Convex Arc Research Articles

Theoretical and Finite Element Analysis of Residual Stress Field for Different Geometrical Features After Abrasive Waterjet Peening

Abrasive waterjet (AWJ) peening can be used for metal surface strengthening by introducing near-surface plastic strain and compressive residual stress. The present studies seldom focus on residual stress by AWJ peening of targets with different geometrical features. In fact, those targets usually exist on some machine parts including gear roots, shaft shoulders, and stress concentration areas. According to Hertz theory of contact and Miao's theoretical model for predicting residual stress of flat surface, this paper developed a theoretical model for investigating residual stress of targets with different geometrical features including concave arc surface, concave sphere surface, convex arc surface, and sphere surface. AWJ peening of targets with different geometrical features and different radii of Gaussian curved surface was simulated by abaqus. Theoretical results were consistent with numerical simulation results and published experimental results (H. Y. Miao, S. Larose, et al., 2010, “An analytical approach to relate shot peening parameters to Almen intensity,” Surf. Coat. Technol., 205, pp. 2055–2066; Cao et al., 1995, “Correlation of Almen arc height with residual stresses in shot peening process”, Mater. Sci. Technol. 11, pp. 967–973.), which will be helpful for predicting residual stress of gear roots, shaft shoulders, and stress concentration areas after AWJ peening. The research results showed that under the same peening parameters, σmax, σtop, dmax, and dbottom in concave surface (including concave arc surface and concave sphere surface) were the maximum; σmax, σtop, dmax, and dbottom in convex surface (including convex arc surface and sphere surface) were the minimum; for concave surface, σtop, σmax, dbottom, and dmax decreased, respectively, with target radius; for convex surface, σtop, σmax, dbottom, and dmax increased, respectively, with target radius.

Low-frequency spectroscopy for quantum multilevel systems

A periodically driven quantum system with avoided-level crossing experiences both non-adiabatic transitions and wave-function phase changes. These result in coherent interference fringes in the system's occupation probabilities. For qubits, with repelling energy levels, such interference, named after Landau-Zener-Stuckelberg-Majorana, displays arc-shaped resonance lines. We demonstrate that in the case of a multi-level system with an avoided-level crossing of the two lower levels, the shape of the resonances can change from convex arcs to concave heart-shaped and harp-shaped resonance lines. In this way, the shape of such resonance fringes is defined by the whole spectrum, providing insight on the slow-frequency system spectroscopy. As a particular example, we consider this for valley-orbit silicon quantum dots.

Study on a method of CNC form milling for the concave convex arc line gear

As general and efficient CNC machining is a fundamental technology for line gear manufacturing, a CNC form milling method for the concave convex arc line gear was studied in this paper. Firstly, line teeth geometry characteristics of the concave convex arc line gear were introduced. On the basis of the space curve meshing principle of the line gear, the machining principle of the concave convex arc line gear was proposed, which makes the machining of the driving line gear and the driven line gear simpler and more efficient. Then, the structural model of a special CNC milling machine tool was shown to explain the machining process. By considering the meshing characteristics of the concave convex arc line gear, the motion laws and mathematical expressions of the specified two axis of the designed special CNC milling machine tool were deduced. Furthermore, a special CNC form milling machine tool was rebuilt, and the samples of concave convex arc line gear were made by it. Then, a strategy for the CNC form milling of the concave convex arc line gear mechanism was proposed, which results in a total machining time of 1 h 18 min 32 s for one pair of the line gear samples designed, while it was 4 h 51 min 2 s by using common NC machining. Finally, the kinematic experiment of the concave convex arc line gear was carried out. The results prove that the CNC form milling method proposed for line gear in this paper is reasonable, practical and efficient.

