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Recent innovative drives in hydraulics could introduce very competitive hybrid hydraulic vehicles (HHV). These drives has been considered and analyzed only in the serial HHV architecture. The series-parallel transmission architecture, also called power-split or e-CVT is highlighted as the most popular concept for full (strong) hybrid electric vehicles (HEV). The examples are one-mode power-split in Toyota Prius and two-mode (compound) power-split in GM-Allison EVT. Ambitions to make the hybrid hydraulic power trains better and more efficient would certainly require deeper analysis of more complex power-split (series-parallel) HHV transmission structures and related optimal controls. This paper presents bond graph based mathematical model of kinematics of a one-mode and a two-mode power-split hybrid hydraulic vehicle transmissions which are based on their hybrid electrical counterpart.

A detailed experimental validation has been carried out to point to limitations of static wet-clutch friction model for typical clutch engagement transients. The model accuracy can be increased by incorporating the fluid film dynamics, as done in the lumped-parameter dynamic clutch model developed at the University of Purdue. That model is extended herein in order to increase its accuracy especially in the case of grooved clutches. The extensions include a description of clutch actuator dynamics and introduction of an empirical scaling factor for the fluid film thickness state equation. More rigorous treatment of fluid dynamics for the grooved clutch is also presented.