A machine tool RTCP precision interpolation method based on three-dimensional curved surface fitting

Abstract

The application belongs to the field of intelligent manufacturing, and particularly relates to a machine tool RTCP precision interpolation method based on three-dimensional curved surface fitting, which comprises the following steps: determining a main motion shaft of a machine tool according to a machine tool topological structure and RTCP functions, setting a motion interval of the main motion shaft, and forming a linkage RTCP detection position combination; obtaining three-direction error values under each linkage RTCP detection position combination; adopting a local weighted regression scattered point smoothing algorithm to fit three-dimensional data, so as to obtain three groups of regression models corresponding to three-direction errors; resetting a plurality of linkage motion position combinations as RTCP precision verification points, and performing verification; if a specified threshold is exceeded, a smoothing coefficient of the step is modified; and if the threshold is within a range, fitting is ended and is used for RTCP precision interpolation and compensation. The application proposes three-dimensional curved surface fitting based on a local weighted regression scattered point smoothing algorithm, combines RTCP error three-direction values and detection positions, and respectively makes three-dimensional graphics for fitting prediction, so that the method is novel and has high fitting interpolation accuracy.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of intelligent manufacturing, and particularly relates to a machine tool RTCP precision interpolation method based on three-dimensional curved surface fitting. BACKGROUND

[0002] Five-axis linkage RTCP (RTP control protocol) precision is an important index for measuring the machining precision of a machine tool, and machine tool error detection based on the RTCP function is a detection method for reflecting the machine tool error through linkage of all axes and keeping the position of a tool tip point unchanged, and the position error of the tool tip point is used to reflect the machine tool error, which has been widely applied in five-axis machine tool precision detection with a rotating shaft.

[0003] In the prior art, a precision detection tool assembled by three micrometers is proposed in a document (Zhang Yun. A five-coordinate dynamic precision detection tool based on RTCP function [J]. Manufacturing Technology and Machine Tool, 2012 (11): 92-94), which can complete the measurement of five-axis linkage RTCP precision, and a patent ZL202010746268.5 proposes a CA type machine tool RTCP precision detection and calibration method based on a measuring head. The above methods mainly use self-made or standard instruments to measure the RTCP precision. Since the RTCP error is a measurement value at a specified motion position combination, for other motion position combinations, one way is to re-measure, but the tool needs to be prepared, and when the number of measured points is too large, the efficiency is extremely low. Another way is to perform interpolation prediction, and there is a certain requirement for the detection interval of the original data. If the interval value is too large, the interpolation accuracy of the RTCP precision is reduced, and if the interval is too small, the detection time of the entire five-axis linkage space will be geometrically multiplied, so it is necessary to complete a certain number of RTCP precision measurements within a reasonable detection interval, and the RTCP precision not at the detection point can also be interpolated and predicted. For this purpose, ZL201910026305.2 proposes a five-axis NC machine tool space error detection method based on RTCP, which inversely calculates and deduces the geometric errors of the machine tool from the RTCP error values of the rotating shaft at different angle combinations, solves the polynomial coefficients after polynomial interpolation of the geometric errors, and performs prediction calculation on the RTCP precision at a specified rotating shaft angle. This method conforms to the principle of error identification and prediction, but the calculation amount involved is large, and up to 41 geometric errors need to be calculated by polynomial fitting, which is time-consuming. SUMMARY

[0004] To solve the problem of low efficiency of five-axis machine tool linkage RTCP error interpolation compensation in the prior art, the application provides a machine tool RTCP precision interpolation method based on three-dimensional curved surface fitting.

