<p>The power output from a high turning angle turbine blade passage depends on many factors and the most important of all is the appropriate pressure distribution along the pressure and suction surfaces of the blades. The operation of a fully choked passage requires the specification of the proper operating pressure ratio to avoid the formation of any compression waves after the geometric throat which would otherwise generate a total pressure loss for the system.</p> <p>With the advancement of computational methods, the two-dimensional supersonic flow field existing after a choked passage is elaborately analysed to avoid the adverse effect of compression waves on the blade performance. For different pressure ratios the characteristic waves as well as the pressure distribution are presented which give a theoretical prediction for the presence of a possible shock wave after the geometric throat of the passage. The shock free operation of the passage definitely increases the power output of the cascade. The stream tube method of pressure distribution is extended for generating the characteristic waves covering the entire supersonic flow field existing near the trailing edge of the fully choked passage of a high turning angle turbine blade passage.</p> / Master of Engineering (ME)

<p>The deformation of circular and elliptical steel diaphragms subjected to hydrostatic pressure is investigated and the different modes of failure of these diaphragms are analysed and compared.</p> <p>An experimental program is carried out to determine the inherent variability of the forming-limit curves where a number of samples from different grades of deep drawing quality steel are hydrostatically bulged to failure. A quantitative metallographic analysis is also performed in an effort to establish a relationship between microstructural parameters and formability.</p> <p>A hypothetical model of ductile fracture is proposed to predict the formability of a sheet which contains a population of voids and is subjected to a non-uniform biaxial straining process. A simulation process is developed for this model using the Marciniak analysis and the extreme value theory. Numerical solutions are obtained to show the influence of material defect parameters and process variables on the distribution of forming limits. Theoretical results are then compared with the experimentally determined forming limit curves.</p> / Doctor of Philosophy (PhD)

<p>An approach to study control problems in complex systems of interacting, mixed variable processes is presented. Discrete event simulation is combined with continuous simulation to provide a versatile method for system modelling and analysis. Provisions are made to include a human model into the model of a real system which allows an accurate reproduction of systems in which human control is an integral part. A special model display unit was built to provide feedback to the model operator, which can be readily connected to a hybrid computer. The display unit permits operation of the model by process people with no detailed knowledge of simulation which is an added advantage.</p> <p>A copper smelter system was modelled and simulated on a hybrid computer which includes discrete as well as continuous processes and requires human control to integrate the process to achieve a maximum output. The system thus represents a good example for a variety of similar systems encountered in industry. Semi-empirical models of smelting processes were developed based on existing knowledge of the processes. Using the display unit the evolutionary development necessary for some models was possible.</p> <p>The simulation model was calibrated and validated to accurately reproduce the real system behaviour. Based on simulation experiments on improved operating technique for controlling aspects of the smelting process was tested and an increase in production was predicted. This operating technique was tested in plant trials and adopted while the predicted production increase was verified.</p> <p>The validated model was then used to develop heuristic decision and forecasting algorithms optimal control of model operations. Based on the realistic model diffrent decision strategies could be tested by observing their success in controlling the simulation model. The control algorithms were refined to give a satisfactory control of the simulation model, without the need of human intervention. The smelter model with the heuristic control can thus serve as a useful tool in developing an on-line control system for the real system, which could be used as a decision making aid to operating personnel.</p> / Doctor of Philosophy (PhD)

