KEVOS® MAKEOS · Power Transmission
Reflected Inertia and Motor Acceleration Torque
What torque must the motor give to accelerate this load through the gearbox, and is the inertia ratio reasonable?
Load inertia reflected through a reduction, inertia ratio, acceleration torque and total motor torque to reach a speed in a given time against a load torque.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load inertia (at the load shaft) | kg·m² | Inertia of everything on the load side, about the load shaft (see the mass moment of inertia tool). |
| Motor rotor inertia | kg·m² | Rotor inertia from the motor data sheet (add gearbox input inertia). |
| Reduction ratio (motor ÷ load speed) | :1 | Gear ratio: motor speed divided by load speed. |
| Gearbox efficiency | % | Gearbox efficiency from the maker. |
| Load speed to reach | rpm | Speed the load must reach. |
| Acceleration time | s | Time allowed to reach that speed from rest. |
| Load torque at the load shaft | N·m | Steady torque at the load shaft from friction, gravity or process. |
Method and formulas
- Reflected inertia = J_L ÷ (i² η); inertia ratio = reflected ÷ J_m.
- Motor angular acceleration α = 2π n_L i ÷ (60 t).
- Motor torque = (J_m + J_L ÷ (i² η)) α + T_L ÷ (i η).
- Example: 2 kg·m² through 10:1 reflects as 0.022222 kg·m² (ratio 18.519); peak motor torque 9.5805 N·m.
Limitations
- Constant acceleration from rest; deceleration and duty cycle (RMS torque) need separate checks.
- Coupling and gearbox inertia should be added to the motor inertia.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a servo or induction motor and gearbox
- Check acceleration time of a conveyor or rotary table
- Choose a gear ratio for inertia matching
Who it is for
- Automation engineers
- Machine designers
What you get
- Reflected load inertia and inertia ratio
- Motor speed
- Acceleration and load torque at the motor
- Peak motor torque
Interpreting the result
- Many servo makers recommend inertia ratios of about 10:1 or less for good tuning; follow your drive maker’s guidance.
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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