Benchmark solutions for the dynamic analysis of general rotor-bearing system with arbitrary linear boundary conditions

Abstract

The rotor unbalance is a major source of rotor vibrations. Rotor vibrations often produce many undesired effects like noise, wear and fatigue, etc. In this paper, we try to seek the benchmark solutions for the unbalance responses of complex rotor-bearing system. The presented approach could be seen as the extension of transfer matrix method (TMM) in some sense. For the TMM, a disk or supporting structure cut off one uniform shaft element into two and someone must use the compatibility condition between these two new elements to derive the transitive matrix. However, for the presented approach, it directly solves the governing equations of uniform shaft elements with consideration of the effects of disks and supporting structures. Thus, this analytical approach is advantageous in reducing the times of matrix multiplication between state matrices and field matrices. One only needs to calculate the inversion of 16 × 16 dynamic stiffness matrix to find the steady state response. It saves the computer memory and is easy to be programmed. In addition, this analytical approach avoids the problems of selecting optimal discretization mesh densities in the case of FEM applications. For arbitrary linear boundary condition, the benchmark solutions are always easy to be obtained. The numerical simulation is carried out and two numerical examples are given to validate the new solutions. In which the finite element method is used as the numerical approach. Simulation results show that the benchmark solutions match very well with the FEM results. The effects of anisotropy in the supporting structures on the rotor's dynamic behavior, which are observed in this work, are also in accordance with many references. This validates the benchmark solutions further.