cyclogramReflecting the load to the motor
A load does not reach the motor as kilograms but as an inertia on the shaft, set by how far it moves per motor turn. Everything behind a gearbox falls with the square of its ratio:
| Mechanism | Load inertia at the motor |
|---|---|
| Ball screw, lead p | m · (p / 2π)² / i² + J_screw / i² |
| Belt or rack, pitch diameter D | (m + m_belt) · (D / 2)² / i² + J_pulleys / i² |
| Rotary table | J_table / i² |
| On the motor shaft | J_coupling, J_gearbox as they are |
Why the ratio matters
A servo controls the load through its own rotor. When the load is many times heavier, the loop has to be tuned soft to stay stable, and the axis settles slowly and overshoots. Up to 10 times the rotor is the usual rule for a standard servo, 5 for a very dynamic axis, up to 30 with a stiff coupling and careful tuning. A stepper follows its ramp with about 5 times direct and 10 through a gearbox. A BLDC motor's maker states a permissible load inertia instead, and an induction motor on a drive has no loop to tune — there the ratio is only a caution.
Finding the gear ratio
ratio with a gearbox = ratio without / i² i needed = i_now · √( ratio / limit )- The default ball screw on the 400 W servo: 2.92. Nothing to do.
- The same screw on the 50 W servo: 30.4, so i = √(30.4 / 10), about 1.8 : 1.
- The default belt drive on the 400 W servo: 492. The page suggests about 7.1 : 1; with it the ratio is 9.76, just under the limit and marked Close. An 8 : 1 gearbox brings it to 7.7.
What a gearbox costs
A gearbox multiplies the motor speed by its ratio — the belt behind 7.1 : 1 turns its motor at 1627 rpm instead of 229 — so check the maximum speed; it loses a little to its efficiency; and it adds its own inertia at the motor shaft, which you can type in step 2. In return the torque the motor must give falls with the ratio: the belt's peak drops to 0.411 N·m.
Questions
Is an inertia ratio of 10 a hard limit?
No. It is the usual rule for a standard servo tuned without effort. Very dynamic axes want 5 or less; a stiff mechanism with careful tuning can run 30. Set your own limit under Limits in step 4.
Does the gearbox's own inertia count?
Yes — it sits on the motor shaft, so it counts in full. Type it with the gearbox in step 2. The suggested ratio counts the rotor only, so check the ratio again with the gearbox in.
Why does the ratio fall with the square of the gear ratio?
Because the load turns i times slower than the motor: its speed falls by i and its kinetic energy, which goes with speed squared, by i². The inertia the motor sees falls by the same i².
Why not take a bigger motor instead of a gearbox?
A heavier rotor lowers the ratio too, but it buys torque the move may not need. A gearbox also lowers the torque the motor must give, so a small motor with a gearbox is often the cheaper answer.
Related guides
- Axis sizing calculatorThe whole guided flow: motion, mechanism, motor, regeneration, and the move as a bar.
- Belt drive motor sizingPulley and motor speed, reflected inertia, torque, belt force — and the gearbox a belt axis needs.
- Servo motor sizingPeak torque at speed, RMS over the cycle, maximum speed and inertia ratio, each with its margin.
- Stepper motor sizingPull-out torque at speed over a safety factor, duty cycle, step rate and inertia ratio.
- Ball screw motor sizingSpeed, reflected inertia, torque per phase, RMS, critical speed and D·N for a ball screw axis.
Every term on this page, defined: the axis and motor sizing glossary.