1. Science
  2. Publications
  3. Information Processing Systems
  4. 4(155)'2018
  5. The effect of an uncertainty of measurements on the interest of incorrectly rejected articles under two-factor control

The effect of an uncertainty of measurements on the interest of incorrectly rejected articles under two-factor control

P. Ruzhin, S. Patsera, V. Derbaba, V. Korsun
Annotations languages:


Description: The subject of work is measurement uncertainty, evaluated by type B, as a source of errors of the first and second kind under the tolerance control in mechanical engineering. The theme of work isthe assessment of the influence of the measurement uncertainty of the normalized geometric parameters of the involute gears on the proportion of incorrectly rejected and incorrectly accepted parts. The purpose of the work is to determine the dependence of the influence of measurement uncertainty, as measured by type B, on the distortion of the results of the tolerance testing of gear wheels. The methodology of the research includes simulation modeling of the manufacture of a batch of gears with specified accuracy requirements for the geometric parameters of the gear in accordance with international standards. In this case, the method of statistical modeling (Monte Carlo) reproduces an array of deviations from the nominal value of the geometric parameter of the ring gear. The following assumptions are made: - the distribution of deviations of the geometric parameter is uniform, the limits of the dispersion interval from the lower to the upper deviations are selected with an increasing correction factor of 1.0027, which corresponds to the accepted level of accuracy of technology in engineering; - the first array of random deviations of the wheel parameter is modeled under the assumption that there is no measurement error, and then generated with a uniform distribution of measurement errors in the form of an additional array; while the boundaries of the interval [а ; а+ ] are symmetric relative to zero. The developed algorithmic model of numerical computer experiments includes modeling blocks of measurement and control procedures for the radial runout of the ring gear and the length of the common normal. This combination of geometric parameters reflects a set of parameters when monitoring the kinematic accuracy of gear wheels. The control procedures are modeled using logical formulas, while suitable wheels are given a shelf-life score of "1", and defective − "0". The software implementation of the algorithmic model is implemented in Microsoft Excel. The sample size formed 1000 parts, which is enough for the acceptable accuracy of plotting dependencies. As a result of research, the dependences of the fraction of incorrectly rejected and incorrectly accepted gears on the measurement uncertainty in two-factor control were obtained. The analysis of the obtained dependences leads to the following conclusions: 1) Two-factor control in the absence of a correlation of arrays of random deviations of two controlled parameters of gear wheels significantly increases the errors of the first and second kind. 2) In order to reduce significantly the error of two-factor control of gears, the measurement uncertainty estimated by type B should be reduced to a value not exceeding 1.155 microns. This can be achieved by using the coordinate measuring machines that come with the appropriate software. 3) The application scope of research results is the production of gears, which are subject to increased requirements for accuracy (starting with 8 degrees of accuracy).


Keywords: measurement uncertainty, tolerance control, errors of the first and second kind, gear wheel, modeling

