CN110082238B - Method for measuring comprehensive wear coefficient of ball screw pair - Google Patents

Method for measuring comprehensive wear coefficient of ball screw pair Download PDF

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CN110082238B
CN110082238B CN201910356893.6A CN201910356893A CN110082238B CN 110082238 B CN110082238 B CN 110082238B CN 201910356893 A CN201910356893 A CN 201910356893A CN 110082238 B CN110082238 B CN 110082238B
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ball screw
screw pair
ball
raceway
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CN110082238A (en
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周长光
周华西
刘迪一
陈斌斌
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Nanjing University of Science and Technology
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/025—Test-benches with rotational drive means and loading means; Load or drive simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/56—Investigating resistance to wear or abrasion
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
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Abstract

The invention discloses a method for measuring a comprehensive wear coefficient of a ball screw pair, and belongs to the field of performance measurement of ball screw pairs. The comprehensive wear coefficient refers to a wear coefficient comprehensively considering the influence of the wear of the screw roller path and the wear of the nut roller path, and can directly reflect the degradation speed of the pretightening force and other performance degradation speeds caused by the pretightening force degradation. The method comprises the following steps: establishing a comprehensive wear coefficient calculation model of the ball screw pair; setting the measurement condition of the comprehensive wear coefficient of the ball screw pair; and measuring the ball screw pair to be measured based on a ball screw pair friction moment measuring method to obtain a measured value of the comprehensive wear coefficient of the ball screw pair. The invention provides a method for accurately measuring the comprehensive wear coefficient of a ball screw pair, fills the blank of the field, has high precision compared with the prior reference empirical value, can more accurately reflect the wear condition of the ball screw pair, and further greatly improves the accuracy of service life prediction.

Description

Method for measuring comprehensive wear coefficient of ball screw pair
Technical Field
The invention belongs to the field of performance measurement of a ball screw pair, and particularly relates to a method for measuring a comprehensive wear coefficient of the ball screw pair.
Background
The ball screw pair is used as a linear positioning transmission part with high precision, high efficiency, high rigidity and high bearing capacity, and is widely applied to the industrial fields of precision machine tools, petroleum drilling, scientific measurement and the like. The abrasion between the ball and the roller path can directly lead to the deterioration of the pretightening force of the ball screw pair, reduce the performances of rigidity, bearing capacity, dynamic characteristics and the like, and even lead to the occurrence of reverse clearance. The wear coefficient can directly reflect the degradation speed of the pretightening force, so that the comprehensive wear coefficient of the ball screw pair has important significance in theoretical research and experimental measurement.
The comprehensive wear coefficient in the wear model of the ball screw pair is mainly related to materials, lubrication states and surface roughness, an accurate mathematical model is difficult to establish, the traditional Archard wear theory is not suitable for the working condition of the ball screw pair, the comprehensive wear coefficient of the ball screw pair can only refer to the test result value of Rabinowicz in 1958 at present, and the materials, the lubrication and the like are greatly different from the current states. The comprehensive wear coefficient is important for performance indexes and performance degradation of the ball screw pair, and research on the current method for measuring the comprehensive wear coefficient of the ball screw pair is blank and needs to be filled.
Disclosure of Invention
The invention aims to provide a method for measuring a comprehensive wear coefficient of a ball screw pair, fill the blank of the field, provide theoretical support and test verification for a performance degradation model of the ball screw pair, and further improve the accuracy of performance degradation and service life prediction of the ball screw pair.
The technical solution for realizing the purpose of the invention is as follows: a method for measuring the comprehensive wear coefficient of a ball screw pair comprises the following steps:
step 1, establishing a comprehensive wear coefficient calculation model of a ball screw pair;
step 2, setting a measurement condition of the comprehensive wear coefficient of the ball screw pair;
and 3, measuring the ball screw pair to be measured based on a ball screw pair friction moment measuring method, and obtaining a measured value of the comprehensive wear coefficient of the ball screw pair.
