first-order sensitivity of the A axis at 0 ℃ and the C axis at 0 ℃.2 represents the first order sensitivity at 45 ° on the a axis and 45 ° on the C axis. 3 represents the first order sensitivity at 0 ° on the A axis and 90 ° on the C axis. 4 represents the first order sensitivity at 90 ° on the a axis and 0 ° on the C axis. 5 represents the first order sensitivity at 90 deg. on the A axis and 90 deg. on the C axis. 6 represents the first order sensitivity at 0 to 90 on the A axis and 0 to 360 on the C axis. Representation of the error term: 1-EYOA、2-EZOA、3-EXOC、4-EYOC、5-EBOA、6-ECOA、7-EAOC、8-EBOC、9- δx(a)、10-δy(a)、11-δz(a)、12-εx(a)、13-εy(a)、14-εz(a)、15-δx(c)、16-δy(c)、17-δz(c)、 18-δx(c)、19-εy(c)、20-εz(c)。
FIG. 5 is a diagram illustrating global sensitivity results in an embodiment of the method of the present invention. In this case, reference numeral 1 indicates the first-order sensitivity of the A axis at 0 ℃ and the C axis at 0 ℃.2 represents the first order sensitivity at 45 ° on the a axis and 45 ° on the C axis. 3 represents the first order sensitivity at 0 ° on the A axis and 90 ° on the C axis. 4 represents the first order sensitivity at 90 ° on the a axis and 0 ° on the C axis. 5 represents the first order sensitivity at 90 deg. on the A axis and 90 deg. on the C axis. 6 represents the first order sensitivity at 0 to 90 on the A axis and 0 to 360 on the C axis. Representation of the error term: 1-EYOA、2-EZOA、3-EXOC、4-EYOC、5-EBOA、6-ECOA、7-EAOC、8-EBOC、9- δx(a)、10-δy(a)、11-δz(a)、12-εx(a)、13-εy(a)、14-εz(a)、15-δx(c)、16-δy(c)、17-δz(c)、 18-εx(c)、19-εy(c)、20-εz(c)。
Detailed Description
In order to solve the problems, the invention provides a method for identifying the geometric errors of double rotating shafts of a five-axis numerical control machine tool based on sensitivity analysis. The method can simply, conveniently and accurately identify the geometric errors, obtain the influence degree of each error element on the total errors, and further improve the processing quality by controlling the key geometric errors. The method comprises the following specific steps:
step 1, performing geometric error modeling by using a multi-body system theory and a homogeneous transformation matrix, and specifically comprising the following steps:
step 1.1, setting a reference coordinate system and a local coordinate system for the numerical control machine tool based on the topological structure relationship of the numerical control machine tool parts, setting the Y-axis local coordinate system to be coincident with the reference coordinate system, wherein the reference coordinate system of the numerical control machine tool is shown in figure 1.
Step 1.2, identifying Geometric Errors of double rotating shafts of the numerical control machine tool, wherein the Geometric Errors include 12 Position-Dependent Geometric Errors (PDGEs) and 8 Position-Independent Geometric Errors (PIGEs), PIGEs of an A shaft are shown in fig. 2, and PIGEs of a C shaft are shown in fig. 3.
And 1.3, constructing an error transformation matrix by using the homogeneous transformation matrix.
Position error E of actual revolution center line of A axis in Y axis directionYOAIs the deviation of the axis of the A-axis in the Y direction, DYOAIs the error transformation matrix:
position error E of actual rotation center line of A axis in Z axis directionZOAIs the deviation of the axis of the A-axis in the Z direction, DZOAIs the error transformation matrix:
the projection of the actual revolution center line of the A axis on the XOZ plane forms an included angle E with the X axisBOAIs the parallelism error of the axis of the A-axis around the Y-axis, TB0AIs the error transformation matrix:
the projection of the actual revolution center line of the A axis on the XOY plane forms an included angle E with the X axisCOAIs the parallelism error of the axis of the A-axis around the Z-axis, TC0AIs the error transformation matrix:
wherein D isYOA、DZOA、TB0A、TC0AIs the 4-term PIGEs error transformation matrix for the A-axis.
Position error E of C-axis actual rotation center line in X-axis directionXOCIs the deviation of the C-axis in the X direction, DXOCIs the error transformation matrix:
the position error of the C-axis actual rotation center line in the Y-axis direction is EYOCIs the deviation of the C-axis in the Y-direction, DYOCIs the error transformation matrix:
the projection of the C-axis actual rotation center line on the YOZ plane and the included angle E of the Z axisAOCIs the parallelism error of the C-axis around the X-axis, TAOCIs the error transformation matrix:
step C, forming an included angle E between the projection of the actual rotation center line of the axis C on the XOZ plane and the axis ZBOCIs the parallelism error of the C-axis around the Y-axis, TBOCIs the error transformation matrix:
wherein D isXOC、DYOC、TAOC、TBOCIs a 4-term PIGEs error transformation matrix for the C-axis.
wherein,
the method is a dual-rotation-axis PDGEs error transformation matrix based on a small-angle approximation principle.
