A method for evaluating the tooth profile and helix deviation of planetary roller screws

Abstract

The present invention provides a planetary roller screw tooth profile and helix deviation evaluation method, including: processing the threaded rod to be evaluated to obtain axial point set data and helix point set data of the threaded rod to be evaluated; correcting the axial point set data to obtain corrected data; based on the coordinate transformation principle, converting the profile point set data between the test axial direction and the design normal direction of the corrected data to obtain converted data; based on the residual square sum minimization principle, evaluating the tooth profile deviation according to the converted data to obtain a first evaluation result; expanding the helix point set data in the tangent direction of the helix starting point to obtain expanded data; based on the helix deviation formula, calculating the helix deviation value of the preset test length in the expanded data according to the expanded data; obtaining a second evaluation result according to the helix deviation value of the preset test length. The present invention solves the problem of inaccurate evaluation of the profile accuracy of planetary roller screws in the prior art.

Description

Technical Field

[0001] The invention relates to the field of precision testing technology, in particular to a planetary roller screw tooth profile and helix deviation evaluation method. Background Art

[0002] Planetary Roller Screw Mechanism (PRSM) is a new type of precision heavy-duty transmission device that can realize the conversion between rotation and linear motion. It is mainly composed of a screw, multiple rollers, and a nut. It is widely used in military and civilian fields such as aerospace, weapons and equipment, and humanoid robots. The stringent requirements of high-end equipment such as high load, high precision, fast response, and long life pose a great challenge to the processing quality of PRSM threads. Therefore, it is particularly important to detect the geometric profile accuracy of PRSM threads.

[0003] PRSM has small pitch and non-standard special-shaped features. Currently, profile detection of PRSM based on profilers and three-coordinate equipment is the main way to reflect its profile processing quality. It has high detection accuracy and test efficiency and is widely used in research and engineering practice. However, profilers can only scan two-dimensional profiles. It is difficult for profilers to scan three-dimensional spiral lines. In addition, there is currently a lack of domestic PRSM profile accuracy assessment standards. The industry mainly uses indicators such as mid-diameter deviation, pitch deviation, and tooth angle deviation to assess PRSM profile accuracy. However, the existing PRSM assessment indicators cannot fully reflect the surface processing quality of the thread teeth. Summary of the invention

[0004] In order to overcome the deficiencies of the prior art, an object of the present invention is to provide a method for evaluating the tooth profile and helix deviation of a planetary roller screw, which solves the problem of inaccurate evaluation of the profile accuracy of a planetary roller screw in the prior art.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A planetary roller screw tooth profile and helix deviation evaluation method, comprising:

[0007] The threaded rod to be evaluated is processed by a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain profile point set data of the threaded rod to be evaluated, wherein the profile point set data includes: axial point set data and helical point set data;

[0008] Correcting the axial point set data to obtain corrected data;

[0009] Based on the coordinate transformation principle, the correction data is converted into the profile point set data between the test axial direction and the design normal direction to obtain the conversion data;

[0010] Based on the residual square sum minimization principle, the tooth shape deviation is evaluated according to the conversion data to obtain a first evaluation result;

[0011] Expanding the spiral point set data in the tangent direction of the spiral starting point to obtain expanded data;

[0012] Based on the spiral deviation formula and the unfolding data, the spiral deviation value of the preset test length in the unfolding data is calculated;

[0013] A second evaluation result is obtained according to the spiral deviation value of the preset test length.

[0014] Preferably, the threaded rod to be evaluated is processed using a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain the profile point set data of the threaded rod to be evaluated, including:

[0015] A high-precision three-dimensional coordinate measuring machine is used to perform contact scanning on the threaded rod to be evaluated, and the threaded rod to be evaluated is clamped by a three-jaw chuck on the worktable. The probe scans the thread profile from top to bottom along the axial direction to obtain axial point set data;

[0016] Set the thread parameters of the threaded rod to be evaluated, make the work turntable rotate at a preset speed, keep the stylus of the worktable in contact with the theoretical middle diameter, and scan the stylus along the spiral line of the threaded rod. After completing a spiral line scan, control the stylus to move downward by one pitch and continue scanning until the spiral line scan of the multi-start thread is completed, and output the spiral line point set data of the threaded rod to be evaluated.

[0017] Preferably, the axial point set data is corrected to obtain corrected data, including:

[0018] Based on the fastest gradient descent method, according to the gradient threshold, the axial point set data is differentiated to obtain the tooth top data, tooth side data and tooth bottom data;

[0019] Based on the method of coinciding the angle bisector with the design axis, the tooth top data, tooth side data and tooth bottom data are corrected for axis inclination to obtain correction data.

