Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring

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.

Keywords

• Mechanical analysis
• machine elements design
• sine-cosine algorithm
• nonlinear optimization model
• closed coil helical spring