质量不平衡转子系统发生碰摩后振动特性分析

1、VIBRATION CHARACTERISTICS ANALYSIS OF THERUB- IMPACT ROTOR SYSTEM WITH MASSUNBALANCE5 JIA Jiiilioiig, HANGTIancp101520 (Key Laboratory of Pi essiire Systems and Safety, Ministry of Education, East Cliina University of Science and Technology, ShangHai 200237) Abstract: Iii this paper, vibration chara

2、cteristics of a rub-inipact Jeffcott rotor system excited by mass unbalance including the eccentric mass and the initbl permanent deflection are investigated. Tlirougli the niiiiieiical calculation, rotating speeds, mass eccentricities, initial p eriiianent deflections and p liase angles between tli

3、e eccentric mass directi on and the rotor initial peniiaueiit deflection direction are used as control parameters to investigate their effect on the nib-iiiipact rotor system with tlie help of bifiu cation diagrams Poiiicare maps, frequency spectnuiis and orbit maps. Result shows that these two kind

4、s of mass imbalance have gi eat but different effect on tlie dyiiaiiiic characteristic of tlie nibbing rotor systeui, Diffeieiit motion chai acted sties appear with the varying of tliese control parameters and complicated motions such as periodic and quasi-periodic vibrations are obseived Correspond

5、ing results can be used to diaguose the nib-iiiipact fault and dea ease tlie effect of mb impact in tlie rotor system witli mass unbalance. Keywords: Rub-impact rotor system; Mass unbalance; Nonlinear motion 0 IntroductionMass unbalance of the rotor is the main factor to increase vibration and bring

6、 unstable characteristics to the whole rotor system 1-2. Since the rotor-stator nib is one of the main faults for large rotary machines, it has attracted great concern and lots of research work has been done by many researchers. Juiiyi Cao 3 investigated nonlinear dynamic characteristics of nib-iinp

7、act rotor system with fractional order damping. From the study, van OUS complicated dynamic behaviors and types of routes to chaos weie found, including period doubling bihircatioit sudden transition and quasi-periodic from periodic motion to chaos. Jawaicti 4 investigated dynamics of a rigid rotor

8、supported by load-sharing between magnetic and auxiliary bearings for a range of realistic design and operating parajueters. Many phenoinena were found and studied Weiuiung Zhang 5 carried out an analytical investigation on the stability of the nib solutions of the rotor system in MEMS. Nuiiieiical

9、calculation deiiioiistialed the complex nonlinear motion fonns in tliis system.Altliougli Hindi work has been done respectively on the research of rotor mass unbalance and rotor-stator nibbing imp act, the vibration characteristics of this kind of nib-iiiipact rotors with mass imbalance have rarely

10、been studied specially in the literature. Due to mass unbalances ubiquity, great effect on the vibration of the nib-iinpact rotor system and rubs large tlireat to the safe operation of the rotor system. Therefore, in tliis papeT attention is paid to the research of vibration characteristics of nib-i

11、m pact rotors with mass imbalance. First-order headline 25 30 351 Physical model and equations40 Riib-iinpact forces Iii the O-xy coordinate system are 6: Fx=-FNcos7-l-FTsiir/=-(l-lir)Kr(x-|iy) (1) Fy=-FNsixi7-Frcos*/=-(l-lir)Kr(ix+y) when rh, the nib happens. Carrying out the Foundations: New Teach

12、er Fluid for Doctor Station, the Ministry of Ediicatioii(20090074120005).Brief autlior introduction: JIA Jiulioug, (1979-) Jemale,Associate professoraiii reseaiclrliitegrity of stiiictiire. E-mail: jliaecust,editai uoiidinieiisional procedure, tlie govemiug iiiotiou equations are as follows:*=rb1.0,

13、 tlie nib doesift ha ppen、and the iioudimeiisioual luotiou equations are: Wlieu R45*+2sX-bc*=o2cosoT+rOcos(i)T+c(0)x *+2iy*4y=ec)2sinfc)T+r*0sin(jT+a0)y(2)=rlPl 0, the nib happeiis. and the nondinieusioiial motion equations are: Wlieii R(1 一R J (x+2 事“七、+K-py J=32 coscoT+rO cos(ijT+a0)x2*+2y+y+K(l-R

14、)(|ix-Fy)=OsinoT+r0sin(c3T+a0)y=KK,Jk/mC2oM, t)= the uatiiral frequency of=xh, y=yh, KWhere:x r00500=1011, T=G)Ot, -ddT. the shaft t)=Q0 the fi eqiiency ratio, e=emh、rSince the iiondiiiiensioiial goveniing equations of motion have been got above, they are &=fu). Tlieii the fourtli-order transfeiied

15、into a set of first order differential equations ii 55RungeKutta method is used to integrate this set of equations. According to the analysis need.some paraineters can be used as tlie control paraineters siich as the rotor rotating speed, the initial pennanent deflection and so on. while otlier para

