Cálculo da distribuição da tensão elétrica em uma máquina copiadora

Abstract

In engineering and other many areas, mathematics is the main scientific basis in the classification and analysis of many phenomena and materials. Analytical analyzes are the main pillars for several areas of knowledge. Technology, in turn, plays a key role in making classical methods of analysis more efficient and practical. Most electrostatic phenomena can be described by partial differential equations, but the resolution of these equations is not always easy. For this reason, computational analyzes are important to validate classical analytical methods. The finite element method is a computational simulation resource with the purpose of validating and making a classical analytical analysis more accessible. The finite element method is very important because its use in industries can reduce the construction costs of a particular machine or product. This work presents a comparison of results obtained through an analytical analysis performed with Laplace’s equation and the results obtained through simulation with finite elements. The present work seeks to validate the simulation of finite elements, as well as highlight its importance and show how its use is an important tool used in engineering. This work presents an analysis with a problem of electrostatics in one dimension. The chosen problem is a copier machine, an electronic device that works based on the action of voltages and electric fields. The finite element method can be performed in one, two, or three dimensions. In this work, the analysis will be carried out in one dimension to prove the functioning of the method, later, similar analyzes can be used in more complex eletrical machines such as transformers, for example, for publication of future works.