Energy-based method for nonlinear characteristics analysis of Belleville springs

• The energy method is proposed and a new analytical solution of the load deformation characteristic of the Belleville springs was obtained.
• Compared with experimental results, the analytical solution has higher precision than the traditional A-L algorithm solution and the FEA method, and the validity of energy method is verified.
• The stiffness characteristic of Belleville spring with supporting surface can be improved and with the increase of the supporting surface width, the stiffness of Belleville spring grows.

In this study, based on the analytical model of circular plane plate with initial bending curvature under large deflection and conical shells theory, the energy method is proposed and a new analytical solution of the load deformation characteristic of the Belleville springs was obtained. Compared with experimental results, the analytical solution has higher precision than the traditional A-L algorithm solution and the FEA method, and the validity of energy method is verified. On this basis, the deformation energy is studied and the analytical solution is applied to the mono-freedom conservative system consisting of a single Belleville spring and mass. The natural frequency of the conservative system under free vibration is analyzed, followed by the discussion on two factors, the ratio of free height and width, the width of supporting surface, which affect load deformation characteristic of Belleville springs.