Highly-accurate 5-axis flank CNC machining with conical tools

A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization based approach is then applied to globally minimize the error between the design surface and the conical envelope. Our computer simulation are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software

Structural studies of thermally stable, combustion-resistant polymer composites

Composites of the industrially important polymer, poly(methyl methacrylate) (PMMA), were prepared by free-radical polymerization of MMA with varying amounts (1–30 wt. %) of sodium dioctylsulfosuccinate (Aerosol OT or AOT) surfactant added to the reaction mixture. The composites with AOT incorporated show enhanced resistance to thermal degradation compared to pure PMMA homopolymer, and micro-cone combustion calorimetry measurements also show that the composites are combustion-resistant. The physical properties of the polymers, particularly at low concentrations of surfactant, are not significantly modified by the incorporation of AOT, whereas the degradation is modified considerably for even the smallest concentration of AOT (1 wt. %). Structural analyses over very different lengthscales were performed. X-ray scattering was used to determine nm-scale structure, and scanning electron microscopy was used to determine μm-scale structure. Two self-assembled species were observed: large phase-separated regions of AOT using electron microscopy and regions of hexagonally packed rods of AOT using X-ray scattering. Therefore, the combustion resistance is observed whenever AOT self-assembles. These results demonstrate a promising method of physically incorporating a small organic molecule to obtain a highly thermally stable and combustion-resistant material without significantly changing the properties of the polymer

Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines

Calabro et al. (2017) changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of magnitude faster. Considering a B-spline basis function as a non-negative measure, each mass matrix row is integrated by its own quadrature rule with respect to that measure. Each rule is easy to compute as it leads to a linear system of equations, however, the quadrature rules are of the Newton-Cotes type, that is, they require a number of quadrature points that is equal to the dimension of the spline space. In this work, we propose weighted quadrature rules of Gaussian type which require the minimum number of quadrature points while guaranteeing exactness of integration with respect to the weight function. The weighted Gaussian rules arise as solutions of non-linear systems of equations. We derive rules for the mass and stiffness matrices for uniform C1 quadratic and C2 cubic isogeometric discretizations. Our rules further reduce the number of quadrature points by a factor of (p+12p+1)d when compared to Calabro et al. (2017), p being the polynomial degree and d the dimension of the problem, and consequently reduce the computational cost of the mass and stiffness matrix assembly by a similar factor

Soil contamination in landfills: a case study of a landfill in Czech Republic

A phytotoxicity test was determined to assess ecotoxicity of landfill soil. <i>Sinapis alba</i> L. was used as a bioindicator of heavy metals. Soil samples 1–8, which were taken from the landfill body, edge of the landfill body, and its vicinity meet the limits for heavy metals Co, Cd, Pb, and Zn specified in the applicable legislation. Hg and Mn threshold values are not established in legislation, but values have been determined for the needs of the landfill operator. For heavy metals Cr, Cu, and Ni sample 2 exceeded the threshold values, which attained the highest values of all the samples tested for Cr, Cu, and Ni. For Cr and Ni the values were several times higher than values of the other samples. The second highest values for Cr, Cu, and Ni showed sample 6 and 7. Both samples exceeded the set limits. An increase in plant biomass was observed in plants growing on plates with soil samples, but no changes in appearance, slow growth, or necrotic lesions appeared. Ecotoxicity tests show that tested soils (concentration of 50 %) collected from the landfill body, edge of the landfill body, and its vicinity reach high percentage values of germination capacity of seeds of <i>Sinapis alba</i> L. (101–137 %). At a concentration of 25 %, tested soil samples exhibit lower values of germination capacity – in particular samples 3 to 8 – yet the seed germination capacity in all eight samples of tested soils ranges between 86 and 137 %

Stretch-minimising stream surfaces

We study the problem of finding stretch-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a stretch minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In general fields, such curves may not exist. How-ever, the divergence-free constraint gives rise to these 'stretch-free' curves that are locally arc-length preserving when infinitesimally propagated. Several families of stretch-free curves are identified and used as initial guesses for stream surface generation. These surfaces are subsequently globally optimised to obtain the best stretch-minimising stream surfaces in a given divergence-free vector field. Our algorithm was tested on benchmark datasets, proving its applicability to incompressible fluid flow simulations, where our stretch-minimising stream surfaces realistically reflect the flow of a flexible univariate object