Non-linear analysis of a flexible rotor system with multi-span bearing supports

The current article deals with the non-linear dynamic behaviours of a flexible rotor system with multi-span bearing supports. The shaft is modelled by using the finite-element method that can take the effects of inertia and shear into consideration. A modified modal synthesis technique with free interface is proposed to reduce the degrees of freedom of the model of a flexible rotor system. In order to keep the accuracy of non-linear analysis and save computational cost, a truncated modal transformation is used to reduce the linear degrees of freedom of the system, whereas non-linear oil-film forces and non-linear degrees of freedom of the system are retained in the physical space. Thus, the non-linear excitation and unbalance force can be easily added to the system equation and the reduced system keeps the non-linearity. In accordance with the physical character of oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at every step of the dynamic iterative procedure. Non-linear oil film forces and their Jacobians are calculated simultaneously without an increase in computing costs and compatible accuracy is obtained. The numerical example shows that the proposed methods not only save computing costs but also have good precision.