[0005] To achieve the above application purposes, the technical scheme provided by the application is as follows:

[0006] A machine tool RTCP precision interpolation method based on three-dimensional surface fitting, comprising the following steps:

[0007] Step S1: According to the topology structure of five-axis machine tool and RTCP function, the main motion axis of five-axis machine tool is determined;

[0008] Step S2: Set the motion interval of the main motion axis to form a series of five-axis linkage RTCP detection position combinations;

[0009] Step S3: Obtain the three-direction error value under each linkage RTCP detection position combination;

[0010] Step S4: Based on the five-axis linkage RTCP detection position combination, the main motion axis position and the three-direction error value are selected as a set of three-dimensional data, and a local weighted regression scatter smoothing algorithm is used to fit the three-dimensional data, and three sets of regression models corresponding to the error in three directions are obtained respectively;

[0011] Step S5: Re-set the multiple five-axis linkage motion position combinations as RTCP precision verification points, and verify based on the three sets of regression models of step S4, if it exceeds the specified threshold, modify the smoothing coefficient of the smoothing algorithm in step S2, if it is within the threshold, end the fitting and use it for RTCP precision interpolation and compensation.

[0012] Further, the specific implementation steps of step S1 are:

[0013] The motion relationship of each axis in the five-axis linkage involved in the RTCP function is as follows:

[0014]

[0015] In the formula, (x t ,y t ,z t ) represents the three-direction coordinate values of the tool tip point in the machine tool coordinate system; X, Y and Z represent the motion coordinate values of the machine tool translation axes X, Y and Z respectively; A and C represent the motion angles of the machine tool rotation axes A and C respectively, and L is the tool length, which is a constant value after selecting the tool;

[0016] Further, step S2 is specifically: setting the motion interval of the main motion axis, and the translation axes will be automatically operated by the machine tool numerical control system according to the RTCP motion relationship of step S1;

[0017] If the motion range of the rotation axis A is ±90° and the motion range of the rotation axis C is ±360°, then set the motion interval angle Δa of the A axis and the motion interval angle Δc of the C axis, then:

[0018] The number of A-axis detection points: Na=180Δa+1, the number of C-axis detection points: Nc=720Δc+1;

[0019] Combining all detection points of the A-axis, all detection points of the C-axis and the movement positions of the translational axes, a series of five-axis linkage RTCP detection position combinations (A i ,C j ,X,Y,Z), i≤Na+1, j≤Nc+1, are obtained, wherein A i represents the ith detection angle of the A-axis, C j represents the jth detection angle of the C-axis, and X, Y and Z respectively represent the X-axis movement coordinate value, the Y-axis movement coordinate value and the Z-axis movement coordinate value of the machine tool translational axes, which are automatically calculated by the numerical control system according to the A-axis and C-axis angles (A i ,C j ) and moved to the instruction position to stop.

[0020] Further, the S3 specifically comprises: acquiring three-direction error values under the five-axis linkage position combination by using an R-test detection instrument, recording the RTCP error three-direction values at each movement position, and denoted as (ekx,eky,ekz), k∈[1,i·j], wherein k represents the kth combination position in the linkage detection position combination; e kx , e ky , e kz represent the X, Y and Z three directions of the RTCP error at the kth combination position.

[0021] Further, the specific implementation steps of the step S4 are as follows:

[0022] S41: based on the five-axis linkage RTCP detection position combination (A i ,C j ,X,Y,Z), selecting the movement positions (A i ,C j ) of the main movement axes, and defining the A-axis angle and the C-axis angle as the X-axis and the Y-axis in the Cartesian coordinate system to form the XY plane in the Cartesian orthogonal coordinate system, and taking one of the RTCP error values (X / Y / Z three directions) at each movement position combination as the Z-axis in the Cartesian orthogonal coordinate system, and forming a three-dimensional data set (Ai,Cj,ekm), m∈[x,y,z], e km represents one of e kx , e ky , e kz , which is described as a series of space point clouds in the Cartesian coordinate system, and the point cloud data is used to construct an original surface;

[0023] S42: adopting a local weighted regression scatter smoothing algorithm to fit the three-dimensional data set of the original surface, and obtaining a movement position range after fitting.

