The Motor That Tripped on Acceleration: Inertia Mismatch, Not Undersized Motor
A servo motor driving a belt axis. The motor tripped on overcurrent every time the axis accelerated. The motor was rated for 400 W. The load was 5 kg. On paper, it should have been fine. The acceleration was 2 m/s². The torque needed was F × r = (5 × 2) × (pulley radius 0.05 m) = 0.5 Nm. The motor was rated for 1.27 Nm. So why was it tripping?
The inertia mismatch
The motor’s rated torque is the continuous torque. The peak torque (for acceleration) is 2-3x that. But the inertia ratio (load inertia / motor rotor inertia) matters. If the load inertia is much larger than the motor’s rotor inertia, the motor has to work harder to accelerate it. The servo drive sees a current spike during acceleration and faults out.
Our motor’s rotor inertia was 0.03 kg·cm². The load (5 kg on a Ø100 pulley) had inertia J = m·r² = 5 × 0.05² = 0.0125 kg·m² = 125 kg·cm². The inertia ratio was 125/0.03 = 4160:1. That’s absurd. The motor was tiny for the load. The catalog torque was fine for steady-state, but the acceleration torque needed to spin up that inertia was enormous.
The inertia ratio rule
| Inertia ratio (load/motor) | Performance | Use case |
|---|---|---|
| <5:1 | Excellent, high bandwidth | Precision positioning |
| 5:1 to 10:1 | Good, standard | Most automation |
| 10:1 to 30:1 | Acceptable, lower bandwidth | Slow moves, long settle |
| 30:1 to 100:1 | Marginal, may overheat | Only with gearbox |
| >100:1 | Will fault or overheat | Undersized motor |
We were at 4160:1. No wonder it tripped.
The fix
Option 1: Bigger motor. A larger motor with more rotor inertia. A 750 W motor has rotor inertia of about 0.2 kg·cm². The ratio drops to 125/0.2 = 625:1. Still too high.
Option 2: Gearbox. A gearbox reduces the reflected inertia by the square of the ratio. With a 10:1 gearbox, the reflected inertia drops by 100x. The 125 kg·cm² load becomes 1.25 kg·cm² at the motor. With the 400 W motor (0.03 kg·cm²), the ratio is 42:1. Acceptable. The gearbox also increases the torque (10x), so the motor has more torque available.
Option 3: Reduce the pulley diameter. The load inertia scales with r². A smaller pulley (Ø50 instead of Ø100) reduces inertia by 4x. But it also reduces the speed for the same motor RPM. The axis would be slower.
We used the gearbox. A 10:1 planetary gearbox. The inertia ratio dropped to 42:1. The motor stopped tripping. The axis accelerated smoothly.
The calculation
For a belt-driven axis, the load inertia at the motor shaft is:
J_load = m · r² + J_pulley
Where m is the total moving mass (kg), r is the pulley radius (m), and J_pulley is the pulley’s own inertia (small, usually negligible). The inertia ratio is J_load / J_motor. For servo motors, keep this under 30:1. If it’s higher, add a gearbox or use a bigger motor.
What we learned
The motor torque was fine for steady-state. The problem was acceleration torque. The servo drive faults on peak current, which happens during acceleration. If the motor trips only on accel (not steady-state), it’s an inertia mismatch. Don’t just turn up the current limit — fix the ratio.
The inertia rule: If the motor faults on acceleration, check the inertia ratio. Keep it under 30:1. Use a gearbox for high-inertia loads. The motor that tripped wasn’t undersized on torque — it was undersized on rotor inertia. A bigger motor or a gearbox fixes it.
