Double-arc ball screw raceway section error identification method

Abstract

The invention discloses a biarc ball screw raceway section error identification method, which comprises the following steps of: acquiring normal section two-dimensional original data of a raceway, fitting the original data through a sliding window to screen outer diameter section data, and completing clamping inclination error correction through least square fitting and coordinate transformation; in combination with a contourgraph hardware measurement parameter, continuously compensating a displacement coupling error to obtain new two-dimensional data; screening out raceway contour data from the new two-dimensional data, dividing the raceway contour data into segments containing complete left and right raceways, and fitting radiuses and circle centers of left and right arcs of each segment; preferentially adopting a geometric analysis method to solve the circle center of the ball for each segment, and switching a grid constraint centering algorithm to carry out iterative positioning in case of failure; and calculating a comparison design value of the contact angle and the nominal lead. Through a dual error correction mechanism and a dual-path circle center solving strategy, the problem of measurement errors caused by clamping inclination and displacement coupling of a contourgraph lever structure in the existing measurement technology is solved, and the measurement precision and the data processing efficiency are both considered.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology for ball screws, specifically to a method for identifying the raceway profile error of a double-circular-arc ball screw. Background Technology

[0002] With its unique advantage of a symmetrical double-arc raceway design, the double-arc ball screw has become a core transmission component for high-end equipment such as CNC machine tools, precision instruments, and humanoid robots. Its two eccentric arc structures can stabilize the contact angle and disperse contact stress, significantly improving load-bearing capacity, axial stiffness, and transmission accuracy stability. Moreover, it exhibits less frictional torque fluctuation and more uniform wear during high-speed operation, resulting in a significantly longer service life compared to single-arc raceways. It is a key basic component for achieving precision transmission in high-end equipment.

[0003] However, the performance advantage of double-arc ball screws highly depends on the machining accuracy of the raceway profile. The raceway grinding process is inherently complex and susceptible to geometric deviations due to multiple factors. Firstly, insufficient machining equipment precision, deviations in grinding wheel dressing parameters, and improper matching of grinding feed rate and speed can directly cause core geometric features such as the raceway radius, center position, and smoothness of the connection between the two arcs to deviate from design values. Secondly, datum deviations during clamping and positioning can cause the screw to tilt, further amplifying the profile measurement error. This ultimately leads to abnormal contact between the balls and the raceway, resulting in either increased local wear, higher transmission temperature, reduced transmission efficiency and smoothness, or, in severe cases, contact angle fluctuations exceeding the design range, compromised axial stiffness stability, and even screw pair jamming, directly impacting the operational accuracy and reliability of high-end equipment. Therefore, accurate and efficient measurement of the raceway profile error of double-arc ball screws is crucial for ensuring performance compliance and is a core industry requirement.

[0004] In existing measurement technologies for the cross-sectional error of double-circular-arc ball screw raceways, they can be broadly classified into two categories based on the type of measurement sensor: contact measurement and non-contact measurement. Contact measurement is the mainstream choice for precision inspection of double-circular-arc raceways because it can accurately reproduce the microscopic morphology of the raceway and is less affected by environmental factors (temperature, humidity, and light). Among these, stylus profilometers are the most widely used. However, the lever mechanism of stylus profilometers has inherent defects: when the stylus contacts the raceway, the probe will move in an arc around a fixed fulcrum, causing the stylus tip displacement to include coupled components in both the horizontal and vertical directions. The resulting "displacement coupling effect" will cause the raw data read by the grating ruler to deviate from the actual morphology of the raceway. If not specifically compensated, this will directly lead to deviations in the subsequent calculation of parameters such as the arc radius and contact angle. At the same time, the tilting error during screw clamping (such as the clamping datum not coinciding with the measurement datum) will cause the outer diameter straight segment and the raceway profile data to tilt as a whole, further amplifying the measurement error.

[0005] Currently, for the detection of raceway profile error in double-arc ball screws, it is necessary to ensure measurement accuracy to accurately identify raceway profile deviations, while also improving measurement efficiency to meet the quality control requirements of mass production scenarios. How to develop a raceway profile error measurement technology that can balance high precision and high efficiency, achieve rapid and efficient processing of massive contour data, and accurately extract key error parameters such as raceway radius, contact angle, and nominal diameter has become an urgent technical challenge to be solved in the field of precision testing of double-arc ball screws. Summary of the Invention

[0006] The purpose of this invention is to provide a method for identifying the raceway profile error of a double-arc ball screw. This method eliminates the influence of errors caused by clamping tilt and displacement coupling of the profilometer lever structure on the measurement results, thereby achieving accurate measurement of the raceway radius, nominal lead, and contact angle.

[0007] The technical solution adopted in this invention is a method for identifying the raceway profile error of a double-circular-arc ball screw, comprising: collecting two-dimensional raw data of the normal profile of the raceway using a stylus-type profilometer; first, filtering the outer diameter segment data through sliding window fitting of the raw data; then, completing the clamping tilt error correction through least-squares fitting and coordinate transformation; combining the hardware measurement parameters of the profilometer, further compensating for displacement coupling error to obtain new two-dimensional data; filtering the raceway profile data from the new two-dimensional data and dividing it into segments containing complete left and right raceways; fitting the radius and center of the left and right circular arcs of each segment; preferentially using the geometric analytical method to solve for the ball center of each segment, and if this fails, switching to the mesh constraint centering algorithm for iterative positioning; calculating the contact angle and nominal lead, and comparing with the design values ​​to complete the raceway profile error identification.