<p>Superplasticity is a hot-working phenomenon exhibited by many metallic alloys and observed above a temperature of about 40% of the absolute melting point. It is characterized by an ultra-fine grain microstructure, an unusually high rate dependence and very low resistance to deformation at low strain rates.</p> <p>The plasticity theories and constitutive equations used in the analysis of secondary creep in structures are shown to be formally applicable to the study of superplastic deformation. A non-linear viscous model, with certain limitations, is employed to analyze superplastic deformation problems.</p> <p>This thesis presents three separate and independent pieces of work. These problems namely; (a) analysis of post-necking geometry in tensile-forming processes, (b) creep testing of superplastic material in sheet form and (c) reverse-extrusion of rate-dependent materials, represent in the author's opinion three most important problems relating to the use of superplastic alloys in industry.</p> <p>In tensile forming processes of superplastic alloys the deformation is unstable and it is shown that geometric non-uniformities develop continuously. The features of such deformation system are illustrated by the numerical analysis of initially non-uniform, tensile bars and thin-walled tubes expanded by internal pressure. Experimental results obtained from testing zinc-aluminum alloy are compared with the numerical results and satisfactory correlation is observed.</p> <p>A technique is presented for obtaining creep data for superplastic sheets using a test in which a strip or indeed the whole sheet is arranged as a cantilever loaded by its own weight. Theory is given for deriving stationary creep parameters from measured deflection rates and for determining a stress, strain-rate curve using the skeletal point method. Tensile and bending creep tests were performed on superplastic zinc-aluminum sheets at room temperature and the creep data from both types of tests are compared.</p> <p>In bulk forming of rate-dependent materials the load requirement are highly dependent on the forming speed. In the present work the traditional analytical method of slip-line field analysis has been extended to accommodate the extrusion of rate-sensitive materials such as superplastic alloys. The volume of the deformation zone and the effective mean strain-rate identified by the slip-line field solutions were incorporated to define a geometric factor which permits the extrusion pressure to be determined for a non-linear viscous material. Experimental results on reverse-extrusion of both as-cast and superplastic zinc-aluminum agree well with theoretical analysis.</p> / Doctor of Philosophy (PhD)

<p>The current emphasis of CAD/CAM technology, in particular the die and mold manufacturing sector, is to verify and optimize the NC code in terms of the productivity and machining accuracy prior to the actual machining. Also, there is a trend towards enhancing the on-line control strategies with the technological data. However, the intricate geometry with sculptured surfaces which is found nowadays in most of dies and molds, together with relative high material hardness, makes the NC verification/optimization process a very demanding and difficult task. In this regard, the development of model-based simulation methodology with functions of geometrical and physical modeling is a fundamental advancement in improving productivity, accuracy, and automation. In the course of the thesis presented, a new model-based simulation methodology for die cavity milling operations is developed. The comprehensive and realistic simulation of the milling process is implemented in the form of an integrated geometrical/physical/interaction environment. The geometric sub-environment constructs the volume swept by the cutter (or the surface swept by the cutting edge), accurately updates the model of the stock as the cutter removes the material, and automatically extracts the immersion geometry from the updated model. Based on the knowledge of the material remaining on the surface, two- and three-axis tool paths are computed. In the semi-finishing operation, a three-axis milling strategy is developed to control the scallop height remaining on the surface and avoid cutting with the dead zone of the cutter. The physical/mechanical sub-environment, integrated with the geometric counterpart, consists of a newly developed force model as well as a mathematical model of tool-structure dynamics. The integrated environment can accurately simulate the closed loop of the machine tool-cutting process. It predicts the instantaneous cutting forces, tool tip deflections, and the onset of chatter vibrations. The finishing operation is simulated based on the true path of the cutting edge. The method developed is able to construct the geometric model of feed marks and scallops remaining on the surface. Experimental measurements confirm the validity of the implemented methodology. First, the chip geometry is extracted, the part is updated, and the NC codes are verified for two- and three-axis milling of free-form surfaces. Second, the instantaneous cutting forces, tool tip deflections, the onset of chatter vibrations are predicted and compared with the experimental measurements. Next, a new three-axis milling strategy is implemented to control the scallop height and avoid cutting with the dead zone of the cutter. Lastly, the model of feed marks and scallop height are constructed, the feed mark profile is extracted and compared with the measurement. The developed system enhances the capabilities of the CAM/CAM systems in terms of increased productivity, improved machining accuracy, and heightened the level of automation</p> / Doctor of Philosophy (PhD)

