Abstract
This study describes the shape synthesis of a metallic flywheel using a non-dominated sorting Jaya algorithm. Generally, the flywheel is used to store the kinetic energy in the machines. Kinetic energy is an essential parameter to measure flywheel performance and can be improved by the optimal shape of the flywheel. In order to the optimal shape of the flywheel, the multi-objective problem with the maximization of the kinetic energy and minimization of von Mises stresses is formulated under appropriate design constraints using the cubic B-spline curve. A flowchart is proposed to solve the two-point boundary value differential equation for the calculation of von Mises stress at each point between the inner and outer radii of the flywheel. The design variables are represented by the control points of the cubic B-spline curve. A posteriori approach-based algorithm as non-dominated sorting Jaya algorithm (NSJaya) is used to solve the formulated optimization problem. This algorithm is based on the concepts of crowding distance and non-dominated sorting approach and gives the optimal Pareto set. The proposed method is applied to the flywheel of the agricultural thresher. The performance of the proposed algorithm is compared with that of non-dominated sorting genetic algorithm (NSGA-II) using hyper-volume performance metric. It is found that the NSJaya algorithm gives better results compared to NSGA-II and a posteriori approach-based algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), and Jaya. The optimal Pareto set for the optimal shape of the flywheel is calculated and outlined in this paper. The designer can choose any solution from the Pareto set for the optimal shape of the flywheel. ANSYS parameter design language (APDL) software is used for the validation of the von Mises stresses in the optimized shapes of the flywheel.
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References
Ahsan M, Farrukh S (2013) A new type of shooting method for nonlinear boundary value problems. Alex Eng J 52(4):801–805
Berger M, Porat I (2017) Optimal design of a rotating disk for kinetic energy storage & H 55(March 1988) 2017
Coello CA (2000) An updated survey of GA-based multiobjective optimization techniques. ACM Comput Surv 32(2):109–143
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Dede T (2018) Jaya algorithm to solve single objective size optimization problem for steel grillage structures. Steel Compos Struct 26(2):163–170
Ebrahimi ND (1988) Optimum design of flywheels. Comput Struct 29(4):681–686
Eby D, Averill RC, Iii WFP, Goodman ED (1999) The optimization of flywheels using an injection island genetic algorithm. AI EDAM 13(5):327–340
Feng L, Mao Z-Z, Yuan P (2012) An improved multi-objective particle swarm optimization algorithm and its application. Kongzhi yu Juece/Control Decis 27(9)
Gao K, Zhang Y, Sadollah A, Lentzakis A, Su R (2017) Jaya, harmony search and water cycle algorithms for solving large-scale real-life urban traffic light scheduling problem. Swarm Evol Comput 37(August 2016):58–72
Gao K, Yang F, Zhou M, Pan Q, Suganthan PN (2019) Flexible job-shop rescheduling for new job insertion by using discrete Jaya algorithm. IEEE Trans Cybern 49(5):1944–1955
Ghotbi E, Dhingra AK (2012) A bilevel game theoretic approach to optimum design of flywheels. Eng Optim 44(11):1337–1350
Gupta S, Agarwal I, Singh RS (2019) Workflow scheduling using Jaya algorithm in cloud. Concurr Comput 1–13
Huang J, Fadel GM (2000) Heterogeneous flywheel modeling and optimization. Mater Des 21(2):111–125
Jiang L, Zhang W, Ma GJ, Wu CW (2016) Shape optimization of energy storage flywheel rotor. Struct Multidiscip Optim 55(2):739–750
Kang F, Xu Q, Li J (2016) Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence. Appl Math Model 40(11–12):6105–6120
Kang F, Li J, Dai J (2019) Prediction of long-term temperature effect in structural health monitoring of concrete dams using support vector machines with Jaya optimizer and salp swarm algorithms. Adv Eng Softw 131(March):60–76
Kharab A, Guenther RB (2012) An introduction to numerical methods: a MATLAB approach
Mortenson ME (2006) Geometric modeling. McGraw Hill Education Private Limited, New Delhi
Norton RL (2011) Kinematics and dynamics of machinery. McGra-Hill Higher Education
Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method in multiobjective problems. In: ACM symposium on applied computing, pp 603–607
Rao RVR (2018) Jaya: an advanced optimization algorithm and its engineering applications. Springer International Publishing AG, part of Springer Nature
Rao RV, Rai DP, Balic J (2016) Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm. J Intell Manuf 28:1–23
Rao RV, Rai DP, Balic J (2017a) Multi-objective optimization of abrasive waterjet machining process using Jaya algorithm and PROMETHEE Method. J Intell Manuf 1–27
Rao RV, Rai DP, Balic J (2017b) A multi-objective algorithm for optimization of modern machining processes. Eng Appl Artif Intell 61(November 2016):103–125
Sandgren E, Ragsdell KM (1983) Optimal flywheel design with a general thickness form representation 105:425–433
Singh P, Chaudhary H (2018a) Optimal design of the flywheel using nature inspired optimization algorithms. Open Agric 3(1):490–499
Singh P, Chaudhary H (2018b) A modified Jaya algorithm for mixed-variable optimization problems. J Intell Syst 1–21
Singh R, Chaudhary H, Singh AK (2017) Defect-free optimal synthesis of crank-rocker linkage using nature-inspired optimization algorithms. Mech Mach Theory J 116:105–122
Timoshenko SP, Goodier JN (1970) Theory of elasticity, 3rd edn. McGraw-Hill
Varshney AC (2004) Data book for agricultural machinery design. Central Institute of Agricultural Engineering, Bhopal
Yu K, Qu B, Yue C, Ge S, Chen X, Liang J (2019) A performance-guided JAYA algorithm for parameters identification of photovoltaic cell and module. Appl Energy 237:241–257
Zeid I (1991) CAD/CAM theory and practice. McGraw-Hill Higher Education
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Singh, P., Chaudhary, H. Optimal shape synthesis of a metallic flywheel using non-dominated sorting Jaya algorithm. Soft Comput 24, 6623–6634 (2020). https://doi.org/10.1007/s00500-019-04302-x
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DOI: https://doi.org/10.1007/s00500-019-04302-x