Detailed Notes: Electromechanical Energy Conversion - 2 | Electrical Machines - Electrical Engineering (EE) PDF Download

 Page 1


ENERGY BALANCE
Attracted-armature relay
• The operation of a simple attracted-armature relay is shown in Fig.
• Assume that initially the switch is open and that there is no
stored field energy
Energy balance equation = 
Function (energy input, 
energy output, 
energy stored, 
energy dissipated)
(External load)
Page 2


ENERGY BALANCE
Attracted-armature relay
• The operation of a simple attracted-armature relay is shown in Fig.
• Assume that initially the switch is open and that there is no
stored field energy
Energy balance equation = 
Function (energy input, 
energy output, 
energy stored, 
energy dissipated)
(External load)
After the switch is closed, the sequence of events falls into four distinct
steps as follows:
• After the switch is closed, the current rises exponentially
• If L
1
is the inductance of the coil for the initial position of the armature,
the initial rate of rise of current is given by di/dt|
t=0+
= V/L
1
Step 1:
ENERGY BALANCE
(External load)
t = 0
Page 3


ENERGY BALANCE
Attracted-armature relay
• The operation of a simple attracted-armature relay is shown in Fig.
• Assume that initially the switch is open and that there is no
stored field energy
Energy balance equation = 
Function (energy input, 
energy output, 
energy stored, 
energy dissipated)
(External load)
After the switch is closed, the sequence of events falls into four distinct
steps as follows:
• After the switch is closed, the current rises exponentially
• If L
1
is the inductance of the coil for the initial position of the armature,
the initial rate of rise of current is given by di/dt|
t=0+
= V/L
1
Step 1:
ENERGY BALANCE
(External load)
t = 0
• The total input electrical energy from the source upto time ‘t’
= i
2
R loss in the magnetizing coil integrated over time (from 0 to t)
+ stored energy in the magnetic field
• During this period the armature experiences an attractive force, but
the various mechanical restraints (external load/force + spring)
prevent it from moving (u = 0)
ENERGY BALANCE
Step 1 (0 < t < t
1
) continued…
(External load)
t = 0
u = 0
Page 4


ENERGY BALANCE
Attracted-armature relay
• The operation of a simple attracted-armature relay is shown in Fig.
• Assume that initially the switch is open and that there is no
stored field energy
Energy balance equation = 
Function (energy input, 
energy output, 
energy stored, 
energy dissipated)
(External load)
After the switch is closed, the sequence of events falls into four distinct
steps as follows:
• After the switch is closed, the current rises exponentially
• If L
1
is the inductance of the coil for the initial position of the armature,
the initial rate of rise of current is given by di/dt|
t=0+
= V/L
1
Step 1:
ENERGY BALANCE
(External load)
t = 0
• The total input electrical energy from the source upto time ‘t’
= i
2
R loss in the magnetizing coil integrated over time (from 0 to t)
+ stored energy in the magnetic field
• During this period the armature experiences an attractive force, but
the various mechanical restraints (external load/force + spring)
prevent it from moving (u = 0)
ENERGY BALANCE
Step 1 (0 < t < t
1
) continued…
(External load)
t = 0
u = 0
Step 2 (t
1
< t < t
2
):
• When the current in the coil reaches an appropriate value, the armature
begins to move (u > 0) when the electro-mechanical force of
attraction (f
E
) = total external mechanical force (f
M
) (load + spring)
• Mechanical energy is required to stretch the spring, drive the external
load and to supply the kinetic energy required by the moving parts
ENERGY BALANCE
t = 0
(External load)
u > 0
Page 5


ENERGY BALANCE
Attracted-armature relay
• The operation of a simple attracted-armature relay is shown in Fig.
• Assume that initially the switch is open and that there is no
stored field energy
Energy balance equation = 
Function (energy input, 
energy output, 
energy stored, 
energy dissipated)
(External load)
After the switch is closed, the sequence of events falls into four distinct
steps as follows:
• After the switch is closed, the current rises exponentially
• If L
1
is the inductance of the coil for the initial position of the armature,
the initial rate of rise of current is given by di/dt|
t=0+
= V/L
1
Step 1:
ENERGY BALANCE
(External load)
t = 0
• The total input electrical energy from the source upto time ‘t’
= i
2
R loss in the magnetizing coil integrated over time (from 0 to t)
+ stored energy in the magnetic field
• During this period the armature experiences an attractive force, but
the various mechanical restraints (external load/force + spring)
prevent it from moving (u = 0)
ENERGY BALANCE
Step 1 (0 < t < t
1
) continued…
(External load)
t = 0
u = 0
Step 2 (t
1
< t < t
2
):
• When the current in the coil reaches an appropriate value, the armature
begins to move (u > 0) when the electro-mechanical force of
attraction (f
E
) = total external mechanical force (f
M
) (load + spring)
• Mechanical energy is required to stretch the spring, drive the external
load and to supply the kinetic energy required by the moving parts
ENERGY BALANCE
t = 0
(External load)
u > 0
• The airgaps are reduced leading to an increase in the inductance of
the arrangement. This causes a reaction in the electrical system in the
form of an induced e.m.f. E
• This e.m.f. tends to reduce the coil current and also permits the
conversion of electrical energy, i.e. it is the reaction to the action
ENERGY BALANCE
Step 2 (t
1
< t < t
2
) continued…
t = 0
(External load)
u > 0
E