Abstract
Nowadays, the increasing demand for high-strength, efficient, quiet, and high-precision gear design leads to the use of various optimization methods. In this study, a new evolutionary optimization algorithm, named adaptive mixed differential evolution (AMDE), based on a self-adaptive approach is introduced. The proposed method is applied to solve the problem of the optimal spur gear tooth profile, where the objectives are to equalize the maximum bending stresses and the specific sliding coefficients at extremes of contact path. The mathematical model of the maximum bending stresses is developed using a finite element analysis (FEA) calculation. The effectiveness of the proposed method is demonstrated by solving some well-known practical engineering problems. The optimization results for the test problems show that the AMDE algorithm provides very remarkable results compared to those reported recently in the literature. Moreover, for the spur gear used in this work, a significant improvement in balancing specific sliding coefficients and maximum bending stresses are found.
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Savsani V, Rao RV, Vakharia DP (2010) Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mech Mach Theory 45:531–541
Prayoonrat S, Walton D (1988) Practical approach to optimum gear train design. Comput Aided Des 20(2):83–92
Yokota T, Taguchi T, Gen M (1998) A solution method for optimal weight design problem of the gear using genetic algorithms. Comput Ind Eng 35:523–526
Thompson DF, Gupta S, Shukla A (2000) Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units. Mech Mach Theory 35:609–627
Deb K, Jain S (2003) Multi-speed gearbox design using multi-objective evolutionary algorithms. ASME J Mech Des 125:609–619
Gologlu C, Zeyveli M (2009) A genetic approach to automate preliminary design of gear drives. Comput Ind Eng 57:1043–1051
Mendi F, Baskal T, Boran K, Fatih EB (2010) Optimization of module, shaft diameter and rolling bearing for spur gear through genetic algorithm. Expert Syst Appl 37:8058–8064
Marjanovic N, Isailovic B, Marjanovic V, Milojevic Z, Blagojevic M, Bojic M (2012) A practical approach to the optimization of gear trains with spur gears. Mech Mach Theory 53:1–16
Wan Z, Zhang SJ (2012) Formulation for an optimal design problem of spur gear drive and its global optimization. Proc Inst Mech Eng part C. J Mech Eng Sci 227(8):1804–1817
Golabi S, Fesharaki JJ, Yazdipoor M (2014) Gear train optimization based on minimum volume/weight design. Mech Mach Theory 73:197–217
Buiga O, Tudose L (2014) Optimal mass minimization design of a two-stage coaxial helical speed reducer with genetic algorithms. Adv Eng Softw 68:25–32
Thoan PV, Wen G, Yin H, Ld H, Nguyen VS (2015) Optimization design for spur gear with stress-relieving holes. Int J Comp Meth-Sing 12(2):1–11
Salomon S, Avigad GC, Purshouse RJ, Fleming P (2015) Gearbox design for uncertain load requirements using active robust optimization. Eng Optimiz 48(4):652–671
Divandari M, Aghdam BH, Barzamini R (2012) Tooth profile modification and its effect on spur gear pair vibration in presence of localized tooth defect. J Mech 28(2):373–381
Atanasovska I, Mitrovic R, Momcilovic D (2013) Explicit parametric method for optimal spur gear tooth profile definition. Adv Mater Res 633:87–102
Bruyère J, Velex P (2014) A simplified multi-objective analysis of optimum profile modifications in spur and helical gears. Mech Mach Theory 80:70–83
Diez-Ibarbia A, Fernandez del Rincon A, Iglesias M, de-Juan A, Garcia P, Viadero F (2015) Efficiency analysis of spur gears with a shifting profile. Meccanica. doi:10.1007/s11012-015-0209-x
Hammoudi A, Djeddou F, Atanasovska I, Keskes B (2015) A differential evolution algorithm for tooth profile optimization with respect to balancing specific sliding coefficients of involute cylindrical spur and helical gears. Adv Mech Eng 7(9):1–11
Storn R, Price KV (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Dechampai D, Tanwanichkul L, Sethanan K, Pitakaso R (2015) A differential evolution algorithm for the capacitated VRP with flexibility of mixing pickup and delivery services and the maximum duration of a route in poultry industry. J Intell Manuf. doi:10.1007/s10845-015-1055-3
Storn R (1996) On the usage of differential evolution for function optimization. In:Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS). pp. 519–523. Berkeley
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE T Evolut Comput 13(2):398–417
Wang Y, Zixing C, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE T Evolut Comput 15(1):55–66
Brest J, Greiner S, Boskovic B, Marjan M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE T Evolut Comput 10(6):646–657
Kim HK, Chong JK, Park KY, Lowther DA (2007) Differential evolution strategy for constrained global optimization and application to practical engineering problems. IEEE T Magn 43(4):1565–1568
Onwubolu GC, Davendra D (2009) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Berlin
Liao TW (2010) Two hybrid differential evolution algorithms for engineering design optimization. Appl Soft Comput 10:1188–1199
Gandomi AH, Yang XS, Alavi HA (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89:2325–2336
Zou D, Liua H, Gaob L, Li S (2011) A novel modified differential evolution algorithm for constrained optimization problems. Comput Math Appl 61:1608–1623
Li H, Zhang L (2013) A discrete hybrid differential evolution algorithm for solving integer programming problems. Eng Optimiz 46(9):1238–1268
Ma W, Wang M, Zhu X (2013) Hybrid particle swarm optimization and differential evolution algorithm for bi-level programming problem and its application to pricing and lot-sizing decisions. J Intell Manuf. doi:10.1007/s10845-013-0803-5
Huang F, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186:340–356
Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. ASME J Mech Des 112:223–229
Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10:629–640
Akay B, Karaboga D (2012) Artificial bee colony algorithm for large scale problems and engineering design optimization. J Intell Manuf 23:1001–1014
Gandomi AH, Yang XS, Alavi AH (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29:17–35
Dong M, Wang N, Cheng X, Jiang C (2014) Composite differential evolution with modified oracle penalty method for constrained optimization problems. Math Probl Eng. doi:10.1155/2014/617905
Rao SS (2009) Engineering optimization theory and practice, 4th edn. Wiley, NewYork
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching-learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Aided Des 43:303–315
Deb K, Srinivasan A (2006) Innovization: innovating design principles through optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp 1629–1636. ACM, New York
Bérubé JF, Gendreau M, Potvin JY (2009) An exact ε-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits. Eur J Oper Res 194(1):39–50
Pedrero JI, Artés M (1996) Determination of the addendum modification factors for gears with pre-established contact ratio. Mech Mach Theory 31:937–945
Henriot G (2007) Engrenages: conception fabrication mise on Œuvre, 8th edn. Dunod, l’Usine Nouvelle, Paris
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Abderazek, H., Ferhat, D. & Ivana, A. Adaptive mixed differential evolution algorithm for bi-objective tooth profile spur gear optimization. Int J Adv Manuf Technol 90, 2063–2073 (2017). https://doi.org/10.1007/s00170-016-9523-2
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DOI: https://doi.org/10.1007/s00170-016-9523-2