Swept Surface Research Articles

Investigation into Yaw Motion Influence of Horizontal-Axis Wind Turbine on Wake Flow Using LBM-LES

The dynamic yaw motion of the wind turbine will affect the overall aerodynamic performance of the impeller and the corresponding wake flow, but the current research on this issue is inadequate. Thus, it is very necessary to study the complicated near-wake aerodynamic behaviors during the yaw process and the closely related blade aerodynamic characteristics. This work utilized the multi-relaxation time lattice Boltzmann (MRT-LBM) model to investigate the integral aerodynamic performance characteristics of the specified impeller and the dynamic changes in the near wake under a sine yawing process, in which the normalized result is adopted to facilitate data comparison and understanding. Moreover, considering the complexity of the wake flows, the large eddy simulation (LES) and wall-adapting local eddy-viscosity (WALE) model are also used in this investigation. The related results indicate that the degree of stability of tip spiral wake in the dynamic yaw condition is inversely related to the absolute value of the change rate of yaw angular speed. When the wind turbine returns to the position with the yaw angle of 0 (deg) around, the linearized migration of tip vortex is changed, and the speed loss in the wake center is reduced at about the normalized velocity of 0.27, and another transverse expansion appeared. The directional inducing downstream of the impeller sweep surface for tip vortex is clearly reflected on the entering side and the exiting side. Additionally, the features of the static pressure on the blade surface and the overall aerodynamic effects of the impeller are also discussed, respectively.

Designing Roller Coaster Loop’s By Using Extended Uniform Cubic B-Spline

Roller coaster is one of the attractions to the public. The design of roller coaster plays an important role for the smoothness and safety of each roller coaster rail. This research is about designing a smooth roller coaster rail loop using extended cubic uniform B-spline method as one of the alternative in designing a smooth roller coaster rail. Two-dimensional design of roller coaster rail loop is form by using extended cubic uniform B-spline with degree 3, 4 and 5 and shape parameter, λ= 0.5, and 1. Then, three-dimensional cubic B-spline is formed by using sweep surface which is translation method. The loop is analysed by the distance between curve and control polygon. Moreover, the G-felt with the different radius of the loop has been calculated. The value of G-felt for each method used will be compared to the G-felt value of the original roller coaster. The result from this research showed that by using extended cubic B-spline method degree 4, λ = 0.5 is the best way to design roller coaster rail because it has the best G-force value compared to others designs.

A Variational Framework for Computing Geodesic Paths on Sweep Surfaces

Sweep is a natural, intuitive, and convenient 3D modeling method in computer-aided design. Sweep surface can be obtained by extruding a 2D cross-sectional profile along a guide curve x=x(t),t∈[a,b]. A small segment of the sweep volume can also be understood by rotating a 2D sectorial generatrix curve around the guide curve. We assume that sweep surfaces have a parametric form Φ=Φ(t,θ), where Φ([t,t+dt],θ) defines the sectorial generatrix curve segment at the angle of θ while rt(θ)=Φ(t,θ),θ∈[0,2π], defines the circumferential closed curve. Geodesic computation on sweep surfaces is a fundamental geometric operation in many scenarios like the manufacturing process of filament winding. In order to compute a geodesic path between two points on sweep surfaces, we propose a variational framework that works on the 2D parametric domain, without the step of discretizing the surface into a polygonal mesh. The solution to the objective function is a polyline curve of n equally spaced vertices that approximates the real geodesic path, where n is a user-specified parameter for accuracy control. We prove that the polyline approaches the real geodesic in quadratic order. Furthermore, it can be easily extended to compute N-round geodesic helix curves. We also discuss various configurations of rt(θ): (1) rt(θ) is a constant, independent of t and θ, (2) rt(θ) depends on only t, independent of θ, and (3) rt(θ) depends on both t and θ. We validate the effectiveness and high performance of our method through extensive experimental results.

Modified iterative approach for predicting machined surface topography in ball-end milling operation

Machined surface topography prediction is an important and useful tool for optimizing cutting parameters. However, accurate prediction of machined surface topography in ball-end milling operation has been extremely challenging, due to the complexity in tool-workpiece interaction induced by the trochoidal motion of cutting edge and computing burden. In this present research, a modified iterative approach was proposed to solve the intersections between the cutting-edge sweeping surface and the discrete Z-vector model of workpiece, which were used to predict the machined surface topography in ball-end milling operation. Firstly, the accurate model of cutting-edge sweeping surface was established utilizing homogeneous coordinate transformation, in which the tool runout was considered. Secondly, the cutting-edge sweeping surface was dispersed into a series of patches in accordance with equal parameter interval, and the in-cut patch was extracted by using the minimum and maximum axial immersion angle of the cutting edge. Thirdly, the intersection between each in-cut patch and discrete Z-vector was solved using the Newton’s method, which was used to update the endpoint of the corresponding discrete Z-vector. Finally, ball-end milling experiments of AISI P20 steel were carried out to validate the proposed approach as well as investigate the effect of cutting parameters on the machined surface topography and roughness. The predicted machined surface topography and roughness were in good agreement with the measured results. Moreover, the proposed approach needs less computing time than the traditional iterative approaches at the same predicting accuracy. This research also provides guidance for optimizing cutting parameters to control surface quality in ball-end milling operation.

