Optimization of Isochronous Motion Characteristics and Output Power Parameters for Gamma‐Type Stirling Engine Based on Response Surface and Grey Relational Analysis

Enhancing the operational performance of Stirling engines is significant for addressing energy issues. This study focuses on the synchronous motion mechanism and power output characteristics of the displacer and piston in a gamma‐type Stirling engine, using response surface methodology (RSM) to analyze five key parameters: the ratio of displacer to piston radius ( H ), distance between expansion space bottom and displacer ( L 1 ), distance between back space top and piston ( L 4 ), displacer mass ( m 1 ), and piston mass ( m 2 ). Under the constraint of synchronous piston motion, optimization for maximum output power is conducted, showing that the maximum output power reaches 97.3242 W when H = 0.302, L 1 = 0.09 m, L 4 = 0.003 m, m 1 = 0.218 kg, and m 2 = 0.245 kg. Laboratory tests verify an 8.81% increase in output power from 85.1 to 92.6 W. Grey relational analysis (GRA) evaluates the influence weights of factors on output power, with the ranking m 2 > H > m 1 > L 1 > L 4 . This study identifies key parameters affecting synchronous characteristics, establishes a high‐fitting model via RSM, and clarifies parameter influence priorities through GRA, providing guidance for Stirling engine optimization.