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

T Widmaier,B Hemming,J Juhanko,P Kuosmanen,V.-P Esala,A Lassila,P Laukkanen,J Haikio

doi:10.1016/j.precisioneng.2016.12.001

Abstract

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 <2000mm) 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 0.5μm for the even harmonics and from 1.5μm to 2.5μm for the odd harmonics, when the standard uncertainty for the four probes is 0.3μm each. The standard uncertainty for roundness deviation is 3.3μm.

Highlights

Roundness is defined by ISO 12181-1 [1] and ISO 12181-2 [2] as a geometrical property of a cross-section of a piece intended to be round
The output from the Monte Carlo simulations with 10 000 runs is shown in Figs. 13–17, where the different standard uncertainties are shown as error bars
Knowledge of measurement uncertainty is a fundamental requirement arising from both practical problems, scientific issues and quality systems

Summary

Introduction

Roundness is defined by ISO 12181-1 [1] and ISO 12181-2 [2] as a geometrical property of a cross-section of a piece intended to be round. Roundness is an important feature of all rotating machines where smooth rotation of the rotors or even surface quality and even thickness of the end product are needed, such as paper machines, steel strip or sheet production, printing machines, engines and generators etc. Measurements of roundness profiles are useful when a specific harmonic component is critical or important, e.g. for vibration excitation. Roundness measuring machines can measure deviation from roundness using a single sensor, as high-accuracy bearing assembly ensures that there is only a small rotational error in the radial direction [3,4,5]. Roundness measurements are usually carried out with the roll placed on a lathe or grinding machine as shown in

Methods

Results

Conclusion