CN111898213B - Matching method based on ball screw and ball nut raceway profile parameters - Google Patents
Matching method based on ball screw and ball nut raceway profile parameters Download PDFInfo
- Publication number
- CN111898213B CN111898213B CN202010578134.7A CN202010578134A CN111898213B CN 111898213 B CN111898213 B CN 111898213B CN 202010578134 A CN202010578134 A CN 202010578134A CN 111898213 B CN111898213 B CN 111898213B
- Authority
- CN
- China
- Prior art keywords
- ball
- raceway
- calculating
- screw
- nut
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
Landscapes
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Length Measuring Devices With Unspecified Measuring Means (AREA)
Abstract
The invention provides a matching method based on ball screw and ball nut raceway profile parameters, which comprises the steps of firstly calculating the profile parameters of a raceway of a to-be-measured ball screw, and constructing a spatial rectangular coordinate system of the to-be-measured ball screw; measuring coordinates of any point of the axial section of the bead screw to perform axial-normal conversion to obtain a corresponding point corresponding phase angle and a corresponding normal plane point coordinate; calculating the center coordinates of the ball circles) to convert the axial coordinates into normal coordinates, and performing least square fitting on the converted normal section data point coordinates to obtain the center coordinates and the left and right arc radiuses of the left and right arc raceways of the lead screw; calculating the contact angle, the axial eccentricity and the radial eccentricity of the ball screw raceway; calculating the pitch and the total pitch between the adjacent raceways; calculating the mean value of the pitch diameters of the ball screws; calculating the profile parameters of the ball nut to be measured; calculating the curve surface and the pitch diameter parameter of the ball nut raceway according to a method for calculating the curve surface and the pitch diameter parameter of the ball screw rotary raceway to be measured; the invention can match the ball screw pair.
Description
Technical Field
The invention belongs to the field of ball screw and ball nut detection, and particularly relates to a matching method based on ball screw and ball nut raceway profile parameters.
Background
The ball screw and the ball nut are used as important components of the ball screw pair and have important influence on the screw pair, and the parameter errors of the spiral raceway curved surfaces of the ball screw and the ball nut directly influence the frictional wear, the precision maintenance, the service life, the rigidity and the vibration noise of the screw pair.
Chinese patent CN 107449372A discloses a laser triangle-based ball screw nut comprehensive parameter detection device and method for measuring key parameters and outer diameter of the inner raceway profile of a nut, so that other parameters can be calculated, the pitch diameters of a ball screw and a ball nut cannot be directly measured, and profile parameters of a whole screw nut are not used for matching a ball screw pair.
Disclosure of Invention
The invention aims to provide a matching method based on the profile parameters of ball screw and ball nut raceways so as to match a ball screw pair.
The technical solution for realizing the purpose of the invention is as follows:
a matching method based on ball screw and ball nut raceway profile parameters comprises the steps of calculating ball screw rotary raceway curved surface and pitch diameter parameters, calculating ball nut raceway curved surface to be detected and pitch diameter parameters, and matching a ball screw pair; the specific implementation mode is as follows:
calculating the parameters of the curved surface and the pitch diameter of the rotary raceway of the ball screw to be measured, and the method comprises the following steps:
step 1, constructing a space rectangular coordinate system of a ball screw to be measured;
step 3, calculating the center coordinates of the ball, converting the axial coordinates into normal coordinates, and performing least square fitting on the converted normal section data point coordinates to obtain the center coordinates and the left and right circular arc radiuses of the left and right circular arc raceways of the lead screw;
step 4, calculating the contact angle, the axial eccentricity and the radial eccentricity of the ball screw raceway: according to the geometric relationship among the profile parameters of the lead screw roller path, obtaining left and right arc contact angles, left and right arc axial eccentricity and left and right arc radial eccentricity;
step 5, calculating the pitch and the total pitch between the adjacent roller paths;
calculating parameters of the curved surface and the pitch diameter of the ball nut raceway to be measured, and specifically comprising the following steps: constructing a spatial rectangular coordinate system of the ball screw to be measured; and calculating the curve surface and the pitch diameter parameter of the ball nut raceway according to a method for calculating the curve surface and the pitch diameter parameter of the ball screw rotary raceway to be measured.
