Ball screw, nut race effective circle arc data point symmetry extraction method

Abstract

The application provides a method for extracting symmetrical data points of effective circular arcs of a ball screw and a nut race. First, a vertical center line of the race is obtained. Then, a ball is simulated to fall into the race along the center line. Approximate contact points of the ball and left and right races are obtained. Then, circular arcs are preliminarily extracted on both sides of the approximate contact points. The centers of the preliminarily extracted circular arcs and contact angles are calculated. Finally, the circular arcs are extracted symmetrically relative to the contact points of the ball and the race according to the centers of the preliminarily extracted circular arcs and the contact angles. The effective circular arcs of the race can be divided.

Description

Technical Field

[0001] This invention belongs to the field of ball screw and ball nut testing, and in particular, it is a method for symmetrical extraction of effective arc data points of the raceway of ball screws and nuts. Background Technology

[0002] Ball screws and ball nuts are crucial components of ball screw assemblies, significantly impacting their performance. Errors in the helical raceway parameters of the ball screw and ball nut directly affect the friction, wear, accuracy retention, lifespan, rigidity, and vibration / noise of the ball screw assembly. Therefore, it is necessary to collect and analyze the raceways of the ball screw and nut.

[0003] A typical ball screw raceway includes two arcs, two chamfers, and an oil reservoir. Since the arcs are the areas in the raceway that contact the balls, it's necessary to extract the effective arc data points before calculating the raceway parameters. The traditional method for extracting these arc data points is radial linear extraction; simply put, a horizontal dividing line divides the raceway into five parts, and the arc portions are extracted. However, this traditional method often fails to capture most of the effective arc data points, and it relies heavily on the experience of the inspectors, resulting in significant fluctuations in the calculated raceway parameters. Therefore, there is an urgent need for a method that can accurately extract the effective arc data points of the raceway. Summary of the Invention

[0004] The purpose of this invention is to provide a method for symmetrically extracting effective arc data points of ball screw and nut raceways, so as to extract the effective arc data points in the raceway.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for symmetrically extracting effective arc data points of ball screw and nut raceways includes the following steps:

[0007] Step 1: Find the vertical centerline of the raceway and divide the raceway into left and right raceways: Take the centerline between the highest and lowest points of the raceway as the horizontal centerline, traverse the intersection points of the horizontal centerline with the left arc and the right arc, and obtain the coordinates of the vertical centerline of the raceway according to the coordinate relationship.

[0008] Step 2: Simulate the ball falling into the raceway and determine the approximate contact angle between the ball and the raceway: Calculate the difference between the distance and radius between the ball's center and the points on the left and right raceways during the ball's fall, and determine the tangency between the ball and the raceway by using the division value; calculate the contact angle between the ball and the left and right raceways.

[0009] Step 3: Preliminary extraction of left and right arc data points: Using the ball drop method to find the center of the ball, take the line connecting the contact point of the ball center and the raceway as the center line. Through the intersection of the dividing line with the left and right raceways, calculate the angle between the line connecting the point on the raceway and the center of the ball and the vertical center line of the raceway. Calculate the difference between the included angle and different dividing angles, and minimize the difference corresponding to each dividing angle to obtain the left and right arc data points.

[0010] Step 4: Finally extract the effective arc data points of the left and right arcs: Calculate the center and radius of the arc by fitting the initially extracted arc data points, and calculate the initial contact angle. Using the center of the fitted arc as the center, and the line connecting the center of the arc and the contact point of the raceway as the centerline, calculate the angle between the line connecting the point on the raceway and the center of the arc and the vertical centerline of the raceway. Calculate the difference between this angle and different dividing angles, minimizing the difference for each dividing angle to obtain the final extracted effective arc data points of the left and right arcs.

[0011] The significant advantages of this invention compared to existing technologies are:

[0012] Compared with existing technologies, the significant advantages of this invention are: 1) It automatically extracts effective arcs, avoiding errors caused by manual arc selection. 2) The extracted arcs are symmetrical about the contact point between the ball and the raceway, encompassing all effective arcs. 3) It divides the extraction into initial and final arc extraction, improving the accuracy of arc extraction. Attached Figure Description

[0013] Figure 1 This is a flowchart of the method of the present invention.