Compared with the prior art, the invention has the following remarkable advantages: 1) the method for measuring the comprehensive wear coefficient of the ball screw pair is provided, and the blank of the field is filled; 2) a relation model between the comprehensive wear coefficient of the ball screw pair and the load, speed, structural parameters and material parameters is established, all influence factors are considered, and the measurement accuracy is improved; 3) the wear depth of the ball screw pair is indirectly obtained by measuring the friction torque of the ball screw pair, and finally the comprehensive wear coefficient of the ball screw pair is obtained, so that the measurement difficulty is greatly reduced, and the data accuracy is high; 4) the method is simple and easy to implement, and can realize the rapid measurement of the comprehensive wear coefficient.
The present invention is described in further detail below with reference to the attached drawings.
Drawings
FIG. 1 is a flow chart of the method for measuring the comprehensive wear coefficient of the ball screw pair of the present invention.
FIG. 2 is a flowchart of a process of measuring a ball screw pair to be measured based on a ball screw pair friction moment measurement method according to the present invention.
Fig. 3 is a schematic diagram of the comprehensive wear coefficient measured by taking a 4010 ball screw assembly as an example in the embodiment of the invention.
Detailed Description
With reference to fig. 1, the method for measuring the comprehensive wear coefficient of the ball screw pair of the invention comprises the following steps:
step 1, establishing a comprehensive wear coefficient calculation model of a ball screw pair;
step 2, setting a measurement condition of the comprehensive wear coefficient of the ball screw pair;
and 3, measuring the ball screw pair to be measured based on a ball screw pair friction moment measuring method, and obtaining the comprehensive wear coefficient of the ball screw pair.
Further, step 1, establishing a comprehensive wear coefficient calculation model of the ball screw pair, specifically:
(1) the relation between the pre-tightening force and the no-load torque of the ball screw pair is as follows:
Figure BDA0002045701850000021
in the formula, FpIs the pre-tightening force of the ball screw pair Mfis the no-load torque of the ball screw pair, alpha is the contact angle between the ball and the roller path, mu is the friction coefficient, and r ismRadius of the screw shaft, rbIs the radius of the ball;
(2) the normal force Q between the ball and the raceway is:
Figure BDA0002045701850000022
in the formula, M is the total number of the effectively loaded balls, and lambda is a lead angle;
(3) the relation between the normal deformation of the ball and the raceway of the ball screw pair and the normal force Q is as follows:
Figure BDA0002045701850000031
in the formula, cKA constant related to the radius of curvature of the contact point of the raceway, cEIs a material constant;
(4) the total depth delta of the lead screw and nut raceway wear is:
Δ＝0-N
in the formula (I), the compound is shown in the specification,0is the initial normal deformation of the roller path,Nthe normal deformation of the roller path is N thousands of turns after the screw rod runs;
(5) wear depth of screw roller path at unit running revolutionWsComprises the following steps:
Figure BDA0002045701850000032
in the formula, LsAnd LnRespectively the effective strokes of the screw and the nut, and N is the total number of revolutions of the ball screw pair; wherein, the unit operation revolution is per ten thousand revolutions;
(6) wear depth of nut raceway per unit running revolutionWnComprises the following steps:
Figure BDA0002045701850000033
(7) in the ball screw pair, a worn region between the balls and the screw raceway or the nut raceway is regarded as a rectangle having a width of 2b, and the area A of the worn regionn′Comprises the following steps:
An′＝2b·LRn′
where b is the minor semi-axis of the ellipse in which the balls contact the raceways, and n' is s, LRn′The total length of the worn ball and screw raceway areas in the ball screw pair, i.e., the thread length corresponding to the effective screw stroke, is represented, and when n ═ n, L is representedRn′The total length of a wear area of a ball and a nut raceway in the ball screw pair is shown, namely the length of a thread corresponding to the effective stroke of the nut;
length L of screw thread corresponding to effective stroke of screw rodRsComprises the following steps:
Figure BDA0002045701850000034
length L of screw thread corresponding to effective stroke of nutRnComprises the following steps:
Figure BDA0002045701850000035
