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. This approach utilizes 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 gains - are then derived using a more intuitive approach and compared to the model derived from first principles.