Numerical Simulation of the Flow around the Ducted Fan of a Quadcopter and Determination of Its Thrust Characteristics in Various Flight Modes

A numerical simulation of the flow induced by rotation of the ducted fan blades of a quadcopter is carried out using the vortex-resolving approach that assumes solution of the full Navier–Stokes equations. Based on the numerical simulation results, the aerodynamic characteristics of the ducted fan are determined in various flight modes with asymmetric airflow over the surface swept by the propeller. In the problem formulation, various angles of the ducted fan rotation plane deviation from the vertical were considered for various flight modes of a multicopter type aircraft as well as characteristics of the non-perturbing incident air flow.

Sweeping surfaces according to type-2 Bishop frame in Euclidean 3-space

This work is concerned with the study of the kinematic-geometry of a special kind of tube surfaces, so-called sweeping surface in Euclidean 3-space [Formula: see text]. It is generated by a plane curve moving through space such that the movement of any point on the surface is always orthogonal to the plane. In particular, the type-2 Bishop frame is considered and some important theorems are obtained. Also, the problem of singularity and convexity of such sweeping surface is discussed. Finally, an application is presented and plotted using computer aided geometric design.

Spacelike Sweeping Surfaces and Singularities in Minkowski 3-Space

We considered the spacelike sweeping surface with rotation minimizing frames at Minkowski 3-space E 1 3 . We presented the new geometric invariant to demonstrate geometric properties and local singularities for this surface. Then, we derived sufficient and necessary conditions of the surface to become developable ruled surfaces. Additionally, its singularities are studied. Finally, examples are illustrated to explain the applications of the theoretical results.

Timelike sweeping surfaces and singularities

We consider a timelike sweeping surface with rotation minimizing frames in Minkowski 3-Space [Formula: see text]. We introduce a new geometric “invariant”, which demonstrates the geometric properties and local singularities of the surface. Subsequently, we give the sufficient and necessary conditions for this surface to be a developable ruled surface. Finally, the singularities of these ruled surfaces are investigated.

Sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-Space

In this paper, we introduce the notion of sweeping surfaces with Natural mate curve of a spatial curve in Euclidean 3-space E3 . We also show that the parametric curves on these surfaces are lines of curvature. Then, we derive the necessary and sufficient condition for the sweeping surface to become a developable ruled surface. In particular, we analyze the necessary and sufficient conditions when the resulting developable surface is a cylinder, cone or tangent surface. Finally, some representative curves are chosen to construct the corresponding developable surfaces which possessing these curves as lines of curvature.

Spatial [formula omitted] closed loops of prescribed arc length defined by Pythagorean-hodograph curves

We investigate the problem of constructing spatial C2 closed loops from a single polynomial curve segment r(t), t∈[0,1] with a prescribed arc length S and continuity of the Frenet frame and curvature at the juncture point r(1)=r(0). Adopting canonical coordinates to fix the initial/final point and tangent, a closed-form solution for a two-parameter family of interpolants to the given data can be constructed in terms of degree 7 Pythagorean-hodograph (PH) space curves, and continuity of the torsion is also obtained when one of the parameters is set to zero. The geometrical properties of these closed-loop PH curves are elucidated, and certain symmetry properties and degenerate cases are identified. The two-parameter family of closed-loop​ C2 PH curves is also used to construct certain swept surfaces and tubular surfaces, and a selection of computed examples is included to illustrate the methodology.

Profile Design Method of Twin-Screw Compressor Rotors Based on the Pixel Solution

A new design method based on pixel solution is proposed to achieve an efficient and high-precision design of a twin-screw rotor profile. This method avoids the complex analytic calculations in the traditional envelope principle. The best approximation of the pixels of the rotor conjugate motion sweeping surface in the lattice screen pixels is illuminated using a specific color. The sweeping surface of the screw rotor single-tooth profile is roughly scanned to capture the base point set of the sweeping surface boundary pixels. The chord length and tilt angle of each interval are calculated using the value of the base point set to adjust the position, phase, and magnification of each interval sweeping surface. Each interval sweeping surface is finely scanned to capture the data point set of the subinterval, and then the data point set is converted to the same coordinate system to generate the conjugated rotor profile. Finally, an example is used to verify the feasibility and adaptability of this method. The approach provided can be used to design screw rotor profiles with high precision.