The matching of the ball screw pair comprises the following specific steps:
step 1, calculating the center distance between the left center of a screw and the right center of a nut;
step 3, calculating the contact deformation of the ball;
and 4, calculating the friction force under the condition of the deformation according to the relation between the friction force and the ball deformation, and adjusting profile parameters of a screw nut by adjusting the screw, the nut and the balls so as to match the ball screw pair.
Compared with the prior art, the invention has the following remarkable advantages:
(1) According to the invention, the contact deformation of the ball is calculated, and the matching degree among the screw, the nut and the ball is analyzed according to the relation between the friction force of the ball screw pair and the contact deformation of the ball, so that the ball screw, the ball nut and the ball are quickly matched.
(2) The invention optimizes the algorithm of the cross section of the shaft section rotating method, can obtain accurate normal section of the raceway, lead and pitch diameter runout of the nut, and is important for evaluating the processing error and the use performance of the screw rod.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a space rectangular coordinate system diagram of the constructed screw nut to be tested.
Fig. 3 is a global cartesian coordinate system diagram.
Fig. 4 is a geometric relationship diagram of the geometric parameters of the raceway profile of the screw nut.
FIG. 5 is a geometric relationship diagram of the pitch diameter and the outer diameter of a ball screw and the center of a ball circle.
Detailed Description
The invention is further described with reference to the following figures and embodiments.
With reference to fig. 1, the matching method based on the parameters of the ball screw and ball nut raceway profiles of the invention comprises the steps of calculating the parameters of the ball screw rotary raceway curved surface and the pitch diameter, and calculating the parameters of the ball nut raceway curved surface and the pitch diameter to be measured; and then the profile parameters of the screw nut are adjusted by adjusting the screw, the nut and the ball to match the ball screw pair, and the specific implementation mode is as follows:
calculating the parameters of the curved surface and the pitch diameter of the rotary raceway of the ball screw to be measured, and the method comprises the following steps:
step 1, constructing a spatial rectangular coordinate system O '-X' Y 'Z' of the ball screw to be tested, and combining with a graph 2, wherein the X 'axis direction is along the axial direction of the ball screw to be tested, and the Y' axis direction is a horizontal direction vertical to the axial direction of the ball screw to be tested; the Z 'axis direction is vertical direction, and passes through a measuring head of a probe when the measurement is started, the Z' axis direction, the measuring head and the measuring head follow the right hand rule, and O 'is the intersection point of the Z' axis and the axis of the ball screw.
step 2.1, establishing a global Cartesian coordinate system
Firstly, a global Cartesian coordinate system O-XYZ is established, as shown in FIG. 3, wherein the X axis coincides with the axis of the lead screw, the Z axis is vertically upward and passes through the lowest point E' of the upper raceway, the Y axis is the horizontal direction perpendicular to the axis direction of the ball screw to be measured, the O point is the intersection point of the axis of the lead screw and the Z axis, and a right-hand rectangular coordinate system is established. The normal cross section is a ball screw axial cross section, and a cross section obtained by rotating a helix angle with the lowest point of the raceway as a rotation center is shown in fig. 3.
Taking any point A of the axial section as an example for conversion analysis, and the coordinate of any point A obtained through experimental measurement is the coordinate of the point A in a measurement coordinate system. The measuring coordinate system is a two-dimensional coordinate system, the abscissa axis of the measuring coordinate system is parallel to the X axis, and the ordinate axis of the measuring coordinate system is parallel to the Z axis.
