Recently, a new power-split hybrid electric vehicle drivetrain has been developed by the Corporate Research and Development Department of the Robert Bosch company and two research cars equipped with this powertrain have been built. Owing to the loop-like arrangement of the shafts in the newly developed Dual-E Transmission, circulating power can arise in this system. In general, circulating power leads to high mesh losses because the power transmitted by some components becomes greater than the input or output power. This paper presents a detailed analysis of circulating power in the Dual-E Transmission. It is shown that the solution of the energy balance equations is given by a linear combination of four basic power flows. The factors in this linear combination, however, cannot be uniquely determined from the energy balance alone. Therefore, the transmission kinematics and dynamics are dealt with in detail. Subsequently, a mathematical description as well as a graphical representation of the circulating-power-free operating range are derived. This elaboration provides a solid basis for the development of a fuel-efficient operating strategy.
