Figure 7. Maximum stress at 300 N.

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.

Figure 8. Maximum deflection at 700 N.

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.

Figure 9. Maximum stress at 700 N.

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.

Figure 12. Governing Equation.

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
Figure 10. Maximum deflection at 2000 N.

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.


Figure 11. Maximum stress at 2000 N.

Simulation results (Figures 4-7) show maximum deflection and Von Mises stress values in both models for specified load parameters. The cylindrical spring design shows limited deflection of 45 mm at 700 N (Figure 8), while the conical spring operates at 2000 N with 80 mm deflection (Figure 10). The conical spring shows maximum compression, negative solid height, and better oscillations compared to the cylindrical spring.

This optimized conical spring design shows the potential to operate in harsh conditions compared to regular springs in a shock absorber. The conical compression spring design can offer superior lateral stability and ride comfort. Negative solid height can be achieved by conical compression springs in a shock absorber, which will help to reduce impacts. The conical spring design can provide better oscillation and wheel-to-ground contact. Nonlinear multiphysics study will be performed for structural design optimization, and development of energy-harvesting, low-cost, high-performance shock absorbers.

This article was written by Asutosh Prasad and Raj C Thiagarajan of ATOA Scientific Technologies, Bengaluru, India. For more information on the COMSOL products used in this project, visit .

Motion Control & Automation Technology Magazine

This article first appeared in the September, 2016 issue of Motion Control & Automation Technology Magazine.

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