[0008] The invention is further characterized by: Specifically, the following steps are included: Step 1: Use a stylus-type profilometer to sample the axial and radial positions of each point on the normal cross-sectional curve of the raceway of the double circular arc ball screw under test, and obtain the raw measurement data. originalData Set the sliding window size and calculate. originalData The approximate derivative of each data point is used to select the data points for the outer diameter section of the lead screw. LinePoint ; data points for outer diameter segment LinePoint Linear fitting was performed using the least squares method, and the clamping tilt angle was calculated using trigonometric functions. TiltAng ; based on raw measurement data originalData The first data point is the center of rotation, and all data points are rotated in the opposite direction. TiltAng Perform coordinate transformation to obtain preliminary correction data. TransData ; Step 2, preliminary correction data TransData Displacement coupling error compensation is performed according to equation (1) to obtain the compensated two-dimensional data.ComData ( x_com , y_com ), (1), in, L 1 represents the probe length. L The length of the major axis of the measuring rod; ζ It is the distance from the tip of the probe to the fulcrum of the probe rod, calculated according to formula (2); dis 1 = Px*PE 1, Px It is the change in pulse in the horizontal direction of the current measuring point relative to the initial point. PE 1 represents the corresponding pulse equivalent; alphai Let the initial angle be calculated according to equation (3); alphac The current position angle is calculated according to equation (4); (2), (3), (4), in, Py It is the pulse change in the rotation of the current measuring point relative to the initial point around the fulcrum of the measuring rod. PE 2 corresponds to the pulse equivalent. L 2 is the length of the minor axis of the measuring rod; Step 3, process the compensated two-dimensional data ComData ( x_com , y_com )according to x_com Sort in ascending order to determine the starting point of the data. sP and end point eP ,as well as y_com maximum value maxYP and minimum value minYP ; Filter out y_com and maxYP The difference does not exceed the threshold δ point set Q Extract point set Q Mid-range sP and eP Connect the two nearest feature points to construct a baseline line YL, and add an auxiliary line BL parallel to YL; filter out the raceway profile data between YL and BL, and extract several segmented point sets from the raceway profile data. Each segmented point set contains data of a complete left and right raceway profile; perform arc least squares fitting on the left and right raceway data in each segmented point set to obtain the radius and corresponding center of the left and right arcs of each raceway segment; Step 4: First, use the geometric analytical method to establish a system of two quadratic equations for each segmented point set to solve for the center of the ball. If the system of equations has no solution, is numerically unstable, or the solution does not meet the geometric constraints, then switch to the grid constraint center-finding algorithm. The grid constraint center-finding algorithm plans the initial search area and generates grid points. After filtering the valid center, iteratively narrows the search area and refines the step size until the step size is less than 0.1μm, and then outputs the center of the ball. Step 5: For each segment, connect the center of the ball bearing circle to the center of the left arc of the raceway. Using the center of the ball bearing circle as a reference, calculate the angle between the line connecting the centers and the vertical direction to obtain the left contact angle of each segment; connect the center of the ball bearing circle to the center of the right arc of the raceway. Using the center of the ball bearing circle as a reference, calculate the angle between the line connecting the centers and the vertical direction to obtain the right contact angle of each segment; calculate the horizontal spacing between the corresponding ball bearing centers of adjacent segments to obtain the nominal lead. Step 6: Compare the contact angle on the left side of the raceway, the contact angle on the right side of the raceway, and the nominal lead with the design values ​​to complete the identification of raceway profile error.

[0009] The approximate derivative in step 1 is calculated as follows: taking each data point as the center, select adjacent data points to form a sliding window, and obtain the window slope through linear fitting. The window slope is the approximate derivative of the current data point. The size of the sliding window is 0.02% to 0.03% of the total amount of the original measurement data.

[0010] Clamping tilt angle in step 1 TiltAng Calculated according to the following formula, TiltAng = arctan ( slope ), in, slope To fit the slope of the straight line.

[0011] In step 3, the auxiliary line BL and the minimum value minYP The vertical distance is ,in r 0 represents the radius of the ball bearing.

[0012] The method for extracting several segmented point sets from the raceway profile data in step 3 is as follows: marking ComData For all intersections with YL and BL, mark the intersection corresponding to YL as A and the intersection corresponding to BL as B, and then... x_com The process involves ascending order integration, dividing each segmented point set into several segments containing complete left and right roller profiles, based on the fact that each segmented point set contains the sequence A→B→B→A.

[0013] The system of two quadratic equations in step 4 is as follows: , in,( x , y Let be the position of the center of the ball to be solved.r 0 represents the radius of the ball bearing. r 1 represents the radius of the left arc of the raceway. r 2 is the radius of the right arc of the raceway, ( a 1, b 1) is the center of the left arc of the raceway, ( a 2, b 2) is the center of the right arc of the raceway.

