CN107748539B - Five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition - Google Patents

Five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition Download PDF

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CN107748539B
CN107748539B CN201710885524.7A CN201710885524A CN107748539B CN 107748539 B CN107748539 B CN 107748539B CN 201710885524 A CN201710885524 A CN 201710885524A CN 107748539 B CN107748539 B CN 107748539B
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CN107748539A (en
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姜忠
丁杰雄
张靖
丁启程
李晴朝
杜丽
王伟
宋智勇
李�杰
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University of Electronic Science and Technology of China
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a five-axis machine tool multi-axis linkage error tracing method based on RTCP detection error feature recognition. The invention has the advantages that the invention not only can evaluate the linkage performance of the machine tool, but also can clearly determine the influence factors influencing the multi-axis linkage performance of the machine tool when the multi-axis linkage performance of the machine tool does not meet the requirements, thereby providing an optimization scheme of the machine tool, and adjusting the factors influencing the multi-axis linkage performance of the machine tool in terms of magnitude, thereby achieving the high-precision requirement of the machine tool.

Description

Five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition
Technical Field
The invention belongs to the technical field of numerical control machines, and particularly relates to a five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition.
Background
The five-axis linkage numerical control machine tool is mainly applied to machining and manufacturing of complex-surface parts such as dies, aerospace and the like. Along with the continuous improvement of the precision and physical property requirements of parts, higher requirements are provided for the multi-axis linkage precision of the numerical control machine tool. The error factors of the numerical control machine tool can be divided into two categories, namely static factors and dynamic factors, wherein the static precision is detected under the working conditions that no cutting load exists and the machine tool does not move or the moving speed is very low.
At present, common numerical control machine tool linkage performance Test instruments mainly comprise a ball bar instrument and an R-Test tester, wherein the ball bar instrument can only be used for testing two-axis or three-axis linkage performance, and the R-Test can be used for detecting the machine tool linkage performance when a plurality of movement axes of a five-axis numerical control machine tool are linked. The club instrument and R-Test manufacturers provide a five-axis machine tool linkage performance detection instrument and corresponding application software, and machine tool linkage errors in the multi-axis linkage of the five-axis machine tool can be detected by using the equipment and the software, but all manufacturers do not provide an error factor tracing method causing the multi-axis linkage errors. In the five-axis machine tool test standard published in international standard ISO10791-6, only a five-axis machine tool multi-axis linkage performance detection method is provided, and a machine tool linkage error tracing method is not provided. Therefore, international standards and manufacturers of detection instruments can only provide a detection instrument and a detection method for detecting five-axis linkage performance at present, and can only indicate whether the machine tool has errors, and when a detection result does not meet the requirement, a specific scheme for adjusting the factors of the machine tool cannot be provided for improving the machining precision of the machine tool.
Disclosure of Invention
The invention aims to solve the problems and provides a five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition, which has simple steps and can effectively trace the source
In order to solve the technical problems, the technical scheme of the invention is as follows: the five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature identification comprises the following steps:
s1, analyzing and determining the linkage error category of the five-axis machine tool according to the structure type of the five-axis machine tool and the influence degree of the motion axis error on the linkage error of the five-axis machine tool, and detecting the multi-axis linkage error of the five-axis machine tool under the condition of each linkage error category;
s2, establishing a mapping relation database between multi-axis linkage errors and five-axis machine tool linkage error categories, representing five-axis machine tool linkage errors through displacement errors of cutter point points in X, Y, Z three directions, and showing the five-axis machine tool linkage errors through a three-dimensional space error graph, wherein X represents a horizontal axis of the cutter point points in a space cutter coordinate system, Y represents a vertical axis of the cutter point points in the space cutter coordinate system, and Z represents a vertical axis of the cutter point points in the space cutter coordinate system;
s3, evaluating the linkage performance of the five-axis machine tool according to the error values of the cutter point detected in the step S2 in the three directions of X, Y, Z;
s4, if the evaluation result of the linkage performance of the machine tool is poor, tracing to obtain the error category influencing the linkage performance of the five-axis machine tool by using an RTCP detection error feature recognition method;
and S5, analyzing the machine tool linkage error influence factors obtained in the quantitative tracing step S4 based on the track similarity, comparing the detected actual errors with the errors in the error library in similarity, and considering that the errors in the error library represent real error values if the similarity is high, namely the multi-axis linkage errors of the currently detected machine tool.
Preferably, the evaluation of the linkage performance of the machine tool in the step S4 is performed by using an image feature recognition method.
