Saratov, Saratov, Russian Federation
Saratov, Saratov, Russian Federation
The run-in method for obtaining the screw surface of a worm is based on the use of the worm gearing principle. In this case, the shaping surface (cutting tool) and the workpiece constitute a gear pair [4; 7]. The use of geometric modeling methods [8; 9] to simulate the process of shaping the working surface is based on the relative movement of intersecting objects in the form of a “workpiece-tool” system. This allows to obtain the necessary geometrical model that accurately reproduces the geometric configuration of the surfaces of the teeth of spatial gears [14; 15], where the producing surface of the tool moves in the selected reference system and its position at an arbitrary time is determined by a certain parameter, the motion parameter. The position of the cutting tool at the beginning and at the end of each pass is calculated using parametric equations, which make it possible to calculate the tool path for accurate processing of spatially complex surfaces [16–19]. In the process of mechanical action of a tool on a solid (workpiece), shaping occurs, which consists in the movement of the tool relative to the workpiece [30; 31]. The use of modern methods of three-dimensional computer graphics allows us to improve and accelerate the process of designing technological operations of tooth profiling, providing the final forms of the surfaces of the teeth in the form of visual and accurate computer-based solid-state models [39; 40]. The method is based on a virtual representation of the process of shaping in the form of intersection of solid-state 3D models of two objects (tools and workpieces), which generally perform a screw relative motion. As a result, the working surfaces of the teeth are formed as the envelopes of the tool producing surface [32–34]. For the formation of fission surfaces, mathematical dependences were obtained, which allow one to describe the mutual motion of a worm, a worm gear and a disk cutter [35–37]. These analytical dependences make it possible to simulate the virtual process of forming the side surfaces of the worm gearing elements [1–3; 5; 6]
worm cutter, worm-gear; computer modeling, geometric modeling, kinematic modeling, simulation modeling, tooth-profiling, mutual intersection of surfaces, gear treatment, dividing surface, initial surface
1. Alekseyev Ye. R., Chernoskova O.V. Resheniye zadach vychislitel'noy matematiki v paketakh Mathcad 12 [Solving Computational Mathematics Problems in Mathcad 12]. Moscow, NT Press Publ., 2006. 496 p. (in Russian)
2. Ammeral, L. Interaktivnaya trekhmernaya mashinnaya grafika [Interactive three-dimensional computer graphics]. Moscow: Sol Sistem Publ. 1992. 317 p. (in Russian)
3. Ammeral, L. Printsipy programmirovaniya v mashinnoy grafike [Principles of programming in computer graphics: a textbook]. Moscow, Sol Sistem Publ., 1992. 224 p. (in Russian)
4. Andojskii V.D. Raschet zubchatih peredach [Calculation of gears]. Moscow, Leningrad Publ., 1955. 269 p. (in Russian)
5. Beklemishev D.V. Kurs analiticheskoy geometrii i lineynoy algebry [The course of analytic geometry and linear algebra]. Moskov, Vyssh. shk. Publ., 1998. 320 p. (in Russian)
6. Bronshtein I.N., Semendyaev K.A. Spravochnik po matematike dlya injenerov i uchaschihsya vtuzov [Directory of mathematics for engineers and colleges students]. Moscow: Nauka Publ., 1986. 544 p. (in Russian)
7. Weits V. L., Volzhenskaya A. M., Kolchin N. I. Geometriya zatsepleniya zubchatykh peredach [Geometry of gearing of gears]. Leningrad, Mashinostroenie Publ., 1978. 136 p. (in Russian)
8. 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)
9. Golovanov N.N. Geometricheskoye modelirovaniye [Geometric modeling]. Moscow, Publishing House of Physics and Mathematics Publ., 2002. 472 p. (in Russian)
10. GOST 18498-89. Peredachi chervyachnyye. Terminy, opredeleniya i oboznacheniya [State Standart 18498-89. Worm gear pairs. Terms, definitions and symbols]. Moscow, Standartinform Publ., 1989. 86 p. (in Russian)
11. 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)
12. 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)
13. 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)
14. Gohman H.I. Teoriya zaceplenii, obobschennaya i razvitaya putem analiza [Link Theory, generalized and developed by analyzing]. Odessa. 1886. 315 p. (in Russian)
15. Dimentberg F.M., Sarkisyan Yu. L., Uskov M.K. Prostranstvennyye mekhanizmy. Obzor sovremennykh issledovaniy [Spatial mechanisms. A review of contemporary research]. Moskva, Science Publ., 1983. 96 p. (in Russian)
16. D'yakonov, V. P. Maple 9.5/10 v matematike, fizike i obrazovanii [Maple 9.5 / 10 in mathematics, physics and education]. Moscow: SOLON-Press Publ., 2006. 720 p. (in Russian)
17. Ilyin V.A., Pozniak E.G. Analiticheskaya geometriya: uchebnik dlya vuzov [Analytical geometry: a textbook for universities]. Moscow, Science Publ., 1999. 224 p. (in Russian)
18. Kalashnikov S.N. Zubchatie kolesa i ih izgotovlenie [The gears and their manufacture]. Moscow: Mashinostroenie Publ. 1983. 264 p. (in Russian)
19. 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)
20. 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 Publ. 2010, I. 4(49), pp. 55-60. (in Russian)
21. 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)
22. Karacharovsky V. Yu., Reshetnikov M. K., Riazanov S. A. Geometricheskoye modelirovaniye i vizual'naya otsenka vintovoy poverkhnosti zuba [Geometric modeling and visual evaluation of the screw surface of the tooth]. Problemy graficheskoy podgotovki studentov tekhnicheskikh vuzov v usloviyakh sovremennogo kompetentnostnogo podkhoda k protsessu obucheniya [Problems of graphic training of students of technical universities in the context of a modern competence approach to the learning process]. Moscow, DGTU Publ., 2015, pp. 59-66. (in Russian)
23. 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 [Problems of geometric modeling in computer-aided design and production]. Moscow, MGIU Publ., 2008, pp. 143-146. (in Russian)
24. 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 [Improving the preparation of students and students in the field of graphics, design and standardization]. Saratov, SGTU Publ. 2010, pp. 152-156. (in Russian)
25. Karacharovskiy, V.YU. , Reshetnikov M.K., Ryazanov S.A. Opredeleniye koordinat tochek evol'ventnoy vinto-voy poverkhnosti chervyachnoy peredachi [Determination of coordinates of points of an involute helical surface of a worm gear]. Problemy graficheskoj podgotovki studentov tekhnicheskih vuzov v usloviyah sovremennogo kompetentnostnogo podhoda k processu obucheniya [Problems of graphic training of students of technical universities in the context of a modern competence approach to the learning process]. DGTU Publ., 2015, pp. 66-73. (in Russian)
26. 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)
27. 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 Publ. 2010, pp. 150-151. (in Russian)
28. Kolchin N.I. Analiticheskii raschet ploskih i prostranstvennih zaceplenii [Analytical calculation of planar and spatial links]. Moscow. Mashgiz Publ. 1949. 210 p. (in Russian)
