Helical compression springs are used to resist compressive forces or store energy in push mode. They are found in many applications that include automotive, aerospace and medical devices. The common configuration of helical compression springs is straight cylindrical shape that has constant coil diameter, constant pitch and constant spring rate. Unlike cylindrical helical compression springs, concave helical compression springs have a larger diameter at each end and a smaller diameter in the middle of the spring. The variable coil diameter enables them to produce desired load deflection characteristics, reduce solid height, buckling and surging, and keep them centered on a larger diameter hole. The unique features of concave helical compression springs also raise their synthesis challenges. In this paper, a method is introduced to synthesize concave helical compression springs. The variable coil diameter of a concave helical compression spring is described by a spline curve. A cylinder with variable diameter is generated by revolving the spline curve on spring axis. The concave helical compression spring is then modeled by wrapping a spring wire on the variable diameter cylinder. The synthesis of a concave helical compression spring is systemized as the optimization of the geometric control parameters of its wrapped spring wire. A synthesis example is presented in the paper to verify the effectiveness and demonstrate the procedure of the introduced method.

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