An Intuitive Derivation of the Dual-Clutch Model for Clutch Shift Dynamics

There are several commercial off-the-shelf software available to study transmission and driveline dynamics. Many of these software require a faithful representation of the transmission topology in order to carry out the analyses. These modeling techniques utilize several redundant degrees of freedom which may not be necessary for studying low frequency (< ~30 Hz) dynamics and may be computationally inefficient. The dual-clutch model has been proposed as a generic 2-DOF model that overcomes some of these drawbacks. In this paper, the dual-clutch model is initially derived from first principles, starting with the equations of motion for a planetary automatic transmission. The model coefficients - the inertia matrix and the matrix of clutch coefficients - are then derived using a more intuitive approach based on energy considerations.