Step 2.2, establishing a spiral equation where the point A is located
Setting the coordinate of the lowest point E' of the upper raceway as (x) in a measurement coordinate system E′ ，y E′ ) The coordinate of the point A in the measuring coordinate system is (x) A ，y A ). The non-rolling path part of the screw has y ordinate in the measuring coordinate system ott The external diameter of the screw of the ball screw pair is D ott . Combining the coordinates of the E 'point and the A point and the relative position of the E' point and the A point to obtain the coordinate of the A point in the global coordinate system O-XYZ
The parameter equation of the spiral line where the point A is located is as follows:
wherein: theta is the phase angle, is positive along the X-axis direction in a counterclockwise way,
is a lead angle of a ball screw pair, P h Is the pitch, X, of a ball screw A Is the X-axis coordinate, Y, of the spiral equation of the point A A Is the Y-axis coordinate of the spiral line equation where the point A is located, Z A And the Z-axis coordinate of the spiral line equation where the point A is located is shown.
Step 2.3, establishing a plane equation of the point correspondence method A, and solving the coordinates of the normal plane points corresponding to the point A
Establishing an A point corresponding method plane equation, wherein the A point corresponding method plane equation is as follows:
the joint type (1) and the formula (2) can obtain:
solving the formula (3) can obtain a general solution of the phase angle theta, and the range of the phase angle theta corresponding to the point A is
The solution interval can therefore be limited to
A unique solution for theta is obtained. And substituting the solved phase angle theta into the formula (1) to obtain the normal plane point coordinate corresponding to the A point.
Step 3, calculating the coordinates (x) of the circle center of the ball sb ，y sb )
Converting the axial coordinate into a normal coordinate according to formulas (1), (2) and (3), and performing least square fitting on the converted normal section data point coordinate to obtain the lead screwCircle center coordinates of left and right circular arc raceways
And the radius r of the left and right circular arcs sL 、r sR 。
Wherein r is b Is the radius of the ball, coefficient A s ，B s Can be obtained by the following formula
Step 4, calculating the contact angle, the axial eccentricity and the radial eccentricity of the ball screw raceway
The contact angle, the axial eccentricity and the radial eccentricity are parameters of the profile of the screw roller path.
The contact angle is the included angle between the load vector transmitted between the roller path and the ball and the vertical plane of the axis of the ball screw and is divided into a left arc contact angle and a right arc contact angle alpha sL And alpha sR . The axial eccentricity is the distance between the circle center of the arc of the lead screw raceway and the circle center of the ball along the axial direction of the lead screw and is divided into a left arc axial eccentricity e and a right arc axial eccentricity e sL And e sR . The radial eccentricity is the radial distance between the arc center of the screw roller path and the ball center along the screw, and is divided into left and right arc radial eccentricities h sL And h sR 。
When the center coordinates of the left and right circular arc raceways of the screw rod
Radius r of left and right circular arc sL 、r sR And the center coordinates (x) of the ball sb ，y sb ) After knowing, and referring to fig. 4, the contact angle α can be obtained according to the geometrical relationship between the parameters of the profile of the screw raceway sL And alpha sR Axial eccentricity e sL And e sR Radial eccentricity h sL And h sR The calculation formula of (2):
step 5, calculating the pitch and the total pitch between the adjacent raceways:
in practical measurement, a plurality of ball paths can be measured in the axial plane of the screw path by one measurement, so that the centers of the balls in the normal plane of the screw path are (x) sbi ，y sbi ) i =1,2.. M, m being the number of tracks acquired, the pitch between the kth and the (k + 1) th track is:
the total pitch p s Comprises the following steps:
the longitudinal coordinate value of the outline sphere center on the screw is obtained as (y) sub1 ，y sub2 ......y subm ) The coordinates of the center of the sphere of the lower contour are (y) sdb1 ，y sdb2 ......y sdbm ) The pitch diameter of the screw of the kth raceway
Comprises the following steps:
calculating parameters of the curved surface and the pitch diameter of the raceway of the ball nut to be measured, and the method comprises the following steps of:
step 1, constructing a spatial rectangular coordinate system O '-X' Y 'Z' of the ball nut to be tested, and combining with a graph 2, wherein the X 'axis direction is along the axial direction of the ball nut to be tested, and the Y' axis direction is a horizontal direction vertical to the axial direction of the ball nut to be tested; the Z' axis direction is vertical, and the three follow the right-hand rule.