Construction of Local Shape Adjustable Surfaces Using Quintic Trigonometric Bézier Curve

Based on quintic trigonometric Bézier like basis functions, the biquintic Bézier surfaces are modeled with four shape parameters that not only possess the key properties of the traditional Bézier surface but also have exceptional shape adjustment. In order to construct Bézier like curves with shape parameters, we present a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis. Then, according to these basis functions, we construct three different types of shape adjustable surfaces such as general surface, swept surface and swung surface. In addition to the application of the proposed method, we also discuss the shape adjustment of surfaces showing with curvature nephogram (with and without fixing the boundaries). However, the modeling examples shows that the suggested approach is efficient and easy to implement.

Ceramic 3D printed sweeping surfaces

Ceramic 3D printing has gained rapid development in recent years. Especially, desktop ceramic 3D printers get more and more popular for designers, artists, and makers to work with clays. As a highly viscous pseudoplastic liquid, the printing material clay produces featured aesthetics, and also indicates several manufacturing constraints. There are barely customized modeling tools for ceramic printing. Targeting for ceramic printing, we present a user-interactive modeling and fabricating framework using sweeping lines as the design tool. We integrate the ceramic printing constraints like self-supporting and collision-free in the modeling stage. Then we propose a customized method for generating the printing file, with the guarantee that the extruder traces a single continuous path without starts and stops. To fulfill this goal, we compute an adaptive zig-zag path along the sweeping surface. During the fabrication, our continuous path avoids the potential collision between the printing head and the physical model. Moreover, we optimize the extrusion amount along with the extruder movement, such that overlap between neighboring layers is appropriate in terms of both model stability and cost-effectiveness. We demonstrate the fabrication process and physical results to validate our method.

A Novel Approach to Profile-Milling for End-Mill Flutes in 4‒Axis CNC Turn-Milling Machines, Part II: Simulation and Verification

As the profile-milling approach to machine end-mill flutes in 4-axis CNC turn-milling machines is developed in the first part of this article, the cutters’ orientations and locations (path) can now be obtained at any moment of the machining. Knowing the cutter’s path, a machining simulation model based on the envelope theory is developed in this part. The model generates a swept surface very essential in performing the simulation and in obtaining the flutes. The model also introduces a simple method to control the core radius of the end-mills and to investigate the effect of type and geometry of cutters on the final shapes of the flutes. Several case studies are presented, and the profile-milling approach of the end-mill flutes in 4-axis CNC turn-milling machines is verified. Therefore, this approach is expected to contribute to the CNC programming techniques of the end-mill flutes in multi-axis profile-milling processes.

A Novel Approach to Profile-Milling for End-Mill Flutes in 4-Axis CNC Turn-Milling Machines, Part I: Mathematical Modeling

In industry, two main operations are used to produce end-mills; grinding and milling. While grinding is more suited for hard end-mills, milling is more attracting in less-hard end-mills since it is more efficient and productive. However, milling the end-mills is currently conducted based on the technical experience, and to the best knowledge of the authors, no mathematical foundation has yet been established. Thus, a profile-milling approach to machine end-mill flutes in 4-axis CNC turn-milling machines is developed and introduced in this work for the first time. The approach employs the cutting edge tangents, and the rake face normals in determining a cutter’s path that ensures an accurate normal rake angle along the rake face. Knowing the cutter’s path, the approach generates a swept surface which is very essential in the profile-milling simulation and in controlling the flutes shapes. However, the profile-milling simulation is conducted in the extended part of this article over several case studies where the developed approach is validated. Overall, this approach is significantly enhancing the CNC programming techniques for multi-axis profile-milling of the end-mill flutes as well as laying a good foundation for the CAD /CAM/CAE of end-mills.

Developable Surfaces Through Sweeping Surfaces

This paper studies the rotation minimizing frames that are associated with spatial curves and the sweeping surfaces which are generated by these frames. Then the necessary and sufficient condition for sweeping surface to be developable ruled surface is derived. In particular, we focused for the resulting developable surface is a cylinder, cone or tangent surface.

