The effects of source loading of the drive motor due to rotating material damping induced self-excited asynchronous whirl and unbalance induced synchronous whirl on the overall steady-state behaviour of a rotor—motor system are studied in this article. The formulation is based on finding the existence of a plausible conservative state of the system where the orbital energies are conserved. This method is very simple and, at the same time, it is physically meaningful. The analysis reveals some interesting non-linear phenomena in non-ideal rotor—motor systems. A bond graph model is used to represent the system dynamics. The analytically obtained whirl characteristics are validated through numerical studies.
OlverP. J., Equivalence, invariants, and symmetry (Cambridge: Cambridge University Press1995).
2.
KirillovO. N., Destabilization paradox due to breaking the Hamiltonian and reversible symmetryInt. J. Non-Linear Mech.42 (2007): 71–87.
3.
Bou-RabeeN. M.MarsdenJ. E.RomeroL. A., Tippe top inversion as a dissipation-induced instabilitySIAM J. Appl. Dyn. Syst.33 (2004): 352–377.
4.
KrechetnikovR.MarsdenJ. E., On destabilizing effects of two fundamental non-conservative forcesPhysica D214 (2006): 25–32.
5.
GeninJ.MaybeeJ. S., Some new stability results in the theory of whirlingSIAM J. Appl. Math.15 (1967): 128–135.
6.
GeninJ.MaybeeJ. S., External and material damped three dimensional rotor systemInt. J. Non-Linear Mech.5 (1970): 281–291.
7.
BhattacharyyaR.MukherjeeA.SamantarayA. K., Harmonic oscillations of non-conservative, asymmetric, two-degree-of-freedom systemsJ. Sound Vibr.264 (2004): 973–980.
8.
NayfehA.MookD., Nonlinear oscillations (New York: Wiley-Interscience1979).
9.
KarnoppD. C.MargolisD. L.RosenbergR. C., System dynamics: modeling and simulation of mechatronic systems (New York: John Wiley & Sons Inc.2006).
10.
MukherjeeA.KarmakarR.SamantarayA. K., Bond graph in modeling, simulation and fault identification (Florida: CRC Press2006).
11.
BorutzkyW., Bond graphs — a methodology for modelling multidisciplinary dynamic systems (San Diego: SCS Publishing House2004).
12.
Dauphin-TanguyG., Les bond graphs (Paris: Hermes Science Europe Ltd.2000).
13.
CohenR.PoratI., Coupled torsional and transverse vibration of unbalanced rotorJ. Appl. Mech.523 (1985): 701–705.
14.
SamantarayA. K., Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effectsNonlinear Dyn. (2009): in press. DOI: 10.1007/s11071-008-9413-8.
15.
SamantarayA. K.MukherjeeA.BhattacharyyaR., Some studies on rotors with polynomial type nonlinear external and internal dampingInt. J. Non-Linear Mech.41 (2006): 1007–1015.
16.
MargolisD. L., Bond graphs and the exploitation of power conserving transformationsComput. Programs Biomed.83—4 (1978): 165–170.
17.
KarnoppD., Power-conserving transformations: Physical interpretations and applications using bond graphsJ. Franklin Inst.2883 (1969): 175–201.
18.
NgwompoR. F.ScavardaS., Dimensioning problems in system design using bicausal bond graphsSimul. Pract. Theory75—6 (1999): 577–587.
19.
GawthropP. J., Physical interpretation of inverse dynamics using bicausal bond graphsJ. Franklin Inst.3376 (2000): 743–769.
20.
MerzoukiR.MedjaherK.DjeziriM. A.Ould-BouamamaB., Backlash fault detection in mechatronic systemMechatronics176 (2007): 299–310.
21.
SugiyamaY.LangthjemM. A., Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systemsInt. J. Non-Linear Mech.42 (2007): 132–145.
22.
SamantarayA. K.BhattacharyyaR.MukherjeeA., On the stability of Crandall gyropendulumPhys. Lett. A372 (2008): 238–243.
23.
SamantarayA. K.BhattacharyyaR.MukherjeeA., An investigation into the physics behind the stabilizing effects of two-phase lubricants in journal bearingsJ. Vib. Control124 (2006): 425–442.
24.
ThomsonW. T.DahlehM. D., Theory of vibration with applications (New Jersey: Prentice Hall1998).
25.
SommerfeldA., Beiträge Zum Dynamischen Ausbau Der FestigkeitslehePhysikal Zeitschr.3 (1902): 266–286.
26.
KononenkoV. O., Vibrating systems with limited excitation (in Russian) (Moscow: Nauka1964).
27.
AlifovA. A.FrolovK. V., Interaction of non-linear oscillatory systems with energy sources (London: Taylor & Francis1990).
28.
EckertM., The Sommerfeld effect: Theory and history of a remarkable resonance phenomenonEur. J. Phys.175 (1996): 285–289.
29.
BlekhmanI. I., Vibrational mechanics: nonlinear dynamic effects, general approach, applications (Singapore: World Scientific2000).
30.
DimentbergM. F.McGovernL.NortonR. L.ChapdelaineJ.HarrisonR., Dynamics of an unbalanced shaft interacting with a limited power supplyNonlinear Dyn.13 (1997): 171–187.
31.
ZukovicM.CveticaninL., Chaotic responses in a stable duffing system of non-ideal typeJ. Vibr. Control136 (2007): 751–767.
32.
SamantarayA. K., A note on internal damping induced self-excited vibration in a rotor by considering source loading of a DC motor driveInt. J. Non-Linear Mech.439 (2008): 1012–1017.