Discrete element analysis of particles flow in convex arc section of large corrugated sidewall belt conveyor

Convex arcs plays a key role in a large corrugated sidewall belt conveyor, which determines the large-capacity, high belt speed can smooth transportation, do not throw material. In order to study the convex arc section of corrugated sidewall belt conveyor conveying the material properties of the particle stream dynamics and logistics particle effects on the conveyor belt to the discrete element theory, by using a nonlinear Hertz Mindlin model built with corrugated sidewall belt conveyor discrete element model machine. The movement of materials with different speed is simulated; The average pressure and the maximum pressure of the base belt and the transverse plate of the corrugated sidewall conveyor belt under different conveyor belt speed were tested, and the average conveyor belt speed of rolling friction coefficient under three different particles were tested; Uniform acceleration of movement of the material flow when turning. Simulation results show that: With the increase of belt speed, the average pressure of corrugated sidewall conveyor increases nonlinearly, and gradually increases with the increase of velocity. The average velocity of the particle unit has nothing to do with the rolling friction coefficient.

Bioinspired sprawling robotic leg and a path-planning procedure

This article shows the characteristics of a sprawling robotic leg inspired by the limb postures of certain reptilian animals known as sprawling-legged creatures. The main part of the robotic limb is based on the eight-bar Peaucellier–Lipkin linkage, and its main attribute is the ability to trace a true straight line, due to the rotational motion of the input link. However, when the eight-bar linkage is modified, it is capable of tracing true circular concave or convex arcs, when two of its constitutive links have distinct and precise lengths. This gives rise to the concepts of concavity and convexity, related to a robotic leg based on the Peaucellier–Lipkin mechanism, such as the one described herein. Our bioinspired robotic leg can trace concave or convex curves, as well as straight lines, making it a reptile-like robotic limb that is very similar to the natural one. We also introduce the concept of rotation center tuning, which refers to the ability of the leg to adapt its posture to the center of rotation of the entire walking machine, resulting in an easy and suitable gait process. The theoretical information is illustrated through the simulation of an example that provides a path-planning procedure, focusing on the rotation center tuning process and a walking gait. The example also includes the design of an elliptical path projected onto the cylindrical workspace and followed by the reptilian foot.

Myanmar-Andaman-Sumatra subduction margin revisited: Insights of arc-specific deformations

We address the role of the concave and convex arcs (as observed from the subducting plate) on the deformation occurring along the Myanmar-Andaman-Sumatra margin. We categorize the pre- and post-seismic deformations of the lithosphere using earthquake database occurring either prior to 26th December 2004 M w 9.3 off-Sumatra mega-event or after the incidence. Analysis under pre-seismic domain shows that area near Sumatra records highest seismicity, which largely drops in the area past the North Andaman, and further increases towards north. Shallowest depth and minimum dip of the subducting lithosphere is recorded at the central segment where the arc transformed into concave shape. The annual moment energy release during earthquake decreases to more than two orders of magnitude past the North Andaman towards north under post-seismic deformation phase. Higher depths of continuity of events are presumably associated with more dipping Benioff zones in both the Indo-Myanmar and Andaman-Nicobar convex arcs. These observations obviously account for tectonic subdivision of the margin near concave shape arc around the central part. Absence of volcanism, presence of splay faults in the back-arc, sharp reduction in seismicity near central segment are interpreted to be caused by major tectonic impact of the NNE-ward converging buoyant Ninety-east Ridge against the Asian Plate. Shallowest dip, small elastic thickness, weak converging Indian lithosphere, and evidences of series of en-echelon blocks off the eastern side of the broken northern Ninetyeast Ridge might be incapable of generating great earthquake in this area.

