Control Techniques
Estun Automation
CODESYS
Crevis
Nexcom / Nexcobot
Leroy-Somer
Servo Systems
AC Drive + Motor
DC Drives
Smart PLC
Panel PC / IPC
Remote I/OMotor Sizing and Servo Motor Selection
Choose your mechanism, enter the load and motion profile, and define the reduction chain. The tool calculates peak and RMS torque, inertia ratio and motor speed, then proposes matching Estun and Control Techniques servo motors with stock status.
How to size a motor: formulas, worked example and FAQSelect Mechanism Type
Lead ScrewLoad Parameters
- mMoving mass (load + carriage)
- pLead: travel per screw revolution
- JsScrew inertia
- JcCoupling inertia
- μGuide friction coefficient
- FOpposing force (process, thrust)
- θIncline angle (90° for vertical axis)
Motion Profile
Choose the speed profile, then describe one move. Torque, speed and RMS are recalculated live from this profile.
Advanced: calculation resolution
Points per cycle; 400 is enough. Raise it only for very short accelerations.
Reduction Chain
No reduction is used in this stage. Motor is directly coupled to the load.
No reduction is used in this stage. Motor is directly coupled to the load.
No reduction is used in this stage. Motor is directly coupled to the load.
- iRatio 1: the motor turns the load directly
- JcCoupling inertia
- JLLoad inertia (from the previous steps)
Safety Margins & Limits
Engineering Warnings
- -
ONX Recommended Motors
Auto MatchSolver Summary
How to size a motor
Motor sizing means finding the motor that lets a mechanism make the required move in the required time. The right motor meets peak torque, continuous (RMS) torque, speed and inertia ratio at the same time. An undersized motor overheats and misses the cycle time; an oversized one adds needless cost, together with its drive.
Ball screw, rack and pinion, conveyor, rotating cylinder, rotary table, feed roll, hoist and user-defined load.
Symmetric trapezoid, custom trapezoid, 1/3 trapezoid and three S-curves; dwell time is part of the cycle.
Belt and pulley, gears, chain and catalogue gearboxes; each stage's ratio, inertia and efficiency are included.
Motors from the Estun EM3 and Control Techniques Unimotor hd catalogues that meet the inertia ratio limit, with stock status.
Motor sizing in six steps
-
1
Find the load inertia (JL)
Express the moving mass and the rotating parts as a single inertia referred to the motor shaft. On a ball screw the linear mass contributes m·(p/2π)², on belts, racks and conveyors m·(D/2)²; add the screw, pulley and coupling inertia.
-
2
Define the motion profile
Enter the distance, move time, acceleration and deceleration times and the dwell. They give the maximum speed and acceleration: for a trapezoid vmax = s / (t − ta), for a 1/3 trapezoid vmax = 1.5·s / t.
-
3
Add the reduction
A stage with ratio i reduces the load inertia seen by the motor by i² and the load torque by i, and raises the motor speed by i. The stage efficiency (η) increases the torque the motor must deliver.
-
4
Split the torque into its components
Acceleration torque (J·α), friction, gravity on inclined and vertical axes, and the process (opposing) force. The largest instantaneous value in the cycle is the peak torque, usually during acceleration.
-
5
Calculate the RMS torque
Weight the square of the torque in each segment of the cycle by its duration and divide by the total cycle time, dwell included. This value determines how hot the motor runs.
-
6
Select the motor
The motor's continuous torque must exceed the RMS torque, its peak torque the required peak torque and its speed the maximum motor speed; the inertia ratio must stay below the limit. Add a margin to each (10 % by default in the tool).
Key formulas
| Quantity | Formula | Note |
|---|---|---|
| Ball screw load inertia | JL = m·(p / 2π)² + Js + Jc | p: lead (m/rev), Js: screw, Jc: coupling |
| Belt, rack, conveyor | JL = m·(D / 2)² + Jkasnak | D: pulley or pinion diameter |
| Rotary table | JL = ½·mt·(Dt / 2)² + n·mw·(Dp / 2)² | table + n workpieces |
| Steel screw inertia | Js = π·ρ·L·d⁴ / 32 | ρ ≈ 7850 kg/m³ |
| Inertia reflected to the motor | Jm = Jc + JL / i² | i = nmotor / nload |
| Motor speed (ball screw) | n = v·60 / p | v: m/s, n: rpm |
| Angular acceleration | α = ωmaks / ta, ω = 2π·n / 60 | rad/s² |
| Ball screw load torque | TL = (F + m·g·(sinθ + μ·cosθ))·p / (2π·η) | θ: incline, μ: friction coefficient |
| Motor torque | T = JM·α + (Jm·α + TL / i) / η | JM: rotor inertia, η: gearbox efficiency |
| RMS torque | Trms = √( Σ Tk²·tk / tçevrim ) | dwell included |
| Inertia ratio | Jm / JM | typically ≤ 10 |
| Mechanical power | P = T·ω = T·n / 9.55 | P: W, T: N·m, n: rpm |
Worked example: ball screw axis
On a horizontal axis a 50 kg carriage is driven through a direct coupling by a Ø25 mm × 1000 mm ball screw with a 20 mm lead (efficiency 0.90). The carriage runs on ball-type linear guides with a friction coefficient of 0.01. The axis travels 300 mm in 0.6 s with a 1/3 trapezoidal profile and dwells for 0.4 s (cycle 1.0 s).
