Use BiArc-curves for contour description of the turbine profiles

В работе рассмотрена возможность использования BiArc-кривых для математического описания турбинных профилей. Приведены элементы теории построения BiArc-кривых. Рассмотрены особенности описания контуров выпуклой и вогнутой частей турбинных профилей с помощью BiArc-кривых. Описан алгоритм автоматического построения контуров турбинных профилей с использованием геометрического критерия качества. Приведены примеры построения турбинных профилей с использованием BiArc-кривых с различными исходными данными.The article analyzes the possibility of using BiArc-curves for the mathematical description of turbine profiles. Confirmed the relevance of the application BiArc-curves in the manufacture of turbine blades. The article presents some of the elements of the theory of building BiArc-curves. The algorithm for determining the coordinates of conjugate points, radii and angles of opening arcs BiArc-curve is shown in the work. Strong influence on the quality of BiArc-curve, provide the coordinates of the point arc connection. Also, the description of certain structural features of convex and concave contours profiles turbines using BiArc-curves. Here the algorithm of automatic construction of a turbine profile using geometric criteria of quality. Optimization problem is solved for each element BiArc-curve using a quadratic fit DSC-Powell. Method of construction of turbine profiles using BiArc-curves programmed in the language c++. Screenshot of dialog boxes and graphics programs can be found in the article. The examples of constructing profiles turbines using BiArc-curves with different initial data. Received confirmation of the possibility to describe the contours of turbine profiles using BiArc-curves

Designing heterogeneous porous tissue scaffolds for additive manufacturing processes

A novel tissue scaffold design technique has been proposed with controllable heterogeneous architecture design suitable for additive manufacturing processes. The proposed layer-based design uses a bi-layer pattern of radial and spiral layers consecutively to generate functionally gradient porosity, which follows the geometry of the scaffold. The proposed approach constructs the medial region from the medial axis of each corresponding layer, which represents the geometric internal feature or the spine. The radial layers of the scaffold are then generated by connecting the boundaries of the medial region and the layer's outer contour. To avoid the twisting of the internal channels, reorientation and relaxation techniques are introduced to establish the point matching of ruling lines. An optimization algorithm is developed to construct sub-regions from these ruling lines. Gradient porosity is changed between the medial region and the layer's outer contour. Iso-porosity regions are determined by dividing the subregions peripherally into pore cells and consecutive iso-porosity curves are generated using the isopoints from those pore cells. The combination of consecutive layers generates the pore cells with desired pore sizes. To ensure the fabrication of the designed scaffolds, the generated contours are optimized for a continuous, interconnected, and smooth deposition path-planning. A continuous zig-zag pattern deposition path crossing through the medial region is used for the initial layer and a biarc fitted isoporosity curve is generated for the consecutive layer with C-1 continuity. The proposed methodologies can generate the structure with gradient (linear or non-linear), variational or constant porosity that can provide localized control of variational porosity along the scaffold architecture. The designed porous structures can be fabricated using additive manufacturing processes

Functionally gradient tissue scaffold design and deposition path planning for bio-additive processes

A layer-based tissue scaffold is designed with heterogeneous internal architecture. The proposed layer-based design uses a bi-layer pattern of radial and spiral layer consecutively to generate functionally gradient porosity following the geometry of the scaffold. Medial region is constructed from medial axis and used as an internal geometric feature for each layer. The radial layers are generated with sub-region channels by connecting the boundaries of the medial region and the layer’s outer contour. Proper connections with allowable geometric properties are ensured by applying optimization algorithms. Iso-porosity regions are determined by dividing the sub-regions into pore cells. The combination of consecutive layers generates the pore cells with desired pore sizes. To ensure the fabrication of the designed scaffolds, both contours have been optimized for a continuous, interconnected, and smooth deposition path-planning. The proposed methodologies can generate the structure with gradient (linear or non-linear), variational or constant porosity that can provide localized control of variational porosity along the scaffold architecture. The designed porous structures can be fabricated using bio-additive fabrication processes

Applying inversion to construct rational spiral curves

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including those, assuming inflection.Comment: 18 pages, 11 figure