Total inertial tolerancing, a new way to drive production

Inertial tolerancing is a new concept of tolerancing which has done a first standardization in France (NF XP E 04-008 (2009). The paper presents a generalization of the inertial tolerancing: total inertia. The goal of total inertial tolerancing is to use the information include in the numeric description of the product. The Total inertial tolerancing defined "consistent functional subset" and different coordinate systems. For each of these subsets, we defined the maximum variability accepted (maximum inertia) from digital target. Inertia is the mean square deviation of the differences between the actual part and the target, measured in accordance with normal to the surface. Each functional subset will be identified by different colors. The purpose of the production is to produce parts with the least variability compared to the numerical shape. The production problem can be represented by two vectors: The vector of the deviations from the target on all measured points, and the vector of the control factors. Thereof, the question is: What is the value to apply on each corrector to minimize the vector of deviations? A reply is given by the total inertial tolerancing of which the link between the maximum inertia and the production is strong. Thus, the problem consists into compute the pseudo-inverse matrix of the relation between the deviation and impact vectors. This pseudo-inverse matrix allows minimizing the least squares deviation, in other words, minimizing the inertia. In this paper, we will present an example of inertial tolerancing specification of a complex part and we will show how to adjust a production with its new approach.