CrossbowCam: a handheld adjustable multi-camera system

This paper presents a novel multi-functional, low-cost handheld multi-camera system (one dimensional camera array) - “CrossbowCam”. The CrossbowCam is suitable for multi-viewpoint image acquisition, smooth switching, alignment and seamless stitching applications. The proposed system differs from the traditional fixed image acquisition systems which are large-sized, high-priced, single functional, and can only captured images at specific locations. With the proposed system, the users can push one single button to change the configuration of the camera array rapidly to divergence (convex arc), parallel (linear), or convergence (concave arc). The three camera configurations can each be suitable for applications such as panorama image stitching, autostereoscopic 3D display, bullet-time (time-freeze) visual effect, 3D scene reconstruction, etc. To rapidly acquire the relationship among cameras after configuration change, we propose a two-stage calibration method to compensate the mechanical misalignment. The first stage adopts the traditional checkerboard calibration method to get the intrinsic parameters (focal length, principal point) and the lens distortion for each camera. The second stage requires no auxiliary tool but utilizes a large number of common feature points from multiple viewpoint images to acquire the extrinsic parameters (translation and rotation matrix) and to compensate the vertical misalignment and the horizontal uneven angle distribution due to the mechanical structure. The proposed system can then insert virtual viewpoint images between actual viewpoint images to allow the viewpoint switching more smoothly. The proposed system has eight cameras with maximum viewing angle of 90° in divergence mode, 38 mm spacing in parallel mode, and imaging radius of 10 m ∼ 0.5 m in convergence mode. We believe that the proposed system can potentially change the consumer habits and becomes the new type of home-use handheld camcorder system in the future.

On the Bernoulli Property of Planar Hyperbolic Billiards

We consider billiards in non-polygonal domains of the plane with boundary consisting of curves of three different types: straight segments, strictly convex inward curves and strictly convex outward curves of a special kind. The billiard map for these domains is known to have non-vanishing Lyapunov exponents a.e. provided that the distance between the curved components of the boundary is sufficiently large, and the set of orbits having collisions only with the flat part of the boundary has zero measure. Under a few additional conditions, we prove that there exists a full measure set of the billiard phase space such that each of its points has a neighborhood contained up to a zero measure set in one Bernoulli component of the billiard map. Using this result, we show that there exists a large class of planar hyperbolic billiards that have the Bernoulli property. This class includes the billiards in convex domains bounded by straight segments and strictly convex inward arcs constructed by Donnay.

Transient dynamic response of a shallow buried lined tunnel in saturated soil

Previous research has produced valuable results on the transient dynamic response of tunnels buried in full-space. However, a half-space model is of more practical interest because tunnels normally have finite buried depths. In this paper, the dynamic response of a lined tunnel is studied where the surrounding soil is described using Biot's theory and the lining is described by the theory of elastodynamics. The half-space straight boundary is approximately represented by a convex arc of large radius. In accordance with Graff's addition theorem, the general solutions in a rectangular coordinate system are converted to ones in a polar coordinate system. The solutions for displacements and stresses of both the soil and the lining as well as the pore pressure of the soil in the Laplace transform domain are derived based on boundary conditions. Time domain solutions are then obtained by the use of inverse Laplace transform. Numerical results are presented showing the distributions of peak values of ground displacements, stresses and pore pressures of the soil.

Design formulae for a concave convex arc line gear mechanism

Abstract. Line gear is a newly developed gear mechanism with point contact meshing according to space curve meshing theory. This paper proposes a new form of line gear with a couple of concave convex arc tooth profiles. It has four characteristics. First, contact curve of the driving line gear is a cylindrical spiral curve. Second, two axes of a pair of line gears are located in the same plane with an arbitrary angle. Third, at the mesh point, normal tooth profiles of a line gear pair are a couple of inscribed circles. Namely, they form a couple of concave convex tooth profiles. Fourth, the tooth profile of a driving line gear is a convex, that of a driven line gear is a concave, and they are interchangeable. If only consider that the arcs of teeth at meshing point are tangent, the actual tooth surfaces may interfere outside of the meshing point. In this paper, the geometric condition of the tooth surface for a concave convex arc line gear mechanism is derived, and the optimal formulae of the tooth profile parameters are derived on basis of interference proof conditions. Finally, the 3-D modeling and kinematic simulation of line gear pairs show that the proposed line gear pairs can perform transmission normally. The proposed method will extend the application of line gear in the conventional power drive.

