CN110095367B - Method for measuring wear coefficient of lead screw raceway - Google Patents
Method for measuring wear coefficient of lead screw raceway Download PDFInfo
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- CN110095367B CN110095367B CN201910355927.XA CN201910355927A CN110095367B CN 110095367 B CN110095367 B CN 110095367B CN 201910355927 A CN201910355927 A CN 201910355927A CN 110095367 B CN110095367 B CN 110095367B
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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- G—PHYSICS
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- 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
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Abstract
The invention discloses a method for measuring a wear coefficient of a raceway of a lead screw, and belongs to the field of performance measurement of ball screw pairs. The method comprises the following steps: establishing a ball screw pair screw raceway abrasion coefficient calculation model; setting the measurement condition of the abrasion coefficient of the screw roller path of the ball screw pair; and measuring the lead screw to be measured based on a stroke error measurement method to obtain the wear coefficient of the ball screw pair lead screw raceway. The abrasion of the screw roller path can cause the degradation of the positioning precision of the ball screw pair, and the abrasion coefficient of the screw roller path can directly reflect the degradation speed of the positioning precision. The invention provides a method for accurately measuring the wear coefficient of a lead screw raceway of a ball screw pair, fills the blank of the field, and particularly directly obtains the wear depth of the lead screw raceway by measuring the stroke error of the lead screw raceway, finally obtains the wear coefficient value of the lead screw raceway, is convenient to measure, has accurate results, and can more accurately reflect the degradation speed of the positioning precision of the ball screw pair compared with the prior reference empirical value.
Description
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 wear coefficient of a screw roller path.
Background
The ball screw pair has the advantages of high positioning precision, high transmission efficiency, high reliability, long service life and the like, so the ball screw pair is widely applied to the fields of machinery, aviation, aerospace, nuclear industry and the like and always occupies most of markets in the application field of linear motion. The positioning accuracy of the ball screw pair can be reduced due to friction and abrasion between the ball and the screw roller path, and when the abrasion amount reaches a certain degree, the accuracy failure of the ball screw pair can occur. And the wear coefficient of the screw raceway of the ball screw pair can directly reflect the degradation speed of the positioning accuracy of the ball screw pair, so that the method has important significance for theoretical research and experimental measurement on the wear coefficient of the screw raceway.
The wear coefficient in the ball screw pair screw raceway wear model is mainly related to materials, lubrication states and surface roughness, and is difficult to analyze and take values theoretically, the traditional Archard wear theory is not suitable for the working condition of a screw, the wear coefficient of the screw raceway at present generally takes an empirical value, and no related test is used for determination. The wear coefficient of the screw roller path is important for the performance index and performance degradation of the ball screw pair, but the research of the existing method for measuring the wear coefficient of the screw roller path of the ball screw pair is blank and needs to be filled.
Disclosure of Invention
The invention aims to provide a method for measuring the wear coefficient of a ball screw roller path of a ball screw pair, fill the blank of the field, provide theoretical support and experimental 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 lead screw raceway wear coefficient measuring method comprises the following steps:
step 2, setting a measuring condition of the abrasion coefficient of the ball screw pair screw roller path;
and 3, measuring the lead screw to be measured based on a stroke error measurement method, and obtaining a measurement value of the wear coefficient of the screw raceway of the ball screw pair.
Compared with the prior art, the invention has the following remarkable advantages: 1) the method for measuring the wear coefficient of the ball screw pair screw raceway is provided, and the blank of the method for measuring the wear coefficient of the ball screw pair screw raceway is filled; 2) a relation model between the wear coefficient of the ball screw pair screw raceway and the load, the speed, the structural parameters and the material parameters is established, all influence factors are considered, and the measurement accuracy is high; 3) the wear depth of the lead screw roller path is obtained by measuring the stroke error of the lead screw roller path, and finally the wear coefficient of the lead screw roller path of the ball screw pair is obtained, so that the precision is high, and the measurement result is accurate and reliable; 4) the method is simple and easy to implement, and can realize rapid measurement of the 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 wear coefficient of the lead screw raceway.
FIG. 2 is a flowchart of a process of measuring a ball screw pair to be measured based on a stroke error measurement method according to the present invention.
Fig. 3 is a schematic diagram of the wear coefficient value of the screw raceway measured by using a 4010 ball screw pair as an example in the embodiment of the present invention.
Detailed Description
With reference to fig. 1, the method for measuring the wear coefficient of the screw raceway comprises the following steps:
step 2, setting a measuring condition of the abrasion coefficient of the ball screw pair screw roller path;
and 3, measuring the lead screw to be measured based on a stroke error measuring method, and obtaining the wear coefficient of the ball screw pair lead screw raceway.