[0014] Figure 2 This is a schematic diagram simulating the falling of balls into the raceway.

[0015] Figure 3 This is a schematic diagram for the initial extraction of arc data points.

[0016] Figure 4 This is a schematic diagram for the final extraction of arc data points. Detailed Implementation

[0017] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0018] Combination Figure 1 The present invention provides a method for symmetrical extraction of the effective circular arc of a ball screw and nut raceway, comprising: determining the vertical centerline of the raceway and dividing the raceway into left and right raceways; simulating a ball falling into the raceway along the raceway centerline to obtain approximate contact points between the ball and the left and right raceways; initially extracting a circular arc from both sides with the approximate contact point as the center, and calculating the center and contact angle of the initially extracted circular arc; and extracting a circular arc symmetrically relative to the contact point between the ball and the raceway based on the center and contact angle of the initially extracted circular arc. Specific implementation details are as follows:

[0019] Step 1: Determine the vertical centerline of the raceway and divide the raceway into left and right raceways.

[0020] The ordinate y of the lowest point of the raceway is found by iterating through the collected data points of the ball screw and nut raceways. min and the y-coordinate of the highest point max Draw a horizontal median line along the midline between the highest and lowest points, with the y-coordinate of the horizontal median line being... mid :

[0021] y mid =(y min +y max ) / 2

[0022] The intersection of the horizontal centerline and the left raceway of the ball screw and nut is pl(x) l ,y l The intersection of the horizontal centerline and the right raceway of the collected ball screw and nut is pr(x). r ,y r p i (x i ,y i (i = 1, 2, ..., n) are i data points on the raceway. Iterate through n data points, and when y appears for the first time... i-1 >y mid And y i+1 <y mid At that time, x l =x i ,y l =y i When y first appears i-1 <y mid And y i+1 >y mid At that time, x r =x i ,y r =y i The x-coordinate of the vertical centerline of the raceway. mid For (x) l +x r ) / 2. If the x-coordinate of the raceway point is less than x mid Then this coordinate point is the left raceway coordinate point. If the x-coordinate of the raceway coordinate point is greater than or equal to x... mid Then the coordinates of the right raceway point are given. The coordinates of the left raceway point are (xl... e ,yl e (e=1,2,…,m), the coordinates of the right raceway are (xr f ,yr f (f = 1, 2, ..., nm).

[0023] Step 2: Simulate the ball falling into the raceway and determine the approximate contact angle between the ball and the raceway.

[0024] The ball bearing's center continuously descends along the midline, as... Figure 2 As shown. Then the center of the ball at any given time (x) d ,y d The differences between the distances to the points on the left and right raceways and the ball radius are d and d, respectively. l and d r .

[0025]

[0026] In the formula, r b The radius of the ball bearing is given.

[0027] For ease of calculation, assume the highest point of the ball's center is located at a distance *r* above the highest point of the raceway, and the lowest point of the center is located at the lowest point of the raceway. The distance the ball moves downwards each time is *d*. Then the coordinates of the ball's center are (x...). d ,y d ).

[0028]

[0029] In the formula, j represents the number of times the ball moves down.

[0030] Calculate the difference between the distance and radius between the ball's center and points on the left and right raceways during the ball's descent. When this difference first falls below the dividing value eps, the ball is considered tangent to the raceway. At this point, the center of the ball's circle when it is tangent to the left arc is (x...). mid ,y ldo The left tangent point A is (x a ,y a When the ball is tangent to the right arc, the center of the ball is (x). mid ,y rdo The right tangent point B is (x b ,y b At this point, the contact angles between the ball and the left and right raceways are α and α, respectively. lo and α ro .

[0031]

[0032] Step 3: Preliminary extraction of left and right arc data points

[0033] like Figure 3 As shown, the center of the ball, obtained by simulating the ball falling into the raceway, is taken as the center, and the line connecting the ball's center and the contact point of the raceway is taken as the center line. Using γ... l Draw dividing lines 1 and 2 on both sides of the left raceway centerline. Dividing line 1 intersects the left raceway at point C, and dividing line 2 intersects the left raceway at point D. Using γ... rDraw dividing lines three and four on either side of the right raceway centerline. Dividing line three intersects the right raceway at point E, and dividing line four intersects the right raceway at point F. The angle between dividing line one and the vertical centerline of the entire raceway is dividing angle θ. c The angle between the second dividing line and the vertical centerline of the entire raceway is the second dividing angle θ. d .

