Multi-mass rotating shaft analysis and identification

Abstract

The frequency response function of a multi-mass rotor system, modelled as a series of interconnected, distributed and lumped elements is considered. The system comprises a number of rigid disc elements mounted on a flexible-distributed shaft. The characteristic determinant of the system model is computed and the overall transfer matrix of the model is derived. The damped natural frequency of the system is established by computation of complex roots of the irrational characteristic determinant of the system, using Nedler and Mead's simplex optimization method. Thereafter, by decomposition of the transfer matrix and considering boundary conditions associated with the bearings, a flexibility matrix is introduced, enabling frequency response functions of the rotor to be computed. The overall system is approximated by a linear multivariable model with second-order transfer function elements. It is shown that an accurate reduced-order model can be obtained by this method, enabling new strategies for vibration control of rotating machinery to be achieved.