A real error-based thread surface reconstruction method for planetary roller screw pair

Abstract

The application provides a real error-based thread surface reconstruction method for a planetary roller screw pair, and belongs to the technical field of three-dimensional reconstruction. A high-precision three-coordinate measuring machine is used to control a work turntable to scan a plurality of axial thread tooth profiles in the circumferential direction and output corresponding point cloud coordinates. A cubic polynomial is used to fit the thread tooth profile curve of the point cloud coordinates and to perform radius compensation according to the diameter of a measuring head. The compensated thread tooth profile curve is used to evaluate and extract thread feature parameters of each thread tooth, which are used as original inputs for subsequent interpolation and three-dimensional reconstruction. The theoretical helical coordinate system and the helical surface equation are corrected based on coordinate transformation. The thread feature parameters of the thread tooth at an unmeasured position are interpolated using a cubic spline. The thread feature parameters of each thread tooth and the angle of each thread tooth on the helix are substituted into the corrected equation to obtain corresponding thread profiles with machining errors. The points on the tooth profile are uniformly dispersed and triangulated to complete the three-dimensional reconstruction of the thread surface.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional reconstruction technology, and in particular to a method for reconstructing the threaded surface of a planetary roller screw pair based on actual errors. Background Technology

[0002] A planetary roller screw mechanism (PRSM) is a transmission device that can convert linear motion into rotary motion, and it has great application prospects in military and civilian fields such as aerospace, navigation, weaponry, and robotics. Its core components, the screw, rollers, and nut, are all high-precision threaded parts. The screw and nut have multi-start straight profile threads, while the rollers have single-start circular arc profile threads.

[0003] Currently, profilometers and coordinate measuring machines (CMMs) are the primary means of assessing the machining quality of PRSM profiles, offering high accuracy and efficiency, and are widely used in research and engineering. However, existing assessments are based on two-dimensional axial sections, providing limited cross-sectional information that cannot fully and accurately reflect the three-dimensional entity. Furthermore, the lack of a comprehensive three-dimensional PRSM model that considers various machining errors has resulted in limited research on PRSM clearance, load-bearing capacity, and contact analysis. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a method for reconstructing the thread surface of a planetary roller screw pair based on actual errors. Based on the detection and evaluation of the two-dimensional axial thread profile, it can quickly complete the reconstruction of a three-dimensional thread surface containing various machining errors, providing a foundation for related research. Furthermore, by adjusting the number of two-dimensional axial thread profiles used as the original input, different reconstruction accuracies can be obtained to meet the needs of different application scenarios.

[0005] To achieve the above objectives, this invention provides a method for reconstructing the thread surface of a planetary roller screw pair based on actual errors, comprising the following steps:

[0006] Step 1: Using a high-precision coordinate measuring machine, control the worktable to scan a number of axial thread profiles in the circumferential direction and output the corresponding point cloud coordinates;

[0007] Step 2: Use a cubic polynomial to fit the thread profile curve to the point cloud coordinates and perform radius compensation based on the probe diameter;

[0008] Step 3: Evaluate and extract the thread feature parameters of each thread tooth based on the compensated thread profile curve, which will serve as the original input for subsequent interpolation and 3D reconstruction.

[0009] Step 4: Correct the theoretical helical coordinate system and helical surface equations based on coordinate transformation;

[0010] Step 5: Use cubic spline interpolation to obtain the thread characteristic parameters of the unmeasured thread teeth;

[0011] Step 6: Substitute the thread characteristic parameters of each thread tooth and its angle on the helix into the corrected equation to obtain the corresponding thread profile including machining errors.

[0012] Step 7: Uniformly discretize the points on the tooth profile and triangulate them to complete the three-dimensional reconstruction of the thread surface.

[0013] Preferably, step one includes: using a high-precision coordinate measuring machine for contact scanning, placing the threaded part to be scanned on the working turntable, scanning the thread profile from top to bottom along the axial direction with the probe, and after completing the scanning of one axial profile, controlling the working turntable to rotate a certain angle to continue scanning until a number of circumferential axial profiles are scanned, and outputting the corresponding thread profile point cloud coordinates.

