Multi-Speed Gearbox Design Using Multi-Objective Evolutionary Algorithms

[+] Author and Article Information
Kalyanmoy Deb, Sachin Jain

Kanpur Genetic Algorithms Laboratory (KanGAL), Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, PIN 208 016, India

J. Mech. Des 125(3), 609-619 (Sep 04, 2003) (11 pages) doi:10.1115/1.1596242 History: Received March 01, 2002; Revised February 01, 2003; Online September 04, 2003
Copyright © 2003 by ASME
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Schematic of a gear train
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A random set of 10,000 feasible solutions, four Pareto-optimal solutions obtained in 2, and 100 nondominated solutions obtained by NSGA-II are shown. Only thickness of 18 gears are varied here.
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NSGA-II solutions for the case of module being an additional variable are shown against four Pareto-optimal solutions of Case I (as reported in 2)
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Variation of gear thickness in obtained solutions
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Variation of gear module in obtained solutions
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The bending stress of NSGA-II solutions are shown against the delivered power
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NSGA-II solutions are shown with two limiting errors in output speeds. Gear teeth and thickness are varied here.
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Proportion of obtained solutions having different maximum percentage error in speed ratios is shown for two cases of optimization (with 5% and 10% limiting error)
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The ratio Bi/Ci for all nine gear-pairs observed in different obtained solutions
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NSGA-II solutions for varying gear module, teeth, and thickness are shown. Nondominated fronts for two different ranges of modules are compared with that obtained in Case III (with a fixed module of 0.28 cm). Open circles indicate results when the module is allowed to vary within [0.10,0.41] cm and the triangles indicate results for modules varying in [0.10,0.73] cm.
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Module m obtained in different nondominated solutions for two cases
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NSGA-II solutions for an additional objective of minimizing center distance are compared with NSGA-II solutions with two objectives (maximizing power and minimizing volume)
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Nondominated solutions for four objectives
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Trade-off between ε and center distance for two-objective NSGA-II and Jain and Agogino’s 2 study




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