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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.

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.