What if the tooth width of the stator should increase beyond a certain value in the design of three-phase indu

Question

What if the tooth width of the stator should increase beyond a certain value in the design of three-phase induction motor?

Examoogle · Accepted Answer

Option D: All of these

Explanation & Concepts:
In an induction motor, the stator tooth width determines the magnetic flux density in the teeth. Increasing the tooth width forces the stator slots to become narrower to maintain the same total peripheral pitch, which necessitates deeper slots to house the required conductor volume, ultimately increasing slot leakage reactance.

Working Principle: The total stator slot pitch is the sum of tooth width and slot width. If tooth width is increased for a constant slot pitch, the available slot width must decrease. To compensate for reduced area, slots must be made deeper. Increased slot depth results in a longer leakage flux path, which is directly proportional to the slot leakage reactance $X_s = \frac{2\mu_0 \pi f N^2 L}{w_s} 	imes \lambda$.

Key Formulas: $X_s \approx \frac{K \cdot f \cdot N^2 \cdot L}{w_s}$ — Slot leakage reactance formula where $w_s$ is slot width; $B_t = \frac{\Phi}{A_t}$ — Tooth flux density where $A_t = w_t \cdot L \cdot N_t$

Key Points: Stator tooth width is limited by the saturation flux density limit of the core material (usually 1.5 to 1.8 Tesla).; Deep slots increase the length of the conductor path, thereby increasing copper losses and leakage reactance.; Higher leakage reactance leads to a decrease in the maximum torque and power factor of the induction motor.; A balance between slot width and tooth width is essential to optimize both electrical and magnetic performance.

Advantages: Higher tooth width reduces magnetic saturation in the teeth.; Reduced flux density minimizes core losses.

Disadvantages: Narrow slots increase winding difficulty and thermal resistance.; Excessive slot depth significantly increases leakage reactance, degrading motor starting torque.

Applications: Design of industrial induction motors where efficiency and starting torque are optimized.; Variable frequency drive (VFD) motor design.

Additional Info: The stator tooth width is generally chosen such that the tooth flux density $B_t$ remains within 1.5 to 1.9 T for silicon steel.. Option B and C are direct physical consequences of reducing the slot width (which happens if tooth width is increased while maintaining constant slot pitch).

Answer: D is correct — Increasing tooth width reduces slot width, forcing deeper slots to maintain conductor volume, which inherently increases leakage reactance.

Exam Tip: In machine design, remember that leakage reactance is proportional to the depth-to-width ratio of the slot; always aim for an aspect ratio that balances copper losses against leakage.

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Option A: Slot width became narrow

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Option B: deep slots required to accommodate conductor/slot

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Option C: leakage reactance increased

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