Manufactoring processes generate surfaces with variable dimensions and geometries. The produced surfaces deviate from their nominal geometry and consequently, critical dimensions and clearaces deviate from their designed values when the parts are assembled. Since it is impossible to check whether the functional requirements fall within their allowable range after the assembly process, geometric tolerances are specified on individual features during the design stage such that, parts whose geometric deviations would cause a violation of the functional requirements when assembled to other parts, would be rejected during the inspection process. Therefore, wrong choice of geometric tolerances could lead to either rejecting good parts, or the acceptance of bad parts leading to an assembly that violates functional requirements. Furthermore, tolerance selection is not limited to the magnitudes of the geometric tolerances. Each feature in the assembly has four geometric variations that need to be controlled. These are size, position, form and orientation. Each of these variations, except variation in size, can be controlled by several types of tolerances and the selection of tolerance types affects the percentage of accepted or rejected parts during inspection. This dissertation presents a novel computer-aided method for the synthesis of magnitudes and types of geometric tolerances in mechanical assemblies. Tolerance selection is formulated as a combinatorial optimization problem, where each feature has seven variables. These are the types of tolerances controlling the orientation, form and position variations, the magnitudes of these tolerances as well as the magnitude size tolerance. A new criterion was developed to allocate geometric tolerances which is the minimum mismatch probability defined as the probability of rejecting a part during the inspection processes which satisfy the functional requirements when assembled to other parts, or accepting one violating the functional requirements when assembled to other parts. In order to evaluate the objective function, a probabilistic analysis method, based on Monte Carlo simulation, was developed to calculate the rejection probabilities of assemblies with geometric tolerances. The surface of each feature in the assembly is represented with a number of points where the coordinates of these points are random variables. In each simulation cycle, the coordinates of the surface points are generated using the probability distribution associated with the manufactoring process. The inspection process is then simulated where the geometric deviations on each feature are checked against the specified tolerances. Finally, the functional requirements are checked. Several methods for parts joining were examined and a new genetic algorithms based method is developed to evaluate the maximum and minimum values of critical clearances. The use of genetic algorithms ensures the arrival to the global minimum and maximum values of the clearance. Due to the large number of random variables, and since the probabilistic analysis is used in every optimization step in the tolerance allocation algorithm, two variance reduction techniques are incorporated with the standard Monte Carlo simulation to reduce sample size. A number of genetic algorithms based routines are used for checking geometric deviations on the generated parts. In many cases the evaluation of geometric deviations involve optimization. The use of global optimizers ensures the correct evaluation of deviations and avoids the unnecessary rejection of good parts. The advantage of using genetic algorithms is demonstrated with several examples used by previous researchers. Furthermore, a new parametric surface interpolation method is developed to approximate the actual surface of the manufactured parts and help in the evaluation of some geometric deviations that cannot be evaluated directly using the generated points. The new tolerance allocation method, presented in this dissertation, attempts to fill a void area in the tolerancing research, which is the selection of the "types" in addition to the magnitudes of geometric tolerances. Although the skill of a tolerancing practitioner is still needed to specify candidate tolerance types for each geometric control, the developed robust mathematical formulation of the problem avoids the random human factors in the selection. The proposed methodology can be extended for incorporation within the computer-aided tolerancing systems to assist designers in selecting geometric tolerances. / Doctor of Philosophy (PhD)

