Motor Sizing, Duty Cycles & Drive Selection

Select the mechanical operating envelope first, then the motor, converter, feedback, transmission, braking path, cooling, and protection as one system. Rated kilowatts at one speed say little about peak acceleration torque, zero-speed heating, field-weakening voltage, or repeated regeneration.

Build the load profile #

For each segment record speed, load torque, acceleration, duration, direction, and dwell. Required motor torque on a common shaft is

$$T_m=J_{eq}\dot\omega+T_{load,ref}+T_{friction}.$$

Map every point onto the motor/drive continuous and peak torque-speed envelope. Peak torque must fit current and demagnetization/commutation limits; continuous and cyclic duty must fit thermal limits.

RMS is useful but conditional #

When copper loss approximately follows torque squared and cooling is comparable across the cycle,

$$T_{rms}=\sqrt{\frac{\sum T_i^2t_i}{\sum t_i}}.$$

Example: 12 N·m for 2 s and 4 N·m for 8 s gives $T_{rms}=6.2$ N·m. This does not by itself validate a 6.2 N·m motor: the 12 N·m peak, acceleration, low-speed cooling, drive current, gearbox, and cycle repetition remain constraints.

Inertia and gearing #

Gearing reduces load inertia reflected to the motor by ratio squared, but raises motor speed and adds efficiency loss, backlash, stiffness, and reflected friction. “Inertia matching” is not a universal equality target; choose ratio to satisfy acceleration, speed, control bandwidth, transmission life, and disturbance sensitivity.

Electrical and thermal boundaries #

Check DC-bus voltage at maximum speed/back EMF, continuous and peak phase current, switching frequency/derating, cable and filter, regeneration destination, braking resistor energy and duty, ambient altitude/temperature, enclosure, and cooling at the actual speed. A shaft-mounted fan provides less cooling at low speed.

Regeneration and stops #

Decelerating inertia returns energy approximately $\Delta E=\tfrac12J(\omega_1^2-\omega_2^2)$. The DC bus, battery/front end, or braking resistor must absorb it. Otherwise bus voltage rises and the drive trips precisely when commanded to stop.

Selection evidence #

Keep the full duty table, reflected quantities, vendor torque-speed curves, thermal assumptions, peak duration/recovery rules, braking calculation, environment/ingress requirement, feedback resolution/accuracy, bearing/shaft loads, and safety stopping concept. Validate with measured current, speed, bus voltage, temperatures, and worst representative cycles after installation.