Abstract
In this chapter, the initially slow and then increasingly rapid awakening of the second scientific age, which goes from Galileo to the present day, is described. Attention is first focused on the first two centuries of scientific activity, from Galileo to Lagrange, because in this time the mechanics establishes itself as queen of the sciences. However, it is emphasized that, in these two centuries, stagnation continues to prevail in the field of gears, which continue to look to the past again and do not immediately benefit from new scientific achievements. Subsequently, attention is focused on the slow detachment from pure empiricism and the equally slow penetration of science into the field of gears. The main scientific contributions are described, which initially concern only the geometric–kinematic aspects. It is also highlighted that, gradually, these aspects begin to be seen from the perspective of the new cutting processes that are gradually conceived and developed. Still later, the attention is focused on the mechanics of solids and on material strength theories that, even in this case, first gradually and then with forced charge, enter the field of gears. In this regard, this brief history only describes the contributions of the pioneers, who have begun new lines of research on gears, starting from Lewis to the present day. Therefore, only the milestones on the state of knowledge concerning the load carrying capacity of the gears in its most diverse aspects are described. To give a concrete demonstration of the fact that gears are ancient science in continuous updating, in the final part of this chapter, brief considerations are presented on the historical aspects of three particular types of damage, which are related to the load carrying capacity of the gears in terms of abrasive wear, micropitting and tooth flank breakage. The chapter closes with epigraphic news on the main monographs and textbooks on gears from 1900 to the present, with a due exception to Olivier’s 1842 treatise, which is probably the first monograph that was written and published on the gears.
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References
Addomine M, Figliolini G, Pennestrì E (2018) A landmark in the history of non-circular gear design: the mechanical masterpise of Dondi’s astrarium. Mech Mach Theory 122:219–232
Airy GB (1827) On the forms of the teeth of wheels. Trans Camb Philos Soc II:279
Akahori H, Sato Y, Nishida Y, Kubo A (2001) Test of the durability of face gears. The JSME international conference, MTP 2001, Fukuoka, Japan
Al-Tubi IS, Long H, Zhang J, Shaw B (2015) Experimental and analytical study of gear micropitting initiation and propagation under varying load conditions. Wear 328–329:8–16
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, July, pp 47–57
Almen JO (1935) Factors influencing durability of spiral bevel gears for automobiles. Automot Ind 73:662–668, 696–701
Almen JO (1942) Dimensional value of lubricants in gear design. SAE J 50, and SAE Technical Paper 420113
Almen JO, Straub JC (1937) Factors influencing the durability of automotive transmission gears. Automot Ind 77:426–432, 488–493
Almen JO, Straub JC (1948) Aircraft gearing, analysis of test and service data. Research Laboratories Division General Motors Corporation, Detroit, Michigan; Source American Gear Manufacturers Association
Amontons G (1699) De la resistance causée dans les machines. Mémoires de Mathematique et de Physique de l’Academie Royale des Sciences, pp 257–282
Archard JF (1953) Contact and rubbing of flat surfaces. J Appl Phys 24(8):981–988
Argyris JH (1954) Energy theorems and structural analysis. Aircr Eng 26:347–356, 383–387, 394
Argyris JH (1955) Energy theorems and structural analysis. Aircr Eng 27:42–58, 80–94, 125–134, 145–158
Argyris JH (1960) Energy theorems and structural analysis. Butterworth Scientific Publications, London
Argyris JH, Kelsey S (1956) The matrix force method of structural analysis and some new applications. Aeron Res Council (London) R&M 3034
Argyris JH, Kelsey S (1956) Structural analysis by the matrix force method with applications to aircraft winds. Wiss Ges Luftfahrt Jahrb, pp 78–98
Aziz IAA, Idris DMN, Ghazali WM (2017) Investigation bending strength of spur gear: a review. In: MATEC web of conferences, 90, 01037, AiGEV 2016
Ball RS (1876) The theory of screws: a study in the dynamics of a rigid body. Hodges, Foster, and Co., Grafton-street, Dublin
Ball RS (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge
Ballarini R (2006) The Da Vinci-Euler-Bernoulli Beam Theory. Mechanical Engineering Magazine Online, June 23
Banerjee PK, Butterfield R (1981) Boundary element methods in engineering science. McGraw-Hill, New York
Basstein G, Sijtstra A (1993) New developments concerning design and manufacturing of face gears. Antriebstechnik 32(11)
Bauschinger J (1897) Mitt Mech Tech Lab. Technischen Hochschule, Munich, nr.25
Beale OJ (1901) A handbook for apprenticed mechanists, 3rd edn. Brown & Sharpe MGF Co., Providence
Becker AA (1992) The boundary element method in engineering: a complete course. McGraw-Hill Book Company, New York
Beermann S, Kissling U (2015) Tooth Flank Fracture—a critical failure mode. Influence of Macro and Micro Geometry. 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
Bell ET (1937) Men of mathematics. Simon & Schuster, New York
Benford RL (1968) Customized motions. Mach Des 151–154
Bennet JA (1991) Geometry and Surveying in early-seventeenth-century England. J Ann Sci 48(4):345–354
Bernoulli J (1691) Specimen alterum Calculi differentialis in demitienda Spirali Logarithmica. Loxodromiis Nautarum & Areis Triangulorum Sphaericorum: una cum Additamento quodam ad Problema Funicularium, aliaque. Acta Eroditorum, June, pp 282–290
Bernoulli J (1692) Lineae Cycloides, Evolutae, Anti-Evolutae, Causticae, Anti-Causticae, Peri-Causticae. Earum usus & simplex relatio ad se invicem. Spira mirabilis. Aliaque. Acta Eroditorum, Maji, pp 207–213
Berthe D, Flamand L, Foucher D, Godet M (1980) Micro-pitting in Hertzian contacts. Trans ASME J Lubr Technol 102:478–489
Bhandari VB (2010) Design of machine elements, 3rd edn. Tata McGraw-Hill Education Private Limited, New Delhi