Further, step 1, establishing a ball screw pair screw raceway abrasion coefficient calculation model, specifically:
(1) in the ball screw pair, a wear region between balls and a screw raceway is regarded as a rectangle having a width of 2b, and an area a of the wear region is expressed as:
A=2b·LR
wherein b is the minor semi-axis of the ellipse of the contact of the ball and the raceway, LRThe total length of the ball and the wear area of the screw raceway in the ball screw pair, i.e. the thread length corresponding to the effective stroke of the screw, is expressed as:
in the formula, LsThe effective stroke of the lead screw is lambda, and the lead angle is lambda;
(2) wear depth of screw roller path at unit running revolutionWsExpressed as:
in which N is the total number of revolutions of the screw, V0For initial measured stroke error of the screw, VNmeasuring a stroke error after the screw rod runs for N ten thousand turns, wherein alpha is a contact angle between a ball and a raceway, wherein the unit running revolution is every ten thousand turns;
(3) total wear volume W between ball and screw raceway contact surfacesVComprises the following steps:
WV=Ws·A·N
wherein M is the total number of the effectively loaded balls;
(5) according to the traditional Archard wear theory, under the action of a normal force Q, the wear volume between the contact surface of a single ball in the ball screw pair and a screw racewayExpressed as:
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 wear coefficient of the ball screw pair screw track, and LtThe sliding distance of a single ball relative to the screw raceway, and Q is the normal force between the ball and the screw raceway;
(6) the sliding distance of the balls with respect to the screw raceway is expressed as:
in the formula, omega is the angular velocity of the screw shaft,the sliding speed of the ball relative to the screw roller path;
wherein the sliding speed of the balls relative to the screw raceway is expressed as:
in the formula, VXAnd VYThe sliding speeds of the balls relative to the screw roller path on the contact ellipse minor semi-axis and major semi-axis respectively;
for the side where the pretension direction is the same as the axial load direction:
for the side of the preload force direction opposite to the axial load direction:
wherein the content of the first and second substances,
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;
(7) the normal force Q between the ball and the screw raceway is:
in the formula, FaThe axial load is applied to the ball screw pair;
(8) combining the formulas in (1) to (7), and establishing a wear coefficient calculation model of the ball screw pair screw raceway as follows:
wherein J is a constant and is represented as:
further, the measuring conditions of the wear coefficient of the ball screw pair screw raceway in the step 2 comprise running-in running rotating speed, axial load, performance monitoring, stroke error measuring conditions, lubricating conditions and running-in rotating speed of the ball screw pair; the specific measurement conditions for setting the wear coefficient of the screw raceway 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 axial load of the auxiliary shaft of the ball screw to be tested to be FaTaking Fa≤30%CaIn which C isaThe dynamic load is rated for the ball screw pair;
(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 an initial stroke error of the screw rod to be measured before running in, and measuring the stroke error of the screw rod 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 measuring the stroke error 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 stroke error measurement method, and obtain a wear coefficient of a ball screw roller path of the ball screw pair, specifically:
step 3-1, measuring initial stroke error V of ball screw pair screw to be measured0;
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 stroke error of the lead screw 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, acquiring the wear coefficient of the screw roller path according to all the stroke error data obtained by measurement.
Further, step 3-3 the measuring of the stroke error of the lead screw of the ball screw pair to be measured specifically comprises:
3-3-1, mounting the ball screw pair to be tested on a stroke error measurement test bed, removing a sealing ring, and standing for t hours to ensure the thermal balance of the screw;
step 3-3-2, c times of forward and reverse stroke error measurement are carried out on the lead screw to be measured, and the measured forward stroke error numerical value of c groups isMeasured c sets of reverse stroke error values of
Step 3-3-3, averaging the forward and reverse stroke error measured values of the ball screw pair measured for the time c, wherein the stroke error measured value is as follows:
recording the revolution number N of the ball screw pair during the measurement of the screw stroke error of the ith ball screw pair to be measurediSum stroke error value Vi(ii) a i 1,2, m, m being the number of travel error measurements,
exemplary preferably, c-5.
Further, in step 3-5, the wear coefficient of the screw raceway is obtained according to all the stroke error data obtained by measurement, specifically:
3-5-1, using the formula Ti=J·(Vi-V0) The m groups of stroke error values are transformed to obtain corresponding Ti;
3-5-2, recording the rotating speed of the ball screw at the time of ith stroke error 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 fitted linear slope is the measured value of the abrasion coefficient of the screw raceway 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 the wear coefficient of a screw raceway of a ball screw pair, which comprises the following steps:
1. and establishing a ball screw pair screw raceway abrasion coefficient calculation model.
