In the design of a three-phase induction motor. The Inside Diameter of rotor lamination can be calculated as

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Examoogle · Accepted Answer

Option B: 𝑫𝒊 = 𝑫𝒓 − 𝟐(𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑹𝒐𝒕𝒐𝒓 𝑺𝒍𝒐𝒕 + 𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑹𝒐𝒕𝒐𝒓 𝑪𝒐𝒓𝒆)

Explanation & Concepts:
The inside diameter of a rotor lamination in a three-phase induction motor is defined by the total outer diameter of the rotor minus twice the combined depth of the rotor slots and the rotor core (yoke). This ensures that the magnetic flux path has sufficient cross-sectional area while accommodating the winding slots.

Working Principle: The rotor of an induction motor consists of a shaft, a core, and slots. The total rotor diameter ($D_r$) encompasses the entire assembly. Since slots are cut from the outer periphery towards the center, and there is a magnetic core depth ($d_c$) at the innermost part, the inner bore diameter ($D_i$) must exclude these depths from both sides of the diameter. Thus, $D_i = D_r - 2 	imes (d_{slot} + d_{core})$.

Key Formulas: $D_i = D_r - 2(d_s + d_c)$ — where $d_s$ is slot depth and $d_c$ is core depth.

Key Points: The rotor core provides the path for magnetic flux.; The slot depth is determined by the size and insulation requirements of the rotor conductors.; The core depth is calculated based on the maximum permissible flux density to avoid magnetic saturation.; The inner diameter ($D_i$) must be sized to fit the motor shaft with a proper interference fit.

Advantages: Ensures structural integrity of the rotor stack.; Optimizes magnetic flux distribution by defining clear core boundaries.

Disadvantages: Improper calculation leads to magnetic saturation of the rotor core.; Too small a core depth increases eddy current losses.

Applications: Design of squirrel cage induction motors.; Design of slip-ring induction motors.

Additional Info: The rotor core depth is often constrained by the mechanical shaft diameter required to carry the torque.. Option A is incorrect as it refers to stator components, while option C adds instead of subtracting.

Answer: B is correct — the inside diameter is the external diameter reduced by twice the sum of slot depth and core depth to account for the radial stack thickness.

Exam Tip: In machine design exams, always remember that diameter calculations for laminated cores involve multiplying the depth factors by 2 because the dimensions are radial and span across the center of the cylinder.

Examoogle · Answer

Option A: 𝑫i = 𝑫r - 𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑺𝒕𝒂𝒕𝒐𝒓 𝑺𝒍𝒐𝒕 - 𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑪𝒐𝒓𝒆

Examoogle · Answer

Option C: 𝑫𝒊 = 𝑫𝒓 + 𝟐(𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑹𝒐𝒕𝒐𝒓 𝑺𝒍𝒐𝒕+𝑫𝒆𝒑𝒕𝒉 𝒐𝒇 𝑹𝒐𝒕𝒐𝒓 𝑪𝒐𝒓𝒆)

Examoogle · Answer

Option D: None of these

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