The non-orthogonal bevel gear is the key component of a four-cylinder double-acting Stirling engine variable incline angle swashplate drive device,which can be used to support the torque of the inclined plate inclination in the angle adjustment of the inclined plate. In order to ensure the reliable and effective operation of the engine,the design of bevel gear and the analysis of fine strength are necessary. Based on this,in view of the high power four-cylinder double-acting Stirling swashplate engine,based on the variable angle of inclined plate transmission device layout requirements,the parameter design research of a Stirling engine nonorthogonal bevel gear transmission system is conducted,three-dimensional model of fine bevel gear contact strength analysis is established. Secondly,simulation analysis is carried out by using the finite element analysis software Workbench to verify the performance of the non-orthogonal bevel gear transmission system. On this basis,the influence of geometrical parameters on meshing properties of bevel gears is discussed. The results show that the maximum shape variables and the maximum stress of the gear are decreased with the increase of the tooth number in a certain range. This conclusion will provide certain theoretical basis for design and dynamic analysis for four-cylinder double-acting Stirling engine variable angle of inclined plate drive system optimization and performance improvement.