5. energy conversion
5.5
Week 12
Energy balance
Fig: 2.1 Electromechanical machine conventions
A machine accepts energy in a variety of forms from its attached terminal systems. By
conversion we take energy input as positive, so that an output is regarded as a negative input.
The machine internally electrical energy- mechanical energy is a motor mechanical energy to
electrical energy is a generator converts some energy, stores some, and dissipates the rest:
these energies are positive if they increase with time. As the prime object of a machine is
conversion to useful output, one of the terminal inputs will normally be negative. Recalling
the principle of conservation of energy which states that energy is neither created nor
destroyed and combining it with the laws of electric and magnetic fields, electric circuits and
Newtonian mechanics, the energy balance can be expressed as:Total terminal energy input internal energy + Dissipation 2.1 for an electromechanical
machine using a magnetic field as the means of conversion, the balance can be stated in more
specific terms as electrical energy input + mechanical energy input
= stored magnetic –field energy + stored mechanical energy + Dissipation
5. energy conversion
Week 12
Reckoned from an initial condition of zero energy, w = o.A comparable relation must apply
to energy changes dw, and also to energy rate dw/dt i.e to power, P. in corresponding
symbols these relations are total energy wf + ws + w
Energy change dwe + dwm = dwf + dws + dw
Energy rate Pe + pm
= dwf + dws
dt
2.2(a)
2.2(b)
+
p 2.2(c)
dt
The rates of change of stored field energy wf and stored mechanical energy, ws, are left in
differential form because there is always a practical limit to storage. A magnetic field can not
grow in strength indefinitely when ferromagnetic materials is employed; and if the kinetic
energy in a flywheel is continually increased, the speed must rise and the wheel may burst
under centrifugal force.
We shall now examine the electromechanical machine in more detail with fig 2.3. The
machine links an electric source of voltages supplying a current; and a mechanical sources
represented by a bar moving to positive directions, thus both vi and fmu are inputs ( The
mechanical source could alternatively be a shaft rotated at angular speed wr by a tongue mm
to give an input power mnwr ). The electrical end of the machine is precisely that of fig 2.1
(a), with opposing v. the mechanical end has the magnetically developed force fe opposing
fm > fm it can reverse speed w so that the mechanical system is driven and absorbs a
mechanical output.
The behavior can now be summarized. With the machine operating in the steady state as a
motor, the applied voltage u drive +I against e to give a total electrical power input pe =
u(+e), of which the part ei is converted. The outcome of conversion is the force fe which
drives the bar against fm to develop the mechanical input pm = fm (-u) which, being
5. energy conversion
Week 12
negative, is actually an output. With the machine as a generator; the bar is driven at speed u
by the force fm to provide the mechanical input pm = fm ( +u), as a result which e now
exceeds u and reverse the current to provide the negative electrical input (i.e output (i.e
output) pe = u (-i) the sum of the inputs (pe +pm) must be rate of rise of internal energy
storage plus the rate of energy dissipation.
A real electromagnetic machine has fairly obvious points of attachment (e.g the electrical
terminals and the shaft) by which it is connected to the electrical and mechanical sources to
form a link between them. But it is very to concentrate source to from link between them.
But it is very convenient attention on the conversion region enclosed by the chain- dotted
line in fig 2.3, for it contains only the essential quantities e and i,. U and fe. Various losses,
and the mechanical storage, are excluded so that attention can be directed on to the physical
process if useful energy conversion by electromagnetic means outside the conversion region
we can account for conduction and core losses associated with the electrical end and
represented rough by the resistance R in fig 2.3, and friction and similar losses on the
mechanical side. It is to be noted that the externally applied force fm is not necessarily equal
to –fe because there may be force-absorbing components of inertial and elasticity in the
mechanical working parts of the machine itself, as well as internal friction.
The machine has new been reduced to an analyzable form. Its behaviors under specified
conditions involves the forces and movement of the mechanical parts, the voltages and
current at the electrical terminals and processes of energy conversion and storage and
dissipation going on inside. Evaluation is based on the well-established principles and laws
summarized in the following table.
5. energy conversion
Week 12
Part of system
Quantities
Principles
Electrical
Voltage, current
Faraday-Lenz and
Kirchhoff laws
Conversion
E.M.F
current
magnetic Magneto- mechanical
field,. Force, displacement
Principles
induction
and
Force, displacement speed
thermal laws Newton law
Mechanical
5.5.1 Block diagram for energy balance equation
The energy balance equation is given by equation 2.2 as electrical energy input mechanical
energy input
= stored magnetic-=field energy + stored mechanical energy + dissipation
The dissipation (energy lossess) arise from three main causes
(ii)
Part of electrical energy is converted directly to heat in the resistance of current path.
(ii)
Part of mechanical energy developed with the device is absorbed in friction ad
windage and converted to heat.
(iii)
Part of the energy absorbed by the coupling field is converted to heat in magnetic
core losses (for magnetic coupling ) or dielectric loss) for electric coupling).
if we associate the various losses with the corresponding energies, equation 2.2 be written as
Electrical energy
Input minus
Resistance losess
mechanical energy
= Output plus friction
and windage losses
increase in energy stored
+
in the coupling field
plus associated losses
5. energy conversion
Week 12
Equation 2.3 is obtained ( for a motor) with the mechanical energy transferred to the R.H.S
of the equality sign and neglecting the energy mechanical stored
energy ( for a machine
without a flywheel and neglecting the mass of the shaft). If there is a flywheel, the stored
mechanical energy is 1/2mu2 or ½ mr2w2
Where m
=
mass of flywheel
V
=
linear velocity of rotating wheel
w
=
angular velocity of rotating wheel
r
=
radius of flywheel
Equation 2.3 may be represented in the form of a block diagram as shown in fig 2.4
Fig 2.4 General representation of electromagnetic energy conversion. Fro a generator action, the
positions of the electrical system and that or the mechanical system will be interchanged.