Magsoft News

3rd Cent bc	Euclid of Alexandria	(325-265 bc)
	writes, among many other works, Optics, dealing with vision theory and perspective.
1st Cent bc
	Chinese fortune tellers begin using loadstone to construct their divining boards, eventually leading to the first compasses. (Mentioned in Wang Ch’ung’s Discourses Weighed in the Balance around 83 B.C.)
1st Cent
	South-pointing divining boards become common in China.
2nd Cent	Claudius Ptolemy	(87-150)
	writes on optics, deriving the law of reflection from the assumption that light rays travel in straight lines (from the eyes), and tries to establish a quantitative law of refraction.
2nd Cent	Hero of Alexandria
	writes on the topics of mirrors and light.
3rd Cent
	True compasses come into use in China.
6th Cent
	Discovery that loadstones could be used to magnetize small iron needles.
11th Cent	Abu Ali al-Hasan ibn al-Haitam (Alhazen)	(965-1039)
	writes Kitab al-manazir (translated into Latin as Opticae thesaurus Alhazeni in 1270) on optics, dealing with reflection, refraction, lenses, parabolic and spherical mirrors, aberration and atmospheric refraction.
11th Cent
	Iron is magnetized by heating it to red hot temperatures and cooling while in south-north orientation.
1086	Shen Kua	(1031-1095)
	writes Dream Pool Essays and makes the first reference to compasses used in navigation.
1150s
	An anonymous author penned the earliest explicit reference to magnets per se, in Roman d’Enéas.
1190s	Alexander Neckam	(1157–1217)
	writes De naturis rerum. It is the first western reference to compasses used for navigation.
13th Cent	Robert Grosseteste	(1168-1253)
	writes De Iride and De Luce on optics and light, experimenting with both lenses and mirrors.
13th Cent	Roger Bacon	(1214-1294)
	is the first to try to apply geometry to the study of optics. He also makes some brief notes on magnetism.
13th Cent	Pierre de Maricourt, a.k.a. Petri Pergrinus	(1269)
	writes Letter on the magnet of Peter the Pilgrim of Maricourt to Sygerus of Foucaucourt, Soldier, the first western analysis of polar magnets and compasses. He also demonstrates in France the existence of two poles of a magnet by tracing the directions of a needle laid on to a natural magnet.
13th Cent	Erazmus Ciolek Witelo	(1230-1275)
	writes Perspectiva around 1270, treating geometric optics, including reflection and refraction. He also reproduces the data given by Ptolemy on optics, though was unable to generalize or extend the study.
13th Cent	Theodoric of Freiberg	(1250-1310)
	working with prisms and transparent crystalline spheres, formulates a sophisticated theory of refraction in raindrops which is close to the modern understanding, though it did not become very well known. (Descartes presents a nearly identical theory roughly 450 years later.)
13th Cent
	Eyeglasses, convex lenses for the far-sightedness were first invented in or near Florence (as early as the 1270’s). Concave lenses for the near-sightedness appeared in the late 15th century.
16th Cent	Girolamo Cardano	(1501-1576)
	elaborates the difference between amber and loadstone.
1558	Giambattista della Porta	(1535-1615)
	publishes his major work, Magia naturalis, analyzing, among many other things, magnetism.
1600	William Gilbert	(1544-1603)
	after 18 years of experiments with loadstones, magnets and electrical materials, finishes his book De Magnete. The work included: the first major classification of electric and non-electric materials; the relation of moisture and electrification; showing that electrification effects metals, liquids and smoke; noting that electrics were the attractive agents (as opposed to the air between objects); that heating dispelled the attractive power of electrics; and showing the earth to be a magnet.
1606
	della Porta is the first to describe the heating effects of light rays.
1618	Francesco Maria Grimaldi	(1618-1663)
	discovers diffraction patterns of light and becomes convinced that light is a wave-like phenomenon. The theory is given little attention.
1621	Willebrord van Roijen Snell	(1580-1626)
	experimentally determines the law of angles of incidence and reflection for light and for refraction between two media.
1629	Nicolo Cabeo	(1585-1650)
	publishes his observations on electrical repulsion, noting that attracting substances may later repel one another after making contact.
1637	René Descartes	(1596-1650)
	publishes his Dioptics and On Meteors as appendices to his Discourse on a Method, detailing a theory of refraction and going over a theory of rainbows which, while containing nothing essentially new, encouraged experimental exploration of the subject.
1644
	Descartes’ Principia philosophiae, describing magnetism as the result of the mechanical motion of channel particles and their displacements, and proposing the absence of both void and action at a distance.
1646	Thomas Browne	(1605–1682)
	coins the term electricity in his Pseudodoia Epidemica.
1657	Pierre de Fermat	(1601-1665)
	formulates the principle of least time for understanding the way in which light rays move.
1660	Otto von Guericke	(1602-1686)
	builds the first electrical machine, a rotating frictional generator.
1661
	Fermat is able to apply his principle of least time to understand the refractive indices of different materials.
1664	Robert Hooke	(1635-1703)
	puts forth a wave theory of light in his Micrographia, considering light to be a very high speed rectilinear propagation of longitudinal vibrations of a medium in which individual wavelets spherically spread.
1665
	Grimaldi’s Prysico-mathesis de lumine coloribus et iride describes experiments with diffraction of light and states his wave theory of light.
1669	Erasmus Bartholin	(1625-1698)
	publishes A Study of Iceland Spar, about his discovery of double refraction.
1675	Robert Boyle	(1627-1691)
	writes Experiments and Notes about the Mechanical Origin or Production of Particular Qualities.
1676	Ole Christensen Römer	(1644-1710)
	demonstrates the finite speed of light via observations of the eclipses of the satellites of Jupiter, although he does not calculate a speed for light. His results were not widely accepted.
1677	Christiaan Huyghens	(1629-1695)
	extends the wave theory of light in his work Treatise on Light, unpublished until 1690.
1687	Sir Isaac Newton	(1642-1727)
	notes magnetism to be a non-universal force and derives an inverse cubed law for two poles of a magnet.
1690
	Huyghens formulates his wave theory of light in Traité de la Lumière, giving the first numerical quote for the speed of light, usually attributed to Römer, of 3.0 x 108 m/s.
1704
	Newton’s research on light culminates in the publication of his Optics, describing light both in terms of wave theory and his corpuscular theory.
1709	Francis Hauksbee	(1666-1713)
	publishes Physico-Mechanical Experiments on various subjects.
1728	James Bradley	(1693-1762)
	discovers the phenomenon of steller aberration, confirming earlier suggestions by Römer that the speed of light is finite.
1729	Stephen Gray	(1670-1736)
	shows static electricity to be transported via substances, especially metals.
1733	Charles-Francois de Cisternai du Fay	(1698-1739)
	discovers that electric charges are of two types and that like charges repel while unlike charges attract.
1745	Ewald Jürgen Georg von Kleist	(1700-1748)
	invents the Leyden jar for storing electric charge.
1746	William Watson	(1715-1789)
	suggests conservation of electric charge.
1746	Jean Antoine Nollet	(1700–1770)
	publishes Essai sur l’electricité des corps.
1747	Benjamin Franklin	(1706-1790)
	proposes that electricity be modeled by a single fluid with two states of electrification, materials have more or less of a normal amount of electric fluid, independently proposing conservation of electric charge, and introducing the convention of describing the two types of charges as positive and negative.
1747
	Watson passes electrical charge along a two mile long wire.
1750	John Michell	(1724-1793)
	demonstrates that the action of a magnet on another can be deduced from an inverse square law of force between individual poles of the magnet, published in his work, A Treatise on Artificial Magnets.
1759	Franz Ulrich Theodosius Aepinus	(1724-1802)
	publishes An Attempt at a Theory of Electricity and Magnetism, the first book applying mathematical techniques to the subject.
1764	Johannes Karl Wilcke	(1732-1796)
	invents the electrophorus, a device which can produce relatively large amounts of electric charge easily and repeatedly.
1766	Joseph Priestley	(1733-1804)
	deduces the inverse square law for electric charges using the results of experiments showing the absence of electrical effects inside a charged hollow conducting sphere.
1772	Henry Cavendish	(1731-1810)
	publishes, An Attempt to Explain some of the Principal Phenomena of Electricity, by Means of an Elastic Fluid.