the calculation methods of the shapes and the profile parameters of the ball nut and the ball screw raceway are the same. The parameter calculation method of the ball nut refers to steps 2 to 6 in the ball screw.
Profile parameters of a screw nut are adjusted by adjusting the screw, the nut and the ball to match the ball screw pair; calculating the contact deformation of the balls, and analyzing the matching degree of the screw, the nut and the balls according to the relation between the friction force of the ball screw pair and the contact deformation of the balls, wherein the specific steps are as follows:
step 1, calculating the center distance between the left center of the screw and the right center of the nut:
the relationship between the screw profile parameter and the nut profile parameter is shown in fig. 5. The distance between the left circle center of the screw rod and the right circle center of the nut is l oln The following were used:
where Δ y is the pitch diameter difference, Δ x is the pitch difference, e nR Is the axial eccentricity of the right raceway in the upper raceway of the nut, e sL Is the axial eccentricity h of the left arc in the upper raceway of the screw rod sL Is the radial eccentricity h of the left arc in the upper raceway of the screw rod nR The radial eccentricity of the right circular arc in the upper raceway of the nut is adopted.
l max ＝r sL +r nR -l oln (13)
wherein r is sL Is the radius of the left circular arc of the upper raceway of the screw rod, r nR Is the right arc radius of the upper raceway of the nut.
And step 3, calculating the contact deformation delta of the ball as follows:
δ＝R b -l max (14)
wherein R is b Is the ball diameter.
And 4, calculating the friction force under the deformation according to the relation between the friction force and the ball deformation, so that profile parameters of a screw nut are adjusted through adjusting the screw, the nut and the ball to match the ball screw pair:
the relationship between the friction force and the ball deformation is:
wherein mu is the friction coefficient between the ball and the raceway, c E Is a material constant, i t Number of thread starts, N c Number of ball cycles, c k Can be calculated according to equation (16).
Wherein Y is s And Y n Auxiliary values of the nut and the screw rod for the first and second elliptical integrals in Hertz theory are respectively; Σ ρ s And Σ ρ n The main curvatures of the contact points of the screw roller path and the nut roller path with the ball are respectively equal to the sum of the main curvatures.
Examples
In this embodiment, a THK4010 screw and a nut matched with the THK4010 screw are used, and coordinates of circle centers of outline raceway balls on the ball screw are calculated according to a formula (4) of the ball screw to be measured, wherein the coordinates are (12.0843, 50.6379), (22.0845, 50.6377), (32.0844 and 50.6379). The center coordinates of the ball screw lower contour raceway are (7.6101, 8.8653), (17.6103, 8.8652), (27.6095, 8.8665).
Data preprocessing, coordinate conversion and arc fitting are carried out on bus contour raceway data points on the lead screw obtained through actual measurement to obtain left and right arc radius and circle center coordinate data, then the left and right arc radius and circle center coordinate data are utilized to calculate raceway profile parameters, and the results are shown in table 1.
TABLE 1 screw raceway accuracy test data fitting results
The pitch of the upper profile of the ball screw can be calculated as p according to equation (9) s1 ＝10.002mm，p s2 =9.992mm. Calculating the pitch of the lower profile of the ball screw to be p' s1 ＝10.002mm，p′ s2 ＝9.999mm。
The average pitch p of the upper profile can be calculated according to equation (10) s =9.997mm, mean pitch p of the lower profile s ′＝10.0005mm。
The pitch diameter of the screw rod is calculated according to the formula (11)
The average pitch diameter d of the ball screw is calculated according to the formula (12) s0 ＝41.7722mm。
According to the embodiment 4, the circle center coordinates of the outline raceway balls on the ball nut to be tested are (14.0731, 50.6323), (24.0732, 50.6326), (34.0843, and 50.6319).