[0024] Further, the step S42 specifically comprises:

[0025] 1) The data set (A i ,C j ,e kx ) is taken as the sample set for training, wherein (A i ,C j ) is the input matrix of sample points, and e kx is the output vector of sample points;

[0026] The mathematical model can be set as: e kx =g(A i ,C j )+ε k , wherein g(A i ,C j ) is a smoothing function, and ε k is an independent distribution random variable with mean 0;

[0027] The weight function of the local weighted regression scatter smoothing algorithm is w(a,c), a and c represent a set of rotation angle values to be interpolated, the smoothing coefficient is f, the data width is r, and the local weighted regression selects a cubic weight function:

[0028]

[0029] Let the range of the smoothing coefficient f be 0

[0030] 2) According to the selected weight function w(a,c), the data around (a,c) is fitted by a polynomial using the weighted least square method with the data in the entire moving window, and the smoothing function g(a,c) is obtained. The formula is as follows:

[0031]

[0032] Thus, the local weighted regression fitting value of the X direction of the point is obtained. The smoothing functions and the local weighted regression fitting values of the Y and Z directions are obtained by using steps 1) and 2), and thus the motion position range of the completed fitting is obtained.

[0033] Further, the selection of the smoothing coefficient f determines the smoothing degree of the fitting of the curved surface data, and needs to be modified multiple times according to the characteristics of the detection data to ensure that the fitting conforms to the data trend.

[0034] Further, the step S5 specifically comprises:

[0035] S51: selecting an angular position within the motion range of the main motion axis according to the motion position range fitted in step S4;

[0036] S52: Combine new motion positions Substitute it into the regression model of step S4 to obtain the local weighted regression fitting values ​​in the X, Y, and Z directions under each combination, thereby obtaining the RTCP error fitting values ​​under other angle combinations of the machine tool;

[0037] S53: Compare the three-dimensional RTCP error detection value of the verification point obtained in S51 with the three-dimensional RTCP error fitting value. If the difference in the X / Y / Z directions is within the specified threshold range, it means that the RTCP error interpolation method based on three-dimensional surface fitting is effective. If it exceeds the threshold, step S42 is repeated to set a new smoothing coefficient f.

[0038] Furthermore, the rule for selecting the angle position in S51 is as follows:

[0039] 1) Take the existing detection angle (A i ,C j ) The value is a fixed value, and the C-axis angle is generated by random integers to obtain several The subscript p represents the total number of randomly generated C-axis angles, forming a new motion position combination

[0040] 2) Take the existing detection angle (A i ,C j ) The value is a fixed value, and the A-axis angle is generated by random integers to obtain several The subscript q represents the total number of randomly generated A-axis angles, forming a new motion position combination

[0041] After obtaining the new detection angle, the RTCP error is detected based on the method in step S2, thereby obtaining a three-way RTCP error detection value for verification.

[0042] Furthermore, the expression of the random integer generation method in step 1) of S51 is randint(1,p orq,[-axis,axis]), where randint is a function for randomly generating integers, its parameter 1 represents a one-dimensional integer vector, p or q represents a one-dimensional integer vector containing p or q integers, [-axis,axis] represents the value range of the integer, and axis represents the angular position limit of the two main motion axes.

[0043] The beneficial effects of the present invention are:

[0044] 1. The application uses detection instruments to obtain a limited number of machine tool RTCP error values, and in view of the randomness and nonlinearity of the RTCP error, a three-dimensional surface fitting based on a local weighted regression scatter smoothing algorithm is proposed, the three-directional values of the RTCP error are combined with the detection positions, and three-dimensional graphics are fitted and predicted respectively, the method is novel and has high fitting interpolation accuracy.

[0045] 2. The RTCP error interpolation method proposed in the application can be expanded to a larger fitting range in the form of three-dimensional graphics, and compared with the RTCP error interpolation method of decoupling error and then calculating inversely, the calculation difficulty is lower, and the method has good practicability. DETAILED DESCRIPTION

[0046] Figure 1 The whole flowchart of the application.

[0047] Figure 2 The application is a schematic diagram of RTCP error detection based on detection instruments.

[0048] Figure 3 It is a schematic diagram of RTCP detection position combination of five-axis machine tool based on main motion shaft.

[0049] Figure 4 It is a three-dimensional surface fitting schematic diagram based on the local weighted regression scatter smoothing algorithm in the application (X-direction error fitting diagram).

[0050] Figure 5 It is a three-dimensional surface fitting schematic diagram based on the local weighted regression scatter smoothing algorithm in the application (Y-direction error fitting diagram).