1775	Alessandro Guiseppe Antonio Anastasio Volta	(1745-1827)
	invents an electrometer, a plate condenser and the electrophorus.
1777	Charles Augustin de Coulomb	(1736-1806)
	research sets a new direction in research into electricity and magnetism.
Early 1780s	Luigi Galvani	(1737-1798)
	uses the response of animal tissue to begin studies of electrical currents produced by chemical action rather than from static electricity. The mechanical response of animal tissue to contact with two dissimilar metals is now known as galvanism.
1785
	Coulomb independently invents the torsion balance to confirm the inverse square law of electric charges. He also verifies Michell’s law of force for magnets and also suggests that it might be impossible to separate two poles of a magnet without creating two more poles on each part of the magnet.
1799
	Volta shows that galvanism is not of animal origin but occurred whenever a moist substance is placed between two metals. This discovery eventually leads to the “Volta pile” a year later, the first electric batteries.
1800
	Volta writes a paper on electricity by contact.
1801	Thomas Young	(1773-1829)
	work on interference revives interest in the wave theory of light. He also accounts for the recently discovered phenomenon of light polarization by suggesting that light is a vibration in the aether transverse to the direction of propagation.
1801	Johann Georg von Soldner	(1776-1833)
	makes a calculation for the deflection of light by the sun assuming a finite speed of light corpuscles and a non-zero mass. (The result, 0.85 arc-sec, was rederived independently by Cavendish and Einstein in 1911, but went unnoticed until 1921.)
1807	Sir Humphrey Davy	(1778–1829)
	prepared a lecture, On Some Chemical Agents of Electricity which came very close to describing the possible relationships of chemical and electrical forces.
1812	Simeon-Denis Poisson	(1781-1840)
	formulates the concept of macroscopic charge neutrality as a natural state of matter and describes electrification as the separation of the two kinds of electricity. He also points out the usefulness of a potential function for electrical systems.
1813	François Étienne de la Roche	(1780-1813)
	Co-researched measurements of specific heat of air as a function of pressure.
1813	Jacques Étienne Bérard	(1789-1869)
	Co-researched measurements of specific heat of air as a function of pressure.
1814	Augustin Jean Fresnel	(1788-1827)
	independently discovers the interference phenomena of light and explains its existence in terms of wave theory.
1817
	Fresnel predicts a dragging effect on light in the aether.
1818
	Fresnel writes an essay on optics and the ether.
1820	Hans Christian Oersted	(1777-1851)
	notes the deflection of a magnetic compass needle caused by an electric current after giving a lecture demonstration. Oersted then demonstrates that the effect is reciprocal. This initiates the unification program of electricity and magnetism.
1820	André Marie Ampére	(1775-1836)
	confirms Oersted’s results and presents extensive experimental results to the French Academy of Science. He models magnets in terms of molecular electric currents. His formulation inaugurates the study of electrodynamics independent of electrostatics.
1820	Jean-Baptiste Biot	(1774-1862)
	co-developed the formula for the strength of the magnetic effect produced by a short segment of current carrying wire.
1820	Felix Savart	(1792-1841)
	co-developed the formula for the strength of the magnetic effect produced by a short segment of current carrying wire.
1825
	Ampére’s memoirs are published on his research into electrodynamics.
1827	Georg Simon Ohm	(1789-1854)
	formulates the relationship between current to electromotive force and electrical resistance.
1828	George Green	(1793-1841)
	introduces the notion of potential and formulates what is now called Green’s Theorem relating the surface and volume distributions of charge. (The work goes unnoticed until 1846.)
1831	Michael Faraday	(1791-1867)
	begins his investigations into electromagnetism.
1832	Carl Friedrich Gauss	(1777-1855)
	independently states Green’s Theorem without proof. He also reformulates Coulomb’s law in a more general form, and establishes experimental methods for measuring magnetic intensities.
1835
	Gauss formulates separate electrostatic and electrodynamical laws, including Gauss’s law. All of it remains unpublished until 1867.
