Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces

The rotor blades of a low pressure (LP) steam turbine stage are subjected to high static and dynamic loads during operation. The static loads are mainly due to the centrifugal force and thermal strains, whereas the dynamic loads are caused by fluctuating gas forces resulting in forced vibrations of the blades. The forced vibrations can lead to high cycle fatigue (HCF) failures causing substantial damage and high maintenance effort. Thus, one of the main tasks in the design of LP steam turbine blading is the vibration amplitude reduction in order to avoid high dynamic stresses that could damage the blading. The vibration amplitudes of the blades in a LP steam turbine stage can be reduced significantly to a reasonable amount if adjacent blades are coupled by shroud contacts that reinforce the blading, see Fig. 1. Furthermore, in the case of blade vibrations, relative displacements between neighboring blades occur in the contacts and friction forces are generated that provide additional damping to the structure due to the energy dissipation caused by micro- and macroslip effects. Therefore, the coupling of the blades increases the overall mechanical damping. A three-dimensional structural dynamics model including an appropriate spatial contact model is necessary to predict the contact forces generated by the shroud contacts and to describe the vibrational behavior of the blading with sufficient accuracy. To compute the nonlinear forced vibrations of the coupled blading, the nonlinear equations of motion are solved in the frequency domain owing to the high computational efficiency of this approach. The transformation of the nonlinear equations of motion into the frequency domain can be carried out by representing the steady-state displacement in terms of its harmonic components. After that transformation, the nonlinear forced response is computed as a function of the excitation frequency in the frequency domain.