(8) wear volume W between ball and screw raceway contact surfacesVsComprises the following steps:
WVs＝Ws·As·N
(9) wear volume W between ball and nut raceway contact surfacesVnComprises the following steps:
WVn＝Wn·An·N
(10) total wear volume W between ball and screw raceway and nut raceway contact surfacesVComprises the following steps:
WV＝WVs+WVn
(11) wear volume between single ball and raceway interface
Figure BDA0002045701850000041
Comprises the following steps:
Figure BDA0002045701850000042
(12) according to the traditional Archard wear theory, under the action of normal force Q, the wear volume between the contact surface of a single ball and a raceway in the ball screw pair
Figure BDA0002045701850000043
Comprises the following steps:
Figure BDA0002045701850000044
wherein H is the hardness value of the surface with lower hardness in the two surfaces which are contacted with each other, K is the comprehensive wear coefficient of the ball screw pair, and LtThe sliding distance of a single ball relative to the raceway;
wherein the sliding distance L of the balls relative to the racewaytComprises the following steps:
Figure BDA0002045701850000045
wherein N is the total number of revolutions of the ball screw assembly, omega is the angular velocity of the screw shaft,
Figure BDA0002045701850000046
the sliding speed of the ball relative to the raceway;
in which the sliding speed of the balls relative to the raceways
Figure BDA0002045701850000047
Comprises the following steps:
Figure BDA0002045701850000048
in the formula, VXAnd VYThe sliding speeds of the balls relative to the raceway in a contact ellipse minor semi-axis and a contact ellipse major semi-axis are respectively;
for the side where the pretension direction is the same as the axial load direction:
Figure BDA0002045701850000049
Figure BDA00020457018500000410
for the side of the preload force direction opposite to the axial load direction:
Figure BDA0002045701850000051
Figure BDA0002045701850000052
wherein the content of the first and second substances,
Figure BDA0002045701850000053
Figure BDA0002045701850000054
in the formula, rbIs the radius of the ball, riIs the radius of the raceway, RSis the bottom diameter of the screw α is the contact angle between the ball and the roller path,sandnrespectively the deformation between the ball and the raceway of the screw and the nut, omega the angular velocity of the screw shaft, omegamIs the revolution angular velocity, omega, of the balls relative to the screw racewayt，ωnAnd ωbAngular velocities ω of rotation of the balls, respectivelyRComponents on the t-axis, n-axis, and b-axis;
(13) combining the formulas in (1) to (12), and establishing a comprehensive wear coefficient calculation model of the ball screw pair as follows:
Figure BDA0002045701850000055
in the formula (I), the compound is shown in the specification,
Figure BDA0002045701850000056
is the initial no-load torque of the ball screw pair,
Figure BDA0002045701850000057
the no-load torque after the ball screw pair runs for N thousands of revolutions is provided, J is a constant, and the method specifically comprises the following steps:
Figure BDA0002045701850000058
further, the measurement conditions of the comprehensive wear coefficient of the ball screw pair in the step 2 comprise running-in running rotating speed, pretightening force level, performance monitoring, friction torque measurement conditions, lubricating conditions and running-in rotating speed of the ball screw pair; the measurement conditions for setting the comprehensive wear coefficient of the ball screw pair are as follows:
(1) setting the running rotating speed of the ball screw pair to be tested as v1Get v1≤v0Wherein v is0The rated rotating speed of the ball screw pair is set;
(2) setting the initial pretightening force of the ball screw pair to be tested to be F1Taking F1≤30％CaIn which C isaRated dynamic load for ball screw pair to be testedLoading;
(3) monitoring the performance of the ball screw pair to be tested in the running-in process to detect whether the ball screw pair to be tested normally operates or not, stopping the test if the ball screw pair to be tested is abnormal, and continuing the test after the fault is eliminated;
(4) setting a timing tail-cutting test method, wherein the tail-cutting time is N ten thousand turns;
(5) setting the initial friction torque of the ball screw pair to be measured before running in, and measuring the friction torque once every N ten thousand revolutions, wherein N can divide N;
(6) and setting to add lubricating grease to the ball screw pair to be tested after the friction torque is measured each time.
Exemplary preferred properties of the ball screw pair to be tested include temperature, noise and vibration.
Exemplary preferred, N ≧ 600, N ≦ 100.
