Geodesic
Formation of nonsmoothness lines in optimization of screw pairs in screw pumps
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 53-64.

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Computer modeling of screw pairs in screw pumps reveals the formation of nonsmoothness lines on the screw surface (with the growth of the height of the helical tooth) conjugate to the smooth helical surface. The mathematical explanation of the appearance of such lines represents considerable interest for the theory and practice of pumps manufacturing. In this paper we show that one can explain the mentioned phenomenon by studying a wider problem, namely, the bifurcation of regressive points on a plane contour conjugate to the smooth one.
Keywords: screw pumps, screw pairs, points of nonsmoothness, bifurcation of regressive points, computer identification of singularities.
Mots-clés : conjugate contour 
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M. I. Kovalyova; V. A. Kostin; Yu. I. Sapronov. Formation of nonsmoothness lines in optimization of screw pairs in screw pumps. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 53-64. http://geodesic.mathdoc.fr/item/IVM_2012_4_a5/

[1] Pevzner B. M., Nasosy sudovykh ustanovok i sistem, Sudostroenie, L., 1971

[2] Baldenko D. F., Bidman M. G., Kalishevskii V. L. i dr., Vintovye nasosy, Mashinostroenie, M., 1982

[3] Valyukhov S. G., Kostin V. A., Sapronov Yu. I., Semenov S. M., Optimizatsiya shesterenchatykh zatseplenii vintovykh poverkhnostei, VorGU, Voronezh, 2005

[4] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Klassifikatsiya kriticheskikh tochek, kaustik i volnovykh frontov, Nauka, M., 1982 | MR

[5] Brus Dzh., Dzhiblin P., Krivye i osobennosti. Geometricheskoe vvedenie v teoriyu osobennostei, Per. s angl., Mir, M., 1988 | MR

[6] Matematicheskii entsiklopedicheskii slovar, Sovetskaya entsiklopediya, M., 1988 | MR

[7] Vinberg E. B., Simmetriya mnogochlenov, MTsNMO, M., 2001

[8] Kovaleva M. I., “Ob osobykh tochkakh na poverkhnosti, sopryazhennoi s vintovoi poverkhnostyu algebroidnogo tipa”, Mezhdunarod. konf., posvyasch. pamyati I. G. Petrovskogo (XXII sovmestnoe zasedanie MMO i semin. im. I. G. Petrovskogo), Tez. dokladov, Izd-vo MGU, M., 2007, 159

[9] Zachepa V. R., Sapronov Yu. I., Lokalnyi analiz fredgolmovykh uravnenii, VGU, Voronezh, 2002

[10] Kovaleva M. I., “K vychisleniyu uglov v tochkakh negladkosti sopryazhennykh konturov”, Vestn. Voronezhsk. un-ta. Ser. Fiz. Matem., 2009, no. 1, 119–125