[0014] The specific steps for the mesh constraint centering algorithm to output the center of the target ball in step 4 are as follows: Step 4.1: Extract the extreme values ​​of the coordinates of the segmented point set, and plan the initial search area as follows: , in,( SP xmin , SP xmax ) represents the range in the X direction, ( SP ymin , SP ymax ) represents the range in the Y direction, ( CP xmin , CP xmax )for ContourPoints Extreme values ​​of the X-coordinate, ( CP ymin , CP ymax )for ContourPoints Extreme values ​​of the Y-coordinate The radius of the ball bearing; At the same time, the initial search step size is set to CoarseStep ; Step 4.2: Generate uniformly distributed grid points based on the initial search region and initial search step size, calculate the number of grid rows and columns, and the coordinates of each grid point generated by traversing the rows and columns, as shown below: , in, cols and rows These are the number of rows and columns of the grid. G px and G py These are the coordinates of the grid points; Step 4.3, for each grid point ( G px , G py ), calculate its to ContourPoints If the squared distance of all points is greater than 1, then the squared distance of all points is greater than 1. If so, then the grid point is a valid circle center; Step 4.4: From all valid center points, select the point with the smallest Y-coordinate as the optimal center point for this round of search, denoted as ( x bc , y bc ); Step 4.5, using the current optimal center as the center, redefine the iterative search region: the X-axis range is set to [ x bc - CoarseStep , x bc + CoarseStep The Y-axis range is set to [ y bc - CoarseStep , y bc [This reduces the search step size;] Step 4.6: If the reduced search step size is less than 0.1μm, the output optimal center is the final ball center position that is tangent to the left and right contours of the raceway. Otherwise, continue the repeated iteration of steps 4.3-4.6.

[0015] Calculated according to the following formula, .

[0016] The reduced search step size is 1 / 5 to 1 / 10 of the original search step size.

[0017] The beneficial effects of this invention are: This invention addresses the problem in existing technologies where the measurement of raceways for double-arc ball screws is susceptible to interference from clamping tilt and displacement coupling errors in the profilometer lever structure. First, it identifies and corrects the tilt angle of the straight segment of the screw's outer diameter using least-squares fitting, eliminating clamping deviations. Then, it compensates for displacement coupling errors by combining parameters such as probe length and probe rod major axis length. This dual correction mechanism effectively reduces system errors, providing high-precision raw data support for subsequent raceway parameter calculations and ensuring the accuracy of measurement results for key parameters such as raceway radius and contact angle. For each raceway segment, when calculating the ball center position, it overcomes the limitation of single-method solutions for ball center determination often resulting in no solution or solutions deviating from actual constraints by employing a dual-path strategy of "geometric analysis + iterative approximation." The analytical method can quickly obtain the center position that meets the tangency condition, while the mesh-constrained center-finding algorithm optimizes through mesh search and distance judgment when the analytical method fails. Once the distance between the current grid point and a point in the contour is detected to be less than the ball radius, the current loop is exited, and the validity of the next grid point is determined. This greatly reduces redundant computation, balances the reliability of centering and the efficiency of processing large amounts of contour data, and avoids invalid calculations. Attached Figure Description

[0018] Figure 1This is a flowchart illustrating Embodiment 1 of the present invention; Figure 2 This is a schematic diagram of the measurement principle of Embodiment 1 of the present invention; Figure 3 These are the original data of the lead screw in Embodiment 1 of the present invention, the selected data points of the lead screw outer diameter, and the straight line of least squares fitting. Figure 4 This is a schematic diagram of the original data and the data point set after tilt correction of the lead screw in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the process of finding the center position of the ball using the mesh constraint center-finding algorithm in Embodiment 1 of the present invention; Figure 6 This is a schematic diagram of the process of finding the center position of a ball using the mesh constraint center-finding algorithm in Embodiment 1 of the present invention. The mesh points where the triangle is located are the points that do not contain the raceway contour data in the first iteration. The final ball center position is marked with a pentagram in the figure. Figure 7 This is a diagram showing the detection results of the lead screw data in Embodiment 1 of the present invention; Figure 8 This is a diagram showing the detection results of the lead screw data in Embodiment 2 of the present invention. Detailed Implementation

[0019] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0020] Example 1 The basic parameters of the double circular arc ball screw under test provided in this embodiment 1 are shown in Table 1.

[0021] Table 1 Basic parameters of the tested lead screw

[0022] The measuring equipment used is a high-precision stylus profilometer (model: SPR2012M-seo, stylus tip radius 25μm, grating ruler resolution 0.1μm). This equipment uses contact scanning between the stylus and the raceway surface, such as... Figure 2 As shown, the stylus-type profilometer is used to scan and sample the axial and radial positions of points on the normal section curve of the raceway of the double-circular-arc ball screw under test, obtaining a two-dimensional coordinate dataset. Approximately 20,000-35,000 data points are generated in a single scan, and a total of 6 independent measurement datasets are collected to eliminate the influence of random errors on the results. All 6 measurement datasets are presented in two-dimensional coordinates (…). x i , y i Stored in the form of ) x i The horizontal coordinate of the stylus along the scanning direction (unit: mm). yi The vertical displacement of the stylus relative to the measurement reference (unit: mm, positive value indicates above the reference plane, negative value indicates below the reference plane), its core data characteristics are highly matched with the raceway geometry.

