Analyzing computation systems for the transmission internal gearing

Evolution of the gearing theory demonstrates a lot of ideas and inventions in the gear mechanisms and formation of a theory based on the conjugate profiles developed by the Russian and Soviet scientists. Basics of the gearing analytical theory became a foundation in solving practical problems in design, development and manufacture of the gear transmissions. For many decades, the system of calculating the gear transmissions prevailed in mechanical engineering. There, diameters of the wheel tops were assigned so that a constant standard radial clearance was maintained in engagement at any offset coefficients. Being convenient for the external gear transmissions, that system often was unusable in implementing transmissions with the small offset coefficients in regard to the internal gear transmissions. GOST 19274–73 “Cylindrical involute internal gear pairs. Calculation of geometry” introduced two new systems for computing diameters of the gear wheel tops with the internal and external teeth. The proposed computation schemes according to GOST 19274-73 and using the existence regions (blocking contours) are analyzed and comparatively assessed.
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References

[1] Gavrilenko V.A. Osnovy teorii evolventnoy zubchatoy peredachi. Moscow, Mashinostroenie Publ., 1969. 431 p. (In Russ.).

[2] Diker Ya.I. Limitations in cutting corrugated gears at large displacements of the initial contour. Vestnik mashinostroeniya, 1955, no. 4, pp. 11–13. (In Russ.).

[3] Bolotovskiy I.A., Guryev B.I., Smirnov V.E. et al. Tsilindricheskie evolventnye zubchatye peredachi vnutrennego zatsepleniya [Cylindrical involute internal gear gears]. Moscow, Mashinostroenie Publ., 1977. 192 p. (In Russ.).

[4] Bolotovskiy I.A., ed. Spravochnik po geometricheskomu raschetu evolventnykh zubchatykh i chervyachnykh peredach [Reference book on geometrical calculation of involute gear and worm gears]. Moscow, Mashinostroenie Publ., 1986. 448 p. (In Russ.).

[5] Groman M.B. On blocking contours of involute gearing. Vestnik mashinostroeniya, 1962, no. 12, pp. 12–17. (In Russ.).

[6] Balakin P.D. Mekhanicheskie peredachi s adaptivnymi svoystvami [Mechanical transmissions with adaptive properties]. Omsk, OmGTU Publ., 1996. 144 p. (In Russ.).

[7] Goldfarb V.I., Tkachev A.A. Proektirovanie evolventnykh tsilindricheskikh peredach. Novyy podkhod [Design of involute spur gears. A new approac]. Izhevsk, Izd-vo IzhGTU Publ., 2004. 94 p. (In Russ.).

[8] Dorofeev V.L., Shevchenko I.V. Blocking contour for the gear designed by the given thickness of teeth on top. Nauka i obrazovanie: nauchnoe izdanie [Science and Education: Scientific Publication], 2011, no. 4. URL: https://www.elibrary.ru/item.asp?id=16257203 (In Russ.).

[9] Vulgakov E.B. Teoriya evolventnykh zubchatykh peredach [Theory of involute gears]. Moscow, Mashinostroenie Publ., 1995. 320 p. (In Russ.).

[10] Dorofeev V.L. [Fundamentals of the technology of computer modelling of fields by the method of complex analytical functions]. Novye tekhnologii upravleniya dvizheniem tekhnicheskikh obektov. Mat. 3-y mezhd. konf. T. 2 [New technologies of controlling the movement of technical objects. Proc. 3rd Int. Conf. Vol. 2]. Rostov-na-Donu, SKNTs VSh YuFU Publ., 2000, pp. 104–109. (In Russ.).

[11] Kopytova O.F. Gears with equalised accelerated sliding gears. Teoriya mekhanizmov i detali mashin, 1974, no. 1, pp. 94–103. (In Russ.).

[12] Litvin F.L., Krylov N.N., Erikhov M.L. Generation of tooth surfaces by two-parameter enveloping. Mech. Mach. Theory, 1975, vol. 10, no. 5, pp. 365–373, doi: https://doi.org/10.1016/0094-114X(75)90036-1

[13] Syzrantsev V.N. Zadacha sinteza realnykh zatsepleniy tsilindricheskikh peredach s lokalizovannym kontaktom. Diss. dok. tekh. nauk [Problem of synthesis of real meshing of cylindrical gears with localised contact. Doc. tech. sci. diss.]. Kurgan, 1989. 407 p. (In Russ.).

[14] Tsukanov O.N. Osnovy sinteza neevolventnykh zubchatykh zatsepleniy v obobshchayushchikh parametrakh [Fundamentals of synthesis of non-involute gears in generalising parameters]. Chelyabinsk, Izd. tsentr YuUrGU, 2011. 139 p. (In Russ.).

[15] Babichev D.T., Storchak M.G., Babichev D.A. [Geometrical synthesis and computer investigation of equal strength spur gears]. Teoriya i praktika zubchatykh peredach. Sb. tr. mezhd. simpoziuma [Theory and practice of gears. Proc. Int. Symposium]. Izhevsk, Izd-vo IzhGTU Publ., 2014, pp. 309–315. (In Russ.).

[16] GOST 19274–73. Peredachi zubchatye tsilindricheskie evolventnye vnutrennego zatsepleniya. Raschet geometrii [State standard GOST 19274–73. Cylindrical involute internal gear pairs. Calculation of geometry]. Moscow, Izd-vo standartov Publ., 1983. 64 p. (In Russ.).

[17] Lopatin B.A., Tsukanov O.N. Design cylindrobevel gears in generalizing parameters. Gearing and Transmissions, 1999, no. 2, pp. 24–35. (In Russ.).