Abstract The steady operation of a turbocharged diesel direct injection (TDI) engine featuring a variable speed ratio mechanism linking the turbocharger shaft to the crankshaft is modelled in the present study. Key parameters of the variable speed ratio mechanism are range of speed ratios, efficiency and inertia, in addition to the ability to control relative speed and flow of power. The device receives energy from, or delivers energy to, the crankshaft or the turbocharger. In addition to the pistons of the internal combustion engine (ICE), also the turbocharger thus contributes to the total mechanical power output of the engine. The energy supply from the crankshaft is mostly needed during sharp accelerations to avoid turbo-lag, and to boost torque at low speeds. At low speeds, the maximum torque is drastically improved, radically expanding the load range. Additionally, moving closer to the points of operation of a balanced turbocharger, it is also possible to improve both the efficiency η, defined as the ratio of the piston crankshaft power to the fuel flow power, and the total efficiency η*, defined as the ratio of piston crankshaft power augmented of the power from the turbocharger shaft to the fuel flow power, even if of a minimal extent. The energy supply to the crankshaft is possible mostly at high speeds and high loads, where otherwise the turbine could have been waste gated, and during decelerations. The use of the energy at the turbine otherwise waste gated translates in improvements of the total fuel conversion efficiency η* more than the efficiency η. Much smaller improvements are obtained for the maximum torque, yet again moving closer to the points of operation of a balanced turbocharger. Adopting a much larger turbocharger (target displacement x speed 30% larger than a conventional turbocharger), better torque outputs and fuel conversion efficiencies η* and η are possible at every speed vs. the engine with a smaller, balanced turbocharger. This result motivates further studies of the mechanism that may considerably benefit traditional powertrains based on diesel engines.