Steady-state dynamics of a non-ideal rotor with internal damping and gyroscopic effects

Abstract

A rotor driven by an ideal source, i.e., a source capable of delivering unlimited amount of power, becomes unstable beyond a certain threshold spin speed due to non-conservative circulatory forces. The circulatory forces considered in this paper arise out of rotating internal damping. If the drive is nonideal then the rotor spin speed cannot exceed the stability threshold. This phenomenon is a type of the Sommerfeld effect. In this work, a DC motor driving four-degrees-of-freedom rotor with internal damping and gyroscopic effects is considered and the corresponding steady-state spin frequency and the whirl orbit amplitude are analytically derived as functions of the parameters of the drive and the rotor system.

Synchronization investigation of vibration system of two co-rotating rotor with energy balance method

“…Substituting equations (25) and (26) into equation (24), the energy balance of the vibrating body in y-direction can be expressed as…”

“…Fang et al 24 applied Zhang's method to investigate the selfsynchronization of two co-rotating rotors coupled with a pendulum rod in a far-resonant vibration system. For investigation of rotor dynamics, K Samantaray et al [25][26][27] considered that the non-ideal rotor and sommerfeld effect influence on the dynamics characteristics, which promotes the development of the dynamics theory of the rotors. In this article, we introduce energy balance method to study the synchronization of the rotor system.…”

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

“…From an extensive survey of the literature, the most common methods used for structural reduction of rotor systems appear to be Guyan Reduction [38,58], Modal Analysis [39,[59][60][61][62][63] and Component Mode Synthesis [20,40,43,[64][65][66]. More specifically research on reduction methods, not necessarily applied to rotor systems, looks to handle damping [59,65,[67][68][69] and gyroscopics [63,[70][71][72] within the systems but rarely together. Other methods such as Krylov-based methods have been applied to structural systems for FEA analysis [73] but are not commonly found in the literature nor are they normally employed in rotor systems.…”

Decomposition of governing equations in the analysis of resonant response of a nonlinear and non-ideal vibrating system

“…The authors present and discuss non-stationary and steady-state responses of the system in the resonance region as well as its passage through resonance based on the analytical and numerical approach. The Sommerfeld effect in rotor dynamics and the influence of external and internal damping on the Sommerfeld effect are the subject of the works [7,8]. Papers [9] and [10] deal with the resonant response of a modified variant of the van der Pol-Mathieu oscillator with nonlinear spring and parametric excitation which is disturbed by a non-ideal source.…”