Adjoint-Based Optimization of Hydrodynamic Lubrication Problems - Κουκολόπουλος, Ελευθέριος (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Μηχανολόγων Μηχανικών, 2016)
In the present thesis, hydrodynamically lubricated contacts are optimized using the continuous adjoint method and a simplified (1D) flow model. Such contacts can be found in almost any mechanical system and they are the main source of friction, which is responsible for power losses, material wear and even total failure of the component. Friction contacts operate under the regime of hydrodynamic lubrication, meaning that a thin fluid film separates the two interacting surfaces, in order to avoid metal to metal contact. So, optimization of the geometry design of sliding surfaces is critical for the reduction of power loss and wear. Optimization is performed aims either the maximization of load capacity or the minimization of the friction coefficient. For the purposes of optimization, the continuous adjoint-based method has been selected. Adjoint-methods belong to the wider category of deterministic optimization methods, which compute and use the derivative of the objective function. They are mathematical tools for the calculation of the gradient of an objective function, satisfying at the same time the primal equations describing the problem. The equation describing the hydrodynamic lubrication problem will be the Reynolds equation. The main benefit of the adjoint method is that the cost of the computation of the derivatives is almost equal to the cost of numerically solving the primal equation and completely independent of the number of design variables. So, several different geometries have been studied, representing the hydrodynamic slider found in mechanical components, with the use of the adjoint optimization method, aiming at the maximization of load capacity and for one case the minimization of friction coefficient additionally. For each different geometry case, the amount of design variables varies and the mathematical formulation is different and for that it is explained for each geometry in detail in the sub-chapters of Chapter 4. The chosen slider geometries are: simple converging slider (optimized for both load capacity and friction coefficient), converging and diverging slider and step slider (only load capacity). One last case has also been studied, where the design variables are the film thickness of each discretization point, meaning that their amount is equal to the number of grid points. Ideally with this method the geometry could take any possible shape and self-adjust to each case.