Magnetic Circuit PDF

Magnetic Circuit Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 2 Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 3 Definitions concerning Magnetic Circuits EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 4 D...

Magnetic Circuit Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 2 Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 3 Definitions concerning Magnetic Circuits EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 4 Definitions concerning Magnetic Circuits EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 5 Composite Series Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 6 How to find Ampere-turns? EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 7 Comparison between Electric Circuit and Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 8 Comparison between Electric Circuit and Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 9 Parallel Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 10 Series-Parallel Magnetic Circuit EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 11 Stacking Factor The stacking factor (also lamination factor or space factor) is a measure used in electrical transformer design and some other electrical machines. It is the ratio of the effective cross-sectional area of the transformer core to the physical cross-sectional area of the transformer core. Transformer cores are usually made up of thin metal sheets stacked in layers. The layers are laminated with varnish or other insulating material. The purpose is to reduce eddy currents in the core, while keeping a high magnetic flux. Since the insulator is non-ferro-magnetic, little, if any, magnetic flux is contained within it. It is mainly in the metal sheets. The insulation takes up a finite space, so the effective area the flux occupies is less than the physical area of the core. The stacking factor is used when calculating the magnetic flux density within the core. Because the flux is confined within a smaller area in a laminated core, the flux density is higher than it would be in a homogenous core. Laminated cores always have a stacking factor less than unity; a stacking factor of unity implies no laminate at all. Stacking factors are typically 0.95 or higher for transformer cores and machine stators. However, cores made from amorphous metal have a stacking factor of around 0.8, compared to 0.96 for silicon steel. EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 12 Leakage flux Leakage flux is defined as the magnetic flux which does not follow the particularly intended path in a magnetic circuit. Taking an example of solenoid one can understand the leakage flux and the fringing both. Most of the flux is set up in the core of the solenoid and passes through the particular path that is through the air gap and is utilised in the magnetic circuit. This flux is known as Useful flux φu. As practically it is not possible that all the flux in the circuit follows a particularly intended path and sets up in the magnetic core and thus some of the flux also sets up around the coil or surrounds the core of the coil, and is not utilised for any work in the magnetic circuit. This type of flux which is not used for any work is called Leakage Flux and is denoted by φl. EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 13 Fringing The useful flux when sets up in the air gap, it tends to bulge outward at (b and b’) as shown in the figure, because of this bulging, the effective area of the air gap increases and the flux density of the air gap decreases. This effect is known as Fringing. Fringing is directly proportional to the length of the air gap that means if the length increases the fringing effect will also be more and vice versa. EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 14 Exercise Problem-1 A laminated soft-iron ring of relative permeability 1000 has a mean circumference of 800 mm and a cross-sectional area 500 mm2. A radial air-gap of 1 mm width is cut in the ring which is wound with 1000 turns. Calculate the current required to produce an air-gap flux of 0.5 mWb if leakage factor is 1.2 and stacking factor 0.9. Neglect fringing. (Answer: 1.64 A) EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 15 Exercise Problem-2 A ring has a diameter of 21 cm and a cross-sectional area of 10 cm2. The ring is made up of semi- circular sections of cast iron and cast steel, with each joint having a reluctance equal to an air-gap of 0.2 mm. Find the ampere-turns required to produce a flux of 8 x 10 -4 Wb. The relative permeabilities of cast steel and cast iron are 800 and 166 respectively. Neglect fringing and leakage effects. (Answer: 1783 AT) EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 16 Exercise Problem-3 A rectangular iron core is shown in Figure below. It has a mean length of magnetic path of 100 cm, cross-section of (2 cm × 2 cm), relative permeability of 1400 and an air-gap of 5 mm cut in the core. The three coils carried by the core have number of turns Na = 335, Nb = 600 and Nc = 600 ; and the respective currents are 1.6 A, 4 A and 3 A. The directions of the currents are as shown. Find the flux in the air-gap.(Answer: 100 μWb) EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 17 Exercise Problem-4 A cast steel d.c. electromagnet shown in Figure has a coil of 1000 turns on its central limb. Determine the current that the coil should carry to produce a flux of 2.5 mWb in the air-gap. Neglect leakage. Dimensions are given in cm. The magnetization curve for cast steel is as under : (Answer: 1.39A) Flux density (Wb/m2) : 0.2 0.5 0.7 1.0 1.2 Amp-turns/meter : 300 540 650 900 1150 EN7032 (ELECTRICAL MACHINES) – MAGNETIC CIRCUIT 18