A rotation axis space grid precision interpolation method based on polynomial fitting

Abstract

The application discloses a rotating shaft space grid precision interpolation method based on polynomial fitting, which comprises the following steps: step 1, obtaining the rotating angle range of the rotating shaft of a machine tool, combining and pairing the rotating detection angles of different rotating shafts to obtain the grid detection points of the rotating shaft in the rotating space according to the rotating angle range; step 2, obtaining the error values and error sensitive directions corresponding to each grid detection point; step 3, in different error sensitive directions, a polynomial function is used to fit the error values of the grid detection points, and the fitting order of the polynomial function is optimized according to the fitting result; and step 4, establishing characteristic space verification points, and using a verification rule combining the polynomial function and the interpolation method to calculate and verify the error values of the characteristic space verification points located in different error sensitive directions.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of machine tool error interpolation fitting, and relates to a rotary shaft space grid precision interpolation method based on polynomial fitting. BACKGROUND

[0002] As an effective post-compensation means, the spatial error compensation and thermal error compensation technology of a numerical control machine tool is widely applied to a five-axis numerical control machine tool. At present, the theory of the spatial error compensation method is relatively mature, and mainstream numerical control system manufacturers also provide corresponding functional modules, for example, VCS of Siemens and 3D compensation of Fanuc can realize the compensation of spatial errors.

[0003] There are mainly two basic modes for realizing the spatial error compensation in the prior art, namely a direct interpolation method and an indirect interpolation method. The direct interpolation method is to calculate the error value of any point in space by using the stored grid point data to perform the operation of geometric error. The indirect interpolation method is to calculate the geometric error value of a machine tool by using the grid point data, to perform polynomial fitting on the geometric error value, and to inversely calculate the error value of any point in space.

[0004] Meanwhile, the prior art ZL201910026305.2 proposes a five-axis numerical control machine tool spatial error detection method based on RTCP, which is to inversely calculate and deduce the geometric error value of the rotary shaft space error under different angle combinations, to perform polynomial interpolation on the geometric error, and to complete the calculation of the rotary shaft space grid precision under the specified angle. The method conforms to the principle of error identification and prediction, but the operation amount is large and the calculation process is time-consuming.

[0005] Moreover, the above prior art does not perform fitting on the error value in the case that the rotary shaft space grid point error is different in different direction sensitivities, thereby causing the problem of insufficient accuracy of the fitting result in a single direction.

[0006] Therefore, in view of the defects of the above prior art, the application discloses a rotary shaft space grid precision interpolation method based on polynomial fitting. SUMMARY

[0007] The application aims to provide a rotary shaft space grid precision interpolation method based on polynomial fitting, which is based on different sensitivity directions to establish a polynomial function to fit the error value in the case that the rotary shaft space grid point error is different in different direction sensitivities, thereby significantly improving the final fitting accuracy.

[0008] The application is implemented by the following technical scheme:

[0009] A rotary shaft space grid precision interpolation method based on polynomial fitting comprises the following steps:

[0010] Step 1, obtain the rotation angle range of the rotating shaft of the machine tool, and combine and pair the rotation detection angles of different rotating shafts according to the rotation angle range to obtain the grid detection point positions of the rotating shaft in the rotation space;

[0011] Step 2, obtain the error value and error sensitive direction corresponding to each grid detection point position;

[0012] Step 3, in different error sensitive directions, a polynomial function is used to fit the error value of the grid detection point position, and the fitting order of the polynomial function is optimized according to the fitting result;

[0013] Step 4, establish a feature space verification point, and use a verification rule combining a polynomial function and an interpolation method to calculate and verify the error value on the feature space verification point in different error sensitive directions.

[0014] In order to better realize the present application, further, the step 3 specifically comprises:

[0015] Step 3.1, obtain the rotation angle vector of the rotating shaft in each error sensitive direction, and use the rotation angle vector as the independent variable and the error value as the dependent variable to establish a polynomial function;

[0016] Step 3.2, the least square method is used to calculate the coefficients of the polynomial function, and the fitting order of the polynomial function is adjusted;

[0017] Step 3.3, the fitting accuracy of the polynomial function under the current fitting order is evaluated by using the root mean square error function, and the optimal fitting order is obtained when the fitting accuracy no longer increases;

[0018] Step 3.4, the polynomial function is optimized based on the optimal fitting order.

