Stepper motor sizing

A stepper is sized on its pull-out torque, not its holding torque, with a safety factor — and it runs warm even standing still. The calculator below, set up with a NEMA 23 stepper, checks all of it for your move: pull-out torque at speed, duty cycle, step rate and inertia ratio.

Holding versus pull-out ↓ Worked example ↓ Where steppers stop ↓

Beta. Every formula is written out under “Show calculation” and checked against published catalogue examples, but check your supplier's data before you order anything. Found a mistake? Write to [email protected].

Holding torque is not what it gives

The holding torque on the catalogue's first line is what a stepper holds at standstill. Turning, it gives its pull-out torque, which starts near the holding torque and falls away with speed as the windings run out of time to fill with current. Without the motor's own curve the page takes it flat up to a corner speed and falling as 1/n beyond, and lets the move use it over a safety factor:

T_pull(n) = T_hold n ≤ n_c T_pull(n) = T_hold · n_c / n n_c < n ≤ n_max usable = T_pull / SF SF = 2 by default step rate = n / 60 · 360 / θ_step steps/s

A worked example

A generic NEMA 23 stepper — 1.2 N·m holding torque, the torque holding to 300 rpm, a 1500 rpm maximum — on the default 10 mm ball screw, moving 100 mm in 1 s in thirds with a 1.5 s dwell:

Where steppers stop

The same motor on the default move — 200 mm in 0.5 s, 3600 rpm at the motor — fails twice. 3600 rpm is past its 1500 rpm maximum, and at 1500 rpm its usable torque is 0.12 N·m against the 0.289 N·m the move needs. Above about 1000 rpm a stepper has little torque left; a servo or a closed-loop stepper suits such a move better.

The duty cycle

A stepper draws its full current standing still, so it heats over the whole cycle, not just while it moves. The page warns — marked Hot — when the motor moves for more than half the cycle: lengthen the dwell, or let the driver reduce the standstill current.

Questions

What safety factor should a stepper have?

2 is the usual rule, 1.5 where the load and the friction are well known. Open loop forgives nothing: a stall is a lost position, found only at the next homing.

Does microstepping change the torque?

It smooths the motion and refines the resolution, but it does not add torque. Size on the pull-out torque your driver's curve gives.

Can I enter the pull-out curve?

Yes. A motor file can carry the pull-out curve as speed–torque pairs, and the page then uses it instead of the generic shape.

Why does the driver's supply voltage matter?

A higher supply fills the windings faster, so the pull-out torque holds to a higher speed. Type the corner speed for your driver and voltage, or use its curve.

What inertia ratio suits a stepper?

About 5 when it drives the load directly and 10 through a gearbox is the usual rule; beyond it the motor tends to miss steps on the ramp.

Sources

Related guides

Every term on this page, defined: the axis and motor sizing glossary.