A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

Sviluppo e applicazione di nuovi criteri per la verifica a fatica multiassiale di componenti strutturali in leghe di acciaio e alluminio

La presente Tesi ha per oggetto lo sviluppo e la validazione di nuovi criteri per la verifica a fatica multiassiale di componenti strutturali metallici . In particolare, i nuovi criteri formulati risultano applicabili a componenti metallici, soggetti ad un’ampia gamma di configurazioni di carico: carichi multiassiali variabili nel tempo, in modo ciclico e random, per alto e basso/medio numero di cicli di carico. Tali criteri costituiscono un utile strumento nell’ambito della valutazione della resistenza/vita a fatica di elementi strutturali metallici, essendo di semplice implementazione, e richiedendo tempi di calcolo piuttosto modesti. Nel primo Capitolo vengono presentate le problematiche relative alla fatica multiassiale, introducendo alcuni aspetti teorici utili a descrivere il meccanismo di danneggiamento a fatica (propagazione della fessura e frattura finale) di componenti strutturali metallici soggetti a carichi variabili nel tempo. Vengono poi presentati i diversi approcci disponibili in letteratura per la verifica a fatica multiassiale di tali componenti, con particolare attenzione all'approccio del piano critico. Infine, vengono definite le grandezze ingegneristiche correlate al piano critico, utilizzate nella progettazione a fatica in presenza di carichi multiassiali ciclici per alto e basso/medio numero di cicli di carico. Il secondo Capitolo è dedicato allo sviluppo di un nuovo criterio per la valutazione della resistenza a fatica di elementi strutturali metallici soggetti a carichi multiassiali ciclici e alto numero di cicli. Il criterio risulta basato sull'approccio del piano critico ed è formulato in termini di tensioni. Lo sviluppo del criterio viene affrontato intervenendo in modo significativo su una precedente formulazione proposta da Carpinteri e collaboratori nel 2011. In particolare, il primo intervento riguarda la determinazione della giacitura del piano critico: nuove espressioni dell'angolo che lega la giacitura del piano critico a quella del piano di frattura vengono implementate nell'algoritmo del criterio. Il secondo intervento è relativo alla definizione dell'ampiezza della tensione tangenziale e un nuovo metodo, noto come Prismatic Hull (PH) method (di Araújo e collaboratori), viene implementato nell'algoritmo. L'affidabilità del criterio viene poi verificata impiegando numerosi dati di prove sperimentali disponibili in letteratura. Nel terzo Capitolo viene proposto un criterio di nuova formulazione per la valutazione della vita a fatica di elementi strutturali metallici soggetti a carichi multiassiali ciclici e basso/medio numero di cicli. Il criterio risulta basato sull'approccio del piano critico, ed è formulato in termini di deformazioni. In particolare, la formulazione proposta trae spunto, come impostazione generale, dal criterio di fatica multiassiale in regime di alto numero di cicli discusso nel secondo Capitolo. Poiché in presenza di deformazioni plastiche significative (come quelle caratterizzanti la fatica per basso/medio numero di cicli di carico) è necessario conoscere il valore del coefficiente efficace di Poisson del materiale, vengono impiegate tre differenti strategie. In particolare, tale coefficiente viene calcolato sia per via analitica, che per via numerica, che impiegando un valore costante frequentemente adottato in letteratura. Successivamente, per validarne l'affidabilità vengono impiegati numerosi dati di prove sperimentali disponibili in letteratura; i risultati numerici sono ottenuti al variare del valore del coefficiente efficace di Poisson. Inoltre, al fine di considerare i significativi gradienti tensionali che si verificano in presenza di discontinuità geometriche, come gli intagli, il criterio viene anche esteso al caso dei componenti strutturali intagliati. Il criterio, riformulato implementando il concetto del volume di controllo proposto da Lazzarin e collaboratori, viene utilizzato per stimare la vita a fatica di provini con un severo intaglio a V, realizzati in lega di titanio grado 5. Il quarto Capitolo è rivolto allo sviluppo di un nuovo criterio per la valutazione del danno a fatica di elementi strutturali metallici soggetti a carichi multiassiali random e alto numero di cicli. Il criterio risulta basato sull'approccio del piano critico ed è formulato nel dominio della frequenza. Lo sviluppo del criterio viene affrontato intervenendo in modo significativo su una precedente formulazione proposta da Carpinteri e collaboratori nel 2014. In particolare, l’intervento riguarda la determinazione della giacitura del piano critico, e nuove espressioni dell'angolo che lega la giacitura del piano critico con quella del piano di frattura vengono implementate nell'algoritmo del criterio. Infine, l’affidabilità del criterio viene verificata impiegando numerosi dati di prove sperimentali disponibili in letteratura.

