Skip to main content
SpringerLink
Log in

Spiral Bevel Gears and Hypoid Gears

  • Chapter
  • First Online:
Gears

Part of the book series: Springer Series in Solid and Structural Mechanics ((SSSSM,volume 10))

Abstract

In this chapter, the geometry of the main types of spiral bevel gears is first defined and considerations about the spiral angle are made. The corresponding cutting processes are then briefly described, and the generation of active flank surfaces of the teeth is defined. The main geometrical quantities of these gears are then determined as well as those concerning the equivalent cylindrical gears obtained using the Tredgold approximation. The load analysis of spiral bevel gears is then performed, also defining the thrust characteristic on shafts and bearings. Subsequently, the concepts concerning these gears are extended to the most general gearing case represented by the hypoid gears. The fundamentals of these gears are then provided, based on the kinematics already described for the hyperboloid gears. Two approaches to theoretical analysis are described, the first of more limited validity, and the second more general, but both capable to provide reliable results in terms of geometric and kinematic characteristics of these types of gears. The load analysis is extended to these types of gears, and some indications on the design choices inherent to them to improve their efficiency are provided. Finally, the unified ISO procedure, which allow us to calculate the geometric quantities of spiral bevel and hypoid gears is summarized.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Artoni A, Gabiccini M, Guiggiani M, Kahraman A (2011) Multi-objective ease-off optimization of hypoid gears for their efficiency, noise, and durability performances. J Mech Des 133(12):267–277

    Article  Google Scholar 

  2. Baxter ML (1961) Basic geometry and tooth contact of hypoid gears. Ind Math 11(2):19–42

    Google Scholar 

  3. Brown MD (2009) Design and analysis of a spiral bevel gear. Master of Engineering in Mechanical Engineering, Rensselaer Polytechnic Institute, Hartford, Connecticut, USA

    Google Scholar 

  4. Buchanan R (1823) Practical essays on mill work and other machinary, with notes and additional articles, containing new researches on various mechanical subjects by Thomas Tredgold. J Taylor, London

    Google Scholar 

  5. Buckingham E (1949) Analytical mechanics of gears. McGraw-Hill Book Company Inc, New York

    Google Scholar 

  6. Coleman W (1975) Computing efficiency for bevel and hypoid gears. Mach Des 47:64–65

    Google Scholar 

  7. Coleman W, Lehmann EP, Mellis DW, Peel DM (1969) Advancement of straight and spiral bevel gear technology, USAAVLABS Technical Report 69-75. U.S. Army Aviation Material Laboratories, Fort Eustis, VA (Virginia), pp 1–267

    Google Scholar 

  8. Falah B, Gosselin C, Cloutier L (1998) Experimental and numerical investigation of the meshing cycle and contact ratio in spiral bevel gears. Mech Mach Theory 33(1/2):21–37

    Article  MATH  Google Scholar 

  9. Fan Q (2006) Computerized modeling and simulation of spiral bevel and hypoid gears manufactured by Gleason face hobbing process. J Mech Des 128(6):1315–1327

    Article  Google Scholar 

  10. Fan Q (2011) Advanced developments in computerized design and manufacturing of spiral bevel and hypoid drives. Appl Mech Mater 86:439–442

    Article  Google Scholar 

  11. Ferrari C, Romiti A (1966) Meccanica Applicata alle Macchine. Unione Tipografica – Editrice Torinese (UTET), Torino

    Google Scholar 

  12. Figliolini G, Stachel H, Angeles J (2019) Kinematic properties of planar and spherical logarithmic spirals: applications to the synthesis of involute tooth profiles. Mech Mach Theory 136:14–26

    Article  Google Scholar 

  13. Galassini A (1962) Elementi di Tecnologia Meccanica, Macchine Utensili, Principi Funzionali e Costruttivi, loro Impiego e Controllo della loro Precisione, reprint 9th edn. Editore Ulrico Hoepli, Milano

