Modelling of cord-rubber composites of bellow air-springs

Due to the complex composite material, the nonlinear material response of the two constituents, the anisotropy, the nearly incompressible rubber matrix and the large displacements and rotations, lots of approaches have been done to cover all these effects. See for example Pidaparti (Pidaparti, Henry, & Soedel 1992) for the modelling of single ply cord-rubber composites, or Cesar de Sa (Cesar de Sa & Owen 1987) and Ferreira (Ferreira, Cesar de Sa, & Marques 2003) for a numerical formulation of reinforced rubber shells. In (Meschke & Helnwein 1994) a smeared constitutive material formulation based on overlay or rebar elements is used to model the material behaviour of cord-rubber composites. This formulation is well suited for global simulations but can not represent the material heterogeneity. The modelling of the heterogeneity of the material was for example subject of the work by Polley (Polley 1999) and Jacob (Jacob 1995), where approaches for the boundary conditions of multi-axial loadings and the modelling of the constitutive material behaviour has been carried out. For simple bellow shapes for example a tube shaped bellow Brüger (Brüger, Merk, & Pelz1 INTRODUCTIONSmarter suspension systems, higher loads and more wishes for comfort lead to a demand in more research for air-spring systems. It is important to understand the reliability and the failure mechanisms under specific loading conditions. There is a need to develop new modelling tools to look more into the details of the composite material and their constituents. This paper presents a method to model cord-rubber composites of bellow airsprings using the finite element method with a multi-scale approach. Bellow type air-springs are widely used in industry. They are used for example in machine basements for vibration isolation or in railway boogies as parts of the suspension system. The latter is the object of this paper but the method will be applicable for any kind of bellow air-spring systems.