[0023] The method for identifying the raceway profile error of the double-circular-arc ball screw provided in Embodiment 1 evaluates the screw, such as... Figure 1 As shown, it includes the following steps: Step 1: Acquire the first set of raw measurement data originalData As shown in Table 2,

[0024] First calculate originalData Each data point in Figure 3 The approximate derivative of the data point (in red) is calculated by taking each data point as the center and selecting adjacent data points to form a sliding window. The size of the sliding window is determined by... ​ The percentage is determined to be 0.02% to 0.03% of the total data volume. This embodiment... ​ The data volume is around 21,000. Therefore, for each ( x i , y i A sliding 5-window is formed by selecting four adjacent data points centered on itself. The slope of this window is obtained through linear fitting, and this slope is used as the approximate derivative of the current data point. Then, data types are distinguished based on the characteristics of the lead screw structure: the lead screw's outer diameter is cylindrical, and its data point trajectory is inclined at an angle when affected by clamping errors. ​ The straight line corresponds to a stable approximate derivative value and an overall linear distribution. However, the raceway has a double-circular-arc concave structure, and its approximate derivative fluctuates with the curvature of the arcs, lacking straight-line characteristics. Therefore, all data points corresponding to the approximate derivatives that conform to the straight-line characteristics are extracted and denoted as the outer diameter segment data. ​ (Two-dimensional coordinate array format) ​ (Middle blue data points).

[0025] Next to ​ Linear fitting was performed using the least squares method to obtain the fitted line ( ​ The slope of the black diagonal line in the middle ​ Then through trigonometric function relationships ​ ( ​ Calculate the tilt angle of the original data caused by clamping deviation. ​ ; after that ​ The first data point is the center of rotation. ​ Perform reverse rotation on all data points. ​ The coordinate transformation is a rotation around the center of rotation in the direction opposite to the direction of inclination.​ Angle adjustment is performed to correct tilt and obtain preliminary corrected data. ​ ( x i ​ i ​ ),like ​ Green data points in the middle.

[0026] Step 2: Read the probe length L 1, L 1 = 45.999816846 mm, length of the major axis of the measuring rod L , L =285.154271604938mm and current position angle ​ Key parameters, defining the initial angle ​ For the data after preliminary correction ​ Displacement coupling error compensation is performed to obtain the compensated two-dimensional data. ​ ( ​ , ​ ), in the following form: (1), in, ​ 1 = ​ 1, ​ It is the change in pulse in the horizontal direction of the current measuring point relative to the initial point. ​ 1 represents the corresponding pulse equivalent. ​ It is the distance from the tip of the probe to the fulcrum of the probe rod, which can be expressed as: (2), Wherein, initial angle ​ It is a constant, specifically represented as follows: (3), Among them, the current position angle ​ Represented as: (4), in, ​ It is the pulse change in the rotation of the current measuring point relative to the initial point around the fulcrum of the measuring rod. ​ 2 corresponds to the pulse equivalent. L 2 is the length of the minor axis of the measuring rod.

[0027] The preliminary correction data is obtained through equation (1). ​ Each coordinate point in a ( x i ​ i​ Displacement coupling error compensation is performed to correct the coupling deviations in the horizontal and vertical coordinates caused by the circular motion of the measuring rod, ultimately obtaining the compensated two-dimensional data. ​ Its format is a two-dimensional coordinate array ( ​ , ​ ).

[0028] Step 3: First, for ​ By horizontal coordinate ​ Sort the data in ascending order to ensure a continuous distribution along the scanning direction; determine the starting point of the data based on the sorted data. ​ ( ​ (Minimum coordinates point) and endpoint ​ ( x_ ​ (largest coordinate point), and ​ maximum value ​ (The highest position corresponding to the outer diameter surface of the lead screw) and the minimum value ​ (Corresponds to the deepest position of the raceway indentation).

[0029] Next, extract the reference feature points of the raceway profile: filter ​ All ​ and ​ The difference does not exceed ​ (The feature point selection threshold is set to 0.125 mm in this embodiment) points to form a point set. Q In the point set Q, find the distance from the starting point. ​ The nearest point (denoted as) ​ ) and distance from the end point ​ The nearest point (denoted as) ​ These two points are the characteristic points representing the boundaries on both sides of the raceway.

[0030] Subsequently, the baseline and auxiliary lines for contour filtering are constructed: connect ​ and ​ Two feature points form a reference straight line YL, which reflects the overall trend of the lead screw's outer diameter surface. Based on the raceway design depth, an auxiliary straight line BL is added parallel to YL. The auxiliary straight line BL intersects with the minimum point... ​ The vertical distance is set based on the ball diameter and thread root diameter parameters, which satisfy... , BL is the radius of the ball bearing. In this embodiment, BL is the minimum point. ​ The vertical distance is 0.07, located below YL, corresponding to the boundary height of the raceway recess. (Mark) ​ For all intersections with YL and BL, mark the intersections corresponding to YL as "yellow" and the intersections corresponding to BL as "blue", and then... ​The data is sorted in ascending order and merged into an array of intersection points with alternating labels. ​ As shown, starting from the first point in the integrated intersection array, segments are extracted according to the alternating label logic. ​ The data in the middle: If two adjacent intersection points are "yellow→blue", then the distance between the two points is... ​ The data is for the left raceway data segment. ​ If two adjacent intersection points are "blue→yellow", then the ComData data between the two points is the right-side scroll rail data segment. ​ Following this logic, the array is traversed to obtain multiple sets of alternating left and right raceway data.

