Servo Motor Sizing
Calculates peak torque, RMS torque, speed and inertia ratio from the motion profile for ballscrew, belt, rack & pinion and rotary table axes; suggests a gearbox ratio and checks your motor against its torque-speed curve. Brand-independent.
// Mechanism
// Motion profile
// Gearbox
// Motor (for checking)
Check the inputs (positive values, acceleration ratio 2–50 %)
// Simulation
Torque-speed diagram
Frequently asked questions
What should the inertia ratio be?
A common rule is that load inertia should not exceed 10 times the rotor inertia. Highly dynamic axes aim for 3–5:1, low-dynamic applications can go up to 20–30:1. A high ratio makes tuning harder and causes oscillation; a gearbox reduces the reflected inertia by the square of the ratio.
Why does RMS torque matter?
Motor heating is determined by the time average of torque squared, so the RMS torque over the cycle must stay below the motor's continuous (rated) torque. Dwell time lowers the RMS torque; on a vertical axis the holding torque during dwell raises it.
What safety factor should I use?
Typically 1.2–2, to cover friction not included in the calculation, efficiency uncertainty, cable chain forces and future load increases. The tool multiplies peak and RMS torque by your factor before comparing them with the motor limits.
How is the gearbox ratio chosen?
The motor's maximum speed sets the upper limit (i ≤ n_motor / n_load). The inertia ratio target sets the lower limit. For a purely inertial load, the ratio that minimises acceleration torque is i_opt = √(J_load / J_m). The tool suggests the standard ratio closest to the optimum within this range.
Trapezoidal or S-curve?
An S-curve limits jerk (rate of change of acceleration), reducing mechanical vibration and overshoot. For the same move time, however, peak acceleration rises (twice as high for a full S-curve), which increases peak torque. Adjust the jerk ratio to see the trade-off.
Which efficiency values are typical?
Typical values: ballscrew 0.85–0.95; lead (trapezoidal) screw 0.3–0.5; timing belt 0.95–0.98; rack & pinion 0.9–0.95; planetary gearbox 0.94–0.97 per stage. Use manufacturer data when available.
What about vertical axes?
Gravity requires continuous torque both while moving and at rest, raising the RMS torque. Because the load falls when power is removed, a motor with a holding brake is needed; some designs add a counterweight or gas spring.
What does this calculation not cover?
Ballscrew critical speed and buckling, bearing and guide life, belt stretch, cable chain forces and drive current limits must be checked separately. The motor torque-speed curve is approximated from the values you enter; use the manufacturer's catalogue curve for the final selection.