Research of Relationships in the Areas of Existence of Non-Involute Gearing by Generalizing Parameters

The objects of this research are areas of existence of non-involute gearings in gears with non-parallel axes, which are an important part of many mechanisms and machines. To fully utilize the geometric-kinematic capabilities of the gearings, a synthesis method is used.  It is applied in generalizing parameters in a generalized area of existence using localized areas of existence corresponding to specific geometric-kinematic indicators of tooth contact. However, there is no information on the relationships in these areas in the literature; therefore, it is impossible to effectively analyze the gearings and select the most rational option for different operating conditions of various types of gears. This paper presents the results of the research of the areas of existence of non-involute gearings synthesized on the basis of the cylindrical involute basic link (gearings of cylindrical-conical gears in generalizing parameters). The areas of existence of gearings of flat-wheel and worm-helical gears are compared.  These gears represent two boundary cases of cylindrical-conical gears. The concepts of a general virtual basic link and the generalizing coordinates for non-involute gearings, synthesized on the basis of the link, are introduced. The assumed forms of generalized and localized areas of existence of such gearings are present. The methods controlling the geometric-kinematic indicators of tooth contact at the synthesis stage of non-involute gearings in generalizing parameters are presented. The results obtained make it possible to determine the most favorable set of geometric-kinematic indicators of the tooth contact for given operating conditions of non-involute gears of various kinds.

References

[1] Davydov Ia.S. Neevol’ventnoe zatseplenie [Evolvente engagement]. Moscow, Mashgiz publ., 1950. 180 p.

[2] Litvin F.L., De Donno M., Peng A. Integrated computer program for simulation of meshing and contact of gear drives. Computer Methods in Applied Mechanics and Engineering, 2000, vol. 181, pp. 71–85.

[3] Litvin F.L., Fuentes A., Zanzi C. Design, generation and stress analysis of two versions of geometry of face-gear drives. Gearing and transmissions, 2004, no. 1, pp. 77–102.

[4] Lopatin B.A., Tsukanov O.N. Tsilindro-konicheskie zubchatye peredachi [Helical-bevel gears]. Cheliabinsk, IuUrSU publ., 2005. 200 p.

[5] Lopatin B.A., Khaustov S.A. Avtomatizirovannaia sistema modelirovaniia i analiza sposobov formirovaniia zub’ev zubchatykh koles [Automated system of modeling and analysis methods of forming the gear teeth]. Vestnik IuUrGU. Ser. Mashinostroenie [Bulletin of the South Ural State University. Ser. Mechanical engineering industry]. 2008, no. 10, pp. 72–77.

[6] Lopatin B.A., Poluektov E.A. Avtomatizirovannyi kompleks rascheta i analiza geometrii tsilindro-konicheskoi peredachi vnutrennego zatsepleniia [Automated complex calculation and analysis of the geometry of helical-bevel gear with internal engagement]. Teoriia i praktika zubchatykh peredach. Sb. tr. mezhdunar. simp. [Theory and practice of gears: collection of works of the international symposium]. Izhevsk, IzhSTU publ., 2014, pp. 227–231.

[7] Poluektov E.A. Sintez vnutrennego priblizhennogo zatsepleniia tsilindro-konicheskikh peredach. Diss. kand. tekhn. nauk [The synthesis of approximate internal meshing helical-bevel gear. Cand. tech. sci. diss.]. Cheliabinsk, 2011. 143 p.

[8] Vulgakov E.B. Teoriia evol’ventnykh zubchatykh peredach [Theory of involute gears]. Moscow, Mashinostroenie publ., 1995. 320 p.

[9] Tsukanov O.N. Osnovy sinteza prostranstvennykh neevol’ventnykh zubchatykh peredach na baze tsilindricheskogo evol’ventnogo iskhodnogo zvena v obobshchaiushchikh parametrakh. Diss. dokt. tekh. nauk [Basics of synthesis of spatial neevolventnyh gears based on cylindrical involute source link in generalizing parameters. Dr. tech. sci. diss.]. Chelyabinsk, 2005. 337 p.

[10] Tsukanov O.N. Osnovy sinteza neevol’ventnykh zubchatykh zatseplenii v obobshchaiushchikh parametrakh [Basics of synthesis of involute gearing in generalising parameters]. Cheliabinsk, IuUrSU publ., 2011. 140 p.

[11] Gol’dfarb V.I. Osnovy teorii avtomatizirovannogo geometricheskogo analiza i sinteza cherviachnykh peredach obshchego vida. Diss. dokt. tekh. nauk [Basic theory of automated geometric analysis and synthesis of worm gears of the general form. Dr. tech. sci. diss.]. Izhevsk, 1986. 32 p.

[12] Kalashnikov D.B. Proektirovanie ploskokolesnykh zubchatykh peredach v obobshchaiushchikh parametrakh. Diss. kand. tekhn. nauk [Design flat wheel gears in generalizing parameters. Cand. tech. sci. diss.]. Cheliabinsk, 2007. 149 p.

[13] Tsukanov O.N., Zizin I.M. Geometricheskii sintez cherviachno-vintovykh zubchatykh peredach v obobshchaiushchikh parametrakh [Geometric synthesis of worm-helical gears in generalizing parameters]. Teoriia i praktika zubchatykh peredach. Sb. tr. mezhdunar. simp. [Theory and practice of gears: Proceedings of the International Symposium]. Izhevsk, IzhSTU publ., 2014, pp. 393–398.

[14] Lopatin B.A. Perspektivy primeneniia v mashinostroenii zubchatykh peredach iz evol’ventno-konicheskikh koles [Prospects for use in mechanical gears of involute-bevel gears]. Aktual’nye voprosy v nauchnoi rabote i obrazovatel’noi deiatel’nosti. Sb. tr. mezhdunar. nauch.-prakt. konf. [Topical issues in scientific research and educational activities: collection of scientific works on materials of the international scientific-practical conference]. Pt. 4, Tambov, 2014, pp. 108–109.

[15] Poluektov E.A., Lopatin S.D. Modifikatsiia profilei zub’ev v tsilindro-konicheskoi peredache vnutrennego zatsepleniia [Modification of tooth profiles in cylindrical-conical internal gear transmission]. Nauka IuUrGU. Sektsii tekhnicheskikh nauk. Мat. 63-i nauch. konf. [Science SUSU. Section of Technical Sciences: a collection of materials of the 63rd conference]. Cheliabinsk, IuUrSTU publ., 2011, pp. 299–302.