Hybrid Simulation of a Dynamic Multibody Vehicle Suspension System Using Neural Network Modeling Fit of Tire Data

Abstract

Multibody models of vehicle suspension systems are a useful tool for investigating road handling performance and passenger harshness of a vehicle under varying conditions. The multibody model describes the nonlinear interactions between the vehicle chassis and the wheel through its suspension kinematic connections. It can be a challenge to model the wheel and road interaction due to the highly nonlinear nature of the tire dynamics. Early tire models in programs such as MSC Adams attempted to fit and interpolate empirical tire data. Interpolation of such a large dataset can be numerically inefficient leading to empirical formulations or utilization of advanced finite element (F.E.) models. Empirical formulations, such as the Magic Formula Tire model and Fiala model, utilize parameters to generalize a tire under pure slip or combined slip conditions. Advanced tire models, such as FTire or RMOD-K, use parametrized nonlinear FE approaches and tread models to represent the tire dynamics. Similar to the empirical models, a neural network is used in this study for function fitting from previously measured data can represent the steady state tire dynamics without the need of manual parametrization. A neural network is used to fit tire test data provided by the Tire Testing Consortium (TTC), which has been utilized by many Formula SAE (FSAE) competition vehicles. A network is created to generate the lateral forces of a tire that will act upon the multibody simulation. Each network has been trained utilizing the gradient descent method with adaptive learning on over 100,000 data points generated from the TTC data. The data is condensed into the weights of a network with 13 hidden neurons. The neural network representing lateral force use a range of slip angles, tire pressures, normal forces, and inclination angles as inputs to generate the lateral force output, which achieve an RMSE of 19.62 lbf (87.18 N) during training. All tire data was generalized under combined slip conditions. A half vehicle model is then constructed in this study with the rigid body components representing a double A-arm suspension typically found in performance vehicles. Ideal dynamic elements has been used to represent the spring, dampers and tire vertical stiffness. A rigid body element for the tire is used to represent the wheel and tire inertias and to apply the tire forces generated by the neural networks. The simulation is then ran under varying tire pressures and steady state conditions, and compared to similar fits using parameterized empirical models. These models show that the nonlinear dynamics of a tire can be incorporated from measured data utilizing neural network models in an efficient and effective way.