Cost optimization of two-stage helical gearboxes with second stage double gear-sets

Keywords: cost optimization, optimization design, gear ratios, optimal gear ratios, helical gearbox

Abstract

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

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Author Biographies

Le Hoang Anh, Vinh Long University of Technology Education

Faculty of Mechanical Engineering

Nguyen Hong Linh, Electric Power University

Faculty of Mechanical and Power Engineering

Nguyen Huu Quang, University of Economics - Technology for Industries

Faculty of Mechanical Engineering

Pham Duc Lam, Nguyen Tat Thanh University

Faculty of Mechanical, Electrical, Electronic and Automotive Engineering

Nguyen Anh Tuan, University of Economics - Technology for Industries

Faculty of Mechanical Engineering

Nguyen Khac Tuan, Thai Nguyen University of Technology

Faculty of Automotive and Power Machinery Engineering

Nguyen Thi Thanh Nga, Thai Nguyen University of Technology

Faculty of Mechanical Engineering

Vu Ngoc Pi, Thai Nguyen University of Technology

Faculty of Mechanical Engineering

References

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.


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Published
2021-11-18
How to Cite
Anh, L. H., Linh, N. H., Quang, N. H., Lam, P. D., Tuan, N. A., Tuan, N. K., Nga, N. T. T., & Pi, V. N. (2021). Cost optimization of two-stage helical gearboxes with second stage double gear-sets. EUREKA: Physics and Engineering, (6), 89-101. https://doi.org/10.21303/2461-4262.2021.001855
Section
Engineering