Multi-objective Optimization of Volute Springs using an Improved NSGA II
الموضوعات :
1 - Department of Mechanical Engineering,
University of Tehran, Iran
الکلمات المفتاحية: Military Motorcar, Volute Spring, Optimization, Nsga II Algorithm Improvement,
ملخص المقالة :
Due to the variable stiffness through their length, their resistance against buckling, damping characteristics due to the friction between their chains, and their small solid length, volute springs are widely used in applications where other mechanisms cannot be employed to provide variable spring stiffness. Meanwhile, the complexities of equations, governing their dramatic non-linear behavior caused the designers to use experimental equations, as well as some simplifications. Therefore, no research has been reported yet that aims to simultaneously optimize the evaluation criteria of these springs (i.e. their weight and energy conservation capacity) considering their strength, stiffness and natural frequency. In this article providing the governing equations for mechanical behaviors of volute springs, the problem of optimized design for this type of springs are addressed as an optimization problem with its constraints, taking into account the aforementioned goals and considerations. To find a set of Pareto front, an improved version of a multi-objective genetic algorithm is employed, performance of which has been improved, adding a migration operator to a classical NSGA II algorithm. To indicate the proposed method efficiency, a volute spring used in a suspension system of a military motorcar was modeled, and its design was optimized. The results show that the functional performance of the designed volute spring, such as minimizing the spring mass and maximizing the stored energy while maintaining design limitations such as dimensions, strength and critical frequency, has been significantly improved.
[1] Schreier, J. R., Konrad, F., Standard Guide to U.S. World War II Tanks & Artillery, 1st ed, Krause Publications,USA,1994, pp. 154–196, ISBN: 0873412974.
[2] Agachev, A. R., Daishev, R. A., Levin, S. F., et al., First-Level Dulkyn Gravitational Wave Detector, Vol. 52, No. 10, 2009, pp. 613–620, https://doi.org/10.1007/s11018-009-9316-1.
[3] Wahl, A. M., Mechanical Springs, 2nd ed, McGraw Hill, New York, 1963.
[4] Kazunori, K., Spring Standards by The Japan Spring Manufacturing Association and The Points in Designing, the Fourth. Hot Formed Volute Springs, Machine Design, Vol. 42, No. 6, 2002, pp. 97-101.
[5] Sterne, B., Characteristics of the VOLUTE SPRING, SAE Technical Paper 420100, 1942, https://doi.org/10.4271/420100.
[6] Sileikis, W., Volute Spring Design, Bulletin of Military Technical Academy, 2015, pp. 97-104.
[7] Kirpichev, V. A., Akiljuk V. S., Surhuanova, Yu. N., and Karaneva, O. V., Residual Stresses and Fatigue Resistance of Cylindrical Volute Springs, VestnikSamarskogo Gosudarstvennogo Seriya Fisiko-MatematicheskieNauki, Vol. 2, No. 17, 2008, pp. 254-257, https://doi.org/10.14498/vsgtu618.
[8] Reck, C., Mueller, M., and Seipel, V., US Patent Application for a “Vehicle”, Docket No.20,070,173,078. Published on 26 July, 2007.
[9] Peng, Q. I., Chen, Q., Hongbin, L., Jian, S. D., et al, A Novel Continuum Manipulator Design Using Serially Connected Double-Layer Planar Springs, IEEE/ASME Transactions on Mechatronics, Vol. 21, No. 3, pp. 1281 – 1292.
[10] Sharvari Dhote, Haitao, L., Zhengbao Y., Multi-Frequency Responses of Compliant Orthoplanar Spring Designs for Widening the Bandwidth of Piezoelectric Energy Harvesters, International Journal of Mechanical Sciences, Vol. 157–158, 2019, pp 684-691, ISSN 0020-7403, https://doi.org/10.1016/j.ijmecsci.2019.04.029.
[11] John, J. P., Larry L. H., and Spencer, P. M., Ortho-Planar Linear-Motion Springs, Mechanism and Machine Theory, Vol. 36, No. 11-12, 2001, pp. 1281-1299,https://doi.org/10.1016/S0094 114X(01) 00051-9.
[12] Ruizhou, W., Xianmin, Z., Optimal Design of a Planar Parallel 3-DOF Nanopositioner with Multi-Objective, Mechanism and Machine Theory, Vol. 112, 2017, pp. 61-83, ISSN 0094-114X, https://doi.org/10.1016/j.mechmachtheory.2017.02.005.
[13] Arora, J. S., Introduction to Optimum Design,5th ed, Elsevier Academic Press, San Diego, California, 2004, ISBN: 9780120641550
Holland, J. H., Adaption in Natural and Artificial Systems,1st ed, MIT Press, Cambridge, MA, 1992.