    Google Scholar 

  14. Giovannozzi R (1965) Costruzione di Macchine, vol II, 4th edn. Casa Editrice Prof. Riccardo Pàtron, Bologna

    Google Scholar 

  15. Handschuh RF, Litvin FL (1991) How to determine spiral bevel gear tooth geometry for finite element analysis. NASA Technical Memorandum 105150, AVSCOM Technical Report 91-C-018, pp 1–9

    Google Scholar 

  16. Handschuh RF, Nanlawala M, Hawkins JM, Mahan D (2001) Experimental comparison of face-milled and face-hobbed spiral bevel gears. NASA Technical Memorandum 2001-210940, ARL-Technical Report-1104, pp 1–8

    Google Scholar 

  17. Henriot G (1972) Traité théorique et pratique des engrenages. Fabrication, contrôle, lubrification, traitement thermique, vol 2. Dunod, Paris

    Google Scholar 

  18. Henriot G (1979) Traité théorique et pratique des engrenages, vol 1, 6th edn. Bordas, Paris

    Google Scholar 

  19. Huston RL, Coy JJ (1981) Ideal spiral bevel gears—a new approach to surface geometry. J Mech Des 103(1):127–132

    Google Scholar 

  20. ISO 23509:2016 (E) Bevel and hypoid gear geometry

    Google Scholar 

  21. Klingelnberg J (ed) (2016) Bevel gear, fundamentals and applications.Spinger, Berlin, Heidelberg

    Google Scholar 

  22. Kolivand M, Kahraman A (2009) A load distribution model for hypoid gears using ease-off topography and shell theory. Mech Mach Theory 44:1848–1865

    Article  MATH  Google Scholar 

  23. Kolivand M, Li S, Kahraman A (2010) Prediction of mechanical gear mesh efficiency of hypoid gear pairs. Mech Mach Theory 45:1568–1582

    Article  MATH  Google Scholar 

  24. Lawrence JD (2014) A catalog of special plane curves. Dover Publications, New York

    Google Scholar 

  25. Lechner G, Naunheimer H (1999) Automotive transmissions: fundamentals, selection, design and application. Springer, Berlin, Heidelberg

    Google Scholar 

  26. Li M, Hu HY (2003) Dynamic analysis of a spiral bevel-geared rotor-bearing system. J Sound Vib 259(3):605–624

    Article  Google Scholar 

  27. Li Q, Jiang JF, Chang YL, Wang LT (2017) Modeling optimization and machining detection of logarithmic spiral bevel gears. Tool Technol 51(3):51–54

    Google Scholar 

  28. Lin C-Y, Tsay C-B, Fong Z-H (2001) Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques. J Mater Process Technol 114:22–35

    Article  Google Scholar 

  29. Litvin FL (1992) Development of gear technology and theory of gearing. NASA Reference Publication 1406, ARL-TR-1500, U.S. Army Research Laboratory, Cleveland. Lewis Research Center, Ohio

    Google Scholar 

  30. Litvin FL (1994) Gear geometry and applied theory. Englewood Cliffs, Prentice Hall Inc, New Jersey

    MATH  Google Scholar 

  31. Litvin FL, Chaing W-S, Lundy M, Tsung W-J (1990) Design of pitch cones for face-hobbed hypoid gears. ASME J Mech Des 112:413–418

    Article  Google Scholar 

  32. Litvin FL, Fuentes A (2004) Gear geometry and applied theory, 2nd edn. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  33. Litvin FL, Gutman Y (1981) Methods of synthesis and analysis for hypoid gear drives of formate and Helixform. Parts 1, 2 and 3. ASME J Mech Des 103(1):83–113

    Google Scholar 

  34. Litvin FL, Petrov KM, Ganshin VA (1974) The effect of geometrical parameters of hypoid and spiroid gears on their quality characteristics. J Eng Ind 96:330–334

    Article  Google Scholar 

  35. Litvin FL, Wang AG, Handschuh RF (1998) Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry. Comput Methods Appl Mech Eng 158:35–64

