An Implicit Ring Tire Model for Multibody Simulation with Energy Dissipation
A rigid ring tire model was developed as the c++ module of a free multibody dynamics software. It takes as input the longitudinal profile of the road and is attached to the wheel element of a multibody simulation. It is intended to evaluate the transient behavior of the tire rolling on a deteriorated road profile. It is tailored for, but not restricted to, applications at low camber angles, limited steering and velocity changes, and continuous contact with the road. It is expected to be accurate under excitation frequencies up to 100 Hz and road deformation up to 10 cm. It takes 45 tire parameters and 20 algorithm parameters and is integrated implicitly except for the road profile. The model has been calibrated and validated against a trusted finite element analysis of Michelin XZA-3 tires mounted on a wheel and axle assembly going over rectangular cleats. The resulting curves showed good agreement with the finite element data. The Nelder-Mead optimization process used on the manually determined parameters was able to increase the average coefficient of determination of the 12 test curves from −0.4 to 0.6. Above 20 km/h, that coefficient was better than 0.8 for every test of the vertical force response to cleats. As for the longitudinal forces, only one curve had a coefficient below 0.5. A variable time-step algorithm was also included in the module and found to reduce the simulation time of the test cases by roughly 85%.ABSTRACT
From left to right: wheel, ring, and patch elements.
Definition of model variables using the geometry shown in Fig. 1.
Experimental and model data for slip forces at 2800-kg load. Experimental data at different loads are shown in pale. (a) Lateral force. (b) Longitudinal force. (c) Aligning moment.
Systems used to (a) compute and (b) apply the rotation-induced forces.
(a) As written in the residual vector and (b) as modeled with the artificial rotation.
Comparison of different contact length equations with the data from Michelin.
Fitting the Schmeitz superellipse to the Rhyne sidewall shape.
Force variations felt at the axle while traveling on a flat road and running into a 20-mm-long rectangular cleat. Axle height fixed at a 27.47-kN static normal load. Initial parameters.
Force variations felt at the axle while traveling on a flat road and running into a 20-mm-long rectangular cleat. Axle height fixed at a 27.47-kN static normal load. Optimized parameters.
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