Dynamics of Electrical Drives Questions and Answers

Answer: C

Rearranging the torque equation gives \( dt = J\,d\omega/(T - T_l) \), and integrating it accounts for the way both torques vary with speed. Only when the difference is constant does the integral reduce to a simple division.

Answer: D

Correct answer: \( J\omega/(T - T_l) \)

With the accelerating torque constant, the acceleration is constant and the equation integrates directly:

Run-up time therefore rises with inertia and falls with the torque margin available. A large inertia with a small margin gives the very long start that is characteristic of fans and centrifuges.

Answer: A

Inertia appears only in the term multiplying the rate of change of speed, so it governs transients and nothing in the steady state. A high-inertia drive is slow to start and slow to stop but is unaffected in its steady behaviour.

Answer: B

Correct answer: \( J_l/i^2 \)

Referring an inertia through a reduction of ratio \( i \) divides it by the square of the ratio:

because the load turns \( i \) times more slowly and the kinetic energies must match. Torque refers with the first power and inertia with the second, which is the single most useful pair of facts in drive sizing - a 10:1 reduction divides the load inertia by a hundred.

Answer: C

Torque refers with the first power of the ratio while inertia refers with the square, which is the single most useful fact in drive calculations. Efficiency of the gearing divides the referred torque further in a real installation.

Answer: D

Equating the kinetic energy of the moving mass to that of an equivalent rotating inertia gives the result directly. The same energy argument produces every referral relation, which is why it is worth remembering in preference to the formulae themselves.

Answer: A

Once inertia and torque are expressed at the motor shaft, the fundamental torque equation applies to the assembly as it stands. Gear ratios and efficiencies are folded into the referred values rather than being carried through the analysis.

Answer: B

Losses in the gearing must be supplied by the motor, so the referred torque is the ideal value divided by the efficiency. During braking the sense reverses and the losses help to retard the load, so the efficiency multiplies instead.

Answer: C

Correct answer: a hoist lifting a fixed weight

The torque a hoist drum must supply is the weight times the drum radius, and neither changes with how fast the drum turns, so the load is constant-torque. A fan is a square-law load, a coiler at constant tension and linear speed is a constant-power load, and a stirrer in a viscous liquid is a viscous load with torque proportional to speed. Conveyors and positive displacement pumps join the hoist in the constant-torque class.

Answer: D

Fans, centrifugal pumps and propellers all move fluid, and the resistance grows with the square of the speed while the power grows with the cube. That cubic law is why a small reduction in fan speed saves so much energy.