Preferably, the step S4 further includes the steps of:
s41, carrying out normalization processing on the cutter point error result graph to form a new cutter point error track graph, wherein the normalization formula is as follows:
Figure BDA0001417636410000021
where Δ is the set of RTCP detection error values, Δ (i) is the ith RTCP detection error, Δ (i)NormalizationFor the ith RTCP detection error after normalization processing, max (delta) is the maximum value in the error value set, and min (delta) is the minimum value in the error value set;
s42, regarding the error track of the tool nose point of the tool normalized in the step S41 as an error track graph of the tool nose point of the tool, regarding the error value of each tool nose point of the tool as a pixel point in the error track graph of the tool nose point of the tool, extracting the boundary of the track in the image, and expressing the boundary by using horizontal and vertical coordinates; in an XOY plane, the coordinate points of the boundary points of the tool nose point error track graph can be represented by a point set (x (k), y (k)), wherein k is the number of the boundary points of the tool nose point error track graph; if the coordinate points are placed in a plurality of UV coordinate systems, UV is represented by letters of the plurality of coordinate systems, the abscissa x (k) corresponds to a real axis coordinate axis of the plurality of coordinate systems, and the ordinate y (k) corresponds to an imaginary axis coordinate axis of the plurality of coordinate systems, then the coordinate points of the XOY plane can be represented by a complex expression (2) in a displacement manner:
s(k)＝x(k)+jy(k) (2)
in formula (2), s (k) represents a complex expression of a coordinate point of the tool nose point error trajectory in the XOY plane, j is a constant, X (k) represents a coordinate value of the tool nose point error trajectory in the XOY plane with respect to the X axis, and Y (k) represents a coordinate value of the tool nose point error trajectory in the XOY plane with respect to the Y axis; assuming that the point set (x (k), y (k)) of the boundary includes N points in total, and the starting point of the boundary is (x (0), y (0)), the end point is (x (N-1), y (N-1)), and the starting point and the end point are arranged in sequence in the counterclockwise direction, the complex expression shown by the formula (2) is a periodic function, and according to the fourier transform theory, the discrete fourier transform of s (k) is shown as follows:
Figure BDA0001417636410000031
s (u) is a Fourier series coefficient, namely a Fourier descriptor, e is a constant, and the Fourier series of the periodic function has a unique Fourier descriptor after being expanded, so that the Fourier descriptor is used as the characteristic of the error track of the tool nose point;
s43, tracing the linkage error category of the five-axis machine tool, extracting a Fourier descriptor in the obtained error trajectory graph of the tool nose point, and then comparing the Fourier descriptor with the Fourier descriptor in the error trajectory graph library constructed in the step S42 to obtain an error trajectory graph with the minimum difference; the difference between the fourier descriptor of the error trace plot and the error map library can be evaluated by accumulating the errors, which is formulated as:
Figure BDA0001417636410000032
in formula (4), the letter E represents the accumulation of errors, ZiRepresents the ith Fourier descriptor, Zi _ galleryAnd n is the number of the Fourier descriptors of the error tracks.
Preferably, the normalization in step S41 means that the tool nose point error trajectory is formed by combining errors in three directions X, Y and Z, the maximum value of the errors in the three directions is normalized to 1, the minimum value is normalized to-1, and the remaining error values are normalized by dividing their own value by the maximum value.
Preferably, the similarity in step S5 is the similarity between the error sequence of the tool nose point measured by the detection machine and the error sequence in the error library.
Preferably, the similarity is assumed that the error trajectory data of the tool nose point obtained by detection is T ═ T (T)1，…，tN) The error trajectory data of the error type obtained in step S3 is Rp＝(rp1，…，rpM) The detected trace data is numbered as i-1 … N, and the dynamic time warping distance between any two points on the two error data numbered as j-1 … M in the standard trace data can be defined as:
Figure BDA0001417636410000033
in formula (5), min { D (i-1, j-1), D (i, j-1), D (i-1, j) } represents the minimum of the three dynamic time warping distances shown, for the detected track data T and the standard track numberAccording to the R, an n × m matrix is constructed, wherein the (i, j) th element in the matrix is two segments of data points TiAnd RjA distance d betweenij(ii) a Here, the euclidean distance is used to calculate the distance between two points:
Figure BDA0001417636410000041
the dynamic warping distance between two elements is the cumulative distance D (i, j), which is the slave element T1，R1) To (T)i，Ri) The minimum cumulative distance between the two, the calculation process of the minimum cumulative distance is as follows: in the dynamic warping algorithm, in order to find the shortest distance between two sequences, it is necessary to set a warping path W ═ W1，w2，…，wK(ii) a The warped path is a continuum formed by some elements on the distance matrix, the path defines a mapping between the time series sum, and the shortest distance between the two series sum can be obtained by comparing along the path; in calculating the distance between two error data, there are many paths that satisfy the above condition, but the warp path here requires a minimum warp cost:
Figure BDA0001417636410000042
in the formula (7), the position loop gain parameter of each motion axis obtained by tracing in this embodiment is: (Kpp)X，KppY，KppZ，KppA，KppB) With (1,0.95,1,1,0.96), KPP is the position loop gain parameter, DTW (T, R) is the value of DTW, and the right side of the medium sign in equation (7) represents the minimum value in the warp path.
