Popov A., Novikov О., Savenkov O., Sadovuy О., Kondrateva А. Influence the misalignment and bending of the rotary shaft on the force factors which appear in its toothed connections

UDC 621.824

 

Popov A., Novikov О., Savenkov O., Sadovuy О., Kondrateva А.

 

The analysis of the influence of the skew and deflection of the shaft, which rotates with high frequency, on the force factors for some gear joints is carried out. It has been established that the values of the dynamic factors do not exceed 1.05-1.15, and the dynamic components of these force factors can reach 30-50% of the values of the level of their static components.

 Key words: rotating shaft, deflection, gear coupling, transmission, axle misalignment, force factors.

References:

  1. Попов А.П. К вопросу исследования моментов от сил трения в зубчатых муфтах. Судовое энергомашиностроение: Тр. Николаев. судостроит. ин-та. Вып.109. С.3-9.
  2. Попов А.П. Зубчатые муфты в судовых агрегатах. Л.: Судостроение, 1985.  240с.
  3. Польченко В.В., Богуславский В.А., Каплюхин А.А. Влияние конструкции зубчатых муфт на нагрузку опор валов. Практика i перспективи розвитку iнструментального партнерства: Вiстн. ДонНГУ – ТРТУ. Донецьк: ДонДТУ, 2003. С.138-143
  4. Попов А.П. Контактная прочность зубчатых механизмов. Николаев: НУК, 2008. 580с.
  5. Попов А.П. Зубчатые механизмы с точечным контактом зубьев. Николаев: Атолл, 2010.  774с.
  6. Савенков О.И. Упругие изгибающие моменты в зубчатых муфтах с модифицированными зубьями. Збірник наукових праць: Миколаїв: НУК, 2011. №5 (440). С.61-
  7. Ханмамедов С.А. Экспериментальное определение изгибающих моментов при статическом нагружении зубчатых муфт. Вісник Національного технічного університету “ХПІ”: Збірник наукових праць. Тематичний випуск: Машинознавство та САПР. Харків: НТУ “ХПІ”. 2012. №22. С.175-
  8. Савенков О.И. Снижение дополнительных силовых факторов в зубчатых муфтах. Вісник Національного університету кораблебудування (загальний за 2011р.) – Миколаїв: НУК, 2012. С.278-
  9. Попов А.П., Мозговой М.Г., Савенков О.И. О влиянии прогиба вращающегося вала на силовые факторы, возникающие в зубчатых соединениях энергетических установок. Інновації в суднобудуванні та океанотехніці: Матеріали Міжнародної науково-технічної конференції. Миколаїв: НУК, 2013. С.175-177.
  10. Подгуренко В.С. Нагрузочная способность зубчатых муфт с учетом погрешностей изготовления зубьев. Вісник аграрної науки Причорномор’я. Вип. №1 (77). С.197-203.
  11. Попов А.П., Мозговой М.Г., Савенков О.И. Пути снижения влияния расцентровок осей судовых энергетических установок Інновації в суднобудуванні та океанотехніці: Матеріали V Міжнародної науково-технічної конференції. Миколаїв: НУК, 2014. С.237-
  12. Попов А.П., Савенков О.И. Влияние смещения осей соединяемых валов на показатели надежности СЭУ. Судова енергетика: стан та проблеми: Тези доповідей Міжнародної науково-технічної конференції. Миколаїв: НУК, 2015.  Ч.1.   С.235-
  13. Popov A. Savenkov O., Marchenko D., Savenkova A. Повышение работоспособности машинных агрегатов при перекосах осей соединяемых валов путём применения высокоэффективных зубчатых муфт. Commission of Motorization and Energetics in Agriculture.  Lublin-Rzesow (Poland).  2016. Vol.18. No2. 9-17.
  14. Попов А.П., Савенков О.И., Марченко Д.Д. Оценка перекосов осей соединяемых валов при использовании зубчатых муфт. Сучасні проблеми взаємозамінності та стандартизації у машинобудуванні: матеріали VІ Всеукраїнської науково-практичної конференції молодих учених і здобувачів вищої освіти, 12-13 квітня 2018 р., м. Миколаїв / Міністерство освіти і науки України; Миколаївський національний аграрний університет. Миколаїв: МНАУ, 2018. С.74-78.
  15. Попов А.П., Дубинский О.Ю., Савенков О.И., Рыбаков А.Б. Причины возникновения расцентровок осей соединяемых валов СЭУ и способы устранения их негативного влияния. Міжнародна науково-практична конференція, присвячена пам’яті професорів Фоміна Ю.Я. і Cеменова В.С. (FS-2019, 24–28 квітня 2019, Одеса – Стамбул – Одеса): матеріали / Одеський національний морський університет. Одеса, 2019. С.169-175.

