Abstract
Springs are important members often used in machines to exert force, absorb energy and provide flexibility. In mechanical systems, wherever flexibility or relatively a large load under the given circumstances is required, some form of spring is used. In this paper, non-traditional optimization algorithms, namely, Ant Lion Optimizer, Grey Wolf Optimizer, Dragonfly optimization algorithm, Firefly algorithm, Flower Pollination Algorithm, Whale Optimization Algorithm, Cat Swarm Optimization, Bat Algorithm, Particle Swarm Optimization, Gravitational Search Algorithm are proposed to get the global optimal solution for the closed coil helical spring design problem. The problem has three design variables and eight inequality constraints and three bounds. The mathematical formulation of the objective function U is to minimize the volume of closed coil helical spring subject to constraints. The design variables considered are Wire diameter d, Mean coil diameter D, Number of active coils N of the spring. The proposed methods are tested and the performance is evaluated. Ten non-traditional optimization methods are used to find the minimum volume. The problem is computed in the MATLAB environment. The experimental results show that Particle Swarm Optimization outperforms other methods. The results show that PSO gives better results in terms of consistency and minimum value in terms of time and volume of a closed coil helical spring compared to other methods. When compared to other Optimization methods, PSO has few advantages like simplicity and efficiency. In the future, PSO could be extended to solve other mechanical element problems.
Highlights
A helical spring or coil spring is a mechanical device, which is normally used to store energy and release it subsequently, to maintain a force between contacting surfaces or to absorb shock.Helical spring is made by twisting a wire or coil with small diameter in the form of helix having rectangular, square, or circular cross section wrapped around an imaginary cylinder, which can undergo considerable deflection without getting permanently distorted
The design variables are as follows Wire diameter, d = x1 Mean coil diameter, D = x2 Number of active coils, N = x3
The design of the closed coil helical spring is considered with the Number of active coils(N), wire diameter(d), mean coil diameter of spring (D), minimum wire diameter(dmin), maximum working load (Fmax), preload compressive force(Fp),allowable shear stress(S), Spring index (C),modulus of rigidity(G), perturbance factor (δ), Stress factor or Wahl factor(Cf), maximum perturbance factor, maximum outside diameter of spring (Dmax), spring stiffness (K), Free length,deflection under the maximum load, deflection under preload, deflection from preload to maximum load and allowable maximum deflection under preload respectively[2,3]
Summary
A helical spring or coil spring is a mechanical device, which is normally used to store energy and release it subsequently, to maintain a force between contacting surfaces or to absorb shock. The gap between two adjacent coils of the helix can be varied according to the desired property. Based on this gap, Volume Minimization of a Closed Coil Helical Spring. BA, PSO and GSA helical springs are classified as open and close coiled helical spring. In closely coiled helical spring, wire is tightly wound so that there is no gap between two adjacent coils of the spring. When the spring wire is closely coiled the plane having each turn is at right angles nearly to the axis of the helix and the wire is subjected to torsion. The load applied is along the axis or parallel to the spring [5]
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