Further, with reference to fig. 2, step 3 is to measure the ball screw pair to be measured based on a ball screw pair friction moment measurement method, and obtain a comprehensive wear coefficient of the ball screw pair, specifically:
step 3-1, measuring initial friction torque M of ball screw pair to be measuredf0；
Step 3-2, installing the ball screw pair to be tested on a ball screw pair abrasion running-in test bed, running in for n thousands of revolutions under set measurement conditions, monitoring the temperature, noise and vibration of the ball screw pair, stopping to check faults if the temperature, noise and vibration are abnormal, and continuing the test after the faults are eliminated;
3-3, measuring the friction torque of the ball screw pair to be measured;
step 3-4, judging the total running revolution of the ball screw pair, and returning to the step 3-2 if the total running revolution is less than N thousands of revolutions; if the total running revolution reaches N thousands of revolutions, the running-in is finished, and the step 3-5 is executed;
and 3-5, processing according to all the friction torque data obtained by measurement to obtain the comprehensive wear coefficient of the ball screw pair to be measured.
Further, 3-3 friction torque measurement is carried out to the ball screw pair that awaits measuring, specifically is:
step 3-3-1, mounting the ball screw pair to be measured on a friction torque measurement test bed, and setting the rotating speed v according to the measurement conditions1Idling for t minutes to fully lubricate the ball screw pair;
step 3-3-2, c times of forward and reverse friction torque measurements are carried out on the ball screw pair to be measured, and the measured forward friction torque value of the c groups is Mp1、Mp2、...、Mpc(ii) a The measured c groups of reverse friction torque values are Mq1、Mq2、...、Mqc；
Step 3-3-3, averaging the measured values of the forward and reverse friction torques of the ball screw pair measured for c times, wherein the measured value of the friction torque of the time is as follows:
Figure BDA0002045701850000061
recording the revolution number N of the ball screw pair during the friction moment measurement of the ith ball screw pair to be measurediAnd the friction torque value Mfi(ii) a i 1,2, m, m is the number of friction torque measurements,
Figure BDA0002045701850000062
further, the step 3-5 is to process all the friction torque data obtained by measurement to obtain the comprehensive wear coefficient of the ball screw pair to be measured, and specifically comprises the following steps:
3-5-1, using the formula
Figure BDA0002045701850000071
The m groups of friction torque values are transformed to obtain corresponding Ti；
3-5-2, recording the rotating speed of the ball screw at the time of the ith friction torque measurement as NiIs a reaction of NiAnd TiIs recorded as a coordinate point (N)i,Ti) Obtaining m coordinate points in total;
3-5-3, using the formula Ti＝KNiAnd performing linear fitting on the m coordinate points by adopting a least square method, wherein the slope of the fitted straight line is the measured value of the comprehensive wear coefficient of the ball screw pair.
The present invention will be described in further detail with reference to examples.
Examples
The invention discloses a method for measuring a comprehensive wear coefficient of a ball screw pair, which comprises the following steps:
1. and establishing a comprehensive wear coefficient calculation model of the ball screw pair.