The invention has the beneficial effects that: the five-axis machine tool multi-axis linkage error tracing method based on feature recognition not only can evaluate the linkage performance of the machine tool, but also can clearly influence the influence factors of the multi-axis linkage performance of the machine tool when the multi-axis linkage performance of the machine tool does not meet the requirements, thereby providing an optimization scheme of the machine tool, adjusting the influence factors of the multi-axis linkage performance of the machine tool in terms of magnitude, and further achieving the high-precision requirement of the machine tool.
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FIG. 1 is a scheme flow chart of a five-axis machine tool multi-axis linkage error tracing method based on feature recognition;
FIG. 2 is a diagram of the substeps of step S4 of the present invention;
FIG. 3 is a schematic of the testing of the present invention;
FIG. 4 is a graph of RTCP detection results of the present invention;
FIG. 5 is a graph showing RTCP detection results when the linkage error is 80% in the case of FIG. 4;
FIG. 6 is a graph of the normalization of the test results according to the present invention;
FIG. 7 is a schematic diagram of boundary extraction of the detection result according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments:
as shown in fig. 1, the five-axis machine tool multi-axis linkage error tracing method based on RTCP detection feature recognition provided by the present invention includes the following steps:
s1, analyzing and determining the linkage error category of the five-axis machine tool according to the structure type of the five-axis machine tool, and detecting the multi-axis linkage error of the five-axis machine tool under the condition of each linkage error category by using a machine tool RTCP technology;
in this embodiment, a five-axis linkage machine tool with linkage performance to be detected is a five-axis numerical control milling machine produced in a country, and is classified into a multi-axis linkage error category according to the influence degree of motion axis errors on machine tool linkage errors, and in this embodiment, the multi-axis linkage errors of the machine tool are represented by combinations of position loop gain parameters of each motion axis. The error presentation form of the five-axis machine tool linkage, namely the tool tip point error, is measured by utilizing the RTCP function of the five-axis machine tool, RTCP is the prior art, and only special description is made here, and corresponding function modules are adopted in machine tools of different machine tools. And detecting the linkage error of the five-axis machine tool by using the RTCP function, as shown in figure 3. The detailed test method and the test process of the RTCP-based five-axis machine tool linkage performance refer to the international standard ISO 10791-6.
S2, establishing a mapping relation database between RTCP detection errors and five-axis machine tool linkage error categories;
the RTCP-based five-axis machine tool multi-axis linkage error in step S1 is represented by the displacement of the tool tip point in X, Y, Z three directions, and the machine tool multi-axis linkage error can be shown by the deviation in three directions in the form of a three-dimensional spatial error graph, as shown in fig. 3. And constructing a mutual mapping relation between the tool nose point error graph of the tool and the linkage error category of the five-axis machine tool, and constructing an error graph library.
S3, evaluating the linkage performance of the five-axis machine tool according to the RTCP detection error;
the linkage performance of the machine tool is evaluated according to the magnitude of the RTCP detection error values in X, Y, Z three directions.
S4, if the evaluation result of the linkage performance of the machine tool is poor, tracing to obtain the error category influencing the linkage performance of the five-axis machine tool by using an RTCP detection error feature recognition method; and (5) measuring the linkage error of the machine tool according to the multi-axis linkage error testing method of the five-axis numerical control machine tool in the step S1, further obtaining a tool nose point error map of the tool, inputting the error map into a mapping relation library of the detection error and the type of the linkage error of the machine tool, and tracing the type of the linkage error of the machine tool by using a characteristic identification technology. In this embodiment, a feature recognition technology based on images is used to trace the type of linkage error of the machine tool. The measured value of the linkage error of the five-axis machine tool is shown in fig. 4, and as shown in fig. 2, the specific implementation of the step S4 includes the following steps:
s41, preprocessing an RTCP detection error result graph;
different error values of the same error type only cause differences in the size of the error trajectory without changing the shape of the error trajectory. If the machine tool linkage error is 80% of the case of fig. 4, the tool nose point error map is shown in fig. 5, and the shape of the tool nose point error trajectory in each plane is substantially the same as that in fig. 4, and the size of the shape is reduced to some extent. Therefore, the error trajectory needs to be normalized to form a new error trajectory diagram of the tool point of the tool.
