Sizing a motor comes down to two questions: how much torque to accelerate the load, and how much to keep it moving. Undersize and it stalls or overheats; oversize and you've wasted money and space.
Acceleration torque dominates
To spin up an inertia J to speed in time t you need T = J·α, where α is the angular acceleration.
For fast-cycling machines this acceleration torque usually dwarfs the steady running load — so start there. Add
the working load torque and any friction to get the peak the motor must deliver. The
Motor Sizing tool does the arithmetic.
The gearbox trick: reflected inertia
A gearbox is an inertia-matching device. It divides the load torque by the ratio, but — crucially — it divides the reflected load inertia by the ratio squared. A 5:1 box makes the load look 25× lighter to the motor. This is why a small motor with the right gearbox beats a big direct-drive motor for high-inertia loads, and why inertia matching (load inertia ≈ motor inertia × ratio²) is a real design target.
A motor drives a load directly. You put a 5:1 gearbox between them, changing nothing else. What does the motor now feel as the load's inertia?
Reflected inertia goes as 1/ratio², so 5:1 divides it by 25. That is why a gearbox is the standard cure for an inertia mismatch, and why the usual target of a 5–10:1 inertia ratio is so easy to hit once you stop trying to do it with a bigger motor. The catch is that torque is multiplied by the ratio but speed is divided by it, so the motor has to spin faster to do the same job — and past about 10:1 the gearbox's own inertia and losses start taking back what you gained.
Try it — the move profile, peak against RMS
Size to the RMS torque, not the peak
A motor can deliver its peak torque briefly but overheats if it runs there continuously. Over a repeating duty cycle, work out the root-mean-square torque — the thermally-equivalent steady torque — and make sure the motor's continuous rating covers it, while its peak rating covers the acceleration spike.
Don't forget
Add a service factor for the unknowns (friction, wear, voltage sag). Check the speed at the operating point too — a motor's torque falls off at high speed, so peak torque and top speed rarely coincide. And confirm the driver/amplifier can supply the peak current the acceleration torque demands.