[0014] Preferably, in step two, after fitting the point cloud coordinates of the thread tooth profile using a cubic polynomial, the radius compensation of the thread tooth profile curve is calculated according to the following formula:

[0015] For the fitted thread profile curve, it can be written in parametric form as r(t), where the tangential velocity is its first derivative:

[0016] v(t) = r'(t);

[0017] After normalization, the unit tangent vector is obtained:

[0018]

[0019] The unit normal vector perpendicular to the tangent needs to be obtained by rotating the tangent by 90°:

[0020] N(t)=(-T y (t),T x (t));

[0021] Based on the probe radius r, the equidistant curves of the thread profile are obtained:

[0022] s(t)=r(t)±rN(t).

[0023] Preferably, in step three, the thread characteristic parameters are determined by the major diameter, pitch diameter, minor diameter, flank angles on both sides, and pitch of the thread profile. The thread characteristic parameters are evaluated and extracted to obtain the machining error of the thread.

[0024] Preferably, the evaluation and determination of the thread feature parameters of each thread tooth in the original input used for subsequent interpolation and 3D reconstruction in step three is performed according to the following steps:

[0025] Using the workpiece coordinate system axis as a reference, the maximum and minimum values ​​of the curves from the axis to the tooth crest and root are respectively taken as the major diameter r of the thread tooth. a and small diameter r f ;

[0026] Search along the tooth flank, parallel to the axis, for positions where the thread thickness and the alveolar width between adjacent threads are close. Use the distance between this position and the axis of the working coordinate system as the mean diameter r. s The pitch p is the sum of the tooth thickness and the alveolar width at that position.

[0027] At the intersection of the pitch diameter and the tooth flank, the acute angle between the left and right tooth flanks and the vertical direction is calculated as the left and right tooth flank angles β of the thread tooth. L β R ;

[0028] To evaluate the radius of the thread arc of a roller, a tangent line is drawn to the tooth profile at the pitch diameter. The acute angle between the tangent line and the horizontal direction is the tooth flank angle. The radius of the thread arc is obtained by fitting the tooth profile arc.

[0029] Preferably, the correction of the theoretical spiral coordinate system based on coordinate transformation in step four includes:

[0030] Establish a fixed coordinate system for the helical surface (O) i -x i ,y i ,z i Choose a point O' on the mean diameter helix. i O' i The rotation angle is θ ij Its spiral ascent is h; with O' i Establish coordinate systems (O') with the origin of the coordinate system as the origin. i -x i1 ,y i1 ,z i1 ) and coordinate system (O' i -x i2 ,y i2 ,z i2 ), where the coordinate system (O' i -x i1 ,y i1 ,z i1 ) is based on coordinate system (O) i -x i ,y i ,z i The coordinate system (O') is obtained by translation. i -xi2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 It is obtained by rotation; where i = S, R, N, S represents the lead screw; R represents the roller; N represents the nut, and j represents different thread teeth;

[0031] Through coordinate transformation, we obtain the coordinate system (O'). i -x i2 ,y i2 ,z i2 ) to coordinate system (O' i -x i1 ,y i1 ,z i1 The conversion process is as follows:

[0032] Coordinate system (O' i -x i2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 The transformation matrix M i1i2 for:

[0033]

[0034] In the formula, μ = ±1, +1 indicates right-handed rotation, and -1 indicates left-handed rotation;

[0035] Coordinate system (O' i -x i1 ,y i1 ,z i1 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii1 for:

[0036]

[0037] Wherein, the spiral ascent amount h is:

[0038] h = θ ij *r ij *tan(ni*p ij / (2*∏*r ij ));

[0039] In the formula, λ ijWhere ni is the helix angle, p is the number of heads, and ni is the number of heads. ij The pitch is r. ij λ is the median diameter; where λ is the median diameter. ij for:

[0040]

[0041] Thus, the coordinate system (O') is obtained. i -x i2 ,y i2 ,z i2 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii2 for:

[0042] M ii2 =M ii1 M i1i2 ;

[0043]

[0044] Preferably, the step four, which involves correcting the theoretical helical surface equation based on coordinate transformation, includes:

[0045] For any point M on the screw helical surface, in coordinate system (O' S -x S2 ,y S2 ,z S2 This is represented as follows:

[0046]

[0047] In the formula, η = ±1, +1 represents the upper surface, where t is taken as L; -1 represents the lower surface, where t is taken as R, and r Sj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Sj Pitch;

[0048] make By coordinate transformation, we can obtain the coordinate system (O) of point M. S -x S ,y S ,z S This is represented as follows:

[0049] r S =M SS2 r S2 ;

[0050]

[0051] For any point M on the roller helical surface, in coordinate system (O' R -x R2 ,y R2 ,z R2 This is represented as follows:

[0052]

[0053] In the formula, r Rj r is the pitch diameter of the roller. PLj r is the radius of the upper arc of the roller. PRj β is the radius of the arc on the underside of the roller. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Rj Pitch;

[0054] make By coordinate transformation, we can obtain the coordinate system (O) of point M. R -x R ,y R ,z R This is represented as follows:

[0055] r Rj =M RR2 r R2 ;

[0056]

[0057] For any point M on the helical surface of the nut, in coordinate system (O' N -x N2 ,y N2 ,z N2 This is represented as follows:

[0058]

[0059] In the formula, r Nj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Nj Pitch;

[0060] make By coordinate transformation, we can obtain the coordinate system (O) of point M. N -x N ,y N ,z N This is represented as follows:

[0061] r Nj =M NN2 r N2 ;

[0062]

[0063] Preferably, in step five, when using the cubic spline interpolation method to interpolate the thread tooth feature parameters, the thread tooth feature parameters obtained by scanning on the same axis are used as feature points, and the different rotation angles of the tooth profile on the helix are used to represent the θ values ​​of different thread parameters. ij As the independent variable, and the thread characteristic parameters of the tooth profile as the dependent variable, the thread characteristic parameters are interpolated to obtain the characteristic parameters of the thread teeth in the unmeasured area, and the characteristic point data after interpolation remains unchanged.

[0064] Preferably, the characteristic parameters of each thread tooth after interpolation in step six and its rotation angle θ on the helix are... ij Substituting the corrected helical coordinate system and helical surface equation, we obtain the thread profile including machining errors.

[0065] Preferably, in step seven, the points on the obtained thread profile containing machining errors are uniformly discretized and triangularly meshed to obtain a three-dimensional reconstruction model of the planetary roller screw pair thread containing machining errors.

[0066] According to the specific technical solution provided by the present invention, compared with the prior art, the present invention has the following technical effects:

[0067] (1) This invention uses a high-precision coordinate measuring machine to control the turntable to scan a certain number of axial thread profiles in the circumferential direction and output the corresponding point cloud coordinates of the thread profiles. The point cloud coordinates are fitted with thread profile curves using a cubic polynomial and radius compensation is performed according to the probe diameter. Based on the compensated thread profile curves, the thread characteristic parameters such as major diameter, pitch diameter, minor diameter, flank angles on both sides, and pitch of each thread tooth are evaluated for subsequent interpolation and the original input for three-dimensional reconstruction.

[0068] (2) Based on coordinate transformation, the equations of the theoretical helical surface and helical line are corrected; the characteristic parameters of the thread tooth at the unmeasured angle position are obtained by using cubic spline interpolation; the characteristic parameters of each thread tooth and its angle on the helical line are substituted into the corrected equation to obtain the corresponding thread tooth profile containing machining error; the points on the tooth profile are uniformly discretized and triangular meshed to complete the three-dimensional reconstruction of the thread surface.