The tool nose point error track is formed by combining errors in X, Y and Z directions, the maximum value of the errors in the three directions is normalized to be 1, the minimum value is normalized to be-1, the other error values are normalized by dividing the value of the error value by the maximum value, and the normalization formula is as follows:
Figure BDA0001417636410000051
where Δ is the set of RTCP detection error values, Δ (i) is the ith RTCP detection error, Δ (i)NormalizationThe error is detected for the ith RTCP after normalization.
The error trajectory plot of the XOY plane as in fig. 4 is shown in fig. 6 by the normalized plot.
S42, extracting the characteristics of the detection error result graph;
and taking the normalized error track as an image, taking each error value as a pixel point, extracting the boundary of the track in the image, expressing the boundary by using horizontal and vertical coordinates, and reducing the two-dimensional data into a one-dimensional function by using a complex description method. Assuming that the boundary of the trajectory is defined by k coordinates as shown in fig. 7, these coordinate points can be represented by a set of points (x (k), y (k)) in the XOY plane. If the coordinate point sets are placed in a complex UV coordinate system, the abscissa x (k) corresponds to the real axis coordinate axis in the complex coordinate system, and the ordinate y (k) corresponds to the imaginary axis coordinate axis in the complex coordinate system, then the coordinate points of the XOY plane can be represented by the complex expression (2).
s(k)＝x(k)+jy(k) (2)
Assuming that the point set (x (k), y (k)) of the boundary comprises N points in total, and the starting point of the boundary is (x (0), y (0)), the end point is (x (N-1), y (N-1)), and the starting point and the end point are arranged in sequence in the counterclockwise direction, the complex expression shown by the formula (2) is a periodic function, and the discrete Fourier change is performed on s (k) according to the Fourier transform theory as shown in the formula.
Figure BDA0001417636410000061
Wherein S (u) is a Fourier series coefficient, i.e., a Fourier descriptor. The Fourier series expansion of the periodic function has a unique Fourier descriptor, so the Fourier descriptor is taken as the characteristic of the error track of the tool point.
S43, identifying linkage error categories of the tracing five-axis machine tool based on the characteristics;
after the error trajectory diagrams of the tool nose point errors on the three planes are obtained by the five-axis machine tool RTCP detection, extracting Fourier descriptors of the error trajectory diagrams, respectively comparing the Fourier descriptors of the three planes with the Fourier descriptors in the error trajectory diagram library constructed in the step S42, and determining the error type of the error trajectory with the minimum difference as the detection error type of the five-axis machine tool. The difference between the fourier descriptor of the error trace plot and the error map library can be evaluated by accumulating the errors, which is formulated as:
Figure BDA0001417636410000062
in the formula ZiRepresents the ith Fourier descriptor, Zi _ galleryAnd n is the number of the Fourier descriptors of the error tracks.
The types of errors obtained by tracing in this embodiment are: and the five-axis linkage error is caused by the fact that the errors of the Y axis and the B axis of the motion axis are larger than the errors of the rest 3 axes.
S5, analyzing and quantifying the similarity of the motion tracks to quantify the machine tool factors obtained in the tracing step 4;
after the five-axis machine tool linkage error type is obtained through tracing by a feature identification tracing method, the accurate value of the error still needs to be accurately analyzed, and the accurate error value tracing can not be obviously realized through error track image identification. The raw error data of the tool point in X, Y, Z contains more detailed information, which provides data support for accurate tracing of the error. The similarity measurement can clearly and accurately represent the difference between two groups of error data, when the similarity value is smaller, the difference of the two sections of data is larger, and if the similarity value is larger, the difference of the two sections of data sequences is smaller. If the measured error sequence of the tool nose point of the tool is very similar to the error sequence in the error library, the five-axis machine tool linkage error value represented by the error sequence in the error library can be regarded as the multi-axis linkage error of the current machine tool to be detected.
Because the data length of each detection error can not be guaranteed to be consistent, the DTW distance can be adopted to represent the similarity between error data.