The center coordinates of the ball of the lower contour raceway of the nut are (9.5982, 8.8703), (19.5993, 8.8699), (29.6095 and 8.8715).
Data preprocessing, coordinate conversion and arc fitting are carried out on the data points of the bus contour raceway on the nut obtained through actual measurement to obtain the radius and circle center coordinate data of the left arc and the right arc, then the parameters of the raceway profile are calculated by utilizing the radius and circle center coordinate data of the left arc and the right arc, and the results are shown in table 2.
TABLE 2 fitting results of nut raceway accuracy test data
The pitch of the upper profile of the ball nut can be calculated as p according to equation (9) n1 ＝10.001mm，p n2 =10.0111mm. Calculating the pitch of the lower profile of the ball nut to be p' n1 ＝10.0011mm，p′ n2 ＝10.0102mm。
The average pitch p of the upper profile can be calculated according to equation (10) n =10.00605mm, mean pitch p of the lower profile n ′＝10.00565mm。
The pitch diameter of the screw is calculated according to the formula (11)
Calculating the average pitch diameter d of the ball nut according to the formula (12) n0 ＝41.7617mm。
According to the formulas (12) and (13), the center distance l between the left center of the screw rod and the right center of the nut can be obtained oln ＝0.6490mm。
Obtaining the maximum distance l of the contact points on the screw rod and the nut raceway according to the formula (14) max ＝6.3448mm。
According to the formula (16), the relation between the ball deformation and the friction torque can be obtained, so that the screw nut ball is matched.
Referring to fig. 2 as an implementation manner, the coordinate value of the raceway generatrix of the ball nut and the lead screw 3 to be measured according to the present invention can be measured by a measuring device, which includes a worktable, an upper moving platform 1, a first probe 2, the ball screw 3 to be measured, a first supporting block 4, a first moving platform 5, a second probe 6, a lower moving platform 7, a horizontal moving platform 8, a second moving platform 9, a second supporting block 10, and the ball nut to be measured;
the horizontal moving platform 8, the first moving platform 5 and the second moving platform 9 are all arranged on the workbench; the workbench is provided with two mutually parallel slide rails, and the bottom of the horizontal moving platform 8 is provided with a slide block which is matched with the slide rails on the workbench; a driving motor is fixed on the workbench, is connected with the horizontal moving platform 8 through a screw mechanism and is used for driving the horizontal moving platform 8 to move horizontally and linearly on the workbench; the first translation platform 5 and the second translation platform 9 are respectively arranged on two sides of the horizontal translation platform 8, and the first support block 4 and the second support block 10 are respectively fixed on the first translation platform 5 and the second translation platform 9; the first supporting block 4 and the second supporting block 10 are used for supporting the ball screw 3 to be tested or the ball nut to be tested; the horizontal moving platform 8 is provided with an upper moving platform 1 and a lower moving platform 7 which are arranged in parallel; two groups of parallel guide rails are arranged on the horizontal moving platform 8 along the height direction, and the upper moving platform 1 and the lower moving platform 7 are matched with the guide rails on the horizontal moving platform 8 through sliding blocks; two groups of motors are fixed on the horizontal moving platform 8, and two groups of electrodes are respectively connected with the upper moving platform 1 and the lower moving platform 7 through a screw rod mechanism and are used for the upper moving platform 1 and the lower moving platform 7 to do linear motion up and down on the horizontal moving platform 8; the first probe 2 and the second probe 6 are respectively fixed on the upper moving platform 1 and the lower moving platform 7; the first probe 2 is located above the lead screw 3 to be tested, the second probe 6 is located below the lead screw 3 to be tested, and the first probe 2 and/or the second probe 6 are/is used for collecting the height value (vertical coordinate) of the ball screw 3 to be tested and/or the ball nut raceway bus to be tested. A grating ruler is arranged on the workbench and used for detecting the position (abscissa) of the collecting point of the first probe 2 and/or the second probe 6; the first probe 2, the second probe 6 and the grating ruler transmit the collected data to the upper computer.