[0034]

[0035] The angle between dividing line three and the vertical centerline of the entire raceway is dividing angle three θ. e The angle between dividing line 4 and the vertical centerline of the entire raceway is dividing angle θ. f .

[0036]

[0037] The difference between the angle between the line connecting the track point and the center of the ball and the vertical centerline of the track and the different dividing angles is:

[0038]

[0039] In the formula d C (i) is the angle between the line connecting the point on the entire raceway and the center of the ball and the vertical centerline of the raceway, and the dividing angle θ. c The difference, d D (i) The angle between the line connecting the point on the entire raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ d The difference, d E (j) The angle between the line connecting the point on the entire raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ e The difference, d F (j) The angle between the line connecting the point on the entire raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ f The difference.

[0040] By traversing the points on the raceway, points C, D, E, and F are found, minimizing the difference corresponding to each dividing angle. The points between C and D are the data points for the initially extracted left arc. The points between E and F are the data points for the initially extracted right arc.

[0041] Step 4: Finally, extract the effective arc data points of the left and right arcs.

[0042] The center and radius of the arc are calculated by fitting the initially extracted arc data points, and the initial contact angle is also calculated. The center of the fitted arc is used as the center point, and the line connecting the center of the arc and the contact point of the raceway is used as the centerline. Dividing lines are drawn to both sides of the centerline with an angle γl'. Dividing lines 1, 2, 3, and 4 intersect the raceway at C', D', E', and F', respectively. The angle between the dividing line and the vertical centerline of the raceway is the dividing angle. The angle between the line connecting a point on the raceway and the center of the arc and the vertical centerline of the raceway is calculated, and the difference between this angle and different dividing angles is calculated. The points on the raceway are traversed to find the points C', D', E', and F' where the difference corresponding to each dividing angle is minimized. C', D', E', and F' are considered the dividing points. The points between C' and D' are the data points on the final extracted left arc. The points between E' and F' are the data points on the final extracted right arc. Figure 4 As shown.

[0043] Example

[0044] In this embodiment, the method of the present invention is used to extract the effective arc data points in the collected ball screw raceway. The extracted effective arc data points include the following: a method for symmetrical extraction of effective arcs in the raceway of ball screws and nuts.

[0045] 1. Determine the vertical centerline of the raceway and divide the raceway into left and right raceways.

[0046] The ordinate y of the lowest point of the raceway is found by iterating through the collected data points of the ball screw and nut raceways. min =59.4058 and the y-coordinate of the highest point max =60.9658. Draw a horizontal median line along the midpoint between the highest and lowest points, with the y-coordinate of the horizontal median line being 60.9658. mid :

[0047] y mid =(y min +y max ) / 2 = 60.1858

[0048] The intersection point pl(x) of the horizontal centerline and the collected data of the left raceway of the ball screw and nut l ,y l The coordinates are (118.6746, 60.1859), and the intersection of the horizontal centerline and the right raceway of the collected ball screw and nut is pr(x). r ,y r The value is (121.7251, 60.1858). i (x i ,y i (i = 1, 2, ..., n) are i data points on the raceway. Iterate through n data points, and when y appears for the first time... i-1 >y mid And y i+1<y mid At that time, x l =x i ,y l =y i When y first appears i-1 <y mid And y i+1 >y mid At that time, x r =x i ,y r =y i The x-coordinate of the vertical centerline of the raceway. mid For (x) l +x r ) / 2.

[0049] x mid =(x l +x r ) / 2 = 120.2026

[0050] If the x-coordinate of the raceway coordinate point is less than x mid Then this coordinate point is the coordinate point of the left arc. If the x-coordinate of the raceway coordinate point is greater than x... mid Then the coordinates of the right arc point are given. The coordinates of the left roller track point are (xl) e ,yl e (e=1,2,…,m), the coordinates of the right raceway are (xr f ,yr f (f = 1, 2, ..., nm).

[0051] 2. Simulate the balls falling into the raceway and determine the approximate contact angle between the balls and the raceway.

