Electromagnetic Levitation (maglev)

Introduction:

If there was something everyone child wanted after the 1989 ‘Back to the Future’ sequel, it was a hover board.  These futuristic skateboards, portrayed in a world three years from now, are skateboards with no wheels that float and glide, possibly a precursor to the flying Jetsons cars. But such a technology, though unavailable to the personal amusement of children world over, is quite readily available in Japan, Shanghai and South Korea in something infinitely more exciting and appealing to juvenile imagination: trains.
The trains in question are known as maglev trains and work on the principle of magnetic levitation. If Archimedes could see the frog that was levitated in the Nijmegen High Field Magnet Laboratory, he would promptly declare ‘Give me a magnet and I shall levitate the Earth’ [This is assuming he never knew that Earth is also a magnet.] Magnetic levitation is a method by which an object is suspended using magnetic fields that counterbalance the gravitational and any other forces acting on it. Magnets lift the train a few inches over the surface of the tracks and also provide the thrust (due to repulsion and attraction between two poles of a magnet) required for motion.
They are in many ways superior to their traditional counterparts. Since these trains do not come in contact with the tracks, there is no friction and thus provide better acceleration and deceleration. The power needed for levitation does not significantly increase its overall power consumption. There is a low level of maintenance as there is little wear and tear rolling resistance [friction]. Maglev trains are unaffected by changes in weather and can operate in extreme weather conditions. Also, maglev trains could theoretically run backwards on the same track as the principle of magnetic levitation is not affected by direction.

Description of the project done:

Theory:

A magnet is defined as an object which attracts magnetic substance towards itself and directs towards earth’s magnetic north pole. Magnets are categorized on two parts: natural magnets and electromagnets. Natural magnets are also called permanent magnets. Permanent magnets are those magnets which has its own persistent magnetic field Electro magnets are the artificial magnets which are created, when an electric current is passed through the solenoid. These are temporary magnets. Magnetic levitation or magnetic suspension is a method to suspend an object in air with no supports other than magnetic field. Here magnetic pressure is used to counteract gravity. Magnetic pressure is energy density associated with magnetic field. It is identical to other types of pressure. Magnetic pressure in S.I. system is given by:

Pmag=B^2/(2μ_0 )

Where P is pressure in Pascal, B is magnetic field in Teslas and µ0 is absolute permeability of space.

Static stability means that any small displacement away from a stable equilibrium causes a net force to push it back to the equilibrium point. Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. Therefore either superconductors should be used or dimagnets. The criterion for stable diamagnets is:

B ∂B/(∂z )=μ_0 ρ g/χ

χ is the magnetic susceptibility

ρ is the density of the material

g is the local gravitational acceleration (−9.8 m/s2 on Earth)

μ0 is the permeability of free space

B is the magnetic field

∂B/∂z is the rate of change of the magnetic field along the vertical axis.

Magnetic field by point charge moving with velocity v is:

B=μ_0/4π  qvsinθ/r^2 

Treating the elementary length dl as a point and assuming the total charge within it is dq, moving with velocity v.

Then, current  i=∂q/∂t and v=∂l/∂t which gives v∂q=i∂l 

Here the quantity idl, called the current element, becomes the source for magnetic field.

∂B=μ_0/4π  i∂lsinθ/r^2 

This is also known as biot-savart law. 

Magnetic field due to a circular loop at a point on the axis of the coil is given by:

B=∫_0^2πr▒∂Bsinβ

=∫▒〖(μ_0/4π〗  i∂lsinθ/r^2 )sinβ

Since sinθ= 90

=〖iμ〗_0/4π ∫_0^2πr▒∂lsinβ/r^2 

So we simply have,

B=μiasinβ/〖2r〗^2 

Writing sinβ and r2 in terms of a and x, we get,

sinβ=a/r=a/√(x^2+a^2 )

∴B=(μ_0 ia^2)/(2(〖x^2+a^2)〗^(3/2) )

For coil with N number of turns,

B’=N.B

This theorem also works as electro dynamic suspension. Electrodynamic suspension is a technique that is used in magnetic levitation. Magnetic levitation is method by which an diamagnetic abject is freely suspended in air though only magnetic pressure. Electrodynamic suspension (EDS) is a form of magnetic levitation in which there are conductors which are exposed to time-varying magnetic fields. This induces currents in the conductors that create a repulsive magnetic field which holds the two objects apart. Electrodynamic suspension can also occur when an electromagnet driven by an AC electrical source produces the changing magnetic field, in some cases; a linear induction motor generates the field.

When a conductive loop experiences a changing magnetic field, from Lenz's law and Faraday's law, the changing magnetic field generates an Electromotive Force (EMF) around the circuit. For a sinusoidal excitation, this EMF is 90 degrees phased ahead of the field, peaking where the changes are most rapid (rather than when it is strongest):

Where N is the number of turns of wire (for a simple loop this is 1) and ΦB is the magnetic flux in webers through a single loop. The above Equation is of Lenz’s law

Since the field and potentials are out of phase, both attractive and repulsive forces are produced, and it might be expected that no net lift would be generated. However, although the EMF is at 90 degrees to the applied magnetic field, the loop inevitably has inductance. The Inductive impedance tends to delay the peak current, by a phase angle dependent on the frequency (since the inductive impedance of any loop increases with frequency).

Where K is impedance of the coil, L is the inductance and R is the resistance

But:

Where, I is the current.

Thus at low frequencies, the phases are largely orthogonal and the currents lower, and no significant lift is generated. But at sufficiently high frequency, the inductive impedance dominates and the current and the applied field are virtually in line, and this current generates a magnetic field that is opposed to the applied one, and this permits levitation.

However, since the inductive impedance increases proportionally with frequency, so does the EMF, so the current tends to a limit when the resistance is small relative to the inductive impedance. This also limits the lift force. Power used for levitation is therefore largely constant with frequency. However there are also eddy currents due to the finite size of conductors used in the coils, and these continue to grow with frequency. Let’s now talk about Lenz law. It is the reason due to which and magnet induces an electromagnet and proceeding magnet has like poles.

Lenz’ law:

 An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.

Lenz's law is shown with the minus sign in Faraday's law of induction

,  

 Which indicates that the induced emf ( ) and the change in flux ( ) have opposite signs

Now, I will describe about few more terms that are or might be introduced during this experiment.

Electrical Impedance:

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current (AC) circuit. Impedance extends the concept of resistance to AC circuits, and possesses both magnitude and phase.

The impedance of an ideal resistor is purely real and is referred to as resistive impedance:

In this case the voltage and current waveforms are proportional and in phase.

Ideal inductors and capacitors have purely imaginary reactive impedance:

The impedance of inductors increases with frequency;

The impedance of capacitors decreases with frequency.

In both cases, for an applied sinusoidal voltage, the resulting current is also sinusoidal, but in quadrature, 90 degrees out of phase with the voltage. However the phases have opposite signs: in an inductor, the current is lagging; in a capacitor the current is leading.

Note the following identities for the imaginary unit and its reciprocal:

Thus we can rewrite the inductor and capacitor impedance equations in polar form:

The magnitude tells us the change in voltage amplitude for given current amplitude through the impedance, while the exponential factors give the phase relationship.

Eddy Currents:

Eddy currents (also called Foucault currents) are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of the conductor. These circulating eddies of current have inductance and thus induce magnetic fields. These fields can cause repulsive, attractive, propulsion and drag effects. The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field changes, then the greater the currents that are developed and the greater the fields produced.

Under certain assumptions (uniform material, uniform magnetic field, no skin effect, etc.) the power lost due to eddy currents can be calculated from the following equations: 

For thin sheets:  

For thin wires:  

Strength of eddy currents:

In very fast changing fields due to skin effect the equations shown above are not valid because the magnetic field does not penetrate the material uniformly. However, in any case increased frequency of the same value of field will always increase eddy currents, even with non-uniform field penetration.

The penetration depth can be calculated from the following equation:

Where: δ - penetration depth (m), f - frequency (Hz), μ - magnetic permeability (H/m), σ - electrical conductivity (S/m)

Hallbach Array:

A Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side. In the diagram, the magnetic field is enhanced on the bottom side and cancelled on the top side (a one-sided flux).

The rotating pattern of permanent magnets (on the front face; on the left, up, right, down) can be continued indefinitely and have the same effect. The effect of this arrangement is roughly similar to many horseshoe magnets placed adjacent to each other, with similar poles touching. 

Objective:

The main objective of this project is to levitate an object (train) in air and propel it by use of only magnet. Magnetic pressure is only the thing that suspends the object (train) in air.   Other objective of this project is constructing a transportation vehicle which does not pollute the environment and does not make noise. Using hybrid maglev technology we can save fuel coz it’s cheaper.  

Significance and Application:

The first patent for a magnetically levitated vehicle was granted in 1968 to U.S. scientists Gordon Danby and James Powell. While maglev transportation was first proposed more than a century ago, the first commercial maglev train made its test debut in Shanghai, China, in 2002, using the train developed by German company Transrapid International. 

It is clear that the future of magnetic levitation lies in mass transit. Our present transport system is blighted by congestion, delays, pollution, rising costs, and most importantly increasing fuel scarcity.

However, there are also a number of technological spinoffs that this technology has the potential to produce. Such field and industry can relate to:

a. Magnetics - High temperature superconductivity, cryogenics, low temperature refrigerators, and superconducting magnet design and construction. 

b. Materials - Fiber reinforced plastics for vehicles and structural concretes. 

c. Electronics - Communication and high power solid-state controls. 

d. Engineering - Vehicle design (aerodynamics and noise mitigation), precision manufacturing, construction and fabrication of concrete structures. 

High technology business will be quick to capitalize on spin-offs that occur as maglev technology evolves. The development of vibration insensitive magnets might be of use in transportable magnetic resonance imaging systems, military magneto-hydrodynamic systems for ship propulsion and other mobile applications. It can further lead to development of magnets which have numerous projected uses for medical applications, shielding of magnetic fields, electric motors, oil exploration, magnetic separation of materials, and superconducting magnetic energy storage. 

Precautions and difficulties:

Being an ambitious project and it a new technology many precautions must be taken and has many difficulties. Well, firstly taking about precautions, following precautions must be taken:

• As magnetic field varies greatly in order of power 3 with distance, precise measurements must be done.

• The required magnetic field increases rapidly for increase in load so load must be taken of lower density.

• Wiring is complex in maglev track, so precautions must be taken that all wiring is properly done.

• High current may cause Excessive dissipation of heat bringing unwanted results.

• Magnetic substance must not be kept near circuit or apparatus.

Many difficulties are also present in maglev technology which can be stated as follows:

• Maglev technology is newly arrived complex technology so, it is hard to understand.

• Calculation must be precise in order of centimeters for wished results.

• Being new technology it is quite expensive.

• Since it is molded or kind of attached with the track, if something happens to the train it is hard to remove it from the track.

• Dissipation of heat is one of many difficulties of this project.

• Hit and trial method should be done for levitating circuit and propulsion circuit.