Two-phase AC servomotor characteristic: The rotor has resistance R and standstill reactance X. State the condition under which the torque–speed curve is approximately linear over a useful range.

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

Introduction / Context:Servomotors used in control systems should offer a reasonably linear torque–speed characteristic around the operating region to simplify design and ensure faithful tracking. Two-phase AC servomotors are designed with intentionally high rotor resistance to achieve this property. Given Data / Assumptions: Two-phase AC servomotor with rotor resistance R and standstill reactance X. Objective: near-linear torque versus speed (or slip) characteristic across the intended operating slip range. Concept / Approach:The air-gap power and electromagnetic torque depend on rotor impedance R + jX_s (seen at slip frequency). A linear torque–speed region is favored when the reactive and resistive parts are comparable—avoiding excessive current phase angles and sensitivity to slip. The design rule-of-thumb is to make rotor reactance roughly equal to rotor resistance at the significant slip frequency, i.e., X ≈ R, which straightens the curve over a practical operating range. Step-by-Step Solution: Consider T ∝ (rotor current)^2 × (resistive component / synchronous speed).Rotor current I ∝ V / √(R^2 + X^2); torque phase sensitivity reduces when R and X are comparable.With X ≈ R the angle of rotor current is ~45°, yielding a smoother, less peaky torque variation vs slip. Verification / Alternative check: Manufacturer data sheets for servomotors show linearized speed–torque when resistance is high and X is of similar magnitude, validating X = R as a practical criterion. Why Other Options Are Wrong: X ≪ R: mostly resistive, low power factor changes and poor torque utilization.X ≫ R: highly reactive, torque becomes very sensitive and non-linear near low slips.R = 0 impossible for real rotor; X = 2R does not generally produce the best linearity. Common Pitfalls: Assuming “large R only” ensures linearity; actually, balance with X is what shapes the characteristic. Final Answer: X = R

Two-phase AC servomotor characteristic: The rotor has resistance R and standstill reactance X. State the condition under which the torque–speed curve is approximately linear over a useful range.

Answer

Explanation