Mathematical modeling of continuous multi-stepped rotor-bearing systems

•This work presents a new method for modeling multi-stepped rotor-bearing systems.•The method is applicable to rotor systems with complex geometries and any number of disks and isotropic bearings.•The equations of motion are discretized leading to uncoupled first-order differential equations.•The present model is evaluated by numerical examples and the results compared to finite element-based models. The mathematical modeling of rotor systems is a challenging task, mainly due to the complex nature of such systems, that might posses multiple rotors, bearings, disks and more. Most approaches in modeling of these systems are based on the well established transfer matrix and finite elements methods. In this work, an alternative method based on the distributed parameter or continuous model is presented. The method presented here can be applied to complex rotor system with multiple-stepped cross-sections and several disks and bearings. The procedure is to obtain the eigenfunctions of the system directly from the equations of motion, thus considering disks and isotropic bearings, as well as damping, on the eigenfunctions. With these functions, which also give the mode shapes, the well known partial differential equations are discretized leading to uncoupled first order differential equations for the modal coordinates, enabling close-form solutions to be obtained. The main difference of the present method from other distributed parameters approaches is that the equations are obtained in the time domain, instead of relying on inverse frequency transforms. Two numerical examples, with a simple and a complex geometry, of rotor systems are presented to evaluate the model.