Application: Machine tools
Gearboxes for CNC rotary and tilting axes: accuracy budget and clamping
How much angular error your part can tolerate, which reducer meets it, and why rotary axes should clamp during heavy cuts. With an accuracy table by part radius.
Key takeaways
- Angular error × part radius = position error on the part. Work out your angle budget first.
- Harmonic drives suit compact 4th axes; cycloidal and RV reducers suit heavier trunnions and interrupted cuts.
- Clamp the axis during heavy cutting so the reducer only positions.
Start with the accuracy budget
A rotary axis error of θ radians moves a feature at radius r by r × θ. The table shows the angular accuracy needed to keep the error at a feature to 0.01 mm:
| Feature radius | Allowed angle |
|---|---|
| 50 mm | 41 arcsec |
| 100 mm | 21 arcsec |
| 200 mm | 10 arcsec |
| 300 mm | 7 arcsec |
Backlash is only one part of this budget; the reducer's transmission error, torsional wind-up under cutting load and thermal growth add to it. Below about 20 arcsec most builders close the loop with an encoder on the table.
Which reducer
| Machine | Reducer | Strength |
|---|---|---|
| Router / small mill 4th axis | Harmonic drive, hollow | Near-zero backlash, compact, through-bore |
| VMC 4th axis, medium trunnion | Precision cycloidal | Stiff, handles interrupted cuts |
| Large trunnion, heavy fixtures | RV reducer | Highest stiffness and moment capacity |
Worked example: holding torque
A 500 N tangential cutting force on a feature 100 mm from the axis creates 500 × 0.1 = 50 N·m on the axis, reversing as the cutter's teeth engage. A harmonic drive's torsional stiffness at low load is its softest region, so under a reversing 50 N·m it winds up measurably. A pneumatic or hydraulic clamp holding the table during the cut removes this load from the gearbox entirely.
References and standards
- ISO 230-2, Test code for machine tools — Determination of accuracy and repeatability of positioning of numerically controlled axes.
- ISO 230-1, Test code for machine tools — Geometric accuracy of machines operating under no-load or quasi-static conditions.
Frequently asked questions
Is a harmonic drive good for a CNC 4th axis?
For compact 4th axes on routers and small mills, yes: near-zero backlash and a hollow bore for the chuck or drawbar. For heavy interrupted cuts, a stiffer cycloidal or RV reducer, or a clamp during cutting, is better.
How accurate does a rotary axis need to be?
Convert your part tolerance to an angle: angle in radians = allowed error ÷ radius. For 0.01 mm at a 100 mm radius that is about 21 arcsec, which needs a zero-backlash-class reducer and often an encoder on the table.
Why clamp a rotary axis during cutting?
Cutting forces are large and fluctuating. A clamp takes them off the reducer, so the drive only positions, which protects accuracy and life.
