Free Engineering Tool
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.
Results
RPM from Surface Speed
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 Type | Recommended Grade | Notes |
|---|---|---|
| Calender rolls | G1.0 – G2.5 | Highest precision required |
| Press rolls (solid/vented) | G2.5 | Standard for most press sections |
| Suction rolls | G2.5 – G6.3 | Shell perforations complicate balancing |
| Dryer cylinders | G2.5 – G6.3 | Condensate shifting changes balance |
| Wire/fabric guide rolls | G2.5 | Small diameter, moderate speed |
| Felt rolls | G6.3 – G16 | Low speed, less critical |
| Reel spool | G2.5 | High 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:
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:
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)
It depends on the roll position. Calender and press rolls in high-speed machines (>1000 m/min) benefit from G2.5. Dryer cylinders typically use G6.3. Guide and felt rolls use G6.3. The general rule: the closer the roll is to the paper web forming and finishing, the tighter the balance requirement.
Paper machine speeds are universally specified as surface (line) speed in m/min, not as RPM. Different diameter rolls all run at the same surface speed (the machine speed), but at different RPMs. This calculator converts for you.
Steam-heated dryer cylinders contain condensate that redistributes based on speed and siphon operation. At low speeds, condensate pools at the bottom (cascading regime) causing vibration. At higher speeds, it forms a uniform ring (rimming regime). Transition between regimes during ramp-up can cause temporary high vibration. Allow the machine to reach steady state before drawing balance conclusions.
Yes, in-situ (field) balancing is common for paper machine rolls, especially for dryer cylinders that are difficult to remove. Use vibration sensors on the bearing housings and a keyphasor on the shaft. Two-plane balancing is typically needed for long rolls (L/D > 0.5). Correction masses are added at dedicated balance weight locations on the roll heads.
Common causes include: cover wear or damage (rubber/polyurethane), corrosion pitting on the shell, condensate system issues in dryer cylinders, thermal distortion, buildup of paper fiber or coating material, and cracking of the shell or heads. Regular vibration monitoring catches these issues early.
Very critical. Unbalance-induced vibration causes barring (regularly spaced marks) on calender and press rolls, uneven moisture profiles in press and dryer sections, and reel defects (corrugation, starring). Balance quality directly impacts paper surface quality and printability.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
