AUTHORS: M. A. Rodriguez-Cabal, Juan Ardila Marín, L.F. Grisales-Noreña, Oscar Danilo Montoya, Jorge Andres Sierra Del Rio
Download as PDF
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.
KEYWORDS: machinery design, drive shaft, particle swarm optimization, ANSYS® simulation
REFERENCES:
[1] S. K. Bhaumik, R. Rangaraju, M. A. Parameswara, M. A. Venkataswamy, T. A. Bhaskaran, and R. V. Krishnan, “Fatigue failure of a hollow power transmission shaft,” Eng. Fail. Anal., vol. 9, no. 4, pp. 457–467, 2002.
[2] R. L. Mott, Machine elements in mechanical design. 2004.
[3] A. M. Cerón, G. A. Charry, and J. J. Coronado, “Análisis de falla del eje de un agitador para tratamiento de agua,” no. 30, pp. 185–190, 2006.
[4] D. Momčilović, Z. Odanović, R. Mitrović, I. Atanasovska, and T. Vuherer, “Failure analysis of hydraulic turbine shaft,” Eng. Fail. Anal., vol. 20, pp. 54–66, 2012.
[5] N. Harle, J. Brown, and M. Rashidy, “A feasibility study for an optimising algorithm to guide car structure design under side impact loading,” Int. J. Crashworthiness, vol. 4, no. 1, pp. 71–92, 1999.
[6] Q. He and L. Wang, “An effective coevolutionary particle swarm optimization for constrained engineering design problems,” Eng. Appl. Artif. Intell., vol. 20, no. 1, pp. 89–99, 2007.
[7] X. Shi and H. Chen, “Particle swarm optimization for constrained circular-arc/linesegment fitting of discrete data points,” Int. J. Model. Simul., vol. 38, no. 1, pp. 25–37, Jan. 2018.
[8] N. E. Mastorakis, “Solving Non-linear Equations via Genetic Algorithms,” Proc. 6th WSEAS Int. Conf. Evol. Comput., vol. 2005, pp. 24– 28, 2005.
[9] C. Giri, D. K. R. Tipparthi, and S. Chattopadhyay, “A genetic algorithm based approach for system-on-chip test scheduling using dual speed TAM with power constraint,” WSEAS Trans. Circuits Syst., vol. 7, no. 5, pp. 416–427, 2008.
[10] R. A. Gallego, A. H. Escobar, and E. M. Toro, Técnicas metaheurísticas de optimización, 2nd ed. Pereira: Universidad Tecnológica de Pereira, 2008.
[11] J. Lampinen, “Cam shape optimisation by genetic algorithm,” CAD Comput. Aided Des., vol. 35, no. 8 SPEC., pp. 727–737, 2003.
[12] M. A. Ait Chikh, I. Belaidi, S. Khelladi, J. Paris, M. Deligant, and F. Bakir, “Efficiency of Bioand Socio-inspired Optimization Algorithms for Axial Turbomachinery Design,” Appl. Soft Comput., 2017.
[13] I. Hanafi, F. M. Cabrera, F. Dimane, and J. T. Manzanares, “Application of Particle Swarm Optimization for Optimizing the Process Parameters in Turning of PEEK CF30 Composites,” Procedia Technol., vol. 22, no. October 2015, pp. 195–202, 2016.
[14] A. Husseinzadeh Kashan, “An efficient algorithm for constrained global optimization and application to mechanical engineering design: League championship algorithm (LCA),” CAD Comput. Aided Des., vol. 43, no. 12, pp. 1769–1792, 2011.
[15] V. V. De Melo and G. L. C. Carosio, “Investigating Multi-View Differential Evolution for solving constrained engineering design problems,” Expert Syst. Appl., vol. 40, no. 9, pp. 3370–3377, 2013.
[16] N. Ben Guedria, “Improved accelerated PSO algorithm for mechanical engineering optimization problems,” Appl. Soft Comput. J., vol. 40, pp. 455–467, 2016.
[17] R. L. Norton, Diseño de máquinas, 1st ed. Prentice Hall, 1999.
[18] J. Kennedy and R. Eberhart, “Particle swarm optimization,” Neural Networks, 1995. Proceedings., IEEE Int. Conf., vol. 4, pp. 1942– 1948 vol.4, 1995.
[19] J. F. Jaramillo Velez and L. F. Noreña Grisales, “Sintonización del d-statcom por medio del método de optimización pso,” 2013.
[20] M. A. Guzmán and A. Delgado, “Optimización de la geometría de un eje aplicando algoritmos genéticos,” Ing. e Investig., vol. 25, no. 2, pp. 15–23, 2005.
[21] MatWeb, “AISI 1040 Steel, cold drawn,” 2018.
[Online]. Available: http://www.matweb.com/search/DataSheet.aspx?Ma tGUID=39ca4b70ec2844b888d999e3753be83a&ckc k=1.
[22] Schaeffler KG, Rodamientos FAG. 2009.
[23] F. P. Beer and E. R. J. Jhonston, Mecanica Vectorial Para Ingenieros “Estatica,” 6th ed. McGRAW-HILL, 1997.