1838
	Faraday explains electromagnetic induction, electrochemistry and formulates his notion of lines of force, also criticizing action-at-a-distance theories.
1838	Wilhelm Eduard Weber	(1804-1891)
	he and Gauss apply potential theory to the magnetism of the earth.
1839
	The potential theory for magnetism developed by Weber and Gauss is extented to all inverse-squared phenomena.
1842	William Thomson a.k.a. Lord Kelvin	(1824-1907)
	writes a paper, On the uniform motion of heat and its connection with the mathematical theory of electricity, based on the ideas of Jean Baptiste Joseph Fourier (1768-1830). The analogy allows him to formulate a continuity equation of electricity, implying a conservation of electric flux.
1845 - 1850
	Faraday introduces the idea of contiguous magnetic action as a local interaction, instead of the idea of instantaneous action at a distance, using concepts now known as fields. He also estabishes a connection between light and electrodynamics by showing that the transverse polarization direction of a light beam was rotated about the axis of propagation by a strong magnetic field (today known as Faraday rotation).
1845 - 1850	Gustav Theodor Fechner	(1801–1887)
	proposes a connection between Ampére’s law and Faraday’s law in order to explain Heinrich Friedrich Emil Lenz’s law (1804-1865).
1846
	Weber proposes a synthesis of electrostatics, electrodynamics and induction using the idea that electric currents are moing charged particles. The interactions are instantaneous forces. Weber’s theory contains a limiting velocity of electromagnetic origin.
1846	William Robert Grove	(1811-1896)
	writes Correlation of physical forces the partial-drag theory of George Gabriel Stokes (1819-1903) is revived for the explanation of stellar aberration.
1849	Armand Hippolyte Louis Fizeau	(1819-1896)
	begins experiments to determine the speed of light.
1851
	Fizeau’s interferometry experiment confirming Fresnel’s theoretical results.
1852
	Stokes names and explains the phenomena of fluorescence.
1854	Bernhard Riemann	(1826-1866)
	makes unpublished conjectures about an investigation of the connection between electricity, galvanism, light and gravity.
1855	Heinrich Friedrich Theodor Kohlrausch	(1780-1867)
	co-determined with Weber a limiting velocity which turns up in Weber’s electrodynamic theory, and that it’s value is about 439,450 km/s.
1855 - 1868	James Clerk Maxwell	(1831-1879)
	completes his formulation of the field equations of electromagnetism. He established, among many things, the connection between the speed of propagation of an electromagnetic wave and the speed of light, and establishing the theoretical understanding of light.
1858
	Riemann generalizes Weber’s unification program and derives his results via a solution to a wave function of a electrodynamical potential (finding the speed of propagation, correctly, to be c). He claimed to have found the connection between electricity and optics. (Results published postumously in 1867.)
1861
	Riemann uses Lagrange’s theorem to deal with velocity-dependent electrical accelerations.
1861	Gustav Robert Kirchhoff	(1824-1887)
	formulates the model of the black body.
1863	John Tyndall	(1820-1893)
	publishes Heat Considered as a Mode of Motion.
1864
	Maxwell publishes A Dynamical Theory of the Electromagnetic Field, his first publication to make use of his mathematical theory of fields.
1865
	Maxwell publishes A Dynamical Theory of the Electromagnetic Field, formulating an electrodynamical formulation of wave propagation using Lagrangian and Hamiltonian techniques, obtaining the theoretical possibility of generating electromagnetic radiation. (The derivation is independent of the microscopic structures which may underlie such phenomena.)
1870	Hermann Ludwig Ferdinand von Helmholtz	(1821-1894)
	developes a theory of electricity and shows Weber’s theories to be inconsistent with the conservation of energy.
1873
	The first edition of Maxwell’s Treatise on Electricity and Magnetism is published.
1874	George Johnstone Stoney	(1826–1911)
	estimates the charge of an electron to be about 10-20 Coulombs and introduces the term electron.
1875	Hendrik Antoon Lorentz	(1853-1928)
	in his doctoral thesis, derives the phenomena of reflection and refraction in terms of Maxwell’s theory.
1875	Sir William Crookes	(1832-1919)
	performs experiments on cathode rays.
1879
