Modeling and Analysis
DOI link for Modeling and Analysis
Modeling and Analysis book
After discussing the role of mathematical models in machine monitoring and fault diagnosis, the basis of the finite element method is introduced. The derivation of the Euler beam element is given in full and the extension to the Timoshenko model is outlined. Whilst these beam elements are simple, it is argued they are extremely effective in modeling many, but not all, machines. The manner in which elements are assembled to yield a complete model is then described and the modeling choices to be made by the analyst are discussed. Using the example of mass imbalance, the chapter shows how some important features of the dynamics can be presented on a Campbell diagram and some differing features are highlighted. However, whilst these diagrams are very helpful, they do not show all relevant data. To extend the scope, systems with damping are discussed and the concept of stability. Finally, the discussion is extended to show how a knowledge of modes shapes can be used to advantage in reducing computation and rapidly estimating the influence of small changes.