Gearbox Heat: The Number You Forgot to Calculate
Every gearbox absorbs a slice of input power as heat. The slice depends on type, stage count, and quality grade. If you size the motor for the load torque and skip the heat check, the gearbox housing tells you about it at 70°C — hot enough to burn a finger, too hot for the grease to last.
The starting equation
P_loss = P_motor × (1 − η)
Where η is the gearbox efficiency. For a 400 W servo through a 2-stage planetary (η = 0.93): P_loss = 400 × 0.07 = 28 W. That 28 W has to leave the gearbox housing. A bare housing in still air dissipates roughly 15–25 W depending on surface area. You’re already over budget.
Efficiency by gearbox type
| Type | η per stage | 2-stage total | Heat at 400 W input |
|---|---|---|---|
| Planetary (standard) | 0.96–0.97 | 0.92–0.94 | 24–32 W |
| Planetary (low-backlash) | 0.94–0.96 | 0.89–0.92 | 32–44 W |
| Helical inline | 0.97–0.98 | 0.94–0.96 | 16–24 W |
| Worm (single stage) | 0.50–0.70 | — | 120–200 W |
| Hypoid / bevel-helical | 0.95–0.97 | 0.90–0.94 | 24–40 W |
Worm gearboxes are the trap. A 0.50 efficiency means half your input power becomes heat. At 400 W that’s 200 W — you need forced air or a water jacket, and even then continuous duty is marginal. The self-locking property that makes worm gearboxes attractive for vertical axes is the same thing that destroys efficiency. Pick planetary or helical-bevel for continuous servo duty.
Continuous vs intermittent duty
The heat equation doesn’t care about duty cycle on its own. What matters is whether the gearbox has time to cool between bursts. An axis that moves 10 seconds out of every 60 averages 17% power, so P_loss averages 5 W — no problem. A conveyor running 24/7 averages 100%, so the housing climbs to equilibrium temperature until P_loss = P_dissipated. Equilibrium is where the housing stops getting hotter.
Find the gearbox’s rated continuous output torque in the catalog. That number already accounts for heat. If your RMS torque (over the motion profile) is below it, the gearbox won’t overheat. If you’re above it, you need either a bigger gearbox, lower duty cycle, or active cooling.
Getting rid of the heat
Mount to metal. A planetary gearbox bolted directly to an aluminum extrusion frame sheds heat through the frame. The extrusion’s surface area is dozens of times the gearbox housing. Use thermal paste between the mounting flange and the frame. This alone drops equilibrium temperature by 15–25°C. The 70°C gearbox in the field was hanging on a thin bracket — no heat path to anything.
Add a fan or heat sink. For larger gearboxes (over 1 kW input), a forced-air fan mounted on the housing increases natural convection by 2–3×. Aluminum heat-sink shrouds bolt over the housing.
Derate the duty cycle. If the motor profile has long high-torque bursts, calculate the RMS torque. The gearbox sees the RMS, not the peak. A 10 N·m peak for 2 seconds every 10 seconds averages about 3 N·m — well within a 10 N·m continuous rating.
The inertia check
Gear ratio selection affects both reflected inertia and torque. A higher ratio reduces the reflected inertia by the square of the ratio — good for servo tuning. But it also multiplies output torque and adds efficiency loss per stage. Don’t over-ratio: a 20:1 gearbox on a light load wastes torque and generates heat for no reason. Match the ratio to the motor’s rated speed (3000 rpm for most servos) and the load’s required speed.
J_reflected = J_load / (ratio)²
Aim for J_reflected / J_motor ≤ 5. If you’re at 20:1 and the ratio is only there to slow the motor down, a larger pulley or a lower motor speed might be the better call.
Quick decision: If you’re choosing between gearbox types for a continuously-running servo axis, the answer is almost always 2-stage planetary (93–95% efficiency) mounted to a metal frame. Worm gearboxes belong on slow, self-locking applications — not on axes that run 24/7.
The number to remember
For any gearbox on a continuously-running axis: calculate P_loss = P × (1 − η). If that number exceeds 25 W, plan the heat path. If it exceeds 50 W, you need active cooling or a bigger unit. The gearbox that ran cool after 8 hours wasn’t the largest one — it had a bolted heat path to the frame.
