How to size a linear actuator

Sizing a linear actuator means proving three things: the actuator's rated load covers the payload with a safety factor, the motor delivers the required torque at the required speed with margin, and the load inertia reflected to the motor is small enough for it to control. Five inputs — payload, speed, travel, orientation, and acceleration time — are enough to check all three. Here is the method the Engineering Decision Engine runs, with a worked example.

Step 1 — Fix the five inputs

Payload is everything the carriage moves, including the tool, gripper, cables and any stacked axis — on a gantry the X axis carries the entire Y actuator. Speed is the commanded plateau speed of the move. Travel is the stroke, which determines the actuator length and, on a screw, the critical speed. Orientation is horizontal or vertical; vertical adds gravity torque and a holding requirement. Acceleration time is how long the move takes to reach speed — 0.25 s is a sensible default for lab and light-assembly axes; 0.1 s is aggressive and roughly doubles acceleration torque.

Step 2 — The load gate

Rated capacity must be at least twice the payload. The 2× factor covers the gripper you add later, the acceleration forces, and the moment loads a catalog rating does not describe. An SBA45 is rated 1 kg direct-drive and 7 kg with its 3:1 gearbox, an SBA60 3.5 kg and 10 kg, an SBA90 7 kg direct and 25 or 50 kg with a 3:1 or 5:1 gearbox, an LSA45 7 kg, an LSA60 15 kg. The engine treats this as a hard gate: a product that fails it is never recommended, however good the torque numbers look.

Step 3 — Required torque at the motor

Convert the linear move to the motor shaft. On a belt, one revolution moves one pulley circumference (65 mm on an SBA45, 160 mm on an SBA90); on a screw, one lead. Motor speed in rev/s is the linear speed divided by that distance. Required torque is the sum of three terms: acceleration torque (total moving inertia × angular acceleration), gravity torque on a vertical axis (payload × g × distance per revolution ÷ 2π ÷ efficiency), and friction or thrust torque. Total moving inertia includes the payload, the carriage, the belt and pulleys or the screw itself, and the motor's own rotor. Belt efficiency is about 95%, a ball screw about 90%, a lead screw 30 to 50% — which is why a lead screw needs noticeably more torque for the same job.

Step 4 — Torque margin at speed

Motors do not deliver their nameplate torque at speed. A stepper's pull-out torque falls steeply with rpm; a servo's continuous torque is nearly flat to its rated speed. Read the available torque from the motor's curve at the rev/s from step 3 — the engine uses the NEMA 17/23/34 stepper curves at 24 V and the NV servo continuous curves at 48 V — and require at least 25% more than the step-3 total. Then sweep the family: the smallest motor that clears 25% wins, because a larger motor adds rotor inertia and cost without adding capability you use.

Step 5 — Inertia mismatch

Divide the load inertia reflected to the motor shaft by the motor's rotor inertia. Above about 10:1 a stepper loses positional accuracy and a servo becomes hard to tune. On belt axes the engine treats 10:1 as a hard maximum; screw axes are exempt because the lead already reduces reflected inertia by the lead-to-circumference ratio squared. When a belt axis exceeds 10:1, a 3:1 or 5:1 planetary gearbox reduces reflected inertia by 9× or 25× — the engine computes the fix, including the gearbox's own inertia, and re-sweeps the motor family.

A worked example

XY system, 2.5 kg payload, 500 mm/s, 500 × 500 mm, stepper, 0.25 s acceleration. The X axis carries the payload plus the Y actuator (2.47 kg including its gearhead): 4.97 kg moving mass. Pulley 20.7 mm → 23.07 rev/s at 500 mm/s. Required torque 5.75 oz-in, all acceleration (horizontal, no thrust). Family sweep on NEMA 17 with the integral 3:1 gearbox: N17-1 clears torque but misses inertia at 12.5:1; N17-2 at 11.0:1; N17-3 passes at 291% torque margin and 8.2:1 mismatch and is selected; N17-4 would also pass at 334% and 6.9:1 but is larger than needed. Speed margin 48%. Move profile: 1.25 s per 500 mm move, 2.5 s out-and-back, 24 cycles/min maximum. Part: SBA45 500 mm motor-down stepper with 3:1 gearbox, $1,800, with a BLC-2T controller.

Common mistakes

Forgetting the stacked axis in the X payload is the most frequent one; the second is choosing a fast screw lead and then discovering the load rating at that lead is 1 kg; the third is sizing a stepper on its holding torque instead of its torque at speed, which can be a factor of three apart at 20 rev/s. Writing the moving-mass chain down — payload, tool, cables, stacked actuator, gearhead — before touching a torque curve prevents most of them.