Winder Acceleration Torque Calculator

Add thick-cylinder roll inertia to steady web-tension torque for a defined line-speed ramp.

Loaded roll mass (kg)Include wound material and core mass represented by the measured roll.Roll outside diameter (mm)Use the diameter at the evaluated ramp condition.Core outside diameter (mm)Must be smaller than roll OD.Target line speed (m/min)Speed reached from rest in the stated ramp time.Acceleration time (s)The model assumes a constant acceleration ramp.Web tension (N)Total force across the web at this condition.Drive-path efficiency (%)Use a verified mechanical efficiency; 100% reports roll demand.

Enter roll, speed, tension and drive data.

What this calculator solves

Steady-state force-times-radius torque can understate demand during start-up. This tool estimates rotational inertia for the current roll and adds the torque needed to reach line speed within the chosen time.

Inputs and units

Use the actual loaded mass and diameters at the evaluated condition. Line speed converts to metres per second at the roll surface; acceleration time is the ramp from rest to that speed.

Calculation method

Roll inertia is approximated as ½m(R²+r²). Angular speed = web speed ÷ outer radius; angular acceleration = angular speed ÷ ramp time. Total roll torque = inertia × angular acceleration + tension × radius.

Worked production example

A 500 kg, 800 mm roll on a 150 mm core reaches 200 m/min in 10 seconds while holding 200 N. Inertia is about 41.41 kg·m²; acceleration adds 34.51 N·m to 80 N·m tension torque. At 90% efficiency, nominal drive demand is 127.23 N·m.

How to use the result

Evaluate both heavy/full and fast/core conditions, then compare torque, speed, power and regenerative limits with the drive supplier. This result supports a commissioning discussion; it does not select a motor by itself.

Common production mistakes

Do not apply full-roll mass at core radius or forget that maximum RPM usually occurs near core. Do not omit deceleration, gearbox ratio, reflected motor inertia or the machine's required safety factor from engineering review.

Assumptions and limitations

The roll is treated as a uniform thick cylinder and the ramp as linear. Density gradients, entrained air, core eccentricity, bearing drag, drivetrain inertia and control response are excluded.

Related workflow and sources

Rockwell's winder engineering handbook separates tension and acceleration demand when sizing center-driven systems. Continue with Taper Tension. Rockwell Winders handbook. Last reviewed: 2026-08-27.