Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

Optimum sweeps of simple polygons with two guards

A polygon P admits a sweep if two mobile guards can detect an unpredictable, moving target inside P  , no matter how fast the target moves. Two guards move on the polygon boundary and are required to always be mutually visible. The objective of this study is to find an optimum sweep such that the sum of the distances travelled by the two guards in the sweep is minimized. We present an O(n²)$O(n^2)$ time and O(n)$O(n)$ space algorithm for optimizing this metric, where n   is the number of vertices of the given polygon. Our result is obtained by reducing this problem to finding a shortest path between two nodes in a graph of size O(n)$O(n)$.     

Comparison of the Effect of a Hydrocarbon Oil and a Terpene Tackifier on the Autohesion of Styrene-Butadiene Rubber

Blends of uncrosslinked styrene-butadiene rubber (SBR) with a terpene tackifier resin or a naphthenic oil have been characterized, and their autohesion and cohesion determined using a T-peel geometry. SBR/oil blends are homogeneous at all proportions, while SBR/resin blends, based on DSC and DMA analysis, undergo bulk phase separation at about 50% resin. However, migration of tackifier to the surface region is proposed at much lower resin contents. Compositions diluted with oil have autohesion similar to the neat SBR. This is attributed to compensating effects; although oil hastens self-bond formation by increasing chain mobility, this is nearly equally balanced by more facile chain separation during bond rupture. In short, oil-diluted compositions are soft and weak. On the other hand, SBR compositions containing small amounts of resin have high autohesion. Resin-diluted specimens deform easily at low strain, just as those containing oil, but intertwined chains of the former have greater resistance to separation, due at least in part to higher glass transition temperatures. It is proposed that autohesion is further enhanced by migration of tackifier to the surface. This causes SBR/resin compositions to be both soft and strong-a necessary condition for high autohesion.     

Relationship between Viscoelastic and Peeling Properties of Model Adhesives. Part 1. Cohesive Fracture

The viscoelastic and peeling properties of polybutadiene/tackifying resin compatible blends have been studied in detail. Viscoelastic properties have been described through the variations of the complex shear modulus, G*(ω), as a function of frequency, ω and peeling properties through the variations of peeling force (F) as a function of peeling rate (V).

After showing the objective character of the peeling curves obtained, the variations of the peeling force and peeling geometry have been studied as a function of volume fraction of the tackifying resin.

In this first paper, the analysis is focused on the first domain of the peeling curves, i.e. the cohesive fracture region. In this region, the peeling properties have been related to the viscoelastic properties in the terminal region of relaxation. It is shown that the longest relaxation time, τ_o, is a reducing parameter of the peeling curves, so a peeling master curve-which is independent of temperature, resin volume fraction and polymer molecular weight-may be defined. Furthermore, the variations of the test geometry as a function of peeling rate have been investigated: the variations of the radius of curvature of the aluminium foil have been analyzed with respect to the viscoelastic behavior of the adhesive, which in fact governs the test geometry.

A detailed analysis of all these features leads to a model which allows one to calculate the peeling curves in the cohesive domain from the adhesive formulation.     

Jet bundle formulation of infinite-dimensional port-Hamiltonian systems using differential operators

We consider infinite-dimensional port-Hamiltonian systems described on jet bundles. Based on a power balance relation we introduce the port-Hamiltonian system representation using differential operators regarding the structural mapping, the dissipation mapping and the input mapping. In contrast to the well-known representation on the basis of the underlying Stokes–Dirac structure our approach is not necessarily based on using energy-variables which leads to a different port-Hamiltonian representation of the analyzed partial differential equations. The presented constructions will be specialized to mechanical systems to which class also the presented examples belong.     

Failure load prediction of structural adhesive joints : Part 2: Experimental study

The objective of this study was to determine how the fracture of adhesive joints depends on elastic beam parameters describing the adherends and the applied loads. The basic specimen geometry was the cracked lap shear joint constructed of aluminium alloy with various adherend and bondline thicknesses. Loads were applied in different combinations of bending, tension and shear to generate a failure envelope for each adhesive and specimen geometry. It was found that crack propagation for precracked specimens occured at a critical strain energy release rate but was also a function of the G_I/G_II ratio and the bondline thickness. The experiments also showed that the loads required to propagate a crack in a precracked specimen were always lower than the loads required to break the fillet. Hence, by treating uncracked joints as being cracked, where the fictitious crack tip is assumed to coincide with the location of the fillet, a conservative estimate of the failure load is obtained.     

Order-k α-hulls and α-shapes

We introduce order-k α-hulls and α-shapes – generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape produces an “inner” shape of the set, with the amount of “digging” into the points controlled by k. As a generalization of k-hull, order-k α-hull is capable of determining “deep” points amidst samples from a multimodal distribution: it correctly identifies points which lie outside clusters of samples.The order-k α-hulls and α-shapes are related to order-k Voronoi diagrams in the same way in which α-hulls and α-shapes are related to Voronoi diagrams. This implies that order-k α-hull and α-shape can be readily built from order-k Voronoi diagram, and that the number of different order-k α-shapes for all possible values of α is proportional to the complexity of order-k Voronoi diagram.     

Effect of granule size and the placement geometry on the efficiency of urea supergranules for wetland rice grown on a permeable soil

In a laboratory experiment 5 cm depth of water was allowed to percolate daily down through a 15 cm thick soil (Typic Ustipsamment) layer. It was observed that leaching losses of urea supergranules (USG)-N could be decreased by about 20% by the placement of four 0.25 g granules at four points instead of one 1 g granule at one point. In field microplots, the placement of approximately 30 granules of 0.30 g size instead of 9 granules of 1.00 g size resulted in reduced leaching of USG-N and, in turn, increased rice yield. In a follow-up field study, the advantage of more frequently placed USG was confirmed. As compared with 1 g USG placed in the usual manner in the center of four rice hills, increasing the density of placement in soil produced 15% more rice grain. Further increase in rice yield could be obtained by increasing the number of USG placed in the soil and decreasing the size of the granule from 1.00 g to 0.70 or 0.35 g. With USG of 0.35 and 0.70 g yields were equal or sometimes even slightly higher than with split application of prilled urea on a heavily percolating, low-CEC, light-textured soil.     

A Projective Framework for Polyhedral Mesh Modelling

We present a novel framework for polyhedral mesh editing with face‐based projective maps that preserves planarity by definition. Such meshes are essential in the field of architectural design and rationalization. By using homogeneous coordinates to describe vertices, we can parametrize the entire shape space of planar‐preserving deformations with bilinear equations. The generality of this space allows for polyhedral geometric processing methods to be conducted with ease. We demonstrate its usefulness in planar‐quadrilateral mesh subdivision, a resulting multi‐resolution editing algorithm, and novel shape‐space exploration with prescribed transformations. Furthermore, we show that our shape space is a discretization of a continuous space of conjugate‐preserving projective transformation fields on surfaces. Our shape space directly addresses planar‐quad meshes, on which we put a focus, and we further show that our framework naturally extends to meshes with faces of more than four vertices as well.