航空发动机高速滚珠轴承振动特性研究.pdf
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1、Chinese Journal of Turbomachinery第65卷,2023年第3期Http:/turbo- Vol.65,2023,No.3Vibration Characteristics of High-Speed Ball Bearing ofVibration Characteristics of High-Speed Ball Bearing ofAero-EnginesAero-Engines*Yun-bing Tang*Jing-xuan ZhangLing-ling ShiXiao-hu Xie(ChangzhouE&ETurbo-PowerCo.,Ltd.)Abst
2、ract:Ballbearingiswidelyusedasrotorsupporting.Itisanon-negligiblesourceofvibrationinaero-engines.Thevibrationcharacteristicsofthehighspeedballbearingarestudiedinthispaper.Bearingkinematicstheoryisappliedtodiscussthebasiccharacteristicsofballbearings.Thevibrationfactorscausedbyballbearingsareanalyzed
3、,andthenthevibrationmodelofballbearingsissetup.Theeffectoftheunbalance,theballpassagevibration,theradialclearanceand the surface waviness are considered.It is found that the ball passage vibration is excited by the contact forcebetween the balls and the races.Increasing the numbers of ball can reduc
4、e the vibration amplitude.The surfacewaviness which is caused due to the geometric imperfection of ball bearings is considered as one of the importantvibrationsourcesofbearingsystems.Keywords:AerospacePropulsionSystem;BallBearing;BallPassageVibration;SurfaceWavinessDOI:10.16492/j.fjjs.2023.03.0010*F
5、unding:National Natural Science Foundation of China(51775267)*Corresponding Author:Yun-Bing Tang,1IntroductionWith the development of science and technology,theperformance of aero-engines is improved constantly.Theball bearing is widely used in aero-engines.Its vibrationproperties exert important in
6、fluences on the dynamic charac-teristics of rotor systems,especially at a high speed.There-fore,the research on the vibration characteristics of ball bear-ings is essential in order to meet the development of the newtype aero-engine 1-5.As the rotor support,the ball bearing needs to bear andresist t
7、he vibration caused by external force.At the sametime,due to the influence of structure and manufacturingtechnology,ball bearing itself will also cause vibration dur-ing operations.The vibration of the ball bearing mainly in-cludes the vibration caused by structural characteristics andthe vibration
8、caused by manufacturing deviation of parts.The vibration caused by the structural characteristics in-cludes the deformation of the inner and outer rings of thebearing caused by the contact force of the rolling elementand the variable stiffness vibration caused by the radial loadof the bearing.The ma
9、nufacturing deviation of parts includesball element roughness,roundness,inner and outer ring wavi-ness,etc.Therefore,it is of great significance for the designand use of ball bearings to study the vibration characteristicsof bearings and their systems.The ball passage vibration which is also called
10、varyingcompliance vibration is studied by Sunnersj firstly 6.Thechaotic behavior and bifurcations can be observed in Ehrichand Tiwari s models 7-8.The studies undertaken by Tiwariinvolved the effect of radial internal clearances9.The effectof the surface waviness is considered by Nizami and Gunhee10
11、-12.The vibration caused by ball bearings is discussed inthis paper.The analytical model taking into account the un-balance,the ball passage vibration,the radial clearance andthe surface waviness altogether is set up.Newmark method isusedtosolvetheequationsandtheresultsareobtained13-14.2Equations of
12、 MotionThe relative motion between the balls and the races hasimportant influence on the vibration characteristics of ballbearings.Fig.1 shows the motion sketch of a ball bearing.ThereforeFig.1The motion sketch of a ball bearing 59Chinese Journal of TurbomachineryVa=Vi=idi2,Vc=Vo=odo2(1)Where,Vais t
13、he ball speed at the pointa,Vcis the ballspeed at the pointc,diis the inner race diameter anddoisthe outer race diameter.When there is no slipping of balls as they roll on the surfaceof races,the speed of the ball(Vb)can be expressed as fol-lows:Vb=Va+Vc2=Vi+Vo2(2)Where,Viis the speed of inner race,
14、Vois the speed of outerrace,iis the angle speed of inner race andois the angelspeed of outer race.Some assumptions are made.The inner race is rigidlyfixed to the rotor.The outer race is fixed rigidly to the sup-port and assumed to be stationary.Thereforei=,o=0(3)Where,is the speed of the bearing.Acc
15、ording to Eqs.(2)and(3),the angular velocity ofthe ball about the center of the inner race isb=Vb(di+do)/4=di(di+do)(4)As the ball bearing rotating,the angeljchanges withtime(Fig.1)and is given byj=2Nb(j-1)+bt(j=1,2,Nb)(5)Where,Nbis the number of the ball bearing and t is the time.The radial displac
16、ement(uj)at thejth ball is given asuj=xcosj+ysinj(6)Where,xandyare displacements of the center of the innerrace.Considering the internal radial clearance(),the con-tact deformation becomesuj=xcosj+ysinj-(7)3The Vibration Caused by Ball BearingA ball bearing is used as the rotor support.It needs toen
17、dure and resist the vibration caused by the exciting force.At the same time,the ball bearing will also excite vibrationby itself,because of the effect of the structure and the fabri-cation technology.The vibration of ball bearings is usuallycaused by the structure characteristics or by the manufactu
18、r-ing process.The vibration caused by structure characteristicsis mainly named as ball passage vibration.Surface waviness,roughness and roundness belong to the manufacturing pro-cess deviation.3.1Ball passage vibrationWhile the ball bearing is rotating,applied loads are sup-ported by a few balls res
19、tricted to a narrow load region.Fig.2shows the load of ball bearings in different time.Note thatthe stiffness of the bearing varies with the cage position.Asthe position of the balls changing with the applied load mov-ing from the loaded to the unloaded zone,the load distribu-tion on the shaft chang
20、es thus producing a relation mo-tion between the inner and outer race.This vibrationwhich is named as ball passage vibration is excited bythe contact force(ball passage force)between the ballsand the races.Ball passage vibration universally occurs in ball bear-ings which bear the radial load.It is g
21、enerated by the loadand the motion of bearings.The frequency of ball passage vi-bration(fvc)is related with the ball number and the anglespeed of the ball.It can be expressed as follows:fvc=vc2=bNb2(8)3.2Vibration due to surface wavinessSurface waviness,roughness and roundness are all thegeometric i
22、mperfection of ball bearings.With the develop-ment of the processing technique,the effects of the rough-ness and the roundness to the vibration are reducing,but theeffect of the surface waviness is still prominent.Althoughball bearings are perfectly manufactured without surfacewaviness,it may be gen
23、erated by load or operating condi-tions.Therefore,the surface waviness becomes an importantsource of the vibration in ball bearings.The surface waviness of ball bearings can be modeledby the sinusoid function 7.Fig.3 shows the surface wavi-ness of the race with the amplitude of the waviness and thew
24、aviness length.It can be expressed as follows:=psin2L(9)Where,pis the maximum amplitude of waviness andisthe waviness length.Take the inner race surface waviness as an example.The surface waviness of the inner race shows in Fig.4.Whereois the center of the ball bearing,bis the ball center,dmis the p
25、itch diameter.Considering the effect of the initial a-mplitude(T),the inner race surface waviness(i)can beexpressed as follows:i=T+()psin2L(10)Where,Tisreplacedbythedeflectionduetothepreload.The waviness length()is the length of the race cir-cumference divided by the waviness number.It can be ex-pre
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