Finite-element Analysis and Optimization for the Column of Numerically Controlled Triaxial Deep Hole Drilling Machine

Solidworks is selected for modeling the 3D-solid structure of the deep-hole drilling machine. Based on parametric modeling and structural optimization theory, the parametric model of column is established. The equivalent stress and maximum principal stress on the column are solved by FEA. The two parameters (column thickness and inner rib thickness) are included. According to the design variables, the main target method is applied for the purpose of optimizing the weight of the column (Chen, Ding, & Guo, 2010). Topology optimization is used to determine the location of the sand holes by ansys software with density method.


Introduction
CNC three-axis drilling machine is a multi-axis deep hole drilling equipment which processes steam generator tube sheet.In the nuclear steam generator tube sheet processing, 1.5 tons of high pressure hydraulic tights jig.The column bears the reaction force of 1.5 tons of high-pressure oil and about 0.5 tons of the axial drilling force.The drilling assembly weight is 11 tons and the center-balance counterpart is 11 tons.Intensity and stiffness affect the accuracy of drilling directly (Li & Shen, 2011).In order to ensure the accuracy of parallel in the processing deep hole, the importance of the column structure is obvious.

Mathematical Modeling
The basic structure of the column includes the column wall, roof, floor, rail and internal ribs.It owns rectangular hollow and nearly symmetrical structure, and internal cross stiffener board.The column material is gray cast iron HT250.The parameters are as follows: Total height of: 5700mm, Length: 1920mm, Width: 2100mm, Wall thickness: 40mm, Roof thickness: 60mm, Rottom plate thickness: 154mm.The geometrical model is shown in Figure 1.

Finite Element Analysis
This is Static analysis.We choose the SOLID95 units, the material properties of gray cast iron HT250: E = 1.2X10 11 N/m 2 , Poisson's ratio is 0.25.The bottom of column constraints and the forces is shown as following.Mesh cell size is 150mm.Solidworks simulation software provides the result of FEA, shown in Figure 2. The first principal stress is 12.3Mpa and the most of the column on the first principal stress are lower than 9.8Mpa.Tensile strength of the iron HT250 is 250Mpa.The ultimate stress of the column is much lower than the ultimate stress of casting material HT250 structural strength.On the condition of not affecting the stiffness of the case, the quality of the column can be reduced (Ni, Yi, & Tong, 2005).Summary of the initial design of the column statics, modal analysis is shown in Table 1.

Optimization Results
The main target method is introduced，In order to save material costs ，the optimization model is expressed as:

S.t.δ ≤ [δ]
Where M: the quality of the column structure; δ: the maximum displacement on the column; [δ]: structure allows displacement.
The optimization results are shown in Table 3.

Topology Optimization
Sand holes are set in an appropriate location.They facilitate the casting process and they can reduce the column quality.Location of sand holes ensure that the stiffness of the structure and the fundamental frequency meet the requirement.
Topology optimization of the mathematical model (Sui, Yang, & Sun, 2000) can be expressed as: (2) : the cell density, : lower limit, take a very small amount of non-zero, F(x): the objective function, : constraint (also known as state variables), : the constraint the upper limit of the condition.
By virtue of experience and intuitive judgment, the column structure is difficult to draw the location of the sand hole.The column structure topology optimization determine the sand holes on the position of the column performance (Cui, Sang, & Wen, 2004).This paper uses Ansys for structural topology optimization; Ansys uses  3.

Discussion
According to parametric model of FEA, we get that strength margin of the column structure is big.So we can propose the column size optimization and topology optimization.The size optimization adjust the location of strengthen the ribs and the location of the layer of ribs.The topology optimization determine the location of the sand holes, reducing the column weight while improving the process of the column (Ding & Lin, 2008).After optimization, the fundamental frequency did not change greatly.Column 7.36% mass reduction, improve material utilization.

Figure 1 .
Figure 1.Geometrical model of the column

Figure 3 .
Figure 3.The FEA of the column Figure 4.
Figure 5. Topological structure of column

Figure 6 .
Figure 6.Optimized structure of the column

Table 1 .
Statics and the modal analysis for the initial design of the column

Table 3 .
The size of column

Table 4 .
Comparison of structure and properties before and after the topology optimization