<p>An experimental study was conducted to investigate fluidelastic instability in multi-span heat exchanger tube arrays. This work is in support of nuclear steam generator design, especially with regard to the U-bend and inlet regions, where tubes are subjected to non-uniform cross flow. The design guidelines defined in the current ASME codes and other recommended semi-emphirical formulas for fluidelastic instability have been based on the extension of experimental results from single span tube bundles. In this study, a specially designed multi-span tube array test rig was used to investigate the effects of partial flow admission. Using this test rig, the water flow can pass across any location along the tube span. Various end supports were used in the different experimental set-ups. Therefore, not only the first mode but also the higher vibration modes can be excited, depending on the location of the flow and tube-support configurations. It has been found that vibration modes higher than the third mode do not have significant vibration displacement. The experiments show that the fluid energy is additive along the span, regardless of the tube mode shape. Response peaks were observed prior to the ultimate fluidelastic instability. By analyzing the corresponding Strouhal numbers, it was found that both vortex shedding and secondary instability mechanisms exist. These two different phenomena may interact and enhance each other. Therefore, high amplitude displacement can be reached even before the ultimate fluidelastic instability. The previous and present experimental data suggest that the energy fraction is a representative parameter in the analysis of the flow induced vibration caused by nonuniform flow velocity distribution. However, existing design guidelines do not always give conservative predictions for the critical velocity. This research reveals that a single correlation of reduced velocity versus mass damping ratio does not follow the same trend in air and liquid flows. An improved design guideline is suggested, which gives consistent conservative flow velocity predictions in multi-span tube arrays. In parallel, an analytical model was developed for the prediction of fluidelastic instability in cross flow multi-span heat exchanger tube arrays. The model is based on concepts developed by Lever and Weaver, as well as Yetisir and Weaver, but is extended to include some crucial factors. Velocity and pressure fluctuations, caused by tube vibration were obtained by using continuity and momentum equations in curvilinear coordinates. Rather than the nonlinear function previously used, a linear area perturbation decay function was introduced to account for the decay of disturbances away from an oscillating tube. Thus, an analytical solution could be obtained. The resulting explicit instability expression is a more convenient tool to analyze effects of various design parameters. The difference between the linear and nonlinear decay functions was found to have a negligible effect on the stability threshold. Critical velocity in both streamwise and transverse directions was calculated, and the latter is lower in the high mass damping ratio range. Therefore, only the instability in the transverse direction needs to be analyzed in that range. On the other hand, there is no clear trend in the low mass damping ratio range, which agrees with many previous research results. This model is a multiple flexible tube model. Tubes directly two rows upstream and downstream of a central tube, neglected in the Yetisir and Weaver model, but are included in the present model. Significant improvement is obtained for the parallel triangular tube arrays. In contrast, little improvement is achieved on the other tube patterns due to the reduced influence of the upstream tube wake. The velocity distribution and mode shape along the tube span were introduced into the model. This is made possible because of the explicit instability equation. Therefore, the present model, in which fluid flow in two-dimensional, but considering tube mode shape in the third dimension, can be used to calculate the fluidelastic instability for multi-span tube arays. The comparison between the theory and experimental data agrees well.</p> / Doctor of Philosophy (PhD)

<p>The topic of this thesis is the phenomenon of ductile fracture, and stems from a government research contract aimed at assessing the utility of different steels designated for cold forging applications.</p> <p>Recourse has been made to experimental data, available in the published literature, of upsetting tests on certain steels in different heat treated conditions. Some upsetting tests have also been performed as part of the present study, and following earlier work conducted at McMaster University, specimens of different geometry were also investigated. The materials were examined metallographically, before and after deformation.</p> <p>It was found that in addition to material characteristics the specimen geometry can have a marked effect on the extent of the deformation before surface cracking. The so-called collar specimen resulted in smaller strains to fracture vis à vis the other specimen geometries investigated.</p> <p>The principal surface strains were determined throughout the course of the upsetting tests by measuring a grid of lines marked on the equatorial free surface of the specimens.</p> <p>A knowledge of the strain path enables the stress history of a point on the equatorial free surface to be determined using simple plasticity theory. The details are described herein. The upsetting tests were also modelled using a finite element technique based on a rigid, work-hardening material. The predicted and measured strains at the free surface of the specimens showed good agreement, and consequently, the predicted stresses agreed with those determined using simple plasticity theory. However, the finite element technique enables the stress history to be determined at any interior point within the specimens.</p> <p>A knowledge of the stress history permits an evaluation of certain damage integrals. The ones proposed by Cockcroft and Latham and Oyane were investigated in the present work, but they failed to provide an adequate account of the observed behaviour in the upsetting tests. Failure based on the attainment of a critical shear seemed more appropriate. The experimental data also demonstrated that the fracture strains, i.e. the.hoop, ε₀₀, and axial strains, ε₀₀/ε₂₂ = -1/2, as proposed by Kuhn.</p> <p>Reliance was also placed on experimental data (gathered by other researchers at McMaster University) from tensile tests performed on spheroidized steels subjected to superimposed hydrostatic pressure. Quantitative metallography had revealed information on certain aspects of void initiation, growth and coalescence as a function of volume fraction of inclusions and hydrostatic pressure.</p> <p>In the present work the void growth stage was predicted using a void growth model due to McClintock, but modified mutatis mutandis to allow for the continuous nucleation of voids. The model is shown to be capable of describing certain experimental observations regarding void growth.</p> <p>McClintock's model was also applied to the data gathered from the upsetting tests. Again it appeared capable of predicting the damage rate and damage accumulation in a manner consistent with experimental observations. Furthermore, it was possible to predict a fracture locus, plotted in ε₀₀-ε₂₂ space and based on the attainment of a critical accumulated damage, which correlated very well with the experimental data. McClintock's model is outlined in the thesis, and discussed in the context of other void growth models given in the published literature.</p> / Doctor of Philosophy (PhD)

