Modeling of measurement errors of general normals teeth and of the indicators sorting

Authors

  • Виталий Анатольевич Дербаба Natіonal mining unіversity Karl Marx Avenue, 19, Dnepropetrovsk, Ukraine, 49600, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.19457

Keywords:

modeling, measurement, error, gears, base tangent length, sorting

Abstract

For the choice of the measuring instruments with an acceptable measurement error, the technique, given in the national standard GOST 8.051-81 is used. However, this technique is applicable only to smooth junctions and does not take into account geometrical features of involute teeth of wheels. The objective of the paper is to determine the dependence of the sorting indicators of base tangents of involute teeth on the limiting random error of measurement.

The method of simulation statistical modeling, adapted in relation to the assigned task was applied. The modeling was carried out both for the case of zero error of measurement, and for the limiting value of the random error, which is taken as input data. It provides the calculation of the percent of incorrectly accepted and incorrectly rejected pairs of teeth. The statistical modeling was conducted on the basis of the random number generator, built in Microsoft EXCEL.

The accepted assumptions concern the choice of the law of normal distribution for deviations of base tangent lengths from the nominal value and uniform law of distribution of random errors of measurement.

The dependences of the number of incorrectly accepted and incorrectly rejected pairs of teeth on limiting values of random error of measurement of base tangent length for degrees of accuracy of gearing 4, 5, 6, 7, 8 with various types of junction were obtained.

The procedure was used in the educational processes when training bachelors, specialists and masters in mechanical engineering.

The technique can be used in drawing up business-plans for decision-making during preparation of engineering production, which is characterized by the stochastic nature

Author Biography

Виталий Анатольевич Дербаба, Natіonal mining unіversity Karl Marx Avenue, 19, Dnepropetrovsk, Ukraine, 49600

Assistant

Department of technology of mountain engineer

References

  1. Kenneth, Hudson Building Materials [Текст].: Bricks and tiles / Hudson Kenneth - chap. 3 - London: Longman, 1972. - pp. 28 – 42.
  2. Огородник, І. В. Тенденції розвитку виробництва керамічної цегли на Україні [Текст] / І. В. Огородник // Строительные материалы и изделия - 2001 – № 1 – с.2 – 3.
  3. The Complete Technology Book on Bricks, Cement and Asbestos / NPCS Board of Consultants & Engineers // NIIR PROJECT CONSULTANCY SERVICES, 2007. – 720 p.
  4. Oliver, John Brick book [Текст] / John Oliver // NZ: Lifetime Books, 2006 - 176 p.
  5. Fernandes Francisco, M. Ancient Clay Bricks: Manufacture and Properties [Текст] / Francisco M. Fernandes, Paulo B. Lourenço, Fernando Castro // Materials, Technologies and Practice in Historic Heritage Structures. Part 1. Springer Netherlands, 2010. - pp 29-48.
  6. Гудков, Ю. В. Пути повышения эффективности производства изделий стеновой керамики [Текст] / Ю. В Гудков, В. Н. Бурмистров // Строительные материалы, 2005 - № 2 - С. 14 - 15.
  7. Kingery, W. Davi Introduction to Ceramics [Текст] / W. David Kingery, H. K. Bowen, Donald R. Uhlmann // Wiley-Interscience, 1976 - 1056 p.
  8. Химическая технология керамики / Под ред. И. Я. Гузмана // М.: ООО РИФ "Стройматериалы", 2003 - 496 с.
  9. Христофоров, А. И. Зависимость свойств керамических изделий от состава и технологических параметров [Текст] / А. И. Христофоров, С. А. Ястребова // Огнеупоры и техническая керамика, 2006 - № 9 — С. 32 - 36.
  10. Kornmann, Michel Clay Bricks and Roof Tiles, Manufacturing and Properties [Текст] / Michel Kornmann // Paris: Lasim, 2007 - 308 p.
  11. Кашкаев, И. С. Производство глиняного кирпича [Текст] / И. С. Кашкаев, Е. Ш. Шейнман // М.: Высш. шк., 1978 — 248 с.
  12. Astashenkov, A. I. (1999). Razrabotka sistemy obespechenija edinstva izmerenij geometricheskih parametrov jevol’ventnyh zubchatyh zaceplenij: avtoref. dis. na soisk. uchen. step. dokt. tehn. nauk: spec. 05.11.15. Metrologija i metrologicheskoe obespechenie. Vserossijskij NII metrologicheskoj sluzhby, 44.
  13. Loktev, D. A. (2009). Sovremennye metody kontrolja kachestva cilindricheskih zubchatyh koles. Metalloobrabotka. Oborudovanie i instrument dlja professionalov, 4, 6-11.
  14. Kel’ton, V., Lou, A. (2004). Imitacionnoe modelirovanie. Klassika SC. [Perevod s angl.] 3rd izd. SPb. Piter. Kiev, Izdatel’skaja gruppa VNV, 847.
  15. Barton, R. R. (1997). Design of Experiments for Fitting Subsystem Metamodels. Winter Simulation Conference, Atlanta, 303 - 310.
  16. Bowden, R. O., Hall, J. D. (1998). Simulation Optimization Research and Development. Winter Simulation Conference, Washington, D.C., 1693 - 1698.
  17. Brennan, R. W., Rogers, P. (1995). Stochastic Optimization Applied to a Manufacturing System Operation Problem. Winter Simulation Conference, Washington D.C., 857-864.
  18. Donohue, J. M. (1994). Experimental Designs for Simulation. Winter Simulation Conference, Orlando, 200-206.
  19. Evans, G. W., Stockman, B., Mollaghasemi, M. Multicriteria (1991). Optimization of Simulation Models. Winter Simulation Conference, Phoenix, 894-900.
  20. Derbaba, V. A., Korsun, V. I., Pacera, S. T. (2010). Vlijanie rasshirennoj neopredelennosti na riski izgotovitelja i zakazchika pri izmerenii dliny obshhej normali. Sistemi obrobki іnformacії, 4(85), 85-89.
  21. Derbaba, V., Korsun, V., Patsera, S. (2010). Influence of the expanded uncertainty on risks of the manufacturer and the customer at measurement of length of the general normal of the cogwheel. Sistemu obrobku informazii, 4(85), 85 - 89.
  22. Derbaba, V. A. Korsun, V. I., Pacera, S. T. (2012). Algoritm imitacionnogo stohasticheskogo modelirovanija tochnosti tolshhiny jevol’ventnogo zuba i pogreshnosti ee izmerenija. Zbіrnik naukovih prac’. Odes’koi derzhavnoi akademіi tehnіchnogo reguljuvannja ta jakostі, 1 (1), 54-61.

Downloads

Published

2013-12-16

How to Cite

Дербаба, В. А. (2013). Modeling of measurement errors of general normals teeth and of the indicators sorting. Eastern-European Journal of Enterprise Technologies, 6(4(66), 48–52. https://doi.org/10.15587/1729-4061.2013.19457

Issue

Vol. 6 No. 4(66) (2013): Mathematics and cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2014 Виталий Анатольевич Дербаба

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.