[0031] Based on the helical periodic characteristics of the double-circular-arc ball screw raceway, and adhering to the principle that "each segment contains a complete left and right raceway profile," the segments are divided using the intersection point label sequence: a continuous label sequence of "yellow (starting outer diameter intersection) → blue (left raceway bottom intersection) → blue (right raceway bottom intersection) → yellow (ending outer diameter intersection)" constitutes a complete segment, corresponding to a complete structure of a left raceway segment plus a right raceway segment. Based on the repetitive pattern of "yellow→blue→blue→yellow," this embodiment extracts four complete sequences from the integrated intersection point array, corresponding to four segmentation point sets, denoted as follows: ​ 1- ​ 4, each ​ Each point set represents a complete raceway.

[0032] Finally, for each paragraph ​ Least square fitting of raceway profile data: respectively ​ left side raceway data ​ Data with the right raceway ​ The circular arc least squares fitting algorithm is used, and each set of data is input ( ​ , ​ The radius of each segment of the left-side raceway arc is obtained by minimizing the sum of squared deviations between the actual coordinates and the fitted arc. r 1 and the radius of the right raceway arc r 2 and the corresponding center coordinates ( a 1, b 1) ( a 2, b 2).

[0033] In this embodiment, there are 4 ​ The fitted arc radius and center coordinates of the left and right contours in the point set are as follows: ​ 1. After fitting, we get ( a 1, b1) is (2.2094822756853675, 0.82903666755116312), r 1 is 0.89165392360897755 mm; ​ 1. After fitting, we get ( a 2, b 2) is (2.3381095248087181, 0.82591165128068877), r 2 is 0.8766187678301659 mm; ​ 2. After fitting, we get ( a 1, b 1) is (4.2108634328852731, 0.85055083163449873), r 1 is 0.91189442487588834 mm; ​ 2. After fitting, we get ( a 2, b 2) is (4.3893507096625182, 0.85896003266214187), r 2 is 0.91463654355786017 mm; ​ 3. After fitting, we get ( a 1, b 1) is (6.2542435672195739, 0.847038500544966), r 1 is 0.917476173913003 mm; ​ 3. After fitting, we get ( a 2, b 2) is (6.3798102650830636, 0.85195401525855325), r 2 is 0.91404953681699275mm; ​ 4. After fitting, we get ( a 1, b 1) is (8.3092154321089815, 0.84842167832582369), r 1 is 0.8963612939588744 mm; ​ 4. After fitting, we get ( a 2, b2) is (8.418344263048957, 0.87005463427913678), r 2 is 0.9183665260015037mm.

[0034] Step 4: Based on the condition that the ball and the left and right arc contours of the raceway are simultaneously internally tangent, the geometric analytical method is first used to solve for each raceway of the lead screw. ​ 1- ​ The positions of the ball bearing centers in each of the four segments are described below: (5), in,( x , y Let be the position of the center of the ball to be solved. For the radius of the ball, ( a 1, b 1) The center position of the fitted circular arc of the left profile of the raceway. r 1 represents the radius of the left contour arc; a 2, b 2) The center position of the fitted circular arc of the right profile of the raceway. r 2 represents the radius of the right contour arc.

[0035] Expanding the system of two quadratic equations and eliminating variables, we obtain the following: x and y The expression for the intermediate variable is: (6), When the discriminant When the value is less than 0, the system of equations has no solution; furthermore, when there are anomalies in the original measurement data or when the abscissas of the fitting centers of the left and right contours are close, i.e. ( a 1 -a 2<1e-3), the denominator of the intermediate variable is close to 0, which may lead to unstable numerical solution. Verify whether the solution meets the actual geometric constraints. If there is no solution, the numerical solution is unstable, or the geometric constraints are not met, switch to the mesh constraint centering algorithm to continue solving for the center position of the ball.

[0036] When using a mesh-constrained center-finding algorithm to iteratively approximate the center position of the search ball, follow these steps: ​ As shown, Step 4.1, plan the initial search area, first extract... ContourPoints X-coordinate extreme values ​​( CP xmin , CP xmax ) and extreme values ​​of the Y coordinate ( CP ymin , CP ymax ); Select (SP xmin , SP xmax The middle 40% of the interval is designated as the X-axis search range to ensure coverage of the core area enclosed by the left and right arcs of the raceway, avoiding an excessively large search range. Based on the assembly constraints of the ball and raceway, the range is limited to... SP ymin (Deepest part of the raceway) to SP ymax (The upper limit position of the ball diameter and raceway depth), as shown in Equation (7), excludes the invalid area outside the raceway; set the initial coarse search step size. CoarseStep The length of the search interval in the X direction ( SP xmax - SP xmin Using 1 / 10 of the step size ensures that the initial search fully covers the effective region while avoiding inefficiency caused by an excessively small step size. (7).

[0037] Step 4.2: Generate grid points and filter valid circle centers, such as... Figure 6 As shown: Based on the initial search area ( SP xmin , SP xmax )×( SP ymin , SP ymax ) and coarse search step size CoarseStep The number of rows and columns of the grid is calculated using equation (8). cols , rows And iterate through rows and columns to generate all uniformly distributed grid points. , ), (8), in, cols and rows These are the number of rows and columns of the grid. G px and G py These are the coordinates of the grid points.

