Sizing a Rotary Index (Dial) Table Motor

Everything that turns with the table contributes inertia about the axis. The table plate itself, as a solid disc, contributes ½·m·r². Each fixture and workpiece, treated as a mass at its mounting radius, contributes m·d², where d is its distance from the axis (use m·d² for a compact mass off-axis; add its own ½·m·r² only if it is large). Sum them all to get the load-side inertia. The parts and fixtures at a large radius often dominate — a light fixture far out can matter more than a heavy hub near the centre — so the radius, squared, is what drives the total.

The motor reflection calculator takes this as a list of component inertias, each flagged as being on the load side (to be reflected) or already on the motor shaft, and sums them — so you enter the table, the fixtures and the parts as separate items rather than pre-combining them by hand.

An index table is almost always geared down — a worm or planetary gearhead between the motor and the table gives the resolution and holding the index needs. Gearing reflects the load inertia to the motor shaft divided by the ratio squared: J_motor_side = J_load / i². Because the ratio is squared, even a modest reduction shrinks a large table inertia to a small number at the motor — which is exactly how a small servo drives a heavy table.

The number that decides whether the drive is well matched is the inertia ratio: the reflected load inertia divided by the motor's rotor inertia. Keep it below roughly 5–10 for a servo that settles quickly and indexes repeatably; too high and the table overshoots and hunts, too low and you are over-motored. The reflection calculator returns the reflected inertia and the ratio directly, so you choose the gearhead ratio and the motor together to land the ratio in a healthy band.

The torque the motor must produce is the friction/load torque plus the torque to accelerate the combined inertia through the index. For a table that indexes an angle θ in a move time t, the peak angular acceleration depends on the motion profile — a triangular (accelerate-then-decelerate) profile has the lowest peak, α = 4·θ/t², while a trapezoidal profile is higher. Working at the motor shaft, multiply the table-side acceleration by the gear ratio, and apply it to the total inertia at the motor (the reflected load plus the rotor): T_accel = (J_reflected + J_rotor)·α_motor.

Add the steady friction/load torque (small for a horizontal table, larger with a heavy vertical load or a stiff bearing) to get the peak motor torque demand, and confirm the motor's rated and peak torque cover it with margin. A shorter index time raises the acceleration — and the torque — as the inverse square, so the move time is the biggest lever on motor size after the inertia itself.

Fixtures and parts at a large radius dominate the inertia — pull them inboard where you can. The index time is the biggest torque lever after inertia, so do not specify a faster index than the cycle needs. Keep the inertia ratio in band by choosing the gearhead ratio and motor together. Check the gearhead's own rated torque and the holding torque needed to resist the process forces at each station. And if the table is vertical or the load is offset, add the gravity torque, which varies with angle and can dominate the sizing.