Skip to main content
SpringerLink
Log in

Localised tooth contact analysis of single envelope worm gears with assembly errors

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper presents the basis of loaded tooth contact analysis and predicts the influence of assembly errors on localised contact stress distribution in single enveloping (cylindrical) worm gearing during a meshing cycle. A method for loaded tooth contact analysis, geometry and kinematics of such gear pairs is developed. The method accounts for the effects of tooth composite deflection caused by bending, shearing, foundation, tooth contact deformation and initial profile separation due to assembly errors. The method includes the determination of contact lines, load and stress distribution due to assembly errors. Because of the complex geometry of worm gear teeth, the tooth bending stiffness is calculated using the slicing technique developed earlier by the authors. Classical Hertz theory is used for calculating contact stress and deformation. A computer program based on the presented method has been developed and used to study the influence of errors on mating teeth contact. It is shown that the governing factors in loaded gears with assembly error are the mesh stiffness and the amount of error which is linked to load sharing between adjacent tooth pairs. A numerical example is presented to further clarify the outlined method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lin CK, Chang CW (2002) Influence of heat treatment on fatigue crack growth of austempered ductile iron. J Mater Sci 37:709–716

    Article  MathSciNet  Google Scholar 

  2. Aslantaş K, Taşgetiren S (2003) Edge spalling formation in a plate due to moving compressive load. Turk J Eng Environ Sci 27:333–338

    Google Scholar 

  3. Taşgetiren S, Aslantaş K (2003) A numerical study of the behavior of surface cracks under dry-sliding conditions. Mater Des 24:273–279

    Article  Google Scholar 

  4. Chue CH, Chung HH (2000) Pitting formation under rolling contact. Theor Appl Fract Mech 34:1–9

    Article  Google Scholar 

  5. Keer LM, Bryant MD (1983) A pitting model for rolling contact fatigue. J Lubric Tech 105:198–205

    Article  Google Scholar 

  6. Sheppard SD, Hills DA, Barber JR (1986) An analysis of fretting cracks. II: unloading and reloading phases. Int J Solids Struct 22:387–396

    Article  Google Scholar 

  7. Hills DA, Comninou M (1985) A normally loaded half-plane with an edge crack. Int J Solids Struct 21:399–410

    Article  Google Scholar 

  8. Magalhaes L, Seabra J, Sa C (2000) Experimental observations of contact fatigue crack mechanisms for austempered ductile iron (ADI) discs. Wear 246:134–148

    Article  Google Scholar 

  9. Magalhaes L, Seabra J (1998) Wear and scuffing of austempered ductile iron gears. Wear 215:237–246

    Article  Google Scholar 

  10. Winter H, Wilkesmann H (1981) Calculation of cylindrical worm gear drives of different tooth profiles. ASME J Mech Des 103:73–81

    Article  Google Scholar 

  11. Octrue M (1988) A new method for designing a worm gear, AGMA Technical Paper 88FTM6. Alexandria, VA

    Google Scholar 

  12. Simon V (2003) Load distribution in cylindrical worm gears. ASME J Mech Des 125:356–364

    Article  Google Scholar 

  13. Fang HS, Tsay CB (1996) Mathematical model and bearing contacts of the ZK-type worm gear set cut by oversize hob cutters. Mech Mach Theor 31(3):271–282

    Article  Google Scholar 

  14. Fang HS, Tsay CB (1999) Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters. Mech Mach Theor 35(12):1689–1708

    Article  Google Scholar 

  15. Su X, Houser DR (2000) Alternative equation of meshing for worm-gear drives and its application to determining undercutting and reverse engineering. ASME J Mech Des 122:207–212

    Article  Google Scholar 

  16. Bercsey T, Horák P (1999) Errors analysis of worm gear pairs. 4th World Congress on Gearing and Power Transmission, Paris, pp 419–423

    Google Scholar 

  17. Shigley JA, Mischke CR, Budynas RG (2004) Mechanical engineering design, 8th edn. McGraw-Hill Inc.

  18. Falah AH, Elkholy AH (2006) Load and stress analysis of cylindrical worm gearing using tooth slicing method. Trans Can Soc Mech Eng 30(1):97–111

    Google Scholar 

  19. Johnson KL (1985) Contact mechanics. Cambridge University Press, London

    Book  MATH  Google Scholar 

  20. Simon VV (2006) Influence of tooth errors and shaft misalignments on loaded tooth contact in cylindrical worm gears. Mech Mach Theor 41:707–724

    Article  MATH  Google Scholar 

  21. Greening JH, Barlow RJ, Loveless WG (1980) Load sharing on the teeth of double enveloping worm gear, contributed by the Design Eng Division of the ASME for presentation at the Intl. Power Transmission & Gearing Conference, San Francisco, August 18–21 paper no. 80-C2/DET-43

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait

    A. H. Falah, M. A. Alfares & A. H. Elkholy

Authors
  1. A. H. Falah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Alfares
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. H. Elkholy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. H. Falah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Falah, A.H., Alfares, M.A. & Elkholy, A.H. Localised tooth contact analysis of single envelope worm gears with assembly errors. Int J Adv Manuf Technol 68, 2057–2070 (2013). https://doi.org/10.1007/s00170-013-4821-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-013-4821-4

Keywords

Search

Navigation