And integrating the error matrixes, wherein the geometric error of the workpiece relative to the cutter is as follows:
and 2.1, sampling the error parameters by adopting a Monte Carlo method, and generating a Sobol sequence to determine the influence of each error on the space error of the machine tool.
Step 2.2, variance-based Sobol sensitivity analysis requires the determination of the number of errors, k, with 20 error terms in both axes of rotation, so k is set to 20.
Step 2.3, generating two parameter sample matrixes of the Sobol sequence A, B, and recording as follows:
wherein xijAn ith (j ═ 1, 2, 3.. n) sample representing the jth (i ═ 1, 2, 3.. k) error element.
Step 2.4, the ith column of the matrix B is changed to the ith column of the matrix A, and the rest columns of the matrix A are unchanged, so that the matrix AB is obtainediAs follows:
the matrix A, B, AB is constructed by the method described aboveiThe total (k +2) N sets of rotation axis error parameters are obtained, thus obtaining (k +2) N sets
The value is obtained. For each group
There is a unique matrix A, B, ABiCorresponding to f (A), f (B), f (AB)i)。
Step 2.5, calculating the first-order sensitivity and the global sensitivity of each error element by a variance calculation formula of system response, wherein the calculation formula is as follows:
Var(Y)＝Var(YA+YB) (3)
Y＝(ya1ya2... yanyb1yb2... ybn)T(6)
wherein y isj1Var (Y) is the standard deviation of Y for the corresponding output values of the input matrix.
Step 2.6, calculating a formula of the first-order sensitivity and the global sensitivity of the error element:
Sirepresenting an error element xiFirst order sensitivity of STiRepresenting an error element xiGlobal sensitivity of (c). Error element xiThe first order sensitivity of (a) represents the direct effect of the error on the machine space error, and the global sensitivity represents the coupled effect of the error on the machine space error.
The sampling ratio of PDGEs and PIGEs of the target five-axis numerical control machine tool is 3: 7, wherein the sampling ranges of the position error and the angle error are (0, 1) mu m and (0, 1)', respectively.
And 3, carrying out sensitivity analysis on the error parameters based on the specific rotation angle position of the rotating shaft. Because the rotating angles of the rotating shafts are different, the influence of various errors of the rotating shafts on the precision of the machine tool is changed. Aiming at the problem of sensitivity of the rotating shaft of the five-axis numerical control machine tool at different corner positions, five groups of specific corner positions and one group of random change of the corner positions in the machining range are set to carry out sensitivity analysis on double rotating shafts of the five-axis numerical control machine tool.
And 3.1, setting the rotation angle of the shaft A to be 0 degrees and the rotation angle of the shaft C to be 0 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.2, setting the rotation angle of the shaft A to be 45 degrees and the rotation angle of the shaft C to be 45 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.3, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.4, setting the rotation angle of the shaft A to be 0 degree and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.5, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 0 degree, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
And 3.6, setting the rotation angle of the shaft A to randomly change within 0-90 degrees, setting the rotation angle of the shaft C to randomly change within 0-360 degrees, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool.
The Sobol sensitivity analysis result of step 3 (as shown in fig. 4 and 5) shows that the errors affecting the processing precision are mainly distributed in the PIGEs part. The PIGEs have a large influence on the space errors of the five-axis numerical control machine tool, the PDGEs have a small influence on the space errors of the five-axis numerical control machine tool, and the key geometric errors in the 20 geometric errors can be identified through a Sobol sensitivity analysis method. The key error in the geometric error affecting the accuracy of the machine tool comes from E in PIGEsY0A、EY0C、EA0CThe first-order sensitivity affecting the machining precision accounts for 67.42% of the 20 geometric errors, and the global sensitivity affecting the machining precision accounts for 26.97% of the 20 geometric errors under the condition of interaction.
Through the Sobol sensitivity analysis result, the geometric errors of the five-axis numerical control machine tool are identified, and the accuracy of the numerical control machine tool can be improved by controlling the key geometric errors.
The sensitivity analysis of the geometric errors of the double rotating shafts of the five-axis numerical control machine tool is completed, and the sensitivity analysis comprises 8 items of geometric errors independent of the position and 12 items of geometric errors related to the position.
The method effectively solves the problem of identification and detection of the geometric errors of the double rotating shafts in the five-axis numerical control machine tool, and provides effective analysis of the geometric error sensitivity of the double rotating shafts of the five-axis numerical control machine tool.
The method carries out sensitivity analysis on the geometric errors of the double rotating shafts of the five-axis numerical control machine tool, and finally obtains the key geometric errors of the double rotating shafts of the five-axis numerical control machine tool. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention, as any modifications, equivalent substitutions, improvements and the like, which are within the spirit and principle of the invention, are intended to be covered by the scope of the invention.
