转子动力学发展与主要问题.

1、A Brief History andState of the Art of Rotor DynamicsByl>r. Rajh TiwarlDvpurtmeM of Mechanical EngineeringIndian Institute of Technology* GuMahati 781039Under AICTtL Spon.red Q1P Short l erm Course ohTheory & Practice of Rotor Dynamics(15-19I IT GuwahatiDr R TiuwiiniOutline of the Presentatio

2、n Inlruductiovi arid Definition Historyfrom Rakine (1869) to Jeffcott (1919)from Stodola (1924) to Lund (1964)from Dimentberg (1965) to till now Development of RotoDynamics Analysis ToolsSoftwares for Rotor Dynamics AnalysisDr R Tiuwi miwAriCdZgeuk iniOutline of the Presentation Dynamic Balancing of

3、 Rotors Condition Monitoring of Rotating Machineries Con elusions & Recent T rendsDr R Tiuwiin»Introductio n A brief history of rotor dynamics field has been documented in the present review paper. It reviews early development of simple rotor models, analyses tools, and physical interpretat

4、ions of various kind of instabilities in rotor-bearing systems. It also reviews developments of analysis methods for the continuous and multi-degrees-ol freedom systems that allowed practicing engineers to apply these methods to real turbomachineries.The paper also summaries work on dynamic balancin

5、g of rotors, vibration based cond帀oning monitoring, and recent trends in the area of rotor dynamics.Dr R Tiuwi 仮iunriFiZcmct in)Introduction A rotor is a body suspended through a set of cylindrical hinges or bearings that allow it to rotate freely about an axis fixed in space- Engineering components

6、 concerned with the subject of rotor dynamics are rotors in machines, especially of turbines, generators motors compressors, blowers and the like. The parts of the machine that do not rotate are referred to with general definition of stator. Rotors of machines have, while in operation, a great deal

7、of rotational energy, and a small amount of vibrational energy.Dr R TiujriiniIntroductio n It is very evident from the fact that a relatively small turbine propels a huge aircraft.The purpose of rotor dynamics as a subject is to keep the vibrationai energy as small as possible. In operation rotors u

8、ndergoes the bending, axial and torsional vibrations.一?History of rotor dynamicsfrom Rakine (1869) to Jeffcott (1919) Rotor dynamics has a remarkable history of developments, largely due to the interplay between its theory and its practice, Rotor dynamics has been driven more by its practice than by

9、 its theory. This statement is particularly rele/ant to the early history of rotor dynamics Research on rotor dynamics spans at least 14 decades of history.Dr R Tiuwi (ftiuariwiitjiefikK iniSingle Mass Rotor Models乞=48£7心A flrxihk rotor mounted on rigid bearingsA rigid rot(»r mounted on fl

10、exible ben ringsF=F° sindXAn c(|uivnknt single degree orrrecdomprinmass systemDr « TiuMiini Rankine (1869) performed the first analysis of a spinning shaft He chose a two-degrees-of-freedom model consisted of a rigid mass whirling in a orbit, with an elastic spring acting in the radial die

11、ction. He predicted that beyond a certain spin speed ： the shaft is considerably bent and whirls around in this bent form： He defined this certain speed as the whirling speed of the shaft. In fact, it can be shown that beyond this whirling speed the radial defection of Rankine*s model increases with

12、out limit.Rankhic rulvr mvdvl dcjrcv rrtrdotii H|>rin|t-ntMwS roh»t model) Today, this speed would be called the threshold speed for divergent instability However, Rankine did add the term whirling to the rotor d 师$国血敝watKuia砒.Krrc hixl) di味mm of the iiNMirl Rankme s neglect of Coriolis acce

13、leration led to erroneous conclusions that confused engineers for one-half century. Whirling refers to the movement of the center of mass of the rotor in a plane perpendicular to the shaft.A critical speed occurs when the excitation frequency (e.g.t the spin speed of unbalnced shaft) coincides with

14、a natural frequency： and can lead to excessive vibration amplitudes3=% =Dr R Tiuwi mhMrieiiy in)A Jcffcott (or Laval) rotor model in general whirling motionDr R Tiuwi mhMrieiiy in) The turbine built by Parsons in 1884 (Parsons, 1948) operated at speeds of around 18.000 rpm. which was fifty times fas

15、ter than the existing reciprocating engineIn 1883 Swedish engineer de Laval developed a single-stage steam impulse turbine (named after him) for marine applications and succeeded in its operation at 42,000 rpm He aimed at the self-centering of the disc above the critical speed, a phenomenon which he

16、 intuitively recognized He first used a rigid rotorf but latter used a flexible rotor and showed that it was possible to operate above critical speed by operating at a rotational speed about seven times the critical speed (Stodola, 1924).Dr R TiuMini It thus became recognized that a shaft has severa