Age-related changes in four-dimensional CMR-derived atrioventricular junction velocities and displacements: Implications for the identification of altered annular dynamics for ventricular function assessment

BackgroundWe determined the age-related changes in atrioventricular junction (AVJ) velocities and displacements by feature tracking cardiovascular magnetic resonance (FT-CMR) in a healthy community-based population. We also investigated the importance of age-matching for the identification of altered AVJ dynamics. MethodsFT-CMR was performed in 230 controls (18–78 years) and in two patient groups each consisting of 40 subjects (group 1: 23–55 years, group 2: 56–80 years). AVJ dynamic parameters, including systolic velocity Sm, early diastolic velocity Em, late diastolic velocity Am, maximal systolic excursion MAPSE and the new parameter sweep surface area velocity SSAV were measured. ResultsIncreasing age in the control group was significantly associated with reductions in Sm, Em, MAPSE (r = −0.40, −0.76, −0.34, all P < 0.001) and an increase in Am (r = 0.45, P < 0.001). For patient group 1, the selection of an age-unmatched control group (56–76 years) underestimated the number of patients with abnormal AVJ dynamics during systole and early diastole (38% vs. 70% for Sm; 20% vs. 60% for Em; 35% vs. 50% for MAPSE). In contrast, for patient group 2, the number of patients with systolic and early diastolic AVJ dynamic abnormalities was overestimated (88% vs. 63% for Sm; 90% vs. 68% for Em; 73% vs. 58% for MAPSE) when compared with age-unmatched controls (24–55 years). Fifty-percent (20/40) of the sub-group of patients with normal left ventricular ejection fraction exhibited abnormal systolic Sm or MAPSE measurements. ConclusionsSignificant correlations exist between age and AVJ dynamics. Age matching is important for evaluating AVJ long-axis function.

Prediction of cutting force of ball-end mill for pencil-cut machining

There are a number of concave circular blending surfaces with minor curvature radius in the corner of curved surface part, like complex mold cavity. Pencil-cut machining has shorter path and completer material remove than other strategies of clean-up machining which make it high efficiency, high precision, and high utilization rate of equipment. In this paper, contact between cutter and concave crescent cylinder (CCC) including cutter workpiece engagement (CWE) and in-cut cutter edge (ICCE) is studied based on an analytic method, and a prediction model of the cutting force for pencil-cut machining with the ball-end mill is established. The cutter, the CCC, and the feed direction for pencil-cut machining are parametrically defined. In cutter contact normal coordinate system, the analytic expressions of tool geometry, CCC, and the cutter sweep surface of the cutter are derived, and then the CWE is obtained by the intersection of the space surfaces, which the CWE in the tool coordinate is realized by the three-dimensional rotation transformation. The cutter edge curve is discreted into a series of infinitesimal element, based on the criteria of the cutter edge element in the CWE, an analytic algorithm to calculate the ICCE is proposed, and the precision of the boundary points can be further improved by the dichotomy. Combining ICCE with instantaneous chip thickness considering cutter run-out and micro-element milling force theories of ball-end mill, the prediction model of cutting force for pencil-cut machining of CCC with ball-end mill is established. A series of pencil-cut machining experiments and simulations were arranged. The performance of pulling milling is better than that of pushing milling. The CWE and ICCE obtained by the analytical method agree well with that of experiment and solid modeling simulation. The cutting force experiments verify the correctness of the milling force predictive model.

A novel extension of the Bézier model and its applications to surface modeling

The construction of Bézier curves and surfaces with shape parameters is one of the most popular areas of research in CAD. In this paper, we present a novel shape-adjustable generalized Bézier curve with multiple shape parameters and discuss its applications to surface modeling in engineering. Firstly, a class of new generalized Bernstein basis functions with explicit expressions is proposed, which is a natural extension of the classical Bernstein basis functions of degree n. Furthermore, the corresponding Bézier curves and surfaces with global and local shape parameters are constructed and their properties are also studied. The shapes of the curves and surfaces can be adjusted intuitively and foreseeably by changing the shape parameters. Secondly, in order to tackle the problem that most complex curves in engineering often cannot be constructed by using a single curve, we derive the necessary and sufficient conditions for C1 and C2 continuity of these new curves. Finally, using shape-adjustable generalized Bézier curves, we construct six different types of engineering surfaces with multiple shape parameters, including general cylinders, bilinear surfaces, ruled surfaces, swung surfaces, swept surfaces and rotation surfaces. The modeling examples show that the proposed methods are effective in geometric modeling.

Surface reconstruction from FE mesh model

Abstract In the computer aided engineering process with finite element analysis, a CAD surface model is sometimes needed for various tasks such as remeshing, shape optimization or design modification. Occasionally, engineers who perform an analysis at the product design stage are given only finite element mesh models; corresponding CAD models can be unavailable. This paper presents a method to extract free-form B-spline surfaces and certain feature curves from a surface mesh model. First, using the k-means clustering method, our process segments given meshes into a number of regions according to principal curvature information; then, region operations are performed. Next, each region is converted to an approximately free-form B-spline surface. In the last step, feature curves to create loft or sweep surfaces are calculated by minimizing the distance error. Some practical examples are also presented to demonstrate the effectiveness and usefulness of our method. Highlights We propose a new method of creating CAD surfaces from given finite element mesh model. Feature curves are extracted for creating sweep or loft surfaces. By using the generated surfaces based on the feature curves, the shape modification can be easily performed in the designing process.