AC self-bearing motors with a bridge configured winding

Magnetic levitation bearings eliminate friction, wear and the need for lubrication and so have high speed capability and potential for vibration control. One noteworthy development in the realm of magnetic levitation is the self-bearing or bearingless motor - an electromagnetic machine that supports its own rotor by way of magnetic forces generated by windings on its stator. Accordingly, various winding schemes have been proposed to accomplish the task of force production. This thesis proposes a novel concept of winding based on a bridge connection for polyphase self-bearing rotating electrical machines with the following advantages: • the connection uses a single set of windings and thus power loss is relatively low when compared with self-bearing motors with conventional dual set of windings. • the motor and levitation controls are segregated such that only one motor inverter is required for the normal torque production and levitation forces are produced by using auxiliary power supplies of relatively low current and voltage rating. The usual way of controlling the motor is retained. • there are many variant winding schemes to meet special needs. • independent power supplies for levitation control offer redundancy for fault tolerance. This thesis dwells specifically on the conceptual design and implementation of the proposed single set of windings scheme. The new connection has been verified to exhibit characteristics of a self-bearing motor via coupled-field finite element analysis: results are crosschecked analytically. Power loss and other aspects such as cost, design implementation are compared to support the newly proposed connection as a potential alternative to present designs.

Optimization of chemical plant simulation using double collocation

A method has been constructed for the solution of a wide range of chemical plant simulation models including differential equations and optimization. Double orthogonal collocation on finite elements is applied to convert the model into an NLP problem that is solved either by the VF 13AD package based on successive quadratic programming, or by the GRG2 package, based on the generalized reduced gradient method. This approach is termed simultaneous optimization and solution strategy. The objective functional can contain integral terms. The state and control variables can have time delays. Equalities and inequalities containing state and control variables can be included into the model as well as algebraic equations and inequalities. The maximum number of independent variables is 2. Problems containing 3 independent variables can be transformed into problems having 2 independent variables using finite differencing. The maximum number of NLP variables and constraints is 1500. The method is also suitable for solving ordinary and partial differential equations. The state functions are approximated by a linear combination of Lagrange interpolation polynomials. The control function can either be approximated by a linear combination of Lagrange interpolation polynomials or by a piecewise constant function over finite elements. The number of internal collocation points can vary by finite elements. The residual error is evaluated at arbitrarily chosen equidistant grid-points, thus enabling the user to check the accuracy of the solution between collocation points, where the solution is exact. The solution functions can be tabulated. There is an option to use control vector parameterization to solve optimization problems containing initial value ordinary differential equations. When there are many differential equations or the upper integration limit should be selected optimally then this approach should be used. The portability of the package has been addressed converting the package from V AX FORTRAN 77 into IBM PC FORTRAN 77 and into SUN SPARC 2000 FORTRAN 77. Computer runs have shown that the method can reproduce optimization problems published in the literature. The GRG2 and the VF I 3AD packages, integrated into the optimization package, proved to be robust and reliable. The package contains an executive module, a module performing control vector parameterization and 2 nonlinear problem solver modules, GRG2 and VF I 3AD. There is a stand-alone module that converts the differential-algebraic optimization problem into a nonlinear programming problem.

Deformations of the pneumatic tyre

A mathematical model is developed for the general pneumatic tyre. The model will permit the investigations of tyre deformations produced by arbitrary external loading, and will enable estimates to be made of the distributions of applied and reactive forces. The principle of Finite Elements is used to idealise the composite tyre structure, each element consisting of a triangle of double curvature with varying thickness. Large deflections of' the structure are accomodated by the use of an iterative sequence of small incremental steps, each of' which obeys the laws of linear mechanics. The theoretical results are found to compare favourably with the experimental test data obtained from two different types of ttye construction. However, limitations in the discretisation process has prohibited accurate assessments to be made of stress distributions in the regions of high stress gradients ..

