Question:
In a wave winding, if \( y_b \) and \( y_c \) are back and commutator pitches respectively, then the front pitch \( y_f \) is given by
In a wave winding, if \( y_b \) and \( y_c \) are back and commutator pitches respectively, then the front pitch \( y_f \) is given by
Show Hint
Remember that for a wave winding, the commutator pitch is always the average of the back and front pitches:
$$y_c = \frac{y_b + y_f}{2}$$
Simply rearrange this fundamental average formula to solve for whichever pitch ($y_b$ or $y_f$) the question asks for!
Updated On: Jun 25, 2026
- \( y_f = 2y_b + y_c \)
- \( y_f = 2y_c - y_b \)
- \( y_f = 2y_b - y_c \)
- \( y_f = y_b - 2y_c \)
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The Correct Option is B
Solution and Explanation
Concept:
In DC machine armature windings, there are two primary configurations: lap winding and wave winding.
• Lap Winding: The finishing end of one coil is connected to a commutator segment adjacent to the segment where its starting end is connected. The coil progresses forward but loops back.
• Wave Winding: The coils are connected in a series-progressive, wave-like fashion around the surface of the armature. The winding progresses continuously around the armature core. Key pitch definitions in armature windings include:
• Back Pitch (\(y_b\)): The distance measured in terms of armature conductors between the two sides of a single coil at the back of the armature core.
• Front Pitch (\(y_f\)): The distance between the second conductor of one coil and the first conductor of the next consecutive coil connected to the same commutator segment at the front end.
• Commutator Pitch (\(y_c\)): The distance between the two commutator segments to which the ends of a single coil are connected.
Step 1: Set up the pitch relationship for a wave winding.
In a simplex wave winding, the total distance advanced around the armature by a single coil loop (comprising both the back progression and the front progression) is related directly to the commutator pitch. The average pitch ($y_{\text{avg}}$) of the winding is defined as the arithmetic mean of the back pitch and front pitch: $$y_{\text{avg}} = \frac{y_b + y_f}{2}$$
Step 2: Relate the average pitch to the commutator pitch.
For a wave winding, the commutator pitch $y_c$ is equal to the average pitch of the winding because the coils continuously advance in the same direction around the armature circle without looping back: $$y_c = y_{\text{avg}}$$ Substituting the expression for average pitch into this equation: $$y_c = \frac{y_b + y_f}{2}$$
Step 3: Rearrange the equation to solve explicitly for front pitch \( y_f \).
To isolate $y_f$, cross-multiply by $2$: $$2y_c = y_b + y_f$$ Subtract $y_b$ from both sides of the equation: $$y_f = 2y_c - y_b$$ This derived relation states that the front pitch equals twice the commutator pitch minus the back pitch. Reviewing the provided options, this perfectly matches option (2).
• Lap Winding: The finishing end of one coil is connected to a commutator segment adjacent to the segment where its starting end is connected. The coil progresses forward but loops back.
• Wave Winding: The coils are connected in a series-progressive, wave-like fashion around the surface of the armature. The winding progresses continuously around the armature core. Key pitch definitions in armature windings include:
• Back Pitch (\(y_b\)): The distance measured in terms of armature conductors between the two sides of a single coil at the back of the armature core.
• Front Pitch (\(y_f\)): The distance between the second conductor of one coil and the first conductor of the next consecutive coil connected to the same commutator segment at the front end.
• Commutator Pitch (\(y_c\)): The distance between the two commutator segments to which the ends of a single coil are connected.
Step 1: Set up the pitch relationship for a wave winding.
In a simplex wave winding, the total distance advanced around the armature by a single coil loop (comprising both the back progression and the front progression) is related directly to the commutator pitch. The average pitch ($y_{\text{avg}}$) of the winding is defined as the arithmetic mean of the back pitch and front pitch: $$y_{\text{avg}} = \frac{y_b + y_f}{2}$$
Step 2: Relate the average pitch to the commutator pitch.
For a wave winding, the commutator pitch $y_c$ is equal to the average pitch of the winding because the coils continuously advance in the same direction around the armature circle without looping back: $$y_c = y_{\text{avg}}$$ Substituting the expression for average pitch into this equation: $$y_c = \frac{y_b + y_f}{2}$$
Step 3: Rearrange the equation to solve explicitly for front pitch \( y_f \).
To isolate $y_f$, cross-multiply by $2$: $$2y_c = y_b + y_f$$ Subtract $y_b$ from both sides of the equation: $$y_f = 2y_c - y_b$$ This derived relation states that the front pitch equals twice the commutator pitch minus the back pitch. Reviewing the provided options, this perfectly matches option (2).
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