(1) The relation between the pre-tightening force and the no-load torque of the ball screw pair is as follows:
Figure BDA0002045701850000072
in the formula, FpIs the pre-tightening force of the ball screw pair Mfis the no-load torque of the ball screw pair, alpha is the contact angle between the ball and the roller path, mu is the friction coefficient, and r ismRadius of the screw shaft, rbIs the radius of the ball;
(2) the normal force Q between the ball and the raceway is:
Figure BDA0002045701850000073
in the formula, M is the total number of the effectively loaded balls, and lambda is a lead angle;
(3) the relation between the normal deformation of the ball and the raceway of the ball screw pair and the normal force Q is as follows:
Figure BDA0002045701850000074
in the formula, cKA constant related to the radius of curvature of the contact point of the raceway, cEIs a material constant;
(4) the total depth delta of the lead screw and nut raceway wear is:
Δ＝0-N
in the formula (I), the compound is shown in the specification,0is the initial normal deformation of the roller path,Nthe normal deformation of the roller path is N thousands of turns after the screw rod runs;
(5) wear depth of screw roller path at unit running revolutionWsComprises the following steps:
Figure BDA0002045701850000081
in the formula, LsAnd LnRespectively the effective strokes of the screw and the nut, and N is the total number of revolutions of the ball screw pair; wherein, the unit operation revolution is per ten thousand revolutions;
(6) wear depth of nut raceway per unit running revolutionWnComprises the following steps:
Figure BDA0002045701850000082
(7) in the ball screw pair, a worn region between the balls and the screw raceway or the nut raceway is regarded as a rectangle having a width of 2b, and the area A of the worn regionn′Comprises the following steps:
An′＝2b·LRn′
where b is the minor semi-axis of the ellipse in which the balls contact the raceways, and n' is s, LRn′The total length of the worn ball and screw raceway areas in the ball screw pair, i.e., the thread length corresponding to the effective screw stroke, is represented, and when n ═ n, L is representedRn′The total length of a wear area of a ball and a nut raceway in the ball screw pair is shown, namely the length of a thread corresponding to the effective stroke of the nut;
length L of screw thread corresponding to effective stroke of screw rodRsComprises the following steps:
Figure BDA0002045701850000083
length L of screw thread corresponding to effective stroke of nutRnComprises the following steps:
Figure BDA0002045701850000084
(8) wear volume W between ball and screw raceway contact surfacesVsComprises the following steps:
WVs＝Ws·As·N
(9) wear volume W between ball and nut raceway contact surfacesVnComprises the following steps:
WVn＝Wn·An·N
(10) total wear volume W between ball and screw raceway and nut raceway contact surfacesVComprises the following steps:
WV＝WVs+WVn
(11) wear volume between single ball and raceway interface
Figure BDA0002045701850000091
Comprises the following steps:
Figure BDA0002045701850000092
(12) according to the traditional Archard wear theory, under the action of normal force Q, the wear volume between the contact surface of a single ball and a raceway in the ball screw pair
Figure BDA0002045701850000093
Comprises the following steps:
Figure BDA0002045701850000094
wherein H is the hardness value of the surface with lower hardness in the two surfaces which are contacted with each other, K is the comprehensive wear coefficient of the ball screw pair, and LtThe sliding distance of a single ball relative to the raceway;
wherein the sliding distance L of the balls relative to the racewaytComprises the following steps:
Figure BDA0002045701850000095
wherein N is the total number of revolutions of the ball screw assembly, omega is the angular velocity of the screw shaft,
Figure BDA0002045701850000096
the sliding speed of the ball relative to the raceway;
wherein the content of the first and second substances,speed of sliding of balls relative to raceways
Figure BDA0002045701850000097
Comprises the following steps:
Figure BDA0002045701850000098
in the formula, VXAnd VYThe sliding speeds of the balls relative to the raceway in a contact ellipse minor semi-axis and a contact ellipse major semi-axis are respectively;
for the side where the pretension direction is the same as the axial load direction:
Figure BDA0002045701850000099
Figure BDA00020457018500000910
for the side of the preload force direction opposite to the axial load direction:
Figure BDA00020457018500000911
Figure BDA00020457018500000912
wherein the content of the first and second substances,
Figure BDA00020457018500000913
Figure BDA0002045701850000101
in the formula, rbIs the radius of the ball, riIs the radius of the raceway, RSis the bottom diameter of the screw α is the contact angle between the ball and the roller path,sandnrespectively the deformation between the ball and the raceway of the screw and the nut, omega the angular velocity of the screw shaft, omegamIs a ballRevolution angular velocity, omega, relative to the screw racewayt，ωnAnd ωbAngular velocities ω of rotation of the balls, respectivelyRComponents on the t-axis, n-axis, and b-axis;
(13) combining the formulas in (1) to (12), and establishing a comprehensive wear coefficient calculation model of the ball screw pair as follows:
Figure BDA0002045701850000102
in the formula (I), the compound is shown in the specification,
Figure BDA0002045701850000103
is the initial no-load torque of the ball screw pair,
Figure BDA0002045701850000104
the no-load torque after the ball screw pair runs for N thousands of revolutions is provided, J is a constant, and the method specifically comprises the following steps:
Figure BDA0002045701850000105
2. and setting the measurement condition of the comprehensive wear coefficient of the ball screw pair.
