ELECTRIC MOTORS Magnetic Circuits

Magnetic Circuits Thus far we’ve got assumed that the supply of the magnetic Weld is an everlasting magnet. This can be a handy place to begin as all of us are aware of magnets, even when solely of the fridge-door selection. However within the majority of motors, the working magnetic Weld is produced by coils of wire carrying a present, so it’s acceptable that we spend a while how we organize the coils and their related iron ‘magnetic circuit’ in order to supply excessive magnetic Welds which then work together with different current-carrying conductors to supply power, and therefore rotation.

Magnetic Circuits

First, we take a look at the only attainable case of the Magnetic Circuits Weld surrounding an remoted lengthy straight wire carrying a gentle present The Xux traces type circles concentric with the wire, the Weld energy is biggest near the wire. As may be anticipated, the Weld energy at any level is immediately proportional to the present.

The conference for figuring out the path of the Weld is that the optimistic path is taken to be the path {that a} right-handed corkscrew have to be rotated to maneuver within the path of the present.

Magnetic Circuits

The determine is considerably synthetic as the present can solely Xow in an entire circuit, so there should all the time be a return path. If we think about a parallel ‘go’ and ‘return’ circuit, for instance, the Weld could be obtained by superimposing the Weld produced by the optimistic present within the go aspect with the Weld produced by the unfavorable present within the return aspect, as proven in Determine.

We observe how the Weld is elevated within the area between the conductors, and decreased within the areas exterior. Though Determine strictly solely applies to an infinitely lengthy pair of straight conductors, it can most likely not come as a shock to study that the Weld produced by a single flip of wire of rectangular, sq., or spherical type could be very a lot the identical as that proven in Determine. This allows us to construct up an image of the Weld that might be produced in air, by the kind of coils utilized in motors, which generally have many turns, as proven for instance in Determine.

The coil itself is proven on the left in Determine whereas the Xux sample produced is proven on the appropriate. Every flip within the coil produces a Weld sample, and when all the person Weld elements are superimposed we see that the Weld contained in the coil is considerably elevated and that the closed Xux paths carefully resemble these of the bar Magnetic Circuits we checked out earlier.

Magnetic Circuits

The air surrounding the sources of the Weld oVers a homogeneous path for the Xux, so as soon as the tubes of Xux escape from the concentrating inXuence of the supply, they’re free to unfold out into the entire of the encircling house. Recalling that between every pair of Xux traces there may be an equal quantity of Xux, we see that as a result of the Xux traces unfold out as they go away the confines of the coil, the Xux density is way decrease exterior than inside, for instance, if the gap ‘b’ says 4 instances ‘a’ the Xux density Bb is 1 / 4 of Ba.

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Though the Xux density contained in the coil is larger than exterior, we’d Wnd that the Xux densities which we may obtain are nonetheless too low to be of use in a motor. What is required Westly is a means of accelerating the Xux density, and secondly a method for concentrating the Xux and stopping it from spreading out into the encircling house.

Magnetomotive force (MMF)

One apparent strategy to improve the Xux density is to extend the present within the coil or so as to add extra turns. And that if we double the present or the variety of turns, we double the entire Xux, thereby doubling the Xux density in every single place. We quantify the flexibility of the coil to supply Xux when it comes to its magnetomotive power (MMF).

The MMF of the coil is solely the product of the variety of turns (N) and the present (I) and is thus expressed in ampere-turns. A given MMF could be obtained with numerous turns of skinny wire carrying a low present, or a couple of turns of thick wire carrying a excessive present: so long as the product NI is fixed, the MMF is similar.

Electrical circuit analogy

We’ve seen that the Magnetic Circuits which is about up is proportional to the MMF driving it. This factors to a parallel with the electrical circuit, the place the present (amps) that Xows is proportional to the EMF (volts) driving it. Within the electrical circuit, present and EMF are associated by Ohm’s Legislation, which is

 

Current ¼ EMF
Resistance

For a given supply EMF (volts), the present depends upon the resistance of the circuit, so to acquire extra present, the resistance of the circuit must be decreased. We are able to make use of an equal ‘Magnetic Circuits Ohm’s legislation’ by introducing the concept of reluctance (R). The reluctance offers a measure of how tough it’s for the magnetic Xux to finish its circuit, in the identical means, that resistance signifies how a lot opposition the present encounters within the electrical circuit. The magnetic Ohm’s legislation is then

Flux ¼ MMF
Reluctance

We see from the equation that to extend the Xux for a given MMF, we have to scale back the reluctance of the magnetic circuit. Within the case of the instance (Determine 1.6), this implies we should substitute as a lot as attainable of the air path with a ‘good’ magnetic materials, thereby decreasing the reluctance and leading to the next Xux for a given MMF. The fabric which we select is nice high quality Magnetic Circuits metal, which for historic causes is normally known as ‘iron’. This brings a number of very dramatic and fascinating beneWts, as proven in Determine

Firstly, the reluctance of the iron paths could be very a lot lower than the air paths which they’ve changed, so the entire Xux produced for a given MMF could be very a lot better. (Strictly talking, subsequently, if the MMFs and cross-sections of the coils in Figures are the identical, many extra Xux traces ought to be proven in Determine than in Determine, however for the sake of readability related numbers are indicated.) Secondly, nearly all of the Xux is convened inside the iron, moderately than spreading out into the encircling air.

