Design optimization of flexure springs for free-piston stirling engines and experimental evaluations with fatigue testing

The free-piston Stirling engine is a closed-cycle regenerative heat engine that converts heat energy into mechanical work, and requires a spring element for vibratory operations of the displacer and power pistons. In this study, the geometry of the flexural spring design was optimized through structural finite element analyses and fatigue test evaluations. First, we constructed a target design space considering the required natural frequency of the displacer spring assembly under the geo-metric constraints of total mass and module height. The design of experiments was employed to construct simulation cases for design factors such as the outer diameter, thickness, and number of spirals in the spring sheet. As a result, the optimized design values were obtained to satisfy the design requirements. We also fabricated a test spring specimen and conducted fatigue tests using a linear actuator system developed to have the same motion as the engine. The test results indicated that the optimized spiral spring had no fracture under operating conditions with the design piston amplitude, revealing the effectiveness of the design method.