Multi-Objective Optimization of a Two-Stage Helical Gearbox with Two Gear Sets in First Stage to Reduce Volume and Enhance Efficiency using the EAMR Technique
Received: 10 October 2024 | Revised: 3 November 2024 | Accepted: 23 November 2024 | Online: 4 December 2024
Corresponding author: Nguyen Khac Tuan
Abstract
This study presents the results of a work employing the Evaluation by an Area-based Method of Ranking (EAMR) methodology to address the Multi-Objective Optimization Problem (MOOP) of a two-stage helical gearbox comprising two gear sets in the initial stage. The objective of this study is to identify the most critical design parameters for minimizing the volume of the gearbox while optimizing its efficiency. In this study, three key design parameters were selected for analysis: the wheel face width coefficients Xba for the first and second stages, as well as the gear ratio of the first stage u1. Furthermore, the EAMR technique was employed to address the Multi-Criteria Decision-Making (MCDM) challenge, with the entropy method used to ascertain the weight criterion for resolving the MOOP. The study's findings offer valuable insights into the optimal values for three primary design parameters, which are essential for the development of a two-stage helical gearbox with two gear sets in the initial stage.
Keywords:
EAMR method, entropy method, helical gearbox, gear ratioDownloads
References
H. Wang and H.-P. Wang, "Optimal engineering design of spur gear sets," Mechanism and Machine Theory, vol. 29, no. 7, pp. 1071–1080, Oct. 1994.
S. Prayoonrat and D. Walton, "Practical approach to optimum gear train design," Computer-Aided Design, vol. 20, no. 2, pp. 83–92, Mar. 1988.
T. T. P. Thao et al., "Determining Optimum Gear Ratios of Mechanical Driven Systems Using Three Stage Bevel Helical Gearbox and Chain Drive," in Advances in Engineering Research and Application, Cham, Switzerland, 2020, pp. 249–261.
L. X. Hung et al., "Calculation of Optimum Gear Ratios of Mechanical Driven Systems Using Two-Stage Helical Gearbox with First Stage Double Gear Sets and Chain Drive," in Advances in Engineering Research and Application, Cham, Switzerland, 2020, pp. 170–178.
H. Zarefar and S. N. Muthukrishnan, "Computer-aided optimal design via modified adaptive random-search algorithm," Computer-Aided Design, vol. 25, no. 4, pp. 240–248, Apr. 1993.
M. M. A. Kader, S. P. Nigam, and G. K. Grover, "A study on mode of failures in spur gears under optimized conditions," Mechanism and Machine Theory, vol. 33, no. 6, pp. 839–850, Aug. 1998.
V. N. Pi, "A new study on the optimal prediction of partial transmission ratios of three-step helical gearboxes with second-step double gear-sets," in Proceedings of the International MultiConference of Engineers and Computer Scientists, Hong Kong, China, 2008, pp. 19–21.
N. K. Tuan et al., "Determining Optimal Gear Ratios of a Two-stage Helical Reducer for Getting Minimal Acreage of Cross Section," MATEC Web of Conferences, vol. 213, 2018, Art. no. 01008.
C. Gologlu and M. Zeyveli, "A genetic approach to automate preliminary design of gear drives," Computers & Industrial Engineering, vol. 57, no. 3, pp. 1043–1051, Oct. 2009.
V. Savsani, R. V. Rao, and D. P. Vakharia, "Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms," Mechanism and Machine Theory, vol. 45, no. 3, pp. 531–541, Mar. 2010.
N. K. Tuan et al., "A Study on Determining Optimum Gear Ratios of Mechanical Driven Systems Using Two-Step Helical Gearbox with First Step Double Gear Sets and Chain Drive," in Advances in Engineering Research and Application, Cham, Switzerland, 2020, pp. 85–93.
N. T. H. Cam, V. N. Pi, N. K. Tuan, L. X. Hung, and T. T. P. Thao, "A Study on Determination of Optimum Partial Transmission Ratios of Mechanical Driven Systems Using a Chain Drive and a Three-Step Helical Reducer," in Advances in Engineering Research and Application, Cham, Switzerland, 2019, pp. 91–99.
F. Mendi, T. Başkal, K. Boran, and F. E. Boran, "Optimization of module, shaft diameter and rolling bearing for spur gear through genetic algorithm," Expert Systems with Applications, vol. 37, no. 12, pp. 8058–8064, Dec. 2010.
V.-T. Dinh et al., "Multi-Objective Optimization of a Two-Stage Helical Gearbox Using MARCOS Method," Designs, vol. 8, no. 3, Jun. 2024, Art. no. 53.
N. Benmoussa, A. Elyamami, K. Mansouri, M. Qbadou, and E. Illoussamen, "A Multi-Criteria Decision Making Approach for Enhancing University Accreditation Process," Engineering, Technology & Applied Science Research, vol. 9, no. 1, pp. 3726–3733, Feb. 2019.
H.-D. Tran, V.-T. Dinh, D.-B. Vu, D. Vu, A.-T. Luu, and N. P. Vu, "Application of the TOPSIS Method for Multi-Objective Optimization of a Two-Stage Helical Gearbox," Engineering, Technology & Applied Science Research, vol. 14, no. 4, pp. 15454–15463, Aug. 2024.
R. J. K. Jalhoom and A. M. R. Mahjoob, "An MCDM Approach for Evaluating Construction-Related Risks using a Combined Fuzzy Grey DEMATEL Method," Engineering, Technology & Applied Science Research, vol. 14, no. 2, pp. 13572–13577, Apr. 2024.
T. Chat and L. Van Uyen, Design and calculation of Mechanical Transmissions Systems, vol. 1. Hanoi, Vietnam: Educational Republishing House, 2007.
D. Jelaska, Gears and gear drives. John Wiley & Sons, 2012.
V.-T. Dinh, H.-D. Tran, D.-B. Vu, D. Vu, N.-P. Vu, and A.-T. Luu, "Application of a Multi-Criterion Decision-Making Method for Solving the Multi-Objective Optimization of a Two-Stage Helical Gearbox," Machines, vol. 12, no. 6, Jun. 2024, Art. no. 365.
X.-H. Le and N.-P. Vu, "Multi-Objective Optimization of a Two-Stage Helical Gearbox Using Taguchi Method and Grey Relational Analysis," Applied Sciences, vol. 13, no. 13, Jan. 2023, Art. no. 7601.
K. M. Ghorabaee, E. K. Zavadskas, M. Amiri, and J. Antucheviciene, "Evaluation by an Area-based Method of Ranking Interval Type-2 Fuzzy Sets (EAMRIT-2F) for Multi-criteria Group Decision-making," Transformations in Business & Economics, vol. 15, no. 3, pp. 76–95, Oct. 2024.
T. T. Hieu, N. X. Thao, P. T. Tien, and L. T. M. Thuy, "Application of MOORA and COPRAS Models to Select Materials for Mushroom Cultivation," Journal of Vietnam Agricultural Science and Technology, vol. 17, no. 4, pp. 322–331, 2019.
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Copyright (c) 2024 Tran Quoc Hung, Vu Duc Binh, Dinh Van Thanh, Lưu Anh Tung, Nguyen Khac Tuan
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