The compressing piston and cylinder of refrigerating compressor frequently come into failures as anti-wearability for metal material is weak. Engineering ceramics is appreciated by designers thanks to its excellent performances. However, it is difficult to machining material because of high hardness. The FEA modules for displacement and stress distributions of compressing piston and cylinder under declared running conditions are established based on the theories of elasto-plasticity and aerodynamics, which reveal the optimal precision conjugation clearance dependence of pressure distributions regularity between friction couple. Based on the FEA analytical results, the feasibility of replacing metal material with Si3N4 ceramics in the friction couple manufacture is researched. Special clamps have been designed to guarantee the superficial quality as mirror surface and tolerances of form and position, technological procedures are programmed, and with satisfactory machining effect.