[0051] Figure 6 It is a three-dimensional surface fitting schematic diagram based on the local weighted regression scatter smoothing algorithm in the application (Z-direction error fitting diagram).

[0052] Figure 7 It is a three-directional RTCP error value (unit: mm) under the motion position combination.

[0053] Figure 8 It is the effect data of fitting.

[0054] Figure 9 It is the result data after taking the absolute value of the difference. DETAILED DESCRIPTION

[0055] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are used to explain the present application but not to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0056] The specific implementation methods of the present application will be described below in combination with the drawings and examples, and the present application is not limited to the embodiments.

[0057] Embodiment 1

[0058] As shown in the figure, a machine tool RTCP precision interpolation method based on three-dimensional surface fitting includes the following steps: Figure 1

[0059] Step S1: According to the topological structure and RTCP function of the five-axis machine tool, the main motion axis of the five-axis machine tool is determined, and the master-slave relationship in the linkage process of each axis is clarified;

[0060] Step S2: Set the motion interval of the main motion axis to form a series of five-axis linkage RTCP detection position combinations;

[0061] Step S3: Obtain the three-direction error values under each linkage RTCP detection position combination by using the detection instrument;

[0062] Step S4: Based on the five-axis linkage RTCP detection position combination, the main motion axis position and the three-direction error value are selected as a set of three-dimensional data, and a local weighted regression scatter smoothing algorithm is used to fit the three-dimensional data to obtain three sets of regression models corresponding to the three directions of error respectively;

[0063] Step S5: Re-set a plurality of five-axis linkage motion position combinations as RTCP precision verification points, and verify based on the three sets of regression models in step S4. If it exceeds the specified threshold, modify the smoothing coefficient of the smoothing algorithm in step S2. If it is within the threshold range, end the fitting and use it for RTCP precision interpolation and compensation.

[0064] Embodiment 2

[0065] As shown in the figure, a machine tool RTCP precision interpolation method based on three-dimensional surface fitting includes the following steps: Figure 1

[0066] Step S1: According to the topological structure and RTCP function of the five-axis machine tool, the main motion axis of the five-axis machine tool is determined, and the master-slave relationship in the linkage process of each axis is clarified;

[0067] Step S2: Set the motion interval of the main motion axis to form a series of five-axis linkage RTCP detection position combinations;​​

[0068] Step S3: and use the detection instrument to obtain the three-direction error values under each combination of the linkage RTCP detection positions;

[0069] Step S4: based on the five-axis linkage RTCP detection position combination, the main motion axis position and the three-direction error values are selected as a set of three-dimensional data, and a local weighted regression scatter smoothing algorithm is used to fit the three-dimensional data, and three sets of regression models corresponding to the three directions of error are obtained respectively;

[0070] Step S5: re-set the multiple five-axis linkage motion position combinations as RTCP precision verification points, and based on the three sets of regression models in step S4, if the threshold is exceeded, the smoothing coefficient of the smoothing algorithm in step S2 is modified, and if it is within the threshold, the fitting is ended and used for RTCP precision interpolation and compensation.

[0071] The specific implementation steps of step S1 are:

[0072] The RTCP function of the five-axis machine tool is closely related to the machine tool topology structure. Taking a CA double swing head type bridge type gantry machining center as an example, the motion relationship of each axis in the five-axis linkage involved in the RTCP function is as follows:

[0073]

[0074] In the formula, (x t ,y t ,z t ) represents the three-direction coordinate values of the tool tip point in the machine tool coordinate system; X, Y and Z represent the motion coordinate values of the machine tool translation axes X, Y and Z respectively; A and C represent the motion angles of the machine tool rotation axes A and C respectively, and L is the tool length, which is a constant value after selecting the tool;

[0075] As can be seen from the formula, the motion coordinate values of the machine tool X, Y and Z are influenced by the tool tip point coordinates (x t ,y t ,z t ) and the rotation axis motion angles (A, C), wherein the influence of (x t ,y t ,z t ) on the translation axis is linear, and the influence of (A, C) on the translation axis is nonlinear. When the five-axis machine tool opens the RTCP function and performs RTCP error detection, the tool tip point coordinates are zero, i.e. (x t ,y t ,z t) = (0, 0, 0), in order to keep the coordinates of the tool tip point unchanged, the change of the tool tip point caused by the rotation axis motion will be compensated by the motion coordinate values of the machine tool translation axes X, Y, Z, so the rotation axes (A axis, C axis) are the main motion axes, but the RTCP error value is the comprehensive error of the five motion axes of the machine tool at the tool tip point.

