A recent method in aero engine production is to fabricate components from smaller pieces, rather than machining them from large castings. This has made laser beam welding popular, offering high precision with low heat input and distortion, but also high productivity. At the same time, the demand for automation of production has increased, to ensure high quality and consistent results. In turn, the need for sensors to monitor and control the laser welding process is increasing. In laser beam welding without filler material, the gap between the parts to be joined must be narrow. Optical sensors are often used to measure the gap, but with precise machining, it may become so narrow that it is difficult to detect, with the risk of welding in the wrong position. This kind of problems can cause severe welding defects, where the parts are only partially joined without any visible indication. This thesis proposes the use of an inductive sensor with coils on either side of the gap. Inducing currents into the metal, such a sensor can detect even gaps that are not visible. The new feature of the proposal is based on using the complex response of each coil separately to measure the distance and height on both sides of the gap, rather than an imbalance from the absolute voltage of each coil related to gap position. This extra information allows measurement of gap width and misalignment as well as position, and decreases the influence from gap misalignment to the position measurement. The sensor needs to be calibrated with a certain gap width and height alignment. In real use,these will vary, causing the sensor to be less accurate. Using initial estimates ofthe gap parameters from the basic sensor, a model of the response can be used to estimate the measurement error of each coil, which in turn can be used for compensation to improve the measurement of the gap properties.The properties of the new method have been examined experimentally, using a precise traverse mechanism to record single coil responses in a working range around a variable dimension gap, and then using these responses to simulate a two coil probe. In most cases errors in the measurement of weld gap position and dimensions are within 0.1 mm.The probe is designed to be mounted close to the parts to be welded, and will work in a range of about 1 mm to each side and height above the plates. This is an improvement over previous inductive sensors, that needed to be guided to the mid of the gap by a servo mechanism.

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This dissertation is a study of methods to automatedly detect and produce approximations of eddy current differential coil defect signatures in terms of a summed collection of Gaussian functions (SoG). Datasets consisting of varying material, defect size, inspection frequency, and coil diameter were investigated. Dimensionally reduced representations of the defect responses were obtained utilizing common existing reduction methods and novel enhancements to them utilizing SoG Representations. Efficacy of the SoG enhanced representations were studied utilizing common Machine Learning (ML) interpretable classifier designs with the SoG representations indicating significant improvement of common analysis metrics.

Electromagnetism and optimal control stand out as a topics that feature impactful applications in modern engineering, as well as challenging theoretical aspects of mathematical analysis. Within this context, a major role is played by the search of necessary and sufficient conditions characterizing optimal solutions, as they are functional to numerical algorithms aiming to approximate such solutions. In this thesis, three standalone topics in optimization sharing the underlying framework of Maxwell-related PDEs are discussed. First, I present an optimal control problem driven by a quasi-linear magneto-static obstacle problem featuring first-order differential state constraints. The non-linearity allows to suitably model electromagnetic waves in the presence of ferromagnetic materials, while the first-order obstacle is relevant for applications in the field of magnetic shielding. Existence theory and the derivation of an optimality system are addressed with an approximation technique based on a relaxation-penalization of the variational inequality. Second, I analyze an eddy current problem controlled through a dipole type source, i.e. a Dirac mass with fixed position and variable intensity: well-posedness of the state equation through a fundamental solution (of a curl curl - Id operator) approach and first order conditions are dealt with. To conclude, I discuss the computation of the topological derivative for shape functionals constrained to low-frequency electromagnetic problems (closely related to the eddy current model), with respect to the inclusion/removal of conducting material; the results are obtained using a Lagrangian approach and in particular the so-called averaged adjoint method. This approach requires the study of the asymptotic behavior of the solutions of some problems defined in the whole space, and the introduction and consequent analysis of appropriate function spaces.

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The optical power of satellites such as the Hubble telescope is directly related to the size of the primary mirror. However, due to the limited capacity of the shuttle bay, progress towards the development of more powerful satellites using traditional construction methods has come to a standstill. Therefore, to allow larger satellites to be launched into space significant interest has been shown in the development of ultra large inflatable structures that can be packaged inside the shuttle bay and then deployed once in space. To facilitate the packaging of the inflated device in its launch configuration, most structures utilize a thin film membrane as the optical or antenna surface. Once the inflated structure is deployed in space, it is subject to vibrations induced mechanically by guidance systems and space debris as well as thermally induced vibrations from variable amounts of direct sunlight. For the optimal performance of the satellite, it is crucial that the vibration of the membrane be quickly suppressed. However, due to the extremely flexible nature of the membrane structure, few actuation methods exist that avoid local deformation and surface aberrations. One potential method of applying damping to the membrane structure is to use magnetic damping. Magnetic dampers function through the eddy currents that are generated in a conductive material that experiences a time varying magnetic field. However, following the generation of these currents, the internal resistance of the conductor causes them to dissipate into heat. Because a portion of the moving conductor's kinetic energy is used to generate the eddy currents, which are then dissipated, a damping effect occurs. This damping force can be described as a viscous force due to the dependence on the velocity of the conductor. While eddy currents form an effective method of applying damping, they have normally been used for magnetic braking applications. Furthermore, the dampers that have been designed for vibration suppression have typically been ineffective at suppressing structural vibration, incompatible with practical systems, and cumbersome to the structure resulting in significant mass loading and changes to the dynamic response. To alleviate these issues, three previously unrealized damping mechanisms that function through eddy currents have been developed, modeled and tested. The dampers do not contact the structure, thus, allowing them to add damping to the system without inducing the mass loading and added stiffness that are typically common with other forms of damping. The first damping concept is completely passive and functions solely due to the conductor's motion in a static magnetic field. The second damping system is semi-active and improves the passive damper by allowing the magnet's position to be actively controlled, thus, maximizing the magnet's velocity relative to the beam and enhancing the damping force. The final system is completely active using an electromagnet, through which the current can be actively modified to induce a time changing magnetic flux on the structure and a damping effect. The three innovative damping mechanisms that have resulted from this research apply control forces to the structure without contacting it, which cannot be done by any other passive vibration control system. Furthermore, the non-contact nature of these dampers makes them compatible with the flexible membranes needed to advance the performance of optical satellites. / Ph. D.