[0020] Preferably, the calculation formula of the gradient threshold is:

[0021]

[0022] Among them, α is the thread angle, S t is the gradient threshold.

[0023] Preferably, the tooth shape deviation is evaluated according to the conversion data based on the residual square sum minimization principle to obtain a first evaluation result, including:

[0024] The thread profile is designed based on the screw, nut and roller, and the axis conversion data is fitted using the least square method to obtain the designed thread profile equation and the average thread profile equation;

[0025] Determine a first auxiliary line equation and a second auxiliary line equation which are parallel to the designed tooth profile trace equation and the average tooth profile trace equation respectively;

[0026] According to the first auxiliary line equation and the second auxiliary line equation, the tooth shape deviation is evaluated to obtain a first evaluation result.

[0027] Preferably, the spiral deviation formula is:

[0028] E i =E i_max -E i_min ;

[0029] ΔL i =max{E i};

[0030] Where, i = {2πrad, 25mm, 100mm, Lu mm}, E i is the helix deviation within any test length, E i_max is the maximum deviation within any test length, E i_min is the minimum deviation within any test length, ΔL i It is the helix deviation within each test length.

[0031] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0032] The present invention provides a planetary roller screw tooth profile and helix deviation evaluation method, including: using a high-precision three-dimensional coordinate measuring machine and a work turntable to process the threaded rod to be evaluated, obtaining the profile point set data of the threaded rod to be evaluated, correcting the axial point set data to obtain the corrected data; based on the coordinate transformation principle, converting the profile point set data between the test axial direction and the design normal direction for the corrected data to obtain the converted data; based on the residual square sum minimization principle, evaluating the tooth profile deviation according to the converted data to obtain the first evaluation result, expanding the helix point set data in the tangent direction of the helix starting point to obtain the expanded data; based on the spiral deviation formula, according to the expanded data, calculating the spiral deviation value of the preset test length in the expanded data; according to the spiral deviation value of the preset test length, obtaining the second evaluation result. The present invention improves the accuracy of the planetary roller screw profile accuracy evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0034] Figure 1 A technical roadmap provided for embodiments of the present invention;

[0035] Figure 2 A schematic diagram of scanning in the axial and helical directions of a thread provided in an embodiment of the present invention;

[0036] Figure 3 The gradient value between two adjacent points on the tooth top, tooth side and tooth bottom provided in the embodiment of the present invention;

[0037] Figure 4 A schematic diagram of the conversion of profile point set data between the test axis and the design normal plane provided by an embodiment of the present invention;

[0038] Figure 5 The tooth shape deviation evaluation diagram and evaluation result diagram provided by the embodiment of the present invention; wherein, Figure 5 (a) is a schematic diagram for evaluating the design of a straight tooth shape. Figure 5 (b) is the evaluation result diagram when the designed tooth shape is a straight line. Figure 5 (c) is the evaluation diagram when the designed tooth shape is an arc. Figure 5 (d) is the evaluation result diagram when the designed tooth shape is an arc;

[0039] Figure 6 A schematic diagram of the spiral line provided by an embodiment of the present invention unfolding along the tangent direction of the starting point;

[0040] Figure 7 The spiral deviation evaluation diagram and evaluation result diagram provided by the embodiment of the present invention are as follows: Figure 7 (a) is a schematic diagram of the helix deviation assessment. Figure 7 (b) is the result diagram of helix deviation evaluation. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] The purpose of the present invention is to provide a method for evaluating the tooth profile and helix deviation of a planetary roller screw, which solves the problem of inaccurate evaluation of the profile accuracy of a planetary roller screw in the prior art.

[0043] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] like Figure 1 As shown, the present invention provides a planetary roller screw tooth profile and helix deviation evaluation method, comprising:

[0045] Step 100: Processing the threaded rod to be evaluated by using a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain profile point set data of the threaded rod to be evaluated, wherein the profile point set data includes: axial point set data and helical point set data;

[0046] Step 200: Correcting the axial point set data to obtain corrected data;

[0047] Step 300: Based on the coordinate transformation principle, the correction data is converted into the profile point set data between the test axis and the design normal direction to obtain the converted data;

[0048] Step 400: Based on the residual square sum minimization principle, the tooth shape deviation is evaluated according to the conversion data to obtain a first evaluation result;

[0049] Step 500: Expand the spiral point set data in the tangent direction of the spiral starting point to obtain expanded data;

[0050] Step 600: Based on the spiral deviation formula, according to the unfolding data, the spiral deviation value of the preset test length in the unfolding data is calculated;

[0051] Step 700: Obtain a second evaluation result according to the spiral deviation value of the preset assessment length.

