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Surface Durability (Pitting) of Spur and Helical Gears

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Gears

Part of the book series: Springer Series in Solid and Structural Mechanics ((SSSSM,volume 11))

Abstract

In this chapter, a general survey is first done on the surface durability (pitting ) of spur and helical gears, also focusing attention on pitting damage and safety factor to be used in their design. The theoretical bases of surface durability are then discussed, with particular reference to the surface and subsurface stress states that occur in sliding and rolling contacts between the mating surfaces of the conjugate flanks of the teeth in relative motion. In this framework, same brief reminder on the elastohydrodynamic lubrication theory is provided, also describing the great influence it exerts on the aforementioned contacts as well as the EDH lubrication conditions necessary to reduce or avoid surface and subsurface fatigue damages in these types of gears. Finally, the procedure for calculating the surface durability of these same gears in accordance with the ISO standards is described, highlighting when deemed necessary as the relationships used by the same ISO are anchored to the theoretical base previously discussed.

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References

  • Bair S (2001) The variation of viscosity with temperature and pressure for various real lubricants. J Tribol 123(2):433–437

    Article  Google Scholar 

  • Barber JR (1992) Elasticity. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Barus C (1893) Isothermals, isopiestics and isometrics relative to viscosity. Am J Sci 45:87–96

    Article  Google Scholar 

  • Beeching R, Nicholls W (1948) A theoretical discussion of pitting failures in gears. Proc Inst Mech Eng 158:317

    Article  Google Scholar 

  • Belajev NM (1917) Bulletin of institution engineers of ways and communications. St. Petersburg

    Google Scholar 

  • Belajev NM (1924) Local stresses in compression of elastic bodies. In: Memoirs on theory of structures. St. Petersburg

    Google Scholar 

  • Bodensieck EJ (1965) Specific film thickness—an index of gear tooth surface determination, In: Paper presented at 1965 aerospace gear systems committee technical division meeting. AGMA, Denver, CO, Sept 1965

    Google Scholar 

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

    Google Scholar 

  • Budynas RG, Nisbett JK (2009) Shigley’s mechanical engineering design, 8th edn. McGraw-Hill Companies Inc., New York

    Google Scholar 

  • Bufler H (1959) Zur Theorie der rollenden Reibung. Ing Arch 27(3):137–152

    Article  MathSciNet  MATH  Google Scholar 

  • Burr AH (1982) Mechanical analysis and design. Elsevier Science Publishing Co., Inc., New York

    Google Scholar 

  • Cameron A (1966) Principles of lubrication. Longmans, London

    Google Scholar 

  • Ciulli E, Piccigallo B (1996) Fondamenti di lubrificazione elastoidrodinamica. ATA 49(3):109–116 (marzo)

    Google Scholar 

  • Cornell RW (1981) Compliance and stress sensitivity of spur gear teeth. J Mech Des 103(2)

    Article  Google Scholar 

  • Dieter GE (1988) Mechanical metallurgy, SI metric edition. Adapted by David Bacon, McGraw-Hill Book Company, London

    Google Scholar 

  • DIN 3990:1987 Tragfähigkeitsberechnung von Stirnrädern

    Google Scholar 

  • Dolan TJ, Broghammer EL (1942) A photoelastic study of stresses in gear tooth fillets. University of Illinois Engineering Experimental Station Bulletin, p 335, Mar

    Google Scholar 

  • Dowson D, Higginson GR (1977) Elastohydrodynamic lubrication, 2nd edn. Pergamon, London

    Google Scholar 

  • Dyson A, Naylor H, Wilson AR (1965–1966) Measurement of oil-film thickness in elastohydrodynamic contacts. In: Proceedings of symposium on elastohydrodynamic lubrication, leeds, vol 180, Pt 3B. England Institution of Mechanical Engineers, pp 119–134

    Google Scholar 

  • Ertel-Mohrenstein A (1984) Die Berechnung der hydrodynamischen Schmierung gekrümmter Oberflächen unter hoher Belastung und Relativbewegung. VDI - Fort - schrittsbericht Reihe 1(115)

    Google Scholar 

  • Faupel JH (1964) Engineering design: a synthesis of stress analysis and materials engineering. Wiley, New York

    Google Scholar 

  • Fontana MG (1987) Corrosion engineering, 3rd edn. Materials Science and Engineering Series. McGraw-Hill International Editions, New York

    Google Scholar 

  • Fromm H (1927) Berechung des Schlupfes beim Rollen deformierbarer Scheiben. Zeitschrift für Angewandte Mathematik and Mechanik (ZAMM) 7:27–58

    Article  MATH  Google Scholar 

  • Frost NE, Marsh KJ, Pook LP (1999) Metal Fatigue. Dover Publications Inc., Minneola, New York

    Google Scholar 

  • Gao S, Srirattayawong S (2014), Computational modeling of the surface roughness effects on the thermal-elastohydrodynamic lubrication problem. In: Proceedings of the international conference on heat transfer and fluid flow, Prague, Czech Republic, 11–12 Aug, Paper no. 192