[0069] (3) This invention can quickly complete the three-dimensional reconstruction of the planetary roller screw pair thread surface with machining error based on two-dimensional axial profile detection. Different reconstruction accuracies can be obtained by adjusting the number of two-dimensional axial thread profiles as the original input, which can meet the usage requirements of different scenarios. It provides a basis for the analysis of the clearance, load and contact of planetary roller screws in real situations, and has important research and engineering application significance. Attached Figure Description

[0070] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 This is a technical roadmap for a method of reconstructing the thread surface of a planetary roller screw pair based on actual error, according to the present invention.

[0072] Figure 2 This is a schematic diagram of thread scanning provided for an embodiment of the present invention;

[0073] Figure 3 This is a schematic diagram of the helical surface coordinate system provided in an embodiment of the present invention;

[0074] Figure 4 This is a schematic diagram of the lead screw thread profile provided in an embodiment of the present invention;

[0075] Figure 5 This is a schematic diagram of the roller thread profile provided in an embodiment of the present invention;

[0076] Figure 6 This is a schematic diagram of the nut thread profile provided in an embodiment of the present invention;

[0077] Figure 7 This is a schematic diagram of tooth profile interpolation reconstruction provided in an embodiment of the present invention;

[0078] Figure 8 The image shows a three-dimensional reconstruction effect provided in an embodiment of the present invention. Detailed Implementation

[0079] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0080] The purpose of this invention is to provide a method for reconstructing the thread surface of a planetary roller screw pair based on real errors. This method can quickly complete the three-dimensional reconstruction of the thread surface of a planetary roller screw pair containing machining errors based on the detection of two-dimensional axial tooth profiles. By adjusting the number of two-dimensional axial thread profiles as the original input, different reconstruction accuracies can be obtained to meet the usage requirements of different scenarios. It provides a basis for the analysis of clearance, load-bearing capacity and contact of planetary roller screws under real conditions, and has important research and engineering application significance.

[0081] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0082] Example 1

[0083] Reference Figures 1-8 This embodiment provides a method for reconstructing the thread surface of a planetary roller screw pair based on machining errors. This method is used to reconstruct the thread surface of a planetary roller screw pair in three dimensions.

[0084] like Figure 1 As shown, the method includes the following steps:

[0085] Step 1: Using a high-precision coordinate measuring machine, control the worktable to scan a number of axial thread profiles in the circumferential direction and output the corresponding point cloud coordinates;

[0086] Among them, reference Figure 2 A high-precision coordinate measuring machine is used for contact scanning. The threaded part to be scanned is placed on the working turntable. The probe scans the thread tooth profile from top to bottom along the axial direction. After completing the scan of one axial tooth profile, the working turntable is controlled to rotate a certain angle to continue scanning until a number of axial tooth profiles in the circumferential direction are scanned, and the corresponding thread tooth profile point cloud coordinates are output. In this embodiment, 20 axial tooth profiles are scanned in the circumferential direction on the threaded part.

[0087] Step 2: Use a cubic polynomial to fit the thread profile curve to the point cloud coordinates and perform radius compensation based on the probe diameter;

[0088] Among them, after fitting the point cloud coordinates of the thread tooth profile using a cubic polynomial, the radius compensation of the thread tooth profile curve is calculated according to the following formula:

[0089] For the fitted thread profile curve, it can be written in parametric form as r(t), where the tangential velocity is its first derivative:

[0090] v(t) = r'(t);

[0091] After normalization, the unit tangent vector is obtained:

[0092]

[0093] The unit normal vector perpendicular to the tangent needs to be obtained by rotating the tangent by 90°:

[0094] N(t)=(-T y (t),T x (t));

[0095] Based on the probe radius r, the equidistant curves of the thread profile are obtained:

[0096] s(t)=r(t)±rN(t).

[0097] Step 3: Evaluate and extract the thread feature parameters of each thread tooth based on the compensated thread profile curve, which will serve as the original input for subsequent interpolation and 3D reconstruction.

