Modeling of the Internal Combustion Engine by Means of Willans Line Approach for the Study of Hybrid Electric Powertrain
Authors: Tarsitano Davide , Mazzola Laura , Cheli Federico , Mapelli Ferdinando 
Published: July 2016

The use of road vehicles has always represented a major contribution to the growth of modern society: it facilitates goods and people mobility, meeting most of the daily needs and it represents a backbone for the development of world economy, (i.e. the industrial field). Nowadays, this mean of transportation, however, given the high number of vehicles on the roads, has a negative impact both on the environment and on the quality of human life. Moreover it leads to an increase in additional costs (i.e. the costs related to environment pollution, global warming and depletion of resources). Such a negative aspect is due to the fact that the drive systems are often characterized by high variability of the load, hence the propulsion system works in areas with low efficiencies and high pollutant emissions. In order to overcome these problems, and to allow the compliance of the road transport system with new European guidelines (i.e White paper, and Horizon 2020), it is necessary to develop innovative technologies able to:

- increase the overall powertrain efficiency;

- introduce a sustainable alternative fuels strategy including also the appropriate infrastructure;

- reduce carbon emission through a decarbonisation approach;

In this perspective, in recent years, the technology of electric and hybrid vehicles has been developed, and nowadays it has become a feasible solution in the context of means of transportation. Car/truck-makers and operators look at further developments and innovation in this field in order to optimise the existing solutions and reduce the production costs.

The current solution for hybrid vehicles aims to couple a conventional engine with an electrical motor; these two propulsion system are coordinated by an opportune algorithm in order to let the conventional engine operate in its higher efficiency range. Hence the technology foresees the action of endothermic and electrical motors. It is then pivotal for the success of this transport the optimisation of the whole system (electrical and endothermic) in terms of efficiency, sizing and of the control algorithm that coordinate the two propulsion systems. For the modeling of the internal combustion engine conventional approaches, based on the numerical simulation of the combustion process, cannot be used because of their complexity in term of time needed for computing activity. For hybrid power train the general approach to simulated a drive cycle, that usually last at least a few minutes, is based on engine map approach [1–2]. The main burden to the described process is the identifications of maps of torque and consumption for the internal combustion engine, which are normally not predictable in detail, nor are provided by the manufacturers, but they can only be determined by means of experimental tests. Such a process can become extremely expensive and time consuming. Hence in this work the concept of virtual optimisation is introduced basing on the identification of torque and fuel consumption maps for internal combustion engines on analytical methods considering the similarities with engine of the same class. In this regard, a model of the system is developed based on the “Willans Line Method” approach, subsequently to a theoretical definition of the model, the identification of maps is carried out for two different engines (one diesel heavy-duty engine and one spark ignition engine) in order to consider the existing configurations of hybrid vehicles. Eventually the calculated maps are validated considering experimental data from existing experimental campaign. Providing the validity of the method and its usefulness in the hybrid vehicle design.