Page 706 - Mechatronics with Experiments

692 MECHATRONICS
Rotor (P.M.)
Ph 1A
Stator
windings:

Phase 1 & 2
Ph 1B
Ph 1C

Ph 1D

Ph 2A Ph 2B Ph 2C Ph 2D
FIGURE 8.67: Two-phase stepper motor. Each phase is wound with two identical windings.
Each phase has four terminal wires. The phase windings can be terminated to configure the
motor for unipolar or bipolar operation.

(c) Connect the phase terminal wires in such a way that the motor can be used as a bipolar wound
motor with parallel connected windings (two identical windings for each phase are connected in
parallel). Draw the amplifier circuit and its connections to motor windings.
(d) What is the main performance difference between bipolar series and bipolar parallel configuration
of the motor?
6. Consider the drive circuit for a three phase brushless DC motor shown in Figure 8.32. Assume
that the rotor has one south and one north pole (like the one shown in Figure 8.29c). Let us focus on
the ON/OFF state of six power transistors (Tr , … , Tr ) in order to generate torque in the forward and
6
1
reverse direction. Determine the sequence of the ON/OFF conditions of the transistors for forward
and reverse torque generation. Assume a nominal rotor position, hence the magnetic field of the rotor,
as the beginning of the commutation cycle. Hint: make a table with columns being the transistors
1 through 6 states, the position of the rotor at the beginning of each transistor state switching sequence,
and the magnetic field vector generated by the stator at a particular switching pattern. The rows should
be six different transistor states for forward torque generation in sequence and similar information for
the reverse torque generation. In an actual motor, the power transistors would be controlled by a PWM
signal to generate a sinusoidal or trapezoidal current as a function of rotor position as opposed to the
ON/OFF switching discussed in this problem. Nonetheless, the ON/OFF switching of transistors is
still useful in understanding the current commutation on DC brushless motors.
7. The torque versus rotor position under constant current conditions for a DC brush-type motor
(Figure 8.28). Assume that for each coil connected to the commutators, the torque is a sinusoidal
function of rotor position under constant current, as shown in the same figure. Plot the torque versus
rotor position for one revolution, under constant current, for the following cases: a) two coils only (and
two commutators), b) four coils (and four commutators), c) eight coils, and d) 16 coils. What is the
benefit of having a large number of commutator segments? Assume that all coils are symmetrically
◦
distributed, that is in the four coil case, the second coil is 180 electrically (1/4 revolution mechanical
degrees) out of phase with the first coil, in the eight coil case each coil is 1∕8 of a revolution
®
®
out of phase from the previous one). Use of MATLAB /Simulink for the plot and calculations is
recommended.
8. Consider a DC motor, current amplifier, a closed loop PD type controller, and a position
feedback sensor (Figures 8.59, 8.64, 2.42). Consider that the motor dynamics is described by its