Table of contents *

Abstract *

INTRODUCTION *

INSERTING THE FILLETS *

DESIGNING THE MESH *

THEORICAL RESULTS *

ANSYS RESULTS *

PROBLEM *

CONCLUSIONS *

We are going to study the stress distribution over a ball valve body that is subjected to an internal pressure. So, we will use the software called ANSYS. We will solve the problem with various meshes and various fillets.

Then, we will try to find an optimal mesh in order to have some good results and an optimal fillet size in order to low the maximal stress without changing too much the geometry. Last but not least, we will complete the report with two graphical outputs from ANSYS, as illustrations.

ANSYS is a design software used by PC or workstation. It uses the finite element method, which one is the main technique for performing stress analysis and strength design for a complex structure. To begin with, the engineer can draw the geometry. Then he makes the mesh and ANSYS do the calculation. The main role of the engineer is to understand and interpret the results. The main problem is that we don’t know how use the ANSYS optimisation modulus. Consequently, we have to change all the mesh each time we want to improve it.

The ball valve body is a three dimensions problem. The system is symmetric (because of both geometry and force), so we can divide the valve in eight parts without changing the results. By this way, we can earn a lot of time for the calculation and simplify the problem. More over, the valve is a pressurised system, so the force is proportional to the surface. As a matter of fact, we can use some little elements while if we had a force applied on a plot, we couldn’t used some very little elements because the force would be infinity.

To begin with, we did not have any fillet but in reality, because of the manufacturing, we should have some.

We inserted the fillets the just after the definition of the initial 2D lines in the original give input file. The fillets were inserted simply using the LFILLT command. Then, we picked the two lines between which the fillet was to be inserted and specified a radius, as shown in fig.1. This radius was constant for both the inside and the outside.

We defined five different areas. These areas were then meshed using a variety of mesh sizes and spacing in order to find the best solution.

We made the mesh using the LESIZE command. This command enables the use of a variety of element sizes. Thus, they are smaller around the critical areas. Like that the calculations are more accurate where the stress is maximal. Furthermore, the elements are larger in areas where the stress is less. Like that, we don’t lose time where it is not important.

The spherical body of the valve, and the cylindrical portion were both meshed using the LESIZE command. The areas 1 and 3 were divided in 10 parts with a space ratio of 0.1.

The areas 4 and 5 were divided in two parts.

The fillet was meshed using a variety of meshes ( you can see it on figure 2 ) with constant sized elements because it was the most important part. Thus, we can compare the effect of the mesh on the calculation.

N.B.

• ANSYS did not accept to do a mesh 1*1 because.
• The mesh 4 was really accurate.
• We can check in figures 4 and 5 that the angles of the elements are almost 90 degrees and if we consider each element the four sizes are almost similar.

In order to compare the stress for a point on a spherical body with the theoretical calculation and ANSYS, we used the Von Mises Theorem. This theorem is used by ANSYS too.

Von Mises Theorem :

Firstly, Lames equations were used to calculate the values of the stress used in the equation above: s _r, s ₂ ,s q

The values required for the ball valve are follows:

This gives the follow results:

Finally: s = 13.48 N / mm²

Finally, we found different maximal stresses depending on the meshes and fillets. As I explained previously, 4 different meshes were used. For each mesh the maximum stress was recorded in the part 2 because it was the most important value and in all cases the maximum was found at the same point on the valve ( you can see it on figure 4 ). We made calculation only one time with the mesh 10*10 because it was long because of the big number of elements. These figures can be found in fig 4 below.

In the close-up of the mesh shown in Fig.4, we can note that a few elements contain more than 2 stress contours. As the elements used were linear, this should not occur and shows that the mesh is not perfect. This leads to errors in the results. Unfortunately this was a problem encountered with all the meshes that were designed. It means that ANSYS results were not completely accurate. As we can see on the figure, only a small number of elements have this problem we can consider that this was an acceptable error.

The overall plot of the stress distribution is shown in Fig.5. These are the results for a 5 mm fillet and a 5*5 mesh. The other meshes and fillets produced a similar pattern of contours.

Our problem was to design a suitable mesh in order to analyse the ball valve problem and to find a good fillet to low the maximal stress. To conclude, we can note the following points:

1 - We can see that the stress is fairly constant for the mesh 2, 3, 4. Nevertheless, the mesh 1 gives some different results. I think that it is not correct. Finally the best mesh is the 4*4. Indeed, with this mesh, the calculations are both fast and correct; They are really near from the 10*10 and really faster. Finally, the more refined the mesh is the longer it takes for ANSYS to solve the equations and the cheaper it is.

2 – On the spherical valve, the average results for the stress is s = 13.44 N / mm² .We can note that is similar to the theoretical result that was 13.48 N / mm² . Last but not least, it confirms the ANSYS results. Nevertheless, the very little error can be the result of the mesh that is not perfect and the rounding of decimal places.

3 – We can note that the bigger is the fillet, the smaller is the stress. Nevertheless we can consider that a too big fillet can change the geometry of the valve. To conclude, the valve is better with a fillet than without. Thus, with a 15 mm fillet the decreasing is 10.5%, in comparison with the result in the notes without a fillet.

Finally, ANSYS was a very useful tool in the analysis of this ball valve body because we solved easily a complex problem which would have been very long and difficult to solve with the analysis method. Furthermore we did optimisation.