Js = π·7850·1·0,025⁴/32 ≈ 3.01 kg·cm²
m·(p/2π)² = 50·(0,02/2π)² ≈ 5.07 kg·cm²
JL ≈ 8.08 kg·cm²
ta = td = 0.2 s
vmax = 1.5·0.3/0.6 = 0.75 m/s
n = 0.75·60/0.02 = 2250 rpm
α ≈ 1178 rad/s²
F = 0.01·50·9.81 ≈ 4.9 N
Tf = 4.9·0.02/(2π·0.9)
Tf ≈ 0.017 N·m
Comparison with two candidate servo motors (continuous / peak torque and rotor inertia from the catalogue):
| 0.4 kW · JM = 0.244 kg·cm² 1.27 / 3.81 N·m |
0.75 kW · JM = 1.64 kg·cm² 2.39 / 7.17 N·m |
|
|---|---|---|
| Peak torque (acceleration) | 1.00 N·m | 1.16 N·m |
| RMS torque (1.0 s cycle) | 0.62 N·m | 0.72 N·m |
| Inertia ratio | 33 | 4.9 |
| Result | Torque is sufficient, inertia ratio far above the limit (10) | Suitable: comfortable ratio, ample torque and speed margin |
On this axis the inertia ratio, not torque, decides the motor. The low-inertia 0.4 kW motor has more than enough torque, but its ratio is 33. A medium-inertia 0.75 kW motor from the same family brings the ratio down to 4.9: the axis tunes easily, runs quietly and settles fast. The alternative is a 2:1 belt on the small motor; the ratio drops to 8.3, but the motor must run at 4500 rpm, high on the torque-speed curve of a motor rated at 3000 rpm.
Motor data from the catalogue on this site (Estun EM3A-04AL, low inertia; EM3J-08A, medium inertia). With the same inputs ONX Motion Sizing also finds JL = 8.08 kg·cm², 2250 rpm and an inertia ratio of 4.9 for the EM3J-08A, and does not propose the 0.4 kW motor because its ratio of 33 exceeds the limit.
Servo motor or induction motor?
Servo motors are used on axes that need positioning, frequent starts and stops and high dynamics: their peak torque can reach about three times their continuous torque and their low rotor inertia allows fast acceleration. For fans, pumps and conveyors running at constant speed, an induction motor with an AC drive is often more economical.
The inertia, torque and speed calculation is the same for both motor types; this tool matches the result to the servo catalogue. For induction motors, see the conveyor motor calculator and AC drives and motors.
Common mistakes
- Ignoring the inertia ratio: even with enough torque, a high ratio makes tuning hard and causes oscillation and long settling times.
- Comparing peak torque with the motor's continuous torque: heating is set by the RMS torque.
- Getting the dwell time wrong: cycles with short dwells raise the RMS torque.
- Forgetting gravity and the brake on vertical axes: the motor holds the load at standstill too and needs a brake.
- Neglecting gearbox efficiency and inertia.
- Leaving no speed margin: the torque a servo motor can deliver drops near its speed limit.
Frequently asked questions
What should the inertia ratio be?
A common upper limit is 10:1, which is also the tool's default. For high dynamics and precise positioning, below 5:1 is preferred. Stiff, backlash-free mechanisms can run at higher ratios, but tuning becomes harder. Follow the motor manufacturer's recommendation for the final limit.
What is RMS torque and why does it matter?
RMS (effective) torque is the thermal equivalent of the torque that varies over the cycle. It determines how hot the motor runs. If the motor's continuous torque is below the RMS torque, the motor overheats over time, even if its peak torque is sufficient.
How much safety margin should I allow?
If the load data is reliable, 10–20 % is a common margin. If friction and process forces are estimates, allow more. In the tool you can set separate margins for peak torque, continuous torque and speed; the default is 10 % each.
When do I need a gearbox?
When the load inertia is much larger than the motor inertia, when the required torque exceeds what the motor can deliver, or when the load speed is far below the motor speed. A gearbox with ratio i reduces the load inertia seen by the motor by i² and the load torque by i, but raises the motor speed by i.
What does an S-curve motion profile change?
It changes acceleration gradually instead of abruptly, which reduces jerk and spares the mechanism, belts and gearbox. To cover the same distance in the same time the maximum acceleration rises, so peak torque is slightly higher than with a trapezoidal profile.
Is the result a final motor selection?
No, it is a preliminary sizing. For the final selection, also check the motor's torque-speed curve, drive current, the energy returned during braking and the braking resistor, mechanical stiffness and resonance. You can send the result to ONX Control engineers with Get Quote.
Is the tool free, and is my data stored?
The tool is free and needs no registration. The values you enter are processed only to produce the result and are not stored unless you send them with Get Quote.