Straight Wedge Research Articles

Modeling of Tribological Processes for Abrasive Wear of Soil-Cutting Part

Abstract. It is shown that simulation modeling of physical processes makes it possible to study the interaction of soil-cutting parts with soil during the observation period of 2-6 hours, when it is required to compress the time scale for creating a new design. (Research purpose) To develop models of the tribological process for abrasive wear of soil-cutting parts based on the combination of simulated loading of friction surfaces with the parameters of the real soil force equivalents. (Materials and methods) This study is based on the simulated loading method and the method of comparing the force equivalents of simulated and real loadings of the friction surfaces of soil-cutting parts using the example of loading flat diagrams. The paper describes the features of non-standard laboratory equipment that facilitates the construction of normal stress diagrams on friction surfaces. As a prototype, a straight wedge opener was investigated. (Results and discussion) As a result the friction surface loading diagrams were obtained with a change in the loosening angles and the range of the stress diagram area from 2,000 to 12,000 square millimeters. The values of force equivalents acting from the real soils of the proposed operating areas were determined. It was noted that combining the characteristics of simulated loading of working parts with the parameters of real soil force equivalents makes it possible to predict the reliability and service life of the created structures of soil-cutting parts. (Conclusions) It has been established that the obtained model of the tribolithic process for abrasive wear of soil-cutting part ensures the superposition of simulated loading results with the values of real soil force equivalents, thus providing a 0.5-1 year reduction in the terms of creating new parts and maintaining the normative indices of technological process reliability and quality.

Wedge disclination description of emergent core-shifted grain boundaries at free surfaces

Emergent grain boundaries at free surface control material properties such as nanomaterial strength, catalysis, and corrosion. Recently the restructuring of emergent boundaries on copper (111) surfaces was discovered experimentally and atomic calculations point to its universality in fcc metal systems. Restructuring is due to a preference for boundaries to shift their tilt axis across the (11¯0) plane towards [112] and ultimately to form low energy [112] core shifted boundaries (CSBs). However, the observed geometry of these emergent boundaries is not reproduced by atomic calculations and the driving force is still controversial due to inconsistencies between the computational continuum analysis and atomic calculations. Here, using atomic calculations that involve a methodical shift of the dislocation core, we confirmed the geometry of emergent boundaries observed in experiment and reconciled the atomic calculations with the elastic analysis through the inclusion of a straight wedge disclination at the free surface.

The emergence of delta shock in the limit process for two‐dimensional steady nonisentropic relativistic Euler flow onto a straight wedge

AbstractIn this paper, we mainly study the limit of solutions to the two‐dimensional steady nonisentropic relativistic Euler flow onto a straight wedge. It turns out that the sequence of shock solutions tends to a delta wave adhering to the wedge surface when the velocity of the incident flow goes to the speed of light and the adiabatic index tends to 1 in turn. Meanwhile, it also verifies that the pressure coefficient in the limit case is consistent with the Newtonian sin‐squared law when the speed of light tends to infinity. To this end, we also derive the generalized Bernoulli equation, Taub adiabat (or the generalized Hugoniot adiabat) and a shock polar, and so forth. Furthermore, we give the construction of the delta wave by the definition of weak solution.

Configurations of Shock Regular Reflection by Straight Wedges

Configurations of Shock Regular Reflection by Straight Wedges

The initiation characteristics of oblique detonation waves induced by a curved surface

Most of the previous studies focus on oblique detonation wave (ODW) produced by an infinite/finite straight wedge; however, there is a lack of research on ODWs induced by a convex or concave curved surface. In this paper, the initiation characteristics of oblique detonation waves induced by a curved surface are studied, the two-dimensional (2D) multi-species Euler equations with a detailed chemical reaction are solved. The effects of the shape and position of the curved surface on the initiation characteristics of the ODW are investigated. The numerical results demonstrate that the wedge with a convex circular arc-surface generates the expansion waves, which makes the shock wave and the combustion wave decoupled and the ODW will not to be initiated. The wedge with a concave circular-arc surface produces the compression waves and promotes the initiation of the ODW. As the curvature of the concave surface becomes greater, the compression waves become stronger, the length of the induction zone gets shorter and the ODW is easy to be initiated. Decreasing the length of the straight wedge makes the compression wave move upstream and the detonation position move forward, it makes the characteristic length of the induction zone decrease.