[0076] Step S2 is specifically: mainly considering the motion range of the main motion axes of the machine tool, setting the motion interval of the main motion axes, and the translation axes will be automatically operated by the machine tool numerical control system according to the RTCP motion relationship of step S1;

[0077] If the motion range of the rotation axis A axis is ±90°, and the motion range of the C axis is ±360°, then set the motion interval angle Δa of the A axis and the motion interval angle Δc of the C axis, then:

[0078] The number of A axis detection points: Na = 180Δa + 1, the number of C axis detection points: Nc = 720Δc + 1;

[0079] After combining all the detection points of the A axis, all the detection points of the C axis, and the motion positions of the translation axes, a series of five-axis linkage RTCP detection position combinations (A i ,C j ,X, Y, Z) are obtained, i≤Na+1, j≤Nc+1, where A i represents the i-th detection angle of the A axis, C j represents the j-th detection angle of the C axis, X, Y, Z respectively represent the motion coordinate values of the machine tool translation axes X axis, Y axis and Z axis, which are automatically calculated and moved to the command position by the numerical control system according to the A axis and C axis angles (A i ,C j ).

[0080] S3 is specifically: using R-test detection instrument to obtain three-direction error values under five-axis linkage position combination, recording RTCP error three-direction values at each motion position, denoted as (e kx ,e ky ,e kz ), k∈[1,i·j], where k represents the k-th combination position in the linkage detection position combination; e kx , e ky , e kz represent X, Y, Z three directions of RTCP error at the k-th combination position.

[0081] Since the RTCP error value at the existing motion position is always limited, the RTCP error values at other angle combinations must be obtained by interpolation fitting, but the RTCP error has randomness, nonlinearity and other characteristics, which are reflected in the characteristics of the original surface as local fluctuation and distortion of the figure, and the locally weighted regression scatter smoothing algorithm (LOWESS algorithm) can handle the heteroscedasticity of the non-linear relationship, effectively resist the change characteristics of the original figure, and is suitable for the processing of the RTCP error.

[0082] The specific implementation steps of step S4 are:

[0083] S41: based on the five-axis linkage RTCP detection position combination (A i ,C j ,X,Y,Z), the motion position (A i ,C j ) of the main motion axis is selected, and the A-axis angle and the C-axis angle are defined as the X-axis and the Y-axis in the Cartesian coordinate system to form the XY plane in the Cartesian orthogonal coordinate system, and the RTCP error value (X / Y / Z three directions) at each motion position combination is taken as one of the directions as the Z-axis in the Cartesian orthogonal coordinate system, and the new combination forms a three-dimensional data set (Ai,Cj,ekm), m∈[x,y,z], e km represents one of e kx , e ky , e kz , which will be described as a series of spatial point clouds in the Cartesian coordinate system, and the point cloud data is subjected to original surface construction;

[0084] S42: the locally weighted regression scatter smoothing algorithm is used to fit the three-dimensional data set of the original surface to obtain the motion position range after fitting.

[0085] Step S42 specifically includes:

[0086] 1) taking the X-direction error e kx of the three-direction RTCP error value as an example, the data set (Ai,Cj,ekx) is taken as a training sample set, wherein (Ai,Cj) is a sample point input matrix, and the X-direction error e kx is taken as an output vector of the sample point;

[0087] A mathematical model can be set as: e kx =g(A i ,C j )+ε k , wherein g(A i ,C j ) is a smoothing function, and ε k is an independent distribution random variable with a mean of 0;

[0088] The weight function of the local weighted regression scatter smoothing algorithm is w(a, c), a and c represent a set of rotation angle values to be interpolated, the smoothing coefficient is f, the data width is r, and the local weighted regression selects a cubic weight function:

[0089]

[0090] Let the smoothing coefficient f range from 0 to 1, the data width r = f·i·j and be rounded, and if the (a, c) value is taken as the center, then the moving window is (a, c) ± r.

