Roll Inertia Calculator
Calculate the moment of inertia for cylindrical rolls, flywheels and drums.
inertia
moment of inertia
roll
flywheel
drum
winder
motor sizing
acceleration
Input values
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Enter values and click Calculate to see results here.
Formula
I = 0.5 × m × r² [kg·m²]
J = I × (2π/60)² [if converting for VFD J parameter]
Worked Example
Given: A steel roll with 400 mm diameter, 200 mm face width, density 7850 kg/m³.
Step 1: Volume = π × 0.2² × 0.2 = 0.02513 m³
Step 2: Mass = 7850 × 0.02513 = 197.3 kg
Step 3: I = 0.5 × 197.3 × 0.2² = 3.95 kg·m²
Use this value when sizing the motor for acceleration time requirements.
Engineering Notes
- Why inertia matters: The motor must overcome inertia during acceleration. Higher inertia = longer acceleration time or larger motor required.
- Acceleration time: t = (I × Δω) / T_motor. For a target acceleration time, the motor torque must exceed the load torque plus the inertia torque.
- VFD tuning: Many VFDs accept an inertia (J) parameter for automatic tuning. Convert I to J using the formula above for your VFD model.
- Core and material: If the roll has a hollow core, subtract the core inertia from the total. A composite roll = solid cylinder + wound material.
References
- IEC 60034-1 — Starting and acceleration