Scalable Fabrication of Bioinspired Controllable Dry Adhesive by Roll‐to‐Roll Slitting

Controllable dry adhesives have attracted significant interest; however, their development and application remain limited owing to their high cost, complexity, and machine precision required for their fabrication. Herein, a scalable roll‐to‐roll technique for fabricating wedge‐shaped controllable dry adhesives for use in robotic grasping tasks is developed. Wedge‐shaped structures with various geometrical dimensions are manufactured, and the structure with optimal wedge dimension (50 μm width and 30° tip angle) demonstrates peak and stable normal adhesion values of 14 and 6.8 kPa, respectively. Moreover, parallel grippers are designed to grasp everyday objects that have flat surfaces and a variety of geometries and surface textures. This novel scalable, low‐cost, and simple method can be used to manufacture a straight and continuous wedge structure in large scale for controllable dry adhesives that can be effectively applied in robotic manipulation tasks.

Numerical investigation on cellular detonation reflection over wedges with rounded corner

Numerical investigations were performed to study the reflection of cellular detonation over wedges with rounded corner, and for comparison, reflections over wedges with straight sharp corner were also calculated. Dynamics of the reflection phenomenon were described by the two-dimensional reactive Euler equations based on the platform of OpenFOAM-7, with the utilization of the adaptive mesh refinement (AMR) technology. The reflection process and the influence of the concave section and wedge angle on the reflection were discussed, as well as the transition from Mach reflection to regular reflection. Different kinds of reflection types including the Direct-Mach reflection (DiMR), the Stationary-Mach reflection (StMR) and the Inverse-Mach reflection (InMR) were observed in the concave section. When the detonation initially propagated to the straight section, the influence of the concave section was “remembered”. Subsequently, the influence was “forgotten” at a certain point, and the reflection was controlled by the straight section. When the wedge angle was smaller than or equal to 50°, the asymptotic self-similarity approached in the far field, and the asymptotical triple-point angles decreased with the increase of wedge angle. The critical angle for the transition from Mach reflection to regular reflection was 64.17° for concave wedge, which was much larger than that of straight sharp corner wedge (51 ± 1°).

Elasticity Boundary-Value Problems for Straight Wedge Disclinations. A Review on Methods and Results

Elasticity Boundary-Value Problems for Straight Wedge Disclinations. A Review on Methods and Results

Study on the initiation characteristics of the oblique detonation wave by a co-flow hot jet

The Oblique Detonation Wave Engine is expected to propel the aircraft to hypersonic speeds. Currently available studies are mainly focused on the initiation characteristics of the oblique detonation wave on a straight wedge. The control method is of great importance for a better thrust performance. However, there lacks the trigger location control method of the oblique detonation wave. In the current research, a co-flow hot jet is utilized to initiate the oblique detonation wave with an initiation length shorter than that on a straight wedge. The performance of the co-flow hot jet under different inflow pressures is discussed in detail. The mechanism for the initiation of the oblique detonation wave by the co-flow hot jet is revealed. It is found that the key for the initiation by the co-flow hot jet is an underexpanded jet, which is featured by a first jet shock wave, a second jet shock wave, an expansion fan, and an intercepting shock wave. The first and second jet shock waves are observed for the first time in the research of the oblique detonation wave. The strength of the first and second jet shock waves is higher than that of the leading shock wave, reducing the initiation length of the oblique detonation wave greatly. This investigation reveals the initiation mechanism of the oblique detonation wave by the co-flow hot jet, which is of great importance for its application in the Oblique Detonation Wave Engine.

Elastic Waves in Cylindrical Metal Wedges with Different Geometries

The article presents results of numerical simulation and experimental studies of elastic wedge wave propagation in cylindrical wedges with positive and negative curvature in the 100–600 kHz frequency range. It is shown that wedge waves in such structures have dispersion and their localization at the edge of the wedge is stronger than that of straight wedges. The results of a study for cases where the inner surface of the wedge is bounded by fluids with different viscosities (water, SAE 10W-30 motor oil, 86% glycerol aqueous solution) are presented.

Hypersonic limit of two‐dimensional steady compressible Euler flows passing a straight wedge

AbstractWe formulate a problem on hypersonic limit of two‐dimensional steady non‐isentropic compressible Euler flows passing a straight wedge. It turns out that the Mach number of the upcoming uniform supersonic flow increases to infinity may be taken as that the adiabatic exponent γ of the polytropic gas decreases to 1. We propose a form of the Euler equations which is valid if the unknowns are Radon measures and construct a measure solution containing Dirac measures supported on the surface of the wedge. It is proved that as , the sequence of solutions of the compressible Euler equations that contains a shock ahead of the wedge converges vaguely as measures to the measure solution constructed. This justifies the Newton theory of hypersonic flow passing obstacles in the case of two‐dimensional straight wedges. The result also demonstrates the necessity of considering general measure solutions in the study of boundary‐value problems of systems of hyperbolic conservation laws.

On regular reflection to Mach reflection transition in inviscid flow for shock reflection on a convex or straight wedge

The regular reflection to Mach reflection ( ) transition in inviscid perfect air for shock reflection over convex and straight wedges is investigated. Provided that the variation of shock intensity only has a second-order effect on the wave transition, the possible cases for the occurrence of the transition for curved shock reflection over a wedge are discussed. For a planar shock reflecting over a convex wedge, four different flow regions are classified and the mechanism of the disturbance propagation is interpreted. It is found that the flow-induced rarefaction waves exist between disturbances generated from neighbouring positions and isolate them. For a curved shock reflecting over a convex wedge, although the distributions of the flow regions are different from those in planar shock reflection, the analysis for the planar shock case can be extended to curved shock cases as long as the wedge is convex. When a diverging shock reflects off a straight wedge, the flow-induced rarefaction waves are absent. However, the disturbances generated earlier cannot overtake the reflection point before the pseudo-steady criterion is satisfied. In the cases considered, the flow in the vicinity of the reflection point will not be influenced by the unsteady flow caused by the shock intensity and the wedge angle variations. This is clearly a local property of the shock–wall interaction, no matter what the history of the shock trajectory is. For validation, extensive inviscid numerical simulations are performed, and the numerical results show the reliability of the pseudo-steady criterion for predicting the transition on a convex wedge.

Initiation of oblique detonation waves induced by a blunt wedge in stoichiometric hydrogen-air mixtures

Two-dimensional, oblique detonation waves (ODWs) in a stoichiometric hydrogen-air mixture are simulated with the reactive Euler equations using a detailed chemical reaction model. This study focuses on blunt wedge induced ODWs, which are not only influenced by inflow parameters but also the size of the blunt body. With the inflow parameters of flight altitude of 30 km and flight Mach number M0 of 8-10, the numerical results demonstrate that the blunt wedge is crucial to initiate the ODW. In the case of M0=10, the straight wedge without the blunt forebody can initiate the detonation. However, decreasing M0 causes the failure of initiation, which can be compensated by increasing the radius R0 of the blunt forebody. By adjusting R0, two initiation procedures are observed and distinguished: one is the wedge-induced initiation and the other is the blunt forebody-induced initiation. Although both have been independently studied before, in this study, their coexistence is demonstrated, and the mechanism is analyzed for the first time. A theoretical analysis based on the classic initiation theory is performed to elucidate the initiation mechanism, giving a good agreement between the critical radius with numerical results.

A revisit of the elastic fields of straight disclinations with new solutions for a rigid core

The classical solutions for straight disclinations in an infinite elastic solid have been obtained by integrating the results for disclination densities. In this paper, the equilibrium equations are solved directly for straight twist and wedge disclinations, subject to the boundary conditions of the defects and rigid body translations/rotations. For a twist or wedge disclination in an infinite solid, the current solutions, based on a core fixed at a point to remove rigid body motion, differ from the classical ones by the constant $$-\hbox {log }r_{i}$$ , where $$r_{i }$$ is the radius of the disclination core. For a wedge disclination in an infinitely long cylinder, additional terms of the form 1 / r in the radial displacement and $$1/r^{2}$$ in the stresses appear in the solutions. The dependence of the current and classical results on the Lame constants highlights significant differences near the disclination line, which will impact studies of disclination relaxation such as crack nucleation and core amorphization. The energy of a singular wedge disclination in a cylinder without a core mostly underestimates that of a wedge disclination with a core.

On Two Alternative Uniformly Asymptotic Procedures for Analyzing the High-Frequency Diffraction of a Complex Source Beam by a Straight Wedge

When spectral wave integrals, representing the radiation and diffraction of electromagnetic waves, are characterized by a first-order saddle point and poles in the integrand, they can usually be evaluated, in essentially closed form, at high frequencies by the leading terms of any of the two well-known alternative uniformly asymptotic procedures, namely, the Pauli–Clemmow method (PCM) and the Van der Waerden method (VWM), respectively. The PCM has the advantage that its leading terms directly yield a solution in the simple ray format of the uniform geometrical theory of diffraction (UTD). On the other hand, it is commonly noted that it is not the leading term of the PCM but that of the VWM which remains valid for the case of complex waves. Nevertheless, it is shown here that the PCM can surprisingly work even for some special complex wave cases, only if certain conditions are met. Indeed, it is demonstrated here that the PCM meets these conditions for the special case of the diffraction of a complex source beam (CSB) by a wedge. Also, the PCM directly yields a UTD like solution for this case. The latter result is significant as it provides a strong justification for obtaining a simple UTD type solution for the more general problem of the diffraction of a CSB incident from an arbitrary direction on a wedge with arbitrary curvature, directly via analytic continuation of the corresponding UTD result available for a curved wedge illuminated by a point source in real space. It is also shown that the VWM solution can be trivially cast in the UTD format, by expressing it as a sum of the PCM solution plus a UTD slopelike correction term; a similar result was obtained previously using a higher order term from a generalization of the PCM procedure given elsewhere.

