质量不平衡转子系统发生碰摩后振动特性分析.pdf

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1、-1-VIBRATION CHARACTERISTICS ANALYSIS OF THE RUB-IMPACT ROTOR SYSTEM WITH MASS UNBALANCE#JIA Jiuhong,HANG Tianqi*5(Key Laboratory of Pressure Systems and Safety,Ministry of Education,East China University of Science and Technology,ShangHai 200237)Foundations:New Teacher Fund for Doctor Station,the M

2、inistry of Education(20090074120005).Brief author introduction:JIA Jiuhong,(1979-),Female,Associate professor,Main research:Integrity of structure.E-mail: Abstract:In this paper,vibration characteristics of a rub-impact Jeffcott rotor system excited by mass unbalance including the eccentric mass and

3、 the initial permanent deflection are investigated.Through the numerical calculation,rotating speeds,mass eccentricities,initial permanent deflections and phase 10 angles between the eccentric mass direction and the rotor initial permanent deflection direction are used as control parameters to inves

4、tigate their effect on the rub-impact rotor system with the help of bifurcation diagrams,Poincare maps,frequency spectrums and orbit maps.Result shows that these two kinds of mass unbalance have great but different effect on the dynamic characteristic of the rubbing rotor system.Different motion cha

5、racteristics appear with the varying of these control parameters,and 15 complicated motions such as periodic and quasi-periodic vibrations are observed.Corresponding results can be used to diagnose the rub-impact fault and decrease the effect of rub impact in the rotor system with mass unbalance.Key

6、words:Rub-impact rotor system;Mass unbalance;Nonlinear motion 20 0 Introduction Mass unbalance of the rotor is the main factor to increase vibration and bring unstable characteristics to the whole rotor system 1-2.Since the rotor-stator rub is one of the main faults for large rotary machines,it has

7、attracted great concern and lots of research work has been done by many researchers.Junyi Cao 3 investigated nonlinear dynamic characteristics of rub-impact rotor 25 system with fractional order damping.From the study,various complicated dynamic behaviors and types of routes to chaos were found,incl

8、uding period doubling bifurcation,sudden transition and quasi-periodic from periodic motion to chaos.Jawaidi 4 investigated dynamics of a rigid rotor supported by load-sharing between magnetic and auxiliary bearings for a range of realistic design and operating parameters.Many phenomena were found a

9、nd studied.Wenming Zhang 5 carried 30 out an analytical investigation on the stability of the rub solutions of the rotor system in MEMS.Numerical calculation demonstrated the complex nonlinear motion forms in this system.Although much work has been done respectively on the research of rotor mass unb

10、alance and rotor-stator rubbing impact,the vibration characteristics of this kind of rub-impact rotors with mass unbalance have rarely been studied specially in the literature.Due to mass unbalances 35 ubiquity,great effect on the vibration of the rub-impact rotor system and rubs large threat to the

11、 safe operation of the rotor system,Therefore,in this paper attention is paid to the research of vibration characteristics of rub-impact rotors with mass unbalance.First-order headline 1 Physical model and equations Rub-impact forces In the O-xy coordinate system are 6:40 cossin(1h)()sincos(1h)()xNT

12、ryNTrFFFr KxyFFFr Kxy=+=+(1)when rh,the rub doesnt happen.When rh,the rub happens.Carrying out the-2-nondimensional procedure,the governing motion equations are as follows:When 1.0Rr h=,the rub doesnt happen,and the nondimensional motion equations are:200200 2coscos()2sinsin()xxxTrTyyyTrT+=+=+(2)45

13、When 1.0Rr h=,the rub happens,and the nondimensional motion equations are:200200 2(1 1)()coscos()2(1 1)()sinsin()xxxKR xyTrTyyyKRxyTrT+=+=+(3)Where:xx h=,yy h=,rKKK=,02CM=,0K M=the natural frequency of the shaft,0=the frequency ratio,meh=,00 rr h=,0Tt=,d dT=.Since the nondimensional governing equati