Description of a propulsion unit used in guiding a walking machine by recognizing a three-point bordered path

A reconfigurable propulsion unit based on the Peaucellier-Lipkin mechanism has the ability to describe exact straight or curved paths depending on the selected ratio between the lengths of two of its links. The Peaucellier-Lipkin mechanism with one degree of freedom is transformed into a more sophisticated parallel kinematic chain by including four more degrees of freedom. The resulting propulsion unit is able to adapt its kinematic structure and reach instant centers of rotation, in accordance with the presence of three points that border a geometric path. A laser sensor mounted on the body of the machine detects each point. Once the machine has detected the exact location of the border of the road, it walks along a curve parallel to that border. Although the proposed research describes only one propulsion unit or leg, the methodology can be applied to all the legs of the walking machine. The novel 5-DOF leg is able to reach different centers of rotation, providing either the concave or convex arcs that satisfy the basic principle of displacement of walking machines.

Generic absence of finite blocking for interior points of Birkhoff billiards

Let $x$ and $y$ be points in a billiard table $M=M(\sigma)$ in$\mathbb{\mathbb{R}}^{2}$ that is bounded by a curve $\sigma$. Weassume $\sigma\in\Sigma_{r}$ with $r\geq2$, where $\Sigma_{r}$is the set of simple closed $C^{r}$ curves in $\mathbb{R}^{2}$ withpositive curvature. A subset $B$ of $M\setminus\{x,y\}$ is calleda blocking set for the pair $(x,y)$ if every billiard pathin $M$ from $x$ to $y$ passes through a point in $B$. If a finiteblocking set exists, the pair $(x,y)$ is called secure in$M;$ if not, it is called insecure. We show that for $\sigma$in a dense $G_{\delta}$ subset of $\Sigma_{r}$ with the $C^{r}$topology, there exists a dense $G_{\delta}$ subset $\mathcal{\mathcal{R}=R}(\sigma)$of $M(\sigma)\times M(\sigma)$ such that $(x,y)$ is insecure in$M(\sigma)$ for each $(x,y)\in\mathcal{R}$. In this sense, for thegeneric Birkhoff billiard, the generic pair of interior points isinsecure. This is related to a theorem of S. Tabachnikov [24]that $(x,y)$ is insecure for all sufficiently close points$x$ and $y$ on a strictly convex arc on the boundary of a smoothtable.

Geometric Aspects of Modifications of Tapered Roller Bearings

The basic analytical relationships for construction of modified tapered roller bearings based on standard bearing type 7000 are dwelt upon. The modification consists in the replacement of rolling elements in the form of tapered rollers with a rectilinear generatrix on casters with a convex arc generatrix. The advantage of the modified-bath roller is shown by means of calculation of the permissible corner re-braid rings and the contact stresses in comparison with the standard roller bearings similar to overall dimensions.

Extremizers for Fourier restriction inequalities: Convex arcs

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

The Application of Radial Basis Function Neural Network in Springback Prediction of Sheet Flanging

Based on the convex (concave) arc sheet flanging experiment data, the springback prediction research in the sheet flanging was carried out, using radial basis function (RBF) neural network (NN) and the dynamic structure design method. By comparing with the experiment results, the validity of this method was verified.

Chapter 24 Geometry of the coastline and morphology of the convergent continental margin of Ecuador

Abstract The pacific border of the South American plate presents a more or less symmetrical sinuosity, with a central concave curvature (the Arica Angle located between two side rays along Chile and Peru) and ending in convex arcs (the Patagonian and Talara arcs, respectively). The width of the continental and coastal margins varies significantly according to the geometry of the border. The continental margin of Ecuador corresponds to the northern part of the Talara Arc. Three different segments showing different coastal geomorphology and continental platform characteristics are identified from north to south: the northern segment (Mataje River–Galera Point) shows a wide continental shelf and slope, the upper subducted slab of the subduction plane presents a low dip; the central segment (Galera Point–Santa Elena) stands in front of the Carnegie Ridge, and presents a moderate uplift in the Manta Peninsula, in front of the Carnegie Ridge, and the upper subduction plane is subhorizontal; the southern segment includes the side and inner coasts of the Gulf of Guayaquil, below the gulf the subduction plane shows a low dip. A comparison with published 3D numerical modelling of curved subduction suggests that the geometry of the continental boundary has a significant effect on uplift or subsidence along the continental margin. Also, the subduction of asperities in the trench, such as the Carnegie Ridge, may change the coastal motion from subsiding to uplifting, as is observed in the Esmeraldas area. There is no clear evidence of a shelf developed during the Last Glacial Maximum (LGM) sea-level lowstand, probably due to the vertical motion – uplift or subsidence – observed all along the coastal margin.

