Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

U. Werner, "Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect," Applied Mathematics, Vol. 4 No. 8A, 2013, pp. 57-74. doi: 10.4236/am.2013.48A009.

 [1] M. I. Friswell, J. E. T Penny, S. D. Garvey and A. W. Lees, “Dynamics of Rotating Machines,” Cambridge Uni versity Press, Cambridge, 2010. [2] J. S. Rao, “Rotor Dynamics,” John Wiley & Sons, New York, 1996. [3] R. Gasch, R. Nordmann and H. Pfützner, “Rotordynamik,” Springer-Verlag, Berlin-Heidelberg, 2002. [4] A. C. Smith, D. G. Dorrell, “Calculation and Measure ment of Unbalanced Magnetic Pull in Cage Induction Motors with Eccentric Rotors, I. Analytical Model,” Pro ceedings of Electric Power Applications, Vol. 143, No. 3, 1996, pp. 193-201. [5] W. Schuisky, “Magnetic Pull in Electrical Machines Due to the Eccentricity of the Rotor,” Electrical Research As sociation Translation, Vol. 295, 1972, pp. 391-399. [6] R. Belmans, A. Vandenput and W. Geysen, “Calculation of the Flux Density and the Unbalanced Pull in Two Pole Induction Machines,” Archiv der Elektrotechnik, Vol. 70, Springer-Verlag, 1987, pp. 151-161. [7] R. L. Stoll, “Simple Computational Model for Calculating the Unbalanced Magnetic Pull on a Two-Pole Turbogen erator Rotor Due to Eccentricity,” IEE Proceedings of Electric Power Applications, Vol. 144, No. 4, 1997, pp. 263-270. doi:10.1049/ip-epa:19971143 [8] T. P. Holopainen, “Electromechanical Interaction in Rotor Dynamics of Cage Induction Motors,” VTT Technical Research Centre of Finland, Ph.D. Thesis, Helsinki University of Technology, Helsinki, 2004. [9] H.-O. Seinsch, “Oberfelderscheinungen in Drehfeldmas chinen,” Teubner-Verlag, Stuttgart, 1992. [10] U. Werner, “Rotordynamische Analyse von Asynchron maschinen mit Magnetischen Unsymmetrien,” Disserta tion, Technical University of Darmstadt, Darmstadt, 2006. [11] U. Werner, “Rotordynamic Model for Electromagnetic Ex citation Caused by an Eccentric and Angular Rotor Core in an Induction Motor,” Archive of Applied Mechanics, 2013. doi:10.1007/s00419-013-0743-8 [12] U. Werner, “Theoretical Vibration Analysis Regarding Ex citation Due to Elliptical Shaft Journals in Sleeve Bear ings of Electrical Motors,” International Journal of Ro tating Machinery, Vol. 2012, 2012, Article ID 860293. doi:10.1155/2012/860293 [13] O. Reynolds, “On the Theory of Lubrication,” Philoso phical Transaction of the Royal Society, Vol. 177, London, 1886. [14] J. Lund and K. Thomsen, “A Calculation Method and Data for the Dynamics of Oil Lubricated Journal Bearings in Fluid Film Bearings and Rotor Bearings System De sign and Optimization,” ASME, New York, 1978, pp. 1-28. [15] A. Tondl, “Some Problems of Rotor Dynamics,” Chap man & Hall, London, 1965. [16] A. A. Gnandoss and M. R. Osborne, “The Numerical So lution of Reynolds’ Equation for a Journal Bearing,” Quar terly Journal of Mechanics and Applied Mathematics, Vol. 17, No. 2, 1964, pp. 241-246. doi:10.1093/qjmam/17.2.241 [17] J. Glienicke, “Feder und Dampfungskonstanten von Gleit lagern für Turbomaschinen und deren Einfluss auf das Schwingungsverhalten eines Einfachen Rotors,” Disserta tion, Technische Hochschule Karlsruhe, Karlsruhe, 1966.? [18] IEC 60034-14, “Rotating Electrical Machines—Part 14: Mechanical Vibration of Certain Machines with Shaft Heights 56 mm and Higher—Measurement, Evaluation and Limits of Vibration Severity,” International Electro technical Commission, 2007. [19] ANSI/API 541, “Form-Wound-Squirrel-Cage Induction Motors-500 Horse Power and Larger,” API, 2004.