[0019] In order to better realize the present application, further, the initial value of the fitting order in the step 3.2 is greater than or equal to 3 orders.

[0020] In order to better realize the present application, further, the root mean square error function in the step 3.3 is specifically:

[0021]

[0022] Wherein: RMSE represents the root mean square error function; num represents the number of rotation intervals of the current rotating shaft; e jm represents the measured error value of the rotating shaft at the jth rotation detection angle; represents the fitted error value of the rotating shaft at the jth rotation detection angle; m represents the error sensitive direction of the rotating shaft; x represents the x direction; y represents the y direction; z represents the z direction.

[0023] For better implementation of the present application, further, the step 4 comprises:

[0024] Step 4.1, establishing a feature space verification point, and measuring a rotation detection angle of the current feature space verification point in different error sensitive directions;

[0025] Step 4.2, judging whether the rotation detection angle belongs to a rotation angle vector in the current error sensitive direction, if the rotation detection angle of the feature space verification point in all error sensitive directions does not belong to the rotation angle vector in any error sensitive direction, then step 4.3 is entered; if the rotation detection angle of the feature space verification point in at least one error sensitive direction belongs to the rotation angle vector in the current error sensitive direction, then step 4.4 is entered;

[0026] Step 4.3, in the rotation angle vector corresponding to the error sensitive direction, two reference angles closest to the current rotation detection angle are called, the called reference angles and the current rotation detection angle are combined to obtain a reference verification point; the called reference angles belong to the error sensitive direction corresponding to the polynomial function of the rotation angle vector, and the rotation detection angle not belonging to the rotation angle vector is taken as an independent variable to be substituted into the called polynomial function for error value fitting;

[0027] Step 4.4, the rotation detection angle belonging to the error sensitive direction corresponding to the polynomial function of the rotation angle vector is called, and the rotation angle not belonging to the rotation angle vector is taken as an independent variable to be substituted into the called polynomial function for error value fitting.

[0028] For better implementation of the present application, further, in step 4.3, based on the result of error value fitting of the reference verification point, the error value of the feature space verification point is calculated by using the inverse distance weighting method.

[0029] For better implementation of the present application, further, if the rotation detection angle of the feature space verification point in all error sensitive directions belongs to the rotation angle vector, the error value of the feature space verification point in the current error sensitive direction is directly output.

[0030] For better implementation of the present application, further, the feature space verification point comprises a first type of point in which the rotation detection angle in at least one error sensitive direction belongs to the rotation angle vector, and a second type of point in which the rotation detection angle in all error sensitive directions does not belong to the rotation angle vector.

[0031] For better implementation of the present application, further, the step 1 comprises:

[0032] Step 1.1, setting a rotation interval angle based on a rotation angle range of a rotation axis;

[0033] Step 1.2, calculating the rotation detection angle of the rotation axis according to the set rotation interval angle;

[0034] Step 1.3, pairing the rotation detection angles of different rotation axes to obtain the grid detection point.

[0035] In order to better realize the present application, further, the calculation formula of the rotation interval angle in step 1.1 is:

[0036] ΔK = (pos_kz-pos_kf) / num;

[0037] Wherein: ΔK represents the rotation interval angle of the current rotation axis; pos_kz represents the positive maximum rotation angle of the current rotation axis relative to the rotation center; pos_kf represents the negative maximum rotation angle of the current rotation axis relative to the rotation center; num represents the rotation interval number of the current rotation axis.

