Bond Graph Modeling and Simulation of a Vibration Absorber System in Helicopters

Abstract

n the last 20 years, computer science has considerably progressed and there has been a resurgence of interest in bond graphs. The evolution of bond graph software has allowed for the full exploitation of its graphical aspects and for its simulation directly from the modeling environment without the need for the modeler to derive the associated dynamic equations. However, within this last decade, few simulations of complex multibody systems modeled with bond graphs have been conducted directly from a graphic software platform. In this context, the objective of this chapter is to show how bond graphs can be used to model and simulate a complex mechatronic system with bond graph simulation software. The multibody system studied in this chapter is a helicopter’s vibration absorber suspension. The structural and modular approach allowed by bond graphs permits a systematic modeling of mechatronic multibody systems. The model is then built as an assembly of components or modules (rigid bodies and compliant kinematic joints) by following the structure of the actual system. This approach was carried out with the use of the parasitic elements method. The bond graph model of the suspension has been verified with another multibody tool for three different excitations (pumping, roll, and yaw). The first part of this chapter will be dedicated to giving the reader an overview of the modeling of multibody systems with bond graphs. BG models of the rigid body and all the basic kinematic joints will be presented. The main existing methods (zero-causal paths ZCPs, Lagrange multipliers, and singular perturbation) for modeling and carrying out simulations of multibody systems will be recalled. The second part of this chapter will present a vector bond graph (also called multibond graph) model of a helicopter’s antivibratory system and the associated simulations. This system is a specific suspension of a helicopter, which filters the vibration coming from the rotor to the fuselage. It is a complex multibody system with four closed kinematic chains (CKC). The dynamic equations of such a CKC system are differential-algebraic equation systems (DAE) that are often difficult to treat and which require specific solving methods. The intention of writing this chapter was to give to bond graph practitioners a detailed and comprehensive method so as to model and conduct simulations of complex multibody systems directly from a bond graph modeling interface.