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We report on the design and implementation of innovative haptic interfaces based on magnetorheological fluids (MRFs). We developed 2-D and quasi-3-D MRF-based devices capable of suitably energizing fluids with a magnetic field in order to build shapes that can be directly felt and explored by hand. We obtained this effect by properly creating a distribution of a magnetic field over time and space inducing the fluid to assume a desired shape and compliance. We implemented different prototypes, synthesized and designed with the help of preliminary simulations by a 3-D finite-element code. In this way, both magnetic field and shear stress profiles inside the fluid could be carefully predicted. Finally, we evaluated and experimentally assessed the performance of these devices. Index Terms--Electromagnetic devices, haptic interfaces, magnetorheological fluid (MRF).

In this paper, the synthesis and design of a new device for the energization and characterization of magneto-rheological fluids (MRF) for haptic interfaces are presented. Due to the core structure and feeding conditions, only a three-dimensional numerical analysis provides an accurate prediction of the electromagnetic quantities and the rheological behavior of an excited specimen. The design constraints are shown in details and the results in terms of magnetic field inside the fluid and its spatial resolution are discussed. Index Terms--Electromagnetic (EM) device, haptic interfaces, magneto-rheological fluid (MRF).

In this paper, the numerical analysis of a complete launch package, composed by a homopolar generator feeding a rail launcher, is described. Because of the nonlinear and time varying characteristics of both generators and launchers, a separate analysis of the two devices is not always able to provide highly accurate previsions about the performance of the overall system. The analysis has been performed here by using an integral formulation that transforms the Maxwell's equations into an equivalent electric network, whose parameters vary together with the evolution of the system. The presence of sliding contacts and the consequent velocity skin effect in both the generator and the launcher have been taken into account. The most important electromechanical quantities have been reported; the results of the simulations shows the effectiveness of the software used for this coupled analysis. Index Terms--Homopolar generator, integral equations, moving conductors, rail launchers, sliding contacts.

In a previous paper, the authors proposed a 'multi-stage' railgun configuration in order to reduce the negative effects of the ablation of material from the rail and insulator walls on the velocity of the mass to accelerate. The railgun was segmented in some stages and the accelerating pellet is pushed by a new plasma armature at every stage. For a given size of the rail, the multi-stage configuration reached a velocity about 20% higher than the one in the single stage, with different mass of the pellet, reducing the ablated mass. The aim of this paper is to perform a deeper analysis of the performance of the multistage railgun in order to characterize the values of the quantities influencing the performances of the railgun in terms of velocity of the pellet. In particular, a series of simulations has been carried out varying the feeding currents, pellet masses, arc masses, and compositions of the propelling plasma arc. The influence of these quantifies has been analyzed in order to study the velocity of the pellet mass and the behavior of the plasma arc in terms of ablated mass, temperature, pressure, and conductivity at every stage. Index Terms--Ablation, multistage railgun, plasma armature, rail launcher.

In this paper a wavelet transform approach is used to solve multiconductor transmission line equations. By using wavelets on the interval, differential and integral operators are represented by sparse matrices. Then the time domain differential equations of multiconductor transmission lines are reduced to algebraic ones. The unknowns of the algebraic system are the coefficients of the wavelet basis functions. Therefore a Fourier-type approach is obtained for transient analysis of transmission lines. The procedure reduces the CPU times with respect to the usual transient analysis obtained by time stepping methods. An initial analysis of the numerical characteristics and performances of the method is carried out considering constant RLCG multiconductor lines. Index terms - Transmission lines, wavelet transform

Hybrid FEM/MOM methods use the equivalence theorem to transform the actual problem into equivalent problems in the exterior and interior regions. In this paper dual edge element differential formulations in terms of two-component vector potentials are used to solve the interior problem. In the exterior problem the Method of Moments (MOM) has been used. A non-linear matrix equation for the problem solution is obtained by forcing the continuity of the actual tangential electric and magnetic fields on the boundary of the non-linear solid bodies. Two-dimensional numerical results are used to show the characteristics of the method. Index terms - Hybrid formulations, Eddy currents

In this paper the transition between the sections of a generator driven induction launcher is investigated. During the transition a possible mismatch of the currents in the sleeve with the driving coils currents can give rise to strong braking force. If the sleeve is not in coaxial position with the barrels, forces in the transverse direction of motion can produce contacts with the flyway tube. Transverse motion of the sleeve has to be considered. The equations of motion are derived assuming a rigid projectile and a flyway restoring force that is proportional to the local deformation. A full 3-D analysis, required because of the departure from the coaxial configuration, has been performed by means of a computer code based on an integral formulation of the Maxwell equations; the resulting equations are those of an electrical time-varying network. Simulations of the behaviour of the system have been performed to search for the optimal initial position of the sleeve in the second section. The results show that smooth transition between the sections is obtained if the energization of the coils of the second section is done in correspondence with the proper positions of the sleeve. Under these conditions the motion is characteryzed by the greater muzzle velocity. Index terms - Linear induction launcher, magnetic force, eddy currents, heating.

The aim of this paper is to define a procedure for the design of induction coilguns in order to obtain thermal and mechanical stress that do not exceed the allowed values in the sleeve. The magnetic vector potential is determined considering a cylindrical sheet current model both for the barrel and the sleeve and solving the related modified Bessel equation. Then the flux, the current density and the propulsive force for each section are determined. By considering the constraints due to mechanical and thermal stress, the maximum muzzle velocity for a one-section launcher is determined. Supposing that the muzzle velocities in the first and in the last section are established, and assuming that all sections, from the second to the last, work with the same mean slip and the same relative velocity, the number of sections and their length are determined. Moreover the surface current density in the barrel is calculated. The design criterion is compared with other criteria, and then used to design an 8km/s muzzle velocity launcher. Index terms - induction coilguns stresses.

In this paper, an equivalent network model for transformer analysis including hysteretic effects is presented. The nonlinear electromagnetic problem is reduced to the analysis of an equivalent network by integrating Ohm's law inside every elementary volume into which the solid bodies of the examined system are subdivided. The model allows the analysis of the electromagnetic field distribution for the evaluation of local saturation effects by using fine discretizations. Furthermore it gives a simple and efficient equivalent circuit of the transformer for external effects determination by using coarse discretizations. Hysteresis effects in the steady state case can be taken into account by an equivalent hysteretic loop obtained from standard measurements. The method has been tested by comparison with experimental data.

Aim of this paper is to compare the features of integral and differential formulations for the solution of transient eddy current problems in nonlinear media. The integral method used in this paper reduces the nonlinear eddy current problem to the analysis of an equivalent network. Two dual edge element differential formulations are also used. Their field estimates automatically verify Faraday's and Ampere's laws and furnish the distribution of the constitutive error in solution domain, which provides a useful tool for the refinement of the discretization. The methods are applied to analyze a massive magnetic circuit characterized by the presence of soft and hard magnetic materials with narrow gaps.

In this paper a method for non linear three dimensional eddy currents and magnetodynamic analysis handling of anisotropic non-linear and hysteretic materials is presented. Taking into account the Coulomb gauge, and expressing the magnetic vector potential as a function of conduction currents and magnetizations, a nonlinear system in the magnetization unknowns and a differential set of equations in the conduction current unknowns are obtained. The nonlinear system is derived imposing the constitutive equation H(B) inside the ferro-magnetic materials allowing the presence of anisotropic non-linear and hysteretic relations. The differential system is derived integrating Ohm's law inside the conductive materials. Considering an hysteretic model characterized by an internal state, like the Preisach one, we know the 'actual' branch in the magnetization loop, and we can schematize hysteresis as a monotonic non-linear time varying phenomenon, to which Newton-like methods can be applied. Numerical simulations comparing anisotropic non-linear reversible and hysteretic cases have shown the model capability to handle 3-D anisotropic and hysteretic constitutive curves, and its numerical robustness.

In this paper an equivalent network model for the three-dimensional analysis of an EML plasma armature is presented. We decompose the plasma armature in elementary volume elements in which a uniform distribution of the current density, momentum density and heat flux Is assumed. A first equivalent electric network is obtained for the determination of the current density and magnetic field distribution in the plasma arc at each time step. Assuming the same plasma arc decomposition, and defining a formal analogy between thermodynamic and electric quantities in the momentum and mass conservation equations, we obtain a second equivalent electric network that allows the determination of the pressure and the mass density distribution and the internal motions in the plasma arc at each time step. Adopting the same procedure, we obtain another equivalent network from the energy equation that allows the determination of the temperature in the plasma arc at each time step. The ionisation coefficient distribution is calculated from Saha's equation. Considering an isothermal plasma with no ablation, calculated results are reported to show the influence of the 3-D model on the distributions of the main thermodynamic quantities of the plasma arc.

In this paper the performances of an electromagnetic launch system constituted by an arc driven railgun powered by a MHD generator are investigated. A small bore plasma driven railgun for fusion fuel pellet injection is examined considering as pulse power source a MHD generator having characteristics taken from operating devices. The analysis of the railgun and generator has been carried out by means of a lumped parameter equivalent network model that takes into account drag force and ablation effects and allows the evaluation of the main electrical and thermodynamic quantity distributions of the plasma arc.

In this paper a hybrid integral-finite difference approach for the analysis of the transient electromagnetic heating effects in three-dimensional conductor bodies, is presented. The electromagnetic analysis is carried out by the discretization of the conductive regions in suitable slabs, that allows the transformation of the Maxwell's equations to the equilibrium equation of an equivalent three-dimensional network. The thermal diffusion equation is solved by means of a finite difference approach in the time domain, using the same gri of the equivalent network above mentioned. The numerical solutions of the electrical and thermal equilibrium equations are performed separately and alternatively, and the values of the temperature dependent physical parameters are updated in time at each step. The method described in the paper has been tested with experimental data with regard to steady and transient state conditions of a bus-bars compartment of a low-voltage power center.

