EDICIÓN Y PUBLICACIÓN DE PELICULAS CON MOVIE MAKER

In this section the trimming of the structure to a more complex shape will be considered. The tessellated surface of the solid model partitions space into a bounded inside region and an unbounded outside region. In order to simplify the computing process, the surfaces of a VS block were tessellated and then any triangle in the inner region was kept while any triangle located in the outer region was deleted. Any triangle intersected by the surface was trimmed and the section inside of the surface kept. Finally a VS block was trimmed to the desired shape. The above process involves a large amount of computing effort but the computing time can be reduced by introducing the bounding box method detailed in Chapter 2. The flowchart of the bounding box method is shown in Figure 4-24.

Figure 4-24 Flowchart of the bounding box method.

As discussed in the section of constructing the VS blocks, the surfaces of each unit cell were tessellated by triangles and these triangles were in one unit cell so that a unit cell can be considered as the common bounding box of triangles in the unit cell. The changes to the procedure can be seen by comparing Figure 4-24 with the flowchart for the revised method shown in Figure 4-25.

Figure 4-25 A revised method for trimming a given triangle by triangles from a tessellated surface.

Further tests were carried out to measure the computing time. Three codes were written to repeat three trimming methods while measuring the computing time. In order to eliminate the effect of other applications when measuring computing time,

A given triangle from a VS block

Compute the bounding box of the

given triangle Triangles (from the VS block) penetrating into bounding box ? Penetrate Record the triangles penetrating into the

bounding box

No action no

Trim the given triangle from recorded triangles Triangulated the trimmed triangle Output the triangulated trimmed triangle yes

For given triangles (from a VS block) in

a same unit cell

Triangles (from the VS block) penetrating into the unit cell (bounding box)? Penetrate Recording the triangles penetrating into bounding box yes No action no Trimming the triangles in the unit

cell by the recorded triangles Triangulated each trimmed triangle Output the triangulated trimmed triangles

the computing time of various trimming times were extracted directly by using the Psutil module discussed in Chapter 3. In these tests, a cylinder (height 32mm, diameter 15mm) with tessellated surface of 240 triangles was created by Magics. A VS block larger than the bounding box of the cylinder was created with various cell sizes which gave different numbers of structure triangles. These triangles were trimmed by the cylinder surface triangles using the three trimming methods and the various computing times were measured. Figure 4-26 shows that one of the trimming methods saves computing time especially as the number of triangles in each cell increases.

Figure 4-27 Computing time taken by three different methods to trim a VS with various numbers of triangles by a cylindrical surface (height 32mm, diameter 15mm) constructed by 240 triangles.

A problem with the commercially available software like Magics is that it can only trim a solid model that has closed surfaces. However in this research, the VS is constructed with open surfaces. Thus further work was carried out to test whether the VS with an open surface could be trimmed using commercial software. Figure 4-28 shows a VS block that was trimmed by the commercial software Magics V9.5.4.7. The trimmed result performed by the new software gives a clearer boundary. Therefore the new trimming function is necessary for trimming VS blocks with open surfaces and cannot be replaced by Magics V9.5.4.7.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06

C omp u tin g time, τ0, (S) Number of triangles, Nt

Trimming triangles one by one

Trimming triangles with bounding box method Trimming triangles with unit cell as a bounding box

Figure 4-28 The trimming functions were performed by Magics and new custom software. After it had been shown that a VS could be trimmed to the desired shape it was necessary to fabricate the part using the SLM. A solid model of an acetabular cup was filled with the RVS as shown in Figure 4-29. The total acetabular cup including the porous structure part and the solid part were fabricated by using the SLM 100 as shown in Figure 4-30. The smooth surface indicates that the trimming function works properly for open surfaces.

Figure 4-29 Illustration of an acetabular cup filled with VS in .stl format.

Trimmed result performed by Magics®

Trimmed result performed by new custom software Z

X Y

Solid section of cup

Porous section of cup filled with RVS ( cell size 1 mm, hole size 80%, percentage of randomisation 60%

Figure 4-30 Fabricated the trimmed result by SLM Realizer 100.

When trimming the VS block, the dimensions of it were controlled to match the original shape of the solid model. The example in Figure 4-31 shows a VS created and trimmed to a cylindrical shape. The model of the cylinder (height 32mm, diameter 15mm) was created by Magics V9.5.4.7 and two VSs with the same parameters were created and trimmed by FreeSteel® and the new custom software. The overall size of a trimmed VS was measured using Magics. As can be seen (Figure 4-31), the size of the cylindrical VS block was the same as that of the original cylinder. While the size of the cylindrical VS (height 36mm and diameter 18.891mm) trimmed by Plateletqt is very different from that of the original cylinder. These results, considering the trimming of the part, indicate that the new trimming method is better at retaining the overall shape and size of the component avoiding further machining which would result in increased cost.

Figure 4-31 Illustration of the tolerance control in the trimming procedures done by different software.