Introduction

Design an electromagnet

The aim of this project is to create a small low voltage electromagnet and optimise it to either lift the largest load or to have the largest range. The restrictions which apply to the design include a limited

power source - 2x D size alkaline cells; and a maximum weight for the active components of 80g.

Theory and Hypothesis An electromagnet is essentially a magnet with its magnetic field created by an electrical current as

opposed to the natural magnetism of a material. This field is created by running an electrical current in a coil. To produce a strong electromagnet, the coil must produce a very large magnetic field and the core

should utilise this magnetic field as efficiently as possible.

This project will focus on the design of the core to most effectively utilise the magnetic flux of the coil and to test different set-ups, which include a basic core, a semi completed “horseshoe” core and a more

elaborate “bell” design core which completes the magnetic circuit. The prediction is that the more complete the magnetic field circuit, the more the magnetic field is used, the more powerful the magnet

becomes for direct lifting.

lifting power vs input power (magnet 1)

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5

0 0.2 0.4 0.6 0.8 1 1.2

Power (W)

Lift (

Kg)

Saturation of core

The Core

Design and Development

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Magnet 1

The ‘workhorse’ coil of magnet 1, used for all testing, here it’s being used in a simple core setup

Yoke for magnet 2

The preliminary design principle trials were

encouraging; this rough ‘horseshoe’ setup lifts 1kg

Simple core - low flux from “diluted” field lines

1

Horseshoe - higher

concentrated flux

Double Horseshoe - Even higher flux from increased efficiency

Double Horseshoe +

yoke - Highest flux

usage/efficiency optimal design

The first part to the design of this electromagnet is the core, and important considerations are the material and the shape of the core.

Different materials such as iron or steel have different permeabilities (the tendency for field lines to travel within the material rather than outside or through air) and according to the formula for the strength of a solenoid, it

is evident that the larger the permeability the stronger the magnet.

B = 4π x10-7 x k x n x I (B = field strength, k = relative permeability, n = turns/length, and I = current) On the right are the relative permeabilities of some materials from which it can be concluded that superpermalloy is the best option, but steel was the most practical option and thus the material of choice as it was easier to obtain and had a high structural strength. The shape of the core has a very significant part in the ‘power’ of the magnet since its strength is determined by the magnetic flux density (the ‘field line’ density), so by concentrating the field, the strength can be increased. After some research and experimenting with small pieces of steel, it was found that the distance the field lines had to travel in the air between the ‘poles’ of the core was related to the concentration of the field lines, following an inverse square relationship. So in other words a shorter distance increased the magnetic flux density. With a simple 8 x 30mm cylindrical steel core, and a coil (diagram 1 and 2), the magnetic field lines are spread over a large area and thus produces a low flux. In this setup the

electromagnet could lift a maximum of around 80g. By exploiting the permeability of the core material, the core itself could be used to complete most of the field ‘circuit’ (lower half of diagram 1 and diagram 3) and thus reduce the air gap, concentrating all the magnetic field into a smaller area which increases the flux density and also utilises nearly all of the magnetic flux which would have otherwise travelled around the core ineffectually. This design significantly improves the strength of the magnet by simply being more efficient at using the magnetic field resulting in a 20 fold increase in power.

Then by completing the circuit with an extra steel component - the yoke (bottom right of diagram 1), which effectively reduces the air gap to near 0. This addition increased the strength again 10 fold. At a near 0 gap the “smoothness” of the surfaces in contact had a very significant effect since a few micrometers meant large proportions of the total air-gap, which explains why rubbing the two surfaces together added another 1.5kg to the pulling strength, while pieces of dust caused losses of up to 2 kg. The first core design diagram (4) was based on the dimensions of the available steel bar and could lift 4.5kg, while itself weighed 59g (inc coil). This core had a problem of insufficient steel mass as it was prematurely saturated (all magnetic domains in the steel

are already oriented the same way) at only 1/2 watt of power input (1/6 of the batteries optimum capacity), which means that there is little increase of pulling power for a further increase in power input so only heat is produced (graph on the right). Another limitation of this design was the centre section (part where bolt passes) which was of significantly lower area than the outer section. And since both have the same amount of magnetic flux passing through, the centre section will saturate first, again meaning more inefficiency.

