THE BIRD-CAGE METHOD USED FOR MEASURING CYLINDRICITY. A PROBLEM OF OPTIMAL PROFILE MATCHING.
The bird-cage method used for measuring cylindricity is reported to be the most effective, as it pro- vides the most detailed information about an analyz ed ob- ject. The average values of profiles measured with the cross- section and the generatrix methods may differ sligh tly, yet this may result from some design imperfections of t he measurement instruments used. In this study, the pr oblem of optimal profile matching is formulated and solved. As a result, the differences between the values of the r egistered profiles at the points of intersection of the scann ing trajecto- ries can be minimized.
Accurate cylindricity evaluation with axis-estimation preprocessing
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.
Wall-to-bed heat transfer in circulating fluidized beds
Heat Transfer from the wall of a circulating fluidized bed to the fast bed suspension has been investigated for several materials. The range of investigation includes dense and dilute phase fast fluidization and pneumatic transport. The overall heat transfer coefficient was found to be a function mainly of cross-sectional average suspension density. Effects of superficial velocity and solids mass flux were obscured by their interrelationship to the suspension density. Two models from the literature are evaluated using present and published data.