Sommerfeld Effect Characterization in Anisotropic Non-ideal Rotor System

Ideal drive is usually considered for analysis of rotor dynamic systems. In reality, all the drives are non-ideal and they provide a limited amount of power. Moreover, the drive dynamics is also influenced by the dynamics of the driven systems. Dynamic analysis of rotor and drive coupling is a very complex task. Increase in input power of drive at resonance region may lead to increase in the transverse vibrations without increasing the rotor spin. At that moment, for a critical power input, the rotor spin speed escapes from resonance region and jumps to a very high rotor speed. This jump phenomenon is known as Sommerfeld effect. This effect is usually seen during coast up and coast down operations. The severity of Sommerfeld effect may lead to persistent large synchronous whirl amplitudes and capture of rotor speed at the resonance frequency, which may damage the rotor, bearings, and other equipment. Thus, smooth passage through resonance during coast up and coast down in rotor dynamic systems requires prior knowledge of its Sommerfeld effect and drive-rotor interaction, based on which, appropriate speed regulation controllers can be developed. In this paper, the characterization of Sommerfeld effect in an unbalanced rotor system is addressed. This unbalanced system is placed on an anisotropic two-degrees-of-freedom foundation and is driven by DC motor. The jump phenomenon of the rotor system, considering an ideal drive, is characterized by the steady-state power balance method. The transient simulation of the said system is carried out with the aid of a bond graph model, and jump voltage required to escape different resonance zone is obtained. Transient solutions may show premature jumps; however, the quasi-static simulation results exactly match with those obtained from steady-state analysis.