During measurement, the horizontal moving platform 8 is driven by the driving motor to move the horizontal moving platform 8 along the axial direction of the ball screw 3 to be measured, the lower tip of the first probe 2 and the upper tip of the second probe 6 sweep from the upper bus and the lower bus of the outer raceway of the ball screw 3 to be measured simultaneously, data points are read at fixed intervals, the upper bus contour and the lower bus contour share one grating ruler during collection, the collected coordinates in the X' axis direction (the axis direction of the ball screw 3 to be measured) are the same, the first probe 2 measures the height value of the upper bus contour of the screw 3 to be measured, and the second probe measures the height value of the upper bus contour of the screw 3 to be measuredAnd the height value of the profile of the bus under the screw rod is measured by the needle 6, and the measured height value is a Z' -axis direction coordinate. The upper bus contour consists of n measured data points, each of which is (x) s1 ，z s1 )，(x s2 ，z s2 )......(x sn ，z sn ) The lower bus contour is composed of n measured data points, respectively (x) s1 ，z′ s1 )，(x s2 ，z′ s2 )......(x sn ，z′ sn ). The horizontal moving platform 8 is driven by a driving motor to move axially along the ball nut 11 to be detected, the upper tip of the first probe 2 sweeps over an upper bus of an inner raceway of the ball nut 11 to be detected, data points are read once at fixed intervals, and the moving distance (coordinate value) in the X' axis direction is collected through a grating ruler; the first probe 2 measures the height value of the bus contour on the nut to be measured, and the measured height value is the Z' -axis direction coordinate. The upper bus contour is composed of n measured data points, respectively (x) n1 ，z n1 )，(x n2 ，z n2 )......(x nn ，z nn ). The horizontal moving platform 8 returns, after the first probe 2 is reset, the lower tip of the first probe 2 is propped against the lower bus of the inner raceway of the nut, the first probe 2 axially moves along the nut 4 to be measured, measurement is continuously carried out in the same way, and the lower bus profile consists of n measured data points which are (x' n1 ，z′ n1 )，(x′ n2 ，z′ n2 )......(x′ nn ，z′ nn )。
Claims (5)
1. A matching method based on ball screw and ball nut raceway profile parameters is characterized by comprising the steps of calculating ball screw rotary raceway curved surface and pitch diameter parameters, calculating ball nut raceway curved surface to be detected and pitch diameter parameters, and matching a ball screw pair; the specific implementation mode is as follows:
calculating the parameters of the curved surface and the pitch diameter of the rotary raceway of the ball screw to be measured, and the method comprises the following steps:
step 1, constructing a spatial rectangular coordinate system of a ball screw to be measured;
step 2, performing axial normal conversion by using the measured coordinates of any point of the axial section of the ball screw to obtain a corresponding phase angle of the point and a corresponding normal plane point coordinate;
step 3, calculating the center coordinates of the ball, converting the axial coordinates into normal coordinates, and performing least square fitting on the converted normal section data point coordinates to obtain the center coordinates and the left and right circular arc radiuses of the left and right circular arc raceways of the lead screw;
step 4, calculating the contact angle, the axial eccentricity and the radial eccentricity of the ball screw raceway: according to the geometrical relationship between the profile parameters of the screw roller path, obtaining left and right arc contact angles, left and right arc axial eccentricity and left and right arc radial eccentricity;