References

1. Dеrbaba, V.А. (2014), “Imitatsionno - statisticheskaya model instrumentalnykh pogreshnostey izmereniya geomet-richeskikh parametrov zubchatykh kolos: dissertatsiya” [Simulation-statistical model of instrumental errors in measuring geo-metrical parameters of gear wheels: dissertation], Dnipro, 109 p.
2. Patsera, S.T., Korsun, V.I., Derbaba, V.A. and Ruzhyn, P.O. (2016), “Alhorytm imitatsiyno-statystychnoho doslidzhen-nya kontrolʹno-vymiryuvalʹnoyi systemy ta yoho prohramna realizatsiya u NI Lab VIEW” [Algorithm of simulation - statistical research of control and measuring system and its program realization at NI Lab VIEW], Information Processing Systems, No. 6(143), 226 p.
3. Derbaba, V.A., Zil, V.V. and Patsera, S.Т. (2014), Evaluation of the adequacy of the statistical simulation modeling method while investigating the components presorting processes, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, No. 5 (143), Dnipro, pp. 45-50, available at: http://scopus.com/inward/record.url?eid=2-s2.0-84914695179&partnerID = MN8TOARS.
4. White, K.P. and Ingalls, R.G. (2017), The basics of simulation, Proceedings of the 2017 Winter Simulation Conference, available at: https://www.informs-sim.org/wsc17papers/includes/files/037.pdf.
5. Nutaro,Y. (2016), A method for bounding, error in multi-rate and federated simulations, Proceedings of the Winter Simu-lation Conference, available at: https://www.informs-sim.org/wsc16papers/087.pdf.
6. Bokrantz, J., Skoogh, A., Andersson, J., Ruda, J. and Lamkull, D. (2015), A Methodology for Continuous Quality As-surance of Production Data Manufacturing Applications, Proceedings of the 2015 Winter Simulation Conference, 5-9 December 2015, California, USA, pp. 2088-2099, available at: https://informs-sim.org/wsc15papers/214.pdf.
7. Fishwick, P., Brailsford, S., Taylor, S.Y., Tolk, A. and Uhrmacher, A. (2014), Modeling for Everyone: Emphasizing the Role of Modeling in STEM Education, Modeling Methodology, Proceedings of the 2014 Winter Simulation Conference, 7-10 December 2014, Georgia, USA, pp. 2786-2796, available at: https://informs-sim.org/wsc14papers/includes/files/251.pdf.
8. Yilmaz, L., Taylor, S.Y., Fujimoto, R. and Darema, F. (2014), Panel: The Future of Research in Modeling & Simulation, Modeling Methodology, Proceedings of the 2014 Winter Simulation Conference, 7-10 December 2014, Georgia, USA, pp. 2797-2811, available at: https://informs-sim.org/wsc14papers/includes/files/252.pdf.
9. Hu, Y., Xiao, J., Rong, G. and Hu, X.(2014), A Structured DEVS Model Representation Based on Extended Structured Modeling, Modeling Methodology, Proceedings of the 2014 Winter Simulation Conference, 7-10 December 2014, Georgia, USA, pp. 2817-2823, available at: https://informs-sim.org/wsc14papers/includes/files/253.pdf.
10. Tolk, A., Heath, B.L., Ihrig, M., Padilla, J.J., Page, E.H., Suarez, E.D., Szabo, E.D., Weirich, P. and Yilmaz, L. (2013), Epistemology of Modeling and Simulation, Modeling Methodology, Proceedings of the 2013 Winter Simulation Conference, 8-11 December 2013, Washington, USA, pp. 1152-1166, available at: https://informs-sim.org/wsc13papers/includes/files/101.pdf.
11. Béchard, V. and Cote, N. (2013), Simulation of Mixed Discrete and Continuous Systems: An Iron Ore Terminal Exam-ple, Modeling Methodology, Proceedings of the 2013 Winter Simulation Conference, 8-11 December 2013, Washington, USA, pp. 1166-1178, available at: https://informs-sim.org/wsc13papers/includes/files/102.pdf.
12. Li, X., Lei, Y., Wang, W., Wang, W. and Zhu, Y. (2013), A DSM-based Multi-Paradigm Simulation Modeling Ap-proach for Complex Systems, Modeling Methodology, Proceedings of the 2013 Winter Simulation Conference, 8-11 December 2013, Washington, USA, pp. 1179-1190, available at: https://informs-sim.org/wsc13papers/includes/files/103.pdf.
13. Kim, S.H., and Whitt, W. (2013), Using Simulation to Study Statistical Tests for Arrival Process and Service Time Models for Service Systems, Modeling Methodology, Proceedings of the 2013 Winter Simulation Conference, 8-11 December 2013, Washington, USA, pp. 1223-1232, available at: https://informs-sim.org/wsc13papers/includes/files/107.pdf.
14. Gore, R. and Diallo, S. (2013), The Need for Usable Formal Methods in Verification and Validation, Modeling Meth-odology, Proceedings of the 2013 Winter Simulation Conference, 8-11 December 2013, Washington, USA, pp. 1258-1268, avail-able at: https://informs-sim.org/wsc13papers/includes/files/110.pdf.
15. Botsyura, O.A. and Zakharov, I.P. (2016), “Sravnitel'nyy analiz razlichnykh sposobov vychisleniya koeffitsiyentov okhvata pri realizatsii bayyesovskogo podkhoda k otsenivaniyu neopredelennosti izmereniy” [Comparative analysis of various methods for calculating coverage factors in the implementation of the Bayesian approach to estimating measurement uncer-tainty], Information Processing Systems, No. 6(143), pp. 20-24.
16. Zakharov, I.P. and Klimova, Ye.A. (2014), “Primeneniye metoda ekstsessov dlya polucheniya dostovernoy otsenki rasshirennoy neopredelennosti” [Using the method of excesses to obtain a reliable estimate of the expanded uncertainty], Information Processing Systems, No. 3(119), pp. 24-28.
17. Zakharov, I.P. (2015), “Neopredelennost' izmereniy dlya chaynikov i nachal'nikov” [Measurement Uncertainty for Dummies and Chiefs], Kharkiv, 52 p.

Reference:
Ruzhyn, P.O., Patsera, S.T., Derbaba, V.A. and Korsun, V.I. (2018), “Vplyv nevyznachenosti vymiriuvan na vidsotky nepravylno zabrakovanykh detalei pry dvokhfaktornomu kontroli” [The effect of an uncertainty of measurements on the interest of incorrectly rejected articles under two-factor control], Information Processing Systems, Vol. 4(155), pp. 140-149. https://doi.org/10.30748/soi.2018.155.20.