    Google Scholar 

  • Giovannozzi R (1965a) Costruzione di Macchine, vol I, Casa Editrice Prof. Riccardo Pàtron, Bologna

    Google Scholar 

  • Giovannozzi R (1965b) Costruzione di Macchine, vol II. Casa Editrice Prof. Riccardo Pàtron, Bologna

    Google Scholar 

  • Gladwell GML (1980) Contact problems in the classical theory elasticity. Alphen aan den Rijn, Sijthoff & Noordhoff International Publishers B.V, The Netherlands, Germantown, Maryland, USA

    Book  MATH  Google Scholar 

  • Greenwood JA (1972) An extension of the Grubin theory of elastohydrodynamic lubrication. J Phys D Appl Phys 5(12):2195–2211

    Article  Google Scholar 

  • Grubin AN, Vinogradova IE (1949) Investigation of the contact of machine component. Central Scientific Research Institute for Technology and Mechanical Engineering (TsNIIMASH), Moscow

    Google Scholar 

  • Hamrock BJ, Dowson D (1977) Isothermal elastohydrodynamic lubrication at point contacts, part III—fully flooded results. Trans ASME Ser F J Lubric Technol 92(2):264–276

    Article  Google Scholar 

  • Herrebrugh K (1968) Solving the incompressible and isothermal problem in elastohydrodynamic lubrication through an integral equation. J Lubric Technol Trans ASME Ser F 90:262

    Article  Google Scholar 

  • Hertz HR (1882) Über die Berührung fester elastischer Körper. Journal für Reine und Angewandte Mathematik (Crelle’s J) 92:156–171

    MATH  Google Scholar 

  • Heywood RD (1952) Designing by photoelasticity. Chapman & Hall Ltd, London

    Google Scholar 

  • ISO 1328-1:2013 Cylindrical gears—ISO system of flank tolerance classification - Part 1: Definitions and allowable values of deviations relevant to flanks of gear teeth

    Google Scholar 

  • ISO 4287:1997 Geometrical product specifications (GPS)—surface texture: profile method—terms, definitions and surface texture parameters

    Google Scholar 

  • ISO 53:1998 Cylindrical gears for general and heavy engineering—standard basic rack tooth profile

    Google Scholar 

  • ISO 6336-2:2006 Calculation of load capacity of spur and helical gears—Part 2: calculation of surface durability (pitting)

    Google Scholar 

  • ISO 6336-5:2016 Calculation of load capacity of spur and helical gears—Part 5: strength and quality of materials

    Google Scholar 

  • ISO/TR 6336-30:2017 Calculation of load capacity of spur and helical gears—Part 30: calculation examples for the application of ISO 6336 parts 1, 2, 3, 5

    Google Scholar 

  • Jacobson BO (1991) Rheology and elastohydrodynamic lubrication, Tribology series 19: Elsevier, Amsterdam

    Google Scholar 

  • Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge, United Kingdom

    Book  MATH  Google Scholar 

  • Johnson KL, Tevaarwerk JL (1977) Shear behavior of elastohydrodynamic oil film. Proc R Soc A 352:215

    MATH  Google Scholar 

  • Juvinall RC (1967) Engineering considerations of stresses, strain, and strength. McGraw-Hill Book Company, New York

    Google Scholar 

  • Juvinall RC (1983) Fundamentals of machine component design. Wiley, New York

    Book  Google Scholar 

  • Juvinall RC, Marshek KM (2012) Fundamentals of machine component design, 5th edn. Wiley, New York

    Google Scholar 

  • Love AEH (1944) A treatise on the mathematical theory of elasticity, 4th edn. Dover Publications, New York

    MATH  Google Scholar 

  • Lugt PM, Morales-Espejel GE (2011) A review of elasto-hydrodynamic lubrication theory. Tribol Trans 54(3):470–496

    Article  Google Scholar 

  • McEven E (1949) Stresses in elastic cylinders in contact along a generatrix. Phil Mag 40:454

    Article  Google Scholar 

  • Morales-Espejel GE (2014) Surface roughness effects in elastohydrodynamic lubrication: A review with contributions. Proc Inst Mechan Eng Part J: J Eng Tribol 228(11):1217–1242

    Article  Google Scholar 

  • Morales-Espejel GE, Wemekamp AW (2008) Ertel-Grubin methods in elastohydrodynamic lubrication—a review. Proc Inst Mechan Eng Part J: J Eng Tribol

    Google Scholar 

  • Mott PH, Roland CM (2009) Limit to Poisson’s ratio in isotropic materials. Chemistry Division, Code 6120, Naval Research Laboratory, Washington DC 20375-5342

    Google Scholar 

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

    Book  Google Scholar 

  • Niemann G, Winter H (1983) Maschinen-Elemente Band II: Getriebe allgemein, Zahnradgetriebe-Grundlagen, Stirnradgetriebe. Springer, Berlin, Heidelberg

    Google Scholar 

  • Niemann G, Winter H, Höhn B-R (2005) Maschinen-Elemente-Band 1: Konstruction und Berechnung von Verbindungen, Lagern, Wellen, 4th edn. Springer, Berlin, Heidelberg

