CN107784174A - A kind of screw support bearings wear-out life computational methods - Google Patents

A kind of screw support bearings wear-out life computational methods Download PDF

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CN107784174A
CN107784174A CN201711020623.5A CN201711020623A CN107784174A CN 107784174 A CN107784174 A CN 107784174A CN 201711020623 A CN201711020623 A CN 201711020623A CN 107784174 A CN107784174 A CN 107784174A
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mrow
msub
msup
msubsup
steel ball
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倪艳光
牛荣军
谢建军
华显伟
王光斌
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Henan University of Science and Technology
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Henan University of Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing

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  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Rolling Contact Bearings (AREA)

Abstract

A kind of screw support bearings wear-out life computational methods, it is related to bearing life computing technique field, including：The analysis of bearing quasi-static testing, bearing wear analysis, obtain the steps such as bearing wear life-span.Beneficial effect of the present invention：Continuous process is carried out sliding-model control by the present invention, the dynamic problem of complexity is converted into simple quasi-static problem, relative to traditional test method, using the abrasion accuracy life of technology of numerical simulation research ball-screw bearing, with research cycle is short, cost is low, and it is very convenient when studying influence of the change of bearing structure parameter to bearing wear accuracy life, it may be repeated, can effectively reduce the R＆D cycle of ball-screw bearing.

