Cusp Volume Research Articles

Adaptive variable layer thickness and perimetral offset planning for layer-based additive manufacturing processes

ABSTRACT This paper presents a methodology to estimate and optimize the process of slicing for a layer-based additive manufacturing process. An objective function for optimizing the process planning parameters is proposed in which perimetral offsets for each layer are considered as a parameter in addition to the layer thickness. The root-mean-square (RMS) value of the deviations between the NURBS representation of the CAD model and its built-up simulation is suggested to estimate a quantitative measure for the uncertainties. The proposed approach eliminates the sophistication of the calculation cusp volume in 3D space and has more compatibility with the corresponding inspection processes. The developed methodology is introduced based on using a metaheuristic algorithm to find the optimal layer thicknesses and perimetral offsets for a built-up model. A data collecting approach is also introduced to reduce the computation time associated with the simulation of the build-up model at each iteration. The developed methodology potentially can be used for layer-based additive manufacturing processes

The Wear Behavior of Various Monolithic Ceramics after Wear Simulation against Human Enamel.

Abstract Purpose: To evaluate and compare the surface roughness (SR), weight loss and volume loss of three monolithic ceramics; monolithic zirconia functional explore (f.explore), lithium disilicate glass ceramic (IPS.e. max CAD), and lithium silicate (Obsidian) and their wear effect on the natural enamel. Materials and Methods Twenty four ceramic disc and twenty four natural tooth antagonist were used. Samples were divided according to ceramic materials into 3 groups (n=8). Group I: f.explore, Group II: Obsidian, and Group III: IPS e.max CAD. SR, weight loss and volume loss of the discs and the enamel were verified before and after exposing the specimens to chewing simulator. Digital and Scanning electron microscopic evaluations were used. Results: The roughness differences changes between all groups was non-significant. While Obsidian antagonist cusp recorded the highest roughness followed by f.explore, whereas, e.max recorded least value. The greatest mean weight loss of materials was recorded in e. max followed by f.explore, where the lowest was recorded for Obsidian significantly.The greatest mean weight loss for antagonist cusp was recorded for f.explore followed by obsidian with insignificant difference ,while the lowest weight loss significantly was recorded in e.max antagonist cusp . The greatest mean volume loss of materials was recorded in e. max followed by f.explore where Obsidian recorded least value significantly. The greatest mean antagonist cusp volume loss was recorded in f.explore followed by e.max , whereas obsidian recorded least value. Conclusions: Obsidian is more wear resistant than e.max and f.explore and produced the least wear in opposing enamel.

Rotating ice cusps on ship's bow shoulder: Full-scale study on the cusp sizes and corresponding peak loads in different ice and operational conditions

The ice loads occurring in ship-ice interaction are uncertain for many reasons. This article addresses some of those uncertainties by studying adjacent frames and identifying cases where the peak ice load occurs on a certain frame. In these cases, we looked at photos of ice to identify what type of an ice response caused the load to peak. We further selected the cases where the peak load was caused by a rotation of an already broken ice cusp. This rotation allowed us to measure the cusp dimensions from the photos, which enabled us to study two research questions. First, how the cusp area distribution is affected by the ice thickness and ship speed. Second, how the peak load distribution is affected by the cusp dimensions and ship speed. Both of these questions were modeled with hierarchical Bayesian models, where the Gaussian process priors compel the distribution parameters to smoothly change in varying conditions. The models predict that the cusp area increases with increasing ice thickness and deceasing ship speed, whereas the peak load increases with increasing cusp volume and decreasing ship speed. The models were tested with posterior predictive checks, which demonstrated good agreement with the models and the measurements.

Developmental origins for semilunar valve stenosis identified in mice harboring congenital heart disease-associated GATA4 mutation.

