Search Results (62)

This paper extends Woźny and Chudy’s linear-complexity Bézier evaluation algorithm (2020) to all parametric curves/surfaces with normalized basis functions via a novel basis function matrix decomposition. The unified framework covers the following: (i) B-spline/NURBS models; (ii) Bézier-type surfaces (tensor-product, rational, and triangular); (iii) enhanced models with shape parameters or non-polynomial basis spaces. For curves, we propose sequential and reverse corner-cutting modes. Surface evaluation adapts to type: non-tensor-product surfaces are processed through index-linearization to match the curve format, while tensor-product surfaces utilize nested curve evaluation. This approach reduces computational complexity, resolves cross-model compatibility issues, and establishes an efficient evaluation framework for diverse parametric geometries. Full article

In order to improve the aerodynamic performance of the voluteless centrifugal fan, a multi-objective optimization design system was established by combining parametric modeling, experimental design, surrogate models, and optimization algorithms, with the static pressure and static pressure efficiency of the fan as the optimization objectives. The design parameters of the blade profile were obtained by fitting the blade profile with a Bézier curve. A mapping relationship between design parameters and optimization objectives was established by combining numerical simulation with a radial basis function neural network, and a genetic algorithm was used to optimize the blade profile. The results indicated a highly significant correlation between design parameters and optimization objectives, with a prediction error of no more than 1% for the surrogate model. The determination coefficients for static pressure and static pressure efficiency were 0.98 and 0.96, respectively. After optimization, the static pressure of the fan increased by 12.7 Pa at the design operating point, and the static pressure efficiency increased by 3.2%. The separation vortex decreased near the trailing edge of the blade suction surface, and the airflow impact at the leading edge of the blade decreased. The entropy production in the flow channel decreased, and the overall flow state of the fluid was improved. Full article

Advanced non-destructive techniques play an important role in detecting surface defects in the context of additive manufacturing, with non-destructive technologies providing surface data for the recognition of surface defects. In this line, it is necessary to implement microscope vision technology for the inspection of surface defects. This study proposes an approach for microsurface defect recognition using affine moment invariants based on microlaser line contouring, allowing for the detection of microscopic holes and scratches. For this purpose, the surface is represented by a Bezier surface to characterize microsurface defects through patterns of affine moment invariants after the surface is contoured via microlaser line projection. In this way, microholes and scratches can be recognized by computing a pattern of affine moment invariants for each region of the target surface. This technique is performed using a microscope vision system, which retrieves the surface topography via microlaser line scanning. The proposed technique allows for the recognition of holes and scratches with a surface depth greater than 20 microns, with a minor relative error of less than 2%. The proposed surface defect recognition approach enhances the literature on recognition techniques performed using visual technologies based on optical microscope systems. This contribution is corroborated through a discussion focused on the recognition of holes and scratches by means of various optical-microscope-based systems. Full article

This research investigates the optimization of airfoil design for fixed-wing drones, aiming to enhance aerodynamic efficiency and reduce drag. The research employs Kulfan CST and Bézier surface parameterization methods combined with global sensitivity analysis (GSA) and machine learning techniques to improve airfoil performance under various operational conditions. Particle swarm optimization (PSO) is utilized to optimize the airfoil design, minimizing drag in cruise and ascent conditions while ensuring lift at takeoff. Computational fluid dynamics (CFD) simulations, primarily using XFOIL, validate the aerodynamic performance of the optimized airfoils. This study also explores the generative design approach using a neural network trained on 10 million airfoil simulations to predict airfoil geometry based on desired performance criteria. The results show important improvements in drag reduction, especially during low-speed cruise and ascent phases, contributing to extended flight endurance and efficiency. These results can be used for small unmanned aerial vehicles (UAVs) in real-world applications to develop better-performance UAVs under mission-specific constraints. Full article

This study presents a generalized approach to Bézier curves and surfaces by utilizing the blending $(\alpha ,\lambda ,s)$-Bernstein basis. The $(\alpha ,\lambda ,s)$-Bernstein basis introduces shape parameters $\alpha$, $\lambda$, and s, which allow for more flexibility and control over the curve’s shape compared to the classical Bernstein basis. The paper explores the properties of these generalized curves and surfaces, demonstrating their ability to maintain essential geometric characteristics, such as convex hull containment and endpoint interpolation, while providing enhanced control over the shape. This work aims to contribute to the fields of computer-aided geometric design and related applications by offering a robust tool for curve and surface modeling. Full article

