ENG
РУС
Search
Menu
About the Edition
Open Access Statement
Editorial Board
Editorial Policy
Editorial Ethics
Rules for peer-review
Rules for presentation of papers
Forms of Submitted Documents
Recommendations for the Design of References to Our Journal
Editorial Staff
Information for Subscribers
Summaries of the Issue
List of Authors
Issues
Publishers license agreement
Procedure of work with personal data
Publications
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
Editor-in-Chief

Nikiforov
Vladimir O.
D.Sc., Prof.
Partners













































doi: 10.17586/2226-1494-2020-20-1-110-117

MATHEMATICAL MODELING OF ANGULAR DIFFERENCE BETWEEN TEETH DIRECTION IN ZONE OF ENGAGEMENT AND COMPLETENESS OF CONTACT IN GEARS

A. I. Abdullayev, G. N. Rasulov, O. F. Ismayilov


Read the full article  ';
Article in русский

For citation:
Abdullayev A.I., Rasulov G.N., Ismayilov O.F. Mathematıcal modelıng of angular dıfference between teeth dırectıon ın zone of engagement and completeness of contact ın gears. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2020, vol. 20, no. 1, pp. 110–117 (in Russian). doi: 10.17586/2226-1494-2020-20-1-110-117


Abstract
The paper presents a mathematical model of the difference in the angles of the teeth direction in the engagement zone of cylindrical and bevel gears, which are widely used in drives of various machines and units, as well as in measuringdevices. A particular solution is considered based on the performed analysis. It is a mathematical model of the difference in the angles of the teeth direction in the engagement zone, covering the factors generated only by structural elements of keyed joints. A numerical experiment revealed a quantitative effect of the angular deviations of the keyed elements on the difference in the angles of the teeth direction in the engagement zone. The difference in the angles of the gear teeth direction turns out to be the main source that affects the teeth contact completeness, which is one of the indicators of the reliability and performance of gears. The elements of keyed joints in the shaft-wheel conjugation are also considered. The analysis is carried out and the effect of design parameter deviations of the keyed joint elements on the nature and position of the locked teeth contact is revealed. Design and technological directions are proposed that minimize the effect of keyed joint errors on the formation of the difference in the angles of the gear teeth direction. Recommendations are given on the use of multi-stage gearboxes of the AN type. They use the keyed joints in conjugations of shaft-wheel only in the drive and driven shafts. We also give recommendations on applying the new design of the keyed joints, providing self-adjustment of one of the teeth (gear) during their engagement. An effective method is proposed for setting up a technological system when cutting a keyway on a shaft.

Keywords: mathematical model, gearing, dimensional chain, keyed joints, contact completeness, difference

References
  1. Abdullaev A.I., Nadzhafov A.M. A qualitative assessment ofr’batch re ducer’s technicallevel. Vestnik mashinostroenija, 2008, no. 12, pp. 6–9. (in Russian)
  2. GutinS.Ya.,VlasovM.Yu.Informationtechnologiesininitialdesign and parameter optimization of parallel-shaft reduction gear units. Moscow, Vysshaya shkola Publ., 2004, 110 p. (inRussian)
  3. EliseevYu.S.,NezhurinI.P.Deformationsandinaccuraciesingearing and theirroleingearoperation.Vestnikmashinostroenija,1999,no.8, pp. 28–31. (in Russian)
  4. Starzhinsky V.E., Basiniuk U.L., Mardasevich A.I., Shalobaev E.V. Analysis of publications for the problem of optimization of gear mechanismarrangement.ThemessengeroftheNTU“KHPI”,2013, no. 40(1013), pp. 156–169. (in Russian)
  5. Productiontechnologyandmethods for quality main tenanceofgear wheel sand pairs.TUTORIAL.Ed.byV.E.Starzhinskii,M.M.Kane. St. Petersburg, Professija Publ., 2007, 832 p. (inRussian)
  6. JohnsonK.L.Contactmechanics.CambridgeUniversityPress,1985.
  7. DrozdovYu.N.,YudinE.G.,BelovA.I.AppliedTribology:Friction, Wear, Lubrication in Technical Systems. Moscow, Eco-Press Publ., 2010, 604 p. (in Russian)
  8. SánchezM.B.,PleguezuelosM.,PedreroJ.I.Approximateequations for the meshing stiffness and the load sharing ratio of spur gears including hertzian effects. Mechanism and Machine Theory, 2017, vol. 109, pp. 231–249. doi:10.1016/j.mechmachtheory.2016.11.014
  9. SánchezM.B.,PleguezuelosM.,PedreroJ.I.Enhancedmodelofload distribution along the line of contact for non-standard involute external gears. Meccanica, 2013, vol. 48, no. 3, pp. 527–543. doi: 10.1007/s11012-012-9612-8
  10. Antoniuk V.E., Pavlovski V.J., Poddubko S.N., Aleksandrova V.S., Nikolaenkova I.N. Longitudinal updating of cogwheels of planetary transfers of mobile cars. Mechanics of Machines, Mechanisms and Materials, 2011, no. 4(17), pp. 37–41. (inRussian)
  11. ZhabinA.I.,KivensonA.I.,SmirnovaE.V.Methodsandfacilitiesfor accuracyimprovementofgearsaccordingtogearedgecontactnorms (review). Vestnik mashinostroenija, 1990, no. 4, pp. 46–50. (in Russian)
  12. Romanov V.V., Spitcyn V.E., Deinekin A.S., Mironenko A.I. Gear pairsofreductionunitswithprofile-longitudinalmodificationofteeth. Eastern-European Journal of Enterprise Technologies, 2009, vol. 4, no. 6(40), pp. 39–44. (in Russian)
  13. Petry-Johnson T.T., Kahraman A., Anderson N.E., Chase D.R. An experimental investigation of spur gear efficiency. Journal of MechanicalDesign,TransactionsoftheASME,2008,vol.130,no.6, pp. 0626011–06260110. doi:10.1115/1.2898876
  14. Yu W., Mechefske C.K. Analytical modeling of spur gear corner contact effects. Mechanism and Machine Theory, 2016, vol. 96, pp. 146–164. doi:10.1016/j.mechmachtheory.2015.10.001
  15. Abdullaev A.I., Rasulov G.N. Dimensional chains in the multistage package reducers. Progressive technologies and systems of mechanical engineering, 2011, no. 1(41), pp. 20–26. (inRussian)
  16. Venttcel E.S. Probability Theory. 10th ed. Vysshaja shkola Publ., 2006, 575 p. (in Russian)
  17. Abdullaev A.I., Nadzhafov A.M. Triple twin cylindrical reduction gear. Patent EA017053В1, 2012. (inRussian)
  18. Najafov A.M., Abdullayev A.I. About results of release testing of triple-reductiondouble-flowpackagegearofsucker-rodpumpmodels SKD 3-1,5-710. The messenger of the  NTU  “KHPI”, 2013, no. 40(1013), pp. 89–93. (in Russian)
  19. Rasulov N.M., Nadirov U.M. Accuracy research of the diametrical sizes forming at gear shaping by stepped cutter. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 5, pp. 893–899. (in Russian). doi: 10.17586/2226-1494-2015-15-5-893-899


Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2024 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.

Яндекс.Метрика