Material Relative Permeability

Steel 50 Iron (99.8%) 150

Iron (99.95%) 10 000 Powdered iron ~2

Brass 1 Air 1

superpermalloy 100 000

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lifting power vs input power (magnet 2)

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5

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15

0 1 2 3 4 5

Power (W)

Lift (

Kg)

The Coil

The improved - magnet 2

Differences in packing density – the smaller wires are likely to pack better in the same dimensions. 1 big wire =4 small wires in diagram

Coil for magnet 1 above, Coil for magnet 2 below

The second core was developed from the first

and is overall of a flatter disc like shape. This is to increase the contact surface area and to allow the ratio of between the centre area and outer area to become closer to a 1:1 ratio. This change had definitely improved the performance of the electromagnet since the lift weight is 3 times higher while the strength of the magnetic

field had actually halved (see 2nd last paragraph this page). The total mass of

steel relative to magnetic field is also increased so the core itself no longer saturates at the max magnetic flux from the coil. This is evident in the graph on the right where there is no sudden flattening of the graph but a smooth curve. For this core, particular care was taken in the machining of the contacting surface accurate to a few hundredths of a millimetre as this proved to be a significant factor in the strength.

The next part to the design was to construct a coil that would produce the maximum flux for the set dimensions and power source. This section of the design is a lot more theory based with some trial and correction when producing the coils. There are several factors that determine the performance of the coil, which are the power input, the wire gauge, the dimensions, and the winding density. The power source in for this project are 2 alkaline D cells, from which the most power that can be practically obtained from it is about 3.5W which can be maintained for a few minutes before some deterioration in the output is observed. Any higher a power draw and the shorter the duration that the peak power is produced, usually 1 minute is the minimum required battery time required. The next choice is to run the batteries in series or parallel. Either combination produces the same watts, but in series a higher voltage is produced and so a thinner wire is needed to draw the same power which in theory is no different but in practice the smaller wires can allow a greater packing density since the small wires are more likely to be divided more accurately into the dimensions of the coil

The thickness of the wire to use for the coil, given the same dimensions and the same voltage input does not influence the strength of the magnetic field significantly. According to the formula for a solenoid, if a thicker wire was used, then more current would be drawn but because the wire is thicker there will be nearly proportionally fewer turns which cancels out the effect, so all that will be changed is the resistance which is altered to maximise the power drawn from the battery. B = 4π x10-7 x k x n x I where k is constant, then there will be little change in the

magnetic field. For the dimensions of the first electromagnet, two coils were made, one with 0.25mm wire and one with 0.4mm wire and they consumed 2W and 3.5W respectively, the latter being the preferred coil. For the second magnet only 1 coil was produced based on predictions from previous coils and it consumed an ideal 3.4W with 0.3125 mm wire. An increase of the diameter of the coil actually has a detrimental effect on the magnetic field output of the coil given the same depth/length of the coil since a larger diameter has a larger circumference and thus more wire is needed to produce 1 turn of the coil. This means that for the same resistance (same length of wire of same diameter), there must be fewer turns and thus less magnetic field output. This is evident between the coils for electromagnet 1 and 2 (see diagram 6) where the coil for the second magnet is of a larger diameter and draws the same power but is only half as powerful as the coil for the first magnet. The overall size of the coil (if an exact dilation) does not change the resistance of the coil but only has the effect of reducing the required thermal dissipation per unit area of the coil and reducing the magnetic flux density since the area increases for the same magnetic energy. Through experimenting it is found that a dissipation of about ½ watt per cm2 is the ideal maximum for an epoxied coil that will reach 100°C in 3 mins of operation. The coils for these electromagnets were at about 1/3 watts per cm2.

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Lifting setup for magnet 2

Conclusion

The aim of the project was to test the difference between a standard core and one which can more effectively utilise the magnetic field of the coil. The hypothesis stated that the more efficient core would create a stronger magnet and the results quite definitely show that this is the case. Between the simple core and the final design, the difference was a 200 fold increase in lifting power, both using the same coil that consumed 3.5watts. A future improvement on the design of the electromagnet would be to increase the overall size of the magnet and allow the coil to take a shape more like that of the coil for magnet 1 since it is more efficient, while the core would be similar to the first core, will be larger to prevent saturation and also to have a larger surface area. Another improvement would be to have the contact area of the centre section equal to the area of the outer section so both have equal flux densities passing through. In terms of efficiency, the electromagnet consumes energy to hold up a mass but according to the definition of work as W=Fs where F is the force and s is the displacement then the magnet is doing no work if it holds the mass stationary in equilibrium against gravity. So the electromagnet is infinitely inefficient since efficiency is work done/energy used.

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