Claims (4)
1. The method for analyzing the geometric error sensitivity of the double rotating shafts of the five-axis numerical control machine tool comprises the following steps of:
step 1, constructing a geometric error mathematical model of a double-rotation shaft by utilizing a multi-body system theory and a homogeneous transformation matrix, and identifying each geometric error;
2, performing Sobol sensitivity analysis based on Monte Carlo sampling on the double rotating shafts of the five-axis numerical control machine tool;
and 3, carrying out sensitivity analysis on the error parameters based on the positions of the specific corners of the double rotating shafts, and carrying out sensitivity analysis on the double rotating shafts by setting five groups of positions of the specific corners.
2. The method for analyzing the geometric error sensitivity of the double rotating shafts of the five-axis numerical control machine tool according to claim 1, wherein in the step 1, a mathematical model of the geometric errors of the double rotating shafts is constructed by using a multi-body system theory and a homogeneous transformation matrix so as to identify the geometric errors of the double rotating shafts, and the method comprises the following steps:
step 1.1, setting a reference coordinate system and a local coordinate system for a numerical control machine tool, and setting a Y-axis local coordinate system to be coincident with the reference coordinate system;
step 1.2, identifying geometric errors of double rotating shafts of the numerical control machine tool;
step 1.3, constructing an error transformation matrix by utilizing the homogeneous transformation matrix;
taking the axis A as an example, obtaining a geometric error transformation matrix of the double rotating shafts through a homogeneous transformation matrix;
position-independent error transformation matrix for axis a:
position-dependent error transformation matrix for the a-axis:
likewise, the position-independent error transformation matrix for the C-axis:
the C-axis position-dependent error transformation matrix:
and integrating the error matrixes, wherein the geometric error of the workpiece relative to the cutter is as follows:
the establishment of the double-rotating-axis mathematical model of the five-axis numerical control machine tool is completed.
3. The method for analyzing geometrical error sensitivity of double rotation axes of a five-axis numerical control machine tool according to claim 1, wherein in the step 2, the Sobol sensitivity analysis based on Monte Carlo sampling comprises the steps of:
step 2.1, sampling the error parameters based on a Monte Carlo method, and generating a Sobol sequence to determine the influence of each error on the machine tool space error;
step 2.2, determining the error number k based on the variance Sobol sensitivity analysis, wherein the dual rotation axes have 20 error items in total, so that k is set to be 20;
step 2.3, generating two parameter sample matrixes of the Sobol sequence A, B, and recording as follows:
wherein xijAn ith (j ═ 1, 2, 3.. n) sample representing a jth (i ═ 1, 2, 3.. k) error element;
step 2.4, the ith column of the matrix B is changed to the ith column of the matrix A, and the rest columns of the matrix A are unchanged, so that the matrix AB is obtainediAs follows:
the matrix A, B, AB is constructed by the method described aboveiThe total (k +2) N sets of rotation axis error parameters are obtained, thus obtaining (k +2) N sets
The value is obtained. For each group
There is a unique matrix A, B, ABiCorresponding to f (A), f (B), f (AB)i)；
Step 2.5, calculating the first-order sensitivity and the global sensitivity of each error element by a variance calculation formula of system response, wherein the calculation formula is as follows:
Var(Y)＝Var(YA+YB) (3)
Y＝(ya1ya2... yanyb1yb2... ybn)T(6)
wherein y isj1Var (Y) is the standard deviation of Y for the output values corresponding to the input matrix;
step 2.6, calculating a formula of the first-order sensitivity and the global sensitivity of the error element:
wherein SiIs the first order sensitivity of the i term error, STiIs the global sensitivity of the i-th error, each error element xiThe first order sensitivity of (a) represents the direct effect of the error on the machine space error, and the global sensitivity represents the coupled effect of the error on the machine space error.
4. The method for analyzing geometric error sensitivity of dual rotational axes of a five-axis numerical control machine tool according to claim 1, wherein in the step 3, the sensitivity analysis of the error parameters is performed based on the positions of the specific rotation angles of the dual rotational axes, and the sensitivity analysis of the dual rotational axes is performed by setting five groups of the positions of the specific rotation angles, including the steps of:
step 3.1, setting the rotation angle of the shaft A to be 0 degrees and the rotation angle of the shaft C to be 0 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
step 3.2, setting the rotation angle of the shaft A to be 45 degrees and the rotation angle of the shaft C to be 45 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
3.3, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
step 3.4, setting the rotation angle of the shaft A to be 0 degrees and the rotation angle of the shaft C to be 90 degrees, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
step 3.5, setting the rotation angle of the shaft A to be 90 degrees and the rotation angle of the shaft C to be 0 degree, carrying out sensitivity analysis on the position of the five-axis numerical control machine tool, and calculating the first-order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
step 3.6, setting the shaft A rotation angle to randomly change within 0-90 degrees and the shaft C rotation angle to randomly change within 0-360 degrees, carrying out sensitivity analysis on the five-axis numerical control machine tool, and calculating the first order sensitivity and the global sensitivity of the five-axis numerical control machine tool;
through the Sobol sensitivity analysis result, the geometric errors of the five-axis numerical control machine tool are identified, and the accuracy of the numerical control machine tool can be improved by controlling the key geometric errors.
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