Magister Legum - LLM

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This thesis presents numerical and experimental investigations into Electrochemical Machining (ECM). The aim is to develop a computer program to predict the shape of a workpiece machined by the ECM process. The program is able to simulate various applications of EC machining which are drilling, milling, turning and shaped tube electrochemical drilling (STED). The program has been developed in a MATLAB environment. In this present work, EC-drilling, EC-milling and EC-turning are analysed as three-dimensional problems whereas STED is simulated in two-dimensions. Experiments have been carried out to verify the accuracy of the predicted results in the cases of EC-milling and EC-turning. The ECM modeller is based on the boundary element method (BEM) and uses Laplace's equation to determine the current distribution at nodes on the workpiece surface. In 3D, the surfaces of the tool and the workpiece are discretised into continuous linear triangular element types whereas in 2D, the boundaries of the tool and workpiece are discretised into linear elements. The ECM modeller is completely self-contained, i.e. it does not rely on any other commercial package. The program contains modules to automatically discretize the surfaces/boundaries of the tool and workpiece. Since the simulation of the ECM process is a temporal problem, several time steps are required to obtain the final workpiece shape. At the end of each time step, the shape of the workpiece is calculated using Faraday's laws. However, the workpiece's shape changes with progressing time steps causing the elements to become stretched and distorted. Mesh refinement techniques are built in the ECM modeller, and these subdivide the mesh automatically when necessary.The effect of time step on the predicted 3D shape of a hole in EC-drilling is investigated. The effect of discontinuity in the slope between neighbouring elements is also studied. Results obtained from the ECM modeller are compared with 2D analytical results to verify the accuracy that can be obtained from the ECM modeller. Milling features ranging from a simple slot to a pocket with a complex protrusion were machined in order to determine the feasibility of the EC milling process. These features were machined on a 3-axes CNC machine converted to permit EC milling. The effect of tool geometry, tool feed rate, applied voltage and step-over distances on the dimensions, shape and surface finish of the machined features were investigated. A pocket with a human shape protrusion was machined using two different types of tool paths, namely contour-parallel and zig-zag. Both types resulted in the base surface of the pocket being concave and the final dimensions of the pockets are compared with the design drawing to determine the effect of tool path type on the accuracy of machining. The ECM modeller was used to simulate the machining of a thin-walled turned component. The machining parameters, i.e. initial gap, rotational speed, and applied voltage, were specified by the collaborating company. Since only a small amount of material had to be removed from the thin-walled component, the tool was held stationary i.e. a feed in the radial or longitudinal direction was not required. By taking advantage of the axi-symmetric nature of a turned component, only a sector of the component was analysed thereby reducing the computing time considerably. The accuracy of the modeller was verified by comparing the predicted time to machine the thin-walled component with the actual machining time. The initial investigations in STED were both experimental and numerical in nature and they studied the effect of applied voltage, tool feed rate and electrolyte pressure on the dimensions of the holes. Later investigations were numerical and an iterative methodology has been developed to calculate a set of feed rates which could machine a specified turbulator shape.

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The aim of this thesis is to prove the existence of the Shilov boundary and the minimal boundary with respect to some function algebras and investigate their topological structures. / Science, Faculty of / Mathematics, Department of / Graduate

Anticosti Island, located in Eastern Canada, displays one of the most complete, best exposed, and most fossiliferous carbonate successions spanning the Ordovician-Silurian (O/S) Boundary in the World. This study develops a new high-resolution framework for the post End-Ordovician extinction strata (~ 260 m thick) exposed in coastal outcrops and recovered from a continuous drill core (La Loutre #1), both located in the western part of the island. In total, eight facies, all associated with a storm-dominated carbonate system, were recognized and organized into a multi-order depositional cycles. A new high resolution isotopic curve with more than 300 data points from well-preserved bulk micrite samples covers the late Hirnantian to Early Aeronian time interval and corresponds to the upper Ellis Bay, Becscie, Merrimack and lower Gun River formations. Two distinct positive carbon isotope excursions are present in the late Hirnantian part of the Ellis Bay Formation (+5‰) and in the lower Aeronian part of the Gun River Formation (+2‰). These positive isotopic carbon excursions provide a distinctive chemostratigraphic signature for regional and global correlations with other O/S sections. Like the Quaternary δ18O marine signal, our δ18O record is largely coupled with multi-order cyclic facies changes. This study demonstrates the importance of glacio-eustasy following the End-Ordovician glacial maxima as one of the primary factors controlling the stratigraphic architecture of paleotropical neritic carbonates during the Early Silurian.

The transient flow in pipe networks is represented by a pair of quasi-linear hyperbolic partial differential equations. The method of characteristics is used to transform these equations to a set of ordinary differential equations, which are then solved, by a first order finite difference technique using suitable boundary conditions. The main purposes of these investigations are: 1) To derive suitable boundary conditions or boundary condition equations for valves, sprinklers, surge tanks and air chambers, and 2) To investigate the effect of these boundary conditions on the transient flow in pipe systems. Several numerical examples are solved on the digital computer using the method of characteristics. The results are compared with those obtained by the graphical method. Although in this thesis the developed boundary conditions are used to study the transient response of the irrigation pipe systems, the boundary conditions, without any modification, can be used to determine the transient conditions in water supply pipe networks or in pipes carrying other liquids. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A thrust anemometer was designed to measure the three components of wind velocity fluctuations in the atmospheric boundary layer over the surface of the sea, and hence to evaluate directly the Reynolds stress of the wind on the sea. The anemometer was shown to be suitable for its intended purpose first by wind tunnel tests and then by comparisons with spectra from measurements in the field by cup and hot-wire anemometers. Spectra and cospectra of wind velocity fluctuations were calculated by analog analysis for thirty-two runs of 32 minutes' duration each at the Spanish Banks experimental site and for one run at another site. The spectra of downwind and of vertical velocity fluctuations were each found to be grouped closely when plotted in normalized form, and an empirical formula was given for the low-frequency end of the vertical velocity spectrum. The correlation of the downwind and vertical velocity fluctuations was found to be -0.5 at low frequencies and to approach zero at higher frequencies. The average value of the drag coefficient of the surface of the sea for the thirty-three runs was .0010 and no significant variation with wind speed was observed over the range 3 to 13 m/sec. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A study of laminar free convection about horizontal plates of finite width with one side heated isothermally and the other insulated is presented in this thesis. This investigation forms part of a continuing program, and its technological origin and significance are discussed in the introduction. The governing partial differential equations comprising the continuity, momentum and energy equations are solved numerically through a finite difference method using a successive-over relaxation technique for a Rayleigh number range from 0.22 to 500, at three values of Prandtl number (0.72, 5.0 and 10.0). The variation of the flow, vorticity and temperature fields with the change of both Grashof and Prandtl numbers is discussed on the basis of the streamline, iso-vorticity and isothermal plots obtained . The effect of Prandtl number alone on the momentum field, energy distribution and heat transfer rate is discussed, by a comparison of the isotherms, streamlines and correlation curves obtained for the three different Prandtl numbers. The theoretical analysis places emphasis on the singular nature of the boundary conditions specified and on the influence of the finite size of the domain of the finite difference scheme. Some results for an upward facing horizontal isothermally heated plate of finite width were also obtained, and were compared to data for the downward facing case. A semi-focussing Schlieren colour system was used order to investigate experimentally the flow behaviour on a horizontal plate with the heated surface facing-downward The experimental results sought were evidence of the non-boundary layer nature of the flow. The evidence of non-boundary layer flow was obtained conclusively. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate