Multi-Objective Optimization Design of the Helical Gear Transmission Based on Coalition Cooperative Game Theory

Abstract

Considering helical gear transmission's economic performance and drive reliability, construct multi-objective optimization model of the helical gear transmission with taking normal module, teeth number of small helical gear, helix angle and the gear width coefficient as design variables and taking the volume of small and large helical gear and opposite number of overlap ratio as objective functions. Propose multi-objective optimization design method based on coalition cooperative game theory where the two design goals are seen as two game players. By calculating the impact factor of design variables to objective functions and fuzzy clustering, the design variables are divided into strategy space of game players. Each game player takes its own revenue function as target and does single objective optimization in its own strategy space in order to get its own best strategy. The best strategies of all players form a combination of one round game and the optimal solution can be obtained through several game rounds. Example results show the effectiveness of game method.

Multi Objective Design Optimization of Helical Gear Pair Using Adaptive Parameter Harmony Search Algorithm

“…The basic goal of optimization is to minimize the volume of the helical gear pair and opposite number of overlap ratio. Detailed study of problem formulation is discussed elsewhere [10].…”

“…According to [10], volume of small and large helical gear is taken as objective function f 1 (X) and the opposite number of overlap ratio is taken as objective function f 2 (X), where, T 1 =440Nm and i =5. The materials considered for the gear pair are given below.…”

“…Normal module (m n ), Teeth number of small helical gear (Z 1 ), Helix angle (β) and the gear width coefficient ( d ) are considered as design variables according to [10]. Hence, the optimal design variables are represented as: X = (x 1 ,x 2 ,x 3 ,x 4 ) T = (m n ,Z 1 ,β, d ) T (1)…”

“…Sabarinath et al [8] successfully extended a recent modified version of harmony search algorithm namely parameter adaptive harmony search (PAHS) to optimize disc brake design and helical compression spring design using weighted sum approach. The problem of multiobjective design of helical gear pair transmission with objective functions namely volume of the helical gear pair and opposite number of overlap ratio involving the design variables such as normal module, helix angle, gear width coefficient and teeth number of small helical gear was solved by Jiang Chong-ming [9] using Matlab toolbox and the same problem was attempted by Meng Rui [10] using Coalition Cooperative Game Theory. In this work, the same problem is attempted by extending parameter adaptive harmony search (PAHS) to solve this gear design problem.…”