Servo Motor Sizing Guide: Torque, Speed and Inertia
A preliminary sizing method from the motion profile to peak torque, RMS torque, maximum speed and reflected-inertia checks.
This content supports preliminary sizing and architecture decisions; it does not replace the selected product manual or machine risk assessment.
1. Gather the mechanical inputs
A reliable servo selection needs load mass or inertia, travel, screw pitch or pulley diameter, ratio and efficiency, friction, incline, target speed, acceleration time and cycle time. Measure unknowns or define a conservative range instead of assigning optimistic values.
- For rotary loads, reflect each component inertia to the motor shaft.
- For linear loads, use the screw, belt or rack conversion.
- Include gearbox inertia and efficiency in the model.
2. Derive motor speed from the mechanism
Maximum motor speed comes from translating load speed through the reduction ratio and transmission geometry to the motor shaft. The result must remain below the permitted motor speed, drive output limit and critical speed of the mechanical components.
3. Calculate acceleration and peak torque
Acceleration torque is total inertia multiplied by angular acceleration. The highest instantaneous motor demand is the worst same-direction combination of acceleration, load and friction torque. Gravity torque is also included for a vertical axis.
T_acc = J_total × αT_peak = T_acc + T_load + T_friction
4. Check thermal suitability with RMS torque
Peak torque checks only the acceleration instant. Motor heating over the cycle is assessed with RMS torque using the torque and duration of every segment. RMS torque must remain below continuous torque capacity at the corresponding speed range.
T_rms = √(Σ(Tᵢ² × tᵢ) / Σtᵢ)
5. Evaluate reflected inertia ratio
After load inertia is reflected to the motor shaft, it is divided by motor rotor inertia. A lower ratio generally makes tuning easier, but there is no single universal acceptance limit. The permitted ratio depends on mechanical stiffness, motion quality, control bandwidth and manufacturer data for the selected servo family.
When reduction ratio i is defined as motor speed / load speed, load inertia reflects to the motor side divided by i². This is why reduction can strongly reduce the inertia seen by the motor.
Inertia ratio = J_load,reflected / J_motorJ_load,reflected = J_load / i² (i = motor speed / load speed)
6. Validate the motor on its torque-speed curve
Plot candidate peak torque, RMS torque and maximum speed on the same torque-speed curve. Supply voltage, drive model, ambient temperature and a braked motor option can change the curve. One nominal catalogue value does not prove the operating point.
7. Close the calculation with commissioning data
At first run, record the drive torque trace, actual acceleration time, position error and regenerative bus rise. If measurement and calculation do not agree, recheck friction, load mass, gearbox efficiency and the motion profile. Preliminary sizing is complete only after this feedback loop.
Frequently asked questions
Can a servo motor be selected only by kW rating?
No. Peak torque, RMS torque, maximum speed, inertia ratio and the actual duty cycle must be validated together.
Is there one correct inertia-ratio limit?
No. The acceptable ratio depends on mechanical stiffness, performance target and manufacturer data. Use the selected family manual.
Technical sources
Sources are publications from standards owners and manufacturers.