A mathematical model to study the driveability and the handling of motorcycles

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A mathematical model to study the driveability and the handling of motorcycles

Musica, R.

A mathematical model is developed to study the motorcycle dynamics. The physical model schematises a classic motorcycle be eleven degrees of freedom. These generalised co-ordinates are defined to describe the small displacements around a configuration of the non-stressed system (case of the elastic displacements of the front fork and of the swing arm) and the large displacements associated to the motion of the motorcycle. Other two small displacements are considered in correspondence to the contact points between the wheels and the soil. These two degrees of freedom are used to force in the system an external excitation simulating the profile effect of the road. The motion equations are obtained using Lagrange's equations. A computer program for the symbolic and numeric computation was utilised to define the oversaid equations starting from the kinetic and potential energy expressions of the system. Damping was also taken into account by a power function. The parameters used to test the model regard a motorcycle with a mass approximately equal to 200 kg and a swept volume of 500 cc. Originally the mathematical model is completely non-linear, but the equations are formidable. In order to use them practically, partial linearisations were performed according to the particular dynamic state to simulate.