Statistical method for the prediction of tolerancing effects in design

This contribution is intended to explain a numerical statistical methodology developed for the analysis of the combined effects of design tolerancing specifications in terms of uncertainty concerning the final threedimensional location of a mechanical element, part of a more complex mechanical assembly to be manufactured. This methodology is based on the use of the Monte-Carlo approach to numerically simulate the propagation of uncertainties related to the location of each mechanical element due to deviations from nominal design conditions allowed by tolerancing. The mechanical assembly geometry (in terms of three-dimensional location of each component) is kept into account by way of a suitable system of reference frames, a number of which is put on each mechanical element. Each reference frame is mathematically defined by a homogeneous matrix. Uncertainty contributions due to tolerancing specifications result in translations and rotations of these references and so in modifications of matrixes terms. By the Monte-Carlo approach a suitable number of possible geometrical situations is generated; computations making use of homogeneous matrixes products take to find out the probability distribution associated to the three-dimensional location variables (degrees of freedom) of each mechanical component. Reference is made to the space program Planck; specifically, this method has been employed to estimate tolerances effects on the misalignments related to the three-dimensional location of some radiometers mounted on a device which is intended to measure deep space short waves radiation.