Vectorial method of minimum zone tolerance for flatness, straightness, and their uncertainty estimation

Flatness and planar straightness are fundamental form tolerances in engineering design and its materialization through manufacturing processes. Minimum zone tolerance is a preferred approach of flatness and straightness for widely accepted ISO and ANSI standards. In this paper, we propose a novel accurate method of minimum zone tolerance based on vectorial calculus of point coordinates. The non-linear minimax formulation of the original flatness or straightness problem is transformed into a set of linear problems. Next, the optimal solution of the envelop planes or lines is reached through vectorial calculus for both flatness and planar straightness. Then, the developed algorithms are compared to a selection of methods with published tests in recent and classic literature on the topic, reaching the best attained accuracies or outperforming them in the trials. Finally, we propose a new decomposition of the uncertainty contributions for analysis and the improvement of sampling strategy. We conclude remarking the practical contributions of the proposals.