# Object-Oriented Mathematical Modelling
--- Applied to Rolling Bearings

** Dag Fritzson**

* SKF Engineering & Research Centre B.V.,*

* Postbus 2350, 3430 DT Nieuwegein, The Netherlands*

** Peter Fritzson, Lars Viklund and Johan Herber**

* Department of Computer and Information Science*

* Linköping University, S-581 83 Linköping, Sweden*

### Abstract:

Machine element analysis has the goal of describing functionality and other
important aspects of machine elements in theoretical form. A rolling bearing
is a typical example of a machine element. The first issue covered in this
paper is how ideas from object-oriented programming and modelling can be applied
to machine element analysis. The models thus obtained are easier to
understand, better structured, and allow a higher degree of re-use than
conventional models. Our conclusion is that an object-oriented model
description is natural for the machine element analyst and is suitable for
machine element analysis.
An equational model of rolling bearings is presented in this paper. The
structure of the model is general, in three dimensions, and applies to many
types of rolling bearings. Part of this generality is obtained by using
parametric surfaces. In order to keep the presentation of the model
understandable, we have simplified many details. Nevertheless, the model and one
solution require approximately **200+200** equations. The model is also
extensible, e.g., simple submodels of detailed properties can be made more
complex without altering the overall structure.

Keywords: machine element, mechanical analysis, modelling,
computer algebra, object-oriented, scientific computing.

Computer Algebra in Industry 2 Edited by A.M. Cohen, L. van Gastel and
S.M. Verduyn Lunel

© 1995 John Wiley & Sons Ltd

Reproduced by permission of John Wiley & Sons Ltd, 1995

** Go to: **

Applications

*Computer Algebra in Industry 2*

Thierry van Effelterre

Last Update: March 24, 1997.