Question 18.3: Analysis of Two-Phase, Four-Pole StepMotor Determine the ful...
Analysis of Two-Phase, Four-Pole Step Motor
Determine the full-step single-phase, full-step two-phase, and half-step current excitation sequences for the PM step motor of Figure 18.10.
Known Quantities: Phase currents.
Find: Full-step sequence for the motor.
Assumptions: The motor currents at the start of the sequence are i_{1}>0 and i_{2}=0.
Analysis: With the initial currents assumed (phase 1 energized), the motor will be at rest if the rotor is in the position shown in Figure 18.10. A single-phase sequence consists of turning on each of the two coils in sequence, reversing the polarity of the currents every other time. Then, the PM rotor will align with the stator poles according to the polarity of the magnetic field generated by each coil’s pole pair. For example, if coil 1 is turned off and coil 2 is turned on with a positive current polarity, the rotor will rotate clockwise by 90^{\circ}. Table 18.1 depicts the (bipolar) sequence of coil currents, and the corresponding motor position.
Table 18.1 Fullstep, single-phase sequence
\begin{array}{ccc}\hline \boldsymbol{i}_{\mathbf{1}} & \boldsymbol{i}_{\mathbf{2}} & {\boldsymbol{\theta}} \\\hline+ & 0 & 0^{\circ} \\0 & + & 90^{\circ} \\- & 0 & 180^{\circ} \\0 & – & 270^{\circ} \\+ & 0 & 0^{\circ} \\ \hline \end{array}
Table 18.2 Fullstep, two-phase sequence
\begin{array}{rrr}\hline \boldsymbol{i}_{\mathbf{1}} & \mathbf{i}_{\mathbf{2}} & \boldsymbol{\theta} \\\hline+ & + & 45^{\circ} \\- & + & 135^{\circ} \\- & – & 225^{\circ} \\+ & – & 315^{\circ} \\+ & + & 45^{\circ} \\ \hline \end{array}
Table 18.3 Half-step sequence
\begin{array}{ccc}\hline \boldsymbol{i}_{\mathbf{1}} & \mathbf{i}_{\mathbf{2}} & \boldsymbol{\theta} \\ \hline + & 0 & 0^{\circ} \\+ & + & 45^{\circ} \\0 & + & 90^{\circ} \\- & + & 135^{\circ} \\- & 0 & 180^{\circ} \\- & – & 225^{\circ} \\0 & – & 270^{\circ} \\+ & – & 315^{\circ} \\+ & 0 & 0^{\circ} \\ \hline \end{array}
If both coils are activated, it is possible to cause the rotor to align between stator poles, also in increments of 90^{\circ}, but shifted in phase by 45^{\circ} with respect to the single-phase stepping sequence. Table 18.2 illustrates this stepping sequence.
Finally, if one combines the two sequences (easily accomplished, since the current commands for the two sequences are distinct), it is possible to obtain increments of 45^{\circ}. Table 18.3 depicts the half-step sequence. Any finer resolution would require increasing the number of windings and teeth in the stator.
Comments: The simplicity of the electronic controls required by this type of machine is one of the very attractive features of step motors.