Static Analysis and Size Optimization for the Bed of Gantry Milling Machine based on ANSYS Workbench

Abstract: Aiming at the phenomenon of heavy structure and high material consumption of the bed of gantry milling machine in machinery industry at present, this paper used the ANSYS Workbench simulation software, through the static analysis of the bed, and combined with its stress and strain contour, to judge whether it meets certain engineering constraints; made the size optimization under the condition of satisfying the condition of stiffness and strength, thus a lightweight design for the bed was realized, in order to achieve the goal of reducing the cost and enhancing the market competitiveness of enterprises.


Introduction
At present, the milling machine is a very wide range of metal cutting machine tools, the gantry milling machine is one of the very common one kind of milling machine, its bed design is particularly important.This bed mainly supporting the working table and processing parts, it is connected with ground effect, and both sides of the bed connected to columns, is one of the components of the milling machine.However, there are different degrees of defects in the design phase of product structure, such as high cost, large supplies, low accuracy and so on, it has become a bottleneck restricting the development of modern manufacturing industry in our country [1].In the design and manufacture of machine tool, the lightweight design of bed is one of key the design problems for designers at present.

The necessity of CAE in the design and application of bed
CAE Technology (Computer Aided Engineering) is a comprehensive process which including product design, engineering analysis, data management, testing, simulation and manufacturing; it is the basis of numerical analysis for all kinds of engineering analysis and calculation methods (such as finite element method, boundary element method, etc.) [2].CAE technology is the analysis of the function modules of the calculation analysis, simulation, optimization design and so on, it combining the computer technology with the modern engineering method.The technology is widely used in aerospace, automotive, machinery manufacturing and other industrial fields.
At present, in most design process of the machine rarely simulation analysis by CAE for the design of each module, generally, some design size only rely on the geometric parameters of the more mature the same type of products which rely on the experience of some old designer values, but most of them is not verified by the simulation analysis software, so it is very necessary to verify the performance by the CAE technology simulation.In recent years, designers had their own judgment and decision ability combined with the optimal design theory and method, which automatically find the optimal design scheme by using computer program on the basis of some optimization algorithms, to achieve the lightweight design for product, and to reduce production cost with low material consumption.At present, ANSYS is one of the most widely used CAE software for enterprise and scientific research in universities.

ANSYS Workbench Simulation analysis
The basic process of ANSYS Workbench simulation analysis can be divided into three parts, pre-processing, solution and post-processing [3].Each process of the whole simulation analysis to deal with the corresponding functional requirements, the whole basic process of ANSYS Workbench simulation analysis as shown in Figure 1.

Pre-processing
The solid model of the bed is built by using 3D software, its length is 6700 mm and width is 1300 mm, the model is shown in Figure 2. Firstly, through the CAD and CAE data sharing transfer mode to achieve the geometric model sharing, the completion of the CAE in the process of geometric modeling in the pre-processing, and the geometric model of the processing is established.Secondly, according to the property of material of the bed of milling machine to set its properties parameters, the parts materials of machine used for gray cast iron HT300 (Elastic modulus: E = 1.45e11 (N/m 2 ), Poisson ratio: μ = 0.26, Density: ρ = 7400 (kg/m 3 )), which Combined machine tool design handbook with enterprise design experience of engineers.Then the discrete model is realized by setting the cell size, and the mesh generation is generated for the next simulation analysis, and the part of the discrete model is shown in Figure 3.

Stress analysis of the bed
According to the actual processing conditions, the main force of the lathe bed are the gravity of work piece, cutting force, weight and gravity of the bed itself, its maximum stress condition is when the largest operating by Working table processing.When the bed size is 6700mm*1300mm, then working table size is 3000mm*1250mm.and the weight is 3.2 tons, so that the cutting force is too small when it respects to the weight, it can be neglected.According to the designer's processing experience, per square area of the table can support the maximum load is 13600 kg for the work piece.

Constraint condition of bed
Because the installation form of bed is directly connected with ground bolt, its anchor bolt can simply set up all constraint, both side of the bed contact with the column are also set up all constraints.

Static analysis
It can solve the calculation after the completion of pre-processing, through the static analysis, it can obtain physical quantities which related to the engineering constraints, such as the total deformation, stress and strain, and so on.The results of static analysis are shown in the following Figure 4 (including the total deformation contour figures, strain contour figures and stress contour figures).

To determine whether to meet the strength of stiffness conditions
Through analyzing the simulation results report file for data extraction, and comparing with material stress and strain limit values, it can determine the strength safety coefficient of the model is whether to consistent with the requirements of the enterprise by checking calculation.According to the above analysis of the stress contour figures and strain contour figures which can report the corresponding data, it is including some of the report data as shown in Figure 5.
With the data of analysis report can be obtained: the maximum deformation is 8.6016E-3 mm, it is 0.86 silk, the maximum deformation is 8.6016E-3 mm, namely 0.86 silk, through combining machine design handbook with engineer experience, it obtains that per meter of machine parts length to allow the maximum deformation is 0.02 mm,the length of parts is 6.7 meters, allows the maximum amount of deformation for 0.134 mm, so it is to meet the requirement of stiffness; and the most stress value for 6.9237 MPa, according to the selected materials for HT300 which material yield limit is 250 Mpa.Then, the size of the bed design meets the stiffness strength condition of engineering constraints.

The size optimization of bed
Size optimization is a form of structure optimization, it refers to in the topology invariant which external shape and internal pore of structural elements, by optimizing to change unit properties for seeking the optimal size of structure element, and to find a kind of optimal method under the condition of meeting certain strength and stiffness requirements [4].In carrying on structure displacement and stress are calculated by finite element method, the optimization process does not need re-meshing, it directly using sensitivity analysis and appropriate mathematical programming method to complete the optimization design of the specified size [5,6].
When the thickness of transverse stiffened plate as design variables ( the primary design variables is 60 mm), maximum displacement, maximum stress values, the maximum strain value as the constraint condition, the bed total volume as the target variable.Then optimizing the design variables (60 mm), the optimal design results are obtained as shown in Figure 6.To meet the stiffness and strength, the volume is decreased (before the optimization model of volume for 8.430e * 008 mm 3 ), the lightweight design is achieved (it can reduce 108 kg after optimization), then the design optimal solution is achieved, so the thickness of transverse stiffened plate is 52 mm for obtaining lightweight design of product.

Conclusion
Through the analysis of the CAE technology, the static analysis of the Bed of Gantry Milling Machine in certain conditions, that with the aid of simulation analysis module and optimization module of this software, and to judge whether it meets certain engineering constraints, the size optimization of this bed was realized with to meet the prerequisite for the stiffness and strength.In this paper, through the simulation analysis, it is used to solve the problem of the estimation error of the product design and the reliability of the verification experience; and through the dimension optimization design, it is used to solve the problem of design level which is difficult to improve by the design level which is based on the individual visual judgment and experience accumulation by the designer, thus reducing the production cost and improving the market competitiveness of enterprises.

Figure 1 .
Figure 1.The basic process of ANSYS Workbench simulation analysis

Figure 2 .Figure 3 .
Figure 2. The 3D modeling model of the bed (a) Total deformation contour figures (b) Strain contour figures (c) Stress contour figures