Electromechanical energy conversion
Electromechanical energy conversion
The advantage of electrical energy over other energies is that it could be transmitted over a long distance without much loss and with high efficiency.The
devices which convert electrical energy into other forms of energy is
known as electromechanical devices and the process is known as
electromechanical energy conversion.The conversion takes place through
either electrical or magnetic medium surrounding the device.The
electromechanical devices could be classified into three categories
primary ,secondary and tertiary.Primary includes the continuous energy
conversion elements such as motors,generators etc ie the linear and
rotating electrical machines.The second category includes transducers
which could work on with even very small input and the tertiary the
force producing devices like electromagnets,solenoids,relays etc
Energy conversion principle
The energy conversion
principle is one and same ie “energy can neither be created nor be
destroyed but could be transformed from one form to another”.In the case
of motors generators etc the input energy is not converted fully into
the output some amount of energy is wasted for ohmic losses ie due to
heating effects as well as friction.so in the case of motor
Total input energy = mechanical energy output + energy stored in magnetic field+ energy wasted for losses.
It is same for generator the difference is that the output energy is electrical and input mechanical.
So if we draw an energy flow diagram for motor it will look as shown below.
Energy flow diagram for motor
Energy flow diagram for a generator
The energy flow equation could be written as
∫d Winput = ∫d W output + ∫d W magnetic field +∫d W heat
Faraday’s Law of electromagnetic induction
The phenomenon by which an emf is induced in a conductor when it is cut by magnetic flux is known as electromagnetic induction.
Faraday’s First Law
It states that,When ever a conductor
cuts a magnetic field or viceversa an emf is induced in it and it setsup
in such a direction so as to oppose the cause of it.
Faraday’s second law
It states that the magnitude of induced emf is equal to the rate of change of flux linkage.
Mathematically
e = -NdØ/dt
e – induced emf
N- number of turns of coil
dØ/dt – rate of change of flux
the minus sign represents that the induced emf or current sets up in a direction so as to oppose the cause of it.
Induced emf
Induced emf could be classified into dynamically induced emf and statically induced emf.
Dynamically induced emf
This is the emf induced due to the motion of a conductor in a magnetic field.
Mathematically
e = Blv volts
e-induced emf
B – flux density of magnetic field in Tesla
l = length of conductor in meters
v- velocity of conductor in m/s
if the conductor moves in an angle θ,the induced emf could be represented as
e= Blvsinθ
the direction of induced emf is given by f lemmings right hand rule.
Statically induced emf
The emf produced in a conductor due to
the change in magnetic field is called statically induce emf .It could
be classified into two
1)self induced emf and 2)mutual induced emf
Magnetic Systems
Magnetic systems could be of two types they are singly exited and multiply exited magnetic systems.
In singly exited
magnetic systems usually one electrical source is employed.It is
generally used to attract or repel hence to make devices like
relays,electromagnets etc.
Single Excited Electromagnetic System
Let us look how an energy build up happens in a single exited electromagnetic system.
Suppose in a relay if
we are giving electrical energy the static part gets magnetized and
attracts the movable armature to it hence a part of that magnetic energy
is converted into mechanical energy.so
Electrical energy input = mechanical energy output + increase in field energy
The above equation is
based on the assumption that there is magnetic core loss in the
conductor and no leakage flux.The above equation could be represented as
idψ = F fld.dx +dW fld (where ‘fld’ stands for field)
It means a change in
electric field due to change in flux(dψ)is equal the force developed
when it moves a distance ‘dx’ and the increase in magnetic field
energy(dW fld) .
Ψ-flux linkage = NØ(N- number of turns in conductors ,Ø-flux across each conductor)
So the above equation could be written after substituting and rearranging
F fld.dx = idψ- dW fld
(dW fld is the energy stored in the medium and is a function of inductance ‘L ‘and distance ‘x’ therefore dW fld = ½ dL(x)i2 )
So a increase in flux linkage dψ = i × dL(x) (got by differentiating)
Therefore the equation colud be written as
F fld.dx = i2 dL(x) – ½ i2dL(x) = ½ i2dL(x)
This equation
indicates that out of the total energy given half of it is converted
into mechanical energy and the other half is stored in the magnetic
field itself.
Let L(x) = N2/S(x) where s –reluctance of magnetic circuit
Then equation becomes
F fld = ½ i2d/dx[N2/S(x)]
=-1/2 (Ni)2/S(x) × dS(x)/dx =1/2Ø2 dS(x)/dx (where Ø = Ni/S)
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Multiple Excited Magnetization systems
This type of system is
much similar to that of an single excited system.In short it could be
assumed as a combination of more than one single excited system.Machines
like alternators,synchronous motor etc requires two excitation or
electrical source for its working and hence it produces two field and
due to the interaction of these field it works.
Mathematically it could be represented as
dWfld(ψ1,ψ2,θ) = i1.dψ1+i2dψ2 -Tflddθ
i1= ∂dWfld(ψ1,ψ2,θ)/∂ ψ1] ψ2,θ
i2= ∂dWfld(ψ1,ψ2,θ)/∂ ψ1] ψ1,θ
Tfld= ∂dWfld(ψ1,ψ2,θ)/∂ θ] ψ1, ψ2
Torque production in rotating machines
When an excitation is
given to rotor and stator of a rotating machine both of it will produce
individual fields and these fields try to align themselves and these
will produce South poles and North poles on the surface of rotor as well
as stator and the interaction of these poles would produce a rotating
torque.
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