Multi-objective Optimization of Volute Springs using an Improved NSGA II

Document Type : Review Articles


Department of Mechanical Engineering, University of Tehran, Iran


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.


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