OBJECT-ORIENTED MATHEMATICAL-MODELING - APPLIED TO MACHINE ELEMENTS

Machine element analysis has a goal of describing function and other a spects of machine elements in a theoretical form. This paper shows how ideas from object-oriented modelling can be applied to machine elemen t analysis. The models thus obtained are both easier to understand, be tter structured, and allow a higher degree of re-use than conventional models. An object-oriented model description is natural and suitable for machine element analysis. As a realistic example an equational mod el of rolling bearings is presented. The structure of the model is gen eral, and applies to many types of rolling bearings. The model and one solution require approximately 200 + 200 equations. The model is exte nsible, e.g. simple submodels of detailed properties can be made more complex without altering the overall structure. The example model has been implemented in a language of our own design, ObjectMath (Object-o riented Mathematical language for scientific computing). Using ObjectM ath, it is possible to model classes of equation objects, to support m ultiple and single inheritance of equations, to support composition of equations, and to solve systems of equations. Algebraic transformatio ns can conveniently be done since ObjectMath models are translated int o the Mathematica computer algebra language. When necessary, equations can be transformed to C+ + code for efficient numerical solution. The re-use of equations through inheritance reduced the size of the model by a factor of two, compared to a direct representation of the model in the Mathematica computer algebra language.