Evaluation of the mixing performance for one novel twin screw kneader with particle tracking

In this article, a novel continuous twin‐screw kneader was proposed. The end‐cross section of the screw rotor consists of convex arcs and cycloidal curves and the rotors profiles were presented. The mixing performance of the novel twin screw kneader was simulated using finite element method (FEM) combined with mesh superimposition technique (MST). Statistical analysis was carried out for flow field using particle tracking technique to research the effect of geometry parameters and working parameters on the mixing performance. To study the dispersive mixing performance, specifically the maximum shear rate, maximum shear stress, maximum mixing index, residence time distribution (RTD) and RTD density function of tracer particles, and dispersive mixing is evaluated using the mixing index in combination with the shear stress. The results show that the changes of centre distance between female and male rotor have little influence on dispersive mixing performance, the lead of rotor has little effect on maximum shear stress and maximum shear rate, while it has an obvious effect on mixing index, cumulative RTD, and RTD density function. The rotor speed has obvious influence on mixing performance, and average residence time of material decreases greatly and the mixing ability is weakened, while the self‐cleaning performance of rotor improved obviously with the increasing of rotor speed. POLYM. ENG. SCI., 54:2407–2419, 2014. © 2013 Society of Plastics Engineers

Numerically Simulating the Aerodynamic Interference Effect of Mean Aerodynamic Force Coefficients on Configurations of Bluff Bodies in Tandem

AbstractIn order to study the aerodynamic interference effects of single and multiple blunt bodies on the rectangular, reverse right angle, reverse inner convex arc, and reverse outer convex arc sections of serial bluff bodies, the finite volume method and the SIMPLE algorithm, the uniform viscous incompressible flow around blunt bodies at a subcritical Reynolds number was simulated by computational fluid dynamics (CFD) technology. The aerodynamic coefficient was analyzed, and the aerodynamic coefficients under various conditions (e.g., different wind angles of attack, chamfer dimensions, and cylinder spacing) were calculated. Results show that the drag and lift, as well as the torque coefficients, of each section of a single blunt decrease in accordance with the sequence of wind flow around the rectangular, reverse right angle, reverse inner convex arc, and reverse outer convex arc sections at different wind angles of attack. The drag and lift, as well as the torque coefficient, of the reverse right angl...

A tight bound for point guards in piecewise convex art galleries

We consider the problem of guarding curvilinear art galleries. A Jordan arc a joining two points, p and q, in the plane is called a convex arc if the closed curve obtained by joining a with the line segment pq encloses a convex set. A piecewise convex art gallery A with n vertices is a simply connected region in the plane whose boundary consists of n convex arcs where A lies on the convex side of each arc. We show that ⌈n2⌉ point guards are always sufficient and sometimes necessary to guard a piecewise convex art gallery with n vertices. We also give a shorter proof for the sufficiency of ⌊2n3⌋ vertex guards, for n⩾2, which was first derived by Karavelas et al.

The Research on Variety of Instantaneous Transmission-Ratio of Gear Pump with Circular-Arc Tooth Profile

According to basic law of tooth profile meshing and principle of higher pair to be replaced with lower pair of planar mechanism, the calculating formula which is used for calculation of transmission ratio of gear pump with circular-arc tooth profile is obtained. The calculating results indicate that stability of transmission ratio of gear pump are very effected by the difference between concave arc radius of tooth profile of pinion and convex arc radius of tooth profile of wheel gear. The smaller the difference of radiuses, the more severe the wave of velocity while meshing.