[0091] 2) According to the selected weight function w(a, c), the weighted least squares method is used to perform polynomial fitting on the data around (a, c) in the entire moving window, and a smoothing function is obtained The formula is as follows:

[0092]

[0093] Thus, the local weighted regression fitting value of the point in the X direction is obtained The smoothing functions and local weighted regression fitting values of the remaining Y and Z directions are obtained by using steps 1) and 2), and thus the motion position range of the completed fitting is obtained.

[0094] The selection of the smoothing coefficient f determines the smoothing degree of the fitting of the curved surface data, and needs to be modified multiple times according to the characteristics of the detection data to ensure that the fitting conforms to the data trend.

[0095] Step S5 is specifically:

[0096] S51: According to the motion position range of the completed fitting in step S4, the angle position selection is performed in the motion range of the main motion axis;

[0097] S52: The new motion position combination is substituted into the regression model of step S4 to obtain the local weighted regression fitting values in the X, Y and Z directions under each combination, and thus the RTCP error fitting values under other angle combinations of the machine tool are obtained;

[0098] S53: The three-direction RTCP error detection values of the verification points obtained in S51 are compared with the three-direction RTCP error fitting values, if the difference values in the X / Y / Z directions are within the specified threshold range, it indicates that the RTCP error interpolation method based on three-dimensional curved surface fitting is effective, if the threshold is exceeded, step S42 is performed again to set a new smoothing coefficient f.

[0099] The selection rule of the angle position in S51 is as follows:

[0100] 1) Take some of the existing detection angles (A i ,C j ) as the center to select the angle position, and the selected angle position is within the range of the existing detection angles. 2) The selected angle position is within the range of the existing detection angles. value is a constant value, the C-axis angle is generated by a random integer generation method, and a plurality of The subscript p represents the total number of randomly generated C-axis angles, and a new motion position combination is formed

[0101] 2) Take some of the existing detection angles (A i ,C j ) values value is a constant value, the A-axis angle is generated by a random integer generation method, and a plurality of The subscript q represents the total number of randomly generated A-axis angles, and a new motion position combination is formed

[0102] After obtaining the new detection angle, the RTCP error detection is performed based on the method of step S2, thereby obtaining the three-direction RTCP error detection value for verification.

[0103] The expression of the random integer generation method in step 1) of S51 is randint(1, p or q, [-axis, axis]), where randint is a function of randomly generating integers, 1 represents a one-dimensional integer vector, p or q represents that the one-dimensional integer vector contains p or q integers, [-axis, axis] represents the value range of the integer, and axis represents the angle position limit value of the two main motion axes.

[0104] Example 3

[0105] On the basis of examples 1 and 2, RTCP error detection and interpolation verification tests were carried out on a CA double swing head machine tool. First, the positioning accuracy of the machine tool translational axis was compensated to reduce the influence on the RTCP error. Second, the R-test measuring instrument was selected as the RTCP error detection instrument and was installed on the machine tool workbench. As shown in FIG. 8, the measurement coordinate system and the measurement origin were set according to the operation steps of the R-test measuring instrument. Figure 2

[0106] According to the CA double swing head machine tool, the main motion axes were determined as the rotating axes A-axis and C-axis, and a certain range of rotating axis swing angle motion was selected, as shown in the linkage position combination in FIG. 9, which was mainly used to verify the accuracy of the algorithm. The A-axis swing angle range was set to -20°-20°, with an interval of 10° each time, and a total of 5 detection points; Figure 3

[0107] The C-axis swing angle range was set to -90°-90°, with an interval of 30° each time, and a total of 7 detection points;

[0108] After combining the A-axis detection points and the C-axis detection points, a total of 35 detection motion position combinations were formed, as shown in FIG. 10.​​Figure 3 The solid points in the figure are the RTCP errors of each combination measured by the R-test instrument. Figure 7 .