The Mechanics of the drawing of polygonal sections from round at elevated temperature

Economic factors such as the rise in cost of raw materials, labour and power, are compelling manufacturers of cold-drawn polygonal sections, to seek new production routes which will enable the expansion in the varieties of metals used and the inclusion of difficult-to-draw materials. One such method generating considerable industrial interest is the drawing of polygonal sections from round at elevated temperature. The technique of drawing mild steel, medium carbon steel and boron steel wire into octagonal, hexagonal and square sections from round at up to 850 deg C and 50% reduction of area in one pass has been established. The main objective was to provide a basic understanding of the process, with particular emphasis being placed on modelling using both experimental and theoretical considerations. Elevated temperature stress-strain data was obtained using a modified torsion testing machine. Data were used in the upper bound solution derived and solved numerically to predict drawing stress strain, strain-rate, temperature and flow stress distribution in the deforming zone for a range of variables. The success of this warm working process will, of course, depend on the use of a satisfactory elevated temperature lubricant, an efficient cooling system, a suitable tool material having good wear and thermal shock resistance and an efficient die profile design which incorporates the principle of least work. The merits and demerits of die materials such as tungsten carbide, chromium carbide, Syalon and Stellite are discussed, principally from the standpoint of minimising drawing force and die wear. Generally, the experimental and theoretical results were in good agreement, the drawing stress could be predicted within close limits and the process proved to be technically feasible. Finite element analysis has been carried out on the various die geometries and die materials, to gain a greater understanding of the behaviour of these dies under the process of elevated temperature drawing, and to establish the temperature distribution and thermal distortion in the deforming zone, thus establishing the optimum die design and die material for the process. It is now possible to predict, for the materials already tested, (i) the optimum drawing temperature range, (ii) the maximum possible reduction of area per pass, (iii) the optimum drawing die profiles and die materials, (iv) the most efficient lubricant in terms of reducing the drawing force and die wear.

A temporary connection for an aluminium space frame

This thesis examines theoretically and experimentally the behaviour of a temporary end plate connection for an aluminium space frame structure, subjected to static loading conditions. Theoretical weld failure criterions are derived from basic fundamentals for both tensile and shear fillet welds. Direct account of weld penetration is taken by incorporating it into a more exact poposed weld model. Theoretical relationships between weld penetration and weld failure loads, failure planes and failure lengths are derived. Also, the variation in strength between tensile and shear fillet welds is shown to be dependent upon the extent of weld penetration achieved/ The proposed tensile weld failure theory is extended to predict the theoretical failure of the welds in the end plate space frame connection. A finite element analysis is conducted to verify the assumptions made for this theory. Experimental hardness and tensile tests are conducted to substantiate the extent and severity of the heat affected zone in aluminium alloy 6082-T6. Simple transverse and longitudinal fillet welded specimens of the same alloy, are tested to failure. These results together with those of other authors are compared to the theoretical predictions made by the proposed weld failure theories and by those made using Kamtekar's and Kato and Morita's failure equations, the -formula and BS 8118. Experimental tests are also conducted on the temporary space frame connection. The maximum stresses and displacements recorded are checked against results obtained from a finite element analysis of the connection. Failure predictions made by the proposed extended weld failure theory, are compared against the experimental results.

Theoretical modelling of the sulcated spring

Replacement of the traditional coil spring with one of more fibre-reinforced plastic sulcated springs is a future possibility. Spring designers of metallic coil springs have design formulae readily available, and software packages specific to coil spring design exist. However, the sulcated spring is at the prototype stage of development, so literature on these springs is very sparse. The thesis contains information on the market for sulcated springs, and their advantages and disadvantages. Literature on other types of fibre reinforced plastic springs has also been reviewed. Design software has been developed for the sulcated spring along similar lines to coil spring design software. In order to develop the software, a theoretical model had to be developed which formed the mathematical basis for the software. The theoretical model is based on a choice of four methods for calculating the flexural rigidity; beam theory, plate theory, and lamination theory assuming isotropic and orthoropic material properties. Experimental results for strain and spring stiffness have been compared with the theoretical model, and were in good agreement. Included in the design software are the results of experimental work on fatigue, and design limiting factors to prevent or warn against impractical designs. Finite element analysis has been used to verify the theoretical model developed, and to find the better approximation to the experimental results. Applications and types of assemblies for the sulcated spring were discussed. Sulcated spring designs for the automotive applications of a suspension, clutch and engine valve spring were found using the design computer software. These sulcated spring designs were within or close to the space of the existing coil spring and yield the same performance. Finally the commercial feasibility of manufacturing the sulcated spring was assessed and compared with the coil spring, to evaluate the plausibility of the sulcated spring replacing the coil spring eventually.