[0038] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0039] (1) According to the different sensitivity of the error of the rotation axis space grid point in different directions, the present application expands the traditional fitting in a single direction to the multi-direction polynomial fitting of the space grid, solving the problem of insufficient fitting accuracy of single direction error value;

[0040] (2) The present application solves the situation of non-grid points in different motion trajectories, especially for non-grid points not on the trajectory, which is different from the traditional four-corner grid point method. The present application constructs a new point from the nearest distance of the non-grid point, reduces the influence of the set grid point on the pre-interpolation position, and improves the fitting accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 The step flowchart of the present application;

[0042] Figure 2 The schematic diagram of the machine tool rotation axis;

[0043] Figure 3 The schematic diagram of U and V rotation trajectories;

[0044] Figure 4 The schematic diagram of non-grid points;

[0045] Figure 5 The schematic diagram of four-order fitting;

[0046] Figure 6 The schematic diagram of three-order fitting;

[0047] Figure 7A schematic view of a quintic fit. DETAILED DESCRIPTION

[0048] The following detailed description is exemplary in nature and is intended to provide further description of the application. All of the technical and scientific terms used in the present application have the same meaning as commonly understood by one of ordinary skill in the art to which the application pertains unless otherwise specifically defined herein.

[0049] It is also noted that the term "comprising" or "comprises" when used in this specification is taken to mean the presence of stated features, integers, steps or components but not to the exclusion of the presence or addition of one or more other features, integers, steps, components or groups thereof.

[0050] For the convenience of description, if the terms "upper", "lower", "left", "right" are used in the present application, they only mean the same direction as the upper, lower, left and right directions of the drawings themselves, and do not limit the structure, but only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present application.

[0051] Term explanation part: The terms "mounting", "connecting", "connecting", "fixing" and the like in the present application should be understood broadly, for example, it can be fixed connection, or detachable connection, or integral; it can be mechanical connection, or electrical connection, it can be direct connection, or indirect connection through intermediate medium, it can be internal connection of two elements, or interaction relationship between two elements, for those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0052] Example 1

[0053] A rotating shaft space grid precision interpolation method based on polynomial fitting of the embodiment, as shown in Figure 1 includes the following steps:

[0054] Step 1, obtaining the rotation angle range of the rotating shaft of the machine tool, combining and pairing the rotation detection angles of different rotating shafts according to the rotation angle range to obtain the grid detection points of the rotating shaft in the rotating space;

[0055] Step 2, obtaining the error value and error sensitive direction corresponding to each grid detection point;

[0056] Step 3, in different error sensitive directions, the error values of the grid detection points are fitted by using a polynomial function, and the fitting order of the polynomial function is optimized according to the fitting result;

[0057] Step 4, the feature space verification points are established, and the error values of the feature space verification points in different error sensitive directions are calculated and verified by using a verification rule combining the polynomial function and the interpolation method.

[0058] The step 1 comprises:

[0059] Step 1.1, setting a rotation interval angle based on the rotation angle range of the rotation axis;

[0060] Step 1.2, calculating the rotation detection angle of the rotation axis according to the set rotation interval angle;

[0061] Step 1.3, pairing the rotation detection angles of different rotation axes one by one to obtain the grid detection points.

[0062] The calculation formula of the rotation interval angle in the step 1.1 is:

[0063] ΔK=(pos_kz-pos_kf) / num;

[0064] Wherein, ΔK represents the rotation interval angle of the current rotation axis; pos_kz represents the positive maximum rotation angle of the current rotation axis relative to the rotation center; pos_kf represents the negative maximum rotation angle of the current rotation axis relative to the rotation center; and num represents the rotation interval number of the current rotation axis.

[0065] The step 3 comprises:

[0066] Step 3.1, obtaining the rotation angle vector of the rotation axis in each error sensitive direction, taking the rotation angle vector as the independent variable and taking the error value as the dependent variable to establish a polynomial function;

[0067] Step 3.2, calculating the coefficients of the polynomial function by using the least square method, and adjusting the fitting order of the polynomial function;

[0068] Step 3.3, evaluating the fitting precision of the polynomial function under the current fitting order by using the root mean square error function, and obtaining the optimal fitting order when the fitting precision no longer increases;

[0069] Step 3.4, optimizing the polynomial function based on the optimal fitting order.