16、ineters keep fixed during every time of calculation. To get the stable result, a small integration step has to be chosen to avoid the ininierical divergence at the point where derivatives of Fx and Fy are discontiniioiis. Iii tliis paper, the integration step is chosen to be 2nZ5OO, i.e., witliin on

17、e period, tliere are 500 times of integral calculation. Generally, long time marcliing computation is required to obtain a convergent orbit. Iii tliis paper, during every calculation, results of the first 500 periods are abandoned and then results of the next 100 periods are got to cairy out various

18、 kinds of analysis. To study tlie vibration characteristics of tlie nibbing rotor system with mass unbalance, bilui catioii diagrams. Poincare maps, fi eqiieiicy spectnuiis and orbit maps are employed Iliey are all usehil and effective ways to illustrate the motion behavior of the rotor system.602 N

19、mnerical simulation of motions of the rotor system652-1 Effect of rotor rotating speedsAltliougli many paianieters siich as the system damping and the fiictional coefficient between the rotor and the stator can be used to investigate tlie vibration cliaractensties of the nib-iiiipact system, the mos

20、t coiniiion and usefill paraineter used is the rotor rotating speed, Tlie whole starting process can be observed by using the rotating speed to siiinilate the nib-inipact rotor-02OS t U ；9X00 7023.11 1 .11丄.1i 11.-1 -HY-L.丄.J1n111-L -J -J,1X1 L 1 A.1 -J,111111i .1( h.丄. J11111-J-1 -J -111*1 J J .k .

21、丄.111 1 .-1 .亠k匚丄.J.051IS22$9X-fi -1-act rotor system keeps synchronous with period-one for the initial deflection ratio ranging fioin 0.0 to *00.8 at co11.0. Further deinonstiation is shown in Fig.9 with r*0 is from 0.0 to As shown in Fig7(b), at(i)=l-5 when tlie initial pennaiient deflection ratio

22、 r0.7, the motion is period-one. From 0,7 to liiglier values of the initial peniiaiieiit deflection ratio, *0=0.8 at the motion keeps quasi-periodic. Further demonstration is sliowii ill Fig.lO with r165 0= Effect of phase angles between the eccentric mass direction and the rotor deflection d

23、irectionAs shown iu above eqiiatious (2) and (3), the pliase angle between the ecceuhic mass directi OU and tlie rotor deflection direction is an important factor to influence the amplitude of the170rotor center, so its ineaniiignil to study its effect on the nib-inipact vibration characteristics of

24、 the rotor system. Fig, 11 are tlie bifurcation diagrams of tlie rotor vibration at different rotating speed ratio u using the phase angle aOI I tw I In J I a i 60 MUfltIto175(c) 0=1.8 (d) 0=2.00Fig. 11 Bifurcation diagram usiugaOQ as the control parauietei180From Figll(a). when 0=1.0, the motion of

25、 tlie rub-impact rotor system keeps synchronous with period-one for the calculating phase angle ranging from 0.0 tol80o-From Fig.ll-(b), when 0=1.5, for the phase augle from 0.0 tol05o, the motion is quasi- periodic. Fonn 95otol80o, the6 http:/www.papeiedu.cu185 motion transits to period-oue motion.

26、 Shown mFig.ll.(c), wlien o increases up to L& tlie motion keeps qiiasi-periodic for the phase angle ranging from 0.0 to86o. then transits to period-one for the rest phase angle. In Fig-11, (d), when o=2-0, the quasi- periodic motion range is for the phase angle from 0.0 to75o, the motion for the re

27、st pliase angle is period-one- A cleartrend can be seen fi oni above analysis that with the increase of rotating speeds, the quasi-periodic inotioii range declines, correspondingly tlie period-oiie motion range increases.3 Conclusions190 111 tliis paper, vibration characteiisties of a nib-iinpact Je

28、ffcott rotor system excited by mass unbalance including the eccentric mass and tlie initial pennanent deflection are investigated- Frominuiierical calculation, rotating speeds, mass eccentricities, initial pennaneiit deflections and phase angles between the eccentric mass direction and rotor iiiitia

29、l pennaneiit deflection direction are used as the control paraineters to investigate their effect on the nib-iiiipact rotor system. Result shows that these two kinds of mass unbalance: eccentric mass and initial pennaneiit deflection has great but different effect on the dyiiaiiiic characteristic of

30、 the nibbing rotor system. Periodic, quasi-periodic iiiotioiis appear witli the varying of these control parametei s. Because the quasi-periodic motion is the route to chaos, it indicates tliat the system has tlie potential to become chaotic. Tliese results can be used to diagnose tlie rub fault and

31、 direct the work to deaease the effect of nib impact in the rotor system with mass unbalance.References1 Liao Y H, and Zliaiig P. Unbalance related rotor precession behavior analysis and modification to tlie holobalaiiciug methodJ. Mechanism andMadiine Theory 45,601- 610. 2010.2 Jal an A K and Mohaiity A R- Model based fault diagnosis of a rotor-beariug systeni for misalignment and unbalance luider steady-state condition卩.Journal of Soun