[0052] If the center of the ball continuously descends along the midline, then the center of the ball at any given time (x) d ,y d The differences between the distances to the points on the left and right raceways and the ball radius are d and d, respectively. l and d r .

[0053]

[0054] For ease of calculation, assume the highest point of the ball's center is located at a distance r = 0.5 above the highest point of the raceway, and the lowest point of the center is the lowest point of the raceway. The distance the ball moves downwards each time is d. Then the coordinates of the ball are (x... d ,y d ).

[0055]

[0056] Calculate the difference between the distance and radius between the ball's center and points on the left and right raceways during the ball's descent. When the difference first falls below 0.00001, the ball is considered tangent to the raceway. At this point, the center of the ball's circle when it is tangent to the left arc is (x...). mid ,y ldo ) = (120.1998, 61.4588), the left tangent point A is (x a ,y a )=(118.7966,60.0542); The center of the ball is (x) when the ball is tangent to the right arc. mid ,y rdo ) = (120.1998, 61.4608), the right tangent point B is (x b ,y b ) = (121.5441, 59.9996). At this time, the contact angles between the ball and the left and right raceways are α and α, respectively. lo and α ro .

[0057]

[0058] 3: Preliminary extraction of left and right arc data points

[0059] The center of the ball, determined by simulating the ball falling into the raceway, is used as the center point, and the line connecting the ball's center and the contact point of the raceway is used as the center line. Using γ... l Draw dividing lines on both sides of the centerline. Dividing line one intersects the left raceway at point C, and dividing line two intersects the left raceway at point D. Dividing line three intersects the right raceway at point E, and dividing line four intersects the right raceway at point F. The angle between dividing line one and the vertical centerline of the raceway is dividing angle θ. c The angle between the second dividing line and the vertical centerline of the raceway is the second dividing angle θ. d .

[0060]

[0061] The angle between the dividing line 3 and the vertical centerline of the raceway is the dividing angle θ. e The angle between the dividing line 4 and the vertical centerline of the raceway is the dividing angle θ. f .

[0062]

[0063] Calculate the angle between the line connecting a point on the raceway and the center of the ball and the vertical centerline of the raceway. Calculate the difference between this angle and the different dividing angles.

[0064]

[0065] By traversing the points on the raceway, we find points C(118.4741, 60.4616), D(119.2051, 59.7337), E(121.1246, 59.6935), and F(121.8816, 60.3940). These points minimize the difference corresponding to each dividing angle. The point between C and D is the initially extracted left arc point. The point between E and F is stored in an array as the initially extracted right arc point.

[0066] 4. Finally, extract the effective arc data points of the left and right arcs.

[0067] The center and radius of the initially extracted arc are calculated by fitting the arc, and the initial contact angle is also calculated. The center of the fitted arc is used as the center point, and the line connecting the center of the arc and the contact point of the raceway is used as the centerline. Dividing lines are drawn to both sides of the centerline at an angle of γl' = 15°. Dividing lines 1, 2, 3, and 4 intersect the raceway at C', D', E', and F', respectively. The angle between the dividing lines and the vertical centerline of the raceway is the dividing angle. The angle between the line connecting a point on the raceway and the center of the arc and the vertical centerline of the raceway is calculated, and the difference between this angle and the different dividing angles is calculated. Traverse the points on the raceway and find the points C'(118.5246, 60.3825), D'(119.1851, 59.7463), E'(121.1891, 59.7306), and F'(121.8631, 60.3665) that minimize the difference corresponding to each dividing angle. Consider C', D', E', and F' as the dividing points. The point between C' and D' is the final left arc point. The point between E' and F' is the final right arc point.

