Abstract: Flexure springs are used in linear compressors and expanders to maintain the clearance seal between the piston and cylinder. The design method of Fermat flexure spring has been put forward. The fermat flexure spring can be obtained by adjusting the space distribution of spiral arms together with the parameters of Fermat curve including base radius r, coefficient of curvature c, start angle  ,curve angle θ, etc. Then the mathematical models were set up to analyze the axial and radial stiffness of the fermat flexure. Geometrically nonlinear static structural analysis and nonlinear dynamics structural analysis which base on the finite element software (ANSYS) and the performance test is made to fermat flexure spring. The feasibility of the method to design Fermat flexure spring, the validity of the numerical analysis and finite element analysis, are proved by comparing the calculated results, simulated results and experimental results.

Key words: Fermat curve, Flexure spring, Natural frequency, Stiffness