**6.4 Quality of surfaces generated by CAD systems**

In many cases it is necessary for modelling three-dimensional boundary conditions that go beyond the requirements of design and ergonomics. Surfaces are required in these cases with a high degree of continuity in order to maintain the smoothness in the shape of the product. The quality of a complex surface generated by a CAD system is related to the model used for its creation in three circumstances:


When you want to develop surfaces for products requiring strict-looking, such as appliances, the external body of a car, etc., small discontinuities in the surfaces of the 3D CAD model can be replicated in the final product, be it cast or stamped. When creating surfaces through the interpolation of two sections and non-planar curves with different radius of curvature, and the need to maintain continuity of the tangential surface created in which the directions of the surface change smoothly, the surface must also have continuity of curvature. Applying tests of light reflection on the product such geometric discontinuities can be found.

Advanced Free Form Manufacturing by Computer Aided Systems – Cax 583

Different computational techniques for solid modelling. The internal representation of a solid object is commonly used to classify the modeller. The internal representation is how the software stores the model. This is different from the external representation, which presents the model on the computer screen. Two techniques of internal representation are: a) B-Rep (Boundary Representation). This representation employs models described by boundaries, proposed by Ian Braid, Cambridge University. b) CSG (Constructive Solid Geometry). This method was proposed by Voelcker and Requicha the University of

Both methods were applied in commercial systems in the late 70's. Other methods of representation of solids were developed, such as octree, quadtree, cell breakdown, among others. However, the methods of representation of solids used in most current CAD systems

In this method, solid objects are built with a combination of simple solid primitives such as cylinders, cubes, cones, spheres, etc. Through Boolean operations (George Boole, 1815-1864, developed the Boolean algebra) addition, subtraction and intersection between solid objects in case of CAD software. When an object is constructed with a CSG modeller, the system saves a history of creation (creating topographic tree), which includes all solid primitives with their size and positioning, and information about all the Boolean operations used to

The hybrid model allows building three-dimensional geometries employed the techniques of combining modelling surfaces in solid modelling. This provides greater versatility to

There are three main techniques, common in CAD systems for the construction of threedimensional geometries: i) primitive geometries ii) intersecting geometries iii) domain-based wireframe geometries. The latter will be the most used, in this case the objects are constructed using geometric information in wireframe, and may be straight lines, curves, arcs, points or a combination thereof. The software uses this field and applies the function selected by the user, which are: operation of revolution or extrusion of a profile on a directional vector; extrusion of a profile on another profile directional; interpolation between curves; migration between cross sections. More complex surfaces, which require patches with three or five boundaries, are more complex representation. These surfaces are found in regions with corners at the

The Computer Aided Engineering (CAE) systems were developed to simulate real applications, and enabling auxiliary steps of projects and manufacturing. There exists CAE

work for the user, can benefit from the best features of both methods.

intersection of surfaces, as well as the junction of three Fillets.

are the CSG (Constructive Solid Geometry) and B-Rep (Boundary Representation).

 Cost less than the CAD surface model. Limited to create complex geometric shapes.

Use relatively simple.

Rochester.

construct the object.

**6.6 CAD hybrid modelling – High end** 

**6.7 Techniques of modelling** 

**7. Application of CAE systems** 

CAD systems have advanced graphical tools to detect such discontinuities in a surface. Figure 25b illustrates a surface with discontinuities. The CAD system identifies the discrete regions through hazards. The parallel strips and gently represent regions consistent with good degree of continuity. The discrete regions are illustrated by the tracks with abrupt changes (Figure 25c). This may occur for mathematical limitations and / or the method used to construct the surface. The surface of Figure 25 (b and c) is a surface Fillet, calculated automatically by the software.

(a) Product (b) Discontinuous surface (c) Abrupt changes in gray bands

Fig. 25. Surface emphasized the problem of discontinuity

The abrupt changes of the bands indicate regions with continuity compromised. However, after identifying these regions and/or surfaces, CAD systems are still not able to help troubleshoot the problem. The reasons that caused specific discontinuities are not presented.

Thus, the user must develop empirical ability to solve or minimize the problem. In the case illustrated in Figure 25, the surface of agreement (Fillet) was calculated by the software with a large number of longitudinal and lateral, creating the problem of continuity observed. Performing a work setting "manual" to delete longitudinal and lateral, it was observed an improvement in continuity of surface.
