The current standards for geometric tolerancing rely on the gauge based
production measurement technology with which the hull of an object is
measured. Due to the use of 3D-coordinate measuring technology it is
possible to determine and classify geometric deviations more differentiated
than by using conventional measuring equipment. Out of this arises the
possibility to transform deviation afflicted geometry into a mathematical
model whose specification basis is identically with the ones of up to date
CAD systems. In this context the present thesis aims at the development of
a mathematical model to describe tolerances and deviations on the basis of
the CAD internal description of geometry. To achieve these existing models
for tolerance integration in CAD systems will be investigated, analyzed and
contrasted to the current standards for tolerancing. The standard systems
deficiencies related to the mathematical description will be argued and
approaches to the mathematical model will be discussed. Based on the
existing works a mathematical model for the representation of deviations in
CAD systems and the calculation of tolerance chains in assemblies will be
developed. The geometrical basic elements plane, cylinder, sphere and cone
will be considered in this. Moreover a demonstration application will be
developed that is based on the mathematical model. This demonstrator
combines the nominal geometry that is created with a CAD system with
further information which includes the deviation parameters of the
mathematical model. The extended information of the CAD model will be used
subsequently to allow the calculation of a tolerance chain with regard to
definite boundary conditions. With that the definition of an arbitrary
tolerance chain by the user is possible. According to this specification
the demonstration application will determine all surfaces belonging to the
tolerance chain, prepare them for calculation and adjacently execute the
calculation according to the mathematical model. To enable the presentation
of the results the demonstration application will be extended by the
capability of modeling deviation afflicted surfaces in the CAD model in a
simplified way. For an additional feedback to the user the calculated
values will be displayed in a table. An examination of possible proceeding
works based on the developed model will be carried out concluding.