Dynamic Models of Bicycles and Motorcycles using Power Flow Approach

Guilherme Nóbrega Martins¹; Mauro Speranza Neto¹; Marco Antonio Meggiolaro¹

¹ Pontifical Catholic University of Rio de Janeiro

doi:10.20906/CPS/CON-2016-0224

Resumo

This paper presents a procedure for the determination of the analytical form of dynamic models for bicycles and/or motorcycles through the characterization of the power flow between its components (driver, handlebars and frame, suspension and wheels/tires, engine, transmission and brakes) including the influence of gyroscopic effect and the interactions between the longitudinal, lateral and vertical dynamics of those vehicles. From the geometrical relations associated to the degrees of freedom of each part of the vehicle (driver, handlebar, frame, and suspension mechanisms and tires/wheels) kinematic relations associated with their speeds are determined. Considering the power flow between the degrees of freedom and also between these, the elements of the transmission (engine, gearbox, chains, tires) and brake (drive, pads, discs, tires) systems, the equilibrium relations between the forces and torques are determined. Finally, taking the inertial, stiffness and damping effects of the various system components into consideration, the equations of motion or state equations that characterize the dynamics of the vehicles are analytically obtained, represented in any reference frame, local or global. This procedure is modular and can be applied to smaller model subsystems (e.g. with fewer components and degrees of freedom). These will later be coupled, also through the power flow, to generate the model of a new subsystem representing the dynamic characteristics of the former system and their interactions. This approach adopts the same basis, concepts and elements of the Bond Graph Technique, without its symbolic notation and graphical representation. As an illustration, the procedure is applied for modeling the longitudinal, vertical and lateral coupled dynamics of a motorcycle, with the purpose of analyzing their stability in the vertical and lateral plane.

Palavras-chave: Bicycles and Motorcycles Dynamics; Kinematic Relations; Power Flow; Equilibrium Relations; Bond Graphs