This study explores the fatigue properties of EN AW-6082-T6 aluminum alloy in the gigacycle range (10⁶–10⁹ cycles), using ultrasonic resonance fatigue testing at 20 kHz in a push–pull mode with a symmetric load cycle (R = −1). A custom-built ultrasonic fatigue machine, developed at TU-Varna, comprising a generator, ultrasonic train (including a high-power transducer, booster, custom-made sonotrode, and specimen), monitoring, data logging systems, and an air-cooling capability, was used for the experiments conducted. A Bezier curve sonotrode, with an amplification ratio of 1:6, was designed and produced for the test. Hourglass-shaped specimens were designed on the base of the dynamic Young’s modulus E = 71.3 GPa, determined through the impulse resonance method (ASTM E1876-01), and validated with FEM analysis for resonance length and stress amplitude. The fatigue testing revealed a fatigue strength reduction of approximately 60 MPa between 10⁶ and 10⁹ cycles. The percentile of failure curves based on a Cactillo–Canteli model fits well with the experimental data and gives a fatigue limit at 10⁹ cycles σl = 104 MPa and “endurance strength” σw = 84 MPa. Surface crack initiation was consistently observed with predominately cleavage transgranular fractures in the fatigue zone. The present research highlights the utility of ultrasonic testing for examining fatigue behavior in the gigacycle regime. Full article

In the field of Computer-Aided Geometric Design (CAGD), a proper model can be achieved depending on certain characteristics of the predefined blending basis functions. The presence of these characteristics ensures the geometric properties necessary for a decent design. The objective of this study, therefore, is to examine the generalized $\alpha$-Bernstein operator in the context of its potential classification as a novel blending type basis for the construction of Bézier-like curves and surfaces. First, a recursive definition of this basis is provided, along with its unique representation in terms of that for the classical Bernstein operator. Next, following these representations, the characteristics of the basis are discussed, and one shape parameter for $\alpha$-Bezier curves is defined. In addition, by utilizing the recursive definition of the basis, a de Casteljau-like algorithm is provided such that a subdivision schema can be applied to the construction of the new $\alpha$-Bezier curves. The parametric continuity constraints for $C^0$, $C^1$, and $C^2$ are also established to join two $\alpha$-Bezier curves. Finally, a set of cross-sectional engineering surfaces is designed to indicate that the generalized $\alpha$-Bernstein operator, as a basis, is efficient and easy to implement for forming shape-adjustable designs. Full article

Developing autonomous navigation techniques for surface vehicles remains an important research area, and accurate global path planning is essential. For mobile robots—particularly for Unmanned Surface Vehicles (USVs)—a key challenge is ensuring that sharp turns and sharp breaks are avoided. Therefore, global path planning must not only calculate the shortest path but also provide smoothness. Bézier Curves are one of the main methods used for smoothing paths in the literature. Some studies have focused on turns alone; however, continuous path smoothness across the entire trajectory enhances navigational quality. Contrary to similar studies, we applied Bézier Curves whose control polygon is defined by an RRT path and thus avoided a multi-objective formulation. In the final stage of our approach, we proposed a control point reduction method in order to decrease the time complexity without affecting the feasibility of the path. Our experimental results suggest significant improvements for multiple map sizes, in terms of path smoothness. Full article

The static aeroelastic characteristics of the distributed propulsion wing (DPW) were studied using the CFD/CSD loose coupling method in this study. The momentum source method of the Reynolds-averaged Navier–Stokes equation based on the k-ω SST turbulence model solution was used as the CFD solution module. The upper and lower surfaces of the DPW were established using the cubic B-spline basis function method, and the surfaces of the inlet and outlet were established using the fourth-order Bezier curve. Finally, a three-dimensional parametric model of the DPW was established. A structural finite-element model of the DPW was established, a multipoint array method program based on the three-dimensional radial basis function (RBF) was written as a data exchange module to realize the aerodynamic and structural data exchange of the DPW’s static aeroelastic analysis process, and, finally, an aeroelastic analysis of the DPW was achieved. The results show that the convergence rate of the CFD/CSD loosely coupled method is fast, and the structural static aeroelastic deformation is mainly manifested as bending deformation and positive torsion deformation, which are typical static aeroelastic phenomena of the straight wing. Under the influence of static aeroelastic deformation, the increase in the lift characteristics of the DPW is mainly caused by the slipstream region of the lower surface and the non-slipstream region of the upper and lower surface. Meanwhile, the increase in its nose-up moment and the increase in the longitudinal static stability margin may have an impact on the longitudinal stability of the UAV. To meet the requirements of engineering applications, a rapid simulation method of equivalent airfoil, which can be applied to commercial software for analysis, was developed, and the effectiveness of the method was verified via comparison with the CFD/CSD loose coupling method. On this basis, the static aeroelastic characteristics of the UAV with DPWs were studied. The research results reveal the static aeroelastic characteristics of the DPW, which hold some significance for engineering guidance for this kind of aircraft. Full article