Assuming that the error track data of the tool nose point obtained by detection is T ═ T (T)1，…，tN) The error trajectory data belonging to the error type obtained in step S3 in the standard error library is Rp＝(rp1，…，rpM) And p represents the p-th error track in the standard error library, and k error tracks are total. The data length of the detection track is N, and the data length of the error track in the standard error library is M. For the sake of clarity, the detected trace data is numbered i 1 … N, and the standard trace data is numbered j 1 … M. The dynamic time warp distance between any point on the two error data can be defined as:
Figure BDA0001417636410000071
for the detected track data T and the standard track data R, a matrix of n × m is constructed, wherein the (i, j) th element in the matrix is two segments of data points TiAnd RjA distance d betweenij. Here, the euclidean distance is used to calculate the distance between two points:
Figure BDA0001417636410000072
the dynamic warping distance between two elements is the cumulative distance, i.e. D (i, j) is the slave element (T)1，R1) To (T)i，Rj) The minimum cumulative distance between. The distance is calculated as follows: in the dynamic warping algorithm, the one-to-one correspondence relationship between points on two sequences is no longer satisfied, and in order to find the shortest distance between two sequences, it is necessary to set a warping path W ═ W1，w2，…，wK. The twisted path isIs a continuum of elements of the distance matrix, the path defining a mapping between the time series and the sum, along which the shortest distance between the two series is obtained by comparison.
It is clear that there are many paths that satisfy the above conditions when calculating the distance between two error data, but the warp path here requires a minimum warp penalty.
Figure BDA0001417636410000081
In the formula (7), the position loop gain parameter of each motion axis obtained by tracing in this embodiment is:
(KppX，KppY，KppZ，KppA，KppB) And (1,0.95,1,1,0.96), KPP is a position loop gain parameter, DTW (T, R) is a value of DTW, and the right side of the medium sign in the formula (7) represents a minimum value in a twisted path, so that the optimization and adjustment of the linkage performance of the machine tool can be guided according to the error parameter.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (5)

1. A five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition is characterized by comprising the following steps:
s1, analyzing and determining the linkage error category of the five-axis machine tool according to the structure type of the five-axis machine tool and the influence degree of the motion axis error on the linkage error of the five-axis machine tool, and detecting the multi-axis linkage error of the five-axis machine tool under the condition of each linkage error category;
s2, establishing a mapping relation database between multi-axis linkage errors and five-axis machine tool linkage error categories, representing five-axis machine tool linkage errors through displacement errors of cutter point points in X, Y, Z three directions, and showing the five-axis machine tool linkage errors through a three-dimensional space error graph, wherein X represents a horizontal axis of the cutter point points in a space cutter coordinate system, Y represents a vertical axis of the cutter point points in the space cutter coordinate system, and Z represents a vertical axis of the cutter point points in the space cutter coordinate system;
s3, evaluating the linkage performance of the five-axis machine tool according to the error values of the cutter point detected in the step S2 in the three directions of X, Y, Z;
s4, if the evaluation result of the linkage performance of the machine tool is poor, tracing to obtain the error category influencing the linkage performance of the five-axis machine tool by using an RTCP detection error feature recognition method;
s5, analyzing the machine tool linkage error influence factors obtained in the quantitative tracing step S4 based on the track similarity, comparing the detected actual errors with the errors in the error library in similarity, and if the similarity is high, determining that the errors in the error library represent real error values, namely the multi-axis linkage errors of the currently detected machine tool;
the similarity in step S5 is the similarity between the error sequence of the tool nose point measured by the detection machine and the error sequence in the error library.
2. The five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition is characterized in that the machine tool linkage performance evaluation in the step S4 is carried out by an image feature recognition method.