<p>The contents of this thesis reflect a general effort in the endeavour of exploring and developing the effective FEM tools for metal forming analysis. There are three major parts in this work. In chapter 2, an unique mathematical derivation of large deformation equations is presented on the basis of a direct linearization of the "future" virtual work equation without using any pseudo stress tensor and corresponding conjugate strain tensor. A major advantage of this derivation is that a clear physical understanding is carried through the whole mathematical process. Therefore distinctive perception on key fundamentals such as: equilibrium equation, strain measure, constitutive relation, stress rotation and residual force evaluation are presented and discussed on a consistent and integrated basis. The code developed in this part of work forms an independent module for 2D bulk forming analysis, while the methodology is carried through the rest of thesis. A particular effort is described in Chapter 3, which addressed the problem and techniques used in dealing with the frictional contact boundary condition which is common in metal forming processes. A typical ring compression problem is used to show the problem and solution. The algorithm and code developed there is a part of the 2D package. Chapter 4 presents a full description of a 3D degenerated shell element formulation based on the consistent large deformation formulation presented in Chapter 2. Various aspects of techniques used in shell elements to prevent elements from locking have been reviewed. A special penalty method is devised to enforce the Kirchhoff constraint which has been missing in the degenerated shell element discretization. The method has successfully prevented 3-node and 4-node elements from shear locking in analysing the typical cup drawing process. At the end of the thesis, a summary of the thesis is presented. Conclusions and recommendations for further work are provided.</p> / Doctor of Philosophy (PhD)

<p>A critical discussion of the formulation methods for the finite clement analysis of nonlinear problems is given, which includes the Lagrangian, the updated Lagrangian, and the Eulerian formulation. It is shown that each formulation is suitable for a specific class of nonlinear problems. In the literature many authors treat updated Lagrangian formulation as an Eulerian formulation. Therefore, the basic differences between the two formulations are critically discussed.</p> <p>Consistent Lagrangian and updated Lagrangian formulation are derived from the virtual work principle expressed in current configuration, then transformed to the proper reference configuration. A detailed Eulerian formulation in the current configuration is derived by means of the virtual work principle. Explicit forms for the stiffness matrices contributing to the total nonlinear stiffness matrix, for the mass matrix, and for the load increments are presented in each case. Differences between the presented Lagrangian and the updated Lagrangian formulations and similar formulations in the literature are found to exist in the number of the stiffness matrices in the final incremental equilibrium equations as well as in the definition of the load increments. These differences as well as those between the existing formulations in the literature are assessed within the framework of the basic equations of the continuum mechanics. Specific forms of constitutive equations for elastic and elasto-plastic response of the materials are presented. A discussion on the use of the stress rates to derive acceptable constitutive equations is also given.</p> <p>For the Lagrangian and the updated Lagrangian formulation two example problems have been solved to demonstrate the applicability of the presented formulations and the effect of the individual stiffness matrices as well as the definition of the follower load which results from the consistent formulation. These problems are elastic, large deformation static analysis of a cantilever under uniformly distributed load and elastic-perfectly plastic dynamic analysis of a pipe-whip problem.</p> <p>To assess the presented Eulerian formulation and to show the effectiveness of the Eulerian finite element analysis using fixed mesh in space: a metal-extrusion problem has been solved. In this approach, the mesh is maintained fixed in space and the increment of stress tensors for a forward incremental step are added to a set of interpolated stress tensors. Then these stresses are interpolated back to obtain the state of stress of the body-points momentarily occupying the fixed integration points of the mesh.</p> / Doctor of Philosophy (PhD)