Technical guide with sources · ROLL Lab
Paper mill cores: reels of paper, tissue and board
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Weight, width, speed
A paper reel loads the core mainly at its ends, where the chucks go in: it needs crush resistance, bending stiffness (ISO 11093-6 and -7) and, on fast machines, a natural frequency well away from the rotation frequency (ISO 11093-8).
Typical sizes
3" and 6" (76 and 152 mm) with walls from 10 to 15 mm and more; larger diameters too for tissue and light papers. The ends can be notched for the chucks to grip.
What to specify
- Guaranteed minimum flat crush to ISO 11093-9 and the test humidity.
- Bending stiffness for long cores.
- ISO 13542 inside diameter tolerances and length tolerances.
- End finish (notches, bevels).
Critical speed, in one formula
A long spinning core behaves like a beam: at a certain speed it starts to resonate. For a core supported at its ends, Euler-Bernoulli beam theory gives the first natural frequency: f = (π / 2L²) · √(E·I / m), where L is the span between supports in m, E the flexural modulus in Pa (ISO 11093-7), I = π·(OD⁴ − ID⁴) / 64 the second moment of area in m⁴ and m the mass per metre in kg/m. The critical speed in rpm is 60 · f.
Three practical consequences. Doubling the length divides the critical speed by four. With the same diameter, a thicker wall changes it little, because stiffness and weight grow together; a larger diameter raises it. Machines run with a wide margin below the critical speed, and the real frequency is measured by modal analysis under ISO 11093-8.
Frequently asked questions
Which core for paper and tissue?
Heavy, wide reels need thick walls and good bending stiffness and, at high speed, attention to critical speed (vibration). 3" and 6" cores are used, with walls from 10 to 15 mm and more.
Sources
- ISO 11093 (parts 6, 7, 8, 9)
- ISO 13542
- CCTI T-158, T-159
- ROLL Lab calculation
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