Preform Optimization of Functional Bevel Gear for Warm Forging Processes
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ght © 2020 KSAE/ 11703 pISSN 12299138/ eISSN 19763832
PREFORM OPTIMIZATION OF FUNCTIONAL BEVEL GEAR FOR WARM FORGING PROCESSES Risky Ayu Febriani, Hong Seok Park*, Saurabh Kumar and Chang Myung Lee School of Mechanical and Automotive Engineering, University of Ulsan, Ulsan 44610, Korea (Received 13 June 2019; Revised 19 November 2019; Accepted 8 December 2019) ABSTRACTOptimizing the design of the preform shapes used in warm forging processes is important for improving quality and reducing cost. The main objective of this study was to optimize the design of a preform shape for a bevel gear to obtain a good product and to improve the efficiency of the warm forging process. Quality parameters included in the fitness function were form-filling, preform volume, and complexity. First, basic principles pertaining to the cross sections, thickness, and concave radius of a bevel gear preform were applied in conjunction with certain theoretical expressions and empirical methods to produce an initial preform shape and initial geometry. Subsequently, mathematical evaluation models of the fitness function were generated to optimize the preform shape. Finally, a genetic algorithm was applied to solve the multi-objective optimization problem, and the best solution was determined considering the accuracy of the results, within the close proximity set generated by the multi-objective genetic algorithm optimization. The optimal preform shape was decreased in weight by approximately 8 % and its flash dimensions were decreased by about 5 % compared to the initial preform shape. This research is expected to improve the efficiency of fabricating bevel gears by means of warm forging processes. KEY WORDS : Preform shape, Bevel gear, Warm forging process, Genetic algorithm
NOMENCLATURE AP AF tP tF rfP rbP B D H Ac Ffilling,n Ai,n AF,n a Ffilling,i Vi Ffilling,i Vi VF Ffilling,i Vi VF rn
Vmin : minimum possible preform volume Vmax : maximum possible preform volume Fvolume,i : volume fitness : radius of individual at cutting plane n ri,n : complexity of individual Ci Cmin : minimum possible complexity Cmax : maximum possible complexity Fcomplexity,i : complexity fitness : flash width fw : flash thickness ft : radial distance of the center of outside diameter Rh : total fitness value Fi w1 : weight factor 1 w2 : weight factor 2 w3 : weight factor 3 wp : workpiece weight I : population size Pc : crossover rate m : mutation rate Tc : termination criterion
: cross section of preform : cross section of final shape : thickness of preform : thickness of final shape : fillet radius of preform : blend-in radius of preform : chamfer length : large diameter : height : depth of adjacent cavity : form-filling of individual at cutting plane n : cross-sectional area of individual at cutting plane n : cross-sectional area of final shape at cutting plane n : amount of flash : form-filling fitness : total volume of the individual : form-filling fitness : total volume of the individual : volume of the final shape : form-filling fitness : total volume of t
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