T-Maps to Model Composite Positional Tolerancing for Patterns of Features

For the first time, Tolerance-Maps (T-Maps) are constructed to model composite positional tolerancing applied to patterns (arrays) of features. The T-Map for a feature is a range (codomain) of points obtained by mapping all the variational possibilities (domain) of a feature within its tolerance zone to a hypothetical Euclidean point space. T-Maps have already been developed for tolerances applied to single features, such as to a simple axis (line), a plane, and a cylinder, but not for the special methods available for tolerancing patterns of features. In this paper, the different pattern tolerancing methods listed in the standards produce distinctions in geometric shape, proportions, and/or dimensions of a T-Map. The T-Map geometry is different when tolerances are specified with composite position tolerancing rather than with two-single-segment control frames. Additional changes to geometry occur when material modifiers are also specified. Two levels of T-Maps are proposed for a pattern of features. One is at the assembly level to ensure the assembly of an engaging pattern of pins and holes, such as the array of pins on an integrated circuit, which are to be inserted into a base. The second is at the part level to model the variations between the two parts that contain the engaging patterns. The assembly-level T-Maps apply to any number of engaging pin/hole features arranged in any pattern: linear, circular, rectangular, or irregular. In this paper, the part-level T-Map is restricted to linear patterns. The different specifications are also compared with a statistical analysis of misalignment for an assembly with a pattern of pins and holes.