    Article  MathSciNet  MATH  Google Scholar 

  36. Maitra GM (1994) Handbook of gear design, 2nd edn. Tata McGraw-Hill Publishing Company Ltd., New Delhi

    Google Scholar 

  37. Merritt HE (1954) Gears, 3th edn. Sir Isaac Pitman&Sons, Ltd, London

    Google Scholar 

  38. Micheletti GF (1958) Lavorazioni dei Metalli ad Asportazione di Truciolo. Libreria Editrice Universitaria Levrotto&Bella, Torino

    Google Scholar 

  39. Mozzi del Garbo GG (1763) Discorso matematico sopra il rotolamento momentaneo dei corpi. Stamperia di Donato Campo, Napoli

    Google Scholar 

  40. Müller H (2007) Face-off: face hobbing vs. face milling. Gear Solution Magazine, 1 Sept 2007

    Google Scholar 

  41. Naunheimer H, Bertsche B, Ryborz J, Novak W (2011) Automotive transmissions: fundamentals, selection, design and application, 2nd edn. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  42. Niemann G, Winter H (1983) Maschinen-Elemente, Band III: Schraubrad-, Kegelrad-, Schnecken-, Ketten-, Rienem-, Reibradgetriebe, Kupplungen, Bremsen, Freiläufe. Springer, Berlin, Heidelberg

    Google Scholar 

  43. Pauline K, Irbe A, Torims T (2014) Spiral bevel gears with optimized tooth-end geometry. Procedia Eng 69:383–392

    Article  Google Scholar 

  44. Pollone G (1970) Il Veicolo. Libreria Editrice Universitaria Levrotto & Bella, Torino

    Google Scholar 

  45. Poritsky H, Dudley DW (1948) Conjugate action of involute helical gears with parallel or inclined axes. Quaterly Appl Mathem VI(3)

    Google Scholar 

  46. Powell DE, Barton HR (1959) Analytical study of surface loading and sliding velocity of automotive hypoid gears. ASME Trans II(2):173–183

    Article  Google Scholar 

  47. Radzevich SP (2010) Gear cutting tools: fundamentals of design and computation. CRC Press, Taylor&Francis Group, Boca Raton, Florida

    Book  Google Scholar 

  48. Radzevich SP (2016) Dudley’s handbook of practical gear design and manufacture, 3rd edn. CRC Press, Taylor&Francis Group, Boca Raton, Florida

    Book  Google Scholar 

  49. Romiti A (1960) Sopra un tipo di ingranaggi conici per assi concorrenti e sghembi, vol XCIV. Atti dell’Accademia delle Scienze di Torino, Torino

    MATH  Google Scholar 

  50. Romiti A (1960) Problemi di dimensionamento, accoppiamento e fabbricazione di ingranaggi conici per uso universale, vol XCIV. Atti dell’Accademia delle Scienze di Torino, Torino)

    MATH  Google Scholar 

  51. Rossi M (1965) Macchine Utensili Moderne. Editore Ulrico Hoepli, Milano

    Google Scholar 

  52. Schiebel A, Lindner W (1954) Zahnräder, Band 1: Stirn-und Kegelräder mit geraden Zähnen. Springer, Berlin, Heidelberg

    Google Scholar 

  53. Schiebel A, Lindner W (1957) Zahnräder, Band 2: Stirn-und Kegelräder mit schrägen Zähnen Schraubgetriebe. Springer, Berlin, Heidelberg

    Google Scholar 

  54. Scotto Lavina G (1990) Riassunto delle Lezioni di Meccanica Applicata alle Macchine: Cinematica Applicata, Dinamica Applicata - Resistenze Passive - Coppie Inferiori, Coppie Superiori (Ingranaggi – Flessibili – Freni). Edizioni Scientifiche SIDEREA, Roma

    Google Scholar 

  55. Sheveleva GI, Volkov AE, Medvedev VI (2007) Algorithms for analysis of meshing and contact of spiral bevel gears. Mech Mach Theory 42:198–215