The smoothing of linear toolpaths plays is critical in improving machining quality and efficiency in five-axis CNC machining. Existing corner-smoothing methods often overlook the impact of spline curvature fluctuations, which may lead to acceleration variations, hindering surface quality improvements. The paper presents a five-axis toolpath corner-smoothing method based on the space of master–slave movement (SMM), aiming to minimize curvature fluctuations in five-axis machining and improve surface quality. The concept of movement space in master–slave cooperative motion is introduced, where the tool tip position and tool orientation are decoupled into a main motion trajectory and two master–slave movement space trajectories. By deriving the curvature monotony conditions of a dual Bézier spline, a G2-continuous tool tip corner-smoothing curve with minimal curvature fluctuations is constructed in real-time. Subsequently, using the SMM and the asymmetric dual Bézier spline, a high-order continuous synchronization relationship between the tool tip position and tool orientation is established. Simulation tests and machining experiments show that with our smoothing algorithm, maximum acceleration values for each axis were reduced by 21.05%, while jerk was lowered by 22.31%. These results indicate that trajectory smoothing significantly reduces mechanical vibrations and improves surface quality. Full article

Nowadays, metaheuristic algorithms have been applied to optimize last lower-surface models. Also, the last lower-surface model has been adjusted through the computational algorithms to perform custom shoe lasts. Therefore, it is necessary to implement nature-inspired metaheuristic algorithms to perform the adjustment of last lower-surface model to the footprint topography. In this study, a metaheuristic genetic algorithm is implemented to adjust the last lower surface model to the footprint topography. The genetic algorithm is constructed through an objective function, which is defined through the last lower Bezier model and footprint topography, where a mean error function moves the last lower surface toward the footprint topography through the initial population. Also, the search space is deduced from the last lower surface and footprint topography. In this way, the genetic algorithm performs explorations and exploitations to optimize a Bezier surface model, which generates the adjusted last lower surface, where the surface is recovered via laser line scanning. Thus, the metaheuristic algorithm enhances the last lower-surface adjustment to improve the custom last manufacture. This contribution is elucidated by a discussion based on the proposed metaheuristic algorithm for surface model adjustment and the optimization methods implemented in recent years. Full article

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks. Full article

The use of advanced brittle composites in engineering systems has necessitated robotic rotary ultrasonic machining to attain high precision with minimal machining defects such as delamination, burrs, and cracks. Longitudinal–torsional coupled (LTC) vibrations are created by introducing helical slots to a horn’s profile to enhance the quality of ultrasonic machining. In this investigative research, modified ultrasonic horns were designed for a giant magnetostrictive transducer by generating helical slots in catenoidal and cubic polynomial profiles to attain a high amplitude ratio ($T_A/L_A$) and low stress concentrations. Novel ultrasonic horns with a giant magnetostrictive transducer were modelled to compute impedances and harmonic excitation responses. A structural dynamic analysis was conducted to investigate the effect of the location, width, depth and angle of helical slots on the Eigenfrequencies, torsional vibration amplitude, longitudinal vibration amplitude, stresses and amplitude ratio in novel LTC ultrasonic horns for different materials using the finite element method (FEM) based on the block Lanczos and full-solution methods. The newly designed horns achieved a higher amplitude ratio and lower stresses in comparison to the Bezier and industrial stepped LTC horns with the same length, end diameters and operating conditions. The novel cubic polynomial LTC ultrasonic horn was found superior to its catenoidal counterpart as a result of an $8.45\%$ higher amplitude ratio. However, the catenoidal LTC ultrasonic horn exhibited 1.87% lower stress levels. The position of the helical slots was found to have the most significant influence on the vibration characteristics of LTC ultrasonic horns followed by the width, depth and angle. This high amplitude ratio will contribute to the improved vibration characteristics that will help realize good surface morphology when machining advanced materials. Full article

In this paper, we make use of an inverse formula that relates the blossom of a NURBS curve, surface or Bézier triangle with its parametrisation, with no explicit reference to the control points and weights of the parametrisation. We make use of this inverse formula to raise and lower the degree elevation and reduction. Full article

Traditionally, ceramic design began with sketches on rough paper and later evolved into using CAD software for more complex designs and simulations. With technological advancements, optimization algorithms have gradually been introduced into ceramic design to enhance design efficiency and creative diversity. The use of Interactive Genetic Algorithms (IGAs) for ceramic design is a new approach, but an IGA requires a significant amount of user evaluation, which can result in user fatigue. To overcome this problem, this paper introduces the LightGBM algorithm and the CatBoost algorithm to improve the IGA because they have excellent predictive capabilities that can assist users in evaluations. The algorithms are also applied to a vase design platform for validation. First, bicubic Bézier surfaces are used for modeling, and the genetic encoding of the vase is designed with appropriate evolutionary operators selected. Second, user data from the online platform are collected to train and optimize the LightGBM and CatBoost algorithms. Finally, LightGBM and CatBoost are combined with an IGA and applied to the vase design platform to verify their effectiveness. Comparing the improved algorithm to traditional IGAs, KD trees, Random Forest, and XGBoost, it is found that IGAs improve with LightGBM, and CatBoost performs better overall, requiring fewer evaluations and less time. Its R² is higher than other proxy models, achieving 0.816 and 0.839, respectively. The improved method proposed in this paper can effectively alleviate user fatigue and enhance the user experience in product design participation. Full article