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.
Highlights
Spindle-bearing systems have been widely applied in mechanisms, such as machine tools, that need relative rotary motion to accomplish desired machining functions
The main purpose of this paper is to demonstrate the application of genetic algorithm (GA) on determining the optimal locations of bearings of motorized spindle shafts, which are the decisions expected to be made by design engineers when they start to plan assembling the bearings and spindle shaft after the spindle and bearing specifications have been specified during the concept design stage
This paper has developed a GA-based optimization approach to search for the optimal locations of bearings installed on a spindle shaft to maximize the first-mode natural frequency (FMNF)
Summary
Spindle-bearing systems have been widely applied in mechanisms, such as machine tools, that need relative rotary motion to accomplish desired machining functions. The eight design variables they considered included material of spindle shaft, diameters and total length of the spindle shaft, bearing initial preload, spacings between the bearings of the front or rear bearing set, spacing between the middle line of the front and rear bearing sets, and spacing of the middle line of the front and rear bearing sets to the end of the cutting tool Their results showed that the first two most important design factors among the eight were related to the locations of the bearings, which implied that the positions bearings installed on the spindle shaft must be determined carefully. The main purpose of this paper is to demonstrate the application of GA on determining the optimal locations of bearings of motorized spindle shafts, which are the decisions expected to be made by design engineers when they start to plan assembling the bearings and spindle shaft after the spindle and bearing specifications have been specified during the concept design stage. The primary conclusions and discussions of this paper are described
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