	Maxwell suggests that an earth-based experiment to detect possible ether drifts could be performed, but that it would not be sensitive enough.
1881	Albert Abraham Michelson	(1852-1931)
	begins his interferometry experiments to detect a luminiferous ether.
1884	Heinrich Rudolf Hertz	(1857-1894)
	develops a reformulation of electrodynamics and shows his and Helmholtz’s theories both amount to Maxwell’s theory.
1884	John Henry Poynting	(1852–1914)
	establishes that for electromagnetic radiation energy can be localized and flow (the first such energy localization principle established).
1885 - 1887	Oliver Heaviside	(1850-1925)
	writes Electromagnetic induction and its propagation over the course of two years, re-expressing Maxwell’s results in 3 (complex) vector form, giving it much of its modern form and collecting together the basic set of equations from which electromagnetic theory may be derived (often called Maxwell’s equations). In the process, He invents the modern vector calculus notation, including the gradient, divergence and curl of a vector.
1887
	Hertz experimentally produces electromagnetic radiation with radio waves in the GHz range, also discovering the photoelectric effect and predicting that gravitation would also have a finite speed of propagation.
1887	Woldemar Voight	(1850-1919)
	working through an analysis of Doppler effects using an elastic model of the luminiferous ether to describe optical properties, produces a set of relations between space and time intervals which are later rediscovered independently by Lorentz and now known as the Lorentz equations (first so-called by Poincaré in 1904).
1889	George Francis Fitzgerald	(1851-1901)
	suggests that bodies contract in the direction of motion against the luminiferous ether by an amount which would account for the null results coming from the Michelson-Morley experiments on ether motion. A more detailed calculation is performed independently by Lorentz in 1895.) Fitzgerald also suggests that the speed of light is an upper bound on any possible speed. (This suggestion reappears in 1900 by Lorentz, in 1904 by Poincaré, and again in 1905 by Einstein.)
1889	John William Strutt a.k.a. Lord Rayleigh	(1842-1919)
	presents a model for radiation in terms of wave propagation.
1890
	Hertz publishes his memoirs on electrodynamics, simplifying the form of the electromagnetic equations, replacing all potentials by field strengths, and deduces Ohm’s, Kirchoff’s and Coulomb’s laws.
1892 - 1904
	Lorentz completes the description of electrodynamics by clearly separating electricity and electrodynamic fields and formulating the equations for charged particles in motion.
1893	Wilhelm Carl Werner Otto Fritz Franz Wien	(1864-1928)
	gives his displacement law of blackbody radiation.
1896
	Wien theoretically derives the radiation distribution law.
1896
	The discovery of X-rays and Becquerel radiation.
1896
	The discovery of the Zeeman effect.
1897	Joseph John Thomson	(1856-1940)
	experimentally determines the charge-to-mass ration of electrons.
1898	Jules Henri Poincaré	(1854-1912)
	suggests that a complete measurement theory must formulate a notion of distant synchronization and discusses its relevance to the apparent constancy of the speed of light.
1899
	Lorentz refines the transformation laws, formulating the notion of local time and local coordinate systems in electrodynamics.
1899	Thomson and Philipp Eduard Anton von Lenard	(1862-1947)
	begin experimental investigations of photoelectric radiation.
1904
	Poincaré uses light signals as a functional technique to establish distant synchronization in application to Lorentz’s electron theory, also putting forth the first formulation of a principle of electrodynamic relativity.
1905	Albert Einstein	(1879-1955)
	analyzes the phenomena of the photoelectric effect and theorizes that light may be taken to be made up of vast amounts of packets of electromagnetic radiation in discrete units.
1905
	Einstein publishes his paper, On the Electrodynamics of Moving Bodies, drawing out the symmetries of Lorentz’s electromagnetic theory, underlying connection in measurement theory and the status of the electromagnetic ether.
1907	Hermann Minkowski	(1864-1909)
	through considerations of the group properties of the equations of electrodynamics, re-interprets Einstein’s relativity theory as a kind of geometry of spacetime, considered as a single medium.