Bidwell S (1883) On the electrical resistance of carbon contacts. Proc R Soc Lond 35:1–18
Birch TW (2012) Automatic transmissions and transaxles. Pearson Education, Upper Saddle River
Blateyron F (2013) The areal field parameters. In: Leach R (ed) Characterization of areal surface texture. Springer, Berlin
Blok H (1937) Measurements of temperature flashes on gear teeth under extreme pressure conditions. Proc Gen Discuss Lubr Inst Mech Eng 2:18–22
Blok H (1937) Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating conditions. Gen Discuss Lubr Proc Inst Mech Eng 2:222–235
Blok H (1937) Les températures de surface dans des conditions de graissage sous pressions extrêmes. In: Proceedings of the 2nd world petroleum congress, Paris, Section IV, III, pp 151–182
Blok H (1937) Surface temperature measurements on gear teeth under extreme pressure lubricating conditions. Power Transm 653–656
Bloomfield B (1947) Designing face gears. Mach Des 19(4):129–134
Bloomfield B (1960) Non-circular gears. Prod Eng 59–66
Bodensieck EJ (1965) Specific film thickness—an index of gear tooth surface determination. Paper presented at 1965 Aerospace gear communications technical division meeting, AGMA (Denver, CO), Sept
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 26–28 Aug 2014. Also Gear Technology
Bordmer JG (1843) On the pitch of spur and bevel wheels and the shape of the teeth of worm wheels and worm working into each other. Minutes Proc Inst Civ Eng 2:32
Bottema O, Roth B (1979) Theoretical kinematics. North-Holland, Amsterdam
Boussinesq J (1885) Application des Potentiels à l’étude de l’équilibre et du mouvement des solides élastiques avec des notes étendues sur divers points de physique mathématique et d’analyse. Gauthier-Villars, Paris
Bowden FP, Tabor D (1939) The area of contact between stationary and between moving surfaces. Proc R Soc Lond A 169(938):391–413
Bradley RE, Sandifer CE (eds) (2007) Leonhard Euler: life, work and legacy. In: Studies in the history and philosophy of mathematics. Elsevier, Amsterdam
Brebbia CA (1978) The boundary element method for engineers. Pentech Press, London
Buchanan R (1808) An essays on the teeth of wheels: comprehending principles, and their application in practice, to, millwork and other machinery. With numerous figures, revised by Peter Nicholson. Printed by and for William Savage, London
Buchanan R (1814) Practical essays on millwork and other machinery, mechanical and descriptive, 3 vols. Printed by Gibson & Sanderson, for J. Taylor, Edinburgh
Buchanan R (1823) Practical essays on mill work and other machinery, with notes and additional articles containing new researches on various mechanical subjects by Thomas Tredgold, vol I and vol II, 2nd edn. J. Taylor, London
Buckingham E (1928) Spur gears. McGraw-Hill, New York
Buckingham E (1949) Analytical mechanics of gears. McGraw-Hill, New York
Burn RP (2012) Another theorem of Cauchy which admits exceptions. Historia Mathematica 39(2):206–210
Buyse F (2017) Galileo, Huygens and the pendulum clock: isochronism and synchronicity. Soc Polit 11(2):7–14
Camus CEL (1733) Sur la figure des dentes des rouës, et des ailes des pignons, pour rendre les horloges plus perfaites. Historie et Mémoires de l’Academie des Sciences, Paris, pp 117–140
Camus CEL, Hawkins JI (1837) A Treatise on the teeth of wheels, demonstrating the best forms which can be given to them for the purposes of machinery, such as mill-work and clock-work, and the art of finding their numbers, translated from the French of M. Camus, 2nd edn. carefully revised and enlarged with Details of the Present Practice of Mill-Wrights, Engine Makers, and other Mechanists. John Isaac Hawkins, James S. Hudson, London
Capechi D (2018) The path to post-galilean epistemology, reinterpreting the birth of modern science. Springer International Publishing AG, Berlin
Carbone GM (2017) Brown & Sharpe and the measure of American industry: making the precision machine tools that enabled manufacturing, 1833–2001. McFarland & Co., Inc., Jefferson
Cardano G (1870) Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum. Item de aliza regula. Henricus Petri, Basel
Castigliano CA (1873) Intorno ai sistemi elastici, Dissertazione presentata da Castigliano Carlo Alberto alla Commissione Esaminatrice della R. Scuola d’Applicazione degli Ingegneri in Torino. Bona, Torino
Cauchy A-L (1821) Cours d’Analyse de l’École Royale Politechnique: Analyse Algébrique. Debure Frères, Paris
Cauchy A-L (1823) Recherches sur l’equilibre et le mouvement intérieur des corps solides ou fluides élastiques ou non élastiques. Bulletin de la Societé Plilomathique 9–13
Cauchy A-L (1828) Sur les équations qui expriment les conditions d’équilibre ou les lois du mouvement intérieur d’un corps solide élastique ou non élastique. Exercises de Mathématiques 3:160–187
Cauchy A-L (1853) Note sur les series dont les divers termes sont des functions continues d’une variable réelle ou imaginaire, entre les limites données. Comptes Rendus de l’Académie des Sciences, Paris 36:454–459
Cayley A (1858) A memoir on the theory of matrices. Philos Trans R Soc Lond 148:17–37
Cerruti V (1881–82) Ricerche intorno all’equilibrio dei corpi elastici isotropi, Atti della Reale Accademia dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, Serie 3, Annata 279, vol 13, pp 81–122; reprint with the same title, Roma, Salviucci, 1882
Chakraborty J, Bhadoria BS (1971) Design of face gears. Mechanisms 6:435–445
Chakraborty J, Bhadoria BS (1973) Some studies on hypoid face gears. Mech Mach Theory 8:339–349
Chauhan V (2016) A review on effect of some important parameters on the bending strength and surface durability of gears. Int J Sci Res Publ 6(3):289–298
Clapeyron BPE (1833) Mémoire sur l’équilibre intérieur des corps solides homogènes. Mémoires présentés par divers savants à l’Académie Royale des Sciences de l’Institut de France, Sciences Mathématiques et Physiques 4:463–562
Clough RW (1960) The finite element method in plane stress analysis. In: Proceedings of the second conference on electronic computation. American Society of Civil Engineers, New York, pp 345–377
Colbourne JR (1987) The geometry of involute gears. Springer, Berlin
Colonnetti G (1918) Applicazione a problemi tecnici di un nuovo teorema sulle coazioni elastiche. Atti R Acc Torino 54:69–83
Colonnetti G (1940) Deformazioni plastiche e deformazioni viscose, Pontificia Academia Scientiarum, Città del Vaticano. Tip. Cuggiani, Roma, pp 155–161
Colonnetti G (1953) Scienza delle Costruzioni: 1. Teoria generale dell’equilibrio, 3rd edn. Edizioni Scientifiche Einaudi, Torino
Colonnetti G (1955) Scienza delle Costruzioni: 2. La statica delle travi e degli archi, 3rd edn. Edizioni Scientifiche Einaudi, Torino
Colonnetti G (1957) Scienza delle Costruzioni: 3. La tecnica delle costruzioni. Le pareti sottili, 3rd edn. Edizioni Scientifiche Einaudi, Torino
Cook RD (1974) Concepts and applications of finite element analysis, 2nd edn. Wiley, New York
Cormac P (1936) A treatise on screws and worm gear, their mills and hobs. Chapman & Hall Ltd, London
Coulomb CA (1773) Essai sur une application des règles de maximis et de minimis à quelques problèmes de Statique relatifs à l’Architecture, aver 2 planches, Mémoires de mathématiques et de physique présentés a l’Academie Royale des sciences par divers savants, & Iûs dans ses assemlées, vol 7, à Paris: De l’Imprimerie Royale, pp 343–382
Coulomb CA (1781) Théorie des machines simples en ayant égard au frottement de leur parties et a la roider des Corages. Piece qui remporté le Prix double de l’Academie des Sciences pour l’année 1781. Mémoires de Mathematique et de Physique de l’Academie Royale des Sciences, pp. 145–173. A Paris, De l’Imprimerie de Montard, Imprimeur-Libraire de la Reine, de Madame, de Madame la Contesse d’Artois, & de l’Academie Royale de Sciences, 1782
Courant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49(1):1–23
Couturat LL (1901) La logique de Leibniz d’après des documents inédits. Felix Alcan, Editeur, Paris
Crosher WP (2014) A gear chronology, significant events and dates affecting gear development. Book Publishers Xlibris LLC, Bloomington
Cunningham FW (1957) Non-circular gears. Transactions of the 5th congress on mechanisms, Purdue University, West Lafayette, Ind., pp 96–103
Davydov JS (1944) Spur and helical involute pinions with crossed axes; influence of errors on accuracy of operation. Ph.D. thesis, maintained in Tomsk Polytechnic Institute (in Russian)
de Condorcet MJAN (1765) Essais sur le calcule intégral. De l’Imprimerie de Didot, Paris
De La Hire F (1694) Traité des Epicycloïdes, & de leurs usages dans les Mechaniques. In: Memoires de Mathematique et Physique. De l’Imprimerie Royale, A Paris
De La Hire F (1695) Traité de mécanique: ou l’on explique toot ce qui est nécessaire dans la pratique des arts, & les propriétés des corps pesants lesquelles ont un plus grand usage dans la physique. De l’Imprimerie Royale, A Paris
Del Monte G (1577) Mechanicorum liber. Apud Hieronymum Concordiam, Pisauri
Denavit J, Hartenberg RS (1955) A kinematic notation for lower pair mechanisms based on matrices. ASME J Appl Mech 22:215–221
Descartes R (1644) Principia Philosophiae. apud Ludovicum Elzevirium, Amstelodami
Descartes R (1637) Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences. Plus la Dioptrique. Les Meteores. Et la Geometrie. Qui sont des essais de fette Méthode. De l’Imprimerie de Ian Maire, Leyde
Disaguliers JT (1734) A course of experimental philosophy, 1st edn., vol I. W. Innys, M. Senex and T. Longman, London
Disaguliers JT (1744) A course of experimental philosophy, 1st edn., vol II. W. Innys, M. Senex and T. Longman, London
Disteli M (1914) Über des Analogen der Savary schen Formel und Konstruktion in der kinematischen Geometrie des Raumes. Zeitschrift für Mathematic und Physik 62:261–309
Dolan TJ, Broghammer EL (1942) A photoelestic study of stresses in gear tooth fillets. Bulletin 335, University of Illinois, Engineering Experimental Station
Dooner DB (2012) The kinematic geometry of gearing, 2nd edn. Wiley, Chichester
Dooner DB, Seireg AA (1995) The kinematic geometry of gearing: a concurrent engineering approach. Wiley, New York
Dowson D, Higginson GR (1959) A numerical solution to the elastohydrodynamic problem. J Mech Eng Sci 1(1):7–15
Dowson D, Higginson GR (1966) Elasto-hydrodynamic lubrication, SI edn. Pergamon Press, Oxford
Dowson D, Higginson GR (1977) Elastohydrodynamic lubrication, 2nd edn. Pergamon, London
Drake S (1978) Galileo at work. His scientific biography. University of Chicago Press, Chicago
Dudley DW (1954) Practical gear design. McGraw-Hill Book Company, New York
Dudley DW (ed) (1962) Gear handbook: the design, manufacture, and application of gears, 1st edn. McGraw-Hill Book Company, New York
Dupont P (1962/63) Nuove dimostrazioni della formula di Eulero-Savary e suo studio storico. Atti Accad Sci Torino Cl Sci Fis Mat Nat 97
Dürer A (1525) Underweysung der Messung, mit dem Zirckel und Richtscheyt in Lienen, Ebnen unnd gantzen Corporen (or Instructions for Measuring with Compass and Ruler). Hieronymus Andreae, Gedruckt zuo Nürenberg
D’Alembert M (1743) Traité de Dynamique, dans lequel les Lois de l’Equilibre & du Mouvement des Corps sont réduites as plus petit nombre possible, & démontrées d’une maniére nouvelle, & où l’on donne un Principle général pour trouver le Mouvement de plusieurs Corps qui agissent les uns sur les autres, d’une maniére quelcomque, A Paris, Chez David l’aîné, Libraire
Ehret P, Dowson D, Taylor CM (1998) On the lubricant transport conditions in elastohydrodynamic conjunctions. Proc R Soc Lond, Ser A 454
Elkholy A (1983) Case depth requirements in carburized gears. Wear 88:S233–S244
Ellenberger M, Collin M-M (1993) La machine à calculer de Blaise Pascal. Nathan, Paris
Ertel AM (1939) Hydrodynamic lubrication based on new principles. Akad Nauk SSSR Prikadnaya Mathematica i Mekhanika 3:41–52
Ertel AM (1945) Hydrodynamic lubrication analysis of a contact of curvilinear surfaces. Dissertation on Proceedings of CNIITMASH, Moscow, pp 1–64
Euler L (1736) Mechanica sive motus scientia analytice exposita, Tomus I et Tomus II, Instar Supplementi Ad Commentar. Acad. Scient. Imper. Petropoli, ex Typographia Academicae Scientiarum
Euler L (1751/54) De Aptissima Figura Rotarum Dentibus Tribuenda. Novi Commentarii Academiae Scientiarum Petropolitanae
Euler L (1762/65) Supplementum the Figura Dentium Rotarum. Novi Commentarii Academiae Scientiarum Petropolitanae, pp 299–317
Fairbairn W (1863) Treatise on mills and millwork, part I. Longmans, Green and Company, London
Fairbairn W (1871) Treatise on mills and millwork, part II. Longmans, Green and Company, London
Fatemi A, Socie DF (1988) A critical plane to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract Eng Mater Struct 11(3):149–165
Fatemi A, Shamsaei N (2011) Multiaxial fatigue: an overview and some approximation models for life estimation. Int J Fatigue 33(8):948–958
Fenner RT (1986) Engineering elasticity, application of numerical and analytical techniques. Ellis Horwood Limited Publishers, Chichester
Ferrari C, Romiti A (1966) Meccanica Applicata alle Macchine. Unione Tipografica-Editrice Torinese, UTET, Torino
Fisher A (1961) The use of speed factors in calculating the load carrying capacity of helical gears. Machinery 98(8):545–552
Fisher R, Kücükay F, Jürgens G, Najork R, Pollak B (2015) The automotive transmission book. Springer International Publishing Switzerland, Cham
Flamant A-A (1892) Sur la répartition des pressions dans un solide rectangulaire chargé trnsversalement. Comptes Rendus des Séances de l’Academie des Sciences, Paris 114:1465–1468
Flanders RE (1909) How many gashes should a hob have? Machinery
Flanders RE (1909) Interchangeable involute gear tooth systems. J Am Soc Mech Eng 1501–1520
Flanders RE (1909) Gear-cutting machinery, comprising a complete review of contemporary American and European practice, together with a logical classification and explanation of the principles involved. Wiley, New York
Ford H, Alexander JM (1963) Advanced mechanics of materials, 2nd edn. Ellis Horwood, Chichester
Foullon A (1563) Usaige et description de l’holometre pour savoir mesurer toutes choses qui sont soubs l’estendue de l’oeil. chez Pierre P. Béguin, A Paris
Francis V, Silvagi J (1950) Face gear design factors. Prod Eng 21:117–121
Franklin J (2017) Discrete and continuous: a fundamental dichotomy in mathematics. J Hum Math 7(2):356–378
Franklin LJ, Smith CH (1924) Effect of inaccuracies on strength of gears. Trans ASME 46
Föppl AO (1897) Vorlesung über technische Mechanik, Band III, Festigkeitslehre. Teubner Verlag, Leipzig
Föppl AO (1909) Mitt Mech Tech Lab. Technischen Hochschule, Munich, nr. 31
Föppl AO (1914) Vorlesung über technische Mechanik, Band IV, Dynamik. Teubner Verlag, Leipzig
Föppl AO, Föppl L (1920) Drang und Zwang: eine höhere festigkeitslehre für ingenieure, 2 vols. R. Oldenbourg, München und Berlin
Galilei G (1594) Delle Meccaniche lette in Padova l’anno 1594 da Galileo Galilei. Memorie del Reale Istituto Veneto di Scienze, Lettere ed Arti, vol XXVI (5). Tipografia C. Ferrari, Venezia (reprint of 1899)
Galilei G (1638) Discorsi e Dimostrazioni Matematiche, intorno a due Nuove Scienze attinenti alla Meccanica & i Movimenti Locali. Appresso gli Elsevirii, Leida
Garro A, Vullo V (1978) Alcune considerazioni sul proporzionamento degli ingranaggi. Atti del VI Convegno Nazionale AIAS, Brescia, 22–24 giugno
Garro A, Vullo V (1979) Acoustic problems in vehicle transmissions. Nauka I Motorna vozila ‘79, Science and Motor Vehicles ‘79, Bled, Slovenija, Jugoslavija, 4–7 June
Gautschi W (2008) Leonhard euler: his life, the man, and his works. SIAM Rev 50(1):3–33
Gere JM, Timoshenko SP (1997) Mechanics of materials. PWS Publishing Company, Boston
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 Aug
Giovannozzi R (1951) Costruzione di Macchine, vol II, 2th edn. Casa Editrice Prof. Riccardo Pàtron, Bologna
Giovannozzi, R (1965) Costruzione di Macchine, vol II, 4th edn. Casa Editrice Prof. Riccardo Pàtron, Bologna
Giovannozzi R (1965) Costruzione di Macchine, vol I, 2nd edn. Casa Editrice Prof. Riccardo Pàtron, Bologna
Gladwell GML (1980) Contact problems in the classical theory of elasticity. Sijthoff & Noordhoff International Publishers B.V., Germantown, Maryland, USA: Alphen aar den Rijn, The Netherlands
Gobler HE (1939) Rollcurve gears. Trans ASME 61:223–231
Gochman CI (1941) Control of spur pinions by means of wires. J Opt Mech Ind 6
Goglia PR, Cusano C, Conry TF (1984) The effects of surface irregularities on the elastohydrodynamic lubrication of sliding line contacts. Part I-Single Irregul ASME J Tribol 106(1):104–112
Goglia PR, Cusano C, Conry TF (1984) The effects of surface irregularities on the elastohydrodynamic lubrication of sliding line contacts. Part II-Wavy Surf ASME J Tribol 106(1):113–119
Goldfarb V, Barmina N (eds) (2016) Theory and practice of gearing and transmissions, in honor of Professor Faydor L. Litvin. Springer International Publishing Switzerland, Berlin
Grant GB (1885) A handbook on the teeth of gears, their curves, properties and practical construction. Grant Gear Works, Boston
Grant GB (1891) Odontics, or, the theory and practice of the teeth of gears. Lexington Gear Works, Lexington
Grant GB (1899) A treatise on gear wheels, 8th edn. Grant Gear Works, Boston
Grubin AN, Vinogradova IE (1949) Investigation of the contact of machine components. Central scientific research institute for technology and mechanical engineering, Book no 30, Moscow, D.S.I.R. translation no 337
Guingand M, de Vaujany J-P, Jacquin C-Y (2005) Quasi-static analysis of a face gear under torque. Comput Methods Appl Mech Eng 194:4301–4318
Hamming PW (1959) Stable predictor-corrector methods for ordinary differential equations. J Assoc Comput Math 6
Hamrock BJ, Dowson D (1977) Isothermal elastohydrodynamic lubrication of point contact: part III—fully flooded results. ASME J Lubr Technol 99(2):264–275
Hamrock BJ, Dowson D (1981) Ball bearing lubrication, the elastohydrodynamics of elliptical contacts. Wiley, New York
Handschuh RF, Lewicki DG, Bossler RB (1994) Experimental testing of prototype face gears for helicopter transmissions. Proc Inst Mech Eng Part G: J Aerosp Eng
Harrison J (1767) The principles of Mr Harrison’s time-keeper with plates of the same. London: W. Richardson & S. Clark
Heath GF, Filler RR, Tan J (2002) Development of face gear technology for industrial and aerospace power transmission. NASA/CR-2002-211320, ARL-CR-0485, 1L18211-FR-01001, May
Hein M, Tobie T, Stahl K (2017) Parameter study on the calculated risk of tooth flank fracture of case-hardened gears. Bull JSME J Adv Mech Des Syst Manuf II(6)
Henchy H (1924) Zur Theorie plastischen Deformationen und hierdurch in Material hervorgerufenen Nebenspannungen. In: Proceedings of 1st international congress for applied mechanics, deft, pp 312–317
Henriot G (1949) Traité Théorique et Pratique des Engrénages, tome I. Dunod, Paris
Henriot G (1950) Traité théorique et pratique des engrenages, tome II, Étude complète du material. Dunod, Paris
Henriot G (1960) Traité théorique et pratique des engrenages, Tome I, Théorie et technologie, 3rd edn. Dunod, Paris
Hertter T (2003) Rechnirischer Festigkeitsnachweis der Ermüdungstragfähigkeit vergüteter und einsatzgehärteter Zahnräder. Ph.D. thesis, Technical University of Munich
Hertz HR (1882) Über die Berührung fester elastischer Körper. Journal für Reine und Angewandte Mathematik (Crelle’s J.) 92:156–171
Heyman J (1998) Structural analysis, a historical approach. Cambridge University Press, Cambridge
Heywood RB (1948) Modern applications of photoelasticity. Proc Inst Mech Eng 158(2):235–250
Heywood RB (1952) Designing by photoelasticity. Chapman & Hall, Lmt., London
Hill R (1950) The mathematical theory of plasticity. Clarendon Press, Oxford
Holditch H (1842) On rolling curves. Trans Camb Philos Soc 7(7):61–82
Holm R (1946) Electric contacts. Hugo Gerbers Forlag, Stockholm
Hooke R (1678) Lectures de Potentia Restitutiva or of Spring explaining the power of springing bodies, to which are added some collections. John Martyn Printer to the Royal Society, London
Hooke R (1679) Lectiones Cutlerianae or a Collection of lectures: physical, mathematical, geographical & astronomical. Printed for John Martyn Printer to the Royal Society, at the Bell in S. Paul’s Charch-yard, London
Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J Aeronaut Sci 540–550
Huber MT (1904) A contribution to fundamentals of the strength of materials. Czasopismo Tow. Technicze Krakow 22:81 (in Polish)
Huygens C (1673) Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae. Apud F. Muguet, MDCLXXIII, Parisiis
Huygens CE (1986) The pendulum clock or geometrical demonstrations concerning the motion of pendula as applied to clocks (trans: Blackwell RJ). Iowa State University Press, Ames
Höhn B-R, Oster P, Emmert S (1996) Micropitting in case-carburized gears—FZG micropitting test. In: International conference on gears, Dresden, Germany, VDI Berichte Nr. 1230, pp 331–334
Imison J (1787) A treatise on the mechanical powers. Printed by the author, and sold by R. Jameson, London
Irgens F (2010) Continuum mechanics. Springer, Berlin
Ishida K (1977) Computer simulation of stresses and deformations of gear case, and of gear teeth taking the influence of gear body into consideration. World Congress on Gearing, Paris, 22–24 June 1977, pp. 309–323
Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge
Jonhson KL (1995) Contact mechanics and the wear of metals. Wear 190(2):162–170
Kapelevich AL (2013) Direct gear design. CRC Press, Taylor & Francis Group, Boca Raton
Karas F (1941) Elastische Formänderung und Lastverteilung beim Doppeleingriff gerader Stirnradzähne, VDI – Forschungheft 406, B, Bd. 12
Katchanov L (1975) Éléments de la Théorie de la Plasticité. Éditions MIR, Moscou
Kelley B-W, Pedersen R (1958) The beam strength of modern gear tooth design. SAE Trans 66:137–157, and SAE Technical Paper 580017, 1958
Keplero I (1596) Prodomus dissertationum cosmographicarum, contineus mysterium cosmographicum, de admirabili proportione orbium coelestium, de que causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & propriis, demonstratum, per quinque regularia corpora geometrica (i.e. Forerunner of the Cosmological Essays, wich contains the secret of the Universe; on the Marvelous Proportion of the Celestial Spheres, and on the True and Particular Causes of the Number, Magnitude, and Periodic Motions of the Heavens; Established by means of the Five Regular Geometric Solids). excudebat Georgius Gruppenbachius, Tubingae
Kissling U, Beermann S (2007) Face gears: geometry and strength. Gear Technol 54–61
Klein M, Höhn BR, Michaelis K, Annast R (2011) Theoretical and experimental investigations about flank breakage in bevel gears. Ind Lubr Tribol 63(1):5–10
Kolchin NI (1949) Analytical calculation of planar and spatial gearings. Mashgiz, Moscow-Leningrad
Kolchin NI (1949) Main problems of the theory of non-circular gearwheels. In: Proceedings of LONITOMASH, 6, Theory and analysis of gearwheels. Mashgiz, Moscow-Leningrad
Kramberger J, Šraml M, Glodez S, Flašker J, Potrč I (2004) Computational model for the analysis of bending fatigue in gears. Comput Struct 82(23):2261–2269
Kulkarni S, Kajale P, Patil DU (2015) Recirculating Ball Screw. Int J Eng Res Sci Technol 4(2):252–257
Kurrer K-E (2008) The History of the Theory of Structures: from arch analysis to computational mechanics. Ernst & Sohn Verlag, Berlin
Lagrange J-L (1788) Méchanique Analitique, 1re éd. Chez La Veuve Desaint, Libraire, A Paris
Lagutin S, Barmina N (2016) Prof. F.L. Litvin: Contribution to the Formation of the Russian School of the theory of gearing. In: Gotfard V, Barmina N (eds) Theory and practice of gearing and transmissions in honor of Professor Faydor L. Litvin. Springer International Publishing Switzerland, Cham
Lalovera A (1660) Veterum Geometrica promota in septem de Cycloide Libris et in duobus adjectis Apprendicibus. apud Arnaldum Colomerium, Toulouse
Lamé G (1852) Leçons sur la théorie mathématique de l’élasticité des corps solides. Bachelier, Imprimeur-Libraire, Paris
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 Technol 54–63
Lasche O (1899) Elektrischer Antrieb mittels Zahnradübertragung. VDI – Zeitschrift 43(48):1487–1493, (49):1528–1533
Lechner G, Naunheimer H (1999) Automative transmissions: fundamentals, selection, design and applications. Springer, Berlin
Leibniz GW (1684) Nova Methodus pro Maximis et minimis, itemque tangentibus, que nec fractas, nec irrationales quantitates moratur, & singulare pro illis calculi genus. Acta Editorum, Lipsiae, pp 467–473
Leibniz GW (2000) Discoveries of Principle of the Calculus in (Acta Editorum) (trans: Beaudry P). Leesburg, VA, USA, Sept, pp 60–61
Leslie J (1829) Elements of natural philosophy, including mechanics and hydrostatics, 2nd edn. Olivier and Boyd, and G.B. Whittaker, London
Levy S (1953) Structural analysis and influence coefficients for delta winds. J Aeronaut Sci 20(7):449–454
Lewicki DG, Handschuh RF, Heath GF, Sheth V (1999) Evaluation of carbonized face gears. The American helicopter society 55th annual forum, Montreal, Canada
Lewis W (1892) Investigation of strength of gear teeth. Proc Eng Club, Philadelphia, Pennsylvania, USA, Oct, pp 16–23
Li S, Kahraman A (2013) A physics-based model to predict micro-pitting lives of lubricated point contacts. Int J Fatigue 47:205–215
Li S, Kahraman A (2013) Micro-pitting fatigue lives of lubricated point contacts: experiments and model validation. Int J Fatigue 48:9–18
Litvin FL (1955) Application of matrices and dual number calculations to analysis of spatial gearings. Proc Leningr Polytech Inst 182 (in Russian)
Litvin FL (1956) Non circular gears: design, theory of gearing, and manufacture, 2nd edn. Gos. Tech. Isdat, Leningrad-Moscow (in Russian)
Litvin FL (1994) Gear geometry and applied theory. PTR Prentice Hall, Prentice Hall Inc., Englewood Cliffs
Litvin FL, Fuentes A (2004) Gear geometry and applied theory, 2nd edn. Cambridge University Press, Cambridge
Litvin FL, Chen YS, Heath GF, Sheth VJ, Chen N (2000) Apparats and method for precision grinding face gears. U.A. Patent No. 6.146.253
Litvin FL, Wang JC, Bossler RB Jr, Chen Y-JD, Heath G, Lewicki DG (1992) Application of face-gear drives in helicopter transmission. In: Proceeding of the 6th international power transmission and gearing conference, Scottsdale, Arizona, 13–16 Sept, and NASA Technical Memorandum 105655, AVSCOM Technical Report 91-C-036
Liu H, Liu H, Zhu C, Zhou Y (2019) A review on micropitting studies of steel gears. Coatings 9(1):42
Logue CH (1922) American mechanist gear book, 3rd edn. revised by R. Trautschold. McGraw-Hill Book Company, Inc., New York
Long H, Al-Tubi IS, Martinze MTM (2015) Analytical and experimental study of gear surface micropitting due to variable loading. Appl Mech Mater 750:96–103
Loveless WG (1984) Cone drive double enveloping worm gearing design & manufacturing. Gear Technol 12–16, 45
Lovász L (2000) Discrete and continuous: two sides of the same? GAFA geometric and functional analysis. Birkhäuser Verlag, Basel, pp 359–382
Mac Curdy E (1938) Leonardo da Vinci notebooks. Jonathan Cape, London
MackAldener M (2001) Tooth interior fatigue fracture and robustness of gears. Doctoral Thesis, KTH Stockholm
MackAldener M, Olsson M (2000) 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 Technol 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 Fract Mech 69(18):2147–2162
Maitra GM (1994) Handbook of gear design, 2nd edn. Tata McGraw-Hill Publishing Company Ltd., New Delhi
Mancosu P (1996) Philosophy of mathematics and mathematical practice in the seventeenth century. Oxford University Press, New York
Mariotte E (1686) Traité du mouvement des eaux. Michallet, Paris
Martin HM (1916) The lubrication of gear teeth. Engineering 102:199–204
Marx GH, Cutter LE (1915) Strength of gear system. Trans ASME 37
Maugin GA (2017) Continuum mechanics through the ages—from the renaissance to twentieth century: from hydraulics to plasticity. Springer, Berlin
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)
McDonnell A (2007) Jesse Ramsden (1735–1800): London’s leading scientific instruments maker. Ashgate Publishing Limited, Aldershot
McMullen FE, Durcan TM (1922) The Gleason works system of bevel gears. Machinery, June
Melosh RJ (1963) Basis for derivation of matrices for the direct stiffness method. J Am Inst Aeronaut Astronaut 1(7):1631–1637
Menabrea LF (1858) Nouveau principe sur la distribution des tensions dans les systèmes élastiques. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences 46:1056–1060
Merritt HE (1935) Worm gear performance. Institution of Mechanical Engineers
Merritt HE (1937) The lubrication of gear teeth. Institution of mechanical engineers, general discussion on lubrication and lubricants, group III, industrial applications, Oct
Merritt HE (1946) Gears, 2nd edn. Sir Isaac Pitman & Sons Ltd, London
Merritt HE (1954) Gears, 3rd edn. Sir Isaac Pitman & Sons Ltd., London
Meyer PB (2011) The Wilson preselector gearbox, armstrong-siddley type. PBM Verlag, Seevetal, Hamburg
Minotti M, Salvini P, Vivio F, Vullo V (2007) Metodo di taglio di viti e ruote in un riduttore a viti e ruota con ricircolazione di sfere. Atti XXXVI Convegno Nazionale AIAS, Ischia, 04–07 Sept
Modugno F (1940) Teoria e Costruzione degli Ingranaggi ad Assi Paralleli con Applicazione ai Riduttori Marini. Arti Grafiche Panetto & Petrelli, S.A. Spoleto
Modugno F (1951) Ingranaggi Cilindrici. Editore Ulrico Hoepli, Milano
Mohr O (1882) Über die Darstellung des Spannungszustandes und des Deformationszustandes eines Körperelementes. Zivilingenieur, p 113
Mohr O (1906) Abhandlungen aus dem Gebiete der technischen Mechanik. Wilhelm Ernst und Sohn, Berlin
Moon FC (2007) The Machines of Leonardo Da Vinci and Franz Reuleaux, Kinematics of machines from the renaissance to the 20th century. Springer, Dordrecht
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 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
Naunheimer H, Bertsche B, Ryborz J, Novak W (2011) Automotive transmissions: fundamentals, selection, design and application, 2nd edn. Springer, Berlin
Navier CLMN (1823) Mémoire sur la flexion des planes élastiques, présenté à l’Académie des Sciences de France, 1820, and publied in the Bulletin des Sciences de la Societé Philo-Mathematique de Paris
Neuber H (1934) Ein neuer Ansatz zur Lösung räumlicher Problem der Elastizitätstheorie. Der Hohlkegel unter Einzellast als Beispiel. Zeitschrift für Angewandte Mathematik und Mechanik 14(4):203–212
Newmark NM (1959) A method of computation for structural dynamics. Proc ASCE 85(EM3):67–94
Newton I (1687) Philosophiae Naturalis Principia Mathematica, 1st edn. Jussu Societatis Regiae ac Typis Josephi Streater, Londinii, Anno MDCLXXXVII
Niemann G (1954) Maschinenelemente: Band 2: Getriebe allgemein, Zahnradgetriebe- Grundlagen, Stirnradgetriebe. Springer, Berlin
Niemann G (1960) Maschinenelemente. Entwerfen, Berechnen und Gestalten im Maschinenbau. Zweiter Band: Getriebe. Getriebearten, Zahnradgetriebe, Stirnräder, Kegelräder und versetzte Kegelräder, Schneckentriebe, zylindrische Schraubenräder, Kettentriebe, Reibräder und Regelreibgetriebe, Reibkupplungen und Reibbremsen, Richtungskupplungen, Freiläufe, Gesperre. Springer, Berlin
Niemann G, Glaubitz H (1950) Zahnfußfestigkeit geradverzahnter Stirnräder aus Stahl, VDI – Zeitschrift 92(33):923–932
Niemann G, Glaubitz H (1951) Zahnfußfestigate geradverzahnter Stirnräder aus Stahl. VDI - Zeirschrift 92(93):1050–1053
Niemann G, Rettig H (1956) Untersuchungen an Blechzahnrädern. Mitt. Forsch. Ges. Blechverarb, Sept
Niemann G, Winter H (1983) Maschinen-Elemente Band II: Getriebe allgemein, Zahnradgetriebe-Grundlagen, Stirnradgetriebe. Springer, Berlin
Niemann G, Winter H (1983) Maschinen-Elemente, Band III: Schraubrad-, Kegelrad-, Schnecken-, Ketten-, Rienem-, Reibradgetriebe, Kupplungen, Bremsen, Freiläufe. Springer, Berlin
Niemann G, Rettig H, Lechner G (1963) Some Possibilities to Increase the Load-Carrying-Capacity of Gears. SAE Technical Paper 630457
Novozhilov VV (1958) Theory of elasticity. Sudpromgiz, Moscow (in Russian, Teoriya uprugosti)
Octrue M, Ghribi D, Sainsot P (2018) A contribution to study the theory flank fracture (TFF) in cylindrical gears. Procedia Eng 213:215–226
Olivier T (1842) Theorié Géométrique des Engrenages destines à transmettre le movement de rotation entre deux axes situés ou non dans un même plane. Bachelier Imprimeur-Libraire, Paris
Ollson U (1953) Non-circular cylindrical gears, Mechanical engineering series (10). Acta Polytechnica, Stockholm
Ollson U (1959) Non-circular bevel gears, Mechanical engineering series (5). Acta Polytechnica, Stockholm
Oster P (1982) Beanspruchung der Zahnflanken unter Bedingungen der Elastohydrodynamik. Doctoral Thesis, Technical Univesity of Munich
Özgüven HN, Houser DR (1988) Mathematical models used in gear dynamics—a review. J Sound Vib 121(3):383–411
Panjkovic V (2014) Friction and hot rolling of steel. CRC Press, Taylor&Frencis Group, Boca Raton
Parent A (1713) Essais et recherches de mathématique et de physique. J. de Nully, Paris
Pascal B (1779) Oeuvres de Blaise Pascal. Chez Detune, La Haye
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–S370
Peterson RE (1933) Stress concentration phenomena in fatigue of metals. Trans ASME J Appl Mech 55:157–171
Peterson RE, Wahl AM (1936) Two- and three-dimensional cases of stress concentration and comparison with fatigue tests. Trans ASME J Appl Mech 58:15–22
Poisson SD (1829) Mémoire sur l’équilibre et le mouvement des corps solides. Mémoires de l’Académie des Sciences de l’Institut de France, Paris 8:357–570
Polder JW (1987) Influence of geometrical parameters on the gear scuffing criterion—part 1. Gear Technol 28–34
Pollone G (1937) Costruzioni Automobilistiche. Il Veicolo. Soc. An. Azienda Anonima Editoriale Libraria, Torino
Pollone G (1957) Costruzioni Automobilistiche. Il Veicolo, 2nd edn. Libreria Editrice Universitaria Levrotto & Bella, Torino
Pollone G (1970) Il Veicolo, 3rd edn. Libreria Editrice Universitaria Levrotto & Bella, Torino
Pomini O (1920) Costruzione di Macchine. IV. Ingranaggi, Cinghie – Corde – Catene di Trasmissione. Ulrico Hoepli Editore Librario della Real Casa, Milano
Przemieniecki JS (1968) Theory of matrix structural analysis. McGraw-Hill, New York
Radzevich SP (2012) Dudley’s handbook of practical gear design and manufacture, 2nd edn. CRC Press, Taylor & Francis Group, Boca Raton
Radzevich SP (2013) Theory of gearing: kinematics, geometry, and synthesis. CRC Press, Taylor & Francis Group, Boca Raton
Radzevich SP (2016) Dudley’s handbook of practical gear design and manufacture, 3rd edn. CRC Press, Taylor & Francis Group, Boca Raton
Radzevich SP (2017) Gear cutting tools: science and engineering, 2nd edn. CRC Press, Taylor & Frencis Group, Boca Raton
Radzevich SP (2018) Theory of gearing: kinematics, geometry and synthesis, 2nd edn. CRC Press, Taylor & Francis Group, Boca Raton
Ramsden J (1777) Description of an engine for dividing mathematical instruments. Publisher William Richardson, London
Ree T, Eyring H (1955) Theory of non-newtonian flow. I. Solid plastic system. J Appl Phys 26(7):793–800
Ree T, Eyring H (1955) Theory of non-newtonian flow. II? Solution system of high polymers. J Appl Phys 26(7):800–809
Rescher N (2012) Leibniz and cryptography. University of Pittsburgh, University Library Systems, Pittsburgh
Reuleaux F (1861) Der Constructeur. Ein Handbuch sum Gebrauch beim Maschinen-Entwerfen. Vieweg und Sohn, Braunschweig (trans: English as The Constructor: a handbook of machine design, in 1893 by H.H. Suplee, Philadelphia)
Reuleaux F (1875) Theoretische Kinematik; grundzüge einer Theorie des Maschinenwesens. Verlag Vieweg & Sohn, Braunschweig
Reye T (1860) Zur theorie der zapfenreibung. Der Civilingenieur 4:235–255
Reynolds O (1876) On rolling friction. Philos Trans R Soc Lond 166:155–171
Ristivojević M, Lazovic T, Venci A (2019) Studying the load carrying capacity of spur gear tooth flanks. Mech Mach Theory 59:125–137
Ritter GDA (1863) Elementare Theorie und Berechnung eiserner Dach-und Brücken- Constructionen. Rümpler, Hannover
Ritter GDA (1865) Lehrbuch der Technischen Mechanik. Baumgärtner, Lipsia
Ritter GDA (1873) Lehrbuch der Höheren Mechanik. Baumgärtner, Lipsia
Rosenfield AR (1990) Wear and fracture mechanics: are they related? Scripta Metallurgica et Materialia 24(5):811–814
Ross AA (1927) High speed gears. American Gear Manufacturers Association Paper
Russo L (2015) La rivoluzione dimenticata. Il pensiero scientifico greco e la scienza moderna, 9th edn. Giangiacomo Feltrinelli Editore, Milano
Rycerz P, Kadiric A (2019) The influence of slide-roll ratio on the extend of micropitting damage in rolling-sliding contacts pertinent to gear applications. Tribol Lett 67(2):1
Saint-Venant, de Barré AJC (1855) De la torsion des prismes, avec des considérations sur leur flexion ainsi que sur l’équilibre des solides élastiques en général et des formules pratiques pour le calcul de leur résistance á divers efforts s’exerçant simultanément. Mém. Acad. Sci. Savants Étrangers, vol XIV, pp 233–560
Sandberg E (1981) A calculation method for subsurface fatigue. In: International symposium in gearing and power transmissions, Tokyo, I, pp S429–S434
Sang E (1838) Essays on the forms of the teeth of wheels. Part I. Wheels with the axes parallel to each other. Edinb New Philos J 24:217
Sang E (1852) A new general theory of the teeth of wheel. Rev Pract Mech J 5
Schiebel A (1912) Zahnräder, I. Teil, Stirn- und Kegelräder mit geraden Zähnen. Verlag von Julius Springer, Berlin
Schiebel A (1913) Zahnräder, II. Teil, Räder mit schrägen Zähnen. Verlag von Julius Stinger, Berlin
Schiebel A, Lindner W (1954) Zahnräder: Erster Band, Stirn- und Kegelräder mit geradenZähnen. Springer Verlaine, Berlin
Schiebel A, Lindner W (1957) Zahnräder: Zweiter Band, Stirn- und Kegelräder mit schrägen Zahnen Schraubgetriebe. Springer Verlaine, Berlin
Schütz W (1996) A history of fatigue. Eng Fract Mech 54:263–300
Shames IH, Cozzarelli FA (1997) Elastic and inelastic stress analysis. Taylor & Francis Ltd., Philadelphia
Sharma VK, Breen DH, Walter GH (1977) An analytical approach for establishing case depth requirements in carburized and hardened gears. Transaction of ASME for presentation at the design engineering technical conference, Sept, Chicago, IL, pp 26–30
Shotter BA (1981) Micropitting: its characteristics and implications on the test requirements of gear oils. In: Performance testing of gear oils and transmission fluids, Institute of Petroleum, pp 53–59, 320–323
Socie DF, Marquis G (1999) Multiaxial fatigue, R-234. SAE International Publisher, New York
Stahl K, Hein M, Tobie T (2018) Calculation of tooth flank fracture load capacity. Gear Solut
Stolze CH (1978) A history of the divergence theorem. Historia Mathematica 5(4):437–442
Stribeck R (1894) Die Abnutzung den Zahnräder und ihre Folgen. VDI – Zeitschrift, Bd. 38:168–170
Stribeck R (1894) Berechnung der Zahnräder. VDI – Zeitschrift, Bd. 38:1182–1187
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
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 Aug 2014
Tredgold T (1820) Elementary principles of carpentry. Printed for J. Taylor, London
Tredgold T (1822) A practical essays on the strength of cast Iron, intended for the Assistance of Engineers, …, with an extensive table of the properties of materials …. Printed for J. Taylor, London
Truesdell CA (1977) A first course in rational continuum mechanics. Academic Press, New York
Truesdell CA (1992) Cauchy and the modern mechanics of continua. Revue d’Histoire des Sciences 45(1):5–24
Tuplin WA (1944) Machinery’s gear design handbook. Machinery Publishing Company Ltd., London
Tuplin WA (1950) Gear tooth stresses at high speed. Proc Inst Mech Eng 163(59):162–175
Turner MJ, Clough RW, Martin HC, Topp LJ (1956) Stiffness and deflection analysis of complex structures. J Aeronaut Sci 23(9):805–823
Veldkamp GR (1967) Canonical systems and instantaneous invariants in spatial kinematics. ASME J Mech 2:329–388
van Musschenbroek P (1729) Physicae Experimentales et Geometricae de Magnete, tuborum capillarium vitreorumque speculorum attraction, magnitudine terrae, coherentia corporum firmorum dissertations. S. Luchtmanz, Lugduni Batavorum, Leyden
von Bach C (1889) Elasticität und Festgkeit. Die für die Technik wichtigsten Sätze und deren erfahrungsmässige Grundlage. Springer, Berlin
von Bach C (1899) Die Maschinen-Element: ihre Berechnung und Konstruktion mit Rücksicht auf die neueren Versuche. Arnold Bergsträsser A. Kröner, Stuttgart
von Mises R (1913) Mechanik der festen Körper im Plastisch-detormablem Zustand. Göttinger Nachrichten, Akad. Wiss, Math-Physik., Kl., 582–592
von Tetmajer L (1886) Methoden und Resultate der Prüfung von Eisen und Stahl und anderer Metalle. Meyer & Zeller, Zürich
Vullo V (2014) Circular cylinders and pressure vessels: stress analysis and design. Springer International Publishing Switzerland, Cham
Vullo V, Vivio F (2013) Rotors: stress analysis and design. Springer, Milan
Wang S, Cusano C, Conry TF (1991) Thermal analysis of elastohydrodynamic lubrication of line contacts using the ree-eyring fluid model. Trans ASME J Tribol 113:232–244
Warwick A (2014) Who invented the automatic gearbox. North West Transmissios Ltd., (ed), Retrieved 11 Oct
Watt J (1781) Sun and planet gear. Watt’s patent, 25 Oct 1781
Whiteside DT (1967–1982) The mathematical papers of Isaac Newton, 8 vols. Cambridge University Press, Cambridge
Wilcox L, Coleman E (1973) Application of finite elements to the analysis of gear tooth stresses. J Eng Ind 95(4):1139–1148
Wildhaber E (1926) Helical gearing. United States Patent Office, Patent No. 1.601.750
Willis R (1841) Principles of mechanism. John W. Parker, London
Wilson EL, Farboomand I, Bathe KJ (1973) Nonlinear dynamic analysis of complex structures. Earthq Eng Struct Dyn 1:241–252
Winter H (1961) Gear tooth strength of spur gears, Part 1. Power Transm 30:404, 516
Winter H (1962) Gear tooth strength of spur gears, Part 2. Power Transm 31:66, 124
Winter H, Hösel Th (1969) Tragfähigkeitsberechnung von Stirn und Kegelrädern nach DIN 3990. Zeitschrift VDI 111:209
Witzig J (2012) Flankenbruch Eine Grenze der Zahnradtragfähigkeit in der Werkstofftiefe. Ph.D. thesis, Technical University of Munich
Woodbury RS (1958) History of the gear-cutting machine. The Technology Press, Massachusetts Institute of Technology, Cambridge
Wöhler A (1870) Über die Festigkeitsversuche mit Eisen und Stahl. Zeitschrift für Bauwesen 20:73–106
Young T (1807) A course of lectures on natural philosophy and the mechanical arts, vols I, II. Joseph Johnson, London
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
Yu Z-Y, Zhou S-P, Liu Q, Liu Y (2017) Multiaxial fatigue damage parameter and life prediction without any additional material constants. Materials, MDPI Basel Switzerland 10(8)
Zammattio C (1974) The mechanics of water and stone. In: Reti L (ed) The unknown Leonardo. McGraw-Hill Co., New York
Zanzi C, Pedrero JI (2005) Application of modified geometry of face gear drive. Comput Methods Appl Mech Eng 194(27–29):3047–3066
Zhou Y, Zhu C, Liu H (2019) A micropitting study considering rough sliding and mild wear. Coatings 9:639–653
Zienkiewicz OC (1969) The finite element method in engineering science. McGraw-Hill, New York
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Vullo, V. (2020). The Second Scientific Age: From Galileo to Today. In: Gears. Springer Series in Solid and Structural Mechanics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-030-40164-1_5
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