14、ons of motion have been got above,they are 50 transferred into a set of first order differential equations()uf u=&.Then the fourth-order Runge-Kutta method is used to integrate this set of equations.According to the analysis need,some parameters can be used as the control parameters such as the roto

15、r rotating speed,the initial permanent deflection and so on,while other parameters keep fixed during every time of calculation.To get the stable result,a small integration step has to be chosen to avoid the 55 numerical divergence at the point where derivatives of xF and yF are discontinuous.In this

16、 paper,the integration step is chosen to be 2/500,i.e.,within one period,there are 500 times of integral calculation.Generally,long time marching computation is required to obtain a convergent orbit.In this paper,during every calculation,results of the first 500 periods are abandoned,and then result

17、s of the next 100 periods are got to carry out various kinds of analysis.To study the 60 vibration characteristics of the rubbing rotor system with mass unbalance,bifurcation diagrams,Poincare maps,frequency spectrums and orbit maps are employed.They are all useful and effective ways to illustrate t

18、he motion behavior of the rotor system.2 Numerical simulation of motions of the rotor system 2.1 Effect of rotor rotating speeds 65 Although many parameters such as the system damping and the frictional coefficient between the rotor and the stator can be used to investigate the vibration characteris

19、tics of the rub-impact system,the most common and useful parameter used is the rotor rotating speed.The whole starting process can be observed by using the rotating speed to simulate the rub-impact rotor system.The parameters used during computations are:=0.12,K=30.0,0.12=.70 00.511.522.53-0.6-0.4-0

20、.200.20.4Rotating speed ratioX 00.511.522.53-0.200.20.40.60.811.2Rotating speed ratioX(a)=0.2 (b)0r=0.8,0/4=;-3-00.511.522.53-0.500.511.5Rotating speed ratioX(c)0r=0.8,0/4=,=0.2 Fig.1 Bifurcation diagram 75 Fig.1.(a)is the bifurcation diagram of the rub-impact rotors vibration which is excited only

21、by the eccentric mass.Fig.1.(b)is the bifurcation diagram of the rub-impact rotors vibration which is excited only by the initial permanent deflection.Fig.1.(c)is the bifurcation diagram of the vibration excited by these two kinds of mass unbalance jointly.Very clearly from Fig.1,80 different shapes

22、 of three diagrams demonstrate that the eccentric mass and the initial permanent deflection have different influence to the vibration of the rubbing rotor system and both contribute a lot to the vibration characteristics of the rub-impact rotor system.As shown in Fig.1.(a),the rub-impact motion exci

23、ted only by the eccentric mass keeps synchronous with period-one for the whole calculating rotating speed range.Fig.2 shows that only one point is correspondingly shown 85 in the Poincare map,only one peak appears in the frequency spectrum,and the orbit of the rotor center is an ellipse.All these fu

24、rther demonstrate the motion is period-one motion.From Fig.1.(b),it can be seen that when the rotating speed ratio is from 0.0 to 1.1,the motion is period-one.From 1.1 to 1.6,the motion is quasi-periodic,then the motion transits to period-one motion again for the higher speed ratios.This can be seen

25、 from Fig.3.It illustrates the rubbing motion excited only by 90 the initial permanent deflection at=1.2.The Poincare map is a closed circle,several peaks appear in the frequency spectrum,and the rotor center orbit is irregular.These prove that the motion is quasi-periodic.From Fig.1.(c),it can be s

26、een that when the rotating speed ratio is from 0.0 to 1.1,the motion is period-one,from 1.1 to 2.4,the motion is quasi-periodic,then the motion transits to period-one 95 motion again for the higher speed ratios.This motion type is clearly different from the one excited only by the eccentric mass in

27、Fig.1.(a)and the one excited only by the initial permanent deflection in Fig.1.(b).Fig.4 demonstrates that the motion in this case at=1.5 is quasi-periodic as analyzed above.-1.5-1-0.500.51-1-0.500.511.5XX -0.4-0.200.20.4-0.4-0.3-0.2-0.100.10.20.30.4XY 01234500.050.10.150.20.250.30.350.4FrequencyX 1