29. Golovanov N. N., Il'yutko D. P., Nosovskiy G. V., Fomenko A. T. Komp'yuternaya geometriya [Computer geometry: studies. allowance for stud. of universities]. Moscow, «Akademiya» Publ., 2006. 512 p. (in Russian)
30. Lashnev S.I. Raschet i konstruirovaniye metallorezhushchikh instrumentov s primeneniyem EVM [Calculation and design of metal-cutting tools using computers]. Moscow, Mashinostroyeniye Publ., 1975. 392 p. (in Russian)
31. 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)
32. Lebedev P.A. Kinematika prostranstvennykh mekhanizmov [Kinematics of spatial mechanisms]. Moscow, Nauka Publ., 1983. 280 p. (in Russian)
33. Litvin F.L. Teoriya zubchatih zaceplenii [Theory of gearing]. Moscow, Nauka Publ. 1968. 584 p. (in Russian)
34. 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)
35. Loskutov V.V., Nichkov A.G. Zuboobrabativayuschie stanki [Gear machines]. Moscow, Mashinostroenie Publ. 1978. 192 p. (in Russian)
36. Muskhelishvili N.I. Kurs analiticheskoy geometrii [The course of analytic geometry]. Moscow: Vysshaya shkola Publ., 1967. 655 p. (in Russian)
37. 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)
38. Reshetnikov M. K., Riazanov S. A. Otsenka parametrov chervyachnykh peredach na osnove meto-dov 3D komp'yuternoy grafiki [Estimation of worm gear parameters based on 3D computer graphics methods]. Geometriya i grafika [Geometry and graphics]. Moscow, INFRA-M Publ., 2018, V. 6, I. 1, pp. 34-38. DOI:https://doi.org/10.12737/article_5ad0971a86af78.65167837. (in Russian)
39. Sal'kov N.A. The Geometric Component Of Technical Innovations. Geometriya i grafika [Geometry and graphics]. Moscow, INFRA-M Publ., 2018, V. 6, I. 2, pp. 85-93. DOI:https://doi.org/10.12737/article_5b55a5163fa053.07622109. (in Russian)
40. Sal'kov N.A. Formirovanie poverhnostej pri kineticheskom otobrazhenii [Formation of Surfaces Under Kinetic Displaying]. Geometriya i grafika [Geometry and graphics]. Moscow, INFRA-M Publ., 2018, V. 6, I. 1, pp. 20-33. DOI:https://doi.org/10.12737/article_5ad094a0380725.32164760. (in Russian)
41. Sandler A.I. Proizvodstvo chervyachnih peredach [Production of worm gears]. Moscow: Mashinostroenie Publ. 2008. 272 p. (in Russian)
42. Svidetel'stvo o gosudarstvennoy registratsii programmy dlya EVM [Certificate of state registration of computer programs] 2015616756 Rossiyskaya Federatsiya, Geometricheskoye tverdotel'noye modelirova-niye zubchatykh peredach so skreshchivayushchimisya osyami vrashcheniya [Geometric solid-state simulation of gears with intersecting axes of rotation] / Karacharovskiy V. YU. (RU), Reshetnikov M. K. (RU), Ryazanov S. A. (RU); zayavitel' i patentoobla-datel' FGBOU VPO «Saratovskiy gosudarstvennyy tekhnicheskiy universitet imeni Gagarina YU.A. (RU)». - № 2015613296; zayavl. 23.04.2015; data gos. regist-ratsii v Reyestre programm dlya EVM 22.06.2015.
43. Karacharovskiĭ V. IU. Chromatic Gradient Appliance Algorithm In Cog Flank Dyeing For Its Flecture Angle Visual Estimate Acquired By Solid State Modeling Method / V.IU. Karacharovskiĭ, Reshetnikov M.K., S.A. Riazanov, V.V. Shpilev, S.V. Borodulina // Research Journal of Pharmaceutical, Biological and Chemical Sciences. - 2015. - Vol. 6. - №4. - P. 202-206. - Bibliography: p. 206(6 name.). - Zag with title screen. URL: http://www.rjpbcs.com/pdf/2015_6(4)/[33].pdf. - ISSN: 0975-8585.
44. Sdvizhkov O.A. Matematika na komp'yutere: Maple 8 [Mathematics on the computer: Maple 8]. Moscow, SOLON-Press Publ., 2003. 176 p.
45. Bernardi L. Maple Programm Guide / L. Bernardi, P. Chin, P. DeMarco, K. Geddes. - Maplesoft, 1996-2014, 664 p.
46. Maple user manual, Maplesoft, 1996-2014, 540 p.
47. Wildhaber E. A new look at wormgear hobbing / E. Wildhaber. American Machinist, 1954, June 21, p. 149-152.