17、l critical speeds and that under certain circumstances these were the same as natural frequencies of a non-rotating shaftDunkerley (1895) found, as a result of nu merous measurements, the relationship known Sday by that of Southwell, by which the fundamental critical speed can be calculated, even fo

18、r complicated cases.Dr R TiwifiiniThe first sentence of Dunkerleys paper reads, "It is well known that every shaft, however nearly balanced, when driven at a particular speed, bends, andt unless the amount of deflection be limited, might even break, although at higher speeds the shaft again run

19、s true This particular speed or critical speed depends on the manner in wnich the shaft is supported, its size and modulus of elasticity, and the sizes, weights and positions of any pulleys it carries? This was the first use of the term criticai speed for the esonance rotational speed Even with the

20、general knowledge of critical speeds, the shaft behaviour at any general speed was still unclear but more was learnt from the calculation of unbalance vibrations, as given by Fdpp I (1 895)Dr R Tiuwi (rtiwAriuriitgenet ini Foppl used an undamped model to show that an unbalanced disc would whirl sync

21、hronously with th© heavy side flying out when the rotation was subcritical and with the heavy side flying in when the rotation was supercritical.Also the behaviour of Lavat rotors (1889) at high speed was con firmed by his theory It is regrettable that what Dunkerley regarded as well known was

22、actually little known.Also practitioners of that day were not aware of the 1895 analysis by the German civil engineer Foppl who showed that a rotor model exhibited a stable solution above Ran kinds whirling speed.Dr R TiuwiiniSyclMoiiaiM wMK iMBayyrtiMaHying In）e The change in phase between the forc

23、e and the response is also shown in Figure below for ihree difference spin speeds i.e. below the critical speed, at the critical speed and above the critical speed.Phase angles, between the foivc iUMl response vcctorx hdew critical speedPIum:between lheforve and ivp<mxr vevko ai critical speedFha

24、v angles bciwwn the orc© 4iid rvqptxiy： vcc<oc> aMvcchtical «pced9»叫）Dr R Tiuwi 仮ini We can not blame them too much since Foppl published his analysis in Der Civiiingenieur, a journal that was probably not well known by contemporary rotor dynamicists.More telling was about the a

25、pparent indifference to the practical work of the Swedish engineer, De Lavalt who in 1889 ran a single stage steam turbine at a supercritical speedDr R Tiuwi 仮iniOne Gan speculate that engineers of the day laboured under a con fusion of concepts equati ng Rankings whirling speed (for prese nt day it

26、 is the threshold speed for diverge nt instability) with Dunkerley's critical speedThis was particularly unfortunate since Rankine was far more emin©rrt than Dunkerley and. as a result, his dire predictions were widely accepted and became responsible for discouraging the development of high

27、 speed rotors for almost 50 years (1869 1916).It was in England in 1916 that things came to the end. Kerr published experimental evidenee that a second critical speed existed, and it was obvious to all that a seco nd critical speed could only be attained by the safe traversal of the first critical s

28、peed-Dr R ThiMiniThe Royal Society of London then commissioned Jeffcott to resolve this conflict between Rankinet theory and the practice of Kerr and de Laval. The first recorded fundamental theory off rotor dynamics can be found in a classic paper of Jeffcott in 1919, in a place where it was more l

29、ikely to be read by those interested in rotor dynamics. Jeffcott confirmed FoppPs prediction that a stable supercritical solution existed and he extendod FoppPs analysis by including external damping (i.e., damping to ground) and showed that the phase of the heavy spot varies continuously as the rot

30、ation rate passes through the critical speed- There is no evidence that Jeffcott was aware of Fdppfs prior work; in fact, Jeffcotfs paper does not contain a singlereference.Dr R ThiMiniDr R Tiuwi 仮iniDr R Tiuwi 仮iniio110*10"152025X35Frequency (Hz)t二fc3M?so1I14厶34 'h1t1t116202S30%40U)Frrquft

31、ncy (bU)Experimental and estimated amplitude and phase responses Dr R Tiujri(rtiwAri0iMf.efne< ini We can appreciate Jeffcotts great contributions if we recall that a flexible shaft of negligible mass with a rigid disc at the midspan is called a Jeffcott rotor (some times it is called the Laval-F

32、dppl-Jeffcott rotor).The bearings are rigidly supported, and viscous damping acts to oppose absolute motion of the disc. This simplified model is also called the Laval rotor named alter de Laval.Dr R Tiuwi 仮iniJeffcott RotorvDr R Tiuwiin)Stodola (1924) to Lund (1964) Developments made in rotor dynam

33、ics up to the beginning of the twentieth century are detailed in the masterpiece book written by Stodola (1924). Among other things, this book includes the dynamics of elastic shaft with discs, the dynamics o1 continuous rotors without considering gyroscopic moment. the secondary resonance phenomeno

