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Ceramic ferrule, which is a major part of fiber optic connectors, requires a high level of precision in the grinding process. Recently, the requirements for high precision and efficiency have gradually increased to match the international competitiveness within the industrial fields of grinding machine. This trend has had a significant effect on industrial fields. In this study, the effects of the grinding conditions regarding the roundness of ZrO₂ ferrule, that apply to the optical fiber connector, were analyzed and measured using the effects of a run-out for the rotation speed of a spindle, the mesh number of a grindstone and the feed rate. Experiments were performed to determine the optimal grinding conditions according to each grinding factor.

We study (1+ε)-factor approximation algorithms for several well-known optimization problems on a given n-point set: (a) diameter, (b) width, (c) smallest enclosing cylinder, and (d) minimum-width annulus. Among our results are new simple algorithms for (a) and (c) with an improved dependence of the running time on ε, as well as the first linear-time approximation algorithm for (d) in any fixed dimension. All four problems can be solved within a time bound of the form O(n+ε^-c) or O(nlog(1/ε)+ε^-c).

In this paper we address the problem of computing the thinnest annulus containing a set of points S ⊂ R^d. For d = 2, we show that the problem can be solved in O(n) expected time for a fairly general family of almost round sets, by using a slight modification of Sharir and Welzl's algorithm for solving LP-type problems. We also show that, for points in convex position, the problem can be solved in (O(n) deterministic time using linear programming. For d = 2 and d = 3, we propose a discrete local optimization approach. Despite the extreme simplicity and worst case O(n^d+1) complexity of the algorithm, we give empirical evidence that the algorithm performs very well (close to linear time) if the input is almost round. We also present some theoretical results that give a partial explanation of this behavior: although the number of local minima may be quadratic (already for d = 2), almost round configurations of points having more than one local minimum are very unlikely to be encountered in practice.

Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.

Let S be a set of points in the plane. The width (resp. roundness) of S is defined as the minimum width of any slab (resp. annulus) that contains all points of S. We give a new characterization of the width of a point set. Also, we give a rigorous proof of the fact that either the roundness of S is equal to the width of S, or the center of the minimum-width annulus is a vertex of the closest-point Voronoi diagram of S, the furthest-point Voronoi diagram of S, or an intersection point of these two diagrams. This proof corrects the characterization of roundness used extensively in the literature.

The selection of appropriate drilling parameters is essential for improving productivity and part quality, therefore, this work mainly concentrates on the investigation of drilling time, burr height, burr thickness, roundness and surface roughness. The drilling experiments were carried out on Magnesium (Mg) AZ91 with High Speed Steel (HSS) tool using the Vertical Milling Machine (VMM). The parameters reckoned are spindle speed and feed rate. Artificial Neural Network (ANN) was concerned with the building of the model that will be used to forecast the responses following the consideration of Response Surface Methodology (RSM). Conventional method of modeling (RSM) yields poorer results which redirected the study with ANN. The Genetic Algorithm (GA)-based ANN has been reckoned for developing the model. With two nodes in the parameter layer and seven nodes in the response layer, six different networks were constructed using variety of nodes in the hidden layers which are 2–6–7, 2–7–7, 2–8–7, 2–6–6–7, 2–7–6–7 and 2–8–6–7. It is observed that the 2–8–7 network offers the best ANN model in predicting the various responses. The prediction results ensure the reliability of the ANN model to analyze the effect of drilling parameters over the various responses.

The single-point incremental forming has been globally accepted as an advanced method of sheet metal forming due to its rapid prototyping and economic benefits. The process has sensitively released the practice of using expensive dies, making it suitable for manufacturing custom-built products in tiny batches. Further, it is getting acceptance in producing parts of shabby machinery. In recent years, superalloys have become the most commonly used materials in the transportation, automotive, aeronautics and marine industries due to their fundamental and structural applications. The input parameters considered in this study are step size, feed rate and tool spindle speed. The effects of all three process parameters on the geometrical accuracy of Inconel 625 superalloy conical parts formed by the single-point incremental forming process are considered in this work. The deviations in roundness, concentricity, half-cone angle and straightness from the target values were considered as response parameters to measure the accuracy. The results showed that the part accuracy could be enhanced by using minimum step size, feed rate and maximum tool spindle speed.

We investigate faithful unitary representations for Polishable ideals, or more generally abelian Polish groups. We give various characterizations for the existence of such representations. The main technical result is to show that the density ideal does not admit any faithful unitary representations.