Accurate cylindricity evaluation with axis-estimation preprocessing

Abstract

Evaluating cylindricity is a very important application in metrology. In this paper, we focus on cylindricity evaluation based on radial form measurements. The standard characterization of cylindricity is the notion of zone cylinder, i.e. the cylindrical crown contained between two coaxial cylinders with minimum radial separation and containing all the data points. Unfortunately, the construction of the zone cylinder is a very complex geometric problem, which can be formulated as a nonlinear optimization. Recently a new method (referred to here as the hyperboloid method) has been discussed, which avoids the direct construction of the zone cylinder of a point set, but approximates it with guaranteed accuracy through a computationally very efficient iterative process based on a linearization of the underlying problem. The iterations can be viewed as the construction of a sequence of “zone hyperboloids” tending to the desired “zone cylinder.” An important requirement of the method, however, is that the initial position of the cylindrical specimen axis be nearly vertical, since significant deviations from this condition essentially invalidate the process. It is the purpose of this paper to remove this shortcoming of the hyperboloid technique by providing a simple procedure for appropriately initializing the data (axis estimation). Axis estimation and the hyperboloid technique constitute an integrated methodology for cylindricity evaluation, which is currently the most effective. The theoretical foundations of the method are reviewed from a viewpoint that highlights its essential features and intuitively explains its effectiveness. The analytical discussion is complemented by experimental data concerning a few significant samples.