(1) In the ball screw pair, a wear region between balls and a screw raceway is regarded as a rectangle having a width of 2b, and an area a of the wear region is expressed as:
A=2b·LR
in the formula, b isMinor semi-axis of the contact ellipse of the ball and the raceway, LRThe total length of the ball and the wear area of the screw raceway in the ball screw pair, i.e. the thread length corresponding to the effective stroke of the screw, is expressed as:
in the formula, LsThe effective stroke of the lead screw is lambda, and the lead angle is lambda;
(2) wear depth of screw roller path at unit running revolutionWsExpressed as:
in which N is the total number of revolutions of the screw, V0For initial measured stroke error of the screw, VNmeasuring a stroke error after the screw rod runs for N ten thousand turns, wherein alpha is a contact angle between a ball and a raceway, wherein the unit running revolution is every ten thousand turns;
(3) total wear volume W between ball and screw raceway contact surfacesVComprises the following steps:
WV=Ws·A·N
wherein M is the total number of the effectively loaded balls;
(5) according to the traditional Archard wear theory, under the action of a normal force Q, the wear volume between the contact surface of a single ball in the ball screw pair and a screw racewayExpressed as:
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 wear coefficient of the ball screw pair screw track, and LtThe sliding distance of a single ball relative to the screw raceway, and Q is the normal force between the ball and the screw raceway;
(6) the sliding distance of the balls with respect to the screw raceway is expressed as:
in the formula, omega is the angular velocity of the screw shaft,the sliding speed of the ball relative to the screw roller path;
wherein the sliding speed of the balls relative to the screw raceway is expressed as:
in the formula, VXAnd VYThe sliding speeds of the balls relative to the screw roller path on the contact ellipse minor semi-axis and major semi-axis respectively;
for the side where the pretension direction is the same as the axial load direction:
for the side of the preload force direction opposite to the axial load direction:
wherein the content of the first and second substances,
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;
(7) the normal force Q between the ball and the screw raceway is:
in the formula, FaThe axial load is applied to the ball screw pair;
(8) combining formulas in (1) to (7), and establishing a wear coefficient calculation model of the lead screw roller path as follows:
where J is a constant and can be expressed as:
2. and setting the measurement condition of the wear coefficient of the ball screw pair screw raceway.
In the embodiment of the invention, a double-nut 4010 type ball screw pair 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 a screw is 1700mm, and the diameter of a 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 axial load to be 8kN and the total running revolution to be 700 thousands of revolutions, and the measurement of the stroke error is carried out once every 100 thousands of revolutions, including the measurement of initial data to obtain 8 groups of data.
3. And measuring the lead screw to be measured based on a stroke error measurement method, and obtaining a measured value of the wear coefficient of the ball screw pair lead screw raceway.
According to the set measuring conditions, the stroke error of the screw is measured:
firstly, the ball screw pair is installed on a workbench, a sealing ring is removed, and the ball screw pair is stood for more than 2 hours to ensure the thermal balance of the screw. Adjusting the axial load of the ball screw auxiliary shaft to about 8kN, measuring according to determined measuring conditions, measuring the stroke error of the screw of the ball screw auxiliary shaft once every 100 ten thousand revolutions, and adding lubricating grease to continue running in after measurement. The ball screw assembly was operated for 700 thousands of revolutions and then stopped for this measurement, and 8 sets of forward and reverse stroke error data corresponding to the number of revolutions were obtained as shown in table 1 below.
TABLE 1 wear coefficient measurement data
Using the formula Ti=KNiFor 8 groups of data (N)i,Ti) linear fitting is carried out, the fitted straight line is shown in figure 3, and the measured abrasion coefficient K of the ball screw pair lead screw raceway is 3.0 × 10-12。
The method directly obtains the wear depth of the screw roller path by measuring the stroke error of the screw roller path, finally obtains the wear coefficient value of the screw roller path, has convenient measurement and accurate result, and can more accurately reflect the degradation speed of the positioning precision of the ball screw pair compared with the prior reference empirical value. The wear coefficient of the lead screw roller path depends on the material, the structure, the load during working and the running speed of the ball screw pair, the method can comprehensively consider the influence factors of the wear condition of the lead screw roller path, measures the corresponding wear coefficient of the lead screw roller path aiming at different types of ball screw pairs and different working conditions, and has important significance for the precision degradation and the service life prediction of the ball screw pair.