Electromagnetic interference from variable speed motor drives

A methodology is presented which can be used to produce the level of electromagnetic interference, in the form of conducted and radiated emissions, from variable speed drives, the drive that was modelled being a Eurotherm 583 drive. The conducted emissions are predicted using an accurate circuit model of the drive and its associated equipment. The circuit model was constructed from a number of different areas, these being: the power electronics of the drive, the line impedance stabilising network used during the experimental work to measure the conducted emissions, a model of an induction motor assuming near zero load, an accurate model of the shielded cable which connected the drive to the motor, and finally the parasitic capacitances that were present in the drive modelled. The conducted emissions were predicted with an error of +/-6dB over the frequency range 150kHz to 16MHz, which compares well with the limits set in the standards which specify a frequency range of 150kHz to 30MHz. The conducted emissions model was also used to predict the current and voltage sources which were used to predict the radiated emissions from the drive. Two methods for the prediction of the radiated emissions from the drive were investigated, the first being two-dimensional finite element analysis and the second three-dimensional transmission line matrix modelling. The finite element model took account of the features of the drive that were considered to produce the majority of the radiation, these features being the switching of the IGBT's in the inverter, the shielded cable which connected the drive to the motor as well as some of the cables that were present in the drive.The model also took account of the structure of the test rig used to measure the radiated emissions. It was found that the majority of the radiation produced came from the shielded cable and the common mode currents that were flowing in the shield, and that it was feasible to model the radiation from the drive by only modelling the shielded cable. The radiated emissions were correctly predicted in the frequency range 30MHz to 200MHz with an error of +10dB/-6dB. The transmission line matrix method modelled the shielded cable which connected the drive to the motor and also took account of the architecture of the test rig. Only limited simulations were performed using the transmission line matrix model as it was found to be a very slow method and not an ideal solution to the problem. However the limited results obtained were comparable, to within 5%, to the results obtained using the finite element model.

Clogging in subsurface-flow treatment wetlands:measurement, modeling and management

This paper reviews the state of the art in measuring, modeling, and managing clogging in subsurface-flow treatment wetlands. Methods for measuring in situ hydraulic conductivity in treatment wetlands are now available, which provide valuable insight into assessing and evaluating the extent of clogging. These results, paired with the information from more traditional approaches (e.g., tracer testing and composition of the clog matter) are being incorporated into the latest treatment wetland models. Recent finite element analysis models can now simulate clogging development in subsurface-flow treatment wetlands with reasonable accuracy. Various management strategies have been developed to extend the life of clogged treatment wetlands, including gravel excavation and/or washing, chemical treatment, and application of earthworms. These strategies are compared and available cost information is reported. © 2012 Elsevier Ltd.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Embedded heat pipes in cofired ceramic substrates for enhanced thermal management of electronics

A novel and new thermal management technology for advanced ceramic microelectronic packages has been developed incorporating miniature heat pipes embedded in the ceramic substrate. The heat pipes use an axially grooved wick structure and water as the working fluid. Prototype substrate/heat pipe systems were fabricated using high temperature co-fired ceramic (alumina). The heat pipes were nominally 81 mm in length, 10 mm in width, and 4 mm in height, and were charged with approximately 50–80 μL of water. Platinum thick film heaters were fabricated on the surface of the substrate to simulate heat dissipating electronic components. Several thermocouples were affixed to the substrate to monitor temperature. One end of the substrate was affixed to a heat sink maintained at constant temperature. The prototypes were tested and shown to successful and reliably operate with thermal loads over 20 Watts, with thermal input from single and multiple sources along the surface of the substrate. Temperature distributions are discussed for the various configurations and the effective thermal resistance of the substrate/heat pipe system is calculated. Finite element analysis was used to support the experimental findings and better understand the sources of the system's thermal resistance. ^

