Dynamic Analysis of Geared Rotors-A Review
Rotor dynamics plays an important role in many engineering fields such as gas turbine, steam turbine, reciprocating and centrifugal compressors, the spindle of machine tools, and so on. Owing to the growing demands for high power, high speed, and light weight of the rotor-bearing system, computations of critical speeds and steady-state response at synchronous and sub critical resonances become essential for system design, identification, diagnosis, and control. The present paper reviews some of the approaches that have been developed to provide a means for understanding and simulations of the characteristics of a geared rotor dynamic system. More emphasis is given on the lateral vibrations of the rotors, effect of coupling of torsional and lateral vibration of rotors especially when the rotors are coupled with gears. Keywords—Critical speed, Geared rotors, Lateral vibrations, Rotor dynamics, Torsional vibrations.
Coupled Torsional-flexural Vibration of a Shaft in a Geared System of Rotors : 1st Report
Coupled torsional-flexural vibration of a shaft in a spur geared system is investigated. Equation of motion which contain the terms of geometrical eccentricity of gears and mass unbalance are introduced. The coupling between torsional and flexural displacements is considered in the equations which assume that surfaces of tooth of meshed gears are always in contact during the rotation. By solving the equation, it is possible to get natural frequencies, mode shapes, and frequency response of the system. It is usual to ignore the effect of the coupling between torsional and flexural vibrations. But comparing the result with them, some new phenomena were revealed. They are: (1) shifts of the critical speeds (2) transformations of the mode shapes (3) a forced vibration which is caused by geometrical eccentricity of a gear.
A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems
The steady-state responses of linear flexible rotor-bearing systems are analyzed by the modified transfer matrix method. The transfer matrix has the advantage of solving the problems in frequency domain with fixed matrix size. This makes the method more economical in analyzing a large degree-of-freedom rotor system than many time-marching integrating methods. In this paper, the modifications of transfer matrix method include that the transfer matrix of shaft is derived from the “continuous system” concept instead of conventional “lumped system” concept, and the paper tries to extend the transfer matrix method to fit synchronous elliptical orbit and nonsynchronous multi-lobed whirling orbit. To demonstrate the applications of the method, three examples are presented; two synchronous and one nonsynchronous.