KEVOS® MAKEOS · Power Transmission
Gear Ratio for Inertia Matching (Optimum Ratio and Motor Torque)
What gear ratio lets this motor accelerate the load with the least torque, what ratio can I actually use within the motor speed, and does the motor have the torque at my chosen ratio?
Gear ratio selection for accelerating a load inertia: reflected inertia, inertia ratio, motor speed, acceleration torque, load torque at the motor and peak motor torque at your chosen ratio (as the reflected inertia tool), the ratio that minimises acceleration torque (load inertia reflected equal to the motor inertia), the best ratio allowed by the motor’s top speed, the motor torque at that ratio, and checks of the chosen ratio against the motor speed and peak torque.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load inertia | kg·m² | Inertia of the load at the gearbox output. |
| Motor inertia | kg·m² | Inertia of the motor rotor (and brake). |
| Chosen ratio | :1 | Gear ratio being considered. |
| Gearbox efficiency | % | Gearbox efficiency. |
| Load speed to reach | rpm | Speed the load must reach. |
| Acceleration time | s | Time to reach it. |
| Load torque | N·m | Steady load torque at the output. |
| Motor top speed | rpm | Highest motor speed. |
| Motor peak torque | N·m | Peak torque the motor and drive can give. |
Method and formulas
- Reflected inertia J_r = J_L ÷ (i² η); motor speed = n_L i; α = 2π n_m ÷ (60 t) (as the reflected inertia tool).
- Motor torque T(i) = (J_m + J_r) α + T_L ÷ (i η).
- Optimum ratio for acceleration i_opt = √[J_L ÷ (η J_m)]; best usable ratio = min(i_opt, n_max ÷ n_L).
- Example: at 10:1 the motor needs 9.5805 N·m; the optimum would be 43.033:1 but the motor speed allows 20:1, needing 5.3558 N·m.
Limitations
- Constant acceleration and rigid transmission; compliance and backlash change real tuning.
- Load torque is taken as constant during acceleration.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a gearbox ratio for a servo axis or indexer
- See how far a ratio is from the optimum
- Check a motor’s peak torque at the ratio
Who it is for
- Automation engineers
- Machine designers
- Controls engineers
What you get
- Reflected inertia, ratio and motor torque at the chosen ratio
- Optimum and best usable ratio
- Speed and torque checks
Interpreting the result
- Near the optimum ratio the torque curve is flat: a ratio within ±30% of it costs little extra torque.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 180–186, 2569–2580. Topic reference; no source tables or recommended settings are reproduced.
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Open the Gear Ratio for Inertia Matching (Optimum Ratio and Motor Torque) calculator
