An intuitive and efficient approach to integrated modelling and control of three-dimensional vibration in long shafts

Abstract

A nonlinear three-dimensional bond graph-based shaft model is presented, in which axial, torsional, and lateral vibrations can be predicted along with contact with external objects. Rigid lumped segments with six degrees of freedom are connected by axial, torsional, shear, and bending springs to approximate continuous system response. Parasitic springs and dampers enforce boundary conditions, contact forces are generated with stiff springs, and sliding friction forces during contact are incorporated using coordinate transformations and dynamic Coulomb friction. The model is easily reconfigurable for different boundary conditions, and the bond graph formalism facilitates the inclusion of (semi-)active control submodels such as electromechanical actuators or dampers. Simulations of a rotating 80-metre oilwell drillstring show realistic axial, torsional and lateral vibration. Active lateral vibration control is implemented, with a proportional controller acting on strain gauge output to attenuate vibration and reduce wellbore contact.