- Load inertia
- 2.500e-2 kg·m²
- Reflected to motor
- 1.000e-3 kg·m²
- Inertia ratio
- 3.7 : 1
- What it means
- Easy to tune for most motion.
The short answer
Inertia ratio = load inertia reflected to the motor ÷ motor rotor inertia, where reflected inertia = load inertia ÷ (gear ratio)². Ratios below about 10:1 are usually easy to tune; above that, response gets slower and resonance more likely, so a gearbox, a higher-inertia motor or a stiffer coupling is often the fix. Each servo maker publishes its own limits.
Formula
Solid disc or cylinder: J = ½ × m × r²Reflected inertia: J_reflected = J_load ÷ i²Inertia ratio = J_reflected ÷ J_motor
How to use it
- Enter the load inertia directly, or its mass and diameter for a solid disc.
- Enter the reduction ratio (1 for direct drive).
- Enter the motor rotor inertia from its data sheet, in the same units.
Assumptions
- Units are kg·m² throughout (1 kg·cm² = 0.0001 kg·m²).
- Gearbox and coupling inertia are not included; add them to the motor inertia side if they are significant.
Frequently asked questions
What inertia ratio is acceptable for a servo?
It depends on the maker and on how stiff the mechanics are. Many guides treat up to about 10:1 as comfortable for general motion, and much lower ratios for high-response axes. Direct-drive and very stiff mechanics can run far higher. Check the motor maker’s sizing guide.
How does a gearbox change inertia ratio?
Reflected inertia falls with the square of the ratio, so a 5:1 reduction divides the load inertia seen by the motor by 25.
What are the signs of a ratio that is too high?
Overshoot, ringing at stop, audible resonance and following-error alarms that only clear when gains are lowered so far that the axis becomes sluggish.