3.Properties_of_Materials

3. Magnetic Properties of MaterialsWhen a voltage is applied to a device composed of materials, a current flows. Magnetic fields within and external to the materials are created. These fields store energy within the device and may be the transfer medium for energy conversion from one electrical system to another.Different materials exhibit different characteristics when placed in a magnetic field. These can be regarded as the magnetic properties of the materials.3.1 RELATIVE PERMEABILITYA current I passing through a coil of wire of N turns will produce a magnetomotive force (mmf ), MM = NIN turnsmagnetic field lineϕl oThe mmf gives rise to a magnetic flux φ, which flows around the coil and through any material in its path. Strictly, a magnetic flux is a concept. Its presence is inferred from the effects that its existence generates. Nothing actually flows, nor is there energy loss. It is a useful concept with which the fundamentals of magnetics can be modelled.The value of flux, for a given mmf causing it, is dependent on the characteristics and dimensions of the materials it passes through. This can be represented by the reluctance R of the material, a concept akin to resistance in conductors. ThusM = φRThe magnetic flux flows through an area A , hence it is a useful to represent the mmf in terms of flux density B . For a uniform flux density M = BARFrom Ampere’s law, the mmf is also equal to the integral of the magnetising force or magnetic field intensity H (another concept) around a closed circuit.M = ∫HdlH is independent of the material and is a measure of the tendency of a moving charge to produce the flux density B. If H is regarded as being constant, then l is the length of the closed path of the magnetic field.M = HlNiThus H =lThe magnetising force H represents the practical and measurable coil dimensions of the number of turns and length, and the current flowing in the coil. It is a parameter most used to illustrate the magnetic properties of materials and is also used in the fundamental theory and development of analytical expressions for electroheating and transformers. However, it is often supplanted in the design phase of devices by parameters that are more familiar and measurable to electrical engineers.When a magnetizing force is applied to a material, it is found that most materials do not significantly affect the magnetic field as compared to that in free space. Paramagnetic materials, for example aluminium (Al), increase the field only slightly. These are attracted to magnets. Diamagnetic materials, for example copper (Cu) and water, decrease the field slightly. These repel magnets.The most useful types of magnetic material are known as ferromagnetic, e.g. iron (Fe), cobalt (Co), nickel (Ni) or their alloys, plus two rare earth metals, gadolinium (Gd) and dysprosium (Dy). They have the ability to increase the field hundreds or thousands of times.There are also ferrimagnetic materials which are iron oxide (ferrite) based. These are used in high frequency applications. Also, powdered iron particles in epoxy resin or plastic are used in electronic transformers or inductor cores (superparamagnetic).3.2 DOMAIN THEORY FOR FERROMAGNETIC MATERIALSThe different classes of magnetism of materials arise from the cancellation of individual atomic magnetic fields. The electrons of the atom behave as a spinning charged sphere and is therefore electrically equivalent to a tiny circulating current. This establishes the magnetic field.eˉ+In most materials, neighbouring atomic fields cancel each other. In ferromagnetic materials the cancellation is not complete. The net effect is an alignment of magnetic fields of atoms in groups called domains. These are of the order of 10-4 to 10-7 m in length.Within each domain there is an intense magnetization equivalent to the saturation value of the material, H 0, shown in a 2 dimensional representation.In un-magnetized material, these domains are randomly orientated in six directions, being the sides of the iron crystal, which is cubic. There is thus a net effect of zero magnetization. However, when an external magnetic field is applied to the previously un-magnetized ferromagnetic material, three bands of effects are observed as the magnetizing force is increased. These can be depicted on a B-H curve.H SaturationRegion IIIRegion I100020002.01.51.0B Region IIThe regions of the B-H curve due to the level of magnetizing force applied are the result of different responses of the domain magnetization. With no applied magnetization force, the domain magnetizations cancel each other.With the application of a magnetizing force, initially the domains nearest inorientation to the direction of the magnetizing force grow in size at the expense of the other domains. This occurs in region I.HIn region II, where a rapid change in the magnetic field is observed, up to the start of saturation, the other domains in each crystal align with the dominant domains.H Finally all the domains rotate in the direction of the applied field and saturation isreached. This is region III.H Saturation does not mean a constant value of B. A large increase in magnetizing force will increase the value of B. Not all domains rotate at the same magnetization level and hence saturation is reached with a continuous change of the B-H curve.For practical design purposes, a value of B somewhere in region III where saturation is occurring, is useful for defining the upper limit of the linear behaviour of the ferromagnetic material. This is referred to as the knee point. Both electroheaters and transformers are designed with this value either set as a fixed parameter, or monitored to ensure that the level is not exceeded.Looking at the curve of B versus H, it is obvious that this is very non-linear. However, as an approximation, both regions I and III can be regarded as small. Also, many devices operate in region II and this can be approximated by a straight line up to the knee leading to saturation. The B-H curve is then linear, passing through the origin. Under these approximations, the factor that indicates how much magnetic flux is produced in a material by a given magnetizing force is called the permeability. This factor is expressed as a ratioBμ =HIt is more commonly represented in its causal formB = µHwhich indicates that the magnetic field is a result of the magnetization.For a magnetic field in free space (air for practical purposes)B = µ0Hwhere μ0 is the permeability of free space = 4π . 