A study has on the modeling of Non Destructive Testing using eddy currents with FLUX 8.10, 3D application has recently been performed at CEDRAT. FLUX has demonstrated its capacity to obtain high-quality results for this kind of application with reasonable computation time. To obtain these results, one needs to pay particular attention to the modeling of the mesh design, formulations, and the description of probe motion during the simulation of such problems.

A technical paper “ Non Destructive Testing with FLUX 3D application has been created that allows the user to easily reproduce this computation and understand the key points of NDT modeling in FLUX.

Problem 8: A block of austenitic stainless steel (resistivity: 7.4e-7 Ω.m-1) contains a rectangular slot representing a flaw. A differential probe moves across the surface of the block. The probe is composed of one inducing solenoid (supplied by a 500 Hz sinusoidal signal) and by two receptive coils (see Figure 1).

Figure 1 :The problem 8.

Each of the two smaller solenoids are in a branch of a Wheatstone’s bridge. An amplifier and a dephasor generate signals proportional to the difference of the magnetic flux in the two receivers. The simulation aimed at fitting the measurements for two different motions of the probe :

- Longitudinal motion: motion parallel to the plane of the crack (the axes of the two coils being in the plane of the crack).

- Transversal motion: motion perpendicular to the plane of the crack ( the axes of the two coils being in the plane perpendicular to the plane of the crack).

The “ Key points � A study of sensitivity has permitted to determine the most significant parameters for the finite element model . A good modeling of NDT devices with FLUX will follow the four following advices:

• Limit the mesh noise inherent in the flux computation.

• Limit the mesh noise inherent in the description of the probe motion.

• Mesh finely the place where eddy currents will appear.

• Use of an adapted formulation in the computation of eddy currents in a cracked geometry.

Figure 2: Geometric representation.

1. Flux computation: The probe has been modeled by non meshed coils. However, in order to ensure a precise computation, the mesh must be well structured in the air space filled by these coils. Thus, the air volumes inhabited by the coils have been geometrically represented. (see Figure 2)To limit the mesh noise, an extrusive mesh generator has been applied on the entire height of the sensor. Similarly, as the computed flux is the difference between the flux seen by the two receivers, the mesh noise is drastically reduced by meshing them identically.(see Figures 3 and 4)

Figure 3: Extrusive mesh generator.

Figure 4: Linked mesh.

Finally, the calculation of the flux itself must be done with the method “FLUX_INDUCTOR” corresponding to a volume integration in the air enclosing the coils (zone modeled by a reduced formulation versus to vector potential) :

An integration of B on a surface normal to the flux or the multiplication of the mean value of the induction on this surface would lead to important approximations.

2. Probe motion: A computation parameterized by the geometrical position of the coils would mean a remeshing of the entire model for each position. Such a remeshing introduces an unacceptable amount of noise compared with the required precision. The new 3D mechanical sets available in the version 8.10 will be used to describe the motion.

It is imperative to keep a constant mesh in the zone where you compute the flux. Thus, a first mechanical set in translation will be created in the air surrounding the coils and the flux will be computed only in this zone. The plate being fixed, we have the choice to define the mechanical sets by following two strategies :

Figure 5: Division in 3 mechanical sets.

Division in 3 mechanical sets (see figure 5):

In blue: mechanical set in translation containing the coils (zone of flux computation): constant mesh

In green: compressible mechanical set

In yellow and magenta: plate and crack, fixed mechanical set : constant mesh

Figure 6: Division in 2 mechanical sets.

Division in 2 mechanical sets (figure 6) :

In blue and green: mechanical set in translation : constant mesh

In yellow, turquoise and magenta: fixed mechanical set, constant mesh

In the 1st case, the device is surrounded by air and an infinite box, the technique of compressible mechanical set is used. In the second case, two blocks are in relative motion, a sliding surface separates them. The boundary conditions are directly defined on external faces.

3. Plate mesh: A correct mesh is necessary in the plate, which is the zone where eddy currents appear. More particularly, the study has shown that the mesh can be structured efficiently by geometrically representing the volumes of the plate over which the probe passes. Then, it is possible to refine the mesh in these zones without generating too many nodes in the rest of the plate (see figure 7). The global mesh of the device represents between 120,000 and 145,000 nodes (with second order element) depending on the chosen configuration.

Figure 7: Plate mesh

4. Formulations: The study has been realized both with scalar and vector potential formulations. Thanks to recent developments, the scalar formulations give results as precise as vector ones and demand less resources (computation time, memory requirement).