3. The five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition is characterized in that the step S4 further comprises the following steps:
s41, carrying out normalization processing on the cutter point error result graph to form a new cutter point error track graph, wherein the normalization formula is as follows:
Figure FDA0002589897680000011
where Δ is the set of RTCP detection error values, Δ (i) is the ith RTCP detection error, Δ (i)NormalizationFor the ith RTCP detection error after normalization processing, max (delta) is the maximum value in the error value set, and min (delta) is the minimum value in the error value set;
s42, regarding the error track of the tool nose point of the tool normalized in the step S41 as an error track graph of the tool nose point of the tool, regarding the error value of each tool nose point of the tool as a pixel point in the error track graph of the tool nose point of the tool, extracting the boundary of the track in the image, and expressing the boundary by using horizontal and vertical coordinates; in an XOY plane, the coordinate points of the boundary points of the tool nose point error track graph can be represented by a point set (x (k), y (k)), wherein k is the number of the boundary points of the tool nose point error track graph; if the coordinate points are placed in a plurality of UV coordinate systems, UV is represented by letters of the plurality of coordinate systems, the abscissa x (k) corresponds to a real axis coordinate axis of the plurality of coordinate systems, and the ordinate y (k) corresponds to an imaginary axis coordinate axis of the plurality of coordinate systems, then the coordinate points of the XOY plane can be represented by a complex expression (2) in a displacement manner:
s(k)＝x(k)+jy(k) (2)
in formula (2), s (k) represents a complex expression of a coordinate point of the tool nose point error trajectory in the XOY plane, j is a constant, X (k) represents a coordinate value of the tool nose point error trajectory in the XOY plane with respect to the X axis, and Y (k) represents a coordinate value of the tool nose point error trajectory in the XOY plane with respect to the Y axis; assuming that the point set (x (k), y (k)) of the boundary includes N points in total, and the starting point of the boundary is (x (0), y (0)), the end point is (x (N-1), y (N-1)), and the starting point and the end point are arranged in sequence in the counterclockwise direction, the complex expression shown by the formula (2) is a periodic function, and according to the fourier transform theory, the discrete fourier transform of s (k) is shown as follows:
Figure FDA0002589897680000021
s (u) is a Fourier series coefficient, namely a Fourier descriptor, e is a constant, and the Fourier series of the periodic function has a unique Fourier descriptor after being expanded, so that the Fourier descriptor is used as the characteristic of the error track of the tool nose point;
s43, tracing the linkage error category of the five-axis machine tool, extracting a Fourier descriptor in the obtained error trajectory graph of the tool nose point, and then comparing the Fourier descriptor with the Fourier descriptor in the error trajectory graph library constructed in the step S42 to obtain an error trajectory graph with the minimum difference; the difference between the fourier descriptor of the error trace plot and the error map library can be evaluated by accumulating the errors, which is formulated as:
Figure FDA0002589897680000031
in formula (4), the letter E represents the accumulation of errors, ZiRepresents the ith Fourier descriptor, Zi _ galleryAnd n is the number of the Fourier descriptors of the error tracks.
4. The five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition as claimed in claim 3, wherein the normalization in step S41 means that the tool nose point error trajectory is formed by combining errors in three directions X, Y and Z, the maximum value of the errors in the three directions is normalized to 1, the minimum value is normalized to-1, and the rest error values are normalized by dividing the self value by the maximum value.
5. The five-axis machine tool multi-axis linkage error tracing method based on RTCP error feature recognition as claimed in claim 1, wherein the similarity is assumed that the error trajectory data of the tool nose point obtained by detection is T ═ T (T)1,…,tN) The error trajectory data of the error type obtained in step S3 is Rp＝(rp1,…,rpM) The detected track data is numbered as i-1 … N, the standard track data is numbered as j-1 … M, and the dynamic time distortion between any points on the two error data is calculatedThe curved distance may be defined as:
Figure FDA0002589897680000032
in formula (5), min { D (i-1, j-1), D (i, j-1), D (i-1, j) } represents the minimum value of the three dynamic time warping distances, and for the detected track data T and the standard track data R, a matrix of n × m is constructed, wherein the (i, j) th element in the matrix is two segments of data points TiAnd RjA distance d betweenij(ii) a Here, the euclidean distance is used to calculate the distance between two points:
Figure FDA0002589897680000033
the dynamic warping distance between two elements is the cumulative distance D (i, j), which is the slave element T1,R1) To (T)i,Rj) The minimum cumulative distance between the two, the calculation process of the minimum cumulative distance is as follows: in the dynamic warping algorithm, in order to find the shortest distance between two sequences, it is necessary to set a warping path W ═ W1,w2,...,wK(ii) a The warped path is a continuum formed by some elements on the distance matrix, the path defines a mapping between the time series sum, and the shortest distance between the two series sum can be obtained by comparing along the path; in calculating the distance between two error data, there are many paths that satisfy the above condition, but the warp path here requires a minimum warp cost:
Figure FDA0002589897680000041
in the formula (7), the position loop gain parameter of each motion axis obtained by tracing is: (Kpp)X,KppY,KppZ,KppA,KppB) With (1,0.95,1,1,0.96), KPP is the position loop gain parameter, DTW (T, R) is the value of DTW, and the right side of the medium sign in equation (7) represents the minimum value in the warp path.
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