Application: Machine building
Gearboxes for rotary index tables: sizing a direct-drive cycloidal table
Direct-drive the table with a cycloidal reducer for stiffness, shock tolerance and accurate stops. Full worked example: inertia, index time, torque, ratio and motor.
Key takeaways
- A cycloidal reducer under the table gives low backlash, high shock capacity and a built-in output bearing.
- Table inertia, index angle and index time set the acceleration torque; the load-to-motor inertia ratio usually decides the motor size.
- Check the off-centre load's tilting moment against the output bearing rating.
The challenge
An index table moves a heavy, often unevenly loaded plate through a fixed angle and must stop exactly on station, cycle after cycle. Every stop is a deceleration shock, and tooling on one side adds a tilting moment. Mechanical cam indexers do this well at one fixed angle; a servo with a cycloidal reducer does it at any angle and any number of stations, which suits flexible assembly lines.
Worked example: four-station table
Steel table plate Ø600 mm × 20 mm, eight fixtures of 3 kg each (two per station) at a 250 mm radius, 90° index in 0.8 s, trapezoidal profile (? ? accelerate, ? ? constant, ? ? decelerate).
| Item | Calculation | Result |
|---|---|---|
| Plate mass | 7,850 kg/m³ × π × 0.3² × 0.02 | 44.4 kg |
| Plate inertia | ½ × 44.4 × 0.3² | 2.00 kg·m² |
| Fixtures | 8 × 3 × 0.25² | 1.50 kg·m² |
| Total J | 3.50 kg·m² |
| Step | Calculation | Result |
|---|---|---|
| Peak table speed | 1.5 × θ ÷ t = 1.5 × 1.571 ÷ 0.8 | 2.95 rad/s (28.1 rpm) |
| Acceleration | ω ÷ (t/3) = 2.95 ÷ 0.267 | 11.0 rad/s² |
| Inertia torque | 3.50 × 11.0 | 38.6 N·m |
| + bearing and seal friction (estimate) | + 5 N·m | 43.6 N·m |
| With service factor 1.5 | 43.6 × 1.5 | 65.4 N·m |
| Ratio 59:1 → motor peak speed | 28.1 × 59 | 1,659 rpm |
| Motor peak torque (90% efficiency) | 43.6 ÷ (59 × 0.9) | 0.82 N·m |
| Table inertia seen by motor | 3.50 ÷ 59² | 1.0 × 10⁻³ kg·m² |
Torque alone would allow a 400 W servo. But a typical 400 W rotor has an inertia around 0.3 × 10⁻⁴ kg·m², giving a load-to-motor inertia ratio of about 33:1, which makes tuning sluggish. A 750 W servo (rotor around 1.1 × 10⁻⁴ kg·m²) brings it to about 9:1. This is common on index tables: inertia matching, not torque, decides the motor.
The reducer's acceleration torque must exceed 65 N·m; an 80-frame precision cycloidal reducer rated around 120 N·m with 240 N·m acceleration torque has ample margin. If two fixtures with 5 kg parts sit on one side at 250 mm, the tilting moment is 10 × 9.81 × 0.25 = 24.5 N·m, far below a typical 500 N·m output bearing rating.
Accuracy on station
At the fixture radius of 250 mm, 1 arcmin of lost motion is 0.073 mm of movement. If the process needs better, use the servo's position loop with a table-side encoder, or add a locating pin or clamp at each station.
References and standards
- ISO 230-2, Test code for machine tools — Determination of accuracy and repeatability of positioning of numerically controlled axes.
- VDI 2143, Motion rules for cam mechanisms (background on index motion profiles).
Frequently asked questions
Can a cycloidal reducer carry the table directly?
Yes. Precision cycloidal reducers with a flange output have a cross-roller or angular-contact output bearing that carries the table's weight and tilting moment, so the table bolts straight onto the output.
What index profile should I use?
A trapezoidal profile with one third accelerating, one third at constant speed and one third decelerating is a good default. Cam-like S-curve profiles reduce vibration further at the cost of a higher peak acceleration.
Do I need a brake or lock on an index table?
For light machining or pressing on the table, a clamp or brake takes the process load off the reducer. For assembly or inspection tables, the reducer's low backlash and the servo's holding torque are usually enough.
