Phase transitions in a resonating free-piston engine generator

The phase difference between the excitation force and the response of a resonating free piston engine generator, has been examined by numerical simulation, for both resonant starting, and self-excited resonant operation. This is achieved by using a simple nonlinear model of a resonating free piston generator, first undergoing resonant starting, then undergoing a self-excited resonant Otto cycle. The resonant starting results show that the system is highly sensitive to very small changes in both amplitude and frequency. The resonant starting results also show that with harmonic excitation at the operational resonant frequency, the response phase is only moderately delayed behind the excitation. Under resonant operating conditions, the phase difference between the fundamental harmonic component of the self-excitation, and the fundamental harmonic component of the displacement response have also been obtained by simulation, and found to be very small, suggesting the excitation and response are almost in phase. The implications of this finding in making the transition from resonant starting to self-excited operation (involving fired combustion) are assessed and appropriate guidance given.