[0038] Step 4.3, calculate each grid point ( G px , G py Point set ContourPoints If the squared distance of all points is greater than the squared radius of the ball, then... If the generated grid point is the center of the circle, then that grid point is a valid center. Geometrically, this means drawing a circle with the generated grid points as centers and the ball bearing radius as the radius. If the circle does not contain the set of points... ContourPoints The point in the middle is the valid center of the circle. If it contains ContourPoints The points in the middle are invalid.

[0039] Step 4.4: Select the point with the smallest Y-coordinate from all valid center points as the optimal center point for this round of search. BestCenter ( x bc , y bc ), adapted to the geometric features of the raceway.

[0040] Step 4.5: Using the current optimal center as the center, narrow the search area. The X-axis range of the new search area is set to [ x bc - CoarseStep , x bc + CoarseStep The Y-axis range is set to [ y bc - CoarseStep , y bc This ensures the search focuses on the optimal region, and then the search step size is updated to 1 / 5 to 1 / 10 of the original step size to improve search accuracy. In this embodiment... CoarseStep = CoarseStep / 5.

[0041] Step 4.6: Repeat the grid generation and valid center selection operations in the new search area, updating the optimal center coordinates. Repeat the above iterative process until the search step size is less than 0.1. μ The process terminates at time m. The optimal center output at this point is the final target center position, which is simultaneously internally tangent to the left and right contours of the raceway. Figure 7 As shown, this is used for subsequent contact angle calculations.

[0042] Based on the above steps, calculate the remaining three segments. ContourPoints The center of the target ball corresponding to the point set.

[0043] In this embodiment, the coordinates of the ball center in each of the four segments were determined after executing equation (6). Since a suitable target ball center coordinate was not found using the geometric analytical method, the proposed mesh-constrained center-finding algorithm was used to iteratively approximate the search for the ball center, ultimately determining its coordinate position. The coordinates of the center of the first ball bearing are (2.28865270416987, 0.773661581892762). The coordinates of the center of the second ball bearing are (4.29831274000996, 0.777384044078394). The coordinates of the center of the third ball bearing are (6.30699270419919, 0.775337515676878). The coordinates of the center of the fourth ball bearing are (8.31567270991955, 0.772539344702049).

[0044] Step 5: Calculate the contact angle and nominal lead 1. Calculate the contact angle The first paragraph of step 4 ContourPoints The contact angles on the left and right sides of the first raceway corresponding to the point set are calculated according to the following logic: For the center of the ball bearing in the first segment (2.28865270416987, 0.773661581892762), connect this center of the ball bearing with the center of the left arc fitting circle (2.2094822756853675, 0.82903666755116312) to form line L1; then connect the target ball bearing center with the center of the right arc fitting circle (2.3381095248087181, 0.82591165128068877) to form line L2. Establish a local coordinate system with the target ball bearing center as the origin, defining the vertically upward direction as the angular reference (i.e., the 0° direction); as... Figure 7 As shown, the angle between line L1 and the vertical direction is denoted as the left contact angle α1, α1 = 44.76°; the angle between line L2 and the vertical direction is denoted as the right contact angle β1, β1 = 42.31°.

[0045] Similarly, the left contact angle α2 of the second raceway is 48.68°, and the right contact angle β2 is 42.02°; the left contact angle α3 of the third raceway is 42.71°, and the right contact angle β3 is 42.66°; and the left contact angle α4 of the fourth raceway is 41.82°, and the right contact angle β4 is 41.11°.

[0046] 2. Calculate the nominal lead. The nominal lead is the horizontal distance between corresponding points of two adjacent raceways of the lead screw. It is calculated based on the horizontal coordinates of the center of each segment of the ball: In this embodiment, the data of the 4 raceways correspond to 3 segment spacings, namely P1=2.00966mm, P2=2.00868mm, and P3=2.00868mm.

[0047] By comparing the measured values ​​with the design values ​​in Table 1, a quantitative evaluation of the raceway profile machining error can be completed. In the national standard GB / T, the accuracy grades of ball screws are mainly defined according to standards such as GB / T 17587.3 and GB / T 1800.1. Ball screw accuracy grades are divided into eight levels: P0, P1, P2, P3, P4, P5, P7, and P10, with P0 being the highest accuracy and P10 the lowest. In this embodiment, the screw contact angle deviation is designed according to the nominal value of the contact angle ±3°, and the lead deviation is designed according to grade P5 (lead tolerance within ±23μm within any 300mm stroke).

[0048] In this embodiment, the left contact angle error of the first raceway segment is 0.24°, and the right contact angle error is 2.69°; the left contact angle error of the second raceway segment is 3.68°, and the right contact angle error is 2.98°; the left contact angle error of the third raceway segment is 2.29°, and the right contact angle error is 2.34°; and the left contact angle error of the fourth raceway segment is 3.18°, and the right contact angle error is 3.89°. The nominal lead errors of these four raceway segments are 9.66μm, 8.68μm, and 8.68μm, respectively. The measurement results show that the nominal lead errors of all four raceway segments are within the allowable error range. Furthermore, the contact angle errors of the first and third raceways are within the allowable error range, indicating that the machining accuracy of these two raceway segments is qualified.

[0049] Example 2 This embodiment uses the second set of original measurement data collected in Embodiment 1 as the detection object. Some data are shown in Table 3 below. Using the same error identification method as in Embodiment 1, the final calculated contact angles are: left side α1 = 42.42°, right side β1 = 38.11°, and nominal lead P1 = 2.00953 mm. Figure 8 As shown, the contact angle on its right side deviates from the design value within the allowable range, indicating that the machining accuracy of the raceway section of the screw is unqualified.

