Modeling and simulation of longitudinal dynamics coupled with clutch engagement dynamics for ground vehicles

During the engagement of the dry clutch in automotive transmissions, clutch judder may occur. Vehicle suspension and engine mounts couple the torsional and longitudinal models, leading to oscillations of the vehicle body that are perceived by the driver as poor driving quality. This paper presents an effective formulation for the modeling and simulation of longitudinal dynamics and powertrain torsional dynamics of the vehicle based on non-smooth dynamics of multibody systems. In doing so friction forces between wheels and the road surface are modeled along with friction torque in the clutch using Coulomb's friction law. First, bilateral constraint equations of the system are derived in Cartesian coordinates and the dynamical equations of the system are developed using the Lagrange multiplier technique. Complementary formulations are proposed to determine the state transitions from stick to slip between wheels and road surface and from the clutch. An event-driven scheme is used to represent state transition problem, which is solved as a linear complementarity problem (LCP), with Baumgarte's stabilization method applied to reduce constraint drift. Finally, the numerical results demonstrate that the modeling technique is effective in simulating the vehicle dynamics. Using this method stick-slip transitions between driving wheel and the road surface and from the clutch, as a form of clutch judder, are demonstrated to occur periodically for certain values of the parameters of input torque from engine, and static and dynamic friction characteristics of tire/ground contact patch and clutch discs.