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.
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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