Abstract
This paper proposes the application of the sinecosine algorithm (SCA) to the optimal design of a closed coil helical spring. The optimization problem addressed corresponds to the minimization of total spring volume subject to physical constraints that represents the closed coil helical spring such as maximum working load, shear stress, and minimum diameter requirements, among other. The resulting mathematical formulation is a complex nonlinear and non-convex optimization model that is typically addressed in literature with trial and error methods or heuristic algorithms. To solve this problem efficiently, the SCA is proposed in this research. This optimization algorithm belongs to the family of the metaheuristic optimization techniques, it works with controlled random processes guided by sine and cosine trigonometric functions, that allows exploring and exploiting the solution space in order to find the best solution to the optimization problem. By presenting as main advantage an easy implementation at any programming language using sequential quadratic programming; eliminating the need to uses specialized and costly software. Numerical results demonstrating that the proposes SCA allows reaching lower spring volume values in comparison with literature approaches, such as genetic algorithms, particle swarm optimization methods, among others. All the numerical simulations have been implemented in the MATLAB software.
Highlights
INTRODUCTION[7], where the authors perform the optimization of different engineering problems by using multiples objective functions, such as: minimizing the weight of a spring, minimizing the weight of a gear train, minimizing the weight of a welded beam, and minimizing the volume of a tank
T HE design of mechanical elements for industrial machinery is a complex and delicate task, since various factors must be considered for its construction, such as: the efforts to which the part will be subjected, the type of material to be used, the correct geometry for the coupling of the elements, among others [1]
This paper proposes the application of the sinecosine algorithm (SCA) to the optimal design of a closed coil helical spring
Summary
[7], where the authors perform the optimization of different engineering problems by using multiples objective functions, such as: minimizing the weight of a spring, minimizing the weight of a gear train, minimizing the weight of a welded beam, and minimizing the volume of a tank. The solution technique proposed by the authors is known as the chaotic gray wolf, the solution method is compared with other articles reported in the literature by demonstrating that the proposed algorithm presented a good performance in comparison with these; the authors do not report the times from the solution Another case is presented in [8], by using a multi objective optimization for designing a helical spring, taking as objective functions the minimization of the weight of the element and the natural frequency. The authors report that the best solution is founded by the Active set, but they do not compare processing times These optimization cases make it clear that performing the optimization of a complete machine is a complex task, is for this reason that the literature is focused on the constructive elements that are more prone to failure or that are widely used regardless of the final application.
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