Saratov, Saratov, Russian Federation
Saratov, Saratov, Russian Federation
The current state of the machine-building production market is such that various modifications of its products are produced by single specimens. This requires that production should, on the one hand, reduce the terms for preparation and production of new products along with increasing the same products’ nomenclature, and on the other hand, it is economically necessary to reduce these products’ factory labor hours and cost along with high quality of manufacturing thereof. Such production’s profitability depends largely on effectiveness of the use of computer equipment and software that will allow virtualization of design and technological processes, which in the final development will allow transfer all stages related to preparing for manufacturing of a new product to mathematical and geometric computer models of manufactured products. This permits to leave only one stage of preparing for manufacturing of a new product — geometric synthesis, taking into account the workspace configuration. Due to the complexity of processes for tooth-profiling and engagement, their exact calculation can be only performed by a computer. A mathematical model of engagement, for example, a worm pair, which takes into account not only geometric parameters, but also the enterprise’s machine capabilities, makes it possible, without manufacturing the worm pair in a metal, to obtain reliable information about all features of the worm pair operation. The modern computers’ processing speed allows in a short time to choose the option that gives the best approximation to consumer’s desired requirements. This paper shows an example for application of the method of geometric computer solid-state modeling for the technological process of worm gear shaping as an envelope of the tool model’s producing surface. The algorithm work consists in the mutual motion and rotation of a part blank and the tool. As a result of mutual intersection of the part blank and the tool surfaces, final shapes of tooth surfaces are formed as precise computer solid-state models. In this paper has been shown the final result for computer shaping of the worm’s working surface. One of the stages for determining the gaps between the working surfaces of the worm and the worm wheel has been described. One of variants for interactive analysis of the worm pair’s computer model is application of the cutting-plane method to obtain a set of sections. The mutual intersection of the worm and worm wheel’s planes and working surfaces makes it possible to determine points’ coordinates and thereon to define the gaps between the working surfaces of the product.
worm-gear, computer modeling, tooth-profiling, mutual intersection of surfaces, tooth treatment.
Зацепление в червячной передаче — это процесс взаимного качения друг по другу двух винтовых поверхностей: непрерывная однопараметрическая последовательность положений поверхностей зуба колеса и зуба червяка с взаимным касанием (теоретически по линии) [17; 18; 23; 25].
1. Andojskii V.D. Raschet zubchatih peredach [Calculation of gears]. Moscow, Leningrad Publ., 1955. 269 p. (in Russian)
2. Bronshtein I.N., Semendyaev K.A. Spravochnik po matematike dlya injenerov i uchaschihsya vtuzov [Directory of mathematics for engineers and colleges students]. Moskva. Nauka Publ. 1986. 544 p. (in Russian)
3. Volkov A.EH. Komp'yuternoe modelirovanie protsessov formoobrazovaniya poverkhnostey rezaniem [Computer simulation of forming cutting surfaces]. IV Mezhdunarodnyj kongress: Konstruktorsko-tekhnologicheskaya informatika [IV International Congress: Design and Technology Informatics]. Moscow, «STANKIN» Publ., 2000, V. 1, pp. 122-126. (in Russian)
4. GOST 19036-81 Peredachi chervyachnye tsilindricheskie. Iskhodnyy chervyak i iskhodnyy proizvodyashchiy chervyak [State Standard 19036-81. Method of measurement. Worm-gearing cylindrical. The original worm and the source producing a worm]. Moscow, Standartinform Publ., 1981. 4 p. (in Russian)
5. GOST 19650-97 Peredachi chervyachnye tsilindricheskie. Raschet geometricheskikh parametrov [State Standard 19650-97. Worm-gearing cylindrical. The calculation of geometrical parameters]. Moscow, Standartinform Publ., 2005. 10 p. (in Russian)
6. GOST 20184-81 Peredachi chervyachnye tsilindricheskie melkomodul'nye. Iskhodnyy chervyak i iskhodnyy proizvodyashchiy chervyak [State Standard 20184-81. Worm-gearing cylindrical fine-grained. The original worm and the source producing a worm]. Moscow, Standartinform Publ., 1981. 5 p. (in Russian)
7. Gohman H.I. Teoriya zaceplenii, obobschennaya i razvitaya putem analiza [Link Theory, generalized and developed by analyzing]. Odessa. 1886. 315 p. (in Russian)
8. Kalashnikov S.N. Zubchatie kolesa i ih izgotovlenie [The gears and their manufacture]. Moscow. Mashinostroenie Publ. 1983. 264 p. (in Russian)