[0052] Furthermore, the threaded rod to be evaluated is processed using a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain the profile point set data of the threaded rod to be evaluated, including:

[0053] A high-precision three-dimensional coordinate measuring machine is used to perform contact scanning on the threaded rod to be evaluated, and the threaded rod to be evaluated is clamped by a three-jaw chuck on the worktable. The probe scans the thread profile from top to bottom along the axial direction to obtain axial point set data;

[0054] Set the thread parameters of the threaded rod to be evaluated, make the work turntable rotate at a preset speed, keep the stylus of the worktable in contact with the theoretical middle diameter, and scan the stylus along the spiral line of the threaded rod. After completing a spiral line scan, control the stylus to move downward by one pitch and continue scanning until the spiral line scan of the multi-start thread is completed, and output the spiral line point set data of the threaded rod to be evaluated.

[0055] Specifically, Figure 2 As shown, a high-precision three-dimensional coordinate measuring machine is used for contact scanning. The threaded rod to be scanned is clamped by a three-jaw chuck on the working turntable. The probe scans the thread profile from top to bottom along the axial direction. After scanning, the axial point set data of the thread profile is output; the thread parameters of the threaded rod are set, and the working turntable rotates at a certain speed to match the axial movement speed of the probe. The probe always maintains contact with the theoretical middle diameter to realize the scanning of the probe along the spiral line direction of the threaded rod. After completing a spiral line scan, the probe is controlled to move down one pitch and continue scanning until the spiral line scan of the multi-start thread is completed, and the spiral line point set data of the threaded rod is output. In this embodiment, two profiles of the threaded rod are scanned axially symmetrically, and 5 leads are scanned at each head in the spiral line direction, and a total of 5 spiral lines are scanned. The point set data of the axial and spiral parts are shown in Tables 1 and 2, respectively, where Table 1 is the axial point set data table, and Table 2 is the spiral line point set data table. Table 1 is as follows:

[0056] Table 1 Axial point set data table

[0057]

[0058]

[0059] Table 2 is as follows:

[0060] Table 2 Spiral point set data table

[0061]

[0062]

[0063] Furthermore, the axial point set data is corrected to obtain corrected data, including:

[0064] Based on the fastest gradient descent method, according to the gradient threshold, the axial point set data is differentiated to obtain the tooth top data, tooth side data and tooth bottom data;

[0065] Based on the method of coinciding the angle bisector with the design axis, the tooth top data, tooth side data and tooth bottom data are corrected for axis inclination to obtain correction data.

[0066] Specifically, Figure 3As shown in the figure, the fastest gradient descent method is highly sensitive to the gradient changes of adjacent sampling data points. Therefore, this method can quickly and accurately distinguish the data segments of the tooth top, tooth side, and tooth bottom. The gradient threshold calculation formula is:

[0067]

[0068] Where α is the thread angle, S t is the gradient threshold.

[0069] Obtain the gradient value between two adjacent points in turn and compare the gradient value S i With the gradient threshold S t relation:

[0070]

[0071] Based on the method of coincidence of the angle bisector and the design axis, the axis inclination correction is performed on the above grouped data.

[0072] Specifically, Figure 4 As shown, the workpiece coordinate system is established at the center of the top of the threaded rod as O i (x i ,y i , z i ), the axis of the threaded rod coincides with the Z axis, A is an arbitrary point on the axial profile, and A is expressed as (x A ,y A , z A ). Therefore, any point A(x A ,y A , z A ) is transformed to the corresponding point A′(x′) on the normal plane A , y′ A , z′ A ), in the workpiece coordinate system O i (x i ,y i , z i ) is expressed as:

[0073] Where M i For any point A(x A ,y A , z A ) to the corresponding point A′(x′) on the normal plane A , y′ A , z′ A ) is the transformation matrix of .

[0074] Further, such as Figure 5 As shown, based on the residual square sum minimization principle, the tooth shape deviation is evaluated according to the conversion data to obtain a first evaluation result, including:

[0075] The thread profile traces of the screw, nut and roller are designed. The thread profile traces of the screw and nut are straight lines, and the thread profile half angle is 45°. The least square method is used to fit the axis conversion data to obtain the designed thread profile trace equation and the average thread profile trace equation.

[0076] Determine a first auxiliary line equation and a second auxiliary line equation which are parallel to the designed tooth profile trace equation and the average tooth profile trace equation respectively;

[0077] According to the first auxiliary line equation and the second auxiliary line equation, the tooth shape deviation is evaluated to obtain a first evaluation result.

