Copyright © Transportation Systems Chania, Greece, 1997 MULTI-BODY SIMULATION SOFTWARE IN THE ANALYSIS OF MOTORCYCLE DYNAMICS Mahbub Gani * David Limebeer ** Robin Sharp *** * CPSE, Imperial College, London SW7 2BY, UK ** CPSE, Imperial College, London SW7 2BY, UK *** SME, Cranfield University, Bedford MK43 OAL, UK Abstract: A linear, straight running model of a motorcycle is developed using multi- body simulation software. The stability properties as a function of forward speed obtained from this model exactly match well established results found by (Sharp 1994b) , which validates the linearised equations of motion derived by the software. This model is used to obtain time response data and FFT analysis identified the same dominant eigenvalues found from the linear model. The counter-steering phenomenon is then predicted using the computer generated system. Finally an enhanced model is used to study the stability properties of a motorcycle under constant acceleration and deceleration. Keywords: Simulation, Linear analysis, Vehicle dynamics, Modelling, Software tools 1. INTRODUCTION Motorcycles are elaborate mechanical systems, comprising a number of masses, each with sev- eral degrees of freedom and complex coupling geometry. The task of deriving the equations of motion of such a system proves to be time con- suming and prone to errors for the dynamicist. The straight running properties of motorcycles have been extensively studied by several authors. The most complete account has been presented by (Sharp 1994b), where a sophisticated model including frame flexibilities, tyre forces, tyre mo- ments and aerodynamic forces is used to predict the eigenvalues of the motorcycle. In contrast, modes of operation of greater complexity, such as certain cornering and acceleration phenomena, have not been studied so thoroughly because the use of manual methods to analyse such cases be- comes quite impractical. When studying straight running behaviour, one can decouple the pitch- plane motion from the lateral motion and anal- yse them independently; even so, the linearised equations of motion take several pages to write down. However, if one wishes to study cornering 227 behaviour, for instance, one has to take account of the many coupling terms arising from interac- tions between in-plane and out-of-plane motions. Tyre forces and moment descriptions also become more elaborate. This makes the process of deriving the equations of motion laborious and subject to error. This means that we do not have a means of predicting the motion of motorcycles analyti- cally under the many circumstances that arise as thousands of riders take to the road . This has a bearing on questions of the safety of motorcyclists, particularly for the police, who frequently need to travel at high speeds and employ advanced maneuvering techniques. Sharp has reported sev- eral accidents that have occurred as a result. of loss of rider control, apparently as the relevant motorcycle entered a lightly damped oscillatory region in the eigenspace (Sharp 1992). In industry, the complexity involved in modelling motorcycles, has lead to the continuing use of rules of thumb to design and manufacture the machines, which prejudices the product improvement. The recent development of multi-body simulation software gives the analyst the opportunity to au-