Multi-objective optimization design of spur gear based on NSGA-II and decision making

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.

Multi-objective optimization of a 2-stage spur gearbox using NSGA-II and decision-making methods

“…The bending and contact stress values are obtained from Eqs. (19) and (20), respectively, while the unmodified allowable bending and contact stress values are obtained from Eqs. (21) and (22).…”

“…The terms expressed in Eqs. (19)(20)(21)(22) are defined as follows: W t tangential load, Z E is the elastic coefficient, Y j is the geometric factor for bending strength, m t transverse module, d w1 pitch diameter of pinion, H B hardness factor. The rest of terms are defined in Table 1.…”

“…Thompson et al [9] considered 17 variables viz three pinion diameters, gear diameters, face-width, diametral pitch, hardness and two shaft diameters, while Huang et al [19] considered module and tooth number in place of the diametral pitch. Two-stage spur gear systems have been considered by Yao [20] with design variables viz. module, tooth number for both stages and overall transmission ratio and applied decision-making methods to the Pareto frontier.…”

A Criterion Utility Conversion Technique for Probabilistic Linguistic Multiple Criteria Analysis in Emergency Management

“…A mass of achievements have been obtained in terms of the information environments (Li, 2008;Liao et al, 2019a;Lu et al, 2020), model structures (Chen, 2019;Haghighi et al, 2019), and the combinations with other methods (Kashef et al, 2018;Mehrabadi & Boyaghchi, 2019). This method has also been applied to solve practical problems (Hamidzadeh et al, 2020;Yao, 2019;Zuo et al, 2019). The studies of the LINMAP method on different information environments and the combination with other methods extended the applications of the LINMAP method.…”

“…When criteria have inter-dependencies, the simple weighted average might cause errors (Liao et al, 2019b). The studies of LINMAP method (Li, 2008;Liao et al, 2019a;Lu et al, 2020;Chen, 2019;Haghighiet al, 2019;Kashef et al, 2018;Mehrabadi & Boyaghchi, 2019;Hamidzadeh et al, 2020;Yao, 2019;Zuo et al, 2019) just used the simple weights of criteria, so their results might be inaccurate. The even swaps method uses the relations of criteria to do the trade-offs, so the idea of trade-offs might be able to fit the challenge of the LINMAP method in terms of criterion relations.…”