According to the embodiment of the invention, a double-nut 4010 type ball screw pair with adjustable pretightening force is selected for measurement and used for testing, the rated dynamic load of a sample is 55KN, the rated rotating speed is 2000r/min, the thread length of the screw is 1700mm, and the diameter of the ball is 6.35 mm. According to the parameters of the sample, the test sets the rotating speed of the ball screw pair to be 1000r/min, the initial pretightening force to be 6800N and the total running revolution to be 1000 ten thousand revolutions, and the no-load torque is measured once every 100 ten thousand revolutions, wherein 11 groups of data are obtained by measuring the initial data.
3. And measuring the ball screw pair to be measured based on a ball screw pair friction moment measuring method to obtain a measured value of the comprehensive wear coefficient of the ball screw pair.
And (3) according to the set measurement conditions, measuring the friction coefficient of the ball screw pair:
firstly, the ball screw pair is arranged on a workbench and idles for 5 minutes at the speed of 1000r/min, so that the ball screw pair is fully lubricated. Adjusting the pretightening force level of the ball screw pair to be about 6800N, measuring according to the determined measuring conditions, measuring the no-load torque of the ball screw pair once every 100 ten thousand revolutions, and adding lubricating grease to run in continuously after the measurement. The ball screw assembly was operated for 1000 thousand revolutions and the measurement was stopped to obtain 11 sets of forward and reverse no-load torque data corresponding to the number of revolutions as shown in table 1 below.
TABLE 1 comprehensive wear coefficient measurement data
Figure BDA0002045701850000111
Using the formula Ti＝KNiFor 10 sets of coordinate points (N)i,Ti) linear fitting is carried out, the fitted straight line is shown in figure 3, and the finally measured comprehensive wear coefficient K of the ball screw pair is 6.9 × 10-12。
The comprehensive wear coefficient value of the ball screw pair is changed along with the change of the rotating speed and the pretightening force of the screw, so that the comprehensive wear coefficient value is taken according to the past empirical value in the performance degradation and service life prediction of the ball screw pair to bring about a great error.

Claims (7)

1. A method for measuring the comprehensive wear coefficient of a ball screw pair is characterized by comprising the following steps:
step 1, establishing a comprehensive wear coefficient calculation model of a ball screw pair; the method specifically comprises the following steps:
(1) the relation between the pre-tightening force and the no-load torque of the ball screw pair is as follows:
Figure FDA0002574491420000011
in the formula, FpIs the pre-tightening force of the ball screw pair Mfis the no-load torque of the ball screw pair, alpha is the contact angle between the ball and the roller path, mu is the friction coefficient, and r ismRadius of the screw shaft, rbIs the radius of the ball;
(2) the normal force Q between the ball and the raceway is:
Figure FDA0002574491420000012
in the formula, M is the total number of the effectively loaded balls, and lambda is a lead angle;
(3) the relation between the normal deformation of the ball and the raceway of the ball screw pair and the normal force Q is as follows:
Figure FDA0002574491420000013
in the formula, cKA constant related to the radius of curvature of the contact point of the raceway, cEIs a material constant;
(4) the total depth delta of the lead screw and nut raceway wear is:
Δ＝0-N
in the formula (I), the compound is shown in the specification,0is the initial normal deformation of the roller path,Nthe normal deformation of the roller path is N thousands of turns after the screw rod runs;
(5) wear depth of screw roller path at unit running revolutionWsComprises the following steps:
Figure FDA0002574491420000014
in the formula, LsAnd LnRespectively the effective strokes of the screw and the nut, and N is the total number of revolutions of the ball screw pair; wherein, the unit operation revolution is per ten thousand revolutions;
(6) wear depth of nut raceway per unit running revolutionWnComprises the following steps:
Figure FDA0002574491420000015
