Analysis of prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape by analytical and finite element methods

•Analytical formulations of axial deflection different springs under axial load.•CAD modeling and FEA of prismatic and non prismatic springs of different coil shapes.•Comparison of stress and deflection in mass-equivalent springs of different geometry.•Approx. analytical formulation for the location and value of max. stress in springs.•Effects of spring shape on damping, vibrational properties in 1D systems and buckling.

This paper presents a methodology for designing prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape using analytical and numerical methods. To start with, simple analytical formulations for obtaining the axial deformation of the springs under axial load have been demonstrated. Next, the processes of obtaining CAD models of the springs and their subsequent finite element analysis (FEA) in commercial softwares have been outlined. In the third part, the different springs have been compared with a common cylindrical spring and their merits compared to a common spring have been demonstrated. Next, a fairly accurate analytical formulation (with maximum error of ∼7-8%) for obtaining the value and location of maximum shear stress for all the springs has been demonstrated. Next, two aspects of non-prismatic springs under dynamic loads, viz. damping introduced in a vibrating system and contribution of the spring to the equivalent mass in a one dimensional vibrating spring mass system due to shape of the spring have been discussed. The last part involves an analytical formulation for the linear elastic buckling of two springs with circular coil shapes. For the majority of the work, emphasis has been on obtaining and using closed form analytical expressions for different quantities while numerical techniques such as FEA have been used for validation of the same.

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