Rotor-to-stator, rub-related, thermal/mechanical effects in rotating machinery

The thermal effects of rotor-to-stator rub, and their influence on the rotor vibrational response, are discussed in this paper. Based on machinery observations, it is assumed in the analysis that velocities of transient thermal effects are considerably lower than that of rotor vibrations, and thermal effects affect only rotor steady-state vibrational responses. These responses would change due to thermally induced bow of the rotor, which can be considered slowly varying in time for the purposes of rotor vibration calculation. 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 of the rotor, unbalance force, and radial constant load force. In the case of an inelastic impact, this causes an on/off step-change in the stiffness of the system. A specially developed transformation is applied to the system model which contains discontinuities, and an averaging technique is then used to analyze stability of the different resonance regimes of rotor motion that were obtained. These regimes are further used to calculate the heat generated during rotor-to-stator contact stages, as a function of thermal conditions and rotor thermal bow modal parameters. The calculated heat input is used as a boundary condition for the rotor heat transfer problem. The latter is treated as quasi-static, which allows the application of an asymptotic method to the problem. The solution at its first approximation is used to adjust the rotor thermal bow value. As a result of this calculation, an ordinary differential equation with complex variables is obtained for the thermal bow, and it is investigated from the stability standpoint.