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The torsional natural frequencies of axles equipped with limited slip differential clutches depend on whether or not the tires and clutches are slipping since the effective inertia at each end of the axle is different for slipping and non-slipping conditions. Limited slip axle vibrations are typically analyzed for one tire slipping and the other not since that is the case for which the limited slip clutches are used. Vibrations often arise, however, during normal turning when both drive tires have good traction.

Safety is considered one of the most important parameters when designing a ground vehicle. The adverse effect of weather on a vehicle can lead to a surge in safety issues and accidents. Several safety assistance systems are available in modern vehicles, which are designed to lessen the negative effects of weather hazards. Although these safety systems can intervene during crucial conditions to avoid accidents, driving a vehicle on snowy or icy terrain can still be a challenging task. Road conditions with the least tire-road friction often results in poor vehicle handling, and without any kind of safety system it can lead to mishaps. With the use of Adams Car software and vehicle dynamics modeling, a realistic relationship between the vehicle and road surface may be established. The simulation can be used to have a better understanding of vehicle handling in snowy and icy conditions, tire-ice interaction, and tire modeling.

A model and simulation results are presented for the torsional dynamics of a rear wheel driveline while the vehicle is coasting in a turn. The model includes the effects of road load and powertrain drag, limited slip differential clutch friction, the inertias of the vehicle, wheels, axles, differential carrier, and driveshaft, the final drive ratio, torsional stiffnesses of the axles and driveshaft, vehicle track width, and radius of the turn. The dynamics of coasting in a turn differ from powered driving due to changes in the inertia loading the driveshaft, the damping effect of the disengaged transmission, and nonlinearities in the clutch friction. Specific focus is given to vibration in the axles and driveshaft due to variations in the torque-speed slope of the clutches, which is determined by the slope of the friction coefficient ‘μ’ versus sliding speed ‘v’ in the limited slip clutches.

Data-driven modeling can help improve understanding of the governing equations for systems that are challenging to model. In the current work, the Sparse Identification of Nonlinear Dynamical systems (SINDy) is used to predict the dynamic behavior of dynamic problems for NVH applications. To show the merit of the approach, the paper demonstrates how the equations of motions for linear and nonlinear multi-degree of freedom systems can be obtained. First, the SINDy method is utilized to capture the dynamic behavior of linear systems. Second, the accuracy of the SINDy algorithm is investigated with nonlinear dynamic systems. SINDy can output differential equations that correspond to the data. This method can be used to find equations for dynamical systems that have not yet been discovered or to study current systems to compare with our current understanding of the dynamical system.