Share This Article:

Optimization of Bearing Locations for Maximizing First Mode Natural Frequency of Motorized Spindle-Bearing Systems Using a Genetic Algorithm

Abstract Full-Text HTML Download Download as PDF (Size:2185KB) PP. 2137-2152
DOI: 10.4236/am.2014.514208    2,572 Downloads   3,344 Views   Citations
Author(s)    Leave a comment


This paper has developed a genetic algorithm (GA) optimization approach to search for the optimal locations to install bearings on the motorized spindle shaft to maximize its first-mode natural frequency (FMNF). First, a finite element method (FEM) dynamic model of the spindle-bearing system is formulated, and by solving the eigenvalue problem derived from the equations of motion, the natural frequencies of the spindle system can be acquired. Next, the mathematical model is built, which includes the objective function to maximize FMNF and the constraints to limit the locations of the bearings with respect to the geometrical boundaries of the segments they located and the spacings between adjacent bearings. Then, the Sequential Decoding Process (SDP) GA is designed to accommodate the dependent characteristics of the constraints in the mathematical model. To verify the proposed SDP-GA optimization approach, a four-bearing installation optimazation problem of an illustrative spindle system is investigated. The results show that the SDP-GA provides well convergence for the optimization searching process. By applying design of experiments and analysis of variance, the optimal values of GA parameters are determined under a certain number restriction in executing the eigenvalue calculation subroutine. A linear regression equation is derived also to estimate necessary calculation efforts with respect to the specific quality of the optimization solution. From the results of this illustrative example, we can conclude that the proposed SDP-GA optimization approach is effective and efficient.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Lin, C. (2014) Optimization of Bearing Locations for Maximizing First Mode Natural Frequency of Motorized Spindle-Bearing Systems Using a Genetic Algorithm. Applied Mathematics, 5, 2137-2152. doi: 10.4236/am.2014.514208.


[1] Bossmann, B. and Tu, J. (2002) Conceptual Design of Machine Tool Interfaces for High-Speed Machining. Journal of Manufacturing Processes, 4, 16-27.
[2] Lin, C.-W. and Tu, J. (2007) Model-Based Design of Motorized Spindle Systems to Improve Dynamic Performance at High Speeds. Journal of Manufacturing Processes, 9, 94-108.
[3] Al-Shareef, K. and Brandon, J. (1990) On the Effects of Variations in the Design Parameters on the Dynamic Performance of Machine Tool Spindle-Bearing Systems. International Journal of Machine Tools and Manufacture, 30, 431-445.
[4] Kang, Y., Chang, Y.-P., Tsai, J.-W., Chen, S.-C. and Yang, L.-K. (2001) Integrated CAE Strategies for the Design of Machine Tool Spindle-Bearing Systems. Finite Elements in Analysis and Design, 37, 485-511.
[5] Li, H. and Shin, Y. (2004) Analysis of Bearing Configuration Effects on High Speed Spindles Using an Integrated Dynamic Thermomechanical Spindle Model. International Journal of Machine Tools and Manufacture, 44, 347-364.
[6] Maeda, O., Cao, Y. and Altintas, Y. (2005) Expert Spindle Design System. International Journal of Machine Tools and Manufacture, 45, 537-548.
[7] Altintas, Y. and Cao, Y. (2005) Virtual Design and Optimization of Machine Tool Spindles. CIRP Annual, 54, 379-382.
[8] Srinivasan, S., Maslen, E. and Barrett, L. (1997) Optimization of Bearing Locations for Rotor Systems with Magnetic Bearings. Journal of Engineering for Gas Turbines and Power, 119, 464-468.
[9] Nelson, H. and McVaugh, J. (1976) The Dynamics of Rotor-Bearing System Using Finite Elements. Journal of Engineering for Industry, Transactions of the ASME, 93, 593-600.
[10] Zorzi, E. and Nelson, H. (1977) Finite Element Simulation of Rotor-Bearing Systems with Internal Damping. Journal of Engineering for Power, Transactions of the ASME, 7, 71-76.
[11] Nelson, H. (1980) A Finite Rotating Shaft Element Using Timoshenko Beam Theory. Journal of Mechanical Design, Transactions of the ASME, 102, 793-803.
[12] Lantto, E. (1997) Finite Element Model for Elastic Rotating Shaft. ACTA Polytechnica Scandinavica, Electrical Engineering Series, 88, 1-73.
[13] Inman, D. (2008) Engineering Vibrations. Pearson Education, Inc., Upper Saddle River.
[14] Holland, J.H. (1975) Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor.
[15] Rao, S.S. (2009) Engineering Optimization: Theory and Practice. John Wiley and Sons, Hoboken.
[16] Huang, M., Chen, K. and Fung, R. (2010) Comparison between Mathematical Modeling and Experimental Identification of a Spatial Slider-Crank Mechanism. Applied Mathematical Modelling, 34, 2059-2073.
[17] Fiandaca, G., Fraga, E. and Brandani, S. (2009) A Multi-Objective Genetic Algorithm for the Design of Pressure Swing Adsorption. Engineering Optimization, 41, 833-854.
[18] Gomes, H. and Silva, N. (2008) Some Comparisons for Damage Detection on Structures Using Genetic Algorithms and Modal Sensitivity Method. Applied Mathematical Modelling, 32, 2216-2232.
[19] Chakraborty, I., Kumar, V., Nair, S. and Tiwari, R. (2003) Rolling Element Bearing Design through Genetic Algorithms. Engineering Optimization, 35, 649-659.
[20] Lin, C.-W. (2001) High Speed Effects and Dynamic Analysis of Motorized Spindles for High Speed End Milling. Ph.D. Thesis, Purdue University, West Lafayette.
[21] Wardle, F., Lacey, S. and Poon, S. (1983) Dynamic and Static Characteristics of a Wide Speed Range Machine Tool Spindle. Precision Engineering, 5, 175-183.
[22] Zill, D., Wright, W. and Cullen, M. (2011) Advanced Engineering Mathematics. Jones & Bartlett Learning, Burlington.
[23] Pham, D. and Karaboga, D. (2000) Intelligent Optimisation Techniques, Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer, New York.
[24] Chong, E. and Zak, S. (2008) An Introduction to Optimization. Wiley-Interscience, Hoboken.
[25] Zalzala, A. and Fleming, P. (1997) Genetic Algorithms in Engineering Systems. IET, London.
[26] Belegundu, A. and Chandrupatla, T. (1999) Optimization Concepts and Applications in Engineering. Prentice Hall, Upper Saddle River.
[27] Montgomery, D. and Runger, G. (2011) Applied Statistics and Probability for Engineers. Wiley, Hoboken.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.