ABSTRACTCongenital heart defects affect ∼2% of live births and often involve malformations of the semilunar (aortic and pulmonic) valves. We previously reported a highly penetrant GATA4 p.Gly296Ser mutation in familial, congenital atrial septal defects and pulmonic valve stenosis and showed that mice harboring the orthologous G295S disease-causing mutation display not only atrial septal defects, but also semilunar valve stenosis. Here, we aimed to characterize the role of Gata4 in semilunar valve development and stenosis using the Gata4G295Ski/wt mouse model. GATA4 is highly expressed in developing valve endothelial and interstitial cells. Echocardiographic examination of Gata4G295Ski/wt mice at 2 months and 1 year of age identified functional semilunar valve stenosis predominantly affecting the aortic valve with distal leaflet thickening and severe extracellular matrix (ECM) disorganization. Examination of the aortic valve at earlier postnatal timepoints demonstrated similar ECM abnormalities consistent with congenital disease. Analysis at embryonic timepoints showed a reduction in aortic valve cushion volume at embryonic day (E)13.5, predominantly affecting the non-coronary cusp (NCC). Although total cusp volume recovered by E15.5, the NCC cusp remained statistically smaller. As endothelial to mesenchymal transition (EMT)-derived cells contribute significantly to the NCC, we performed proximal outflow tract cushion explant assays and found EMT deficits in Gata4G295Ski/wt embryos along with deficits in cell proliferation. RNA-seq analysis of E15.5 outflow tracts of mutant embryos suggested a disease state and identified changes in genes involved in ECM and cell migration as well as dysregulation of Wnt signaling. By utilizing a mouse model harboring a human disease-causing mutation, we demonstrate a novel role for GATA4 in congenital semilunar valve stenosis.This article has an associated First Person interview with the joint first authors of the paper.

Intelligent Process Planning for Additive Manufacturing

Abstract This paper introduces an intelligent approach for process planning of additive manufacturing (AM) in digital environment. A global adaptive slicing algorithm is developed and embedded in the introduced concept, which determines the layer thicknesses and widths based on the minimization of the deviations between the CAD model boundary and its stepped approximation. It is discussed that there are different metrics to measure the deviations such as cusp height, cusp volume and surface roughness criteria. A new criterion is developed to globally minimize the overall volumetric deviations of the final product from the desired geometric model. The proposed methodology uses the locally optimized layer thicknesses as the inputs to calculate the globally optimized layer thicknesses and the optimal contour for each layer. The global optimization problem is highly nonlinear that can be solved with a metaheuristic algorithm such as Simulated Annealing.

Densities of hyperbolic cusp invariants of knots and links

We find that cusp densities of hyperbolic knots in S 3 S^3 include a dense subset of [ 0 , 0.6826 … ] [0,0.6826\dots ] and those of links are a dense subset of [ 0 , 0.853 … ] [0,0.853\dots ] . We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between the cusp volume and the crossing number of a link, and show that cusp crossing density for links is bounded above by 3.1263 … 3.1263\dots . Moreover, there is a sequence of links with cusp crossing density approaching 3. For two-component hyperbolic links, cusp crossing density is shown to include a dense subset of the interval [ 0 , 1.6923 … ] [0,1.6923\dots ] and for all hyperbolic links, cusp crossing density is shown to include a dense subset of [ 0 , 2.120 … ] [0, 2.120\dots ] .

Geometric estimates from spanning surfaces

We derive bounds on the length of the meridian and the cusp volume of hyperbolic knots in terms of the topology of essential surfaces spanned by the knot. We provide an algorithmically checkable criterion that guarantees that the meridian length of a hyperbolic knot is below a given bound. As applications we find knot diagrammatic upper bounds on the meridian length and the cusp volume of hyperbolic adequate knots and we obtain new large families of knots with meridian lengths bounded above by four. We also discuss applications of our results to Dehn surgery.

Cusp volumes of alternating knots

We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some applications to Dehn surgery. Another consequence is that there is a universal lower bound on the cusp density of hyperbolic alternating knots.

