Application of Monte Carlo simulation for estimation of uncertainty of four-point roundness measurements of rolls

T. Widmaier, Björn Hemming (Corresponding Author), J. Juhanko, P. Kuosmanen, Veli-Pekka Esala, Antti Lassila, Pasi Laukkanen, J. Haikio

Research output: Contribution to journalArticleScientificpeer-review

25 Citations (Scopus)


Large-scale rotors in the paper and steel industry are called rolls. Rolls are reground at regular intervals and roundness measurements are made throughout the machining process. Measurement systems for roundness and diameter variation of large rolls (diameter <2000 mm) are available on the market, and generally use two to four sensors and a roundness measurement algorithm. These methods are intended to separate roundness of the rotor from its movement. The hybrid four-point method has improved accuracy, even for harmonic component amplitudes. For reliable measurement results, every measurement should be traceable with an estimation of measurement uncertainty. In this paper, the Monte-Carlo method is used for uncertainty evaluation of the harmonic components of the measured roundness profile under typical industrial conditions. According to the evaluation, the standard uncertainties for the harmonic amplitudes with the hybrid method are below 0.5 μm for the even harmonics and from 1.5 μm to 2.5 μm for the odd harmonics, when the standard uncertainty for the four probes is 0.3 μm each. The standard uncertainty for roundness deviation is 3.3 μm.
Original languageEnglish
Pages (from-to)181-190
Number of pages10
JournalPrecision Engineering
Issue numberDecember
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed


  • harmonic amplitude
  • measurement uncertainty
  • Monte Carlo
  • paper machine roll
  • roundness

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