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Paper Machine Roll Balance Calculator

Calculate operating RPM from surface speed, permissible residual unbalance per ISO 21940, centrifugal force from unbalance, and correction mass for paper machine rolls.

ISO 21940 G2.5 – G6.3 Paper Rolls
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Results

Permissible Residual Unbalance (Total)
Operating RPM
Per-Plane Unbalance
Specific Unbalance (eccentricity)
Centrifugal Force at Tolerance Limit
Correction Mass at Roll OD

RPM from Surface Speed

RPM = (Surface Speed [m/min]) / (π × D [m])

Paper machine speeds are specified as web surface speed in m/min. The roll RPM depends on the roll diameter.

Typical Balance Grades for Paper Machine Rolls

Roll TypeRecommended GradeNotes
Calender rollsG1.0 – G2.5Highest precision required
Press rolls (solid/vented)G2.5Standard for most press sections
Suction rollsG2.5 – G6.3Shell perforations complicate balancing
Dryer cylindersG2.5 – G6.3Condensate shifting changes balance
Wire/fabric guide rollsG2.5Small diameter, moderate speed
Felt rollsG6.3 – G16Low speed, less critical
Reel spoolG2.5High speed, affects winding quality

Paper industry note: Rolls operating above 1000 m/min benefit from G2.5 or better. Dryer cylinders with condensate management (siphons, turbulence bars) may show apparent unbalance changes during operation due to condensate redistribution.

Centrifugal Force from Unbalance

The centrifugal force generated by unbalance at the tolerance limit is:

F = m × e × ω² = U_per × ω² / 1000 [N]

Where U_per is in g·mm and ω in rad/s. This force rotates at shaft speed and is transmitted to the bearings and support structure.

Correction Mass Calculation

The correction mass to be added or removed at a given radius:

m_corr = U_per / r [g]

Where r is the correction radius in mm (typically at the roll OD or at a specific correction plane location).

Special Considerations for Paper Rolls

  • Suction rolls: Shell perforations create periodic mass variations. Balance should be checked after re-drilling or shell replacement.
  • Covered rolls (rubber/polyurethane): Cover thickness variations affect balance. Re-balance after re-covering.
  • Dryer cylinders: Condensate redistribution during startup causes transient unbalance. Allow stabilization before measuring.
  • Variable crown rolls: Hydraulic crown pressure changes can affect balance state.
  • Thermal crown: Uneven heating can cause temporary bowing — check that thermal steady state is reached before balancing.

Vibration Limits for Paper Machine Rolls

Paper machines require very low vibration levels for paper quality. Typical bearing housing velocity limits:

  • Calender rolls: < 1.0 mm/s RMS (affects paper surface quality)
  • Press rolls: < 2.0 mm/s RMS
  • Dryer cylinders: < 2.5 mm/s RMS
  • Wire/felt guide rolls: < 2.0 mm/s RMS
  • Reel spool: < 1.5 mm/s RMS (affects winding quality)
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