A fluid solid interaction model of lubricated soft contacts with application to windscreen wipers

Abstract

Developing reliable Fluid-Solid-Interaction models are important for understanding the tribological behaviour in compliant contacts in lubricated conditions. This is particularly important for applications such as seals and windscreen wipers, which play a significant role in e.g. the automobile industry. This thesis presents a thorough modelling and computational solution framework aimed at the numerical simulation of a wiper blade sliding against glass in a wide range of lubrication regimes in steady-state conditions. Three modules each containing a unique algorithm are demonstrated to handle the coupling between the fluid flow and the solid deformation and capture the transition between different lubrication regimes. Whilst the hydrodynamic pressure is obtained by solving the Reynolds equation with Finite Difference method and Gauss-Seidel iterative scheme, the interaction between asperities can be described using analytical formulations based on Persson’s theory or the boundary element method (BEM) which solves the contact problem deterministically. As the latter provides more flexibility dealing with any given rough surfaces (measured or computer generated), it is employed here together with the Fast Fourier Transform (FFT) technique and the Conjugate Gradient (CG) iterative method to determine the variation of the real contact areas and the interfacial separation with respect to the applied load. These relations are represented as fitted functions and act as solid solvers in the presented FSI model. The effect of the thermodynamic correction, the continuum correction, the fractal correction and the surface property Hurst exponent, which usually affects the accuracy of the numerical analysis, are assessed in a systematic manner to provide general guidance for the employment of the BEM. Elastic deformation, which is critical in determining the film thickness, is calculated by means of an innovative Reduced Stiffness Method, which is based on the finite element method and model condensation techniques. This approach has been validated for both linearly elastic and non-linearly elastic (hyper-elastic and viscoelastic) materials in static and sliding conditions. Depending whether the contact behaviour is associated with small or large strain deformations, the initial stiffness matrix or the deformed stiffness matrix can be extracted from the finite element model at a certain state and incorporated into the FSI model to account for the finite deformation of compliant solids due to geometric and material nonlinearity, respectively. The proposed model has been compared with experimental measurements and has shown a good agreement in terms of friction prediction for elastomer specimens of triangular cross-section. For real wiper blades, simulations have shown that the accuracy of model predictions is sensitive to quantities such as the roughness, the input configuration and the reduced stiffness matrix employed, which are evaluated regarding their relative importance. Suggestions on how to obtain improved performance and further investigations aimed at clarifying the behaviour of these complex systems in different scenarios have also been proposed.