Vakhonina L., Potryvaieva N., Sadovyi О. Fine elastic circular inclusion in the area of harmonic vibrations of an unlimited body under smooth contact

UDC 539. 3

 

Vakhonina L.

Potryvaieva N.

Sadovyi О.

Modern problems of dynamic fracture mechanics, improvement of means of non-destructive testing and flaw detection require further development and improvement of methods for solving problems of dynamic interaction of thin-walled inclusions with the environment. An important case of inclusions is a circular (disc-shaped) inclusion. This is primarily due to the fact that thin disc-shaped reinforcements are quite common in machine parts and building structures. Thin inclusions are not only stress concentrators, but are also used as fillers in composites. When creating composite materials, the matrix is often filled with coin-like reinforcing elements of high rigidity. Therefore, it is inclusions of this shape that have always been given a lot of attention, which requires the solution of problems on the stress-strain state of bodies with inhomogeneities such as thin inclusions.

Methodology. The solution method is based on the representation of displacements in the matrix through discontinuous solutions of the Lamé equations for harmonic vibrations. This made it possible to reduce the problem to Fredholm integral equations of the second kind with respect to functions associated with jumps of normal stress and radial displacement to included ones. After the realization of the boundary conditions on the sides of the inclusion, a system of singular integral equations is obtained to determine these jumps.

Results. In the case of real materials, taking into account the elasticity of the inclusions significantly affects the value of the stress intensity factors. The values of the stress intensity factors obtained taking into account the elasticity for some materials may exceed, and for some be much smaller than those corresponding to the absolutely rigid inclusion. Taking into account the stiffness of the inclusion also significantly changes the dependence of the voltage intensity coefficients on the wave number. It becomes more complex with many highs and lows. Moreover, the maximum values of voltage intensity factors can be several times higher than the corresponding values for absolutely rigid inclusions.

 Originality. Determination of problems about harmonious communication of non-interconnected body with disk-like inclusions in the minds of smooth contact. Previously, such a task was tied for an absolutely hard inclusionю.

Practical value. The data obtained can be used in the calculations of machine parts and structures in which it is necessary to take into account elastic inclusions.

Key words: elastic inclusions, cylindrical waves, matrix, stress intensity factor

 

References:

  1. Litvin O.V. Popov V.G. (2002) Izgibnye kolebanija tonkogo uprugogo vkljuchenija v neogranichennoj srede pri vzaimodejstvii s uprugimi volnami.  Teoreticheskaja i prikladnaja mehanika. Vip.38. S. 131-140.
  2. Kit H.S., Kunets Ya. I., Yemets V.F. (1999) Elastodynamics scattering from a thinwallad inclusions of low rigidity.International Journal of Engineering Science. 37. P. 331-343.
  3. Kit G.S., Kunec V.V., Mihas’kiv V.V. (2004) Vzaimodejstvie stacionarnoj volny s tonkim diskoobraznym vkljucheniem maloj zhestkosti. Izvestija RAN.   Mehanika tverdogo tela.  №5. S. 83-89.
  4. My`xas`kiv V.V., Kaly`nyak O.I. (2005) Nestacionarni zburennya try`vy`mirnoyi pruzhnoyi matry`ci z zhorstky`m dy`skovy`m vklyuchennyam. Fizy`ko–ximichna mexanika materialiv. T. 41, # 2.  S. 7-15.
  5. Vahonina L.V., Popov V.G. (2002) Osesimmetrichnye kolebanija prostranstva s tonkim zhestkim krugovym vkljucheniem // Teorija i praktika processov izmel’chenija, razdelenija, smeshenija i uplotnenija. Odessa: OGMA.  Vyp. 9. S. 28-34.
  6. Vahonina L.V., Popov V.G. (2003) Vzaimodejstvie uprugih voln s tonkim zhestkim krugovym vkljucheniem v sluchae gladkogo kontakta. Teoreticheskaja i prikladnaja mehanika.    Vyp. 38. S. 158-166.
  7. Popov G.Ja. (1999) Postroenie razryvnyh reshenij differencial’nyh uravnenij teorii uprugosti dlja sloistoj sredy s mezhfaznymi defektami. Doklady RAN. T.364, № 6. S.769-773.
  8. Kit G.S., Mihas’kiv V.V., Haj O.M. (2002) Analiz ustanovivshihsja kolebanij ploskogo absoljutno zhestkogo vkljuchenija v trehmernom uprugom tele metodom granichnyh jelementov. Prikladnaja matematika i mehanika. T. 66, Vyp. 5. S. 855-863.
  9. Gradshtejn I.S., Ryzhik I.M. (2011) Tablicy integralov, summ rjadov i proizvedenij. M. 1108s.
  10. Rakhmanov Evguenii A. (2016) Orthogonal Polynomials Walter De Gruyter Incorporated. 510 с.
  11. Suetin P.K.(2005) Klasicheskie ortogonal’nie mnogochleny – 3-e izd., pererab. i dop. M.: Fizmat. 480s.
  12. Zemanian A.H. (2010) Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications (Dover Books on Mathematics). 400 с.
  13. My`xas`kiv V.V., Kunecz` Ya.I., Mishhenko V.O. (2003) Napruzhennya u try`vy`mirnomu tili z tonky`m podatly`vy`m vklyuchennyam za frontom impul`sny`x xvy`l`.  Fizy`ko–ximichna mexanika materialiv.  T. 39, # 3.  S. 63–68.

