Tom Gustafsson

Nonlinear Reynolds equation for hydrodynamic lubrication

Abstract We derive a novel and rigorous correction to the classical Reynolds lubrication approximation for fluids with viscosity depending upon the pressure. Our analysis shows that the pressure dependence of viscosity leads to additional nonlinear terms related to the shear rate and arising from a non-negligible cross-film pressure. We present a comparison of the numerical solutions of the classical Reynolds equation and our modified equation and conclude that the modified equation leads to the prediction of higher pressures and viscosities in the flow domain.

Development of Nanostructured Al2O3-Ni HVOF Coatings

HVOF thermal spraying has been developed to deposit dense Al2O3-coatings for improved protective properties. As compared to generally used plasma sprayed coatings HVOF coatings can be prepared much denser and thus are better suited for applications where protective properties of the coating are needed. In this paper we describe the development of HVOF spraying technologies for nanocrystalline Al2O3- and Al2O3-Ni-coatings. The microstructure and the mechanical properties of these novel coatings are reported and compared to a conventionally processed Al2O3-coating.

A POSTERIORI ESTIMATES FOR CONFORMING KIRCHHOFF PLATE ELEMENTS

We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported, and free boundary conditions subject to both distributed and concentrated (point and line) loads. Extensive numerical computations are presented to verify the functionality of the estimators.

On Finite Element Formulations for the Obstacle Problem - Mixed and Stabilised Methods

Abstract We discuss the differences between the penalty, mixed and stabilised methods for the finite element approximation of the obstacle problem. The theoretical properties of the methods are discussed and illustrated through numerical examples.

Process Optimization for Nanostructured HVOF -Sprayed Al2O3-Based Ceramic Coatings

Special mechanical properties have widely been demonstrated with bulk nanocrystalline materials. An increasing effort has been made to transfer such improvements also into thermal sprayed ceramic coatings. This paper focuses on such efforts in alumina-based ceramic coatings. The optimization of process conditions and effect of different process parameters on the mechanical performance of high velocity oxy-fuel (HVOF) sprayed ceramic coatings is discussed.

An adaptive finite element method for the inequality-constrained Reynolds equation

Abstract We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.

A stabilised finite element method for the plate obstacle problem

We derive a residual a posteriori estimator for the Kirchhoff plate bending problem. We consider the problem with a combination of clamped, simply supported and free boundary conditions subject to both distributed and concentrated (point and line) loads. Extensive numerical computations are presented to verify the functionality of the estimators.

Stochastic Galerkin approximation of the Reynolds equation with irregular film thickness

Abstract We consider the approximation of the Reynolds equation with an uncertain film thickness. The resulting stochastic partial differential equation is solved numerically by the stochastic Galerkin finite element method with high-order discretizations both in spatial and stochastic domains. We compute the pressure field of a journal bearing in various numerical examples that demonstrate the effectiveness and versatility of the approach. The results suggest that the stochastic Galerkin method is capable of supporting design when manufacturing imperfections are the main sources of uncertainty.