Abstract
In this chapter, a general survey is first done on the tooth fatigue breakage of spur and helical gears, which can manifest itself in the form of tooth flank fatigue fracture (TFF) or tooth interior fatigue fracture (TIFF). The mechanics that trigger these two types of tooth fatigue breakage as well as the characteristics that distinguish one type of damage from the other are described. The fundamentals on the TIFF and TFF calculation methods developed so far are then briefly recalled. Attention is then focused mainly on the fatigue crack initiation criterion, on a refined TFF-risk assessment model as well as on a practical-oriented TFF calculation approach. Some insights on the multiaxial stress state that may originate TIFF and TFF crack initiation as well as the weakest link theory and classical multiaxial criteria are described, focusing attention on a general fatigue criterion for multiaxial stress to be included in the framework of the shear stress intensity hypothesis (SIH). Finally, the procedure for calculating the tooth flank fracture load capacity of cylindrical spur and helical case-carburized gears with external teeth in accordance with the ISO standards is described, highlighting when deemed necessary how the formulae used by the same ISO are rooted in the theoretical and experimental bases previously discussed.
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Al BC, Langlois P (2015) Analysis of tooth interior fatigue fracture using boundary conditions from an efficient and accurate loaded tooth contact analysis. In: British Gears Association (BGA) Gears 2015 Technical Awareness Seminar, 12th of November 2015, Nottingham, U.K. (also Gear Solutions, Feb. 2016)
Al BC, Patel R, Langlois P (2016) Finite element analysis of tooth flank fracture using boundary conditions from LTCA. In: CTI Symposium USA, Novi, MI, 11–12 May 2016
Al BC, Patel R, Langlois P (2017) Comparison of tooth interior fatigue fracture load capacity to standardized gear failure models. Gear Solutions, pp 47–57
Batdorf SB (1977) Some approximate treatments of fracture statistics for polyaxial tension. Int J Fract 13:5–11
Batdorf SB, Crose JG (1974) Statistical theory for the fracture of brittle structures subjected to nonuniform polyaxial stresses. J Appl Mech 41:459–464
Batdorf SB, Heinisch HL (1978) Weakest link theory reformulated for arbitrary fracture criterion. J Am Ceram Soc 61:355–358
Beermann S, Kissling U (2015) Tooth flank fracture—a critical failure mode. Influence of Macro and Micro Geometry. In: KISSsoft User Conference India
Belajev NM (1917) Bulletin of Institution Engineers of Ways and Communications, St. Petersburg
Belajev NM (1924) Local stresses in compression of elastic bodies, in memoirs on theory of structures, St. Petersburg
Boiadjiev I, Witzig J, Tobie T, Stahl K (2014) Tooth flank fracture-basic principles and calculation model for a sub-surface-initiated fatigue mode of case-hardened gears. In: International Gear Conference, Lyon, France. Also Gear Technology, 2015 26–28 August 2014
Ding Y, Rieger N (2003) Spalling formation mechanism for gears. Wear 254(12):1307–1317
Elkholy A (1983) Case depth requirements in carburized gears. Wear 88:S233–S244
Evans AG (1978) A general approach for the statistical analysis of multiaxial fracture. J Am Ceram Soc 61:302–308
Fernandes PJL, McDuling C (1997) Surface contact fatigue failures in gears. Eng Fail Anal 4(2):99–107
Findley WN (1959) A theory for the effect of mean stress on fatigue of metals under combined torsion and axial load or bending. J Eng Indus 301–306
Föppl L, Föppl A (1947) Drang und Zwang, Band III—Eine höhere Festigkeitslehre für Ingenieure, Leibnitz Verlag, München
Ghribi D, Octrue M (2014) Some theoretical and simulation results on the study of the tooth flank breakage in cylindrical gears. In: International Gear Conference 2014, Lyon, France, 26–28 August 2014
Häfele P, Dietmann H (1994) Weiterentwicklung der Modifizierten Oktaederschubspannungshypothese (MOSH). Konstruktion 46:52–58
