Rotordynamics and bond graphs: basic models

Abstract

Basic rotordynamic models such as for the Jeffcott [H. H. Jeffcott, Lateral vibration of laded shafts in the neighborhood of a whirling speed–Thee ffect of want of imbalance, Philos.Mag. 37, 1919, pp. 304–314] and Stodola–Green [A. Stodola, Dampf-und Gasturbinen, Springer-Verlag, Berlin, 1924, R.Green, Gyroscopic effects of the critical speeds of flexible rotors, J Appl Mech, 15 (1948), pp. 369–376] rotors are developed in a bond graph formalism. The equations of motion for a general rotor with an imbalance are derived from Lagrange's equations to include most rotordynamic phenomena including gyroscopic effects. The implementation into the bond graph models using both multibond and scalar bonds is given and discussed. An example of bond graph models for the classical Jeffcott rotor is included and the derivation of the complete state equations from the scalar bond graph is shown in detail. A more complex bond graph-modelling example using the Stodola–Green model mounted on a stiff shaft with bearing elasticity and damping is also included. Simulation results for both the models are shown. The purpose of a bond graph implementation of such rotordynamics models is to explore the modular and foundational pieces of the bond graph in more complex rotordynamic or mechatronic models and visualize the rotordynamic phenomena from the energy flow and visual perspectives.