[0109] First, the three-dimensional values ​​of the RTCP error are combined with the detection angle to make the original three-dimensional graphics of the point cloud data. Then, the three-dimensional surface fitting is performed based on the local weighted regression scatter point smoothing algorithm model. The smoothing coefficient f is set to 0.25, as shown in the attached figure. Figure 4 、 Figure 5 and Figure 6 As shown, the fitting effect is as follows Figure 8 .

[0110] Use the obtained verification point angle combination, as shown in the attached Figure 3 Substitute the hollow points in the figure into the local weighted polynomial regression model obtained above, and compare the three-way RTCP error detection value of the verification point with the three-way RTCP error fitting value. The absolute value of the difference is as follows:

[0111] Angle combination Δx (mm) Δy (mm) Δz (mm) (-10,-75) 0.0021 0.0025 0.0026 (-10,-14) 0.0016 0.007 0.0037 (-10,15) 0.0001 0.0004 0.0015 (-15,-30) 0 0.0039 0.0002 (-2,-30) 0.003 0.0001 0.0005 (16,-30) 0.005 0.0012 0.0001

[0112] It can be seen from the table that the maximum fitting error is <0.01 mm, which is a relatively high fitting accuracy and can be used for interpolation prediction of machine tool RTCP error.

[0113] It will be easily understood by those skilled in the art that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting, characterized in that: The steps include: Step S1: Determine the main motion axis of the five-axis machine tool according to the topological structure of the five-axis machine tool and the RTCP function; Step S2: Setting the motion interval of the main motion axis to form a series of five-axis linkage RTCP detection position combinations; Step S3: Obtain the three-way error value under each linkage RTCP detection position combination; Step S4: Select the main motion axis based on the five-axis linkage RTCP detection position combination The error values ​​between the position and one of the X-axis, Y-axis and Z-axis are regarded as a set of three-dimensional data. The local weighted regression scatter point smoothing algorithm is used to fit the three-dimensional data, and three sets of regression models corresponding to the three directional errors are obtained. Indicates the i-th detection angle of the A-axis, Indicates the j-th detection angle of the C-axis, i is less than or equal to the number of detection points on the A-axis plus 1, and j is less than or equal to the number of detection points on the C-axis plus 1; Step S5: Reset multiple groups of five-axis linkage motion position combinations as RTCP accuracy verification points, and verify them based on the three groups of regression models in step S4. If the specified threshold is exceeded, the smoothing coefficient of the smoothing algorithm in step S4 is modified. If it is within the threshold range, the fitting is terminated and used for RTCP accuracy interpolation and compensation.

2. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 1, characterized in that, The specific implementation steps of step S1 are: The motion relationship of each axis in the five-axis linkage involved in the RTCP function is as follows: In the formula Indicates the three-dimensional coordinate values ​​of the tool tip in the machine tool coordinate system; X 、 Y 、 Z They represent the X-axis motion coordinate value, Y-axis motion coordinate value, and Z-axis motion coordinate value of the machine tool translation axis respectively; A 、 C They represent the A-axis motion angle and C-axis motion angle of the machine tool rotation axis respectively. L It is the tool length, which is a fixed value after the tool is selected.

3. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 2, characterized in that, The step S2 specifically includes: setting the motion interval of the main motion axis, and the translation axis will be automatically operated by the machine tool numerical control system according to the RTCP motion relationship of step S1; If the A-axis motion range of the rotary axis is ±90° and the C-axis motion range is ±360°, then set the A-axis motion interval angle. Δa , set the C-axis motion interval angle Δc , then: Number of detection points on A-axis: , Number of C-axis detection points: ; After combining all the detection points of the A-axis, all the detection points of the C-axis, and the motion positions of the translation axis, a series of five-axis linkage RTCP detection position combinations are obtained. , where X, Y, and Z represent the X-axis motion coordinate value, Y-axis motion coordinate value, and Z-axis motion coordinate value of the machine tool translation axis respectively. The CNC system calculates the motion coordinate value based on the A-axis and C-axis angles. Automatically calculates and moves to the command position and stops.

4. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 3, characterized in that: The S3 is specifically as follows: using the R-test detection instrument to obtain the three-dimensional error value under the five-axis linkage position combination, and recording the three-dimensional value of the RTCP error at each motion position, which is recorded as ,in k Indicates the first position in the linkage detection position combination. k combination positions; 、 、 Indicates in k The X, Y, and Z directions of the RTCP error under the combined position.

5. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 4, characterized in that: The specific implementation steps of step S4 are: S41: Position detection combination based on five-axis linkage RTCP , select the motion position of the main motion axis , and define the A-axis angle and the C-axis angle as the X-axis and Y-axis in the Cartesian coordinate system to form the XY plane in the Cartesian coordinate system. At the same time, the RTCP error value under each motion position combination takes one of the X-axis, Y-axis and Z-axis as the Z-axis in the Cartesian coordinate system. The newly combined three-dimensional data set , , Indicates belonging 、 、 One of them is to describe it as a series of spatial point clouds in the Cartesian coordinate system and construct the original surface of the point cloud data; S42: Using a local weighted regression scatter point smoothing algorithm to fit the three-dimensional data set of the original surface, and obtain a motion position range for completing the fitting.

6. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 5, characterized in that: Step S42 specifically includes: 1) Dataset As a training sample set, Input matrix for sample points, X direction error As the output vector of sample points; The mathematical model is: , where is a smooth function, is an independently distributed random variable with mean 0; The weight function of the local weighted regression scatter point smoothing algorithm is , Represents a set of rotation angle values ​​to be interpolated, and the smoothing coefficient is f , the data width is r , the local weighted regression selects the cubic weight function: Let the smoothing coefficient f Range , data width And round up, if The value is the center, then the moving window is ± r； 2) According to the selected weight function , using the weighted least squares method, the data within the entire moving window The surrounding data are fitted with a polynomial and a smooth function is obtained , the formula is as follows: Thus, we get this point X Locally weighted regression fitted value of direction , using steps 1) and 2) to get the rest Y 、 Z The smoothing function of the direction and the local weighted regression fitting value are used to obtain the motion position range for completing the fitting.

7. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 6, characterized in that: The smoothing coefficient f The choice of determines the smoothness of the surface data fitting, and needs to be modified multiple times according to the characteristics of the test data to ensure that the fitting conforms to the data trend.

8. The machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 6 is characterized in that: The step S5 is specifically as follows: S51: selecting an angular position within the motion range of the main motion axis according to the motion position range fitted in step S4; S52: Combine new motion positions 、 Substitute into the regression model of step S4 to obtain X 、 Y 、 Z The local weighted regression fitting value of the direction is used to obtain the RTCP error fitting value under other angle combinations of the machine tool; S53: Compare the obtained three-dimensional RTCP error value of the verification point with the three-dimensional RTCP error fitting value. If the difference in the three directions of X / Y / Z is within the specified threshold range, it means that the RTCP error interpolation method based on three-dimensional surface fitting is effective. If it exceeds the threshold, repeat step S42 and set a new smoothing coefficient. f .

9. A machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 8, characterized in that: The rules for selecting the angle position in S51 are as follows: 1) Take the existing detection angle In The value is a fixed value, and the C-axis angle is generated by random integers to obtain several , the subscript p represents the total number of randomly generated C-axis angles, forming a new motion position combination ; 2) Take the existing detection angle In The value is a fixed value, and the A-axis angle is generated by random integers to obtain several , the subscript q represents the total number of randomly generated A-axis angles, forming a new motion position combination ; After obtaining the new detection angle, the RTCP error is detected based on the method in step S3, thereby obtaining a three-way RTCP error detection value for verification.

10. The machine tool RTCP precision interpolation method based on three-dimensional surface fitting according to claim 9, characterized in that: The expression for generating the random integer in step 1) of S51 is: , is a function that randomly generates integers, whose parameter 1 is represented as a one-dimensional integer vector. p or q Represents a one-dimensional integer vector containing p or q integers, Indicates the range of integer values. axis Indicates the angular position limits of the two main motion axes.

Images