Page 70 - Electric Machinery Fundamentals

46 ELECTRIC MACHINERY FUNDAMENTALS

(d) This task is ideally suited for MATLAB. We can take advantage of MAT LAB's
vectorized calculations to determine the velocity of the bar for each value of
force. The MATLAB code to pelform this calculation is just a version of the
steps that were performed by hand in part c. The program shown below calcu-
lates the current, induced voltage, and velocity in that order, and then plots the
velocity versus the force on the bar.

% M- flle ' ex! 10 m
% M-f i le to calculate and plot the velocity of
% a linear mot or as a func tion of load .
VB = 120 i % Batter y v oltage (V)
r 0 . 3 ; % Resist ance (ohms )
1 1 ; % Bar l ength (m)
B 0 . 6 ; % Flux den s i t y (T)

% Sel ect the forces to apply t o the bar
F = 0 : 10 : 50 ; % Fo r ce (Nl
(
% Calculate the c u rrents fl owing i n t h e motor .
i = F . f 11 • B ) ; % Current (A)

% Calcul ate the induced voltages on t h e bar .
eind = VB - i • r; % Induced voltage (V)

% Calculate the velocit ies of the bar .
v_bar = eind . f 11 • B) ; % Velocity (rn/ s)

% Plot the veloc ity of t he ba r versus force .
plot (F , v_bar) ;
i
t i t l e ('pl ot of Veloci t y versus Applied For ce ) ;
xlabe l (I Force (N) I) ;
ylabe l ('Ve loc ity (rols) I ) i
a xis «(0500 2 00J);
The resulting plot is shown in Figure 1- 28. Note that the bar slows down more
and more as load increases.
(e) If the bar is initially unloaded, then eind = VB' If the bar suddenly hits a region
of weaker magnetic field, a transient will occur. Once the transient is over,
though, eind will again equal V n -
This fact can be used to determine the final speed of the bar. The initial speed was
120 m/s. Thejinal speed is
VB = eind = v sfll
VB
VSS = Bl
l20V
(0.08 T)(IO m) = ISO mI,

Thus, when the flux in the linear motor weakens, the bar speeds up. The same behavior oc-
curs in real dc motors: When the field flux of a dc motor weakens, it turns faster. Here,
again, the linear machine behaves in much the same way as a real de motor.