Sanjin Troha, Željko Vrcan, Dimitar Karaivanov, Madina Isametova

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The application of multi-criteria optimization to two-carrier two-speed planetary gear trains is outlined in this paper. In order to determine the mathematical model of multi-criteria optimization variables, the objective functions and conditions must be determined first. Two-carrier two-speed planetary gear trains with brakes on coupled shafts are analyzed in this paper. The mathematical model covers the determination of the set of the Pareto optimal solutions as well as the method for selecting an optimal solution from this set. A numerical example is provided to illustrate the procedure in which the optimal two-speed planetary gear train is selected and defined by design parameters.


Multi-criteria Optimization, Two-speed Planetary Gear Trains, Pareto Optimal Solutions, Coupled Shafts

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Tudose, L., Buiga, O., Jucan, D.,Stefanache, C., 2008, Multi-objective optimization in helical gears design, The Fifth International Symposium about Design in Mechanical Engineering-KOD 2008, Novi Sad, Serbia, pp. 77-84.

Tkachev, A., Goldfarb, V., 2009, The concept of optimal design for spur and helical gears, The 3rdInternational Conference Power Transmissions '09, October 2009, Chalkidiki, Greece, pp.59-62.

Rosić, B., 2001, Multicriterion optimization of multistage gear train transmission, Facta Universitatis-Series Mechanical Engineering, 1(8), 2001, pp. 1107-1115.

Brüser, P.,Grüschow, G., 1989,Otimierung von Planetengetrieben,Antiebstechnik, 2, pp. 64-67.

Troha, S., 2011, Analysis of a planetary change gear train’s variants, (in Croatian), PhD Thesis, University of Rijeka, Engineering Faculty, Rijeka, Croatia.

Kudrjavtsev, V. N., Kirdyiashev, I. N., 1977,Planetary gears, (in Russian), Handbook, Mashinostroenie, Leningrad.

Arnaudow, K., Karaivanov, D., 2005, Systematik, Eigenschaften und Möglichkeiten von zusammengesetzten Mehrsteg-Planetengetrieben, Antriebstechnik, 5, pp. 58-65.

Ivanov, A.N., 1990, Evaluation of diametric dimensions of planetary gearboxes in the design phase, (in Russian),Vestnikmashinostroenie, 7, pp. 16-19.

Lechner, G., Naunheimer, H.,1999, Automotive Transmissions, Springer-Verlag, Heidelberg.

Jelaska, D., 2012, Gears and Gear Drives, University of Split, Croatia.

Stefanović-Marinović, J., Troha, S., Milovančević, M., 2017, An application of multicriteria optimization to the two-carrier two-speed planetary gear trains, Facta Universitatis-Series Mechanical Engineering, 15(1), pp. 85-95.

Stefanović-Marinović, J., Petković, M., Stanimirović, I., Milovančević, M., 2011, A model of planetary gear multicriteria optimization, Transactions of FAMENA, 35(4), pp. 21-34.

Sriatih, A., Yedukondalu, G., Jagadeesh, A., 2011, Mechanical efficiency of planetary gear trains: An Estimate, Mechanical Engineering Research, 1(1), pp. 97-102.

Del Castillo, J.M., 2002, Theanalytical expression of the efficiency of planetary gear trains, Mechanism and Machine Theory, 37, pp. 197-214.

Stefanović-Marinović, J., 2008, Multicriterionoptimization of planetary power transmission gear pairs, (in Serbian), PhD Thesis, University of Niš, Faculty of Mechanical Engineering, Niš, Serbia.

Niemann, G., Winter, H., 1989, Maschinenelemente, Band II, zweite völlig neubearbeite Auflage, Springer-Verlag Berlin.

International Organization for Standardization, 2006, Calculation of load capacity of spur and helical gears, International standard ISO 6336-2.

Troha, S., Žigulić, R., Karaivanov, D., 2014, Kinematic operating modes of two-speed two-carrier planetary gear trains with four external shafts, Transactions of FAMENA, 38(1), pp. 63-76.

Troha, S., Lovrin, N., Milovančević, M., 2012, Selection of the two–carrier shifting planetary gear train controlled by clutches and brakes, Transactions of FAMENA, 36(3), pp. 1-12.

Troha, S., Petrov, P., Karaivanov, D., 2009, Regarding the optimization of coupled two carrier planetary gears with two coupled and four external shafts, Machine building and electrical engineering, 1, pp. 49–56.



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