28、00(a)Poincare map (b)orbit (c)spectrum of frequency Fig.2 Motion excited by=0.2 at=1.5 -4-0.90.9511.051.1-0.8-0.6-0.4-0.200.2XX -1.5-1-0.500.511.5-1.5-1-0.500.511.5XY 0246800.20.40.60.81FrequencyX(a)Poincare map (b)orbit (c)spectrum of frequency 105 Fig.3 Motion excited by 0r=0.8,0/4=at=1.2 0.40.60.

29、811.21.4-1.5-1-0.500.511.5XX -1.5-1-0.500.511.5-1.5-1-0.500.511.5XY 01234500.10.20.30.40.50.60.70.8FrequencyX(a)Poincare map (b)orbit (c)spectrum of frequency Fig.4 Motion excited jointly by and 0r at=1.5 110 2.2 Effect of the eccentric mass Eccentric mass is one of the mass unbalance to excite the

30、motion of the rotor system,so its essential to study its effect on dynamic characteristic of the rub-impact rotor system.Fig.3 are bifurcation diagrams of rotors vibration at different rotating speeds using the mass eccentricity 115 ratio as the control parameter.The initial permanent deflection is

31、not included in this analysis and is set as 0.0.0.050.10.150.20.250.30.3500.10.20.30.40.50.60.70.8Mass eccentricity ratioX 0.050.10.150.20.250.30.35-0.5-0.20.10.40.71Mass eccentricity ratioX(a)=1.0 (b)=1.5 Fig.5 Bifurcation diagram usingas the control parameter 120 -0.500.511.52-0.500.511.52XX -1.5-

32、1-0.500.511.5-1.5-1-0.500.511.5XY 01234500.20.40.60.81FrequencyX(a)Poincare map (b)orbit (c)spectrum of frequency Fig.6 Motion with=0.3 at=1.0 125 -5-0.40.50.60.70.80.40.60.811.21.41.61.82XX -1.5-1-0.500.511.5-1.5-1-0.500.511.5XY 01234500.20.40.60.81FrequencyX(a)Poincare map (b)orbit (c)spectrum of

33、frequency Fig.7 Motion with=0.3 at=1.5 130 As shown in Fig.5.(a),when the rotating speed ratio is not high like 1.0,the motion of the rub-impact rotor system keeps synchronous with period-one for the whole calculating range.Further demonstration is shown in Fig.6 with=0.3 at=1.0 that only one point

34、is correspondingly shown in the Poincare map,only one peak appears in the frequency spectrum,and the orbit of the rotor center is an ellipse.All these further demonstrate the motion is 135 period-one motion.As shown in Fig.5.(b),at=1.5 when the mass eccentricity ratio is from 0.0 to 0.26,the motion

35、is period-one.From 0.26 to higher values of the mass eccentricity ratio,the motion keeps quasi-periodic.In Fig.7 with=0.3 at=1.5,the Poincare map is a closed circle,several peaks appear in the frequency spectrum,and the rotor center orbit is irregular.These prove that the 140 motion is quasi-periodi

36、c.2.3 Effect of the initial permanent deflection The initial permanent deflection is another one of the mass unbalance to excite the motion of the rotor system,its also important to study its effect on dynamic characteristic of the rub-impact rotor system.Fig.8 is bifurcation diagrams of rotors vibr

37、ation at different rotating speeds using 145 the initial permanent deflection ratio 0r as the control parameter.The mass eccentricity is not included in this analysis and is set as 0.0.0 is fixed as/4.0.20.40.60.810.30.50.70.91.1Initial deflection ratioX 0.20.40.60.81-0.500.511.5Initial deflection r

