Cost optimization of two-stage helical gearboxes with second stage double gear-sets
In practice, the cost of a gearbox plays a very important role in the trade. Therefore, reducing the cost of gearboxes is an important task not only when manufacturing the gearboxes but also when designing them. In order to reduce the cost of a gearbox, there are many solutions in which determining the optimal partial gear ratios of a gearbox is an effective measure. This is because it not only the size, the mass but also the cost of a gearbox depends greatly on the partial gear ratios. This work presents a method for calculating the cost function of two-stage helical gearboxes with second-stage double gear-sets based on the mass of the components that construct the gearbox. The cost objective function is minimized to achieve the optimal transmission ratios. Furthermore, screening experiments are carried out with nine important input parameters that have significant effects on the optimum transmission ratio of the second stage. These parameters are the total gearbox ratio, the coefficient of wheel face width of the first stage, coefficient of wheel face width of the second stage, the allowable contact stress of the first stage, the allowable contact stress of the second stage, the output torque, the cost of gearbox housing, the cost of gears, and the shaft cost. The experimental results of were analysed by using the Analysis of Variance (ANOVA) method with the help of Minitab 19 software. The results demonstrate that the effective weight of the input parameters and their interactions on the output response was investigated. Also, a regression model for computing the optimal transmission ratio of the second stage was proposed. This brings significance not only in the design process but also in manufacturing since the gearbox cost can decrease
Hong, T. T., Cuong, N. V., Ky, L. H., Tuan, N. K., Pi, V. N. (2019). Calculating optimum gear ratios of two step bevel helical reducer. International Journal of Applied Engineering Research (IJAER), 14 (16), 3494–3499. Available at: https://www.ripublication.com/ijaer19/ijaerv14n16_05.pdf
Kudryavtsev, V. N., Derzhavets, Yu. A., Gluharev, E. G. (1971). Design and Calculus of Gearboxes. Leningrad: Mashinostroenie Publishing, 328.
Trinh Chat, L. V. U. (1996). Calculation of mechanical driven systems. Ha Noi: Education Publisher.
Milou, G., Dobre, G., Visa, F., Vitila, H. (1996). Optimal design of two step gear units, regarding the main parameters. VDI Berichte, 1230, 227.
Pi, V. N., Tuan, N. K., Hung, L. X., Tung, L. A. (2019). A New Study on Determination of Optimum Gear Ratios of a Two-Stage Helical Gearbox. Lecture Notes in Mechanical Engineering, 107–115. doi: https://doi.org/10.1007/978-981-13-8297-0_14
Pi, V. N., Tuan, N. K. (2016). Optimum Determination of Partial Transmission Ratios of Three-Step Helical Gearboxes for Getting Minimum Cross Section Dimension. Journal of Environmental Science and Engineering A, 5 (11). doi: https://doi.org/10.17265/2162-5298/2016.11.004
Buiga, O., Tudose, L. (2014). Optimal mass minimization design of a two-stage coaxial helical speed reducer with Genetic Algorithms. Advances in Engineering Software, 68, 25–32. doi: https://doi.org/10.1016/j.advengsoft.2013.11.002
Tuan, N. K., Pi, V. N., Thi Hong Cam, N., Thao, T. T. P., Thanh, H. K., Hung, L. X., Tham, H. T. (2018). Determining Optimal Gear Ratios of a Two-stage Helical Reducer for Getting Minimal Acreage of Cross Section. MATEC Web of Conferences, 213, 01008. doi: https://doi.org/10.1051/matecconf/201821301008
Pi, V. N. (2000). A new and effective method for optimal calculation of total transmission ratio of two step bevel-helical gearboxes. Proceedings of the International Colloquium on Mechannics of Solids, Fluids, Structures & Interaction, 716–719.