Comparative analysis of mass and cost indicators of single-phase transformers and reactors with rectangular and hexagranium cross sections of armored rods twisted magnetic core

UDC 621.314

А. Sadovuy, assistant
А. Cherepovskaya, 4th year student
Mykolaiv National Agrarian University

Goal.To implement new technical solutions to improve the configuration of magnetic circuits of active elements. To develop mathematical models of optimization comparative analysis of electromagnetic system variants of single-phase transformers with a twisted magnetic core.
Methodology.To solve the problems of practical use of new designs of the active part of single-phase EMC, it is necessary to carry out an optimization comparative analysis of mass and cost indicators. ISС optimization is performed on the basis of mathematical models with partial or integral optimization criteria, while observing the identity of power, electromagnetic load and voltage of the windings, taking into account a set of independent and dependent control variables.
Results.The main technical solutions of electromagnetic systems of single-phase transformers are proposed, and also mathematical models of quadrilateral and hexagonal EMC of the compared variants are given. It is shown that existing twisted single-phase induction static devices do not sufficiently satisfy the requirements of compactness and reliability of electrical engineering and radio electronic devices. Improvement of reliability and mass and cost indexes are achieved on the basis of the use of “wasteless” technology for the production of twisted magnetic cores.
Originality.The structural transformation of single-phase induction static devices with a twisted magnetic core is considered for the first time in order to reduce resource intensity and increase reliability. The transformation of structures is based on the use of combined twisted elements of a trapezoidal cross-section of hexagonal sections of rods. Thus, the longevity of the insulation increases depending on the change in the bending of coil turns in the angular zones from 90 ° to 120 °, and the material capacity decreases by 6-6.9%.
Practical value.The proposed solutions and the method of structural optimization will allow to reduce the indices of the mass and the loss of active power of the ISU based on the twisted magnetic circuit for electrical equipment of various equipment. References – 8, figures – 1, tables.

Keyword: single-phase transformer and reactor, twisted magnetic core, mass-index indicators, optimization, controlled variables.

Comparative analysis of mass and cost indicators of single-phase transformers and reactors with rectangular and hexagranium cross sections of armored rods twisted magnetic core.

References:
1. Stavinskiy A.A. Genezis struktur i predposyilki usovershenstvovaniya transformatorov i reaktorov preobrazovaniem konturov elektromagnitnyih sistem (sistemyi s shihtovannyimi i vityimi magnitoprovodami) / A.A. Stavinskiy // Elektrotehnіka і elektromehanіka. –2011.– #6 – s.33–38.
2. Balyan R.H. Transformatoryi dlya radioelektriki. – M.: Sov. Radio, 1971.-720s.
3. Tihomirov P.M. Raschet transformatorov: Uchebnoe posobie dlya vuzov. – 5-e izd. Pererab. i dop. – M.: Energoatomizdat, 1986 – 528s.
4. Flanagan W.M. Handbook of transformers desing and application / W.M. Flanagan. – Boston : Mc Graw Hill, 1993. – 232 p.
5. Sadovoy A.S. Variantyi i preobrazovanie struktur odnofaznyih transformatorov i reaktorov s vityimi magnitoprovodami / A.S. Sadovoy – Visnik Kremenchutskogo natsіonalnogo unіversitetu Imenі Mihayla Оstrogradskogo. – Kremenchuk : KrNU, 2017. – Vip. 2/2017(103). – S.15- 20.
6. Patent na korisnu model #65005. Ukraina. Magnіtoprovіd іnduktsіynogo statichnogo pristroyu. [Tekst] / Stavinskiy A.A., Stavinskiy R.A., Avdeeva O.A., Sadoviy O.S., Tsiganov O.M. – #u201104986; zayav. 20.04.11 ; opub. 25.11.11, Byul. #22. – 3 s. : il.
7. Stavinskiy R.A. Netraditsionnyie tehnicheskie resheniya, postanovka zadachi i metod strukturnoy optimizatsii induktsionnyih staticheskih ustroystv // Vіsnik KDU. – Kremenchuk: KDU, 2010. – Vip 4 / 2010(63), ch.2. – S.91-94.
8. Stavinskiy A.A. Metod sravnitelnogo analiza staticheskih elektromagnitnyih sistem, otlichayuschihsya strukturoy i konfiguratsiey elementov / A.A. Stavinskiy R.A. Stavinskiy, E.A. Avdeeva // Electrotechnic and computer systems. : Scientific and Technical Journal. – #14 (90) – Odessa, 2014.– S.53-60.

