Optimization of a drive shaft using PSO algorithm

Abstract

Mechanical design involves several continuous variables associated with the calculation of elements that compose the parts implemented in different processes. However, when the values associated with several design variables are selected, the range of each such variable may result in infinite solutions or oversized solution spaces. Thus, the choice and fit of different variables related to the mechanical parts under analysis pose a challenge to designers. This is the case of drive shaft design: the variables that represent the diameters of several transversal sections of each of its elements directly affect its weight and resistance to mechanical stresses. Therefore, the selection of variables should not be at random. This article presents the optimization of the design of a drive shaft composed of three transversal sections using the metaheuristic technique particle swarm optimization (PSO). Such problem is solved to obtain an optimal and reliable part. For that purpose, a nonlinear mathematical model was developed to represent this problem as a function of the physical features of the mechanical system. The objective function is the reduction of the weight of the shaft and the variables are the diameters of each section. The set of constraints in this problem considers the general equation to design a fatigue-safe shaft as well as a constructive constraint to establish the minimum step distance for coupling the mechanical elements. Due to the nonlinearity of the mathematical model, this work proposes PSO as optimization technique. This algorithm has proven to be an efficient tool to solve continuous nonlinear problems. Finally, the solution provided by the optimization technique is validated in ANSYS® software, thus demonstrating that the answer meets all the design criteria previously selected. © 2018, World Scientific and Engineering Academy and Society. All rights reserved.