A micro-opto-electro-mechanical system (MOEMS) for microstructure manipulation

Microstructure manipulation is a fundamental process to the study of biology and medicine, as well as to advance micro- and nano-system applications. Manipulation of microstructures has been achieved through various microgripper devices developed recently, which lead to advances in micromachine assembly, and single cell manipulation, among others. Only two kinds of integrated feedback have been demonstrated so far, force sensing and optical binary feedback. As a result, the physical, mechanical, optical, and chemical information about the microstructure under study must be extracted from macroscopic instrumentation, such as confocal fluorescence microscopy and Raman spectroscopy. In this research work, novel Micro-Opto-Electro-Mechanical-System (MOEMS) microgrippers are presented. These devices utilize flexible optical waveguides as gripping arms, which provide the physical means for grasping a microobject, while simultaneously enabling light to be delivered and collected. This unique capability allows extensive optical characterization of the structure being held such as transmission, reflection, or fluorescence. The microgrippers require external actuation which was accomplished by two methods: initially with a micrometer screw, and later with a piezoelectric actuator. Thanks to a novel actuation mechanism, the "fishbone", the gripping facets remain parallel within 1 degree. The design, simulation, fabrication, and characterization are systematically presented. The devices mechanical operation was verified by means of 3D finite element analysis simulations. Also, the optical performance and losses were simulated by the 3D-to-2D effective index (finite difference time domain FDTD) method as well as 3D Beam Propagation Method (3D-BPM). The microgrippers were designed to manipulate structures from submicron dimensions up to approximately 100 μm. The devices were implemented in SU-8 due to its suitable optical and mechanical properties. This work demonstrates two practical applications: the manipulation of single SKOV-3 human ovarian carcinoma cells, and the detection and identification of microparts tagged with a fluorescent "barcode" implemented with quantum dots. The novel devices presented open up new possibilities in the field of micromanipulation at the microscale, scalable to the nano-domain.

Development of thresholds for surface preparation in repair systems with wet lay -up fiber reinforced polymers

Bonded repair of concrete structures with fiber reinforced polymer (FRP) systems is increasingly being accepted as a cost-efficient and structurally viable method of rapid rehabilitation of concrete structures. However, the relationships between long-term performance attributes, service-life, and details of the installation process are not easy to quantify. Accordingly, there is currently a lack of generally accepted construction specifications, making it difficult for the field engineer to certify the adequacy of the construction process. ^ The objective of the present study, as part of the National Cooperative Highway Research Program (NCHRP) Project 10-59B, was to investigate the effect of surface preparation on the behavior of wet lay-up FRP repair systems and consequently develop rational thresholds that provide sufficient performance. ^ The research program was comprised of both experimental and analytical work for wet lay-up FRP applications. The experimental work included flexure testing of sixty-seven (67) reinforced concrete beams and bond testing of ten (10) reinforced concrete blocks. Four different parameters were studied: surface roughness, surface flatness, surface voids and bug holes, and surface cracks/cuts. The findings were analyzed from various aspects and compared with the data available in the literature. As part of the analytical work, finite element models of the flexural specimens with surface flaws were developed using ANSYS. The purpose of this part was to extend the parametric study on the effects of concrete surface flaws and verify the experimental results based on nonlinear finite element analysis. ^ Test results showed that surface roughness does not appear to have a significant influence on the overall performance of the wet lay-up FRP systems with or without adequate anchorage, and whether failure was by debonding or rupture of FRP. Both experimental and analytical results for surface flatness proved that peaks on concrete surface, in the range studied, do not have a significant effect on the performance of wet lay-up FRP systems. However, valleys of particular size could reduce the strength of wet lay-up FRP systems. Test results regarding surface voids and surface cracks/cuts revealed that previously suggested thresholds for these flaws appear to be conservative, as also confirmed by analytical study. ^

Embedded Heat Pipes in Cofired Ceramic Substrates for Enhanced Thermal Management of Electronics

A novel and new thermal management technology for advanced ceramic microelectronic packages has been developed incorporating miniature heat pipes embedded in the ceramic substrate. The heat pipes use an axially grooved wick structure and water as the working fluid. Prototype substrate/heat pipe systems were fabricated using high temperature co-fired ceramic (alumina). The heat pipes were nominally 81 mm in length, 10 mm in width, and 4 mm in height, and were charged with approximately 50-80 mL of water. Platinum thick film heaters were fabricated on the surface of the substrate to simulate heat dissipating electronic components. Several thermocouples were affixed to the substrate to monitor temperature. One end of the substrate was affixed to a heat sink maintained at constant temperature. The prototypes were tested and shown to successful and reliably operate with thermal loads over 20 Watts, with thermal input from single and multiple sources along the surface of the substrate. Temperature distributions are discussed for the various configurations and the effective thermal resistance of the substrate/heat pipe system is calculated. Finite element analysis was used to support the experimental findings and better understand the sources of the system's thermal resistance.