Issue 3 (95), 2017

Comparative analysis weight-and-cost indicators singlephase transformers and reactors with rectangular and hexagonal crosssections of rods of twisted magnetic core

UDC 621.3.042

A. Sadovoy

At this time, single-phase transformers and reactors are widely used in various fields of electrical engineering and one of the main metal elements of electrical engineering complexes. Therefore there are requirements to reduce material consumption and losses. The improvement of static induction devices leads to increasing the technical level of complexes in general. One of the most common designs of electromagnetic systems of single-phase induction static devices is a planar rod with twisted or laminated magnetic cores.
Solving the problem of comparative structural analysis it is used the method of optimizing the objective function which contains the technical conditions of the dimensionless parameters, and also the relative geometric controlled variables. Extremum relative components of the objective function is a function of the winding box winding conductive material and three universal identical geometric controlled variables are applied to any of the existing options of electromagnetic systems.
In these embodiments, according to the principle of equivalence of electromagnetic the same materials are used and the average numbers of the amplitudes of the magnetic induction flux in the rods and yokes are used. The filling factor of magnetic by steel is important, as well as methods of cooling performance and static induction devices.
The results of the comparative analysis of mathematical models have shown that the design of a twisted magnetic rod with hexagonal rods provides a significant reduction in the average weight and cost of a single-phase electromagnetic systems, according to equivalents with rectangular cross-section rods.

Key words: magnetic core, single-phase transformer, weight-and-cost indicator, controllable geometric variables.

Comparative analysis weight-and-cost indicators singlephase transformers and reactors with rectangular and hexagonal crosssections of rods of twisted magnetic core.

References:
1. Bal’jan R.H. Transformatory dlja radiojelektriki. – M.: Sov. Radio, 1971.-720s.
2. Tihomirov P.M. Raschet transformatorov: Uchebnoe posobie dlja vuzov. – 5-e izd. Pererab. i dop. – M.: Jenergoatomizdat, 1986 – 528s.
3. Majorec A.M. Magnitoprovody silovyh transformatorov (tehnologija i oborudovanie) / A.M. Majorec, G.I. Pshenichnyj, Ja.Z. Checheljuk i dr. : – M. : Jenergija, 1973 –272 s.
4. Patent na korisnu model’ №65005. Ukraїna. Magnіtoprovіd іndukcіjnogo statichnogo pristroju. [Tekst] / Stavins’kij A.A., Stavins’kij R.A., Stavins’ka O.A., Sadovij O.S.,Ciganov O.M. – №u201104986; zajav. 20.04.11 ; opub. 25.11.11, Bjul. №22. – 3 s. : il.
5. Stavinskij R.A. Netradicionnye tehnicheskie reshenija, postanovka zadachi i metod strukturnoj optimizacii indukcionnyh staticheskih ustrojstv // Vіsnik KDU. – Kremenchuk: KDU, 2010. – Vip 4 / 2010(63), ch.2. – S.91-94.
6. Stavins’kij A.A. Metod sravnitel’nogo analiza staticheskih jelektromagnitnyh sistem, otlichajushhihsja strukturoj i konfiguraciej jelementov / A.A. Stavins’kij R.A. Stavins’kij, E.A. Avdeeva // Jelektrotehnicheskie i komp’juternye sistemy. : Nauchno-tehnicheskij zhurnal. – №14 (90) – Odessa, 2014.– S.53-60
7. Blincov V. S. Transformatory dlja vstraivanija v obolochki ogranichennogo diametra ob#ektov special’noj tehniki i postanovka zadachi ih usovershenstvovanija / V. S. Blincov, R. A. Stavinskij, E. A. Avdeeva, A. S. Sadovoj // Elektrotehnіka і elektromehanіka : naukovo-praktichnij zhurnal. – № 2 – Harkіv, 2012. – S. 16–21.

Issue 4 (92), 2016