The new reduced formulation versus T0 has been used in the air surrounding the coils. The plate is modeled by a TΩ formulation (Electric vector potential, Total magnetic scalar potential) with edge interpolation. The equivalent nodal formulation is not satisfactory for NDT application as the crack makes the plate concave and the concavity leads to imprecise local computations of eddy currents with nodal interpolation.

The Studied Cases:

Beyond the sensitive study, different simulations have been performed: longitudinal and transversal motion, use of compressible mechanical set or use of sliding technique. Finally, the crack being very fine, we have the choice to represent it by a volume composed by air or by a surface on which is assigned a specific surface constraint. (see Figure 8 )

Figure 8: Mesh distribution for the defect.

The Results:

The results obtained by FLUX fits very well to the measurements. Similarly, the sliding technique and the compressible have both given satisfaction .( see Figures 9 and 10)

Figure 9: Results with the compressible mechanical set.

Figure 10: Results with the sliding surface.

Finally, the representation of the crack as a surface gives equivalent results. The surface constraint assigned to the crack requires that the local direction of eddy currents is parallel to the edges of the crack (TXN=0). We can conclude that it is not necessary to physically represent the crack itself but only the consequence of its presence on the eddy currents distribution. (see Figure 11)

Figure 11: Results with a surface crack.

The result of the computation being the difference of two close quantities, the quality of the results is very sensitive to the respect of the “key points� presented above. Without taking care when constructing the model, the results could look like the following. (see Figure 12)

Figure 12: Results using a global remeshing.

Costs:

Concerning the computation time, the scalar formulations and a fine but controlled mesh allow a reasonable computation time. Results for the 30 positions of the probe are obtained in half a working day. This makes FLUX a powerful and efficient tool for NDT applications.

This study is based on the benchmark Problem No. 8 of TEAM WORKSHOP: “A Coil over a crack” realized by Jean-Claude VERITE (EdF, Direction Etudes et Recherches). This problem has been presented in COMPEL.

Pioneering the field of computation of electromagnetic fields related to ships, FLUX has become a known and renowned reference in the world. This leadership has a long history: • The partnership developed with the LMN, Laboratoire de Magnétisme du Navire, that has enabled since long time to develop the tools needed for the modelling of this application as well as validation of the results versus measurements. • Xavier Brunotte, the technical manager of CEDRAT has lead its PhD on this application in 1991. The topic was: “Modelling of infinity and account for thin magnetic regions. Application to modelling of ship magnetisation”. • Christophe GUERIN, a major actor on FLUX physical aspects in CEDRAT’s Development Team, has developed the “shell regionsâ€? during its PhD in 1994. The topic was: “Determination of Eddy currents losses in transformer tanks. Modelling of thin regions and account for saturation in magnetic material in harmonic states”.

This leadership is also explained by a long list of advanced technical features, such as:

1/ The Shell region is a major feature for ship magnetisation. It enables to consider the hull as a surface and not as a volume. Considering the difference of dimensions between the length of the structures and the thickness of the hull, this enables to consider much larger structures with high accuracy. The shell region represents the hull as a surface, its thickness being introduced as “virtual thickness” and taken accurately into account. The variation of the field through this thickness is taken into account providing accurate field at the opposite side, whatever the variation of the field.

Example of a source field defined as parametric expression: Axis=1: along X; Axis=2: along Y; Axis=3: along Z.
2/ The parametric application which enables in one file to obtain the results for the 3 directions, using a simple formula. The multi axis model enables to solve for any parametric orientation of the source field. Results are then obtained easily for all directions at any distance of the ship. The formula manager of FLUX enables also to express easily the expression to obtain : Bz, Bz-µ0*H0, …

Simple model: hull considered has a surface with virtual thickeness

|B| induced by a earth field along X axis: influence of boxes and wall of ship

HO in X direction, Z=250mm, Bz.

HO in Y direction Z=250mm, Bz.

HO in Z direction, Z=250 mm, Bz - mu*0*HO.

3/ The infinite box that enables to model the open boundary cases, taking into account the field up to the infinite.

2 degaussing coils, Z=250mm, Bz.

4/ The coil shape data base that enables to describe either parameterized standard coils from database, either any kind of customized shapes of coils. The coils are independent of the mesh. So parametric computations versus their position in the system are extremely easy to obtain.

Part of shell described with nurbs imported on step format from Solidworks and meshed in FLUX.