[0098] The general thread profile is determined by thread characteristic parameters such as major diameter, pitch diameter, minor diameter, flank angles on both sides, and pitch. The determination of the thread profile is the basis for its three-dimensional reconstruction, and the evaluation of the thread characteristic parameters can include machining errors.

[0099] The evaluation and determination of the thread feature parameters of each thread tooth in the original input used for subsequent interpolation and 3D reconstruction are performed according to the following steps:

[0100] Using the workpiece coordinate system axis as a reference, the maximum and minimum values ​​of the curves from the axis to the tooth crest and root are respectively taken as the major diameter r of the thread tooth. a and small diameter r f ;

[0101] Search along the tooth flank, parallel to the axis, for positions where the thread thickness and the alveolar width between adjacent threads are close. Use the distance between this position and the axis of the working coordinate system as the mean diameter r. s The pitch p is the sum of the tooth thickness and the alveolar width at that position.

[0102] At the intersection of the pitch diameter and the tooth flank, the acute angle between the left and right tooth flanks and the vertical direction is calculated as the left and right tooth flank angles β of the thread tooth. L β R ;

[0103] To evaluate the radius of the thread arc of a roller, a tangent line is drawn to the tooth profile at the pitch diameter. The acute angle between the tangent line and the horizontal direction is the tooth flank angle. The radius of the thread arc is obtained by fitting the tooth profile arc.

[0104] The pitch diameter obtained by the above method is its single pitch diameter, and the workpiece coordinate system axis is used as the reference. The eccentricity error of the asymmetry of the threads on both sides is also included in the pitch diameter.

[0105] Step 4: Correct the theoretical helical coordinate system and helical surface equations based on coordinate transformation;

[0106] Among them, reference Figure 3 The correction of the theoretical spiral coordinate system based on coordinate transformation includes:

[0107] Establish a fixed coordinate system for the helical surface (O) i -x i ,y i ,z i Choose a point O' on the mean diameter helix.i O' i The rotation angle is θ ij Its spiral ascent is h; with O' i Establish coordinate systems (O') with the origin of the coordinate system as the origin. i -x i1 ,y i1 ,z i1 ) and coordinate system (O' i -x i2 ,y i2 ,z i2 ), where the coordinate system (O' i -x i1 ,y i1 ,z i1 ) is based on coordinate system (O) i -x i ,y i ,z i The coordinate system (O') is obtained by translation. i -x i2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 It is obtained by rotation; where i = S, R, N, S represents the lead screw; R represents the roller; N represents the nut, and j represents different thread teeth;

[0108] Through coordinate transformation, we obtain the coordinate system (O'). i -x i2 ,y i2 ,z i2 ) to coordinate system (O' i -x i1 ,y i1 ,z i1 The conversion process is as follows:

[0109] Coordinate system (O' i -x i2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 The transformation matrix M i1i2 for:

[0110]

[0111] In the formula, μ = ±1, +1 indicates right-handed rotation, and -1 indicates left-handed rotation;

[0112] Coordinate system (O'i -x i1 ,y i1 ,z i1 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii1 for:

[0113]

[0114] Wherein, the spiral ascent amount h is:

[0115] h = θ ij *r ij *tan(ni / p ij / (2*Π*r ij ));

[0116] In the formula, λ ij Where ni is the helix angle, p is the number of heads, and ni is the number of heads. ij The pitch is r. ij λ is the median diameter; where λ is the median diameter. ij for:

[0117]

[0118] Thus, the coordinate system (O') is obtained. i -x i2 ,y i2 ,z i2 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii2 for:

[0119] M ii2 =M ii1 Mi 1i2 ;

[0120]

[0121] Additionally, refer to Figures 4-6 The correction of the theoretical helical surface equation based on coordinate transformation includes:

[0122] For any point M on the screw helical surface, in coordinate system (O' S -x S2 ,y S2 ,z S2 This is represented as follows:

[0123]

[0124] In the formula, η = ±1, +1 represents the upper surface, where t is taken as L; -1 represents the lower surface, where t is taken as R, and r Sj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Sj Pitch;