Claims

1. A method for symmetrically extracting effective arc data points of the raceway of a ball screw and nut, characterized in that, Includes the following steps: Step 1: Find the vertical centerline of the raceway and divide the raceway into left and right raceways: Take the centerline between the highest and lowest points of the raceway as the horizontal centerline, traverse the intersection points of the horizontal centerline with the left arc and the right arc, and obtain the coordinates of the vertical centerline of the raceway according to the coordinate relationship. Step 2: Simulate the ball falling into the raceway and determine the approximate contact angle between the ball and the raceway: Calculate the difference between the distance and radius between the ball's center and the points on the left and right raceways during the ball's fall, and determine the tangency between the ball and the raceway by using the division value. Calculate the contact angles between the balls and the left and right raceways; Step 3: Preliminary extraction of left and right arc data points: Using the ball drop method to find the center of the ball, take the line connecting the contact point of the ball center and the raceway as the center line. Through the intersection of the dividing line with the left and right raceways, calculate the angle between the line connecting the point on the raceway and the center of the ball and the vertical center line of the raceway. Calculate the difference between the included angle and different dividing angles, and minimize the difference corresponding to each dividing angle to obtain the left and right arc data points. Step 4: Finally extract the effective arc data points of the left and right arcs: Calculate the center and radius of the arc by fitting the initially extracted arc data points, and calculate the initial contact angle. Using the center of the fitted arc as the center, and the line connecting the center of the arc and the contact point of the raceway as the centerline, calculate the angle between the line connecting the point on the raceway and the center of the arc and the vertical centerline of the raceway. Calculate the difference between this angle and different dividing angles, minimizing the difference for each dividing angle to obtain the final extracted effective arc data points of the left and right arcs.

2. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 1, characterized in that, Step 1 specifically includes: (1) The ordinate of the horizontal median is : , These are the ordinates of the lowest and highest points of the raceway, respectively. (2) Traverse the intersection points of the horizontal centerline with the left arc and the right arc. When the first occurrence and hour, , When it first appears and hour, , The x-coordinate of the vertical centerline of the raceway for If the x-coordinate of the raceway point is less than If the x-coordinate of the raceway point is greater than or equal to the x-coordinate of the raceway point, then the point is the left raceway point. Then the coordinate point is the right roller coordinate point; in The intersection of the horizontal centerline and the left raceway of the ball screw and nut. It is the intersection of the horizontal centerline and the right raceway of the ball screw and nut.

3. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 1, characterized in that, Ball core The differences between the distance to the points on the left and right raceways and the radius are as follows: In the formula, Where is the radius of the ball bearing. The coordinates of the left raceway point are... These are the coordinates of the right raceway point.

4. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 1, characterized in that, The coordinates of the center of the ball are : Let x be the x-coordinate of the vertical centerline of the raceway. y is the ordinate of the highest point of the raceway; r is the distance between the highest point of the ball's center and the highest point of the raceway; d is the distance the ball's center moves down each time; j is the number of times the ball moves down.

5. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 1, characterized in that, The contact angles between the ball and the left and right raceways are respectively and : in The center of the ball is where the ball is tangent to the left arc. The left tangent point where the ball and raceway are tangent. The center of the ball is where the ball is tangent to the right arc. This is the right tangent point where the ball and raceway are tangent.

6. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 1, characterized in that, The formula for calculating the angle of division is: Where γ l γ is the angle between the centerline of the left raceway and either the first or second dividing line on either side; r The angle between the center line of the right raceway and either the third or fourth dividing line on either side; θ is the dividing angle between dividing line 1 and the vertical centerline of the entire raceway; d θ is the dividing angle between dividing line two and the vertical centerline of the entire raceway. e θ is the dividing angle between dividing line three and the vertical centerline of the entire raceway. f The dividing angle between the dividing line and the vertical centerline of the entire raceway is the angle between the dividing line and the dividing line. and These are the contact angles between the ball and the left and right raceways, respectively.

7. The method for symmetrically extracting effective arc data points of ball screw and nut raceways according to claim 6, characterized in that, The difference between the angle between the line connecting the point on the raceway and the center of the ball and the vertical centerline of the raceway and the different dividing angles is: In the formula The angle between the line connecting the point on the raceway and the center of the ball and the vertical centerline of the raceway, and the dividing angle. The difference, The angle between the line connecting the point on the raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ d The difference, The angle between the line connecting the point on the raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ e The difference, The angle between the line connecting the point on the raceway and the center of the ball and the vertical centerline of the raceway and the dividing angle θ f The difference, The center of the ball is where the ball is tangent to the left arc. The center of the ball is where the ball is tangent to the right arc. The coordinates of the left raceway point are... These are the coordinates of the right raceway point.

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