Representation and conversion of dimension units in CAD data models

This paper presents a knowledge-based approach to represent the dimension units of numerical values in CAD data models. Although numerical quantities are associated with dimension units in typical engineering data, these units are missing in most product data models. Some extended data models allow to store information about dimension units, but this information is limited to a fixed and predefined number of units. The presented approach helps to model parts of the semantics of product data by extending numerical values to semantic entities that can be converted automatically. Further, the evaluation of simple units (e.g. mm und cm) or more complex units (e.g. N=kg*m/s2) in arithmetical operations (e.g. addition, multiplication or division) is described. The approach works on any set of units with any complexity. Users are able to define new units by so-called reduce and substitute rules. In order to evaluate dimension units in arithmetical operations, all units are converted first into a standard form, using the defined reduce and substitute rules. Next, the dimension unit of the complete operation is calculated by reducing fractions, combining units, calculating numerical values, and converting the result of the complete operation into the desired unit. This paper also describes an implementation of the presented approach that integrates the concept of representing and evaluating dimension units in a shared CAD database system.