    Article  MATH  Google Scholar 

  56. Shih YP, Fong ZH, Lin GC (2007) Mathematical model for a universal face hobbing hypoid gear generator. J Mech Des 129(1):38–47

    Article  Google Scholar 

  57. Simon V (2007) Computer simulation of tooth contact analysis of mismatched spiral bevel gears. Mech Mach Theory 42:365–381

    Article  MATH  Google Scholar 

  58. Simon V (2009) Design and manufacture of spiral bevel gears with reduced transmission errors. ASME J Mech Des 131(4):041007-1–041007-11

    Google Scholar 

  59. Spear GM, King CB, Baxter ML (1960) Helixform bevel and hypoid gears. ASME Trans 82-B(III):179–190

    Article  Google Scholar 

  60. Stachel H, Figliolini G, Angeles J (2019) The logarithmic spiral and its spherical counterpart. J Ind Des Eng Graph 14(1):91–98

    Google Scholar 

  61. Stadtfeld HJ (1993) Handbook of bevel and hypoid gears: calculation. Rochester Institute of Technology, Manufacturing and Optimization, Rochester

    Google Scholar 

  62. Stadtfeld HJ (2011) Tribology aspects in angular transmission systems, Part VII: hypoid gears. Gear Technol 66–72

    Google Scholar 

  63. Stadtfeld HJ (2014) Gleason bevel gear technology. Gleason Works, Rochester

    Google Scholar 

  64. Su J, Fang Z, Cai X (2013) Design and analysis of spiral bevel gears with seventh-order function of transmission error. CSAA, Chin J Aeronaut 26(5):1310–1316

    Article  Google Scholar 

  65. Suh S-H, Jung D-H, Lee E-S, Lee S-W (2003) Modeling, implementation, and manufacturing of spiral bevel gears with crown. Int J Adv Manuf Technol 21:775–786

    Article  Google Scholar 

  66. Townsend DP (1991) Dudley’s gear handbook. McGraw-Hill, New York

    Google Scholar 

  67. Tsai YC, Chin PC (1987) Surface geometry of straight and spiral bevel gears. J Mech Transmissions Autom Des 109(4):443–449

    Article  Google Scholar 

  68. Vimercati M (2007) Mathematical model for tooth surfaces representation of face-bobbed hypoid gears and its application to contact analysis and stress calculation. Mech Mach Theory 42(6):668–690

    Article  MATH  Google Scholar 

  69. Vimercati M, Piazza A (2005) Computerized design of face hobbed hypoid gears: tooth surface generation, contact analysis and stress calculation. AGMA Fall Technical Meeting, Paper N. 05FTM05

    Google Scholar 

  70. Wang J, Lim TC, Li M (2007) Dynamics of a hypoid gear pair considering the effects of time-varying mesh parameters and backlash nonlinearity. J Sound Vib 308:302–329

    Article  Google Scholar 

  71. Wang P-Y, Fong Z-H (2005) Adjustability improvement of face-milling spiral bevel gears by modified radial motion (MRM) method. Mech Mach Theory 40:69–89

    Article  MATH  Google Scholar 

  72. Wildhaber E (1946) Basic relationship of hypoid gears. Am Machinist, XC, February, pp 14, and 28, March, p 14, June, pp 6 and 20, July, p 18, and August, pp 1 and 15

    Google Scholar 

  73. Wildhaber E (1956) Surface curvature. Prod Eng 27:184–191

    Google Scholar 

  74. Zhang Y, Litvin FL, Handschuh RF (1995) Computerized design of low-noise face-milled spiral bevel gears. Mech Mach Theory 30(8):1171–1178

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Rome “Tor Vergata”, Rome, Italy

    Vincenzo Vullo

Authors
  1. Vincenzo Vullo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincenzo Vullo .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vullo, V. (2020). Spiral Bevel Gears and Hypoid Gears. In: Gears. Springer Series in Solid and Structural Mechanics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-36502-8_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-36502-8_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36501-1

  • Online ISBN: 978-3-030-36502-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation