Abstract
In this chapter, the fundamentals of general rigid kinematic pairs are first described and the hyperboloid pitch surfaces are defined. These concepts are then applied to the generation of cylindrical crossed helical gear pairs. The main geometrical quantities of these types of gears are then defined and their kinematic quantities are determined, particularly those correlated with the lengthwise sliding and sliding velocity. Subsequently, the load analysis of this gears is performed and the thrust characteristic on shafts and bearings are defined. Other important kinematic quantities related to the rolling and sliding motions of the mating teeth surfaces are then defined and the instantaneous and average efficiencies of these gears are analytically determined. Finally, short notes are given regarding the fundamentals of profile-shifted toothing for crossed helical gears.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ball RS (1876) The theory of screw: a study in the dynamics of a rigid body. Hodges, Foster&Co, Dublin
Buckingham E (1949) Analytical mechanics of gears. McGraw-Hill Book Company Inc, New York
Ceccarelli M (2000) Screw axis defined by Giulio Mozzi in 1763 and early studies on helicoidal motion. Mech Mach Theory 35:761–770
Colbourne JR (1987) The geometry of involute gears. Springer, New York Inc, New York Berlin Heidelberg
Dobrovolski V, Zablonski K, Mak S, Radtchik A, Erlikh L (1971) Éléments de Machines. Édition MIR, Moscou
Dudley DW (1962) Gear handbook. The design, manufacture, and application of gears, McGraw-Hill, New York
Euler L (1765) Theoria Motus Corporum Solidorum seu Rigidorum ex primis nostrae cognitionis principiis stabilita et ad omnes motus, qui in huius modi corpora cadere possunt, accomodata, Rostochii et Gryphiswaldiae Litteris et Impensis A. F. Röse
Ferrari C, Romiti A (1966) Meccanica Applicata alle Macchine, Unione Tipografica – Editrice Torinese (UTET), Torino
Giovannozzi R (1965) Costruzione di Macchine, vol II. 4th edn. Casa Editrice Prof. Riccardo Pàtron, Bologna
Henriot G (1979) Traité théorique et pratique des engrenages, vol 1. 6th edn. Borda, Paris
Herrmann R (1928) Evolventen-Stirnrädgetriebe. Julius Springer, Berlin
Levi-Civita T, Amaldi U (1929) Lezioni di Meccanica Razionale—Vol. 1: Cinematica—Principi e Statica, 2nd edn. Reprint 1974, Zanichelli, Bologna
Litvin FL, Fuentes A (2004) Gear geometry and applied theory, 2nd edn. Cambridge University Press, Cambridge
Merritt HE (1954) Gears, 3rd edn. Sir Isaac Pitman & Soins Ltd, London
Minguzzi E (2013) A geometrical introduction to screw theory. Eur J Phys 34:613–632
Mozzi del Garbo GG (1763) Discorso matematico sopra il rotolamento momentaneo dei corpi, Stamperia Donato Campo, Napoli
Niemann G, Winter H (1983) Maschinen-Element Band III:Schraubrad-, Kegelrad-, Schneckn-, Ketten-, Riemen-, Reibradgetriebe, Kupplungen, Bremsen, Freiläufe, Springer, Berlin, Heidelberg
Pollone G (1970) Il Veicolo. Libreria Editrice Universitaria Levrotto & Bella, Torino
Poritsky H, Dudley DW (1948) Conjugate action of involute helical gears with parallel or inclined axes. Q Appl Math 6(3):193–214
Radzevich SP (2016) Dudley’s handbook of practical gear design and manufacture, 3rd edn. CRC Press, Taylor & Francis Group, Boca Raton, Florida
Schiebel A (1913) Zahnräder, II Teil, Räder mit schrägen Zähnen. Verlag con Julius Springer, Berlin
Schiebel A, Lindner W (1954) Zahnräder, Band 1: Stirn-und Kegelräder mit geraden Zähnen, Springer, Berlin, Heidelberg
Schiebel A, Lindner W (1957) Zahnräder, Band 2: Stirn-und Kegelräder mit schrägen Zähnen Schraubgetriebe, Springer, Berlin, Heidelberg
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
Spiegel MR, Lipschutz S, Spellman D (2009) Vector Analysis, Schaum’s Outlines, 2nd edn. McGraw-Hill, New York
Tang KT (2006) Mathematical methods for engineers and scientists. Springer, Berlin, Heidelberg
Townsend DP (1991) Dudley’s gear handbook, 2nd edn. McGraw-Hill, New York
Vaisman I (1997) Analytical geometry. World Scientific Publishing Co, Singapore
Zwirner G (1961) Istituzioni di Matematiche, Parte Prima, 5th edn. CEDAM-Casa Editrice Dott. Antonio Milani, Padova
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Vullo, V. (2020). Crossed Helical Gears. In: Gears. Springer Series in Solid and Structural Mechanics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-36502-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-36502-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36501-1
Online ISBN: 978-3-030-36502-8
eBook Packages: EngineeringEngineering (R0)