Hein M, Tobie T, Stahl K (2017) Parameter study on the calculated risk of tooth flank fracture of case-hardened gears. In: Bulletin of the JSME, Journal of Advanced Mechanical of Design, Systems, and Manufacturing, II, (6)
Heindenreich R, Zenner H, Richter I (1983) Dauerschwingfestigkeit bei mehrachsiger Beanspruchung, Forschungshefte FKM, Heft 105
Henchy H (1924) Zur Theorie plastischen Deformationen und hierdurch in Material hervorgerufenen Nebenspannungen. In: Proceedings 1st International Congress for Applied Mechanics, Deft, pp 312–317
Hertter T (2003) Rechnirischer Festigkeitsnachweis der Ermüdungstragfähigkeit vergüteter und einsatzgehärteter Zahnräder. Ph. D. thesis, Technical University of Munich
Hill R (1950) The mathematical theory of plasticity. Oxford University Press, Oxford
Höhn BR, Oster P, Hertter T (2010) A calculation Model for rating the gear load capacity based on local stresses and local properties of the gear material. In: International Conference on Gears, Garching, Germany, VDI
Huber MT (1904) A contribution to fundamentals of the strength of materials. Czasopismo Tow. Technicze Krakow 22:81 (in Polish)
ISO 6336-5:2016 Calculation of load capacity of spur and helical gears—Part 5: Strength and quality of materials
ISO/TR 15144-1:2014 Calculation of micropitting load capacity of cylindrical spur and helical gears—Part 1: Introduction and basic principles
ISO/TS 6336-22:2018 Calculation of load capacity of spur and helical gears—Part 22: Calculation of micropitting load capacity
ISO/TS 6336-4:2019 Calculation of load capacity of spur and helical gears—Part 4: Calculation of tooth flank fracture load capacity
Johnson KL (1985) Contact Mechanics, Cambridge University Press, Cambridge, United Kingdom
Klein M, Höhn BR, Michaelis K, Annast R (2011) Theoretical and experimental investigations about flank breakage in bevel gears. Indus Lubrication Tribol 63(1):5–10
Lamon J (1988) Statistical approaches to failure for ceramic reliability assessment. J Am Ceram Soc 71:106–112
Lang OR (1979) The dimensioning of complex steel members in the range of endurange strength and fatigue life. Zeitschrift fuer Werkstofftechnik 10:24–29
Lang OR (1988) Berechnung und Auslegung induktiv gehärteter Bauteile, Berichtsband zur AWT-Tagung, Induktives Randschichthärten, Darmstadt
Langlois P, Al BC, Harris O (2016) Hybrid hertzian and FE-based helical gear-loaded tooth contact analysis and comparison with FE. Gear Technology, pp 54–63
Liu J (1999) Weakest Link Theory and Multiaxial Criteria. In: Macha E, Bedkowki W, Lagoda T (eds) Multiaxial fatigue and fracture. Elsevier, New York, pp 55–68
Liu J, Zenner H (1993) Berechnung der Dauerschwingfestigkeit bei mehrachsiger Beanspruchung, Mat.-Wiss. und Werkstofftech., 24, part 1: pp 240–249; part 2: pp 296–303 and part3: pp 339–347
MackAldener M (2001) Tooth interior fatigue fracture and robustness of gears. Doctoral thesis, KTH Stockholm
MackAldener M, Olsson M (2000a) Interior fatigue fracture of gear teeth. Fatigue Fract Eng Mater Struct 23(4):283–292
MackAldener M, Olsson M (2000b) Design against tooth interior fatigue fracture. Gear Technolog, pp 18–24
MackAldener M, Olsson M (2001) Tooth interior fatigue fracture. Int J Fatigue 23:329–340
MackAldener M, Olsson M (2002) Analysis of crack propagation during tooth interior fatigue fracture. Eng Fracture Mech 69(18):2147–2162
Martens H, Hahn M (1993) Vergleichspannungshypothese zur Schwingfestigkeit bei Zweiachsiger Beanspruchung ohne und mit Phasenverschiebungen, Konstruktion, 45, pp 196–202
Maxwell JC (1856) Letter to Lord Kelvin, Dec. 18 (pertinent portion of letter quoted by Nadai, Theory of flow and Fracture of solids, Vol II, p 43)
Mises RV (1913) Mechanik der festen Körper im Plastisch-detormablem Zustand. Göttinger Nachrichten, Akad. Wiss, Math-Physik., Kl., pp 582–592
Munz D, Fett T (1989) Mechanisches Verhalten Keramischer Werkstoffe. Springer, Berlin
Nadai A (1933) Theories of strength. ASME J Appl Mech 1(3):111–129
Nadai A (1937) Plastic behavior of metals in the strain hardening range. J Appl Phys 8:205–213
Nadai A (1950) Theory of flow and fracture of solids, vol I. McGraw-Hill Book Company Inc., New York
Nadai A (1963) Theory of flow and fracture of solids, vol II. McGraw-Hill Book Company Inc., New York
