Abstract
Optimization design of spur gear is a complicated work because the performance characteristics depend on different types of decision variables and objectives. Traditional single-objective optimization design of the spur gear always results in poor outcomes relative to other objectives due to objectives’ competition with each other. Therefore, this study works on the spur gear design based on the multi-objective optimization model of elitist non-dominated sorting genetic algorithm (NSGA-II). In the model, gear module, teeth number, and transmission ratio are decision variables, while center distance, bearing capacity coefficient, and meshing efficiency are objectives. Final optimal solutions are picked out from Pareto frontier calculated from NSGA-II using the decision makers of Shannon Entropy, linear programming technique for multidimensional analysis of preference (LINMAP), and technique of order preference by similarity to an ideal solution (TOPSIS). Meanwhile, a deviation index is used to evaluate the reasonable status of the optimal solutions. From triple-objective and dual-objective optimization results, it is found that the optimal solution selected from LINMAP decision maker shows a relatively small deviation index. It indicates that LINMAP decision maker may yield better optimal solution. This study could provide some beneficial information for spur design.
Highlights
Gears are used in a great deal of mechanical devices for transmitting power from one part of a machine to another.[1]
Three optimal solutions selected from Shannon Entropy (SE), LINMAP, and TOPSIS decision makers are compared in Table 3, which are (85.2, 86.7, 0.961), (115, 208, 0.964), and (108, 174, 0.960)
In order to evaluate the reasonable status of each optimal solution, a deviation index shown in equation (20) is used to assess/quantify the goodness of the obtained optimal solutions.[13,32,33,34]
Summary
Gears are used in a great deal of mechanical devices for transmitting power from one part of a machine to another.[1]. Due to most of power transmission systems requiring light weight, efficient, and low-cost elements, Tamboli et al.[11] optimized a heavy-duty gear reducer with helical gear pair based on the minimum volume. Multi-objective optimization methods have been widely applied in the gear design because it allows decision maker to consider trade-offs between the competing objectives.[13] Wei and Lin[14] performed a multiobjective optimization design for a helical gear using finite element method and Taguchi method. Ye et al.[17] established a multi-objective optimization model for tractor’s NGW planetary gear, where the mechanism’s smallest volume and highest efficiency were taken as the objective functions, while reliability conditions of planetary transmission and gears’ fatigue strength, the planetary gear’s tooth configuration conditions, and structural conditions were taken as the constraints.
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