3D Optimization of Gear Train Layout Using Particle Swarm Optimization Algorithm

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131, Iran

2 Modern Manufacturing Technologies Research Center, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131, Iran

Abstract

Optimization of the volume/weight in the gear train is of great importance for industries and researchers. In this paper, using the particle swarm optimization algorithm, a general gear train is optimized. The main idea is to optimize the volume/weight of the gearbox in 3 directions. To this end, the optimization process based on the PSO algorithm occurs along the height, length, and width of the gearbox to achieve the smallest possible gearbox. The constraints are divided into three types named geometrical, design and control constraints. The optimization process is presented for two and three-stage gear trains and by choosing different values for the gear ratio, input power and hardness of gears. The practical graphs for the optimum value of the weight/volume and all necessary design parameters of gearbox such as the number of stages, position, modulus of gears, face width of gears, and diameter of shafts are also presented. The results are validated by comparing with the results reported in the previous publications.

Keywords

Main Subjects

[1] Gologlu, M. Z., A genetic approach to automate preliminary design of gear drives, Computers & Industrial Engineering, 57, 2009, 1043-1051.
[2] Patwal, R. S., Narang, N., Garg, H., A novel TVAC-PSO based mutation strategies algorithm for generation scheduling of pumped storage hydrothermal system incorporating solar units, Energy, 142, 2018, 822-837.
[3] Panda, S., Biswal, B. B., Jena, S. D., Mishra, D., An approach to weight optimization of a spur gear, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 231(2), 2016, 189-202.
[4] Cheng, R., Jin, Y., A social learning particle swarm optimization algorithm for scalable optimization, Information Sciences, 291, 2015, 43-60.
[5] Chong, J. S. L., A design method of gear trains using a genetic algorithm, International Journal of Precision Engineering and Manufacturing, 1-1, 2000, 62-70.
[6] Zolfaghari, A., Goharimanesh, M., Akbari, A. A, Optimum design of straight bevel gears pair using evolutionary algorithms, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(6), 2017, 2121-2129.
[7] Miler, D., Lončar, A., Žeželj, D., Domitran, Z, Influence of profile shift on the spur gear pair optimization, Mechanism and Machine Theory, 117, 2017, 189-197.
[8] Garg, H., Sharma, S. P., Multi-objective reliability-redundancy allocation problem using particle swarm optimization, Computers & Industrial Engineering, 64(1), 2013, 247-255.
[9] P. Alexandru, D. M., C. Alexandru, Design and simulation of a steering gearbox with variable transmission ratio, Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci, 226, 2013 2538–2548.
[10] Garg, H., A hybrid PSO-GA algorithm for constrained optimization problems, Applied Mathematics and Computation, 274, 2016, 292-305.
[11] Garg, H., Solving structural engineering design optimization problems using an artificial bee colony algorithm, Journal of Industrial and Management, 10(3), 2014, 777-794.
[12] Harish, G., A Hybrid GA-GSA Algorithm for Optimizing the Performance of an Industrial System by Utilizing Uncertain Data. In V. Pandian (Ed.), Handbook of Research on Artificial Intelligence Techniques and Algorithms, 620-654, Hershey, PA, USA: IGI Global, 2015.
[13] Tudose, L., Buiga, O., Ştefanache, C., Sóbester, A., Automated optimal design of a two-stage helical gear reducer, Structural and Multidisciplinary Optimization, 42(3), 2010, 429-435.
[14] Rui, L., Tian, C., Jianwei, W., Xiaopeng, W, Multi-objective optimization design of gear reducer based on adaptive genetic algorithm, 12th International Conference on Computer Supported Cooperative Work in Design, 16-18, 229-233, 2008.
[15] Kang, J. S., Choi, Y.-S., Optimization of helix angle for helical gear system, Journal of Mechanical Science and Technology, 22(12), 2008, 2393-2402.
[16] Mendi, F., Başkal, T., Boran, K., Boran, F. E., Optimization of module, shaft diameter and rolling bearing for spur gear through genetic algorithm, Expert Systems with Applications, 37(12), 2010, 8058-8064.
[17] Abderazek, H., Ferhat, D., Ivana, A., Adaptive mixed differential evolution algorithm for bi-objective tooth profile spur gear optimization, The International Journal of Advanced Manufacturing Technology, 90(5), 2010, 2063-2073.
[18] Jafari Fesharaki, J., Golabi, S., Optimum pattern of piezoelectric actuator placement for stress concentration reduction in a plate with a hole using particle swarm optimization algorithm, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229(4), 2015 614–628.
[19] T. Yokota, T. T., M. Gen, A solution method for optimal weight design problem of the gear using genetic algorithms. Comput. Ind. Eng., 35, 1998, 523-526.
[20] V. Savsani, R. V. R., D.P. Vakharia, Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms, Mechanism and Machine Theory, 45, 2010, 531-541.
[21] Swantner, A., Campbell, M. I., Topological and parametric optimization of gear trains. Engineering Optimization, 44(11), 2012, 1351-1368.
[22] N. Marjanovic, B. I., V. Marjanovic, Z. Milojevic, M. Blagojevic, M. Bojic, A practical approach to the optimization of gear trains with spur gears, Mechanism and Machine Theory, 53, 2012, 1-16.
[23] T.H. Chong, I. B., G.-J. Park, A new and generalized methodology to design multi-stage gear drives by integrating the dimensional and the configuration design process, Mechanism and Machine Theory, 37, 2002, 295-310.
[24] L.P. Pomrehn, P. Y. P., Discrete Optimal Design Formulations With Application to Gear Train Design, ASME Journal of Mechanical Design, 117, 1995, 419-424.
[25] Thompson, D. F., Gupta, S., Shukla, A., Tradeoff analysis in minimum volume design of multi-stage spur gear reduction units, Mechanism and Machine Theory, 35(5), 2000, 609-627.
[26] H. Zarefar, S. N. M., Computer-aided optimal design via modified adaptive random-search algorithm, Comput. Aided Des, 25, 1993, 240–248.
[27] S. Salomon, G. A., R.C. Purshouse, P.J. Fleming, Gearbox design for uncertain load requirements using active robust optimization, Engineering Optimization, 48, 2016, 652-671.
[28] M. Ciavarella, G. D., Numerical methods for the optimisation of specific sliding, stress concentration and fatigue life of gears, International Journal of Fatigue, 21(5), 1999, 465-474.
[29] H. Wang, H.-P. W., Optimal engineering design of spur gear sets, Mech. Mach. Theory, 29, 1994, 1071-1080.
[30] Wang, Optimized tooth profile based on identified gear dynamic model, Mechanism and Machine Theory, 42, 1994, 1058-1068.
[31] S. Golabi, J. J. Fesharaki., M. Yazdipoor, Gear train optimization based on minimum volume/weight design, Mechanism and Machine Theory, 73, 2014, 197-217.
[32] Fundamental rating factors and calculation methods for involute spur and helical gear teeth. American Gear Manufacturers Association, 1995, 2101-C95.
[33] R.G. Budynus, J. K. N., Shigley's Mechanical Engineering Design, McGraw-Hill, 2011.
[34] Kennedy, J. E., R.C. Particle Swarm Optimization. In  IEEE International Conference on Neural Networks, 1942–1948, Nagoya, Japan, 1995.
[35] Garg, H., Performance analysis of an industrial system using soft computing based hybridized technique, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(4), 2017, 1441-1451.
[36] Garg, H., Performance analysis of complex repairable industrial systems using PSO and fuzzy confidence interval based methodology. ISA Transactions, 52(2), 2013, 171-183.