electromechanical energy conversion ppt 2
TRANSCRIPT
Lecture 4 - EE743Lecture 4 - EE743
Electromechanical Energy Conversion
Professor: Ali KeyhaniProfessor: Ali Keyhani
2
Electromechanical Energy Conversion
The electromechanical energy conversion theory allows the representation of the electromagnetic force or torque in terms of device variables, such as the currents and the displacement of the mechanical systems.
An electromechanical system consists of an electric system, a mechanical system, and a means whereby the electric and mechanical systems can interact.
3
Electromechanical Energy Conversion
Consider the block diagram depicted below.
ElectricSystem
Coupling Field Mechanic
System
WE = We + WeL + WeS
Energy supplied by an electric source
Energy transferred to the coupling field by the electric system
Energy losses of the electric system. Basically, I2R
Energy stored in the electric o magnetic field
4
Electromechanical Energy Conversion
The energy transferred to the coupling field can be represented by
WWMM = = W Wmm + + W WmLmL + + WWmSmSEnergy supplied by a mechanical source
Energy transferred to the coupling field from the mechanical system
Energy losses of the mechanical system
Energy stored in the moving member and compliance of the mechanical system
WWFF = = W Wee + + W Wmm Total energy transferred to the coupling field
Energy transferred to the coupling field by the electric system
Energy transferred to the coupling field from the mechanical system
WWFF = = W Wff + + W WfLfL Energy stored in the electric system
Energy dissipated as heat (I2R)
5
Electromechanical Energy Conversion
The electromechanical systems obey the law of conservation of energy.
Energy Balance in an Electromechanical System
WWFF = W = Wf f + W + WfLfL = W = We e + W + Wmm
WE
WeL
WeS
WfLWmL
Wf WmS
WM
6
Electromechanical Energy Conversion
If the losses are neglected, we will obtain the following formula,
WWFF = W = We e + W + Wmm
Energy transferred to the coupling field by the electric system
Energy transferred to the coupling field from the mechanical system
7
Electromechanical Energy Conversion
Consider the electromechanical system given below,
xx0
N+
-
ef
iLr
V
+
-
k
f
fe
D
m
8
Electromechanical Energy Conversion
The equation for the electric system is-
The equation for the mechanical system is-
fedt
diLriV
fexxKdt
dxD
dt
dxmf )( 02
2
9
Electromechanical Energy Conversion
The total energy supplied by the electric source is -
The equation for the mechanical system is-
dtdt
dxfdxfWM
dtie
dt
diLridtiVW fE
10
Electromechanical Energy Conversion
Substituting f from the equation of motion-
dxfexxKdt
dxD
dt
dxmdxfW
system mechanical
the from field couplingthe to dtransferre
energy Total springthe in stored
Energy Potential
(Wall)friction the due
loss Heatmass the in stored
energy Kinetic
E
)( 02
2
11
Electromechanical Energy Conversion
dxfidtedW
dxfidteW
WWeW
Recall
dxfW
eff
eff
Mf
eM
*
12
Electromechanical Energy Conversion
If dx=0 is assumed, then
0
dxf
fEf
idW
dtidt
didteWW
13
Electromechanical Energy Conversion
Recalling the normalized magnetization curve,
),( xi d
idW f
diWc
i
14
Electromechanical Energy Conversion
0
),(
),(),(
),(
dx
f diii
xiW
dxx
xidi
i
xid
xi
15
Electromechanical Energy Conversion
0
),(
),(),(
),(
dx
c dxi
diW
dxx
xid
xidi
xii
16
Electromechanical Energy Conversion
From the previous relationship, it can be shown that for one coil,
01
*
0
*
0
)(
)(
dxj jjf
i
f
i
f
diW
case, general a For
idxLiW
i xL diW
17
Electromechanical Energy Conversion
For two coupled coils,
For the general case with n-coupled coils,
22
22211212
11 2
1
2
1iLiiLiLW f
n
p
n
qqppqf iiLW
1 12
1
18
Electromagnetic Force
xx0
N+
-
ef
iLr
V
+
-
k
f
fe
D
m
Recalling,
19
Electromagnetic Force
dt
de
dWdWdxf
dxfidteW
WWeW
f
fee
eff
Mf
20
Electromagnetic Force
fe
fe
dWdidxf
didtidt
didtedW
dxx
xidi
i
xid
),(),(
dxx
xiWdi
i
xiWdW ff
f
),(),(
Substituting for d and dWf in fedx=id dWf, it can be shown
fe dWx
ixif
,
21
Electromagnetic Force
Recall, d
idW f
diWc
i
x
W
xixif
x
W
xi
x
W
WiW
fe
fc
fc
),(
22
Electromagnetic Force
x
Wxif
x
W
xi
xixif
x
W
xixif
WiWWWi
ce
ce
fe
cfcf
),(
),(
),(