step 5, calculating the pitch and the total pitch between the adjacent roller paths;
step 6, calculating the mean value of the pitch diameters of the ball screws;
calculating parameters of the curved surface and the pitch diameter of the ball nut raceway to be measured, which are as follows: constructing a space rectangular coordinate system of the ball screw to be detected; calculating the curve surface and the pitch diameter parameter of the ball nut raceway according to a method for calculating the curve surface and the pitch diameter parameter of the ball screw rotary raceway to be measured;
the ball screw pair matching method comprises the following specific steps:
step 1, calculating the center distance l between the left center of the screw and the right center of the nut oln Comprises the following steps:
where Δ y is the pitch difference, Δ x is the pitch difference, e nR Is the axial eccentricity of the right raceway in the upper raceway of the nut, e sL Is the axial eccentricity h of the left arc in the upper raceway of the screw rod sL Is the radial eccentricity h of the left arc in the upper raceway of the screw rod nR The radial eccentricity is the right arc in the upper raceway of the nut;
step 2, the maximum distance l of the contact points on the screw rod and the nut raceway max Comprises the following steps:
l max ＝r sL +r nR -l oln
wherein r is sL Is the radius of the left arc of the upper raceway of the screw rod, r nR The radius of the right circular arc of the upper raceway of the nut;
and step 3, calculating the contact deformation delta of the ball as follows:
δ＝R b -l max
wherein R is b Is the diameter of the ball;
step 4, calculating the friction force under the condition of the deformation according to the relation between the friction force and the ball deformation, and adjusting profile parameters of a screw nut by adjusting the screw, the nut and the balls to match the ball screw pair;
the relationship between the friction force and the ball deformation is:
where mu is the coefficient of friction between the balls and the raceways, c E Is a material constant, i t Number of thread starts, N c Number of ball cycles, Y s And Y n Auxiliary values of the nut and the screw rod for the first and second kinds of elliptic integrals in Hertz theory are respectively; sigma rho s Sum Σ ρ n The main curvatures of the contact points of the screw roller path and the nut roller path with the ball are respectively equal to the sum of the main curvatures.
2. The matching method according to claim 1, wherein in the step 2 of calculating the curved surface of the raceway of the ball screw to be measured and the pitch diameter parameters, axial normal conversion is performed, and the method specifically comprises the following steps:
2.1, establishing a global Cartesian coordinate system;
step 2.2, establishing a spiral equation of any point of the shaft section;
and 2.3, establishing a normal plane equation corresponding to any point of the axial section, and solving the normal plane point coordinates corresponding to any point of the axial section.
3. The matching method according to claim 1, wherein the step 3 of calculating the center coordinates of the ball in the step 3 of calculating the curved surface and the pitch diameter parameters of the rotary raceway of the ball screw to be measured(x sb ，y sb ) Comprises the following steps:
wherein A is s ，B s Is a coefficient of r b Is the ball radius;
respectively are the coordinates of the centers of the left and right circular arc raceways of the screw rod; r is sL 、r sR Respectively a left arc radius and a right arc radius.
