Thermal Bending of the Rotor Due to Rotor-to-Stator Rub - Paul Goldman (International Journal of Rotating Machinery, 2000)
The rotor thermal bending due to the rotor-to-stator rubbing can lead to one of three types of observed rotor lateral motion: (1) spiral with increasing amplitude, (2) oscillating between rub]no-rub conditions, and (3) asymptotical approach to the rotor limit cycle. Based on the machinery observations, it is assumed in the analytical part of the paper that the speed scale of transient thermal effects is considerably lower than that of rotor vibrations, and that the thermal effect reflects only on the rotor steady-state vibrational response. This response would change due to thermally induced bow of the rotor, which can be considered to slowly vary in timefor the purpose of rotor vibration calculations. Thus uncoupled from the thermal problem, the rotor vibration is analyzed. The major consideration is given to the rotor which experiences intermittent contact with the stator, due to predetermined thermal bow, unbalance force, and radial constant load force. In the case of inelastic impact, it causes an on/off, step-change in the stiffness of the system. Using a specially developed variable transformation for the system with discontinuities, and averaging technique the resonance regimes of motion are obtained. These regimes are used to calculate the heat generated during contact stage, as a function of thermal bow modal parameters, which is used as a boundary condition for the rotor heat transfer problem. The latter is treated as quasi-static, which reduces the problem to an ordinary differential equation for the thermal bow vector. It is investigated from the stability standpoint.