[0125] make By coordinate transformation, we can obtain the coordinate system (O) of point M. S -x S ,y S ,z S This is represented as follows:

[0126] r S =M SS2 r S2 ;

[0127]

[0128] For any point M on the roller helical surface, in coordinate system (O' R -x R2 ,y R2 ,z R2 This is represented as follows:

[0129]

[0130] In the formula, r Rj r is the pitch diameter of the roller. PLj z is the radius of the upper arc of the roller. PRj β is the radius of the arc on the underside of the roller. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Rj Pitch;

[0131] make By coordinate transformation, we can obtain the coordinate system (O) of point M. R -x R ,y R ,z R This is represented as follows:

[0132] r Rj =M RR2 r R2 ;

[0133]

[0134] For any point M on the helical surface of the nut, in coordinate system (O' N -x N2 ,y N2 ,z N2 This is represented as follows:

[0135]

[0136] In the formula, r Nj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Nj Pitch;

[0137] make By coordinate transformation, we can obtain the coordinate system (O) of point M. N -x N ,y N ,z N This is represented as follows:

[0138] r Nj =M NN2 r N2 ;

[0139]

[0140] Step 5: Use cubic spline interpolation to obtain the thread characteristic parameters of the unmeasured thread teeth;

[0141] In this method, when using cubic spline interpolation to interpolate thread tooth feature parameters, the thread tooth feature parameters obtained by scanning along the same helix are used as feature points. During interpolation, the different rotation angles of the tooth profile on the helix are used to represent the θ values ​​of different thread parameters. ij As independent variables, the thread characteristic parameters of the tooth profile are used as dependent variables. The thread characteristic parameters are interpolated to obtain the characteristic parameters of the thread teeth in the unmeasured area. After interpolation, the characteristic point data must be retained unchanged.

[0142] In this embodiment, with 20 axial tooth profiles as the original input, the interpolation accuracy of the major, medium, and minor diameters, pitch, and arc radius is about 1 μm, and the interpolation accuracy of the tooth flank angle is about 0.1°.

[0143] Step Six, Refer to Figure 7 The thread characteristic parameters of each thread tooth after interpolation and its rotation angle θ on the helix are calculated. ij Substituting the corrected helical coordinate system and helical surface equation, we obtain the corresponding thread profile including machining errors;

[0144] Step 7, Refer to Figure 8 By uniformly discretizing and triangulating the points on the obtained real thread profile, the three-dimensional reconstruction model of the real thread of the planetary roller screw pair in this embodiment can be obtained.

[0145] The beneficial effects of this invention are as follows:

[0146] (1) This invention uses a high-precision coordinate measuring machine to control the turntable to scan a certain number of axial thread profiles in the circumferential direction and output the corresponding point cloud coordinates of the thread profiles. The point cloud coordinates are fitted with thread profile curves using a cubic polynomial and radius compensation is performed according to the probe diameter. Based on the compensated thread profile curves, the thread characteristic parameters such as major diameter, pitch diameter, minor diameter, flank angles on both sides, and pitch of each thread tooth are evaluated for subsequent interpolation and the original input for three-dimensional reconstruction.

[0147] (2) Based on coordinate transformation, the equations of the theoretical helical surface and helical line are corrected; the characteristic parameters of the thread tooth at the unmeasured angle position are obtained by using cubic spline interpolation; the characteristic parameters of each thread tooth and its angle on the helical line are substituted into the corrected equation to obtain the corresponding thread tooth profile containing machining error; the points on the tooth profile are uniformly discretized and triangular meshed to complete the three-dimensional reconstruction of the thread surface.

[0148] (3) This invention can quickly complete the three-dimensional reconstruction of the planetary roller screw pair thread surface with machining error based on two-dimensional axial profile detection. Different reconstruction accuracies can be obtained by adjusting the number of two-dimensional axial thread profiles as the original input, which can meet the usage requirements of different scenarios. It provides a basis for the analysis of the clearance, load and contact of planetary roller screws in real situations, and has important research and engineering application significance.