Pi, V. N., Thi Phuong Thao, T., Thi Hong, T., Khac Tuan, N., Hung, L. X., Anh Tung, L. (2019). Determination of optimum gear ratios of a three stage bevel helical gearbox. IOP Conference Series: Materials Science and Engineering, 542, 012007. doi: https://doi.org/10.1088/1757-899x/542/1/012007
Thao, T. T. P., Hong, T. T., Van Cuong, N., Ky, L. H., Tu, N. T., Hung, L. X., Vu, N. P. (2019). Determining Optimum Gear Ratios of Mechanical Driven Systems Using Three Stage Bevel Helical Gearbox and Chain Drive. Lecture Notes in Networks and Systems, 249–261. doi: https://doi.org/10.1007/978-3-030-37497-6_29
Tung, L. A., Hong, T. T., Cuong, N. V., Ky, L. H., Tu, N. T., Hung, L. X., Vu, N. P. (2019). A Study on Determination of Optimum Gear Ratios of a Two-Stage Worm Gearbox. Lecture Notes in Networks and Systems, 76–84. doi: https://doi.org/10.1007/978-3-030-37497-6_8
Cuong, N. M., Tham, H. T., Hong, T. T., Van Cuong, N., Ky, L. H., Tu, N. T. et. al. (2019). Calculation of Optimum Gear Ratios of Two-Step Worm Gearbox. Lecture Notes in Networks and Systems, 179–188. doi: https://doi.org/10.1007/978-3-030-37497-6_21
Pi, V. N., Tuan, N. K., Hung, L. X., Dung, N. T. Q., Hien, B. T. (2019). Determining Optimum Gear Ratios of a Worm—Helical Gearbox for Minimum Acreage of the Cross Section. Lecture Notes in Mechanical Engineering, 89–96. doi: https://doi.org/10.1007/978-981-13-8297-0_12
Pi, V. N., Thi Hong, T., Hung, L. X., Anh Tung, L., Khac Tuan, N. (2019). A study on determination of optimum gear ratios of a worm -helical gearbox. IOP Conference Series: Materials Science and Engineering, 635, 012010. doi: https://doi.org/10.1088/1757-899x/635/1/012010
Pi, V. N. (2008). Optimal determination of partial transmission ratios for four-step helical gearboxes with first and third step double gear-sets for minimal mass of gears. Applied Computing Conference, 53–57. Available at: http://www.wseas.us/e-library/conferences/2008/istanbul/acc/acc_07.pdf
Pi, V. N. (2008). Optimal calculation of partial transmission ratios for four-step helical gearboxes with first and third-step double gear-sets for minimal gearbox length. MATH'08: Proceedings of the American Conference on Applied Mathematics, 29–32.
Pi, V. N. (2007). A new study on the optimal prediction of partial transmission ratios of three-step helical gearboxes with second-step double gear-sets. Wseas Transactions on Applied and Theoretical Mechanics, 2 (11), 229–238. Avaialble at: https://www.researchgate.net/profile/Vu-N/publication/237522436_A_new_study_on_the_optimal_prediction_of_partial_transmission_ratios_of_three-step_helical_gearboxes_with_second-step_double_gear-sets/links/54356dfa0cf2bf1f1f2b0645/A-new-study-on-the-optimal-prediction-of-partial-transmission-ratios-of-three-step-helical-gearboxes-with-second-step-double-gear-sets.pdf
Golabi, S., Fesharaki, J. J., Yazdipoor, M. (2014). Gear train optimization based on minimum volume/weight design. Mechanism and Machine Theory, 73, 197–217. doi: https://doi.org/10.1016/j.mechmachtheory.2013.11.002
Cam, N. T. H., Hong, T. T., Cuong, N. V., Ky, L. H., Tung, L. A., Tu, N. T. et. al. (2019). Calculating Optimum Gear Ratios of Mechanical Drive Systems Using Two-Stage Helical Gearbox with Second-Stage Double Gear Sets and Chain Drive for Minimum Gearbox Length. Lecture Notes in Networks and Systems, 155–163. doi: https://doi.org/10.1007/978-3-030-37497-6_18
Vu, N.-P., Nguyen, D.-N., Luu, A.-T., Tran, N.-G., Tran, T.-H., Nguyen, V.-C. et. al. (2020). The Influence of Main Design Parameters on the Overall Cost of a Gearbox. Applied Sciences, 10 (7), 2365. doi: https://doi.org/10.3390/app10072365
Density, Specific Weight and Specific Gravity. Available at: https://www.engineeringtoolbox.com/density-specific-weight-gravity-d_290.html
Römhild, I., Linke, H. (1992). Gezielte Auslegung Von Zahnradgetrieben mit minimaler Masse auf der Basis neuer Berechnungsverfahren. Konstruktion, 44 (7-8), 229–236.
Copyright (c) 2021 Le Hoang Anh, Nguyen Hong Linh, Nguyen Huu Quang, Pham Duc Lam, Nguyen Anh Tuan, Nguyen Khac Tuan, Nguyen Thi Thanh Nga, Vu Ngoc Pi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.