The analytical expression of the time behaviour of the current density due to a electric discharge on a three dimensional conducting slab has been obtained by means of an analytical method. The electric discharge is modeled by a current pulse injected in the slab. The current injection point can be arbitrarily positioned on the surface of the slab. The diffusion equation was solved in the s domain using the technique of the separation of variables. The time behaviour of the current density was determined applying the inverse Laplace transform to the solution. The analytical results were compared with results obtained with two numerical methods, the first based on an equivalent network formulation and the second based on a Finite Difference Time Domain method. The electromagnetic field in space has been simply determined from the knowledg of the current density distribution.

In this paper a method based on an integral formulation for nonlinear three dimensional eddy currents and magnetostatic analysis is presented. The method is based on the subdivision of the conductive regions in elementary volume elements in which a uniform current density J and magnetization M is assumed. Integrating Ohm's law inside the conductive regions, a system of nonlinear equations that can be integrated combining a modified Newton-Rapshon and a single-step time-marching method is obtained. Calculated results for TEAM problem 13 (magnetostatic) and problem 10 (eddy currents) are reported.

The RFEC (Remote Field Eddy Current) technique is a relatively new method of testing thick walled tubes, that rely on the use of very low intensity electromagnetic fields. In the conventional RFEC technique defect detection is carried out considering the phase difference between the exciting and pickup signals. Depending on the electric and magnetic characteristics of the tube material, the probe output signal does not always allow easy defect detection. In this paper the use of a differential probe, in order to have a clearer defect detection, is proposed and its response is analysed considering both sinusoidal steady state or sinusoidal pulse excitations. The electromagnetic analysis of the system is carried out by means of an equivalent network model, that allows easy modeling of axysimmetric defects.

The knowledge of the magnitude and of the spatial and temporal distributions of electric and magnetic fields radiated during the ignition of the plasma armature of arc-driven railguns, can be a useful tool for the correct design of the shielding and of the location of electronic apparatuses controlling the launchers. In this paper the electromagnetic fields radiated by a railgun during its operation are evaluated at different points around the launcher, The radiation is determined, assuming a temporal and spatial form of the current in the plasma arc, and integrating Maxwell equations directly in the time domain. In general the evaluation of the obtained electromagnetic fields expressions requires a numerical integration, while when it is possible to assume particular spatial and temporal form of the arc current, analytical expressions have been derived.

Current filament models have been widely used for the electromagnetic analysis of induction launchers and electromagnetic devices. In this paper two functions of the eigenvalues of the filament parameter matrix were determined in order to evaluate: - the errors on the system solution, induced by approximate calculations of the matrix parameters; - the influence on the solution, of a variation of the filament number of the discretization. These functions allow an estimate of the solution convergence, and accuracy, avoiding the numerical or analytical integration of the differential equation set of the system. The launcher has been modeled by means of a coordinate system coherent with the moving armature, with the hypotheses of piecewise constant velocity of the armature, in order to have not time dependent elements in the system matrix.

This paper describes an approach to simulate the behaviour of electromagnetic rail launchers. The problem of the three-dimensional electromagnetic diffusion of the current is solved by discretizing the conductors in suitable elementary volumes, forming an equivalent network, whose electrical parameters are calculated by the subdividing geometry adopted. The thermal and the mechanical behaviour of the system are also considered, and the parameters of the network are updated step by step in time, taking into account the variation of the resistances and of the self- and mutual inductances due to the motion of the armature, and the increase of electrical resistivity due to the increase in temperature.

The analysis of the effects of the application of an external magnetic field on the behaviour of plasma-driven railguns is carried out. An evaluation of the quantity of material ablated from the rail and insulator walls, of the mass leakage from the rear of the arc, and an estimate of secondary arc formation is carried out modeling the characteristic quantities of the plasma arc by means of an adimensional model that was suitably adapted in order to reproduce some experimental data.

In this paper an integral approach for the analysis of three-dimensional transient electromagnetic heating effects is presented. The conductor bodies are decomposed in elementary parallelepipeds and the centers of nearby parallelepipeds are connected in order to obtain a three-dimensional grid. The electrical and thermal equilibrium equations applied to this grid allow the evaluation of the current density and the temperature distribution inside the conductors of the system. The characteristics of the presented approach are shown simulating the tests provided in the experimental verifications of switch gear and controlgear assemblies.

In this paper a quasi-analytical model for the analysis of eddy currents distributions and forces in axisymmetric systems with conductors in motion is presented. The model is based on the analytical solution of the vector potential formulation of the Maxwell Equations for a sinusoidal steady state regime relating to an axially infinite geometry with conductors moving at a constant velocity. When the conductors move at a constant velocity, the model allows the analysis of axially infinite geometries for every kind of excitation waveforms. Finite axial geometries are considered, for iron free systems, superimposing two solutions relating to axially infinite geometries. The model can be used for the analysis of different devices, and a particularly useful application for the analysis of the transient induced voltage in a Non Destructive Testing system is shown.