Cylindrical compression springs are wound in the form of a helix of a wire on cylindrical geometry. The major stresses produced are shear due to twisting. The applied load is parallel to the axis of spring. The cross section of the wire may be round, square, or rectangular. Figure 2 shows the cylindrical compression spring model used in this application. The cylindrical compression spring is rigidly attached with two circular rings at both ends.

Conical compression springs are wound in the form of a helix of a wire on conical geometry. The major stresses produced are also shear due to twisting, and tensile and compressive stress due to bending. Figure 3 shows a conical compression spring design used in this experiment. In this design, both ends of the springs are rigidly attached with two different diameter circular rings.

#### Numerical Modeling Simulation

In this application, the damping performance of cylindrical and conical compression springs is analyzed numerically. The numerical model is developed with the solid mechanics interface of COMSOL Multiphysics software (COMSOL, Inc., Burlington, MA). A linear stationary analysis is performed to obtain desired deflection and stress at various loading conditions.

Figures 2 and 3 represent the CAD models of respective spring designs used in this investigation. Both models are designed to have same coil diameter, free length, number of active coils, and material properties.

• Material Density (⍴) = 7850 kg/m3
• Young’s Modulus (E) = 200 GPa
• Poisson’s Ratio (ν) = 0.33

Individual spring models are assumed to be fixed at the bottom end, and compressive force is applied to the top end. The radial deflection is neglected for the current application. A varying compressive load of 100 N to 2000 N is applied parametrically in the linear stationary study environment.

#### Governing Equation

The differential equation shown in Figure 12 (where x = Displacement, k = Spring Stiffness, and m = Loaded Mass) is implemented for both spring designs, and solved in the solid mechanics physics environment of COMSOL Multiphysics.

#### Results 