Computational analysis for dynamic response of a rotating shaft on flexible support structure with clearances

A finite element-based formulation for modelling the dynamic behavior of a rotating flexible shaft supported by a flexible support structure is presented. The coupling effect between the rigid-body rotation and the flexible deformation of the shaft is considered and represented by non-linear coupling terms in the mass matrix and forcing vectors in the global system of equations. The rigid-body rotation is treated as one of the degrees of freedom (d.o.f.) of the entire system. The interaction between the rotating shaft and the flexible support is modelled by either linear or non-linear springs distributed around the circumference of the shaft. The coupling between the flexibility of the shaft and the flexibility of the support structure are considered. The flexible d.o.f. of both the shaft and the support structure are represented as a set of retained and internal d.o.f. of a Craig–Bampton formulation. An additional transformation is performed when the rigid-body d.o.f. is coupled with the internal and the retained d.o.f. in a Craig–Bampton basis. The equations of motion are solved in the time domain using a modified Newmark method for time integration, in which the Newton–Raphson method is used for handling the non-linear behavior within each time step. Analyses are performed to validate the new development for different combinations of load condition, spring type, and rigid-body rotation.