Engineering · Motors & Drives
Gearbox Ratio and Reflected Inertia
What do the motor shaft see when a gearbox sits between it and the load?
A gearbox divides speed and multiplies torque by the ratio, but it also hides the load: the motor feels the load inertia divided by the ratio squared. This page shows the maths with live numbers: speed and torque through a gearbox, reflected inertia and the inertia ratio, a belt conveyor drive, a rotary table drive, the gear ratio that needs the least motor torque, and a comparison of gearbox types.
Speed out is the motor speed divided by the ratio. Torque out is the motor torque times the ratio times the efficiency. Power out is the motor power times the efficiency, so the gearbox never makes power; the difference is lost as heat.
The load inertia seen by the motor is the load inertia divided by the square of the ratio, so a ratio of 10 makes a load feel 100 times lighter. The motor also has to spin the gearbox input inertia. A low inertia ratio gives a stiff, easy-to-tune drive; a high one gives slow settling, overshoot and resonance. The limit depends on the coupling stiffness and on the motor maker’s advice.
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The moving mass is the belt, the product and the equivalent mass of the structure that moves with it. The total linear force is rolling resistance, friction and any incline. The extra inertia is for pulleys and rollers that turn with the belt.
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The load torque is friction plus the process torque. For indexing, add the torque that accelerates the load and the motor rotor itself. The peak torque is what the motor and drive must deliver for a short time.
At a low ratio the motor must supply a large torque to move the load. At a high ratio the load looks light, but the motor has to accelerate its own rotor much faster. The sum has a minimum. The speed limit of the motor sets the highest usable ratio. For a pure inertia load the best ratio is the square root of the load inertia divided by the motor inertia.
| Type | Efficiency | Backlash | Typical ratio | Good for |
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| Parameter | Typical range | Notes |
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Efficiency, backlash and inertia-ratio limits depend on the gearbox maker, the coupling and the motor. The values here are typical, to be checked against the catalogues. Isolate and lock out before working on a drive.