Description

A kind of screw support bearings wear-out life computational methods
Technical field
The present invention relates to bearing life computing technique field, specifically a kind of screw support bearings wear-out life calculates Method.
Background technology
Because abrasion has complexity and multifarious feature so that traditional experimental study method and classical calculus meter Calculation method can not solve the problems, such as actual wear well, although test method(s) closer to reality, it require that expending a large amount of Human and material resources, and research cycle is long, cost is high.
With intelligent simulation going deep into tribological field, technology of numerical simulation, which has become, solves the problems, such as Dynamic wear One of important method.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of ball-screw bearing wear-out life computational methods, solve mesh Preceding ball-screw bearing wear-out life calculates the problems such as inaccurate.
The present invention is that technical scheme is used by solving above-mentioned technical problem：A kind of screw support bearings wear-out life meter Calculation method, comprises the following steps：
Step 1: bearing is set in conventional coordinates { o；X, y, z } in when inner ring, outer ring, the spin velocity of retainer and steel ball Respectively ωi、ωo、ωmAnd ωb, then by the rotational velocity of steel ball in coordinate system { o'；Obtained in x', y', z'} to coordinate axial projection To three component ωx', ωy'And ωz', wherein coordinate system { o'；X', y', the z'} origin of coordinates are located at the steel ball centre of sphere, x' axles and x Axle is parallel, and radially, the coordinate system is rotated z' axles with the revolution speed of steel ball around x-axis；
Step 2: analyzing the motion state of screw support bearings, outer ring raceway is fixed, and inner ring raceway is with ωiRotation, steel The ball centre of sphere is with angular velocity omegamRevolved round the sun around fixed coordinate system origin o, thus according to inner ring raceway absolute angular velocities ωiIn can obtaining, Outer ring relative to retainer relative angular velocity omegaim、ωomAnd the autobiography angular velocity omega of steel ballb：
Step 3: according to the contact relation of steel ball and interior raceway, in rotating direction, sliding or cunning of the inner ring raceway relative to steel ball Dynamic speed uyiDetermined by the linear differential of raceway and steel ball, thus obtain uyiAnd steel ball is perpendicular to the sliding speed of rotating direction uxi；
Step 4: similarly, sliding or cunning of the outer ring raceway relative to steel ball can obtain by the contact relation of steel ball and outer ring raceway Dynamic speed uyoAnd steel ball is perpendicular to the sliding speed u of rotating directionxo；
Step 5: the wear-out life t of bearing is：
Wherein,ux、uy Value be uxi、uyiOr uxo、uyo, Qu taken ux、uyObtained maximum is substituted into after calculating, and a, b grow for Elliptical Contacts region Semi-minor axis length；QmaxRepresent the maximum of instantaneous normal direction load, ωsAutomatic rotary component for steel ball relative to raceway；X, y is to connect Region any point is touched,A values are aiOr ao, α values are αiOr αo, p takes A and α is substituted into after calculating obtained minimum value, KsThe coefficient of waste between steel ball and raceway is represented, H represents Vickers hardness, Z tables Show the number of steel ball, eoRepresent end-play increment allowable.
ω is sought in step of the present inventionx', ωy'And ωz'Specific method be：
ωx'=ωbcosβcosβ' (1)
ωy'=ωbcosβsinβ' (2)
ωz'=ωb sinβ (3)
Wherein β is the attitude angle of steel ball rotation axis and the angle, i.e. steel ball of x'o'y' planes；β ' is the steel ball axis of rotation in x'o' Projection and the angle of x' axles in y' planes.
Relative angular velocity omega of the inside and outside circle relative to retainer is sought in step 2 of the present inventionim、ωomAnd steel ball from Pass angular velocity omegabSpecific method be：
In formula, Ti' for outer ring raceway pure rolling point is contacted on major axis with steel ball to the distance of the centre of sphere, To' it is inner ring raceway and steel Pure rolling point is to the distance of the steel ball centre of sphere, α on ball contact major axisoFor steel ball and outer raceway contact angle, αiConnect for steel ball and interior raceway Feeler.
U in step 3 of the present inventionyiAnd uxiCircular be：
Wherein, aiFor the major semiaxis length of elliptic contact surface projection；RiFor the radius of curvature of inner ring Contact Ellipse textured surface；dm For pitch diameter, its value is the half of inside and outside raceway diameter sum；DwFor steel ball size.
Sliding or sliding speed u of the outer ring raceway relative to steel ball in step 4 of the present inventionyoAnd steel ball perpendicular to The sliding speed u of rotating directionxoCircular be：
Wherein, a0For the semi-minor axis length of elliptic contact surface projection；RoFor the radius of curvature of outer ring Contact Ellipse textured surface； ωomIt is the relative retainer in outer ring or relative { o；X, y, z } coordinate system rotating speed.
K of the present inventionsValue be Ks≈1.77×10-8λ-1, wherein λ is film lubrication parameter.
E of the present inventionoTake the 20% of initial play.
