Control-oriented modeling of a vehicle drivetrain for shuffle and clunk mitigation

Flexibility and backlash of vehicle drivelines typically cause unwanted oscillations and noise, known as shuffle and clunk, during tip-in and tip-out events. Computationally efficient and accurate driveline models are necessary for the design and evaluation of torque shaping strategies to mitigate this shuffle and clunk. To accomplish these goals, this paper develops a full-order physics-based model and uses this model to develop a reduced-order model (ROM), which captures the main dynamics that influence the shuffle and clunk phenomena. The full-order model (FOM) comprises several components, including the engine as a torque generator, backlash elements as discontinuities, and propeller and axle shafts as compliant elements. This model is experimentally validated using the data collected from a Ford vehicle. The validation results indicate less than 1% error between the model and measured shuffle oscillation frequen-cies. The reduced-order model is derived by lumping 24 inertia elements into 2 elements, 3 stiffness and damping elements into 2 elements, and 2 backlashes into 1 element. As part of the reduced-order model development, the paper (i) investi-gates the effect of using a simplified tire model; (ii) investigates the effect of lumping transmission and final drive backlashes; and (iii) evaluates the ROM for shuffle and clunk control. Simulation results show that the ROM replicates the behavior of the FOM with less than 5% error in predicting shuffle frequency, thus making it suitable for the design of torque shaping controllers to mitigate shuffle and clunk