Combined dynamic and thermodynamic modeling of beta-type stirling engine with hypocycloid gear mechanism

Abstract

This study introduces a novel dynamic–thermodynamic modeling approach for a Beta-type Stirling engine incorporating a customized hypocycloid gear mechanism with a specific gear ratio of 1:2. This particular ratio offers a distinct advantage over previously studied gear configurations by enabling perfectly linear motion of both the power and displacer pistons. As a result, lateral forces are eliminated, allowing all gas expansion forces to contribute directly to useful work, thereby reducing frictional and structural losses. Compared to the widely used and mechanically efficient rhombic drive, the proposed mechanism delivers superior performance while simplifying the kinematic layout, achieving a mechanical effectiveness of 97 %.

The developed model couples thermodynamic gas force generation with multibody dynamic analysis using a Lagrangian formulation. Gas forces derived from instantaneous cycle pressure are applied to the dynamic model and updated at each iteration to compute the acceleration of the output shaft. Gear friction losses are calculated using elastic contact theory, enabling accurate prediction of dynamic losses. Validation against MSC ADAMS simulations confirms the model’s accuracy in predicting both piston motion and torque response.

The proposed system achieves higher thermal efficiency (13.1 % vs. 11.9 %) and second-law efficiency (40.1 % vs. 36.6 %) than the rhombic mechanism under comparable operating conditions, including swept volume, charge pressure, and temperature range, delivering 1958 W at 1496 rpm. A scaled configuration with 50 % reduced swept volume outputs 871 W at 1387 rpm. These results highlight the potential of the hypocycloid-driven Stirling engine for compact and efficient energy conversion in renewable and waste heat recovery applications.