Estimation of Natural Frequencies and Mode Shapes of a Shaft Supported by more than Three Bearings

Atul B. Meshram^1, , Girish D. Mehta² and Jayant P. Modak³

¹M.Tech Student, P.C.E. Nagpur, MH, India

²Assoc. Professor, P.C.E. Nagpur, MH, India

³Emeritus Professor, P.C.E. Nagpur, Pincode 440019, MH, India

Cite this paper:
Atul B. Meshram, Girish D. Mehta and Jayant P. Modak. Estimation of Natural Frequencies and Mode Shapes of a Shaft Supported by more than Three Bearings. Journal of Mechanical Design and Vibration. 2014; 2(1):11-24. doi: 10.12691/jmdv-2-1-2

Abstract

The present paper emphasizes on the estimation of natural frequencies and mode shapes of a shaft supported by more than three bearings. In advent of this, a counter shaft of already developed experimental setup has been considered. The natural frequencies and mode shapes of counter shaft are deteremined analytically by adopting Holzer's method and the results obtained are then compared with the results of software based approach. By adopting the same method, Stresses in the shaft and amplitudes of rotors are also estimated. Based on the obtained data the generallised mathematical models have been formulated for the prediction of stresses in shaft and amplitudes of rotors. Significant independent variables which influence the phenomenon i.e. development of stresses and amplitudes of rotor have been accounted in terms of a group of pie terms. These group of pi terms are accoplished with the help of dimensional analysis technique and they are used to formulate the mathematical models. In this paper the qualitative and quantitative analyses of the established mathematical models are also carried out.

Keywords:
countershaft natural frequency mode shapes shear stress mathematical model

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