The beneficial effects of the invention are as follows：This method is in rolling bearing quasi-static testing analytic approach and bearing wear theoretical foundation Screw support bearings are carried out with wear-out life analysis, screw support bearings wear-out life appraising model is established in innovation, predicts bearing Wear-out life under normal operating conditions.Compared with prior art, continuous process is carried out sliding-model control by the present invention, will be multiple Miscellaneous dynamic problem is converted into simple quasi-static problem, relative to traditional test method, is studied using technology of numerical simulation The abrasion accuracy life of ball-screw bearing, have that research cycle is short, cost is low, and in the change of research bearing structure parameter It is very convenient during influence to bearing wear accuracy life, it may be repeated, can effectively reduce grinding for ball-screw bearing Send out the cycle.
Brief description of the drawings
Fig. 1 is bearing parts rotational angular velocity vector figure of the present invention；
Fig. 2 is local coordinate system reference chart of the present invention；
Fig. 3 is steel ball and interior raceway contact situation schematic diagram.
Marked in figure：1st, outer raceway groove, 2, steel ball, 3, interior raceway groove, 4, axis, 5, steel ball rotation axis, 6, pitch circle.
Embodiment
As illustrated, a kind of screw support bearings wear-out life computational methods, comprise the following steps：
Step 1: bearing is set in conventional coordinates { o；X, y, z } in when inner ring, outer ring, the spin velocity of retainer and steel ball Respectively ωi、ωo、ωmAnd ωb, then by the rotational velocity of steel ball in coordinate system { o'；Obtained in x', y', z'} to coordinate axial projection To three component ωx', ωy'And ωz'：
ωx'=ωbcosβcosβ' (1)
ωy'=ωbcosβsinβ' (2)
ωz'=ωbsinβ (3)
Wherein coordinate system { o'；X', y', the z'} origin of coordinates are located at the steel ball centre of sphere, and x' axles are parallel with x-axis, z' axles radially to Outside, the coordinate system is rotated with the revolution speed of steel ball around x-axis, and β is steel ball rotation axis and the angle of x'o'y' planes, i.e. steel ball Attitude angle；β ' is projection and the angle of x' axle of the steel ball axis of rotation in x'o'y' planes；
Step 2: analyzing the motion state of screw support bearings, outer ring raceway is fixed, and inner ring raceway is with ωiRotation, steel The ball centre of sphere is with angular velocity omegamRevolved round the sun around fixed coordinate system origin o, thus according to inner ring raceway absolute angular velocities ωiFormula can be passed through (4) relative angular velocity omega of the inside and outside circle relative to retainer is obtained in~(6)im、ωomAnd the autobiography angular velocity omega of steel ballb：
In formula, Ti' for outer ring raceway pure rolling point is contacted on major axis with steel ball to the distance of the steel ball centre of sphere, To' it is inner ring raceway Pure rolling point is contacted on major axis with steel ball to the distance of the steel ball centre of sphere, αoFor steel ball and outer raceway contact angle, αiFor steel ball and interior rolling Road contact angle；
Step 3: according to the contact relation of steel ball and interior raceway, in rotating direction, sliding or cunning of the inner ring raceway relative to steel ball Dynamic speed uyiDetermined by the linear differential of raceway and steel ball, uyiComputational methods be：
Wherein, aiFor the major semiaxis length of elliptic contact surface projection；RiFor the radius of curvature of inner ring Contact Ellipse textured surface；dm For pitch diameter, its value is the half of inside and outside raceway diameter sum；DwFor steel ball size；
Sliding speed u of the steel ball perpendicular to rotating directionxiComputational methods be：
Step 4: similarly, sliding or cunning of the outer ring raceway relative to steel ball can obtain by the contact relation of steel ball and outer ring raceway Dynamic speed uyoAnd steel ball is perpendicular to the sliding speed u of rotating directionxo：
Wherein, a0For the semi-minor axis length of elliptic contact surface projection；RoFor the radius of curvature of outer ring Contact Ellipse textured surface； ωomIt is the relative retainer in outer ring or relative { o；X, y, z } coordinate system rotating speed；
Step 5: the wear-out life t of bearing is：
Wherein,ux、uy Value be uxi、uyiOr uxo、uyo, Qu taken ux、uyObtained maximum is substituted into after calculating, and a, b grow for Elliptical Contacts region Semi-minor axis length；QmaxRepresent the maximum of instantaneous normal direction load, ωsAutomatic rotary component for steel ball relative to raceway；X, y is to connect Region any point is touched,A values are aiOr ao, α values are αiOr αo, p takes A and α is substituted into after calculating obtained minimum value, KsThe coefficient of waste between steel ball and raceway is represented, H represents Vickers hardness, Z tables Show the number of steel ball, eoRepresent end-play increment allowable.
The KsValue be Ks≈1.77×10-8λ-1, wherein λ is film lubrication parameter.
The eoTake the 20% of initial play.
Continuous process is carried out sliding-model control by the present invention, and the dynamic problem of complexity is converted into simple quasistatic asks Topic, relative to traditional test method, the abrasion accuracy life of ball-screw bearing is studied using technology of numerical simulation, has and grinds Study carefully that the cycle is short, cost is low, and it is very square when studying influence of the change of bearing structure parameter to bearing wear accuracy life Just, it may be repeated, can effectively reduce the R＆D cycle of ball-screw bearing.

