Question

The step angle of a 3-\(\phi\) (A, B, C), 6 stator pole, 4 rotor teeth stepper motor if excited sequentially i.e, A, AB, B, BC, C, CA, and so on is:

• A. \(3.75^\circ\)
• B. \(30^\circ\)
• C. \(15^\circ\)
• D. \(7.5^\circ\)

Hint:

To quickly find the step angle for any non-standard or half-step sequence, use the formula $\beta = \frac{360^\circ}{N}$, where $N$ is the total number of unique electrical states per mechanical revolution. For half-stepping, $N = 2 \times m \times N_r = 2 \times 3 \times 4 = 24$ steps. Thus, $\beta = \frac{360^\circ}{24} = 15^\circ$.

Answer 1

The Correct Option is C

Concept: The step angle (\(\beta\)) of a stepper motor is the angular displacement of the rotor per input command pulse. In a conventional full-step operating mode, the motor changes excitation from one single phase directly to the next single phase (e.g., A $\rightarrow$ B $\rightarrow$ C). However, when the switching sequence alternates between a single phase and two phases simultaneously (e.g., A $\rightarrow$ AB $\rightarrow$ B $\rightarrow$ BC $\rightarrow$ C $\rightarrow$ CA), it operates in half-step mode. In half-step mode, the number of steps per revolution is exactly doubled compared to full-step mode, which reduces the structural step angle by half: \[ \beta_{\text{full}} = \frac{360^\circ}{m \cdot N_r} \quad \text{or} \quad \frac{N_s - N_r}{N_s \cdot N_r} \times 360^\circ \] \[ \beta_{\text{half}} = \frac{\beta_{\text{full}}}{2} \] where $m$ is the number of phases, $N_s$ is the number of stator poles, and $N_r$ is the number of rotor teeth.

Step 1: Extract the mechanical parameters given.
* Number of phases (\(m\)) = 3 (Phases A, B, C) * Number of stator poles (\(N_s\)) = 6 * Number of rotor teeth (\(N_r\)) = 4

Step 2: Calculate the standard full-step angle.
Using the formula for full-step operation of a multi-phase variable reluctance or permanent magnet stepper motor: \[ \beta_{\text{full}} = \frac{360^\circ}{m \times N_r} \] Substituting the values: \[ \beta_{\text{full}} = \frac{360^\circ}{3 \times 4} = \frac{360^\circ}{12} = 30^\circ \]

Step 3: Analyze the given excitation sequence to determine the mode.
The sequence given is: $\text{A} \rightarrow \text{AB} \rightarrow \text{B} \rightarrow \text{BC} \rightarrow \text{C} \rightarrow \text{CA}$. This is a standard 1-phase-on, 2-phases-on alternating scheme. Because it introduces an intermediate stable alignment step between full steps, the motor is half-stepping.

Step 4: Compute the resulting half-step angle.
\[ \beta_{\text{half}} = \frac{\beta_{\text{full}}}{2} = \frac{30^\circ}{2} = 15^\circ \] Thus, the step angle under this specific excitation sequence is exactly \(15^\circ\), which matches Option (C).