34、n due to gravity effect, the balancing of rotors, and methods of determini ng approximate values of critical speeds of rotors with variable cross sections. He presented a graphical procedure to calculate critical speeds, which was widely used He shewed that these supercritical solutions were stabili

35、zed by Coriolis accelerations (which eventually gives gyroscopic effects). The unwitting constraint of these accelerations was the defect in Rankine*s model. It is interesting to note that Rankine's model is a sensible one for a rotor whose stiffness tri one directron is much greater than its st

36、iffness in the quadrature direction. Indeed, it is now well known that such a rotor will have regions of divergent instability. It is less well known that Prandtl (1918) was 1he first to study a Jeffcott rotor with a non-circular cross-section (i.e., elastic asymmetry in the rotor). In Jeffcott'

37、s analytical model the disk did not wobble As aresult, the angular velocity vector and the angular momentum vector were colinear and no gyroscopic moments were generated Dr R Tiujriini(u) A simpty supported shaft uidi a disc at the mid-span(b) A simply supported shaft with a disc iier the bearing(c&

38、gt; A camilever shaft with u point disc al the free endV(d) A cantilever shaft with a rigid disc al lhe free endDr R Tiuwi (rtiwariwihfi/fiKf iniGyroscopic effectsA Jeffcott r<Mr u it h u disc from the midspam in ihc y-7 planeFigure 5 23 Disc element in x-y planeFtyure 5.29 Emk tn"/ plxii; r

39、tiwariSnijemet iniDr R Tiuwi miueri®iitgerw in)Dr R Tiuwi miueri®iitgerw in)This restriction was removed by Stodola (1924). Natanzon (194& 1952), Bogdanoff (1947), Green (1948) and Foppl (1948) studied effect of gyroscopic moment on natural frequencies and critical speedsThe gyroscopic

40、 moment has the effect of making the natural frequencies dependence on rotor speed, while the same time doubling their number. Along with other parameters, the ratio of diametral to polar moment of inertia plays an important role.Dr R Tiuwi miueri®iitgerw in)Campbell Diagram05001000150020002500

41、3000SpinSpooa (radtc)Campbell Diagram for nMor bearing systemDr R Tixiini About a decade latter (1933), the study of asymmetrical shaft systems and asymmetrical rotor systems beqan. The former are systems with a directional in the shaft stiffness and the latter are those with a directional d iff ere

42、 nee in rotor inertia. Two-pole generator rotors and propeller rotors are examples of such systems As these directional differences rotate with the shaft, terms with time-varying coefficients appear in the governing equationsThese systems therefore fall into the category of parameterically excited s

43、ystems, which leads to instability in the rotor system.Dr R Tiuxi(ftiuaritiiiht/fna iniPZL SwhMi hcoptcriMnufKtwcrX cwmv 禎 Lmnrvfi MM»rwb $yvvuVibration monitoring tor complex moclunical structures arwl rotatmg machines M of key importance in many industrial rU like «erd<wuticsA tHcHhla

44、dcd propdl代Or R Tiuwi(tiwari*iitg.efiw< in) The most characteristic property of asymmetricaS systems is the appears nee of unstable vibrations in some rotatio nal speed ranges* In 1933, Smith obtained a poineer work in the form of simple formulas that predicted the threshold spin speed for superc

45、ritical instability varied with bearing stifiness and with the ratio of external to internal viscous damping.To quote from Smith's paper. the increase ofdissymmetry of the bearing stiffness and in the intensity of external damping relative to in怕rnal damping raises the threshold speed . . . and

46、this threshold speed is always higher than either critical speed."Dr R Tiuwi 仮2亦帀仗ew iniThe formula for dam pi ng was obtained in depe ndently by Crandall (1961) some 30 years later. Dick (1948) also studied behaviour of shaft having sections with unequal principal modulii.The system is stable

47、provided/ 、cH +仇 >0血< ,+ 4k CH(D； = k/rnTherea什er rotor dynamics expanded to consider various other effects.As the rotational speed increased above the first critical speed, the huge amount of kinetic energy stored in the rigid- body rotational mode of a high speed rotor is available to fuel a

48、 wide variety of possible self-excited vibration mechanisnns.However, the rotor dynamicists respite from worrying about instability was brief.In the early 1920s a supercritical in stability in built-up rotors was encountered andt shortly thereafter, first shown by Newkirk (1924) and Kimball (1924) t

49、o be a manifestation of rotor internal damping (i.e.t damping between rotor components).阶仮如叭曲讪Then. Newkirk and Taylor (1925) described an instability caused by the nonlinear action of the oil wedge in a journal bearing, which was named as oil whip. Robertson (1932, 1934, 1935a and 1935b ) also studied certain problems of vibratory motion and stability of rotors Baker (1933) described self-excited vibrations due to contact between rotor and stator.Kapitsa (193