Reflection of a converging cylindrical shock wave segment by a straight wedge

As a converging cylindrical shock wave propagates over a wedge, the shock wave accelerates and the angle between the shock wave and the wedge decreases. This causes the conditions at the reflection point to move from what would be the irregular reflection domain for a straight shock wave into the regular reflection domain. This paper covers a largely qualitative study of the reflection of converging shock wave segments with Mach numbers between 1.2 and 2.1 by wedges inclined at angles between \(15^\circ \) and \(60^\circ \) from experimental and numerical results. The sonic condition conventionally used for predicting the type of reflection of straight shock waves was found to also be suitable for predicting the initial reflection of a curved shock wave. Initially regular reflections persisted until the shock was completely reflected by the wedge, whereas the triple point of initially irregular reflections was observed to return to the wedge surface, forming transitioned regular reflection. After the incident shock wave was completely reflected by the wedge, a shock wave focusing mechanism was observed to amplify the pressure on the surface of the wedge by a factor of up to 100 for low wedge angles.

Elastic fields of straight wedge disclinations axially piercing bodies with spherical free surfaces

Linear elasticity problem for a straight wedge disclination, which axially pierces a hollow sphere (a spherical layer), is solved analytically. The disclination displacements, stresses and dilatation are given in the form of series with Legendre polynomials. The related elasticity problems for a wedge disclination in a bulk elastic sphere and those one treading a spherical cavity are addressed, as well. It is demonstrated that the found solutions satisfy the boundary conditions on spherical free surfaces including the disclination emerging points. The distribution and the magnitude of the disclination elastic fields in spherical bodies strongly depend on the presence and the size of the inner cavity. For the correct treatment of elasticity for a disclination penetrating through a spherical pore, it is necessary to take into account strictly the boundary conditions on the remote external boundaries of the elastic body.

The Hardy inequality and the heat flow in curved wedges

We show that the polynomial decay rate of the heat semigroup of the Dirichlet Laplacian in curved planar wedges that are obtained as a compactly supported perturbation of straight wedges equals the sum of the usual dimensional decay rate and a multiple of the reciprocal value of the opening angle. To prove the result, we develop the method of self-similar variables for the associated heat equation and study the asymptotic behaviour of the transformed non-autonomous parabolic problem for large times. We also establish an improved Hardy inequality for the Dirichlet Laplacian in non-trivially curved wedges and state a conjecture about an improved decay rate in this case.

A Novel Ray Tracing Algorithm for Scenarios Comprising Pre-Ordered Multiple Planar Reflectors, Straight Wedges, and Vertexes

An algorithm is presented for calculating the positions of the scattering centers of a ray undergoing multiple reflections and multiple diffractions from edges and/or vertexes, in a scenario comprising a collection of reflecting plates illuminated by a point source. Through the application of the image theorem, the new ray tracing algorithm generalizes a previous solution, already present in the literature, which efficiently calculates the diffraction centers in the case of multiple edge diffraction. The effectiveness of the proposed algorithm is positively tested by some numerical examples.

Generalization of UTD Double Diffraction to the Case of Impenetrable Wedges With Relatively General Boundary Conditions

In the framework of the uniform geometrical theory of diffraction (UTD), a novel high-frequency solution is provided which allows the description of the rays doubly diffracted by a pair of impenetrable straight wedges, with relatively general boundary conditions, under a spherical wave illumination. Such a UTD solution is heuristically derived by imposing the continuity of the total field at the shadow boundaries of the first order (i.e., geometrical optics + UTD wedge single diffracted ray field) UTD solution. It is the extension, to the case of double diffraction, of the first order solutions proposed by Luebbers and by Burnside and Burgener; it allows a uniform description of the field at any observation point, including those aspects where transition regions overlap and the cascading of UTD single wedge diffraction coefficients fails. The proposed solution does not consider surface wave effects and, for the special case of two perfectly conducting wedges, it reduces to the formulation present in the literature, of which it can be considered a generalization. Indeed, it requires the same special functions involved in UTD double diffraction by two perfectly conducting wedges. The double diffracted ray field is expressed in analytical closed form, providing a deeper understanding of the physics involved in double diffraction, and a new powerful tool to be employed in any modern ray-based code.