[0050]

[0051] Example 3 In this embodiment, the third set of original measurement data collected in Embodiment 1 is used as the detection object. Some data are shown in Table 4 below. Using the same error identification method as in Embodiment 1, the contact angle α1 on the left side of the first raceway is 47.12°, the contact angle β1 on the right side is 39.7°, and the nominal lead P1 is 2.00827mm. The deviation of the right contact angle from the design value is not within the allowable range, and it is determined that the machining accuracy of the cross section of the screw raceway is unqualified.

[0052]

[0053] Example 4 In this embodiment, the fourth set of original measurement data collected in Embodiment 1 is used as the detection object. Some data are shown in Table 5 below. Using the same error identification method as in Embodiment 1, the contact angle α1 on the left side of the first raceway is 46.83°, the contact angle β1 on the right side is 40.11°, and the nominal lead P1 is 2.00813mm. The deviation of the right contact angle from the design value is not within the allowable range, and it is determined that the machining accuracy of the cross-section of the screw raceway is unqualified.

[0054]

[0055] Example 5 In this embodiment, the fifth set of original measurement data collected in Embodiment 1 is used as the detection object. Some data are shown in Table 6 below. Using the same error identification method as in Embodiment 1, the final calculation results are: left contact angle α1=47.07°, right contact angle β1=39.10°, and nominal lead P1=2.00809mm. The right contact angle deviates from the design value within the allowable range, and it is determined that the machining accuracy of the cross section of the screw raceway is unqualified.

[0056]

[0057] Example 6 In this embodiment, the 6th set of original measurement data collected in Embodiment 1 is used as the detection object. Some data are shown in Table 7 below. Using the same error identification method as in Embodiment 1, the contact angle α1 on the left side of the first raceway is 47.08°, the contact angle β1 on the right side is 39.10°, and the nominal lead P1 is 2.00835mm. The deviation of the right contact angle from the design value is not within the allowable range, and it is determined that the machining accuracy of the cross-section of the screw raceway is unqualified.

[0058]

[0059] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for identifying a double-arc ball screw raceway section shape error, characterized in that, The method comprises the following steps: Collecting the normal section two-dimensional original data of the raceway by using a stylus profilometer, and performing fitting and screening on the outer diameter section data of the original data by using a sliding window, and then performing least square fitting and coordinate transformation to complete clamping tilt error correction; combining the profilometer hardware measurement parameters, and continuing to compensate the displacement coupling error to obtain new two-dimensional data; screening the raceway profile data from the new two-dimensional data and dividing the raceway profile data into segments containing complete left and right raceways, fitting the radius and center of each segment left and right circular arc; solving the ball center by using a geometric analytical method for each segment, and switching to a grid constraint center-finding algorithm for iterative positioning when the geometric analytical method fails; calculating the contact angle and nominal lead, and comparing the design value to complete the raceway section error identification.

2. The double-arc ball screw raceway profile error identification method according to claim 1, characterized in that, The method comprises the following steps: Step 1, the axial position and radial position of each point on the normal section curve of the double circular arc ball screw raceway to be measured are sampled by using a stylus profilometer, to obtain original measurement data originalData ; Set the size of the sliding window, calculate originalData the approximate derivative of each data point, and filter out the data points of the outer diameter section of the screw LinePoint ; the data points of the outer diameter section LinePoint Linear fitting is performed by using the least square method, and the clamping inclination angle is calculated by using the trigonometric function relationship TiltAng ; the first data point of the original measurement data originalData is taken as the rotation center, and all data points are rotated in the opposite direction TiltAng Coordinate transformation is carried out to obtain the preliminary corrected data TransData ; Step 2, preliminary correction of data TransData According to formula (1), displacement coupling error compensation is performed to obtain compensated two-dimensional data ComData ( x_com , y_com ), (1)， wherein, L 1 is the length of the probe needle, L is the length of the long axis of the measuring rod; ζ is the distance from the vertex of the probe needle to the fulcrum of the measuring rod, calculated according to equation (2); dis 1 = Px*PE 1, Px is the pulse change amount of the current measuring point relative to the initial point in the horizontal direction, PE 1 is the corresponding pulse equivalent; alphai is the initial angle, calculated according to equation (3); alphac is the current position angle, calculated according to equation (4); (2)， (3)， (4)， wherein, Py is the current measurement point relative to the initial point around the measurement rod fulcrum rotation pulse change, PE 2 is the corresponding pulse equivalent, L 2 is the length of the short axis of the measuring rod; Step 3, process the compensated two-dimensional data ComData ( x_com , y_com )according to x_com Sort in ascending order to determine the starting point of the data. sP and end point eP ,as well as y_com maximum value maxYP and minimum value minYP ; Filter out y_com and maxYP The difference does not exceed the threshold δ point set Q Extract point set Q Mid-range sP and eP Connect the two nearest feature points to construct a baseline line YL, and add an auxiliary line BL parallel to YL; filter out the raceway profile data between YL and BL, and extract several segmented point sets from the raceway profile data. Each segmented point set contains data of a complete left and right raceway profile; perform arc least squares fitting on the left and right raceway data in each segmented point set to obtain the radius and corresponding center of the left and right arcs of each raceway segment; Step 4, for each segment point set, a geometric analytical method is used to establish a bivariate quadratic equation set to solve the ball center; if the equation set has no solution, the numerical value is unstable or the solution does not meet the geometric constraint, the grid constraint center-finding algorithm is switched to; the grid constraint center-finding algorithm plans an initial search area and generates grid points, screens effective centers, iteratively reduces the search area and refines the step length until the step length is less than 0.1 μm, and outputs the ball center; Step 5, for each segment, the ball center and the left circular arc center of the raceway are connected, the included angle between the center line and the vertical direction is calculated based on the ball center, and the left side contact angle of each segment is obtained; the ball center and the right circular arc center of the raceway are connected, the included angle between the center line and the vertical direction is calculated based on the ball center, and the right side contact angle of each segment is obtained; the distance between the ball centers corresponding to adjacent segments in the horizontal direction is calculated, and the nominal lead is obtained; Step 6, the raceway left side contact angle, the raceway right side contact angle and the nominal lead are compared with the design value to complete the raceway section error identification.

