Estimation of rolling process variation by usage of a Monte-Carlo method

Estimation of rolling process variation by usage of a Monte-Carlo method


download PDF

Abstract. Rolling simulation, especially for groove rolling, is heavily dominated by use of finite element methods, but simulating a full pass sequence often takes several hours. Simpler models offer high-speed simulation within seconds at the expense of resolution and accuracy. In mechanical engineering, Monte-Carlo approaches are well known for analysis of fabrication tolerances in component assembly. By usage of fast simulation cores, this technique becomes available for analysis of process variations in groove rolling, since computational costs are crucial due to the need of hundreds or thousands of simulation runs. Rolling process variations can be classified in two groups: first, variations of the input material, such as actual dimensions, temperature and microstructure state; second variations occurring during processing, such as transport times, environment temperature and tool wear. The regarded process was the operation of the experimental semi-continuous rolling plant at the Institute of Metal Forming (IMF). Simulations were carried out by use of the open source rolling framework PyRolL, developed at IMF. The main part of process parameters was considered as constant, but some were described as a statistical distribution. For each simulation run a set of actual sample values of the distributed parameters was drawn using a random number generator. Selected result values were described by use of statistical methods to analyze the variational behavior of the process in behalf of the two variation classes.

Rolling Simulation, PyRolL, Monte Carlo Method, Process Variations

Published online 4/19/2023, 8 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: WEINER Max, RENZING Christoph, SCHMIDTCHEN Matthias, PRAHL Ulrich, Estimation of rolling process variation by usage of a Monte-Carlo method, Materials Research Proceedings, Vol. 28, pp 1575-1582, 2023


The article was published as article 170 of the book Material Forming

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] C. Lemieux, Monte Carlo and Quasi-Monte Carlo Sampling, Springer New York, (2009). ISBN: 978-0-387-78165-5.
[2] C.-Y. Lin, W.-H. Huang, M.-C. Jeng, J.-L. Doong, Study of an Assembly Tolerance Allocation Model Based on Monte Carlo Simulation, J. Mater. Process. Technol. 70 (1997) 9-16.
[3] Zhengshu Shen, Gaurav Ameta, J.J. Shah, J.K. Davidson, A Comparative Study Of Tolerance Analysis Methods, J. Comput. Inform. Sci. Eng. 5 (2005) 247-256.
[4] J.-Y. Dantan, A.-J. Qureshi, Worst-Case and Statistical Tolerance Analysis Based on Quantified Constraint Satisfaction Problems and Monte Carlo Simulation, Computer-Aided Design 41 (2009) 1-12.
[5] A.-J. Qureshi, J.-Y. Dantan, V. Sabri, P. Beaucaire, N. Gayton, A Statistical Tolerance Analysis Approach for Over-Constrained Mechanism Based on Optimization and Monte Carlo Simulation, Computer-Aided Design 44 (2012) 132-142. 2011.10.004.
[6] H. Yan, X. Wu, J. Yang, Application of Monte Carlo Method in Tolerance Analysis, Procedia CIRP. 13th CIRP Conference on Computer Aided Tolerancing 27 (2015) 281-285.
[7] C. Rausch, M. Nahangi, C. Haas, W. Liang, Monte Carlo Simulation for Tolerance Analysis in Prefabrication and Offsite Construction, Automat. Constr. 103 (2019) 300-314.
[8] M. Weiner, M. Schmidtchen, U. Prahl, A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part I: Model Development and Case Studies, Adv. Eng. Mater. 24 (2022).
[9] M. Weiner, T. Zienert, M. Schmidtchen, J. Hubálková, C.G. Aneziris, U. Prahl, A New Approach for Sintering Simulation of Irregularly Shaped Powder Particles – Part II: Statistical Powder Modelling, Adv. Eng. Mater. (2022) 202200443.
[10] M. Weiner, C. Renzing, M. Stirl, and M. Schmidtchen. PyRolL. Version 1.0.5. Institute of Metal Forming, TU Bergakademie Freiberg. URL:
[11] M. Weiner, C. Renzing, R. Pfeifer, M. Schmidtchen, U. Prahl. Supplemental Material to ’Estimation of Rolling Process Variation by Usage of a Monte-Carlo Method’ at ESAFORM2023. 2022.
[12] P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau,
E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K. Jarrod Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, I. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, SciPy 1.0 Contributors, SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python, Nat. Methods 17 (2020) 261-272.
[13] pandas-dev/pandas: Pandas (2020).
[14] W. McKinney, Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference (2010), pp. 56-61.
[15] A. Hensel, T. Spittel. Kraft- und Arbeitsbedarf bildsamer Formgebungsverfahren, VEB Deutscher Verlag für Grundstoffindustrie, 1978.
[16] A. Hensel, P. Poluchin, W. Poluchin, Technologie der Metallformung. Deutscher Verlag für Grundstoffindustrie, 1990.
[17] G. Zouhar, Umformungskräfte beim Walzen in Streckkaliberreihen, Akademie Verlag Berlin, 1960.
[18] J. H. Hitchcock, W. Trinks, Roll Neck Bearings. Report of Special Research Committee on Roll Neck Bearings, ASME (1935) 51.
[19] A. E. Lendl, Rolled Bars – Part I – Calculation of Spread between Non Parallel Roll Surfaces, Iron and Steel 21.14 (1948) 397-402.
[20] A. E. Lendl, Rolled Bars – Part II – Application of Spread Calculation to Pass Design, Iron and Steel 21 (1948) 601-604.
[21] A. E. Lendl, Rolled Bars – Part III – Application of Spread Calculation to Diamond Passes, Iron and Steel 22 (1949) 499-501.
[22] Z. Wusatowski, Fundamentals of Rolling, Pergamon Press, 1969.