Axis and motor sizing calculator

What the six steps work out

1. The motion. The distance or angle and the move time; the dwell at the end, the move back to the start and the rest at home, each switched on or off; a trapezoidal or S-curve profile; the orientation, the guide friction and any external force. Out come the peak speed, acceleration and jerk — over the whole cycle.
2. The actuator and the load. A ball screw, a belt drive, a rack and pinion, a rotary table or a pneumatic cylinder, an optional gearbox, and the parts that move. Out come the travel per motor turn and the inertia the motor sees.
3. The motion, drawn. Position, speed, acceleration and motor speed over the cycle, and the mechanism's own limits — a screw's critical speed and D·N, the force in a belt or at a rack's teeth. A cylinder's stroke is drawn as its air allows.
4. The motor. A servo, a stepper, a BLDC motor or an AC induction motor on a drive: the torque in every phase, the RMS over the cycle, and four checks with their margins, drawn on the motor's speed–torque map; up to two more motors can stand beside it, judged on the same move, each by its own kind's rules, on one map and in one table. A cylinder has no motor: here it gets its force, each way, and its stroke time.
5. Regeneration. The energy that comes back while the axis brakes, against what the drive's bus can absorb — and the brake resistor when it cannot.
6. Send to Cyclogram. The move becomes a bar on your cycle diagram: the move out, the stay at the end, the move back.

Guides by topic

Each guide opens the same calculator, set up for its question, and works through the formulas with a full example underneath.

• Ball screw motor sizingSpeed, reflected inertia, torque per phase, RMS, critical speed and D·N for a ball screw axis.
• Belt drive motor sizingPulley and motor speed, reflected inertia, torque, belt force — and the gearbox a belt axis needs.
• Rack and pinion motor sizingPinion and motor speed, the inertia the motor sees, torque, the force at the teeth — and the gearbox.
• Rotary table motor sizingTable and motor speed, the inertia of discs and parts off the axis, the indexing torque — and the gearbox.
• Pneumatic cylinder stroke timeForce out and in, the load ratio, the stroke time the air allows, and the air each cycle costs.
• Move time and motion profilePeak speed, acceleration and jerk from a distance and a move time; trapezoid, triangle and S-curve.
• 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.
• Inertia ratioThe load's inertia at the motor through a screw, a belt or a gearbox, and the ratio that fixes it.
• Brake resistor sizingThe energy an axis returns while braking, what the drive's bus takes, and the resistor for the rest.
• Ball screw critical speedHow fast a screw may turn for its root diameter, length and supports, and the nut's D·N limit.

How the numbers are checked

Every result has a “Show calculation” with the formula and your numbers in it. The mechanism torques come from calculation packages that are tested against Oriental Motor's published ball-screw, belt and index-table selection examples, within 0.5 %, and the cylinder's forces against a handbook's 6-bar table within 1 %. The torque the page samples over the cycle is held against the closed-form phase torques to 1 part in 100 000, and the default cases are worked by hand in the test suite — every number on these pages is recomputed there before each release.

The page is in beta. The motors in the list are generic — typical sizes of each kind, not a maker's catalogue — and the envelope of a motor without its own curves is the generic shape of its kind. A cylinder's stroke time comes from an empirical model and is indicative once the load passes half the cylinder's force.

Questions