[0070] The root mean square error function in the step 3.3 is specifically:

[0071]

[0072] Wherein: RMSE represents the root mean square error function; num represents the rotation interval number of the current rotation axis; e jm represents the error value actually measured by the rotation axis at the jth rotation detection angle; represents the error value fitted by the rotation axis at the jth rotation detection angle; m represents the error sensitive direction of the rotation axis; x represents the x direction; y represents the y direction; and z represents the z direction.

[0073] The step 4 comprises:

[0074] Step 4.1, establishing a feature space verification point, and measuring the rotation detection angle of the current feature space verification point in different error sensitive directions;

[0075] Step 4.2, judging whether the rotation detection angle belongs to the rotation angle vector in the current error sensitive direction, if the rotation detection angle of the feature space verification point in all error sensitive directions does not belong to the rotation angle vector in any error sensitive direction, then step 4.3 is entered; if the rotation detection angle of the feature space verification point in at least one error sensitive direction belongs to the rotation angle vector in the current error sensitive direction, then step 4.4 is entered;

[0076] Step 4.3, in the rotation angle vector of the corresponding error sensitive direction, two reference angles closest to the current rotation detection angle are called, the called reference angles and the current rotation detection angle are combined to obtain a reference verification point; the called reference angles belong to the error sensitive direction corresponding to the polynomial function of the rotation angle vector, and the rotation detection angle not belonging to the rotation angle vector is taken as an independent variable to be substituted into the called polynomial function to fit the error value;

[0077] Step 4.4, the rotation detection angle belongs to the error sensitive direction corresponding to the polynomial function of the rotation angle vector, and the rotation angle not belonging to the rotation angle vector is taken as an independent variable to be substituted into the called polynomial function to fit the error value.

[0078] Further, the initial value of the fitting order in the step 3.2 is greater than or equal to 3 orders.

[0079] Further, in the step 4.3, based on the fitting result of the error value of the reference verification point, the inverse distance weighting method is used to calculate the error value of the feature space verification point.

[0080] Further, if the rotation detection angle of the feature space verification point in all error sensitive directions belongs to the rotation angle vector, the error value of the feature space verification point in the current error sensitive direction is directly output.

[0081] Further, the feature space verification point position includes a class of point positions in which the rotation detection angle in at least one error sensitive direction belongs to the rotation angle vector, and a class of point positions in which the rotation detection angle in all error sensitive directions does not belong to the rotation angle vector.

[0082] Embodiment 2:

[0083] A rotation axis space grid precision interpolation method based on polynomial fitting in the embodiment is improved on the basis of embodiment 1, as shown in Figure 2 and Figure 3 As shown in the drawings, taking a CA double swing head bridge type machine tool as an example, the CA double swing head bridge type machine tool has two rotation axes, i.e., a rotation A axis and a rotation C axis, and rotation interval angles of the rotation A axis and the rotation C axis are set as follows:

[0084]

[0085] Wherein, ΔKa represents the rotation interval angle of the rotation A axis; pos_kaz represents the positive maximum rotation angle of the rotation A axis relative to the rotation center; pos_kaf represents the negative maximum rotation angle of the rotation A axis relative to the rotation center; and numA represents the rotation interval number of the rotation A axis.

[0086] ΔKc represents the rotation interval angle of the rotation C axis; pos_kcz represents the positive maximum rotation angle of the rotation C axis relative to the rotation center; pos_kcf represents the negative maximum rotation angle of the rotation C axis relative to the rotation center; and numC represents the rotation interval number of the rotation C axis.

[0087] The rotation A axis is rotated according to the above ΔKa and numA to obtain a plurality of groups of rotation detection angles A i , wherein 1≤i≤numA+1; the rotation C axis is rotated according to the above ΔKc and numC to obtain a plurality of groups of rotation detection angles C j , wherein 1≤j≤numC+1. The rotation detection angles of the rotation A axis and the rotation C axis are paired and combined to obtain a plurality of grid detection point positions (A i , C j ).