(7) on rollIn the ball screw pair, the worn region between the balls and the screw raceway or the nut raceway is regarded as a rectangle having a width of 2b, and the area A of the worn regionn′Comprises the following steps:
An′＝2b·LRn′
where b is the minor semi-axis of the ellipse in which the balls contact the raceways, and n' is s, LRn′The total length of the worn ball and screw raceway areas in the ball screw pair, i.e., the thread length corresponding to the effective screw stroke, is represented, and when n ═ n, L is representedRn′The total length of a wear area of a ball and a nut raceway in the ball screw pair is shown, namely the length of a thread corresponding to the effective stroke of the nut;
length L of screw thread corresponding to effective stroke of screw rodRsComprises the following steps:
Figure FDA0002574491420000021
length L of screw thread corresponding to effective stroke of nutRnComprises the following steps:
Figure FDA0002574491420000022
(8) wear volume W between ball and screw raceway contact surfacesVsComprises the following steps:
WVs＝Ws·As·N
(9) wear volume W between ball and nut raceway contact surfacesVnComprises the following steps:
WVn＝Wn·An·N
(10) total wear volume W between ball and screw raceway and nut raceway contact surfacesVComprises the following steps:
WV＝WVs+WVn
(11) wear volume between single ball and raceway interface
Figure FDA0002574491420000023
Comprises the following steps:
Figure FDA0002574491420000024
(12) according to the traditional Archard wear theory, under the action of normal force Q, the wear volume between the contact surface of a single ball and a raceway in the ball screw pair
Figure FDA0002574491420000025
Comprises the following steps:
Figure FDA0002574491420000026
wherein H is the hardness value of the surface with lower hardness in the two surfaces which are contacted with each other, K is the comprehensive wear coefficient of the ball screw pair, and LtThe sliding distance of a single ball relative to the raceway;
wherein the sliding distance L of the balls relative to the racewaytComprises the following steps:
Figure FDA0002574491420000031
wherein N is the total number of revolutions of the ball screw assembly, omega is the angular velocity of the screw shaft,
Figure FDA0002574491420000032
the sliding speed of the ball relative to the raceway;
in which the sliding speed of the balls relative to the raceways
Figure FDA0002574491420000033
Comprises the following steps:
Figure FDA0002574491420000034
in the formula, VXAnd VYThe sliding speeds of the balls relative to the raceway in a contact ellipse minor semi-axis and a contact ellipse major semi-axis are respectively;
for the side where the pretension direction is the same as the axial load direction:
Figure FDA0002574491420000035
Figure FDA0002574491420000036
for the side of the preload force direction opposite to the axial load direction:
Figure FDA0002574491420000037
Figure FDA0002574491420000038
wherein the content of the first and second substances,
Figure FDA0002574491420000039
Figure FDA00025744914200000310
in the formula, rbIs the radius of the ball, riIs the radius of the raceway, RSis the bottom diameter of the screw α is the contact angle between the ball and the roller path,sandnrespectively the deformation between the ball and the raceway of the screw and the nut, omega the angular velocity of the screw shaft, omegamIs the revolution angular velocity, omega, of the balls relative to the screw racewayt，ωnAnd ωbAngular velocities ω of rotation of the balls, respectivelyRComponents on the t-axis, n-axis, and b-axis;
(13) combining the formulas in (1) to (12), and establishing a comprehensive wear coefficient calculation model of the ball screw pair as follows:
Figure FDA00025744914200000311
in the formula (I), the compound is shown in the specification,
Figure FDA00025744914200000312
is the initial no-load torque of the ball screw pair,
Figure FDA00025744914200000313
the no-load torque after the ball screw pair runs for N thousands of revolutions is provided, J is a constant, and the method specifically comprises the following steps:
Figure FDA0002574491420000041
step 2, setting a measurement condition of the comprehensive wear coefficient of the ball screw pair;
and 3, measuring the ball screw pair to be measured based on a ball screw pair friction moment measuring method, and obtaining the comprehensive wear coefficient of the ball screw pair.
