Resonance of a Spring Opposed Free Piston Engine Device

Recent free piston engine research reported in the literature has included development efforts for single and dual cylinder devices through both simulation and prototype operation. A single cylinder, spring opposed, oscillating linear engine and alternator (OLEA) is a suitable architecture for application as a steady state generator. Such a device could be tuned and optimized for peak efficiency and nominal power at unthrottled operation. One of the significant challenges facing researchers is startup of the engine. It could be achieved by operating the alternator in a motoring mode according to the natural system resonant frequency, effectively bouncing the translator between the spring and cylinder, increasing stroke until sufficient compression is reached to allow introduction of fuel and initiation of combustion. To study the natural resonance of the OLEA, a numeric model has been built to simulate multiple cycles of operation. The MATLAB^® model combines differential relationships (for cylinder pressure and translator dynamics), empirical relationships (for heat transfer and friction), and simplifications (for gas exchange and a mechanical spring) to describe the primary dynamic elements acting on the translator. The translator is excited from rest by a sinusoidal forcing function which is defined by frequency and force amplitude. As an example, an engine with a 1 kg translator mass, 30 mm bore, maximum stroke of 45 mm, atmospheric intake pressure, and spring stiffness of 250 kN/m is given. When the motor applies a sine wave at 85 Hz with peak force at 400 N, the steady state stroke is found to be 30 mm with a compression ratio of 20 after 70 strokes. For the same system motored at a forcing frequency of 75 Hz, the resulting steady state stroke is reduced to 17 mm and the compression ratio to 3.2. Knowledge of the natural resonance for a given device will enable controlled motoring to achieve a desired stroke and compression ratio. This paper investigates the resonant nature of the OLEA and parametrically explores the forcing amplitude and frequency.