Motor inertia and torque calculator
A gearbox reduces reflected inertia by the square of its ratio, which is usually the only practical way to match a large load to a small motor.
kg m2
kg m2
rpm
s
N m
Peak motor torque required
1.1972N m
- Reflected load inertia
- 0.0005 kg m2
- Inertia ratio
- 1.000 Excellent — easy to tune
- Torque to accelerate
- 1.0472 N m
- Reflected friction torque
- 0.1500 N m
- Peak mechanical power
- 250.7
- Angular acceleration
- 1047.20 rad/s2
- Inertia ratio is within the usual guideline
- 1
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- Load inertia = 0.05
- Motor inertia = 0.0005
- Gear ratio = 10
- Target speed = 2000
- Acceleration time = 0.2
- Friction torque at the load = 1.5
- Reflected load inertia = 0.05 / 10^2 = 0.0005
- total_inertia = 0.0005 + 0.0005 = 0.001
- Inertia ratio = 0.0005 > 0 ? 0.0005/0.0005 : 0 = 1
- omega = 2000 * 2 * pi / 60 = 209.44
- Angular acceleration = 0.2 > 0 ? 209.44/0.2 : 0 = 1047.2
- Torque to accelerate = 0.001 * 1047.2 = 1.0472
- Reflected friction torque = 1.5 / 10 = 0.15
- Peak motor torque required = 1.0472 + 0.15 = 1.1972
- Peak mechanical power = 1.1972 * 209.44 = 250.74
- Inertia ratio is within the usual guideline = 1 <= 10 ? 1 : 0 = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- reflected inertia = load inertia / gear ratio squared
- torque = total inertia x angular acceleration + friction
A ratio under 10:1 is the usual servo guideline, and under 5:1 for high-bandwidth work. Steppers tolerate more because they run open loop.
The gearbox also divides the speed, so a high ratio can push the motor past its own speed limit.