Modelling of parametric excitation of a flexible coupling–rotor system due to misalignment

A flexible diaphragm coupling, connecting two rotating shafts, is investigated for its dynamic characteristics, when subjected to parallel offset misalignment. The diaphragm coupling is a constant velocity coupling which becomes asymmetric once misaligned. Asymmetry creates directional difference or spatial variation of stiffness, as shown by a quasi-static finite element (FE) analysis using ABAQUS software. As the shafts rotate, this spatial variation in stiffness makes the diaphragm coupling–rotor system model to become time-varying. The time-varying direct and cross–coupled stiffness terms of the coupling are synthesized from the FE model and used in the governing equations of motion of the coupling–rotor system. This leads to a parametrically excited system due to the time-periodic stiffness coefficients of the coupling. Using Simulink, numerical integration has been performed to find the response of the system for both mass unbalance and inclination unbalance excitations that arise due to the tilt of the principal axes of the diaphragm due to parallel misalignment. The responses obtained clearly indicate the effect of parametric excitation at one-fourth, one-third, and one-half of the principal parametric resonance. To verify this model, an experimental setup has been developed for the coupling–rotor system model with misalignment. The experimental results clearly show the asymmetry between the two lateral direction responses, as predicted by the model.