Generalized optimal lattice covering of finite-dimensional Euclidean space

A generalization of the classical problem of optimal lattice covering of R-n is considered. Solutions to this generalized problem are found in two specific classes of lattices. The global optimal solution of the generalization is found for R-2. (C) 1998 Elsevier Science Inc. All rights reserved.

Surface characterization of 6H-SiC (0001) substrates in indentation and abrasive machining

Surface characterization of 6H-SiC (0001) substrates in indentation and abrasive machining was carried out to investigate microfracture, residual damage, and surface roughness associated with material removal and surface generation. Brittle versus plastic deformation was studied using Vickers indention and nano-indentation. To characterize the abrasive machining response, the 6H-SiC (0001) substrates were ground using diamond wheels with grit sizes of 25, 15 and 7 mum, and then polished with diamond suspensions of 3 and 0.05 mum. It is found that in indentation, there was a scale effect for brittle versus plastic deformation in 6H-SiC substrates. Also, in grinding, the scales of fracture and surface roughness of the substrates decreased with a decrease in diamond grit size. However, in polishing, a reduction in grit size of diamond suspensions gave no significant improvement in surface roughness. Furthermore, the results showed that fracture-free 6H-SiC (0001) surfaces were generated in polishing with the existence of the residual crystal defects, which were associated with the origin of defects in single crystal growth. (C) 2003 Elsevier Ltd. All rights reserved.

Machining of micro aspherical mould inserts

This paper reports a parametric investigation and development of grinding technologies for micro aspherical mould inserts using parallel grinding method. The parametric investigation revealed that at nanometric scale the undeformed chip thickness has little influence on the surface finish of ground inserts. The grinding trace spacing has a slightly larger influence on the surface finish. A new technique was developed to true and dress the resin bonded micro wheels with mesh size of #3000, which produced a satisfactory wheel form accuracy and relatively high grain packing density. A form error compensation technique was also developed, with which mould inserts of submicron form accuracy were consistently produced. Using the developed technologies, micro aspherical inserts of diameters ranging from 200 mu m to 1000 mu m with surface finish of around 10 nm and form error of similar to 0.2-0.4 mu m were successfully fabricated. (c) 2005 Elsevier Inc. All rights reserved.

Effect of hardness on three very different forms of wear

Different abrasive wear tests have been applied to materials with hardnesses ranging from 80 HV (aluminium) to 1700 HV (tungsten carbide). The tests were: dry sand rubber wheel (DSRbrW); a similar test using a steel wheel (DSStlW); a new combined impact-abrasion test (FIA). The DSRbrW results were as expected, giving generally decreasing wear with increasing hardness. White cast irons and tool steels containing coarse, hard carbide particles performed better than more homogeneous materials of comparable hardness. When normalized to load and distance, the DSStlW results for the homogeneous materials were similar to the DSRbrW results. The multi-phase materials performed poorly in the DSStlW test, with volume loss for high-speed steel (880 HV) higher than that of aluminium. Within this group, wear increased with increasing hardness. These unexpected results are explained in terms of (a) differential friction coefficients of wheel and specimen, (b) increased fracture of sand, and (c) introduction of microfracture wear mechanisms. The FIA combined impact-abrasion results lacked clear correlations with hardness. The span of relative wear rates was similar to that reported for materials in ball mills. White cast irons at maximum hardness performed fairly poorly and showed evidence of microfracture. (C) 1997 Elsevier Science S.A.

Laboratory wear testing of polyurethane elastomers

A dry sand-rubber wheel abrasion test was used to investigate the wear behaviour of polyurethanes. The dry sand-rubber wheel abrasion test (DSRW test) is an approved ASTM test designed primarily for testing metals, therefore, in this study the set of test conditions was optimized for use with polyurethane elastomers. The wear performance of polyurethanes was assessed for the range of Shore hardness 85A to 65D, and a correlation was identified between the wear rate and the sample hardness. Polyurethane elastomers can be separated into three classes according to their hardness and wear performance, and each class shows a different dependence on the specimen temperature. This work has implications for use of the DSRW test for the prediction of field performance of polyurethanes. (C) Elsevier Science S.A.

A fuzzy max-flow min-cut theorem

Interval-valued versions of the max-flow min-cut theorem and Karp-Edmonds algorithm are developed and provide robustness estimates for flows in networks in an imprecise or uncertain environment. These results are extended to networks with fuzzy capacities and flows. (C) 2001 Elsevier Science B.V. All rights reserved.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.