Similar fillings and isolation of cusps of hyperbolic 3-manifolds

We deepen the analysis of certain classes Mg,k of hyperbolic 3-manifolds that were introduced in a previous work by B. Martelli, C. Petronio and the author. Each element of Mg,k is an oriented complete finite-volume hyperbolic 3-manifold with compact connected geodesic boundary of genus g and k cusps. We prove that several elements in Mg,k admit nonhomeomorphic hyperbolic Dehn fillings sharing the same volume, homology, cusp volume, cusp shape, Heegaard genus, complex length of the shortest geodesic, length of the shortest return path, and Turaev?Viro invariants. Let N be a complete finite-volume hyperbolic 3-manifold with (possibly empty) geodesic boundary and cusps C1,?,Ch,Ch+1,?,Ck. According to Neumann and Reid, the cusps C1,?,Ch are said to be geometrically isolated from Ch+1,?,Ck if any small deformation of the hyperbolic structure on N induced by Dehn filling Ch+1,?,Ck does not affect the Euclidean structure at C1,?,Ch. We show here that the cusps of any manifold in Mg,k are geometrically isolated from each other. On the contrary, any element in Mg,k admits an infinite family of hyperbolic Dehn fillings inducing nontrivial deformations of the hyperbolic structure on the geodesic boundary.

Cusp size bounds from singular surfaces in hyperbolic 3-manifolds

Singular maps of surfaces into a hyperbolic 3-manifold are utilized to find upper bounds on meridian length, ℓ \ell -curve length and maximal cusp volume for the manifold. This allows a proof of the fact that there exist hyperbolic knots with arbitrarily small cusp density and that every closed orientable 3-manifold contains a knot whose complement is hyperbolic with maximal cusp volume less than or equal to 9. We also find particular upper bounds on meridian length, ℓ \ell -curve length and maximal cusp volume for hyperbolic knots in S 3 \mathbb {S}^3 depending on crossing number. Particular improved bounds are obtained for alternating knots.

The application of an inclined end mill machining strategy on 3-axis machining centres

An inclined end mill machining strategy offers an effective machining method for manufacturing low curvature free-form surfaces. The machined surface profile is a close match to the required surface geometry, and standard end mills are available at competitive prices. The amount of surface finishing work is therefore reduced, and the inclined cutting action prolongs the tool life. Although this machining strategy has these advantages, it is not commonly used in manufacturing industry, because it needs the facilities of costly 5-axis machining centres and appropriate post processors are required to generate the NC codes for these advanced machine tools. This paper proposes a simple method which extends the machining capability of the conventional 3-axis machining centre to give the same specifications as a 5-axis machine, and therefore allow the inclined end mill machining strategy to be used on 3-axis machines. The method involves tilting the workpiece instead of tilting the end mill during the machining process. The tool paths are determined by the workpiece rotation and cutter contact point offset equations. The amount of excess material on the machined surface is minimized by choosing optimum pitching and rolling angles at the work set-up stage. The experimental results indicate that the quality of the machined surfaces is improved in comparison with the surfaces machined by ball-nosed cutters, e.g. the resulting cusp volume is reduced by 64%. The research suggests that the need for advanced and expensive 5-axis machining could be satisfied in a more economical machining environment. As a result, the machining cost of the products may be significantly reduced.

Hyperbolic Invariants of Knots and Links

Tables of values for the hyperbolic volume, number of symmetries, cusp volume and conformal invariants of the cusps are given for hyperbolic knots through ten crossings and hyperbolic links of $2, 3$ and $4$ components through $9$ crossings. The horoball patterns and the canonical triangulations are displayed for knots through eight crossings and for particularly interesting additional examples of knots and links.

Hyperbolic invariants of knots and links

Tables of values for the hyperbolic volume, number of symmetries, cusp volume and conformal invariants of the cusps are given for hyperbolic knots through ten crossings and hyperbolic links of 2 , 3 2, 3 and 4 4 components through 9 9 crossings. The horoball patterns and the canonical triangulations are displayed for knots through eight crossings and for particularly interesting additional examples of knots and links.