Claims (7)

  1. A kind of 1. screw support bearings wear-out life computational methods, it is characterised in that：Comprise the following steps：
    Step 1: bearing is set in conventional coordinates { o；X, y, z } in when inner ring, outer ring, the spin velocity of retainer and steel ball Respectively ωi、ωo、ωmAnd ωb, then by the rotational velocity of steel ball in coordinate system { o'；Obtained in x', y', z'} to coordinate axial projection To three component ωx', ωy'And ωz', wherein coordinate system { o'；X', y', the z'} origin of coordinates are located at the steel ball centre of sphere, x' axles and x Axle is parallel, and radially, the coordinate system is rotated z' axles with the revolution speed of steel ball around x-axis；
    Step 2: analyzing the motion state of screw support bearings, outer ring raceway is fixed, and inner ring raceway is with ωiRotation, steel The ball centre of sphere is with angular velocity omegamRevolved round the sun around fixed coordinate system origin o, thus according to inner ring raceway absolute angular velocities ωiIn can obtaining, Outer ring relative to retainer relative angular velocity omegaim、ωomAnd the autobiography angular velocity omega of steel ballb：
    Step 3: according to the contact relation of steel ball and interior raceway, in rotating direction, sliding or cunning of the inner ring raceway relative to steel ball Dynamic speed uyiDetermined by the linear differential of raceway and steel ball, thus obtain uyiAnd steel ball is perpendicular to the sliding speed of rotating direction uxi；
    Step 4: similarly, sliding or cunning of the outer ring raceway relative to steel ball can obtain by the contact relation of steel ball and outer ring raceway Dynamic speed uyoAnd steel ball is perpendicular to the sliding speed u of rotating directionxo；
    Step 5: the wear-out life t of bearing is：
    <mrow> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>pe</mi> <mi>o</mi> </msub> </mrow> <mrow> <mo>(</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mo>/</mo> <mi>H</mi> <mo>)</mo> <msub> <mi>ZQ</mi> <mi>u</mi> </msub> </mrow> </mfrac> </mrow>
    Wherein,ux、uy's Value is uxi、uyiOr uxo、uyo, Qu taken ux、uyObtained maximum is substituted into after calculating, and a, b are Elliptical Contacts region length Half shaft length；QmaxRepresent the maximum of instantaneous normal direction load, ωsAutomatic rotary component for steel ball relative to raceway；X, y is contact Region any point,A values are aiOr ao, α values are αiOr αo, p taken a Obtained minimum value, K are substituted into after calculating with αsThe coefficient of waste between steel ball and raceway is represented, H represents Vickers hardness, and Z is represented The number of steel ball, eoRepresent end-play increment allowable.
  2. A kind of 2. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The step In seek ωx', ωy'And ωz'Specific method be：
    ωx'=ωbcosβcosβ' (1)
    ωy'=ωbcosβsinβ' (2)
    ωz'=ωbsinβ (3)
    Wherein β is the attitude angle of steel ball rotation axis and the angle, i.e. steel ball of x'o'y' planes；β ' is the steel ball axis of rotation in x'o' Projection and the angle of x' axles in y' planes.
  3. A kind of 3. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The step Relative angular velocity omega of the inside and outside circle relative to retainer is sought in twoim、ωomAnd the autobiography angular velocity omega of steel ballbSpecific method For：
    <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msup> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>-</mo> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> <mrow> <mn>1</mn> <mo>+</mo> <mfrac> <mrow> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>-</mo> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <msup> <msub> <mi>T</mi> <mi>o</mi> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> <msup> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;omega;</mi> <mi>b</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>&amp;omega;</mi> <mi>i</mi> </msub> </mrow> <mrow> <mfrac> <mrow> <msub> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>o</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> <mo>+</mo> <msub> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>o</mi> </msub> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <msub> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msup> <mi>cos&amp;beta;cos&amp;beta;</mi> <mo>&amp;prime;</mo> </msup> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>sin&amp;beta;sin&amp;alpha;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>-</mo> <msub> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mi>i</mi> </msub> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    In formula, Ti' for outer ring raceway pure rolling point is contacted on major axis with steel ball to the distance of the centre of sphere, To' it is inner ring raceway and steel ball Pure rolling point is contacted on major axis to the distance of the steel ball centre of sphere, αoFor steel ball and outer raceway contact angle, αiFor steel ball and interior raceway contact Angle.
  4. A kind of 4. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The step U in threeyiAnd uxiCircular be：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>y</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>m</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>-</mo> <mo>{</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> </msub> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mfrac> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>+</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </msub> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mfrac> <msub> <mi>sin&amp;alpha;</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>cos&amp;alpha;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>u</mi> <mrow> <mi>x</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mo>{</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>}</mo> <mo>&amp;times;</mo> <msub> <mi>&amp;omega;</mi> <msup> <mi>y</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, aiFor the major semiaxis length of elliptic contact surface projection；RiFor the radius of curvature of inner ring Contact Ellipse textured surface；dm For pitch diameter, its value is the half of inside and outside raceway diameter sum；DwFor steel ball size.
  5. A kind of 5. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The step Sliding or sliding speed u of the outer ring raceway relative to steel ball in fouryoAnd steel ball is perpendicular to the sliding speed u of rotating directionxo's Circular is：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>y</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>m</mi> </msub> <mn>2</mn> </mfrac> <msub> <mi>&amp;omega;</mi> <mrow> <mi>o</mi> <mi>m</mi> </mrow> </msub> <mo>+</mo> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> </msub> <msub> <mi>&amp;omega;</mi> <mrow> <mi>o</mi> <mi>m</mi> </mrow> </msub> </mfrac> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>+</mo> <mfrac> <msub> <mi>&amp;omega;</mi> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> </msub> <msub> <mi>&amp;omega;</mi> <mrow> <mi>o</mi> <mi>m</mi> </mrow> </msub> </mfrac> <msub> <mi>sin&amp;alpha;</mi> <mi>o</mi> </msub> <mo>-</mo> <msub> <mi>cos&amp;alpha;</mi> <mi>o</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mrow> <mi>o</mi> <mi>m</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>u</mi> <mrow> <mi>x</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>D</mi> <mi>w</mi> </msub> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msubsup> <mi>a</mi> <mi>o</mi> <mn>2</mn> </msubsup> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&amp;rsqb;</mo> <mo>&amp;times;</mo> <msub> <mi>&amp;omega;</mi> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, a0For the semi-minor axis length of elliptic contact surface projection；RoFor the radius of curvature of outer ring Contact Ellipse textured surface；ωom It is the relative retainer in outer ring or relative { o；X, y, z } coordinate system rotating speed.
  6. A kind of 6. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The Ks's Value is Ks≈1.77×10-8λ-1, wherein λ is film lubrication parameter.
  7. A kind of 7. screw support bearings wear-out life computational methods according to claim 1, it is characterised in that：The eoTake The 20% of initial play.
CN201711020623.5A 2017-10-26 2017-10-26 A kind of screw support bearings wear-out life computational methods Pending CN107784174A (en)

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