2. The method for measuring the comprehensive wear coefficient of the ball screw pair according to claim 1, wherein the measuring conditions of the comprehensive wear coefficient of the ball screw pair in the step 2 comprise running-in running rotating speed, pretightening force level, performance monitoring, friction torque measuring conditions, lubricating conditions and running-in revolution of the ball screw pair; the measurement conditions for setting the comprehensive wear coefficient of the ball screw pair are as follows:
(1) setting the running rotating speed of the ball screw pair to be tested as v1Get v1≤v0Wherein v is0The rated rotating speed of the ball screw pair is set;
(2) setting the initial pretightening force of the ball screw pair to be tested to be F1Taking F1≤30％CaIn which C isaRated dynamic load of the ball screw pair to be measured;
(3) monitoring the performance of the ball screw pair to be tested in the running-in process to detect whether the ball screw pair to be tested normally operates or not, stopping the test if the ball screw pair to be tested is abnormal, and continuing the test after the fault is eliminated;
(4) setting a timing tail-cutting test method, wherein the tail-cutting time is N ten thousand turns;
(5) setting the initial friction torque of the ball screw pair to be measured before running in, and measuring the friction torque once every N ten thousand revolutions, wherein N can divide N;
(6) and setting to add lubricating grease to the ball screw pair to be tested after the friction torque is measured each time.
3. The method for measuring the comprehensive wear coefficient of the ball screw pair according to claim 2, wherein the properties of the ball screw pair to be measured comprise temperature, noise and vibration.
4. The method for measuring the comprehensive wear coefficient of the ball screw pair as recited in claim 3, wherein N is more than or equal to 600 and N is less than or equal to 100.
5. The method for measuring the comprehensive wear coefficient of the ball screw pair according to claim 4, wherein the step 3 of measuring the ball screw pair to be measured based on the ball screw pair friction moment measuring method to obtain the comprehensive wear coefficient of the ball screw pair comprises the following steps:
step 3-1, measuring initial friction torque M of ball screw pair to be measuredf0；
Step 3-2, installing the ball screw pair to be tested on a ball screw pair abrasion running-in test bed, running in for n thousands of revolutions under set measurement conditions, monitoring the temperature, noise and vibration of the ball screw pair, stopping to check faults if the temperature, noise and vibration are abnormal, and continuing the test after the faults are eliminated;
3-3, measuring the friction torque of the ball screw pair to be measured;
step 3-4, judging the total running revolution of the ball screw pair, and returning to the step 3-2 if the total running revolution is less than N thousands of revolutions; if the total running revolution reaches N thousands of revolutions, the running-in is finished, and the step 3-5 is executed;
and 3-5, processing according to all the friction torque data obtained by measurement to obtain the comprehensive wear coefficient of the ball screw pair to be measured.
6. The method for measuring the comprehensive wear coefficient of the ball screw pair according to claim 5, wherein the step 3-3 of measuring the friction torque of the ball screw pair to be measured specifically comprises the following steps:
step 3-3-1, mounting the ball screw pair to be measured on a friction torque measurement test bed, and setting the rotating speed v according to the measurement conditions1Idling for t minutes to fully lubricate the ball screw pair;
step 3-3-2, c times of forward and reverse friction torque measurements are carried out on the ball screw pair to be measured, and the measured forward friction torque value of the c groups is Mp1、Mp2、...、Mpc(ii) a The measured c groups of reverse friction torque values are Mq1、Mq2、...、Mqc；
Step 3-3-3, averaging the measured values of the forward and reverse friction torques of the ball screw pair measured for c times, wherein the measured value of the friction torque of the time is as follows:
Figure FDA0002574491420000051
recording the revolution number N of the ball screw pair during the friction moment measurement of the ith ball screw pair to be measurediAnd the friction torque value Mfi(ii) a i 1,2, m, m is the number of friction torque measurements,
Figure FDA0002574491420000052
7. the method for measuring the comprehensive wear coefficient of the ball screw pair according to claim 6, wherein the step 3-5 of processing the friction torque data obtained by measurement to obtain the comprehensive wear coefficient of the ball screw pair to be measured specifically comprises the following steps:
3-5-1, using the formula
Figure FDA0002574491420000053
The m groups of friction torque values are transformed to obtain corresponding Ti；
3-5-2, recording the rotating speed of the ball screw at the time of the ith friction torque measurement as NiIs a reaction of NiAnd TiIs recorded as a coordinate point (N)i,Ti) Obtaining m coordinate points in total;
3-5-3, using the formula Ti＝KNiAnd performing linear fitting on the m coordinate points by adopting a least square method, wherein the slope of the fitted straight line is the measured value of the comprehensive wear coefficient of the ball screw pair.
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