Abstract
Evolutionary structural optimization (ESO) method is based on a simple idea that the optimal structure can be produced by gradually removing the ineffectively used material from the design domain. ESO seems to have some attractive features in engineering aspects: simple and fast. In this paper, ESO is applied to optimize shaft shape for the rotating machinery by introducing variable size of finite elements in optimization procedure. The goal of this optimization is to reduce total shaft weight and resonance magnification factor (Q factor), and to yield the critical speeds as far from the operating speed as possible. The constraints include restrictions on critical speed, unbalance response and bending stresses. Sensitivity analysis of the system parameters is also investigated. The results show that new ESO method can be efficiently used to optimize the shape of rotor shaft system with frequency and dynamic constraints.
Similar content being viewed by others
References
Choi, B. G. and Yang, B. S., 2000, “Optimum Shape Design of Rotor Shafts Using Genetic Algorithm,”Journal of Vibration and Control 6 (2), pp. 207–222.
Choi, B. K. and Yang, B. S., 2001, “Multiobjective Optimum Design of Rotor-Bearing Systems with Dynamic Constraints Using Immune-Genetic Algorithm,”ASME Trans. Journal of Engineering for Gas Turbines and Power 123, pp. 78–81.
Choi, B. K. and Yang, B. S., 2001, “Optimal Design of Rotor-Bearing Systems Using Immune-Genetic Algorithm. ASME Trans,”Journal of Vibration and Acoustics 123, pp. 398–401.
Chu, D. N., Xie, Y. M., Hira, A. and Steven, G. P., 1996, “Evolutionary Structural Optimization for Problems with Stiffness Constraints,”Finite Elements Analysis Design 21, pp. 239–251.
Diewald, W. and Nordmann, R., 1990, “Parameter Optimization for the Dynamics of Rotating Machinery,”Proceedings of 3rd International Conference on Rotor Dynamics, Lyon, France, pp. 51–55.
Doizelet, D. and Bondoux, D., 1990, “Application of Optimization Techniques for Hypercritical Rotors,”Proceedings of the 3rd International Conference on Rotor Dynamics, Lyon, France, pp. 57–62.
Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Co., Massachusetts.
Holland, J., 1975, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor.
Lagaros, N. D., Papadrakakis, M., Kokossalakis, G., 2002, “Structural Optimization Using Evolutionary Algorithms,”Computers and Structures 80, pp. 571–589.
Nelson, H. D. and McVaugh, J. M., 1976, “The Dynamics of Rotor-Bearing Systems Using Finite Elements. ASME Trans,”Journal of Industry for Engineering 98 (2), pp. 71–75.
Querin, O. M., Steven, G. P. and Xie, Y. M., 1998, “Evolutionary Structural Optimization (ESO) Using a Bidirectional Algorithm,”Engineering Computations 15 (8), pp. 1031–1048.
Rajan, M., Rajan, S. D., Nelson, H. D. and Chen, W. J., 1987, “Optimal Placement of Critical Speeds in Rotor Bearing Systems,”ASME Trans. J. Vibration, Acoustics, Stress and Reliability in Design 109, pp. 152–157.
Rechenberg, I., 1973, Evolution Strategy: Optimization of Technical Systems According to the Principles of Biological Evolution, Frommann-Holzboog, Stuttgart (in German).
Schwefel, H. P., 1981, Numerical Optimization for Computer Models Wiley & Sons, UK.
Shiau, T. N. and Chang, J. R., 1993, “Multi-objective Optimization of Rotor-Bearing System with Critical Speed Constraints,”ASME Trans. J. Eng. Gas Turbines Power 115, pp. 246–255.
Shiau, T. N. and Hwang, J. L., 1990, “Optimum Weight Design of a Rotor Bearing System with Dynamic Behavior Constraints,”ASME Trans. J. Eng. Gas Turbines Power 112, pp. 454–462.
Tanskanen, P., 2002, “The Evolutionary Structural Optimization Method: Theoretical Aspects,”Computer Methods in Applied Mechanics and Engineering 191, pp. 5485–5498.
Vance, J. M., 1988, Rotordynamics of Turbomachinery, John Wiley & Sons, New York.
Wang, J. H. and Shih, F. M., 1990, “Improve the Stability of Rotor Subjected to Fluid Leakage by Optimum Diameters Design,”ASME Trans. J. Vibration, Acoustics, Stress and Reliability in Design 112, pp. 59–64.
Xie, Y. M. and Steven, G. P., 1993, “A Simple Evolutionary Procedure for Structural Optimization,”Computational Structure 49, pp. 885–896.
Xie, Y. M. and Steven, G. P., 1996, “Evolutionary Structural Optimization for Dynamic Problems,”Journal of Computer and Structure 58, pp. 1067–1073.
Xie, Y. M. and Steven, G. P., 1997, Evolutionary Structural Optimization, Springer-Verlag, Berlin.
Zhao, C., Steven, G. P. and Xie, Y. M., 1996, “Evolutionary Natural Frequency Optimization of Thin Plate Bending Vibration Problems,”Journal of Structural Optimization 11, pp. 244–251.
Zhao, C., Steven, G. P. and Xie, Y. M., 1996, “General Evolutionary Path for Fundamental Natural Frequencies of Membrane Vibration Problems: Towards Optimum from Below,”Structural Engineering Mechanics 4, pp. 513–527.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, YH., Tan, A., Yang, BS. et al. Optimum shape design of rotating shaft by ESO method. J Mech Sci Technol 21, 1039–1047 (2007). https://doi.org/10.1007/BF03027653
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF03027653