[0088] An O-XYZ coordinate system is established in the rotation space, and when the rotation detection angle of the rotation A axis is a constant value and the rotation C axis rotates, the motion trajectory of the intersection of the axis of the rotation A axis and the axis of the rotation C axis in the rotation space is a first circular arc trajectory parallel to the XY plane, and the rotation direction of the first circular arc trajectory is defined as the U direction. When the rotation detection angle of the rotation A axis is 0°, only the rotation C axis rotates, and the intersection of the axis of the rotation A axis and the axis of the rotation C axis is a fixed point.

[0089] Similarly, when the rotation detection angle of the rotating C-axis is a constant value and the rotating A-axis rotates, the trajectory of the intersection point of the axis of the rotating A-axis and the axis of the rotating C-axis in the rotation space is a second circular arc trajectory parallel to the YZ plane, and the rotation direction of the second circular arc trajectory is defined as the V direction. When the rotation detection angle of the rotating C-axis is 0°, only the rotating A-axis rotates, and the intersection point of the axis of the rotating A-axis and the axis of the rotating C-axis is a fixed point.

[0090] The intersection point of the first circular arc trajectory in the U direction and the second circular arc trajectory in the V direction in the rotation space forms a plurality of grid detection points, each of which contains a group of rotation detection angles A of the rotating A-axis i and a group of rotation detection angles C of the rotating C-axis j . After the grid detection points are established, a ball head inspection rod and a detection instrument are installed at the spindle end of the machine tool, and an NC pause program is set in the machine tool control system when the rotating shaft moves to the grid detection point. When the rotating shaft rotates to the grid detection point, the deviation value between the actual ball center of the ball head inspection rod and the theoretical ball center is collected by the detection instrument, which is the error value, and the error value is denoted as (e kx ,e ky ,e kz ), k ∈ [1, i, j].

[0091] Where e kx represents the error value in the x direction, e ky represents the error value in the y direction, and e kz represents the error value in the z direction, and the meanings of i and j are the same as those in formula (1).

[0092] Further, the detection instrument is any one of an R-test detection instrument, a ball rod detection instrument, and a laser detection instrument.

[0093] For the two error sensitive directions of the U direction and the V direction, a polynomial function about the U direction and the V direction is established, specifically:

[0094] The first circular arc trajectory in the U direction is defined as Similarly, the second circular arc trajectory in the V direction is defined as

[0095]

[0096] Where: ui represents the trajectory along the U direction obtained by corresponding different rotation detection angles A of the rotating A-axis i ; and vj represents the trajectory along the V direction obtained by corresponding different rotation detection angles C of the rotating C-axis j .

[0097] Further, the polynomial function for the U direction and the V direction is constructed as:

[0098]

[0099] wherein: E pu represents the polynomial function error value fitting result for the U direction; E pv represents the polynomial function error value fitting result for the V direction; a0 is a constant term; a1-a n represents the coefficient of the polynomial function, the least square method is used to determine the coefficient of the polynomial function; n represents the fitting order of the polynomial function.

[0100] In order to optimize the fitting order of the polynomial function, the root mean square error function is introduced to judge the fitting accuracy of the polynomial function to the error value under the current fitting order, and the root mean square error function is specifically:

[0101]

[0102] Based on the above formula (3), the root mean square error functions for the U direction and the V direction are respectively:

[0103]

[0104] wherein: RMSE u represents the root mean square error function for the U direction; RMSE v represents the root mean square error function for the V direction; the meanings of numA and numC are the same as those of the above formula (1); e jmA represents the error value actually measured by the rotating A axis at the jth rotating detection angle; represents the error value fitted by the rotating A axis at the jth rotating detection angle; e jmC represents the error value actually measured by the rotating C axis at the jth rotating detection angle; represents the error value fitted by the rotating C axis at the jth rotating detection angle; m represents the error sensitive direction of the rotating axis; x represents the x direction; y represents the y direction; z represents the z direction.

[0105] Combined with formula (2) and formula (4), the fitting order n is iteratively adjusted, when the error value fitting accuracy corresponding to the current fitting order is obtained through the root mean square error function calculation, which is higher than that of the previous fitting order, then the fitting order is increased, otherwise the current fitting order is output and no longer increased.

