Frequency-based design of a free piston Stirling engine using genetic algorithm

This paper focuses on the frequency-based design of a FPSE (free piston Stirling engine) using a GA (genetic algorithm). First, a mathematical description of the FPSE is presented. The engine design parameters including mass and stiffness of power and displacer pistons and cross-sectional area of the displacer rod are considered as unknown variables. Then, based on a desirable operating frequency, positions of closed-loop poles of the engine system are selected. The unknown design parameters are thus found via an optimization scheme using GA. A new objective function based on the eigenvalues of the state matrix of the FPSE is proposed and GA is used to obtain the optimal values of design variables so that the objective function is minimized. Next, the effectiveness of the proposed design is evaluated through numerical simulation. Two mathematical approaches are presented to compute the phase difference between the motions of power and displacer pistons. Furthermore, the generated work and power of the FPSE are found based on the computed phase angle. Finally, the designed FPSE is constructed and primarily tested. It is found that the simulation results are in a good agreement with the experiment through which validity of the presented design technique is affirmed.