A theoretical model of amplitude-dependent dynamical stiffness for cord-rubber air springs

Based on the principle of minimum complementary energy, a theoretical model considering the additional dynamic stiffness caused by the structural deformation of the cord-rubber diaphragm is proposed. The capability of modeling the dynamic stiffness change of the rolling lobe air spring provides guidance for material selection and the design of the diaphragm structure. The directly measured geometric parameters in the proposed model have physical meanings, while the relevant material parameters can be identified by combining the mechanics of composite materials and the Payne effect theory of rubber diaphragm structures. Three air springs with different designs and structures were selected for the indicator test and compared with the theoretical value. The comparison results show that the relative error was less than 3%, which verifies the universality and accuracy of the proposed dynamic stiffness theory of the rubber diaphragm. The results demonstrate that the amplitude-dependent additional stiffness generated by the rubber diaphragm is significant, and the lobe bending moment has the most considerable stiffness contribution to the rolling lobe air spring at low amplitudes. In the end, the changing trend of the entire dynamic stiffness with different design factors is given. The rubber diaphragm stiffness theory of rolling lobe air springs proposed in this paper provides powerful assistance for material selection and shape design for car air springs.