[0149] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for reconstructing the thread surface of a planetary roller screw pair based on actual errors, characterized in that, Includes the following steps: Step 1: Using a high-precision coordinate measuring machine, control the worktable to scan a number of axial thread profiles in the circumferential direction and output the corresponding point cloud coordinates; Step 2: Use a cubic polynomial to fit the thread profile curve to the point cloud coordinates and perform radius compensation based on the probe diameter; Step 3: Evaluate and extract the thread feature parameters of each thread tooth based on the compensated thread profile curve, which will serve as the original input for subsequent interpolation and 3D reconstruction. Step 4: Correct the theoretical helical coordinate system and helical surface equations based on coordinate transformation; Step 5: Use cubic spline interpolation to obtain the thread characteristic parameters of the unmeasured thread teeth; Step 6: Substitute the thread characteristic parameters of each thread tooth and its angle on the helix into the corrected equation to obtain the corresponding thread profile including machining errors. Step 7: Uniformly discretize the points on the tooth profile and triangulate them to complete the three-dimensional reconstruction of the thread surface.

2. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, Step one includes: using a high-precision coordinate measuring machine for contact scanning, placing the threaded part to be scanned on the working turntable, scanning the thread tooth profile from top to bottom along the axial direction with the probe, and after completing the scanning of one axial tooth profile, controlling the working turntable to rotate a certain angle to continue scanning until a certain number of axial tooth profiles in the circumferential direction are scanned, and outputting the corresponding thread tooth profile point cloud coordinates.

3. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, In step two, after fitting the point cloud coordinates of the thread tooth profile using a cubic polynomial, the radius compensation of the thread tooth profile curve is calculated according to the following formula: For the fitted thread profile curve, it can be written in parametric form as r(t), where the tangential velocity is its first derivative: v(t) = r'(t); After normalization, the unit tangent vector is obtained: The unit normal vector perpendicular to the tangent needs to be obtained by rotating the tangent by 90°: N(t)=(-T y (t),T x (t)); Based on the probe radius r, the equidistant curves of the thread profile are obtained: s(t)=r(t)±rN(t).

4. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, In step three, the thread characteristic parameters are determined by the major diameter, pitch diameter, minor diameter, flank angles on both sides, and pitch of the thread profile. The thread characteristic parameters are evaluated and extracted to obtain the machining error of the thread.

5. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 4, characterized in that, The evaluation and determination of the thread characteristic parameters of each thread tooth in the original input used for subsequent interpolation and 3D reconstruction in step three are performed according to the following steps: Using the workpiece coordinate system axis as a reference, the maximum and minimum values ​​of the curves from the axis to the tooth crest and root are respectively taken as the major diameter r of the thread tooth. a and small diameter r f ; Search along the tooth flank, parallel to the axis, for positions where the thread thickness and the alveolar width between adjacent threads are close. Use the distance between this position and the axis of the working coordinate system as the mean diameter r. s The pitch p is the sum of the tooth thickness and the alveolar width at that position. At the intersection of the pitch diameter and the tooth flank, the acute angle between the left and right tooth flanks and the vertical direction is calculated as the left and right tooth flank angles β of the thread tooth. L β R ; To evaluate the radius of the thread arc of a roller, a tangent line is drawn to the tooth profile at the pitch diameter. The acute angle between the tangent line and the horizontal direction is the tooth flank angle. The radius of the thread arc is obtained by fitting the tooth profile arc.

6. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, The fourth step, which involves correcting the theoretical spiral coordinate system based on coordinate transformation, includes: Establish a fixed coordinate system for the helical surface (O) i -x i ,y i ,z i Choose a point O' on the mean diameter helix. i O' i The rotation angle is θ ij Its spiral ascent is h; with O' i Establish coordinate systems (O') with the origin of the coordinate system as the origin. i -x i1 ,y i1 ,z i1 ) and coordinate system (O' i -x i2 ,y i2 ,z i2 ), where the coordinate system (O' i -x i1 ,y i1 ,z i1 ) is based on coordinate system (O) i -x i ,y i ,z i The coordinate system (O') is obtained by translation. i -x i2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 It is obtained by rotation; where i = S, R, N, S represents the lead screw; R represents the roller; N represents the nut, and j represents different thread teeth; Through coordinate transformation, we obtain the coordinate system (O'). i -x i2 ,y i2 ,z i2 ) to coordinate system (O' i -x i1 ,y i1 ,z i1 The conversion process is as follows: Coordinate system (O' i -x i2 ,y i2 ,z i2 ) by coordinate system (O' i -x i1 ,y i1 ,z i1 The transformation matrix M i1i2 for: In the formula, μ = ±1, +1 indicates right-handed rotation, and -1 indicates left-handed rotation; Coordinate system (O' i -x i1 ,y i1 ,z i1 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii1 for: Wherein, the spiral ascent amount h is: h6θ ij *r ij *tan(is*p ij / (2*Π*r ij )) In the formula, λ ij Where ni is the helix angle, p is the number of heads, and ni is the number of heads. ij The pitch is r. ij λ is the median diameter; where λ is the median diameter. ij for: Thus, the coordinate system (O') is obtained. i -x i2 ,y i2 ,z i2 ) to coordinate system (O) i -x i ,y i ,z i The transformation matrix M ii2 for: M ii2 =M ii1 M i1i2 ; 7. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 6, characterized in that, The fourth step, which involves correcting the theoretical helical surface equation based on coordinate transformation, includes: For any point M on the screw helical surface, in coordinate system (O' S -x S2 ,y S2 ,z S2 This is represented as follows: In the formula, η = ±1, +1 represents the upper surface, where t is taken as L; -1 represents the lower surface, where t is taken as R, and r Sj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Sj Pitch; make By coordinate transformation, we can obtain the coordinate system (O) of point M. S -x S ,y S ,z S This is represented as follows: r S ＝M SS2 r S2 ； For any point M on the roller helical surface, in coordinate system (O' R -x R2 ,y R2 ,z R2 This is represented as follows: In the formula, r Rj r is the pitch diameter of the roller. PLj r is the radius of the upper arc of the roller. PRj β is the radius of the arc on the underside of the roller. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Rj Pitch; Let the formula By coordinate transformation, we can obtain the coordinate system (O) of point M. R -x R ,y R ,z R This is represented as follows: r Rj ＝M RR2 r R2 ； For any point M on the helical surface of the nut, in coordinate system (O' N -x N2 ,y N2 ,z N2 This is represented as follows: In the formula, r Nj β is the lead screw pitch diameter. Lj The upper tooth lateral angle, β Rj p is the lateral angle of the lower tooth. Nj Pitch; make By coordinate transformation, we can obtain the coordinate system (O) of point M. N -x N ,y N ,z N This is represented as follows: r Nj ＝M NN2 r N2 ； 8. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, In step five, when interpolating the thread tooth feature parameters using the cubic spline interpolation method, the thread tooth feature parameters obtained by scanning along the same axis are used as feature points, and the different rotation angles of the tooth profile on the helix are used to represent the different thread parameters at angle θ. ij As the independent variable, and the thread characteristic parameters of the tooth profile as the dependent variable, the thread characteristic parameters are interpolated to obtain the characteristic parameters of the thread teeth in the unmeasured area, and the characteristic point data after interpolation remains unchanged.

9. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, The interpolated characteristic parameters of each thread tooth and its rotation angle θ on the helix in step six are described in step six. ij Substituting the corrected helical coordinate system and helical surface equation, we obtain the thread profile including machining errors.

10. The method for reconstructing the thread surface of a planetary roller screw pair based on actual error according to claim 1, characterized in that, In step seven, the points on the obtained thread profile containing machining errors are uniformly discretized and triangularly meshed to obtain a three-dimensional reconstruction model of the planetary roller screw pair thread containing machining errors.

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