Von Mises stress evaluation for a mechanical part using the CATIA finite element method.

Ghionea, Ionut ; Munteanu, Gabriel ; Beznila, Hortensia 等

1. INTRODUCTION

For many equipments and particularly for the machinery manufacturers, the resistence structure design is the most important component that has to be analyzed with FEM instruments; the structure comprises the whole mechanical system having a strictly loads absorbtion, ensure a specific meaning (e.g.: the relative movement between the subassemblies), together with the static and dynamic stability or to guarantee a nominal stiffness established by the designer in his specifications (Constantinescu et al., 2006).

Increasing the strength, the stability and the durability are the main required characteristics of an assembly comprising as well subassemblies, joints and pieces. So, for a specific product, the engineers should always consider constraints like: the number and intensity of the static loads as well as dynamic ones, the maximum strains values, different safety factors (for bucking, breaking or fatigue), the susceptibility at execution, mounting or errors appeared in operation, frequency characteristics, steady afterflow speed, product cycle of life, weight, material and moment of inertia, different loads stiffness, static and dynamic stability or simultaneous loads response (Ispas & Ghionea, 2001).

The FEM analysis of a structure is in fact a numeric computation review. Hence, for a specific geometrical model, particular loads and seat constraints well known will result the required values of the deformation, stress, bearing reaction and natural frequency (Ghionea, 2007).

2. THE FINITE ELEMENT METHOD ANALYSIS

2.1 Initial data

The current analysis comprises the FEM applied for an arm type piece shown in figure 1.

[FIGURE 1 OMITTED]

To accomplish the functional meaning, the structure has an assembly and a connection surface where the load is applied (Barlier & Poulet, 1999).

The solid model has been built in CATIA Part Design module, having a steel material with the characteristics shown in figure 2: Young's modulus of 2 x [10.sup.11] N/[m.sup.2], Poisson's ratio of 0.266, density of 7,860 kg/[m.sup.3], thermal extension ratio of 1.17 x [10.sup.-5] K, yield streght of 2.5 x [10.sup.8]N/[m.sup.2].

By applying the material characteristics, the specification tree is completed with the Material=Steel element. To start the FEM analysis, the user can access the CATIA Generative Structural Analysis module to set up the type of statical analysis as Static Case.

2.2 The methodology

Although CATIA software defines a default net of nodes in the process named digitization, it is higly recommended for experienced users to edit this net and establish the dimension of the finite element (Size), the maximum deviation of the virtual digitized model from the real model (Absolute sag), the type of the element (Element type) with a double click on OCTREE Tetrahedron Mesh element from the specification tree.

A new dimension of the finite element of 2 mm has been established, a deviation of 1 mm and a linear type of element are the new coordinates. On the every surface of the bearings from the bottom of the structure, the user applies the Clamp restrains as shown in figure 3.

[FIGURE 3 OMITTED]

On the surface of the bore from the upper part of the structure, is applied a distributed force of 150 N from interior to exterior in the opposite direction of the X axis. In the specification tree, the Distributed Force.1 element becomes available.

The force is represented by a four red arrows symbol, and characterized by a value and direction. All the parameters can be introduced in the appropriate fields from the dialog box as figure 4 shows.

[FIGURE 4 OMITTED]

2.3 The outputs

As the restrains and loading are established, the next step is to calculate the model behaviour running the Compute routine. At the end of the calculus, the user may decide to view the results from the Image menu. The specification tree is being completed based on the inserted images.

The figure 5 shows an output as Von Mises Stress type of image. A variety of parameters might be studied, but the present study analyses the structure behaviour considering the deformation, principal stress and precision.

[FIGURE 5 OMITTED]

In order to identify the maximum and minimum stress values it is used the Information instrument to show the results.

In the Figure 6 is presented the window with stress value as well as the colour scale of Von Mises image. The lowest stress values correspond to the bottom of the scale, close to blue; the higher are the red ones at the scale top; between these are quite safe yellow and green shades.

To draw conclusions, we have picked from the dialog window the choose the exact values: minimum of 0 to a maximum of 2.2x108 N/m2. Knowing the yield strenght of the material of 2.5x108 N/m2, it can be considered that the structure will resist to a distributed load force of 150 N, but the operational safety is nearby the maximum limit and an increase of more than 10% is dangerous and not recommended.

[FIGURE 6 OMITTED]

2.4 Optimizing the model

To verify the accuracy of the results we performe a specific test with Precision software instrument as well as locate the zones containing the biggest errors, based on the Image Extrema software instrument (see fig. 7). Hence, the global error is calculated at 41.9%; such error seems to be high but it indicates in fact all the differences between the proposed virtual model and the real structure.

[FIGURE 7 OMITTED]

Therefore, it is imperative to optimize the model running the New Adaptivity software instrument and filling in a suitable value--for the start: 25%. To reiterate the computation in 5 steps is imperative for the analysis to refine model and to reach the established goal. The net is also refined by increasing it's accuracy from 2 to 1 mm with Minimum Size instrument. Definitely, all these improvements of the virtual model increase the computing time for analysis (Ghionea, 2007).

Analysis of the optimized model results shows an enhanced error, but +4.58% more than the initial target of 25%. Overall, an improvement of +12.36% has been achieved, but regarding the Von Mises outputs, the new model analysis shows an increased maximum stress value, from 2.20 x [10.sup.8] N/[m.sup.2] to 2.34 x [10.sup.8] N/[m.sup.2] (figure 8). For an increased precision and higher improved model, the user may continue an iterative analysis and to refine the model. The goal is to decrease the target of the global error, but the outputs of the maximum stress must not exceed the admissible steel yield strength.

[FIGURE 8 OMITTED]

3. CONCLUSION

On the sequences of CAD--FEM--CAM an iterative process of design--computing--execution is being realised, comprising both analysis and synthesis FEM routines applied to the virtual model or prototype. Experienced and explained above, each reiteration brings a new improvement for the model or prototype until the goal is attained.

4. REFERENCES

Barlier, C. & Poulet, B. (1999). Memotech. Genie mecanique, productique mecanique. Deuxieme edition (Memotech. Mechanical engineering, mechanical manufacturing). Editions Casteilla, ISBN2-7135-2063-0, Paris.

Constantinescu, N. I., Sorohan, St. & Pastrama, St. (2006). The practice of finite element modeling and analysis. Printech Publishing House, ISBN 978-973-718-511-2, Bucharest

Ghionea, I. (2007). A practical approach in the finite element method study of a mechanical part. Scientific Bulletin, Serie C, Volume XXI, Fascicle: Mechanics, Tribology, Machine Manufacturing Technology, North University of Baia Mare pp. 251-258, ISSN-1224-3264, , 2007, Baia Mare.

Ghionea, I. (2007). Proiectare asistata in CATIA v5. Elemente teoretice si aplicatii. Computer aided design in CATIA v5. Theoretical elements and applications. BREN Publishing House, ISBN 978-973-648-654-8, Bucharest.

Ispas, C., Ghionea, I., (2001). Stude of computer design and management in the conception and development phases of a product. Optimum Technologies, Technologic Systems and Materials in the Machines Building Field, University of Bacau, ISSN 1224-7499, Bacau.

Fig. 2. Physical characteristics of the structure steel material.

PartBody\Material Steel

'Steel\Steel.1.1\Young Modulus' 2e+011N_m2
'Steel\Steel.1.1\Poisson Ratio' 0,266
'Steel\Steel.1.1\Density' 7860kg_m3
'Steel\Steel.1.1\Thermal Expansion' 1,17e-005_Kdeg
'Steel\Steel.1.1\Yield Strength' 2,5e+008N_m2