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A simulation study was conducted to examine the transition from SI combustion to HCCI combustion in a two-stroke free piston engine fuelled with propane. Operation of the free piston engine was simulated based on the combination of three mathematical models including a dynamic model, a linear alternator model and a thermodynamic model. The dynamic model included an analysis of the piston motion, based on Newton's second law. The linear alternator model included an analysis of electromagnetic force, which was considered to be a resistance force for the piston motion. The thermodynamic model was used to analysis thermodynamic processes in the engine cycle, including scavenging, compression, combustion, and expansion processes. Therein, the scavenging process was assumed to be a perfect process. These mathematical models were combined and solved by a program written in Fortran.