4. The matching method according to claim 3, wherein the contact angle α of the left arc and the right arc in the step 4 in the calculation of the parameters of the curved surface and the pitch diameter of the rotary raceway of the ball screw to be measured sL And alpha sR Axial eccentricity e of left and right circular arcs sL And e sR And the radial eccentricity h of the left and right circular arcs sL And h sR The calculation formula is as follows:
5. the matching method according to claim 1, wherein the step 6 of calculating the mean value of the ball screw pitch diameters in the step 6 of calculating the curved surface and the pitch diameter parameters of the rotary track of the ball screw to be measured
Comprises the following steps:
wherein y is ubk Is the longitudinal coordinate value y of the outline sphere center on the k raceway screw dbk The longitudinal coordinate value of the spherical center of the lower profile of the screw of the kth raceway is shown.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010578134.7A CN111898213B (en) | 2020-06-23 | 2020-06-23 | Matching method based on ball screw and ball nut raceway profile parameters |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010578134.7A CN111898213B (en) | 2020-06-23 | 2020-06-23 | Matching method based on ball screw and ball nut raceway profile parameters |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111898213A CN111898213A (en) | 2020-11-06 |
| CN111898213B true CN111898213B (en) | 2022-10-14 |
Family
ID=73206406
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010578134.7A Active CN111898213B (en) | 2020-06-23 | 2020-06-23 | Matching method based on ball screw and ball nut raceway profile parameters |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111898213B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108871229A (en) * | 2018-06-11 | 2018-11-23 | 南京理工大学 | A kind of measurement method of ball nut spiral interior rollaway nest curved surface and outer diameter |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8257191B2 (en) * | 2009-08-27 | 2012-09-04 | Nike, Inc. | Golf clubs and golf club heads having digital lie and/or other angle measuring equipment |
-
2020
- 2020-06-23 CN CN202010578134.7A patent/CN111898213B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108871229A (en) * | 2018-06-11 | 2018-11-23 | 南京理工大学 | A kind of measurement method of ball nut spiral interior rollaway nest curved surface and outer diameter |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111898213A (en) | 2020-11-06 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110954021B (en) | Vortex disc measuring method and device based on numerical control motion platform | |
| CN109780965B (en) | Cylindrical surface multi-element detection device and method based on concentric circle grid traversal optimization | |
| CN108871229B (en) | Method for measuring curved surface and outer diameter of spiral inner raceway of ball nut | |
| CN111993159A (en) | In-place non-contact detection method for shaft workpieces | |
| CN109059766B (en) | Method for detecting inner ring groove position of deep groove ball bearing | |
| CN103543010A (en) | High-speed screw and screw pair comprehensive examination test bed | |
| CN105758360B (en) | A kind of steering bearing blowout patche raceway groove parameter measurement instrument and its measurement method | |
| JP3687896B2 (en) | Measuring device for pulley for continuously variable transmission | |
| CN105783658A (en) | Special device for detecting VL-type universal joint inner star wheel raceway pitch diameter and detection method | |
| CN109737884A (en) | A kind of quiet dynamic deformation amount on-Line Monitor Device of axial workpiece and method | |
| CN107314731A (en) | Detect the cubing and the detection method using the cubing of the cage out star wheel equation of the ecentre | |
| CN113970299A (en) | Device for vertically measuring outline of elongated piece with high precision | |
| CN115077452A (en) | Detection method for crankshaft of ultrahigh-precision RV reducer | |
| CN109827538A (en) | A kind of bar straightness detection device and its straightness detection method | |
| CN107339967B (en) | Roundness measuring instrument | |
| CN111879277A (en) | Double-spiral gear symmetry measuring method based on CNC gear measuring center | |
| CN105466381A (en) | Concave arc radius detection and arc degree determination apparatus and method | |
| CN111898213B (en) | Matching method based on ball screw and ball nut raceway profile parameters | |
| CN109141329B (en) | Ball screw online measurement method based on one-dimensional trigger type measuring head | |
| CN111272088B (en) | Measuring algorithm for profile pitch diameter of sliding block of rolling linear guide rail pair | |
| CN206440215U (en) | Hole diameter detection apparatus for manufacturing the desk-top cage of high accuracy | |
| CN114562962A (en) | Equipment coaxiality measuring method based on laser tracker | |
| CN211651524U (en) | Diameter and roundness on-line monitoring device for expanded diameter pipeline | |
| CN203811302U (en) | Detection workbench for axle residual stress | |
| CN208902084U (en) | A kind of detection device of super large type bearing ring outer diameter |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CB03 | Change of inventor or designer information |
Inventor after: Wu Jian Inventor after: Ou Yi Inventor after: Wang Kai Inventor before: Ou Yi Inventor before: Wu Jian Inventor before: Wang Kai |
|
| CB03 | Change of inventor or designer information |