10-7 H/m.With a ferromagnetic material, the relative permeability µr (dimensionless) is the ratio of its B compared to that for free space, for a given H. HenceB = µ0µr HFor the same magnetization, the magnetic flux density is much greater for ferromagnetic materials, since µr >> 1. For mild steel, μr = 100 is a typical value, however, for silicon steel used as transformer laminations, μr typically varies from 1500 – 3000. For special core steels, µr can be as high as 10,000.For paramagnetic materials such as aluminium, µr > 1 (slightly), and for diamagnetic materials such as copper and water, µr < 1 (slightly). For practical purposes, all insulation and all non-ferrous metals, such as copper and aluminium, and stainless steel, can be taken to have a relative permeability of 1.An alternative way of looking at the meaning of permeability is that the effect of the applied H field can be split from that due to the material magnetic field intensity H o.B = µ0H + µ0H0 (13)or μ0µr H = μ0H + μ0H 0 (14) thusµr = 1 +HH 0(15)Here µ0H 0 is the magnetic polarization produced within the material and µr is the magnetization within a domain.For ferromagnetic materials, the relative permeability μr varies depending on the composition of the metal and the metallurgical processes that it is subjected to. Below the saturation level, the ratio of B:H and hence permeability, is approximately constant. This ratio is little affected by temperature until it approaches the Curie temperature of 760 o C. There is usually some decay in the value of μr as this point is approached, at which the relative permeability becomes unity.Above the Curie point, the thermal energies of ferromagnetic materials dominate over the domain coupling. The material loses its ferromagnetic properties and μr drops to 1. The material then shows paramagnetic properties where the magnetic dipoles are randomly orientated.The ac excitation curve of magnetic material more or less coincides with the dc magnetization curve as saturation is approached. The magnetization curve of a particular steel may not be available and hence the reference usually must be to a curve typical of that class of material.3.3 HYSTERESIS LOOPWhen the applied ac field is removed, the magnetization of the material is permanently altered. The B-H curve does not retrace itself.BHB resH cThis is due to domain boundaries not returning to their original position. There remains a residual magnetization flux density B res . To reduce the field to zero, a magnetizing force H c (coercive force) is necessary, applied in the reverse direction.With an alternating magnetizing force, a complete loop characteristic is traced. This is known as the hysteresis loop. Here, B lags H .Experimental Derivation of the B-H CharacteristicA coil is wound around a core and a dc current I is passed through it. A second (search) coil of N turns is also wound on the core.The current is varied through the use of a resistor in series with the coil. As it changes, the flux also changes. This induces an electromotive force (emf) in the search coildtd Ne φ =This emf is input to an integrating flux meter which gives a measure of the flux in the core.∫t dt e 0 = ∫t dt dtd N 0 φ=∫φφd N=NφBy varying the current in both the positive and the negative directions, the core material B-H curve can be drawn.The stages of the test procedure are1 For an un-magnetized core and the switch open, I = 0 and hence ϕ = 01→2 The switch is closed to give I positive. The current is increased by adjusting the resistance R. The trace of ϕ versus I is drawn until saturation is reached.2→3 The current I is then decreased to zero. There is some residual magnetic flux (residual magnetism) in the core at point 3.3→4 The polarity of the applied voltage is reversed and the current I is increased in the negative direction until the magnitude is that previously reached in the forward direction.4→5 The current I is then decreased to zero.5→2 The current I is increased positively to its maximum value.3.4 HYSTERESIS LOSSESEnergy is lost during the growth and rotation of domains. This energy is in the form of heat and is known as hysteresis losses. This hysteresis loss is only present whenthe magnetic material is exposed to a time-varying magnetic field. For ferromagnetic material, these losses can be significant.Experiment shows that the hysteresis energy loss is proportional to f B xwhere f is the frequency of the applied fieldB is the magnetic flux densityx is the Steinmetz factor (1.5 - 2.5) which depends on the steel quality and impurities.The loss is proportional to the area swept out by the hysteresis loop. For transformers, to get a high power transfer efficiency, it is desirable to minimize this hysteresis loop area. Consequently the materials used for cores are those which show low residual magnetism and require a low coercive force to reduce the magnetization to zero.BH3.5 EDDY CURRENTSIf a piece of iron is in a magnetic field, an internal electric current is set up in the material through Faraday's Law of induced emf. The current direction obeys Lenz's Law and is thus opposite to the winding current direction.vilwBiThe ac flux induces a voltage in the iron which causes the eddy currents to flow. Iron has resistivity so there are heating losses due to the circulating current. The current density varies with depth from the surface.For sinusoidal flux variations, the eddy current loss per unit volume (W/m 3) is given byP e = ρπ6 2222w B fTo reduce the losses, materials can be selected which have very high resistivity, e.g. silicon steel cores, and/or the distance w can be reduced, since P e is proportional to w 2. In practice, transformer cores are laminated with alternating layers of iron and insulation. The insulation gives electrical isolation between each iron layer.metal insulationiBThe laminations are aligned parallel to the flux direction. There is a uniform flux density in each lamination. This maintains the overall core cross-sectional area and allows the flux density to be below the saturation level of the steel.Because of the insulation, the eddy currents are now confined to each lamination. Essentially the area of the current path has been decreased and to a lesser extent so has the current path length. Overall, the path resistance has been increased.There is a need to trade between losses and the thinness of laminations. As laminations get smaller, so the percentage of insulation in the core increases. There is thus a resultant decrease in the core steel and overall flux that the core can carry before it saturates.The ratio of the volume of actual magnetic material to the total volume (magnetic material plus insulation) of the core is known as the stacking factor. Typically this value is 0.9-0.95.While eddy currents are suppressed in transformer cores to reduce losses and increase the power transfer efficiency, induction heaters use eddy currents for heating metal workpieces.The rate of heat development in a ferromagnetic material at a temperature well below its Curie point, depends on the combined effect of both hysteresis and eddy current losses [1]. The percentages of these components vary with the material, its temperature, the grain size, the base dimension of the part, the flux density and the frequency.The greater the thickness, the more the eddy current loss dominates. For induction heating applications, the hysteresis loss is relatively small and can be ignored. However, for transformers with thin steel laminations, the hysteresis loss usually dominates.。