[0106] After the polynomial function optimization in the U direction and the V direction, three kinds of characteristic space verification points can be established, which are respectively:

[0107] The first kind: non-grid detection points on the first circular arc track but not on the second circular arc track;

[0108] The second kind: non-grid detection points on the second circular arc track but not on the first circular arc track;

[0109] Third: neither on the first arc trajectory nor on the second arc trajectory of the non-grid detection point.

[0110] The verification rule of the combination of the polynomial function and the interpolation method is used to calculate and verify the error values of the feature space verification point on different error sensitive directions:

[0111] Given any one feature space verification point (A' i , C' j ), it is judged whether A' i belongs to the rotation angle vector A cj = [A1, A2…A i ] of the rotation A axis, and whether C' j belongs to the rotation angle vector C Ai = [C1, C2…C j ] of the rotation C axis, wherein A' i represents the rotation detection angle of the rotation A axis corresponding to the feature space verification point; C' j represents the rotation detection angle of the rotation C axis corresponding to the feature space verification point.

[0112] The judgment result is as follows:

[0113] 1. If A' i belongs to A cj , and C' j belongs to C Ai , then directly output the error value corresponding to the feature space verification point (A' i , C' j ) at this time as the result.

[0114] 2. If A' i belongs to A cj , and C' j does not belong to C Ai , then call the polynomial function E pu corresponding to A' i , and introduce C' j at this time as the independent variable into E pu to fit the error value.

[0115] 3. If A' i does not belong to A cj , and C' j belongs to C Ai , then call the polynomial function E pv corresponding to C' j , and introduce A' i at this time as the independent variable into E pv to fit the error value.

[0116] 4. If A' i Not A cj , and C' j It doesn't belong to C either Ai , then traverse A cj , in A cj Select the one closest to A' i The two rotation detection angles A iq With A it , where A iq A' i Previously closest to A' i The rotation detection angle, A it A' i Then closest to A' i Rotation detection angle; similarly, traverse C Ai , in C Ai Select the one closest to C' j The two rotation detection angles C jq with C jt , where C jq C' j Previously closest to C' j The rotation detection angle, C jt C' j Then closest to C' j The rotation detection angle.

[0117] Then A' i , C' j 、A iq 、A it 、C jq 、C jt The four reference verification points are combined as follows:

[0118] (A' i , C jq )、(A' i , C jt )、(A iq , C' j )、(A it , C' j );

[0119] For (A' i , C jq )、(A' i , C jt ), due to C jq with C jt Belongs to C Ai , then (A' i , C jq )、(A' i , Cjt ) According to the third point judgment result above, the error value is fitted to obtain the fitting result: and

[0120] Targeting (A iq , C' j )、(A it , C' j ), due to A iq With A it Belongs to A cj , then (A iq , C' j )、(A it , C' j ) According to the second judgment result above, the error value is fitted to obtain the fitting result: and

[0121] Because (A' i , C' j ) is actually (A' i , C jq )、(A' i , C jt )、(A iq , C' j )、(A it , C' j ) is the intersection of the lines, then the inverse distance weighted method is used to calculate (A' i , C' j ) The error fitting result is:

[0122]

[0123] in Indicates the feature space verification point (A' i , C' j ) corresponding error value; Indicates the reference verification point (A' i , C jq )、(A' i , C jt ) corresponding error value; Indicates the reference verification point (A iq , C' j )、(A it , C' j ) corresponds to the error value.

[0124] The rest of this embodiment is the same as that of embodiment 1, so it will not be described again.

[0125] Example 3:

[0126] The rotational axis space grid precision interpolation method based on polynomial fitting of the embodiment is improved on the basis of embodiments 1 or 2, and the space grid precision test verification work is carried out in the CA double swing head bridge type machine tool. Before the test, the laser interferometer is used to complete the compensation of the translational axis positioning precision of the CA double swing head bridge type machine tool, the R-test measuring instrument is selected as the detection tool of the rotational axis space grid error, and the CA double swing head bridge type machine tool experiment is carried out in a constant temperature environment to improve the accuracy of the rotational axis space error measurement as much as possible.

