Today Computer Aided Tolerance (CAT) software is readily available for tolerance analysis of rigid part assemblies, but even if these tools provide good results they have not been widely used (Turner & Gangoiti, 1991; Chase et al., 1997b; Salomons et al., 1998; Prisco & Giorleo, 2002). The CAT system known as CE/TOL® is based on the vector loop model. Many commercial CAT software packages are based on the variational model, such as eM-TolMate of UGS®, 3-DCS of Dimensional Control Systems®, VisVSA of UGS®. Commercial CATs are not completely true to the GD&T standards and need improvement after a better mathematical understanding of the geometric variations. The user needs expertise and great experience combined with a through understanding of the packages’ theoretical base plus modeling principles to build a valid model and obtain relatively accurate results. Computer Aided Tolerance software efficiently deals with mechanical assemblies where the feature to align are planes, hole-pin, but it hardly treats of free-form surfaces to connect.
A CAT software shares the same user interface and the same database of a CAD package; the CAT information is stored within the CAD model with no need of translation.
The CAT software used in the following of this work is eM-TolMate of UGS® and, therefore, further information about this package has been discussed in the following. EM-TolMate involves the building of the model through the feature definition, the tolerance specification, the assembly and the measurement definitions.
The feature definition process must be performed for each component of the final assembly (there must be a separate CAD model for each component); it uses the existing CAD geometry of the model to create its own features. Therefore, full associativity with CAD entities is assured. The basic features supported in eM-TolMate are plane, pin (cylindrical, tapered, threaded), hole, point, tab, slot, constant profile surface, constant cross section, sphere, surface of revolution, general 3D surface. Edge features (for thin-walled parts) are also available. In many cases, the user needs to mathematically derive some feature from existing features (e. g. line of intersection between a plane and a parallel cylinder, centroid of several points or best fit line between several points).
The tolerance specification allows the user to define the dimensional or geometric tolerances supported by the existing international standards of GD&T (ASME and ISO). There is no limit on the number of tolerances applied to a feature. Diameter modifier and material modifier (MMC and LMC) may be added to tolerances applied to a feature of size. Available statistical distributions are normal (default), uniform, triangular, exponential, gamma, Weibull, Laplace or Pearson distribution.
The assembly definition creates an empty CAD model which represents the assembly. The sequence of assembly, represented by a tree structure, has to be defined by using the source components into the correct position of the assembly tree. Afterwards the assembly operations have to be specified by the selection of the mating features that are involved in each operation. Except for the first component of the assembly, the assembly operation has to be defined for each component which will be constrained to the target features of the components inserted before it in the tree. The constraint scheme can be isostatic, but also under or overconstrained.
The measurement definition specifies the geometric relationship that is to be put under control in the assembly or in the single part. EM-TolMate supports various types of measurements: linear distance, angle, clearance, virtual size.
The built model is simulated according to Monte Carlo technique in a statistical approach. EM-TolMate determines simulation order for each feature on each component, the tolerance priority order and the tolerance degree of control (i. e. the degrees of freedom constrained by the tolerance on a feature). The system warns the user about any lack of completeness or ambiguity in tolerancing scheme (e. g. loops, unreferenced datums). Based on this information, eM-TolMate uses random numbers to create several sets of feature variations from nominal geometry, according to the specified tolerances. The simulations (one for each set of variations) proceed based on the mating features specified by the user and components are assembled into position relative to each other. Finally, measurements of the actual assembly are performed and the results are stored in memory. Worst-case limits can be estimated when the sample size of simulations are big enough and setting the estimated limits to "Actual". To assure a high level of accuracy, a large number of simulations has to be carried out.
The user performs the results analysis phase interactively after the simulations are finished. There are two kinds of results: the variation analysis, which computes statistical parameters and reports the overall variation range for each measurement, and the contributors analysis, which determines the sources of variation and presents this information in a sorted list. The user may view the results analysis on the screen or output the information to a file in various file formats.