Recently planar magnetic technologies have been widely used in power electronics, due to good cooling and ease of fabrication. High frequency operation of magnetic components is a key to achieve high power density and miniaturization. However, at high frequencies, skin and proximity effect losses in the planar windings become significant, and parasitics cannot be ignored. This piece of work deals with the modeling and design of planar integrated magnetic component for power electronics applications. First, one-dimensional eddy current analysis in some simple winding strategies is discussed. Two factors are defined in order to quantify the skin and proximity effect contributions as a function of frequency. For complicated structures, 2D and 3D finite element analysis (FEA) is adopted and the accuracy of the simulation results is evaluated against exact analytical solutions. Then, a planar litz structure is presented. Some definitions and guidelines are established, which form the basis to design a planar litz conductor. It can be constructed by dividing the wide planar conductor into multiple lengthwise strands and weaving these strands in much the same manner as one would use to construct a conventional round litz wire. Each strand is subjected to the magnetic field everywhere in the winding window, thereby equalizing the flux linkage. 3D FEA is utilized to investigate the impact of the parameters on the litz performance. The experimental results verify that the planar litz structure can reduce the AC resistance of the planar windings in a specific frequency range. After that, some important issues related to the planar boost inductor design are described, including core selection, winding configuration, losses estimation, and thermal modeling. Two complete design examples targeting at volume optimization and winding parasitic capacitance minimization are provided, respectively. This work demonstrates that planar litz conductors are very promising for high frequency planar magnetic components. The optimization of a planar inductor involves a tradeoff between volumetric efficiency and low value of winding capacitance. Throughout, 2D and 3D FEA was indispensable for thermal & electromagnetic modeling. / Master of Science

The report examines the factors which may be a contributing cause to the problems that are present when ferritic stainless steel are eddy current tested in a warm condition. The work is carried out at Fagersta Stainless AB in Fagersta which manufactures stainless steel wire. In the rolling mill there is an eddy current equipment for detection of surface defects on the wire. The ferritic stainless steels cause a noise when testing and this noise complicates the detection of defects.Because of this, a study was made of how the noise related to factors such as steel grade, temperature, size and velocity. By observing the signal and with the possibilities to change the equipment settings the capability to let a signal filter reduce the noise level were evaluated. Theories about the material's physical properties have also been included, mainly the magnetic properties, electrical conductivity and the material's tendency to oxidize.Results from the tests show that a number of factors do not affect the inductive test significantly and to use a filter to reduce the noise level does not seem to be a viable option. The level of noise does not relate to the presence of superficial particles in form of oxides.The ferritic stainless steels showed some difference in noise level. Which noise level there was did match well with the steels probability for a precipitation of a second phase, and precipitation of austenite may in this case contribute to noise when using an eddy current instrument.The noise is probably due to some physical material property that varies within the thread.

This dissertation investigates a new design for a magnetostrictive actuator that employs individually controlled coils distributed axially along the magnetostrictive rod. As a quantitative goal, the objective is to show that the multi-coil actuator can operate effectively at frequencies as high as 10,000 Hz with 900 N force and 50 microns of displacement. Conventional, single coil actuators with the same parameters for force and displacement develop significant attenuation in their response at frequencies above the first longitudinal vibration resonance at about 2750 Hz. The goal of the research is to investigate whether multiple coils can effectively increase the frequency range a least four times the range of conventional magnetostrictive actuators. This document derives a new mathematical model of the actuator that represents the spatial distributions of magnetic field and vibration, devises a control design that takes advantage of the multiple inputs to control the displacement of the actuator while consuming minimum electrical power, and describes a prototype multi-coil actuator and experimental system developed to test the idea. The simulations of the multi-coil actuator and control design demonstrate successful transient operation of the actuator over the targeted frequency range with feasible levels of input power and current. Experimental tests of the design, although limited by a computer sampling rate less than 10,000 Hz, are able to validate the predictions of the developed model of the actuator and reproduce the simulated control performance within the constraints of the experimental system.