In the design of single-phase induction motor. The flux density in stator teeth is given by

Question

Examoogle · Accepted Answer

Option A: $B_{ts} = \frac{\Phi_m}{W_{ts} 	imes (S_s/p) 	imes L_i}$

Explanation & Concepts:
The flux density in the stator teeth of a single-phase induction motor is determined by the ratio of the total flux per pole to the total cross-sectional area of the teeth under one pole. Since the flux is divided among the teeth corresponding to a specific pole, the effective area is calculated as the product of the tooth width, the number of teeth per pole, and the net core length.

Working Principle: The total flux $\Phi_m$ produced by a pole must pass through the teeth located under that pole. The number of teeth per pole is given by $S_s/p$, where $S_s$ is the total number of stator slots and $p$ is the number of poles. The cross-sectional area per pole is therefore $W_{ts} 	imes (S_s/p) 	imes L_i$. Flux density $B_{ts}$ is defined as the flux divided by this effective area.

Key Formulas: $B_{ts} = \frac{\Phi_m}{W_{ts} 	imes (S_s/p) 	imes L_i}$ — Flux density in stator teeth; $A_{total} = W_{ts} 	imes (S_s/p) 	imes L_i$ — Total cross-sectional area of teeth per pole

Key Points: $\Phi_m$ represents the maximum flux per pole.; $W_{ts}$ is the width of a single stator tooth.; $S_s/p$ represents the number of teeth per pole.; $L_i$ is the net axial length of the stator core.

Advantages: Allows optimization of stator geometry for magnetic saturation.; Ensures uniform flux distribution across teeth.

Disadvantages: High flux density leads to increased core losses.; Higher saturation levels result in increased magnetizing current.

Applications: Design of fractional horsepower induction motors.; Magnetic circuit calculation in electric machines.

Additional Info: The net length $L_i$ is usually calculated as $L_i = K_s 	imes L$, where $K_s$ is the stacking factor (typically 0.9 to 0.95).. Options B and C incorrectly multiply the flux by the area, which is dimensionally inconsistent with flux density.

Answer: A is correct — The formula for flux density in stator teeth is the ratio of total flux per pole to the total area provided by the teeth under that pole.

Exam Tip: Always verify dimensional consistency: Flux density ($Wb/m^2$) must equal Flux ($Wb$) divided by Area ($m^2$).

Examoogle · Answer

Option B: $B_{ts} = \Phi_m 	imes W_{ts} 	imes (S_s/p) 	imes L_i$

Examoogle · Answer

Option C: $B_{ts} = \Phi_m 	imes W_{ts} 	imes (S_s/p) 	imes 2L_i$

Examoogle · Answer

Option D: $B_{ts} = \frac{\Phi_m}{W_{ts} 	imes (S_s/p) 	imes 2L_i}$

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