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Rain erosion induced by raindrops impacting wind turbine blades at high velocity can change the aerodynamic characteristics of the blades and increase maintenance costs. Previous numerical studies on rain erosion have not considered the curvature of the blade leading-edge surfaces and assumed them to be flat surfaces. This study established a fluid-solid coupled numerical model combining the finite element method and smooth particle hydrodynamics. It models a water droplet with a diameter of 2.74 mm impacting the curved leading-edge surface of wind turbine blades with radii of curvature of 1.35 mm, 6.75 mm, 67.5 mm, and infinite at 110 m/s, and the effects of the radius of curvature on the impact response were analyzed. The results show that as the radius of curvature of the leading-edge surface increases, the surface obstructs the water droplet more significantly, and the lateral jetting of the water droplet is enhanced. A larger radius of curvature causes more droplet impact energy to be transferred to the curved surface, increasing the contact force between the water droplet and the surface. The increased transferred impact energy results in higher stress and plastic strain values. The decrease in the radius of curvature of a curved surface increases the error in the stress and strain results obtained by assuming it to be a flat surface.

ABSTRACTWire and Arc Additive Manufacturing (WAAM) with high efficiency and low-cost is an economical choice for the rapid fabrication of medium-to-large-sized metallic components and has attracted great attention from scholars and entrepreneurs in recent years. However, defects such as porosity, and humps, could occur occasionally after each layer of deposition on weld bead surfaces due to disturbances and process abnormities. Detection and quantitative evaluation of weld bead defects is crucial to ensure successful deposition and the quality of the entire component. In this paper, a novel defect detection and evaluation system was developed for WAAM utilizing machine vision technology. The system incorporated new defect detection algorithms based on analysing the 2D curvature of the weld bead height curve and the 3D curvature of the weld bead point cloud. Furthermore, a defect evaluation algorithm was developed based on reconstructing the normal weld bead contour using geometric features extracted from the accumulated point cloud. This system enables the automatic detection of weld bead morphology during the WAAM process, offering important information about the location, type, and volume of defects for effective interlayer repairs and enhanced part quality.

A method of forming a curved orthogonal coordinate system on a plane and a technique of constructing new surface shapes with curved trapezoidal plans are presented. Multiple examples of curved trapezoidal plans based on different directrix curves and surfaces with the given plans, including combinations of surfaces with different conjugate directrix curves, are illustrated. The proposed technique of surface forming may be used in architecture and construction for development of thin-walled space structures in both urban and industrial buildings. But for the analysis of thin shells, geometric characteristics of the middle surface of the shell are usually used. Vector equation of surfaces with curved trapezoidal plan was used to obtain the formulas for the fundamental form coefficients and surface curvatures. Examples of calculation of the fundamental form coefficients and curvatures of surfaces with particular directrix curves and vertical coordinate functions are presented.

The curvature variation regularity of the blade surface is complex and requires a high level of machining accuracy. In order to research the influence of interpolation tolerance on the machining accuracy of blade surface at different positions, the non-uniform rational b-spline was used to build the blade surface and analyze the curvature variation regularity at different positions, and the distribution regularity of interpolation tolerance at different curvature positions on interpolation moving points was explored based on the NC (Numerical Control) program. In addition, the NC interpolation principle is used to analyze the effect of different interpolation tolerance parameters on the machining accuracy of blade surfaces, and the appropriate interpolation moving point coordinates were obtained through the five-axis coordinate system transformation theory, and the five-axis cutting simulation and experiment were carried out. The results show that there are many interpolation moving points at the position with large curvature. With interpolation tolerances of 0.1 mm, 0.03 mm and 0.003 mm, the interpolation errors obtained in the regions with large curvature are 0.005 mm, 0.0034 mm and 0.0025 mm, respectively. The smaller the interpolation tolerance, the smaller the interpolation error. What is more, the smaller the interpolation tolerance is, the more obvious the improvement of interpolation accuracy will be when the interpolation tolerance is reduced. Besides, when sampling length of 250 μm, the surface roughness (Ra) detected at the small curvature position and the large curvature position are 0.434 and 1.070μm respectively. The surface roughness is better in position with smaller curvature, however, it is worse in position with larger curvature. The analytical regularity is in good agreement with both simulation and experiment values. It provides a reference for improving NC machining accuracy for similar blade surfaces.