[0078] Specifically, the designed tooth profile traces of the screw and nut are straight lines. The least squares method is used to fit the axial tooth side data to obtain the designed tooth profile trace and the average tooth profile trace equations:

[0079]

[0080] In the formula, k des is the slope of the designed tooth profile trace, b des is the intercept of the designed tooth trace, k act is the average tooth profile slope, b act is the mean tooth trace intercept;

[0081] In (b des -δ, b des +δ) to find the equations of two auxiliary lines that include the actual thread axial profile and are parallel to the designed thread trace line:

[0082]

[0083] In the formula, δ is the auxiliary line intercept to search for extreme values, b i is the intercept of the auxiliary line, i = {des_u, des_d};

[0084] In (b act -δ, b act +δ) to find the equations of two auxiliary lines that include the actual thread axial profile and are parallel to the average thread profile trace:

[0085]

[0086] In the formula, δ is the auxiliary line intercept to search for extreme values, b i is the intercept of the auxiliary line, i = {act_u, act_d};

[0087] Within the range of measurement, the average tooth profile trace intersects the actual axial profile at P(x p , z p ), Q(x q , zq ) above and below. The equations of the two auxiliary lines passing through points P and Q are:

[0088]

[0089] Where b i is the intercept of the auxiliary line, i = {sub_u, sub_d};

[0090] The total tooth profile deviation, tooth shape deviation and tooth inclination deviation of each tooth side are:

[0091]

[0092] The roller tooth profile trace is designed as an arc. The least square method is used to fit the axial tooth side data to obtain the designed tooth profile trace and the average tooth profile trace equation:

[0093]

[0094] In the formula, (x des ,y des ) is the center of the designed arc of the roller, r des is the arc radius of the roller design, (x act ,y act ) is the center of the roller fitting arc, r act Fit the arc radius to the roller;

[0095] In (r des -δ, r des +δ) to find the equations of the two auxiliary arcs that contain the actual thread axial profile and are parallel to the designed tooth profile trace:

[0096]

[0097] In the formula, δ is the auxiliary arc search extreme value, r i is the radius of the auxiliary arc, i = {des_u, des_d};

[0098] In (r act -δ, r act +δ) to find the equations of two auxiliary lines that include the actual thread axial profile and are parallel to the average thread profile trace:

[0099]

[0100] Where δ is the auxiliary arc search extreme value, r i is the radius of the auxiliary arc, i = {act_u, act_d};

[0101] Within the range of measurement, the average tooth profile trace intersects the actual axial profile at P(x p , zp ), Q(x q , z q ) above and below. The equations of the two auxiliary lines passing through points P and Q are:

[0102]

[0103] In the formula, r i is the radius of the auxiliary arc, i = {sub_u, sub_d};

[0104] The total tooth profile deviation, tooth shape deviation and tooth inclination deviation of each tooth side are:

[0105]

[0106] After calculation, within the measuring range, the total tooth profile deviation of the arc tooth side is 5.09~9.17μm, the tooth shape deviation is 4.56~5.07μm, and the tooth inclination deviation is 0.04~0.54μm.

[0107] Specifically, Figure 6 As shown in the figure, the end point of the three-dimensional spiral point set is taken as the starting point, the direction of rotation is determined, and the spiral point set is expanded according to the tangential direction of the starting point to obtain the point set data for evaluating the spiral deviation. The theoretical spiral is the hypotenuse of a right triangle after expansion:

[0108]

[0109] Among them, β is the helix angle, n is the number of helical coils, Ph is the thread lead, a is the right angle side adjacent to β, and b is the right angle side opposite to β.

[0110] Further, such as Figure 7 As shown, the helix deviation is defined as the maximum algebraic difference between the actual helix and the theoretical helix in the axial direction. Within any test length, the helix deviation is calculated, and the helix deviation formula is:

[0111] E i =E i_max -E i_min ;

[0112] ΔL i =max{E i};

[0113] Where, i = {2πrad, 25mm, 100mm, Lu mm}, E i is the helix deviation within any test length, E i_max is the maximum deviation within any test length, E i_min is the minimum deviation within any test length, ΔL iis the helix deviation within each test length. According to calculation, the helix deviation within the test range of 2πmm is 2.17-3.28μm, the helix deviation within the range of 25mm is 2.28-3.29μm, the helix deviation within the range of 100mm is 2.35-3.37μm, and the helix deviation within the range of Lu mm is 2.41-3.6μm.

