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

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Author(s)  

Chi-Wei Lin

Affiliation(s)

Department of Industrial Engineering and Systems Management, Feng Chia University, Taichung, Taiwan.

ABSTRACT

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.

KEYWORDS

Optimal Design, Motorized Spindle System Design, Finite Element Method, Genetic Algorithm, First Mode Natural Frequency

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. 

 

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