cyclogramThe angle, the time and the speed
A rotary axis moves an angle instead of a distance; the profile is the same — accelerate, cruise, decelerate, dwell — in degrees. The table sits on the motor or behind a gearbox, and one motor turn turns it 360° / i.
ω_peak = θ / (t_move · (1 − (f_a + f_d) / 2)) rad/s n_table = ω_peak / 2π · 60 rpm n_motor = n_table · i α = ω_peak / t_accel90° in 0.5 s, in thirds, peaks at 4.71 rad/s — 45 rpm at the table — and accelerates at 28.3 rad/s².
What turns: discs, and parts off the axis
Almost everything on a table is a disc or close to one. A disc about its own centre is m·d²/8; a part whose centre sits a distance r from the axis adds m·r² on top — the parallel-axis rule — and that term is usually the larger. Step 2 takes each disc with its distance from the axis.
J_disc = m · d² / 8 about its own centre J_offset = m · d² / 8 + m · r² centre at r from the axis J_load = Σ J / i²A 1.5 kg fixture Ø80 mm sitting 120 mm out: 1.5 · 0.08² / 8 = 1.2 × 10⁻³ kg·m² about its own centre, plus 1.5 · 0.12² = 2.16 × 10⁻² for where it sits — 2.28 × 10⁻² kg·m² in all, the offset eighteen times the disc.
Torque
A table's torque is almost all inertia: a level table's weight loads its bearings, not the motor. The page adds the bearings' friction torque and any external torque, both at the table, divided by the efficiencies and the gear ratio.
T_static = (T_external + T_friction) / (η · i) α_motor = α · i T_accel = T_static + J_load · α_motor / η + J_trans · α_motor / η_t + J_rotor · α_motorThe default table, 0.01 kg·m² straight on the 400 W servo: 0.283 N·m while accelerating, −0.283 N·m braking, nothing at constant speed, and 0.164 N·m RMS over the 1 s cycle.
The gearbox
Direct, the servo drives 385 times its own rotor inertia. A rotary table nearly always wants a reducer, and the reflected inertia falls with the square of its ratio:
i = √( (J_load / J_rotor) / 10 ) = √( 385 / 10 ) ≈ 6.2The page suggests about 6.3 : 1, which brings the ratio to 9.69 — Close — and 7 : 1 to 7.85. Through 6.3 : 1 the motor turns at 284 rpm and the peak falls to 0.0519 N·m: the gearbox, not the motor, now carries the table.
Worked example
| Quantity | By hand | Result |
|---|---|---|
| Peak speed | (π/2) / (0.5 · 2/3) | 4.71 rad/s, 45 rpm |
| Acceleration | 4.71 / (0.5 / 3) | 28.3 rad/s² |
| Torque accelerating / braking | (0.01 + 2.6 × 10⁻⁵) · 28.3 | 0.283 / −0.283 N·m |
| RMS torque over 1 s | 0.283 · √(2/6) | 0.164 N·m |
| Inertia ratio, direct | 0.01 / 2.6 × 10⁻⁵ | 385 |
| Inertia ratio through 6.3 : 1 | 0.01 / 6.3² / 2.6 × 10⁻⁵ | 9.69 |
Questions
Does the weight of the table matter?
On a level table, only through its inertia: the weight loads the bearings, not the motor. A table on a tilted axis is out of balance when its load is — type that as an external torque in step 1.
How do I enter the parts around the table?
As discs, each with its mass, its diameter and its distance from the axis — or as one disc carrying the mass of all of them at the same distance. For any other shape, type its inertia from the CAD model.
Which angle and time for an indexing table?
The index angle is 360° over the number of stations: eight stations is 45°. The move time is the part of the machine's cycle the table may take to index; the rest is the dwell while the stations work.
Why does a rotary table need a gearbox?
Because nearly all of its load is inertia, and the inertia the motor sees falls with the square of the ratio. A few kilograms of fixtures well out from the axis easily show a small servo hundreds of times its rotor inertia.
What is the table drive efficiency?
For a table with its own drive inside — a worm, a belt or a cam — the share of the torque that reaches the table. A table straight on the gearbox has nothing in between: leave it at 1.
Sources
- Oriental Motor, Technical Reference, selection calculations — the index-table example. The test suite works it and meets the printed load inertia and acceleration torque within 0.5 %.
- The parallel-axis theorem — J = J_centre + m · r² for a part off the axis.
Related guides
- Axis sizing calculatorThe whole guided flow: motion, mechanism, motor, regeneration, and the move as a bar.
- Inertia ratioThe load's inertia at the motor through a screw, a belt or a gearbox, and the ratio that fixes it.
- Servo motor sizingPeak torque at speed, RMS over the cycle, maximum speed and inertia ratio, each with its margin.
- Move time and motion profilePeak speed, acceleration and jerk from a distance and a move time; trapezoid, triangle and S-curve.
- Brake resistor sizingThe energy an axis returns while braking, what the drive's bus takes, and the resistor for the rest.
Every term on this page, defined: the axis and motor sizing glossary.