38、atioX(a)=1.0 (b)=1.5 Fig.8 Bifurcation diagram using0ras the control parameter 150 -0.500.511.52-1.5-1-0.500.51XX -1.5-1-0.500.511.5-1.5-1-0.500.511.5XY 01234500.20.40.60.81FrequencyX(a)Poincare map (b)orbit (c)spectrum of frequency Fig.9 Motion with0r=0.8 at=1.0-6-0.70.80.911.11.21.3-1-0.500.51XX -

39、1.5-1-0.500.511.5-1.5-1-0.500.511.5XY 01234500.20.40.60.81FrequencyX 155(a)Poincare map (b)orbit (c)spectrum of frequency Fig.10 Motion with0r=0.8 at=1.5 As shown in Fig.8.(a),when the rotating speed ratio is at 1.0,the motion of the rub-impact rotor system keeps synchronous with period-one for the

40、initial deflection ratio ranging from 0.0 to 160 1.0.Further demonstration is shown in Fig.9 with 0r=0.8 at=1.0.As shown in Fig.7.(b),at=1.5 when the initial permanent deflection ratio 0r is from 0.0 to 0.7,the motion is period-one.From 0.7 to higher values of the initial permanent deflection ratio,

41、the motion keeps quasi-periodic.Further demonstration is shown in Fig.10 with 0r=0.8 at=1.5.165 2.4 Effect of phase angles between the eccentric mass direction and the rotor deflection direction As shown in above equations(2)and(3),the phase angle between the eccentric mass direction and the rotor d

42、eflection direction is an important factor to influence the amplitude of the rotor center,so its meaningful to study its effect on the rub-impact vibration characteristics of the 170 rotor system.Fig.11 are the bifurcation diagrams of the rotor vibration at different rotating speed ratio using the p

43、hase angle 0 as the control parameter with 0r=0.8,=0.2.0306090120150180-0.20.10.40.711.3Phase angleX (a)=1.0 (b)=1.5 0306090120150180-0.5-0.20.10.40.711.31.5Phase angleX 0306090120150180-0.5-0.20.10.40.711.31.5Phase angleX 175(c)=1.8 (d)=2.0 Fig.11 Bifurcation diagram using0(o)as the control paramet

44、er From Fig.11.(a),when=1.0,the motion of the rub-impact rotor system keeps synchronous with period-one for the calculating phase angle ranging from 0.0 to180o.From Fig.11.(b),when 180=1.5,for the phase angle from 0.0 to105o,the motion is quasi-periodic.Form 95oto180o,the http:/-7-motion transits to

45、 period-one motion.Shown in Fig.11.(c),when increases up to 1.8.the motion keeps quasi-periodic for the phase angle ranging from 0.0 to 86o,then transits to period-one for the rest phase angle.In Fig.11.(d),when=2.0,the quasi-periodic motion range is for the phase angle from 0.0 to75o,the motion for

46、 the rest phase angle is period-one.A clear 185 trend can be seen from above analysis that with the increase of rotating speeds,the quasi-periodic motion range declines,correspondingly the period-one motion range increases.3 Conclusions In this paper,vibration characteristics of a rub-impact Jeffcot

47、t rotor system excited by mass unbalance including the eccentric mass and the initial permanent deflection are investigated.From 190 numerical calculation,rotating speeds,mass eccentricities,initial permanent deflections and phase angles between the eccentric mass direction and rotor initial permane

48、nt deflection direction are used as the control parameters to investigate their effect on the rub-impact rotor system.Result shows that these two kinds of mass unbalance:eccentric mass and initial permanent deflection has great but different effect on the dynamic characteristic of the rubbing rotor

49、system.Periodic,195 quasi-periodic motions appear with the varying of these control parameters.Because the quasi-periodic motion is the route to chaos,it indicates that the system has the potential to become chaotic.These results can be used to diagnose the rub fault and direct the work to decrease

50、the effect of rub impact in the rotor system with mass unbalance.200 References 1 Liao Y H,and Zhang P.Unbalance related rotor precession behavior analysis and modification to the holobalancing methodJ.Mechanism and Machine Theory 45,601-610.2010.2 Jalan A K and Mohanty A R.Model based fault diagnos