9. Kalashnikov S.N., Kalashnikov A.S., Kogan G.I. Proizvodstvo zubchatih koles: spravochnik [Production of gears: directory]. Moscow. Mashinostroenie Publ. 1990. 464 p. (in Russian)
10. Karacharovskii V.YU., Riazanov S.A. Vizualizatsionnaya otsenka geometricheskikh kharakteristik kontaktiruyushchey poverkhnosti v chervyachnykh peredachakh na osnove primeneniya metodov 3D komp'yuternoy grafiki [Application of 3D computer graphics and solid modeling in the design processes gear cutting]. Vestnik Saratovskogo gosudarstvennogo tehnicheskogo universiteta [Bulletin of the Saratov State Technical University]. Saratov. SGTU. 2010. i. 4(49), pp. 55-60. (in Russian)
11. Karacharovskii V.YU., Riazanov S.A. Vizual'naya otsenka parametrov lokalizovannogo kontakta v chervyachnykh peredachakh na osnove primeneniya metodov 3D komp'yuternoy grafiki [Visual assessment of localized exposure settings in worm gears on the basis of application of methods of 3D computer graphics]. Vestnik Saratovskogo gosudarstvennogo tehnicheskogo universiteta [Bulletin of the Saratov State Technical University]. Saratov, SGTU Publ. 2011, I. 2(56), pp. 73-77. (in Russian)
12. Karacharovskii V.YU., Riazanov S.A. Geometricheskoe modelirovanie formoobrazovaniya prostranstvennykh poverkhnostey pri vintovom otnositel'nom dvizhenii [Geometric modeling of spatial shaping of surfaces by helical relative motion]. Problemy geometricheskogo modelirovaniya v avtomatizirovannom proektirovanii i proizvodstve: 1-ya Mezhdunar. nauch. konf. [Problems of geometric modeling in computer-aided design and production: 1st Intern. sci. Conf.]. Moscow, MGIU Publ., 2008, pp. 143-146. (in Russian)
13. Karacharovskii V.YU., Riazanov S.A. Obobshchennaya model' tverdotel'nogo zuboreznogo instrumenta s izmenyaemoy kriviznoy proizvodyashchey poverkhnosti [The generalized model of solid-state gear-cutting tool with a variable curvature of the generating surface]. Sovershenstvovanie podgotovki uchaschihsya i studentov v oblasti grafiki, konstruirovaniya i standartizacii: mejvuz. nauch.-metod. sb. [Improving the preparation of students and students in the field of graphics, design and standardization: interuniversity. scientific-method. Sat.]. Saratov, SGTU Publ. 2010, pp. 152-156. (in Russian)
14. Karacharovskii V.YU., Reshetnikov M.K., Riazanov S.A. Primenenie metodov komp'yuternoy 3D grafiki i tverdotel'nogo modelirovaniya pri razrabotke tekhnologicheskikh protsessov zubonarezaniya [Imaging evaluation of geometrical characteristics of the contact surface in worm gears on the basis of application of methods of 3D computer graphics]. Vestnik Saratovskogo gosudarstvennogo tehnicheskogo universiteta [Bulletin of the Saratov State Technical University]. Saratov, SGTU Publ. 2010, V. 4(49), I. 1, pp. 55-60. (in Russian)
15. Karacharovskii V.YU., Riazanov S.A. Razrabotka tsifrovykh tekhnologiy tverdotel'nogo modelirovaniya protsessov formoobrazovaniya prostranstvennykh zubchatykh peredach dlya realizatsii na mnogokoordinatnykh stankakh [The development of digital technologies solid modeling of forming processes of spatial gears for sale on multi-axis machine tools]. Pyatyi Saratovskii salon izobretenii, innovacii i investicii [The Fifth Saratov Salon of Inventions, Innovations and Investments]. Saratov. SGTU. 2010. Ch. 1, pp. 150-151. (in Russian)
16. Kolchin N.I. Analiticheskii raschet ploskih i prostranstvennih zaceplenii [Analytical calculation of planar and spatial links]. Moscow. Mashgiz Publ. 1949. 210 p. (in Russian)
17. Lashnev S.I. Formoobrazovanie zubchatih detalei reechnimi i chervyachnimi instrumentami [Shaping the rack gear parts and tools worm]. Moscow, Mashinostroenie Publ. 1971. 216 p. (in Russian)
18. Litvin F.L. Teoriya zubchatih zaceplenii [Theory of gearing]. Moscow, Nauka Publ. 1968. 584 p. (in Russian)
19. Lopato G.A., Kabatov N.F., Segal M.G. Konicheskie i gipoidnie peredachi s krugovimi zubyami [Bevel and hypoid gears with circular teeth]. Moscow, Mashinostroenie Publ. 1977. 423 p. (in Russian)
20. Loskutov V.V., Nichkov A.G. Zuboobrabativayuschie stanki [Gear machines]. Moscow, Mashinostroenie Publ. 1978. 192 p. (in Russian)
21. Lyashkov A.A. Geometricheskoe i komp'yuternoe modelirovanie formoobrazovaniya poverhnostej detalej [Geometrical and computer modeling of forming surfaces of the parts]. OMSK, OmGTU Publ. 2013. 89 p. (in Russian)
22. Lyashkov A.A. Modelirovanie formoobrazovaniya slozhnykh poverkhnostey detaley [Simulation of forming complex surfaces parts]. Metalloobrabotka [Metalworking]. 2010, I. 4, pp. 36-42. (in Russian)
23. Frenkel I.N. Peredachi spiroidnie s cilindricheskimi chervyakami. Raschet geometrii: metodicheskie ukazaniya [Transfer spiroid cylindrical worms. Calculation of geometry: guidelines]. Moscow, Rotaprint VNIINMASh Publ. 1977. 66 p. (in Russian)
24. Sandler A.I. Proizvodstvo chervyachnih peredach [Production of worm gears]. Moscow. Mashinostroenie Publ. 2008. 272 p. (in Russian)
25. Wildhaber E. A new look at wormgear hobbing / E. Wildhaber. American Machinist, 1954, June 21, p. 149-152.