Claims (8)
1. A lead screw raceway wear coefficient measuring method is characterized by comprising the following steps:
step 1, establishing a ball screw pair screw raceway abrasion coefficient calculation model; the method specifically comprises the following steps:
(1) in the ball screw pair, a wear region between balls and a screw raceway is regarded as a rectangle having a width of 2b, and an area a of the wear region is expressed as:
A=2b·LR
wherein b is the minor semi-axis of the ellipse of the contact of the ball and the raceway, LRThe total length of the ball and the wear area of the screw raceway in the ball screw pair, i.e. the thread length corresponding to the effective stroke of the screw, is expressed as:
in the formula, LsThe effective stroke of the lead screw is lambda, and the lead angle is lambda;
(2) wear depth of screw roller path at unit running revolutionWsExpressed as:
in which N is the total number of revolutions of the screw, V0For initial measured stroke error of the screw, VNmeasuring a stroke error after the screw rod runs for N ten thousand turns, wherein alpha is a contact angle between a ball and a raceway, wherein the unit running revolution is every ten thousand turns;
(3) total wear volume W between ball and screw raceway contact surfacesVComprises the following steps:
WV=Ws·A·N
wherein M is the total number of the effectively loaded balls;
(5) according to the traditional Archard wear theory, under the action of a normal force Q, the wear volume between the contact surface of a single ball in the ball screw pair and a screw racewayExpressed as:
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 wear coefficient of the ball screw pair screw track, and LtThe sliding distance of a single ball relative to the screw raceway, and Q is the normal force between the ball and the screw raceway;
(6) the sliding distance of the balls with respect to the screw raceway is expressed as:
in the formula, omega is the angular velocity of the screw shaft,the sliding speed of the ball relative to the screw roller path;
wherein the sliding speed of the balls relative to the screw raceway is expressed as:
in the formula, VXAnd VYThe sliding speeds of the balls relative to the screw roller path on the contact ellipse minor semi-axis and major semi-axis respectively;
for the side where the pretension direction is the same as the axial load direction:
for the side of the preload force direction opposite to the axial load direction:
wherein the content of the first and second substances,
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;
(7) the normal force Q between the ball and the screw raceway is:
in the formula, FaThe axial load is applied to the ball screw pair;
(8) combining the formulas in (1) to (7), and establishing a wear coefficient calculation model of the ball screw pair screw raceway as follows:
wherein J is a constant and is represented as:
step 2, setting a measuring condition of the abrasion coefficient of the ball screw pair screw roller path;
and 3, measuring the lead screw to be measured based on a stroke error measuring method, and obtaining the wear coefficient of the ball screw pair lead screw raceway.
2. The lead screw raceway wear coefficient measurement method according to claim 1, wherein the measurement conditions of the ball screw pair lead screw raceway wear coefficient in step 2 include a ball screw pair running-in operation rotation speed, an axial load, performance monitoring, a stroke error measurement condition, a lubrication condition, and running-in revolution; the specific measurement conditions for setting the wear coefficient of the screw raceway 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 axial load of the auxiliary shaft of the ball screw to be tested to be FaTaking Fa≤30%CaIn which C isaThe dynamic load is rated for the ball screw pair;
(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 an initial stroke error of the screw rod to be measured before running in, and measuring the stroke error of the screw rod 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 measuring the stroke error each time.
3. The lead screw raceway wear coefficient measurement method of claim 2, wherein the properties of the ball screw pair under test include temperature, noise, and vibration.
4. The lead screw raceway wear coefficient measurement method according to claim 3, wherein N is equal to or greater than 600 and N is equal to or less than 100.
5. The lead screw raceway wear coefficient measurement method according to claim 4, wherein the step 3 of measuring the ball screw pair to be measured based on a stroke error measurement method to obtain the ball screw raceway wear coefficient of the ball screw pair specifically comprises:
step 3-1, measuring initial stroke error V of ball screw pair screw to be measured0;
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 stroke error of the lead screw 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, acquiring the wear coefficient of the screw roller path according to all the stroke error data obtained by measurement.
6. The lead screw raceway wear coefficient measurement method according to claim 5, wherein the step 3-3 of measuring the stroke error of the lead screw of the ball screw pair to be measured specifically is:
3-3-1, mounting the ball screw pair to be tested on a stroke error measurement test bed, removing a sealing ring, and standing for t hours to ensure the thermal balance of the screw;
step 3-3-2, c times of forward and reverse stroke error measurement are carried out on the lead screw to be measured, and the measured forward stroke error numerical value of c groups isMeasured c sets of reverse stroke error values of
Step 3-3-3, averaging the forward and reverse stroke error measured values of the ball screw pair measured for the time c, wherein the stroke error measured value is as follows:
7. the lead screw raceway wear coefficient measurement method of claim 6, wherein c is 5.
8. The lead screw raceway wear coefficient measurement method according to claim 7, wherein the step 3-5 of obtaining the wear coefficient of the lead screw raceway based on all the stroke error data obtained by measurement is specifically:
3-5-1, using the formula Ti=J·(Vi-V0) The m groups of stroke error values are transformed to obtain corresponding Ti;
3-5-2, recording the rotating speed of the ball screw at the time of ith stroke error 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 fitted linear slope is the measured value of the abrasion coefficient of the screw raceway of the ball screw pair.
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