Skip to main content
Log in

Optimum shape design of rotating shaft by ESO method

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    MATH  Google Scholar 

  • Holland, J., 1975, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor.

    Google Scholar 

  • Lagaros, N. D., Papadrakakis, M., Kokossalakis, G., 2002, “Structural Optimization Using Evolutionary Algorithms,”Computers and Structures 80, pp. 571–589.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • Rechenberg, I., 1973, Evolution Strategy: Optimization of Technical Systems According to the Principles of Biological Evolution, Frommann-Holzboog, Stuttgart (in German).

    Google Scholar 

  • Schwefel, H. P., 1981, Numerical Optimization for Computer Models Wiley & Sons, UK.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tanskanen, P., 2002, “The Evolutionary Structural Optimization Method: Theoretical Aspects,”Computer Methods in Applied Mechanics and Engineering 191, pp. 5485–5498.

    Article  MATH  Google Scholar 

  • Vance, J. M., 1988, Rotordynamics of Turbomachinery, John Wiley & Sons, New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Xie, Y. M. and Steven, G. P., 1993, “A Simple Evolutionary Procedure for Structural Optimization,”Computational Structure 49, pp. 885–896.

    Article  Google Scholar 

  • Xie, Y. M. and Steven, G. P., 1996, “Evolutionary Structural Optimization for Dynamic Problems,”Journal of Computer and Structure 58, pp. 1067–1073.

    Article  MATH  Google Scholar 

  • Xie, Y. M. and Steven, G. P., 1997, Evolutionary Structural Optimization, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Young-Su An.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03027653

Keywords

Navigation