Orientation, sphericity and roundness evaluation of particles using alternative 3D representations

Sphericity and roundness indices have been used mainly in geology to analyze the shape of particles. In this paper, geometric methods are proposed as an alternative to evaluate the orientation, sphericity and roundness indices of 3D objects. In contrast to previous works based on digital images, which use the voxel model, we represent the particles with the Extreme Vertices Model, a very concise representation for binary volumes. We define the orientation with three mutually orthogonal unit vectors. Then, some sphericity indices based on length measurement of the three representative axes of the particle can be computed. In addition, we propose a ray-casting-like approach to evaluate a 3D roundness index. This method provides roundness measurements that are highly correlated with those provided by the Krumbein's chart and other previous approach. Finally, as an example we apply the presented methods to analyze the sphericity and roundness of a real silica nano dataset.Postprint (published version

Instrument support with precise lateral adjustment Patent

Centering device with ultrafine adjustment for use with roundness measuring apparatu

Metric trees of generalized roundness one

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is to identify some large classes of countable metric trees that have generalized roundness precisely one. At the outset we consider spherically symmetric trees endowed with the usual combinatorial metric (SSTs). Using a simple geometric argument we show how to determine decent upper bounds on the generalized roundness of finite SSTs that depend only on the downward degree sequence of the tree in question. By considering limits it follows that if the downward degree sequence $(d_{0}, d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| = \aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the trees that satisfy this condition are all complete $n$-ary trees of depth $\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits of Cantor trees. The remainder of the paper deals with two classes of countable metric trees of generalized roundness one whose members are not, in general, spherically symmetric. The first such class of trees are merely required to spread out at a sufficient rate (with a restriction on the number of leaves) and the second such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table

Wet granulation in laboratory-scale high shear mixers: Effect of chopper presence, design and impeller speed

The effect of the main means of agitation in a high shear mixer has been investigated in this study. Granulation runs have been performed on a fine cohesive microcrystalline cellulose powder (Avicel 105, d50 = 20 μm) often used as a pharmaceutical excipient in tablet formulations in two bowls of a Mi-Pro® laboratory high shearmixer with a capacity of 0.9 and 1.9 L, respectively. Torque curves recorded during granulation are found to allow good control of the process while increasing impeller speed is found to generally reduce granule size and the onset of breakage seems to occur for similar values of impeller tip speed. As a general rule, the chopper allows for better binder distribution in the Mi-Pro® and is found to be necessary for successful granulation at low to moderate impeller speeds. For high impeller speeds in excess of 4.4 m/s with or without a chopper, similar granule sizes and growth mechanisms are observed. Granule roundness was found to increase with impeller speed up to a certain speed after which granule roundness has been found to decrease with increasing impeller speed most probably because of increased breakage of the granules. Dry granule strength has been found to increase with increasing impeller speed, presenting only a slight decrease at the highest impeller speed studied

Some remarks on generalized roundness

By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian groups of rank $\geq 2$ equals 1. This answers a question of J-F. Lafont and S. Prassidis.Comment: 3 page

The effects of lapping load in finishing advanced ceramic balls on a novel eccentric lapping machine

HIPed (Hot Isostatically Pressed) silicon nitride ball blanks were lapped from diameter 13.255 mm to diameter 12.7 mm by a novel eccentric lapping machine. A maximum material removal rate of 68 μm/hour has been achieved under a nominal lapping load of 43 N/ball. It was found that the material removal rate was increasing almost linearly with the lapping load within this load range. When the lapping load was higher than 43 N/ball, the material removal rate started to drop and the lapped ball roundness error started to increase. At the highest nominal lapping load of 107 N/ball, surface and subsurface damages were found on the lapped balls. Because of eccentric loading effect, the actual load on individual ball could be 25~28% higher than the nominal lapping load. The surface residual stresses of lapped balls under different lapping loads were measured, and it was found that the lapping load had less effect than previous HIP process. Rolling contact fatigue tests were conducted on balls lapped at nominal loads of 43N/ball and 107 N/ball. No failure occurred on the ball lapped at 43 N/ball after 138 million stress cycles. Ball lapped at 107 N/ball was failed after 13.3 million stress cycles with a shallow spall with flat bottom inside. This research suggests that the lapping load for advanced ceramic balls in conventional concentric lapping could be doubled from 20N/ball to 40 N/ball without degrading the surface quality of lapped balls

CF6 jet engine diagnostics program. High pressure turbine roundness/clearance investigation

The effects of high pressure turbine clearance changes on engine and module performance was evaluated in addition to the measurement of CF6-50C high pressure turbine Stage 1 tip clearance and stator out-of-roundness during steady-state and transient operation. The results indicated a good correlation of the analytical model of round engine clearance response with measured data. The stator out-of-roundness measurements verified that the analytical technique for predicting the distortion effects of mechanical loads is accurate, whereas the technique for calculating the effects of certain circumferential thermal gradients requires some modifications. A potential for improvement in roundness was established in the order of 0.38 mm (0.015 in.), equivalent to 0.86 percent turbine efficiency which translates to a cruise SFC improvement of 0.36 percent. The HP turbine Stage 1 tip clearance performance derivative was established as 0.44 mm (17 mils) per percent of turbine efficiency at take-off power, somewhat smaller, therefore, more sensitive than predicted from previous investigations

CF6 jet engine performance improvement: High pressure turbine roundness

An improved high pressure turbine stator reducing fuel consumption in current CF6-50 turbofan engines was developed. The feasibility of the roundness and clearance response improvements was demonstrated. Application of these improvements will result in a cruise SFC reduction of 0.22 percent for new engines. For high time engines, the improved roundness and response characteristics results in an 0.5 percent reduction in cruise SFC. A basic life capability of the improved HP turbine stator in over 800 simulated flight cycles without any sign of significant distress is shown