published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

<p>The purpose of this thesis was to study the influence of manufacturing variations on gear performance. The manufacturing variations inherent in different manufacturing methods were studied to include the effect of real surfaces. Real surfaces have surface irregularities at least on some scale, which can significantly influence how loads are transmitted at the gear contact. To some extent, the lubricant design can help to prevent contact that could lead to tooth failures by forming a protective surface boundary layer. An experimental study was used to consider the compositions of these layers with a surface analysis method.</p><p>In Paper <strong>A</strong> a robust design approach was used to find out to what extent the current standard for calculation of surface durability treats manufacturing variations and the choice of lubricant. The results show that the simplest calculation method used is not enough to predict the effect of these on surface durability. Additionally, the standard quality levels are poorly incorporated in the standard calculating procedures for surface durability, and the quality of the gear tooth is restricted to include only a few parameters.</p><p>In Paper <strong>B</strong> a pin-on-disc machine was used to evaluate the tribofilm formation by the additives and the corresponding wear occurring in the boundary lubrication regime in environmentally adapted lubricants. Studies of the additive and base fluid interaction were carried out using glow discharge-optical emission spectroscopy. It was found that the chemically reacted surface boundary layers played an important role in terms of wear. More specifically, the oxide layer thickness had significant influence on wear. The findings also demonstrate the complexity of lubrication design formulations coupled to these layers. For example, it was found that the pre-existing surface boundary layer (before any lubricant had been added) played an important role in allowing the lubricant to react properly with the surfaces.</p><p>The aim of Paper <strong>C</strong> was to contribute to the knowledge of how different surface topographies, tied to manufacturing methods, influence the early life contact conditions in gears. Topographical measurements of differently manufactured tooth flanks were used as data input to a contact analysis program. The variation in surface topography inherent in the manufacturing method was found to have a strong influence on the contact area ratio.</p>

<p>Boundary integral equation techniques are useful in thenumerical simulation of scattering problems for wave equations.Their advantage over methods based on partial di.erentialequations comes from the lack of phase errors in the wavepropagation and from the fact that only the boundary of thescattering object needs to be discretized. Boundary integraltechniques are often applied in frequency domain but recentlyseveral time domain integral equation methods are beingdeveloped.</p><p>We study time domain integral equation methods for thescalar wave equation with a Galerkin discretization of twodi.erent integral formulations for a Dirichlet scatterer. The.rst method uses the Kirchho. formula for the solution of thescalar wave equation. The method is prone to get unstable modesand the method is stabilized using an averaging .lter on thesolution. The second method uses the integral formulations forthe Helmholtz equation in frequency domain, and this method isstable. The Galerkin formulation for a Neumann scattererarising from Helmholtz equation is implemented, but isunstable.</p><p>In the discretizations, integrals are evaluated overtriangles, sectors, segments and circles. Integrals areevaluated analytically and in some cases numerically. Singularintegrands are made .nite, using the Du.y transform.</p><p>The Galerkin discretizations uses constant basis functionsin time and nodal linear elements in space. Numericalcomputations verify that the Dirichlet methods are stable, .rstorder accurate in time and second order accurate in space.Tests are performed with a point source illuminating a plateand a plane wave illuminating a sphere.</p><p>We investigate the On Surface Radiation Condition, which canbe used as a medium to high frequency approximation of theKirchho. formula, for both Dirichlet and Neumann scatterers.Numerical computations are done for a Dirichlet scatterer.</p>

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Very accurate methods, based on boundary integral techniques, are developed for the study of multiple, interacting fluid interfaces in an Eulerian fluid. These methods are applied to the evolution of a thin, periodic layer of constant vorticity embedded in irrotational fluid. Numerical regularity experiments are conducted and suggest that the interfaces of the layer develop a curvature singularity in infinite time. This is to be contrasted with the more singular vorticity distribution of a vortex sheet developing such a singularity in a finite time.

The evolution of the large scale structures and the mean field were investigated in axisymmetric and plane mixing layers. Some aspects of the linear instability of an axisymmetric jet have been demonstrated. The axisymmetric geometry admits two additional length scales with relation to the two-dimensional shear layer: the radius of the jet column and the azimuthal wavelength. The importance of these two length scales in governing the instability of an axisymmetric jet was explored. The special case of a thin axisymmetric shear layer was analyzed and the results stressing the evolution of different azimuthal modes were compared with some phase-locked data which was produced by subjecting the jet to axisymmetric and helical excitation. The importance of the initial spectral distribution in a natural jet was demonstrated when it is used as an input to the amplification curve obtained from linear stability theory to predict a measured spectral distribution at a further downstream location. The inclusion of the nonlinear terms in the stability analysis reveals two main interactions: mean flow-wave interaction and wave-wave interaction. The modification of the mean flow of an axisymmetric jet was examined by exciting two azimuthal modes simultaneously. The interaction resulted in an azimuthal modulation of the mean velocity profile having a cosine shape. Effectively, the geometry of the jet was modified without changing the geometry of the nozzle. The coupling between an excited periodic disturbance and the mean flow was analyzed and the spatial evolution of both were compared with experimental results obtained in a plane mixing layer. The behavior of the concommittant Reynolds stresses is discussed in detail. The conditions under which one disturbance will transfer energy to another were derived and demonstrated in an axisymmetric jet. The interaction between a large amplitude plane wave with a weak subharmonic component was shown to enhance the amplification rate of the subharmonic. It was further shown that the nonlinear interaction between two azimuthal modes can produce a third azimuthal mode which was not initially present in the flow. The coupling between a fundamental wave and its subharmonic in a parallel plane mixing layer was demonstrated numerically.