Spark-ignited internal combustion engines are known to exhibit a decreased brake efficiency in part-load operation. Similarly to cylinder deactivation, the x-stroke operation presented in this paper is an adjustable form of skip-cycle operation. It is an effective measure to increase the efficiency of an internal combustion engine, which has to be equipped with a variable valve train to enable this feature. This paper presents an optimization procedure for the exhaust valve timings applicable to any valid stroke operation number greater than four. In the first part, the gas spring operation, during which all gas exchange valves are closed, is explained, as well as how it affects the indicated efficiency and the blow-by mass flow. In the second part, a simulation model with variable valve timings, parameterized with measurement data obtained on the engine test, is used to find the optimal valve timings. We show that in 12-stroke operation and with a cylinder load of 5 Nm, an indicated efficiency of 34.3% is achieved. Preloading the gas spring with residual gas prevents oil suction and thus helps to reduce hydrocarbon emissions. Measurements of load variations in 4-, 8-, and 12-stroke operations show that by applying an x-stroke operation, the indicated efficiency remains high and the center of combustion remains optimal in the range of significantly lower torque outputs.

The electric hybridization of vehicles with an internal combustion engine is an effective measure to reduce ${\mathrm{CO}}_2$ emissions. However, the identification of the dimension and the sufficient complexity of the powertrain parts such as the engine, electric machine, and battery is not trivial. This paper investigates the influence of the technological advancement of an internal combustion engine and the sizing of all propulsion components on the optimal degree of hybridization and the corresponding fuel consumption reduction. Thus, a turbocharged and a naturally aspirated engine are both modeled with the additional option of either a fixed camshaft or a fully variable valve train. All models are based on data obtained from measurements on engine test benches. We apply dynamic programming to find the globally optimal operating strategy for the driving cycle chosen. Depending on the engine type, a reduction in fuel consumption by up to 32% is achieved with a degree of hybridization of 45%. Depending on the degree of hybridization, a fully variable valve train reduces the fuel consumption additionally by up to 9% and advances the optimal degree of hybridization to 50%. Furthermore, a sufficiently high degree of hybridization renders the gearbox obsolete, which permits simpler vehicle concepts to be derived. A degree of hybridization of 65% is found to be fuel optimal for a vehicle with a fixed transmission ratio. Its fuel economy diverges less than 4% from the optimal fuel economy of a hybrid electric vehicle equipped with a gearbox.