The Gearbox That Reversed Into Position
We picked a standard (economy) planetary gearbox for a positioning axis. The gearbox was rated for 10 arc-minutes of backlash. On the machine, when the axis reversed direction, it took a small jump before catching up. The positioning accuracy was ±0.1 mm, but the spec called for ±0.03 mm. The backlash was the problem: 10 arc-minutes at the output, through a 5 mm lead screw, translated to about 0.015 mm of lost motion. Combined with other errors (coupling wind-up, screw backlash), the total was over spec. We upsized to a precision gearbox with 1 arc-minute backlash. The reversal jump disappeared. The mistake was picking the cheapest gearbox, not accounting for backlash in the total accuracy budget.
Gearbox backlash selection is matching the gearbox’s lost motion to the system’s accuracy requirement. This article covers the backlash ratings and when to pay for precision.
What Is Backlash?
Backlash is the lost motion when the gear reverses direction. The gear teeth have clearance between them. When the input reverses, the output doesn’t move until the gears re-engage. This angle (in arc-minutes or arc-seconds) is the backlash.
Backlash shows up as a dead zone at reversal. Command the axis to move +10 mm, then -10 mm. The actual position lags by the backlash amount before the motion starts.
Backlash Ratings (Arc-Minutes)
Gearboxes are rated by backlash (in arc-minutes at the output shaft):
| Class | Backlash | Typical Cost | Best For |
|---|---|---|---|
| Economy (standard) | 10–20 arc-min | Base | Conveyors, transport, no precision |
| Precision | 3–8 arc-min | 1.5–2× base | General positioning |
| Low-backlash (precise) | 1–3 arc-min | 2–3× base | CNC, dispensing, precision |
| Zero-backlash (preloaded) | <1 arc-min (or zero) | 3–5× base | High-precision, metrology |
1 arc-minute is 1/60 of a degree = 0.0167°. At the output of a 10:1 gearbox, a 1 arc-min backlash means the input can rotate 10 arc-min before the output moves. Translated through a 5 mm lead screw: 1 arc-min at the output = (1/60) × (5/360) = 0.00023 mm. Very small. But 10 arc-min = 0.0023 mm. Combined with other errors, it adds up.
Step 1: Translate Backlash to Linear Position Error
The gearbox backlash at the output, through the screw lead, becomes a linear position error:
e_backlash = backlash_rad × lead / (2π)
Where backlash_rad is the backlash in radians (arc-min × π/10800), and lead is the screw lead (mm/rev).
For 10 arc-min backlash: backlash_rad = 10 × π/10800 = 0.0029 rad. Lead = 5 mm. e = 0.0029 × 5 / (2π) = 0.0023 mm. For 1 arc-min: e = 0.00023 mm.
This is just the gearbox backlash. Add the screw backlash (if not preloaded), coupling wind-up, and linear encoder error. The total accuracy budget is the sum.
Step 2: Accuracy Budget
The system’s total position error is the sum of all error sources:
- Gearbox backlash: 0.002 mm (for 10 arc-min).
- Screw backlash (if not preloaded): 0.01–0.05 mm. Use preloaded nut to eliminate.
- Coupling wind-up (torsional): 0.001–0.005 mm (under load).
- Screw lead error: 0.01–0.05 mm per 300 mm (from manufacturing).
- Encoder resolution: see article 77.
If the spec is ±0.03 mm total, the gearbox backlash must be a small part of that. A 10 arc-min gearbox (0.002 mm) is fine. But if the spec is ±0.01 mm, use a 1 arc-min gearbox (0.0002 mm) to leave room for other errors.
The backlash rule: Calculate the linear error from the gearbox backlash: e = backlash_rad × lead / 2π. Add it to the total accuracy budget. If the spec is tight (under ±0.05 mm), use a precision gearbox (under 3 arc-min). For general positioning (±0.5 mm), an economy gearbox is fine. The gearbox that jumped on reversal was 10 arc-min — over the budget for a precision axis.
Types of Gearboxes
Planetary Gearbox
The standard for servo drives. Coaxial (input and output on the same axis). High torque capacity. Backlash from 1 arc-min (precision) to 20 arc-min (economy). Most common.
Harmonic (Strain Wave) Gearbox
Zero backlash (the flexspline preloads the gear teeth). Very high reduction ratios (50:1, 100:1) in one stage. But lower torque capacity and more expensive. For robots and precision rotary axes.
Worm Gearbox
Right-angle (input perpendicular to output). Self-locking (the worm can’t back-drive). But low efficiency (50–70%). Backlash is high (30+ arc-min). Not for precision positioning. For conveyors and right-angle drives.
| Type | Backlash | Efficiency | Best For |
|---|---|---|---|
| Planetary (economy) | 10–20 arc-min | 95% | Conveyors, transport |
| Planetary (precision) | 1–5 arc-min | 95% | Servo positioning |
| Harmonic | <1 arc-min (zero) | 70–80% | Robots, rotary axes |
| Worm (right-angle) | 30+ arc-min | 50–70% | Conveyors, right-angle, self-locking |
Backlash Changes Over Time
Gearboxes wear. The backlash increases as the gears wear in. A new gearbox at 3 arc-min might be 5 arc-min after a year. The precision is degraded.
- Preloaded gearboxes: The gears are spring-loaded to take up backlash. They maintain low backlash over time (but generate more heat and friction).
- Lubrication: Proper lubrication slows wear. A gearbox run dry wears fast.
- Don’t oversize: A gearbox loaded at 20% of its rating lasts longer than one loaded at 90%. De-rate for life.
Right-Angle vs. In-Line
For a servo-driven axis, the gearbox can be in-line (coaxial) or right-angle (90°).
- In-line (coaxial): The motor and screw are on the same axis. Compact length. Standard for linear axes.
- Right-angle: The motor sticks out to the side. Saves axial length (the motor is perpendicular). For tight spaces. But slightly more backlash and cost.
Use in-line when the motor can be inline with the screw. Use right-angle when the motor would hit something (space constraints).
A Gearbox Selection Checklist
- What is the required accuracy? (mm total.)
- Calculate e_backlash = backlash_rad × lead / 2π.
- Is the gearbox backlash within the accuracy budget?
- What type? (Planetary, harmonic, worm?)
- What ratio? (See article 54.)
- In-line or right-angle? (Space.)
- What is the rated torque? (Continuous and peak.)
- Does the reflected inertia match? (J_reflected = J_load / i².)
- Is the gearbox preloaded? (For maintaining low backlash.)
- What lubrication? (Grease packed, or oil?)
- Is the gearbox rated for the RPM? (Input speed limit.)
- Is there a warranty? (Backlash specification over time?)
The Bottom Line
Gearbox backlash selection is part of the accuracy budget. The gearbox that jumped on reversal was an economy 10 arc-min unit in a precision axis. Translate the backlash to linear error (e = backlash × lead / 2π), add it to the total error budget, and pick a precision gearbox (under 3 arc-min) for tight specs. For general transport, economy is fine. The axis that reverses without a jump wasn’t the most expensive gearbox — it was one whose backlash fit the accuracy budget.
