Mathematical model of cylindrical form tolerance

Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y14.5.1M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of tolerance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.