Nøkleby JO (1981) Fatigue under multiaxial stress conditions. Report MD-81001, Div. Masch. Elem., The Norwey Institute of Thecnology, Trondheim/Norwegen
Novozhilov VV (1958) Theory of elasticity. Sudpromgiz (in Russian, Teoriya uprugosti), Moscow
Octrue M, Ghribi D, Sainsot P (2018) A contribution to study the Theory Flank Fracture (TFF) in cylindrical gears. Procedia Eng 213:215–226
Oster P (1982) Beanspruchung der Zahnflanken unter Bedingungen der Elastohydrodynamik. Doctoral thesis, Technical Univesity of Munich
Papadopoulos IV (1994) A new criterion of fatigue strength for out-of-phase bending and torsion of hard metal. Int J Fatigue 16:377–384
Paul P (1968) Generalized pyramidal fracture and yield criteria. Int J Solids Struct 4:175–196
Pedersen R, Rice RL (1961) Case crushing of carburized and hardened gears. SAE Technical Paper 610031 and SAE Transactions, SAE Transactions, Warrendale, PA, pp S360–370
Ristivojević M, Lazovic T, Venci A (2019) Studying the load carrying capacity of spur gear tooth flanks. Mech Mach Theory 59:125–137
Sandberg E (1981) A calculation method for subsurface fatigue. In: International symposium in gearing and power transmissions, Tokyo, I, pp S429–434
Shames IH, Cozzarelli FA (1997) Elastic and inelastic stress analysis. Revised Printing, Taylor & Francis Ltd., Philadelphia
Sharma VK, Breen DH, Walter GH (1977) An analytical approach for establishing case depth requirements in carburized and hardened gears. In: Transaction of ASME for presentation at the design engineering technical conference, Chicago, IL, pp 26–30
Simbürger A (1975) Festigkeitsverhalten zäher Werkstoffe bei einer mehrachsigen phasenverschobenen Schwingbeanspruchung mit körperfesten und veränderlichen Hauptspannungsrichtungen, Diss., TH Darmstadt
Sonsino CM (2007) Course of SN-curves especially in the high-cycle fatigue regime with regard to component design and safety. Int J Fatigue 29(12):2246–2258
Sponzilli JT, Remus GE, Clarke TM, Sawdo EJ (2000) Steel quality requirements for heavy duty off-highway gearing, SAE Technical Paper 2000-01-2566
Stahl K, Hein M, Tobie T (2018) Calculation of tooth flank fracture load capacity. Gear Solution, Sri Lanka
Suresh S (1998) Fatigue of materials, 2nd edn. Cambridge University Press, Cambridge
Tallian TE (1992) Failure Atlas for Hertz contact machine elements. ASME Press, New York
Thomas J (1997) Flankentragfähigkeit and Laufverhalten von hart-feinbearbeiteten Kegelrädern. Doctoral thesis, Technical University of Munich
Timoshenko SP (1953) History of strength of materials. McGraw-Hill Book Company Inc, New York
Timoshenko SP, Goodier JN (1951) Theory of elasticity, 2nd edn. McGraw-Hill Book Company Inc, New York
Tobe T, Kato M, Inoe K, Takatsu N, Morita I (1986) Bending strength of carburized C42OH spur gear teeth. ISME, pp 273–280
Tobie T, Höhn B-R, Stahl K (2013) Tooth flank breakage-influences on subsurface initiated fatigue failures of case-hardened gears. In: Proceedings of the ASME 2013 power transmission and gearing conference, Portland, OR, 4–7 August 2014
Townsend DP (1992) Gear handbook. McGraw-Hill Book Company inc., New York
Vullo V (2014) Circular cylinders and pressure vessels: stress analysis and design. Springer International Publishing Switzerland, Cham-Heidelberg
Weibull W (1939) A statistical theory of strength of materials, Ingeniörs Vatenskaps Akademiens Handlinger, Nr. 151, Generalstabens Litografiska Anstalts Förlag, Stockholm
Witzig J (2012) Flankenbruch Eine Grenze der Zahnradtragfähigkeit in der Werkstofftiefe. Ph.D. thesis, Technical University of Munich
Yu M (2002) Advances in strength theories for materials under complex stress state in the 20th Century. ASME Appl Mech Rev 55(3):169–218
Zenner H, Richter I (1977) Eine Festigkeitshypothese für die Dauerfestigkeit bei beliebigen Beanspruchungskombinationen. Konstruktion 29:11–18
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Vullo, V. (2020). Tooth Flank Breakage Load Carrying Capacity 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_11
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