[0127] The rotational angle range of the rotational A axis of the CA double swing head bridge type machine tool is [-110°, 110°], and the rotational angle range of the rotational C axis is [-360°, 360°]. A part of the rotational angle range of the rotational A axis and the rotational C axis is selected for the measurement of the space grid error, and the parameters are set as follows:

[0128] The rotational angle range of the rotational A axis is selected as -20°-20°, and the rotational interval angle is set as 5°, so that:

[0129] A cj =[-20,-15,-10,-5,0,5,10,15,20];

[0130] The rotational angle range of the rotational C axis is selected as -90°-90°, and the rotational interval angle is set as 15°, so that:

[0131] C Ai =[-90,-75,-60,-45,-30,-15,0,15,30,45,60,75,90];

[0132] After combining A cj and C Ai , a total of 117 space grid detection points are formed. Taking the space point error data of the rotational angle of the rotational A axis as -15° as an example, the specific implementation steps are described, as shown in the following table:

[0133]

[0134]

[0135] The three-dimensional error values are adaptively fitted by a polynomial function, and the recommended polynomial order is obtained, as follows:

[0136] Error direction RMSE (3rd order) RMSE (4th order) RMSE (5th order) X 0.001906 0.00185 0.001935 Y 0.001809 0.001901 0.002028 Z 0.002282 0.002386 0.002266

[0137] According to the above, as shown in Figure 4 , for the error values of the X direction of the grid detection point, a fourth-order polynomial fitting is adopted; as shown in Figure 5 , for the error values of the Y direction of the grid detection point, a third-order polynomial fitting is adopted; asFigure 6 As shown in FIG, a fifth-order polynomial fitting is used for the Z-direction error value of the grid detection point.

[0138] Three feature space verification points are set, such as Figure 4 The specific angle combinations of the triangle points, square points, and cross points shown are as follows:

[0139] Rotation A axis -5° 7° -2° 12° Rotation C axis 40° -60° -33° 10°

[0140] Based on formula (5) in Example 2, the error values ​​under different rotation detection angle combinations are obtained as shown in the following table:

[0141] Angle combination Δx (mm) Δy (mm) Δz (mm) (-5°,40°) 0.0016 0.0037 0.0016 (7°,-60°) 0.0002 0.0024 0.0006 (-2°,-33°) 0.0018 0.0049 0.0004 (12°,10°) 0.0027 0.0002 0.0013

[0142] It can be seen from the above table that the maximum fitting error value is <0.005mm, which is a relatively high fitting accuracy and can be used for interpolation prediction of machine tool RTCP error.

[0143] The rest of this embodiment is the same as that of embodiment 1 or 2, and thus will not be described in detail.

[0144] The above are only preferred embodiments of the present invention and do not limit the present invention in any form. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention fall within the scope of protection of the present invention.

Claims

1. A method for interpolation of spatial grid precision of rotating axis based on polynomial fitting, characterized in that: The following steps are involved: Step 1: Obtain the rotation angle range of the machine tool's rotation axis, and combine and pair the rotation detection angles of different rotation axes according to the rotation angle range to obtain the grid detection point positions of the rotation axis in the rotation space; Step 2: Obtain the error value and error-sensitive direction corresponding to each grid detection point; Step 3: In different error-sensitive directions, a polynomial function is used to fit the error values ​​of the grid detection points, and the fitting order of the polynomial function is optimized according to the fitting results; Step 4: Establish feature space verification points, and use a verification rule combining polynomial function and interpolation method to calculate and verify the error values ​​of the feature space verification points in different error-sensitive directions; The step 4 comprises: Step 4.1: Establish feature space verification points and measure the rotation detection angles of the current feature space verification points in different error-sensitive directions; Step 4.2: Determine whether the rotation detection angle belongs to the rotation angle vector in the current error-sensitive direction. If the rotation detection angles of the feature space verification point in all error-sensitive directions do not belong to the rotation angle vector in any error-sensitive direction, proceed to step 4.

3. If the rotation detection angle of the feature space verification point in at least one error-sensitive direction belongs to the rotation angle vector in the current error-sensitive direction, proceed to step 4.

4. Step 4.3: retrieve the two reference angles closest to the current rotation detection angle in the rotation angle vector corresponding to the error-sensitive direction, and combine the retrieved reference angles with the current rotation detection angle to obtain a reference verification point; retrieve the polynomial function corresponding to the error-sensitive direction of the rotation angle vector in which the reference angle belongs, and substitute the rotation detection angle that does not belong to the rotation angle vector as an independent variable into the retrieved polynomial function to perform error value fitting; Step 4.4: retrieve the polynomial function corresponding to the error-sensitive direction of the rotation detection angle belonging to the rotation angle vector, and substitute the rotation angle that does not belong to the rotation angle vector as an independent variable into the retrieved polynomial function to perform error value fitting.

2. The method for interpolation of rotation axis space grid precision based on polynomial fitting according to claim 1, characterized in that: The step 3 specifically includes: Step 3.1, obtain the rotation angle vector of the rotation axis in each error-sensitive direction, and establish a polynomial function with the rotation angle vector as the independent variable and the error value as the dependent variable; Step 3.2, calculate the coefficients of the polynomial function using the least squares method and adjust the fitting order of the polynomial function; Step 3.3, use the root mean square error function to evaluate the fitting accuracy of the polynomial function under the current fitting order, until the fitting accuracy no longer increases and the optimal fitting order is obtained; Step 3.4: Optimize the polynomial function based on the optimal fitting order.

3. The method for interpolating the spatial grid precision of a rotating axis based on polynomial fitting according to claim 2, characterized in that: The root mean square error function in step 3.3 is specifically: ； in: Describes the root mean square error function; num represents the number of rotation intervals of the current rotation axis; It represents the error value measured at the jth rotation detection angle of the rotation axis; represents the error value of the rotation axis at the jth rotation detection angle; m represents the error-sensitive direction of the rotation axis; x represents the x-direction; y represents the y-direction; and z represents the z-direction.

4. The method for interpolating the spatial grid precision of a rotating axis based on polynomial fitting according to claim 2, characterized in that: The initial value of the fitting order in step 3.2 is greater than or equal to 3.

5. The method for interpolation of rotation axis space grid precision based on polynomial fitting according to claim 1, characterized in that: In step 4.3, based on the result of the error value fitting of the reference verification point, the error value of the feature space verification point is calculated using the inverse distance weighted method.

6. The method for interpolation of rotation axis space grid precision based on polynomial fitting according to claim 5, characterized in that: If the rotation detection angles of the feature space verification point in all error-sensitive directions belong to the rotation angle vector, the error value of the feature space verification point in the current error-sensitive direction is directly output.

7. The method for interpolating the spatial grid precision of a rotating axis based on polynomial fitting according to claim 6, characterized in that: The feature space verification points include a first type of point whose rotation detection angle in at least one error-sensitive direction belongs to a rotation angle vector, and a second type of point whose rotation detection angles in all error-sensitive directions do not belong to a rotation angle vector.

8. A method for interpolating rotation axis space grid precision based on polynomial fitting according to any one of claims 1 to 4, characterized in that: The step 1 comprises: Step 1.1, set the rotation interval angle based on the rotation angle range of the rotation axis; Step 1.2, calculate the rotation detection angle of the rotation axis according to the set rotation interval angle; Step 1.3: Pair the rotation detection angles of different rotation axes one by one to obtain grid detection points.

9. The method for interpolating the spatial grid precision of a rotating axis based on polynomial fitting according to claim 8, characterized in that: The calculation formula for the rotation interval angle in step 1.1 is: ； in: Indicates the rotation interval angle of the current rotation axis; Indicates the maximum positive rotation angle of the current rotation axis relative to the rotation center; Indicates the maximum negative rotation angle of the current rotation axis relative to the rotation center; num indicates the number of rotation intervals of the current rotation axis.

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