    Google Scholar 

  • Poritsky H (1950) Stresses and deflections of cylindrical bodies in contact. Trans ASME Ser E J Appl Mech 17:191

    MATH  Google Scholar 

  • Radaj D, Vormwald M (2013) Advanced methods of fatigue assessment. Springer, Berlin, Heidelberg

    Book  Google Scholar 

  • Raptis KG, Costopoulos TN, Papadopoulos GA, Tsolakis AD (2010) Rating of spur gear strength using photoelasticity and the finite element method. Am J Eng Appl Sci 3(1):222–231

    Article  Google Scholar 

  • Reynolds O (1876) On rolling friction. Philos Trans R Soc Lond 166:155–171

    Google Scholar 

  • Ristivojević M, Lazovic T, Vinci A (2019) Studying the load carrying capacity of spur gear tooth flanks. Mech Mach Theory 59:125–137

    Article  Google Scholar 

  • Roelands CJA (1966) Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils. Ph.D. thesis, Technische Hogeschool, V.R.B., Groningen

    Google Scholar 

  • Rolfe ST, Barsom JM (1977) Fracture and fatigue control in structures: applications of fracture mechanics. Prentice-Hall Inc., Englewood Cliffs, New Jersey

    Google Scholar 

  • Saada AS (1993) Elasticity: theory and applications, 2nd edn. Krieger Publishing Company, Malabar, Florida

    MATH  Google Scholar 

  • Sackfield A, Hills DA (1983) Some useful results in the classical Hertz contact problem. J Strain Anal 18:101

    Article  Google Scholar 

  • Sadeghi F, McClung WD (1991) Formulas used in thermal elastohydrodynamic lubrication. STLE Tribol Trans 34(4):588–596

    Article  Google Scholar 

  • Schijve J (2009) Fatigue of structures and materials. Springer, Berlin, Heidelberg

    Book  MATH  Google Scholar 

  • Shipley EE (1967) Gear failures. Machine Design, 7 December

    Google Scholar 

  • Smith JO, Liu CK (1953) Stresses due to tangential and normal loads on an elastic solid with application to some contact stress problems. Trans ASME Ser E J Appl Mech 20:157

    Google Scholar 

  • Sperka P, Krupka I, Hartl M (2016) Surface roughness effects under high sliding EHL conditions. Jpn Soc Tribol 11(1):34–39

    Google Scholar 

  • Stachowiak GW, Batchelor AW (2014) Engineering tribology, 4th edn. Elsevier, Amsterdam

    Google Scholar 

  • Stephens RI, Fatemi A, Stephens RR, Fuchs HO (2001) Metal fatigue in engineering, 2nd edn. Wiley, New York

    Google Scholar 

  • Tallian TE (2000) Failure atlas for Hertz contact machine elements, 2nd edn. ASME Press, New York

    Google Scholar 

  • Tanaka S, Yamada T, Hattori N, Ogata K (1991) Influence of pitch errors on surface failure of spur gears. In: Proceedings of the international conference on motion and power transmissions, JSME, 23–26 Nov 23–26, pp 1084–1088

    Google Scholar 

  • Thomas HR, Hoersch VA (1930) Stresses due to the pressure of one elastic solid upon another. University of Illinois, Engineering Experiment Station, Bulletin no. 212, July, pp 1–56

    Google Scholar 

  • Timoshenko SP (1940a) Strength of materials, Part I: elementary theory and problems, 2nd edn. D. Van Nostrand Company Inc., Toronto

    MATH  Google Scholar 

  • Timoshenko SP (1940b) Strength of materials, Part II: advanced theory and problems, 2nd edn. D. Van Nostrand Company Inc, Toronto

    MATH  Google Scholar 

  • Timoshenko S, Goodier JN (1951) Theory of elasticity. McGraw-Hill Book Company Inc., New York

    MATH  Google Scholar 

  • van Leeuwen H (2009) The determination of the pressure-viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements. Proc Inst Mech Eng 223, Part J: J Eng Tribol 1143–1163

    Google Scholar 

  • Vullo V (2014) Circular cylinders and pressure vessels: stress analysis and design. Springer, Cham, Heidelberg

    Book  Google Scholar 

  • Whitehouse D (2012) Surfaces and their measurement. Butterworth-Heinemann, Boston

    Google Scholar 

  • Wymer DG, Cameron A (1974) Elastohydrodynamic lubrication of a line contact. Proc Inst Mech Eng 188:221–238

    Article  Google Scholar 

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Authors and Affiliations

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

    Vincenzo Vullo

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  1. Vincenzo Vullo
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Correspondence to Vincenzo Vullo .

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Vullo, V. (2020). Surface Durability (Pitting) of Spur and Helical Gears. In: Gears. Springer Series in Solid and Structural Mechanics, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-38632-0_2

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  • DOI: https://doi.org/10.1007/978-3-030-38632-0_2

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  • Online ISBN: 978-3-030-38632-0

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