Magnetic circuits and Electromechanical energy conversion
Electromechanical Energy Conversion
Energy exists in many form like mechanical energy, electrical energy, magnetic energy etc. The process of conversion of one form of energy into another form is called conversion of energy. Conversion of another form of energies to electrical energy is used nowadays to produce electricity. It is very useful and adavantageous process as energy in electrical form can be transmitted, utilized and controlled more easily, reliably and efficiently.
The process of conversion of electrical energy to mecahnical energy or viceversa is called electromechanical energy conversion. For example, an electric motor converts electrical energy to mechanical energy while an electrical generator converts mechanical energy to electrical energy. However, this process is reversible except the losses involved in the process. Therefore, in electromechanical energy conversion, one form of energy changes to another form along with the losses.
Basic principles & Conservation of energy:
According to the principle of conservation of energy, "Energy can neither be created nor destroyed, it can only be changed from one form to another". This is principle involved in electromechanical conversion. Thus, when a current carrying conductor is placed in magnetic field, it experiences a force which tends to move it. If the conductor is free to move in the direction of the magnetic force, torque is produced. This is the principle of electric motor. While in electric generator, an externally applied force makes the conductor move in a direction opposite to the magnetic force, mechanical energy is converted to electrical energy.
Thus, the conversion of one form of energy into another must satisfy the principle of conservation of energy. All electromechanical energy conversion takes place with the help of any medium of of elctric or magnetic field of the conversion device. One category of devices is transducers which is used for measurement and control. They generally operate under linear input output conditions with relatively small signals. This includes microphone, pickups, sensors, loudspeakers etc. The second category involves force producing devices like solenoids, relays and electromagnets. The third category involves the continuous energy conversion equipments like motors or generators.
Advantages of Electromechanical Energy Conversion:
The advantages of electromechanical energy conversion are:

It can be used for both steady state and transient analysis.

This technique is used for designing and optimising the devices for specific requirement.

It gives more physical insight into the operation of all these devices.

It is used to develop electromechanical energy conversion devices that can be used in analysis of their performance.

The conventional approach can be introduced at any stage, to study the effect of saturation, commutation etc.
Physical phenomenon involved in conversion:
In magnetic system, a coil is wound on a magnetic frame and excited by electrical sources. So the energy can be stored or generate from magnetic system. It is divided into two categories:
1. Single Excited Magnetic field system:
In this type, the conversion device consist a single electrical input and magnetic coupling field. This system includes the lossless coil having N number of turns is excited by a voltage V such that current is increased from 0 to 1. A flux is developed which depends on MMF (magnetomotive force) and the reactance of magnetic path. The magnetic field produced establish a force on the armature and reduce the air gap.
Assume

The fluxlinkage/ current relationship is linear.

Hysteresis and eddycurrent loss are neglected.

The coil has negligible leakage flux and all the flux follows magnetic flux.

The magnetic field predominates and electric field effect are neglected.
As the armature is stationary then,
dw_{n} =0
dw_{e} = dw_{m} + dw_{f} + dw_{loss}
dw_{e} = dw_{f}
i.e. when all the core loss is neglected then incremental energy input is stored as field energy.
but dw_{e} = e. I.dt
so e= df/dt
then dw_{f} = I.df
where, f= flux linkage
2. Multiple Excited Magnetic field system:
This system has more than one independent source of excitations. This system produce rotational motion. The fixed part of system is called stator and moving part is called armature.
The rotor is mounted on a shaft and free to rotate between poles of stator. The stator with Ns turns is excited with a Vs voltage source so that a current Is flows in the coil.
As the rotor with Nr turns is energized with Vr voltage such that current Ir flows in the coil. The current can be fed into motor either through fixed brushes or through rotor mounted. The MMF produced by both rotor and stator winding are in the same directions and torque produced is in anticlockwise direction.
Energy Balance:
For any energy conversion device, total input energy is converted into output energy and energy dissipated. For motor, energy balance equation can be written as:
Total electrical energy input = Mechanical energy output + Total energy stored + total energy dissipated
For generator, energy balance equation can be written as:
Total mechanical energy input = Electrical energy output + Total energy stored + total energy dissipated
As we know that in motor electrical energy is converted into mechanical energy while viceversa in case of generator.
Assume the following terms:

Total electrical energy input = W_{ei}

Total mechanical energy output = W_{mo}

Energy stored in any device = Energy stored in magnetic field W_{es} + Energy stored in mechanical system W_{ms}