3. The double circular-arc ball screw raceway profile error identification method according to claim 2, characterized by, The calculation method of the approximate derivative in step 1 is as follows: taking each data point as the center, adjacent data points are selected to form a sliding window, and the window slope is obtained by linear fitting, which is the approximate derivative of the current data point, and the size of the sliding window is 0.02% to 0.03% of the total data amount of the original measurement data.

4. The double-arc ball screw raceway profile error identification method according to claim 2, characterized in that, The clamping inclination angle described in Step 1 TiltAng The calculation is made according to the following formula, TiltAng = arctan ( slope )， wherein, slope is the slope of the fitted straight line.

5. The double-arc ball screw raceway profile error identification method according to claim 2, characterized in that, The auxiliary line BL mentioned in step 3 and the minimum value minYP The vertical distance is ,in r 0 represents the radius of the ball bearing.

6. The double-arc ball screw raceway profile error identification method according to claim 2, characterized in that, The way of extracting several segmented point sets from the raceway profile data in step 3 is as follows: marking all intersection points of YL and BL, marking the intersection point corresponding to YL as A and the intersection point corresponding to BL as B, and integrating in ascending order, dividing several segmented point sets containing complete left and right raceway profiles according to the sequence of A→B→B→A contained in each segmented point set. ComData The way of extracting several segmented point sets from the raceway profile data in step 3 is as follows: marking all intersection points of YL and BL, marking the intersection point corresponding to YL as A and the intersection point corresponding to BL as B, and integrating in ascending order, dividing several segmented point sets containing complete left and right raceway profiles according to the sequence of A→B→B→A contained in each segmented point set. x_com The way of extracting several segmented point sets from the raceway profile data in step 3 is as follows: marking all intersection points of YL and BL, marking the intersection point corresponding to YL as A and the intersection point corresponding to 7. The double circular-arc ball screw raceway profile error identification method according to claim 2, characterized by, The bivariate quadratic equation set in step 4 is: ， wherein, x , y ) is the center position of the ball to be solved, r 0 is the radius of the ball, r 1 is the radius of the left raceway arc, r 2 is the radius of the right raceway arc, a 1, b 1) is the center of the left raceway arc, a 2, b 2) is the center of the right raceway arc.

8. The double circular-arc ball screw raceway profile error identification method according to claim 2, characterized by, The specific steps of the grid constraint center-finding algorithm for outputting the target ball center in step 4 are as follows: Step 4.1, the coordinate extreme value of the segment point set is extracted, and the initial search area is planned as: ， wherein, SP xmin , SP xmax is the X-direction range, SP ymin , SP ymax is the Y-direction range, CP xmin , CP xmax is the ContourPoints X-coordinate extreme value in the middle, CP ymin , CP ymax is the ContourPoints Y-coordinate extreme value in the middle, radius of the ball At the same time, set the initial search step size as CoarseStep ; Step 4.2, based on the initial search area and the initial search step, generate a grid point with uniform distribution, calculate the grid row and column number, and generate the coordinates of each grid point traversed by the row and column, as follows: ， wherein, cols and rows are the number of rows and columns of the grid, respectively, G px and G py are the coordinates of the grid points; Step 4.3, for each grid point ( G px , G py ), calculate its to ContourPoints If the squared distance of all points is greater than 1, then the squared distance of all points is greater than 1. If so, then the grid point is a valid circle center; Step 4.4, from all the valid circle centers, select the point with the smallest Y coordinate as the best circle center for this round of search, denoted as (x, y) (4.4). x bc , y bc ) ; Step 4.

5. Redefine the iterative search region with the current best circle center as the center: X direction range set as [ x bc - CoarseStep , x bc + CoarseStep ], Y direction range set as [ y bc - CoarseStep , y bc ], and reduce the search step size; Step 4.6, if the reduced search step is less than 0.1 μm, the output of the best circle center is the final ball center position that is simultaneously inscribed in the left and right profiles of the raceway, otherwise continue the repeated iteration of steps 4.3-4.

6.

9. The double circular-arc ball screw raceway profile error identification method according to claim 8, characterized by, The calculated according to the formula, 。 10. The double circular-arc ball screw raceway profile error identification method according to claim 8, characterized by, The reduced search step is 1 / 5-1 / 10 of the original search step.

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