Understanding bone surface curvatures is crucial for the advancement of bone material design, as these curvatures play a significant role in the mechanical behavior and functionality of bone structures. Previous studies have demonstrated that bone surface curvature distributions could be used to characterize bone geometry and have been proposed as key parameters for biomimetic microstructure design and optimization. However, understanding of how bone surface curvature distributions correlate with bone microstructure and mechanical properties remains limited. This study hypothesized that bone surface curvature distributions could be used to predict the microstructure as well as mechanical properties of trabecular bone. To test the hypothesis, a convolutional neural network (CNN) model was trained and validated to predict the histomorphometric parameters (e.g., BV/TV, BS, Tb.Th, DA, Conn.D, and SMI), geometric parameters (e.g., plate area PA, plate thickness PT, rod length RL, rod diameter RD, plate-to-plate nearest neighbor distance NNDPP, rod-to-rod nearest neighbor distance NNDRR, plate number PN, and rod number RN), as well as the apparent stiffness tensor of trabecular bone using various bone surface curvature distributions, including maximum principal curvature distribution, minimum principal curvature distribution, Gaussian curvature distribution, and mean curvature distribution. The results showed that the surface curvature distribution-based deep learning model achieved high fidelity in predicting the major histomorphometric parameters and geometric parameters as well as the stiffness tenor of trabecular bone, thus supporting the hypothesis of this study. The findings of this study underscore the importance of incorporating bone surface curvature analysis in the design of synthetic bone materials and implants.

The problem of the size dependence of physical properties is one of the most intriguing when we transit to the nano-level. Experiments have shown that this effect is characteristic of the elastic modulus of many polymeric nanofibers obtained by electrospinning. Existing explanations of this effect did not offer a general understanding of the physical nature of this phenomenon. In this study, we propose a universal model of this phenomenon. We consider the structure of fibers within the framework of the core-shell model, in which the shell is approximated by a thin elastic surface. The analysis of deformation is based on the fundamental laws of the mechanics of deformation of twisted thin shells and, unlike the theories proposed earlier, does not require any additional artificial arguments. This approach made it possible to obtain a simple analytical expression for the size dependence of the elastic modulus, which represents it as the sum of the bulk modulus of the core and two additional moduli proportional to D–1 and D–3, respectively. The resulting model corresponds to all available (from published sources) experimental data, related to polymer of very different chemical structure, and therefore can be considered as universal.

The main goal of this study is determining the influence of surface curvature on 3D scanning accuracy of dental castings. The hypothesis is that 3D scanning errors occur on the geometry (surfaces) of a higher curvature on the dental anatomy. Ten dental castings (five mandibular and five maxillar) were 3D scanned with four different dental 3D scanners. As a reference device Atos Core industrial 3D scanner was used. Using a qualitative-quantitative approach of dividing every tooth in three areas (OS - occlusal surface, CSB - crown surface buccal side, CSP - crown surface palatal side) and observing the frequency of maximal deviation for each area a deviation map was obtained, which shows on what area, are the biggest deviations and in which frequency they emerge. In total 160 teeth were analysed. To conclude, 3D scanning errors occur more frequently on the geometry (surfaces) of a higher curvature on the dental anatomy. Future work suggests conducting a full numerical analysis to find a correlation between the accuracy of 3D scanned teeth surface and a surface curvature. Comparing the 3D scanning deviation to the calculated curvature of the surface could unveil which curvature is hard to 3D scan and generates errors.

