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It's important to monitor the longitudinal friction at the tire/road interface for automotive dynamic control systems like ABS and ASR. Of all the tire friction models the empirical model provides a good illustration on longitudinal wheel forces. An improved exponential friction model based on vehicle driving states was proposed in this paper, the model can monitor the friction characteristics between the tire and road surface for longitudinal braking. Its validity was proven using experiments and comparison with the Pacejka Magic Formula (MF) model and others.

Neutral-idle strategy has been applied for years to improve the fuel consumption of automatic transmission cars. The updated demand is the use of expanded slipping control strategy for further improvement of the transmission efficiency and response speed. However, one major drawback of the continuous slipping clutches is the high tendency to produce shudder or low frequency variation. In this research, a special neutral-idle shudder phenomenon is presented. This special shudder is not only related to slipping clutches but also related to the vibration and structure of the powertrain system. Simulations and experiments are conducted to give an insight view of this phenomenon. The analysis reveals that this special shudder is caused by both torsional vibration of the driveline and rigid-body vibration of the powertrain system. A positive feedback loop between those two kinds of vibrations leads to this special neutral-idle shudder.