Energy dissipated = Energy dissipated in (magnetic core + electrical circuit + mechanical system)
The energy balance equation can be rewritten as:
W_{ei }= _{ }W_{mo } +W_{es } +W_{ms} + losses
This can further be derived to
W_{elec.} = W_{mech.} + W_{field}
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where, W_{elec }is net input electrical energy and W_{mech} is converted mechanical energy and W_{field } is the total energy absorbed by the coupling field.
Energy stored in Magnetic system:
Consider any magnetic system having coil with N turns. Flux is produced which depends on MMF (N.i) and the reluctance of the coil. This magnetic field creates north and south poles. If armature of the device is not allowed to move, then mechanical work done is zero.
W_{elec.} = 0 + W_{field}
This shows that when armature (movable part) is kept fixed then electrical energy is converted to magnetic field.
dW_{elec.} = dW_{field}
When the armature is kept in open position then most of the mmf is consumed in air gap. So, W_{field} = 1/2 . L. i^{2 },
where L is the self inductance of the device which is defined as magnetic flux linkage per ampere current i.e. L= f/i.
Magnetic circuits:
Any closed circuit in which there is some magnetic field which is represented as lines of magnetic flux is called magnetic circuit. It is made up of electromagnet having magnetic field associated with the metal core. All the magnetic field lines constitute the magnetic flux. The term magnetic insulator is not defined in magnetic circuit as magnetic field lines can pass through any device or medium even air too.
Magnetomotive force:
Due to MMF, magnetic flux is produced in magnetic circuit. It plays very important role for the working of any motor, generator etc. It is defined as the work done in moving unit magnetic pole in magnetic circuit. It is equivalent to the product of current flowing through the coil and number of turns of the coil. Its unit is ampereturns.
Magnetic field strength:
Magnetic field strength is used to measure the intensity of magnetic field. It is represented by H and measured in ampere per meter (A/m). It depends on the total number of magnetic field lines crossing an area, which is density of field lines. It depends on the type of material.
Analogy between electric and magnetic circuits:
In electrical circuit, voltage or E.M.F. is represented by E (in volts) which is analogous to M.M.F. in magnetic circuit represented by F_{m} (in Ampere turn).
In electrical circuit, current is represented by I (in ampere) which is analogous to flux in magnetic circuit represented by F_{l} (in weber).
In electrical circuit, resistance is represented by R (in ohm) which is analogous to reluctance in magnetic circuit represented by S (in H^{1}).
Reluctance:
It is defined as resistance in magnetic circuit , so it opposes the presence of magnetic flux. Its unit is A/ Wb or H^{1}. As in electrical circuit, current flows through the path of least resistance. Similarly in magnetic circuit, magnetic flux flows through the path of least reluctance.It is the property of any magnetic material. Materials which are easily magnetised have low reluctance while the nonmagnetic material have high reluctance. Reluctance is directly proportional to the length of the magnetic path and inversely proportional to the area of the core and permeability.
Permeability:
Permeability is defined as the ability of any material to help the formation of magnetic field within itself. It plays the role of resistivity in magnetic circuit. So, it tells us the capability of magnetization of any magnetic material. Materials which are easily magnetised have high permeability while the nonmagnetic material have low permeability. More the value of permeability, higher the flux will flow and lesser will be the reluctance. So, reluctance is directly proportional to the length of the magnetic path and inversely proportional to the area of the core and permeability.
Losses:
There are mainly two types of magnetic losses in magnetic circuit
1. Hysteresis loss This plays the major role in any magnetic circuit. Hysteresis loss is given by the energy consumed in magnetising and demagnetising of any magnetic material. If the process of magnetisation is carried through a complete cycle, the energy wasted in the process is proportional to the area of the hysteresis loop and shape of hysteresis loop depends on the nature of ferromagnetic material. Hysteresis loss is proportional to

Area enclosed by hysteresis loop.

Frequency.

Volume of magnetic material.
And, area of hysteresis loop depends on the flux density of the material. It increases the temperature of any magnetic material. The hysteresis loss is given by: P_{h} = n.V.f.B^{1.6}_{max}
2. Eddy current loss Eddy current is produced due to the circulating current. The power loss due to these circulating current is called eddy current loss. It also increases the temperature of magnetic material. It depends on the emf induced and the resistance offered by magnetic material. It can be reduced by using laminated core. The eddy current depends on:

Thickness of the material.

Frequency.

Max value of flux density.

Volume of material.

Quality of material.
So, eddy current loss is P_{e} = K.B^{2}_{max}.f^{2}.t^{2}.V
where K= eddy current coefficient.
BH curve:
It is defined as the curve between flux density (B) and magnetic field strength (H). When we increase field strength, flux density also increases proportionally but upto a certain limit. This is because there is a limit that the flux can be generated in any magnetic material. Any further increase in the value of field strength does not affect the flux density. This is called saturation point. As the magnetic field strength increases, molecules of the magnet become aligned in the direction of the field causing an increase in the value of flux density.
Applications of permanent magnets:
While the use of permanent magnet is constantly increasing day by day, so some of its important applications are as follow

It eliminates the use of field winding. So, efficiency is increased.

Due to material science, some alloy can be changed to very strong and reliable permanent magnet.

It helps to reduce the size and weight of the machine by producing strong flux density in the air gap.

These make the machines more compatible and precise.

A ring of permanent magnet is used in electron gun's yoke.
Ex 1. A circuit coil of 500 turns with a mean diameter of 50cm is rotated about a vertical axis in the earth's field at 40 revolutions per second. Find the instantaneous value of emf induced in the coil when its plane P is parallel. Take value of H as 14.3 AT/m.
Soln. Given H= 14.3 AT/m
r = 50/2 = 25 cm
We know that E = Nw f sint
where f= BA = mHA
f= 4* 22/7 * 10^{7} * 14.3* 22/7 * 0.25*0.25
f= 2.46 * 10^{7} Wb
w = 40 * 2* 22/7 rad/sec
here plane is parallel so t = 90^{o}
then e= 500*42*2*22/7*2.46*10^{7}
e = 0.032volt.
Ex 2. A conductor carries a current of 150A. The length of conductor is 2m and is placed in a magnetic field whose magnetic flux density is 0.35T. Determine force.
Soln. I = 50A
L= 20m
B = 0.35T
Force = BILN = 0.35*150*2N = 105N.