5/ The advanced imports capabilities and the automatic mesh generator that enables to import DXF, STEP, IGES, PRO-E, CATIA or AUTODESK files.

6/ The 64B solver that will be proposed with V9.3 in spring 2006 will be the last improvement introduced in FLUX. It will bring the capability to consider much larger configuration, the present limit being slightly above 1 000 000 nodes.

Mesh discontinuities of the top of an ellipsoid and connection with surrounding mesh of the air.

7/ The experience and the quality of the support you will benefit from our support team for these applications.

HO in X direction, Z=250mm, Bz along a path placed under the ship, centered in Y.

Some examples are shown in the presented pictures. We remain at disposal for any further information and are ready to bench to enable you to join the community of worldwide navies using FLUX.

Introduction
To some extent, the winding of a switched reluctance machine [SR motor] could be treated as an air‑gap winding, where the eddy currents in the conductors could be significant. This is most noticeable on the leading (”motoring”) side of a coil between the unaligned and aligned position, which is quite a complex magnetic circuit. For this reason a transient finite element analysis is desirable to verify the affect of eddy currents.

Figure 1a:Mesh of low voltage.

Figure 1b: standard voltage for SR models.

FLUX2D modelling
Eddy‑current modelling of a SR motor has some special features and requirements. In this study, two main models were created. Both represent an 8/6 SR motor; the essential difference between them is that one is for low voltage operation (4 turns per pole, 8mm squared conductors) and the other is for standard voltage operations (25 turns per pole, 2mm rounded conductors. This is shown in Figs. 1 (a) and (b). A fine mesh is required around the stator conductors for precise determination of the eddy currents and in the air gap, for satisfactory estimation of performance. There are 14,067 surface elements for the low voltage model and 15,672 surface elements for the standard voltage model. The conductors assumed a constant resistivity of copper (Ï?Cu=1.72×10-8Ωm). The control circuit is simple and uses a single pulse control, with a constant voltage source as shown in Fig. 2 (a) and (b). This circuit also provided the correct connection for the series‑connected conductors; because of the large number of conductors in Fig 2 (b) only one phase was simulated.

Figure 2a: Electric circuit of low voltage

Figure 2b: Standard voltage SR models.

Simulation
It was anticipated that the p.u. eddy current loss will be much higher in the low voltage model by virtue of its large conductors. The transient FE magnetic analysis included rotor movement. Waveforms and performance obtained from FLUX 2D and compared to SPEED PC-SRD – the results are shown in Table 1. The PC-SRD model has more phase turns but the current was adjusted to produce the same torque.

Table 1: Main parameters of the analytical and FE models.
Low voltage SR model
The phase current waveforms are shown in Fig. 3 (a). This is the mean current across a conductor. The highest distortion of current density was in the surface conductors of the coil on the rotor side and, more significantly, on the motoring side. The loss factor (= total loss / DC loss) was found to vary between 1.38 and 9.15 per period. Fig. 3 (b) shows the current density distribution across the conductors on the motoring side. The view is from top right corner on the motoring side of the coil.

Figure 3a: Current waveforms.

Figure 3b: 3Ddistribution of current density for low voltage model.

Standard voltage SR Model
In this case, when the radius of a conductor was significantly smaller than the skin depth, the variation of losses was not so severe and is kept below 9 percent per period. The maximum value of the loss factor was 1.09. The torque waveform and current density distribution are shown in Fig. 4. As can be observed, the current density is practically uniform, except for the outer conductors. This is in contrast to the thick square conductors for the low voltage model.

Figure 4a: Torque waveform.

Figure 4b: 3D distribution of current density for standard voltage model.

Conclusion
The eddy‑current loss is high in the low voltage SR model with thick conductors. According to the finite‑element results, the difference between maximum and minimum loss was almost 600% with a loss factor of about 9. Thus precise calculation of eddy currents is essential otherwise they could lead to the insulation failure and burning of the winding as well as poor performance. It was also computed that the losses due to eddy currents do not exceed about 9% of the DC loss for conductors with a radius of about one quarter of the skin‑depth.

This article is reproduced with permission of the authors, Martin Klauz and David Dorrell from the SPEED Laboratory.