Читать книгу Computer Aided Design and Manufacturing - Zhuming Bi - Страница 37

Any matter for an object in the world exists in one of four distinct states, i.e. solid, liquid, gas, and plasma. The solid state is a common state for the majority of products around us. To investigate the behaviours of solids, it is necessary to know its geometry and shape. Similarly, to investigate the behaviours of fluid, gas, or plasma in a certain volume, the geometry and shape of boundary surfaces of a fine volume is also needed to be defined.

For centuries, geometry has played its crucial role in the development of many scientific and engineering disciplines such as astronomy, geodesy, mechanics, ballistics, civil and mechanical engineering, ship building, and architecture. The importance of the study on geometry has been shown in this century in automobile and aircraft manufacturing. Since geometry is primarily visual, geometry becomes a unique and particularly exciting branch of mathematics. Geometry became a branch of mathematics at the end of the nineteenth century; however, great designs in the history were always inspired by observation and intuition on geometric shapes (Gallier 2008). Geometric modelling is a branch of applied mathematics and computational geometry; it studies the methods and the algorithms for the mathematical representation of geometries and shapes. Geometric modelling serves for the visualization of objects and lays the foundation for computer graphics, which is the construction of models of scenes from the physical world and their visualization as images.

Geometric modelling is as important to computer aided technologies as the governing equilibrium equations are to classical engineering fields such as mechanics and thermal fluids. As shown in Figure 2.1, the design of a part, product, or system usually begins with geometric modelling, so that the physical objects to be designed can be represented virtually in computers. Geometric modelling techniques and algorithms are used to model objects, and the dimensions and spatial constraints of objects are inputs via graphic user interfaces (GUI) of modelling tools. Once the objects are modelled, any information associated with the objects can be utilized in the design processes or decision‐making supports involved in a product lifecycle. For example, virtual geometric models can be used by computer graphics to visualize the designs before physical products are made. Engineering drawings needed in manufacturing processes can be directly generated from solid models of products, and all of the annotations relating to dimensioning and tolerance can be included in the drawings. If a product is a machine with relative motions among system components, a motion study can be defined upon the computer aided design (CAD) model to investigate the relations of driving forces and motions. In addition, engineering analysis can be performed at any stage of the product design process. In the following chapters, you will learn how virtual models of products can be utilized to solve design problems in mould designs, engineering analysis, simulation of manufacturing processes, evaluation of system sustainability, and so on.

Figure 2.1 Role of geometric modelling in computer aided systems (CAD).