[0114] The beneficial effects of the present invention are as follows:

[0115] (1) Use a high-precision three-dimensional coordinate measuring machine to control the work turntable to scan the small pitch non-standard special-shaped threads of the planetary roller screw in the axial and spiral directions to obtain the profile point set data;

[0116] (2) With regard to the tooth profile deviation, based on the fastest gradient descent method, the axial profile point set data of the threaded tooth is divided into the tooth top, tooth side, and tooth bottom data, and the axial inclination correction is performed on the axial profile point set data; based on the principle of coordinate transformation, the profile point set data conversion between the test axial surface and the design normal surface is realized; and the tooth profile deviation is evaluated based on the principle of minimizing the residual sum of squares.

[0117] (3) With regard to the helix deviation, the three-dimensional helix point set data is expanded in the tangent direction of the helix starting point; the helix deviation is evaluated based on the maximum difference between the measured helix and the theoretical helix.

[0118] (4) The present invention can quickly evaluate the accuracy of the corrected planetary roller screw thread profile data, obtain the thread tooth profile deviation and helix line deviation values ​​under normal design, accurately reflect the surface processing quality of each thread tooth, and provide a basis for analyzing the transmission stability and load uniformity of the planetary roller screw under real conditions. It has important research and engineering application significance.

[0119] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0120] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A planetary roller screw tooth profile and helix deviation evaluation method, characterized in that: include: The threaded rod to be evaluated is processed by a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain profile point set data of the threaded rod to be evaluated, wherein the profile point set data includes: axial point set data and helical point set data; Correcting the axial point set data to obtain corrected data; Based on the coordinate transformation principle, the correction data is converted into the profile point set data between the test axial direction and the design normal direction to obtain the conversion data; Based on the residual square sum minimization principle, the tooth shape deviation is evaluated according to the conversion data to obtain a first evaluation result; Expanding the spiral point set data in the tangent direction of the spiral starting point to obtain expanded data; Based on the spiral deviation formula and the unfolding data, the spiral deviation value of the preset test length in the unfolding data is calculated; Obtaining a second assessment result according to the spiral deviation value of the preset assessment length; Correcting the axial point set data to obtain corrected data includes: Based on the fastest gradient descent method, according to the gradient threshold, the axial point set data is differentiated to obtain the tooth top data, tooth side data and tooth bottom data; Based on the method of coinciding the angle bisector with the design axis, the tooth top data, the tooth side data and the tooth bottom data are corrected for axis inclination to obtain correction data; The tooth shape deviation is evaluated according to the conversion data based on the residual square sum minimization principle to obtain a first evaluation result, including: The thread profile is designed based on the screw, nut and roller, and the axis conversion data is fitted using the least square method to obtain the designed thread profile equation and the average thread profile equation; Determine a first auxiliary line equation and a second auxiliary line equation which are parallel to the designed tooth profile trace equation and the average tooth profile trace equation respectively; According to the first auxiliary line equation and the second auxiliary line equation, the tooth shape deviation is evaluated to obtain a first evaluation result.

2. A planetary roller screw tooth profile and helix deviation evaluation method according to claim 1, characterized in that: The threaded rod to be evaluated is processed by a high-precision three-dimensional coordinate measuring machine and a work turntable to obtain the profile point set data of the threaded rod to be evaluated, including: A high-precision three-dimensional coordinate measuring machine is used to perform contact scanning on the threaded rod to be evaluated, and the threaded rod to be evaluated is clamped by a three-jaw chuck on the worktable. The probe scans the thread profile from top to bottom along the axial direction to obtain axial point set data; Set the thread parameters of the threaded rod to be evaluated, make the work turntable rotate at a preset speed, keep the stylus of the worktable in contact with the theoretical middle diameter, and scan the stylus along the spiral line of the threaded rod. After completing a spiral line scan, control the stylus to move downward by one pitch and continue scanning until the spiral line scan of the multi-start thread is completed, and output the spiral line point set data of the threaded rod to be evaluated.

3. A planetary roller screw tooth profile and helix deviation evaluation method according to claim 1, characterized in that: The calculation formula of the gradient threshold is: Among them, α is the thread angle, S t is the gradient threshold.

4. A planetary roller screw tooth profile and helix deviation evaluation method according to claim 1, characterized in that: The spiral deviation formula is: AND i =And i_max -AND i_min ; ΔL i =max{E i }; Where, i = {2πrad, 25mm, 100mm, Lu mm}, E i is the helix deviation within any test length, E i_max is the maximum deviation within any test length, E i_min is the minimum deviation within any test length, ΔL i It is the helix deviation within each test length.

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