Scaffold surface curvature is crucial to guide cell growth and form tissues, and the Young’s modulus of an implant should match the tissue in the implant site. Usually, the curvature and modulus are coupled with volume fraction. Inspired by the lattice slip phenomenon, we propose two structural design methods, linear slip transformation (LST) and rotational slip transformation (RST), to distort an original structure for largely tuning its curvature distribution and Young’s modulus within the restrictions of fixed structural type, volume fraction, and fabricated material. Here samples were additively manufactured using Ti6Al4V. Compared to original triply periodic minimal surfaces (TPMS) based lattices, the curvature distribution spectrum was largely broadened, and negative curvatures were introduced by both LST (generating symmetrical curvature distribution) and RST (generating asymmetrical curvature distribution). Additionally, LST and RST can continuously adjust the Young’s modulus of the original lattice and obtain a drop up to 90 % with 0.3 vol fraction, which can be expected to match soft trabecular bones. Interestingly, the resulting structures show elastic anisotropy and slip-induced deformation. The proposed approaches can be applied to biomedical applications and used to adjust lattice properties for use in energy, aerospace, and optics.

To address the problem of low overall machining efficiency of free-form surfaces and difficulty in ensuring machining quality, this paper proposes a MATLAB-based free-form surface division method. The surface division is divided into two stages: Partition area identification and area boundary determination. In the first stage, the free-form surface is roughly divided into convex, concave, and saddle regions according to the curvature of the surface, and then the regions are subdivided based on the fuzzy c-means clustering algorithm. In the second stage, according to the clustering results, the Voronoi diagram algorithm is used to finally determine the boundary of the surface patch. We used NURBS to describe free-form surfaces and edit a set of MATLAB programs to realize the division of surfaces. The proposed method can easily and quickly divide the surface area, and the simulation results show that the proposed method can shorten machining time by 36% compared with the traditional machining method. It is proved that the method is practical and can effectively improve the machining efficiency and quality of complex surfaces.

An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the K−ω SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar (Pr = 0.71) and a turbulent Prandtl number, Prt, of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in Cp, Cf, and Us predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of Cp and Cf) and in Us profiles just upstream of the bubble. The Reynolds analogy, based on the St/(Cf/2) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of u′ and v′ or positive Reynolds shear stresses ( > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in and turbulence production as well as an evident negative slope on the constant shear layer.

Surface curvature affects adhesion forces, deformations of surfaces in contact, leakage of mechanical seals, friction, wear, paintability, and electrical conductivity. However, potential benefits of surface curvature have not yet been fully utilized. One problem is the lack of comparison data helping to make an informed decision on the selection of curvature characterization method. In this paper, five multiscale curvature characterization methods, namely Nowicki, Bigerelle-Nowicki, Gleason-Heron, Kalin, and Bartkowiak are compared. The comparison was conducted on large image databases of computer-generated fractal surfaces, sine waves and real engineering surfaces. Specifically, the methods were evaluated for their ability to differentiate between surfaces that: (i) exhibit increasing curvature complexity, (ii) have varying curvatures at a single scale, and (iii) represent minute multiscale curvature changes encountered in real engineering applications. The results obtained indicate that the Bigerelle-Nowicki method exhibits the best overall performance.

Though the importance of curvature continuity on compressor blade performances has been realized, there are two major questions that need to be solved, i.e., the respective effects of curvature continuity at the leading-edge blend point and the main surface, and the contradiction between the traditional theory and experimental observations in the effect of those novel leading-edge shapes with smaller curvature discontinuity and sharper nose. In this paper, an optimization method to design continuous-curvature blade profiles which deviate little from datum blades is proposed, and numerical and theoretical analysis is carried out to investigate the continuous-curvature effect on blade performances. The results show that the curvature continuity at the leading-edge blend point helps to eliminate the separation bubble, thus improving the blade performance. The main-surface curvature continuity is also beneficial, although its effects are much smaller than those of the blend-point curvature continuity. Furthermore, it is observed that there exist two factors controlling the leading-edge spike, i.e., the curvature discontinuity at the blend point which dominates at small incidences, and the nose curvature which dominates at large incidences. To the authors’ knowledge, such mechanisms have not been reported before, and they can help to solve the sharp-leading-edge paradox.