Magnetomotive force (MMF)

We are able to subsequently form the iron elements of the magnetic circuit as proven in Determine with a purpose to information the Xux to wherever it’s wanted. And Wally, we see that contained in the iron, the Xux density stays uniform over the entire cross-section, there being so little reluctance that there is no such thing as a noticeable tendency for the Xux to crowd to 1 aspect or one other. Earlier than shifting on to the matter of the air-gap, we should always observe {that a} query which is usually requested is whether or not it will be significant for the coils to be wound tightly onto the magnetic circuit, and whether or not,

if there’s a multi-layer winding, the outer turns are as efficient because the inside ones. The reply, fortunately, is that the entire MMF is set solely by the variety of turns and the present, and subsequently each full flip makes the identical contribution to the entire MMF, no matter whether or not it occurs to be tightly or loosely wound.

After all, it does make sense for the coils to be wound as tightly as is practicable since this not solely minimizes the resistance of the coil (and thereby reduces the warmth loss) but in addition makes it simpler for the warmth generated to be performed away to the body of the machine.

The air-gap

In motors, we intend to make use of the excessive Xux density to develop power on current-carrying conductors. We’ve now seen find out how to create a excessive Xux density contained in the iron elements of a magnetic circuit, however, in fact, it’s bodily not possible to place current-carrying conductors contained in the iron. We, subsequently, organize for an air-gap within the magnetic circuit, as proven in Determine.

We’ll see shortly that the conductors on which the power is to be produced can be positioned on this air-gap area. If the air-gap is comparatively small, as in motors, we Wnd that the Xux jumps throughout the air-gap as proven in Determine, with little or no tendency to balloon out into the encircling air. With many of the Xux traces going straight throughout the air-gap, the Xux density within the hole area has the identical excessive worth because it does contained in the iron.

Within the majority of magnetic circuits consisting of iron elements and a number of air-gaps, the reluctance of the iron elements could be very a lot lower than the reluctance of the gaps. At West sight, this will appear shocking because the distance throughout the hole is a lot lower than the remainder of the trail by means of the iron.

The truth that the air-gap dominates the reluctance is solely a mirrored image of how poor air is as a Magnetic Circuits medium, in comparison with iron. To place the comparability in perspective, if we calculate the reluctances of two paths of equal size and cross-sectional space, one being in iron and the opposite within the air, the reluctance of the air path will usually be 1000 instances better than the reluctance of the iron path.

Returning to the analogy with the electrical circuit, the position of the iron elements of the magnetic circuit could be likened to that of the copper wires within the electrical circuit. Each oVer little opposition to Xow is wasted in conveying the Xow to the place it’s usefully exploited) and each could be formed to information the Xow to its vacation spot. There’s one essential distinction, nevertheless.

Within the electrical circuit, no present will Xow till the circuit is accomplished, after which all the present is convened contained in the wires. With an iron magnetic circuit, some Xux can Xow even earlier than the iron is put in. And though many of the Xux will subsequently take the straightforward route by means of the iron, some will nonetheless leak into the air, as proven in Determine. We won’t pursue leakage Xux right here, although it’s typically essential, as can be seen later.

Reluctance and air-gap flux densities

If we neglect the reluctance of the iron elements of a magnetic circuit, it’s straightforward to estimate the Xux density within the air-gap. Because the iron elements are then in impact ‘excellent conductors’ of Xux, not one of the supply MMF (NI) is utilized in driving the Xux by means of the iron elements, and all of it’s obtainable to push the Xux throughout the air-gap. The state of affairs depicted in Determine.

subsequently reduces to that proven in Determine, the place an MMF of NI is utilized immediately throughout an air-gap of size g. To find out how a lot Xux will cross the hole, we have to know its reluctance. As may be anticipated, the reluctance of any a part of the magnetic circuit depends upon its dimensions, and on itsMagnetic Circuits properties, and the reluctance of an oblong ‘prism’ of air, of cross-sectional space A and size g as in Determine is given by

the place m=0 is the so-called ‘major magnetic fixed’ or ‘permeability of free house’. Strictly, as its identify implies, m0 quantiles theMagnetic Circuits properties of a vacuum, however for all engineering functions, the permeability of air can be m0. The worth of the first Magnetic Circuits fixed (mo) within the SI system is 4 107 H/m; moderately surprisingly, there is no such thing as a identify for the unit of reluctance.

Magnetic circuits in motors

The reader could also be questioning why a lot consideration has been centered on the gapped C-core magnetic circuit when it seems to bear little resemblance to the magnetic circuits present in motors. We’ll now see that it’s truly a brief step from the C-core to a magnetic motor circuit and that no essentially new concepts are concerned. The evolution from C-core to motor geometry is proven in Determine,

which ought to be largely self-explanatory, and pertains to the Weld system of a d.c. motor. We observe that the West stage of evolution leads to the unique single hole of size g being cut up into two gaps of size g/2, rejecting the requirement for the rotor to have the ability to flip.

Magnetic circuits in motors

On the similar time, the only magnetizing coil is cut up into two to protect symmetry. Relocating the magnetizing coil at a unique place across the magnetic circuit is in fact so as, simply as a battery could be positioned anyplace in an electrical circuit Subsequent, the only Magnetic Circuits path is cut up into two parallel paths of half the unique crosssection, every of which carries half of the Xux: and Wally, the Xux paths and pole-faces are curved to match the rotor.

Magnetic Circuits The coil now has a number of layers with a purpose to Wt the obtainable house Magnetic Circuits , however as mentioned earlier this has no hostile impact on the MMF. The air-gap continues to be small, so the Xux crosses Magnetic Circuits radially to the rotor.

In this Article I wrote On Magnetic Circuits In Magnetic Circuits We Learn Following Points.

  • Magnetic Circuits
  • Magnetomotive force (MMF)
  • Electrical circuit analogy
  • The air-gap
  • Reluctance and air-gap flux densities
  • Magnetic circuits in motors

In This Article We Learn Total 6 Points in magnetic circuits

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