Rounded Corners Research Articles

Effect of Dimple Intrusions and Curvature Radius of Rounded Corner Triangular Duct on Fluid Flow and Heat Transfer

The sharp corner significantly affects the flow through triangular duct. In the corners, flow gets stagnant, which results in poor heat transfer. Therefore, in the present study, one corner of the duct is kept rounded with variable curvature radius values (Rc). The curvature radius is selected in such a way that it varied from the minimum value (i.e., Rc = 0.33 times duct height; h) to a maximum value (i.e., Rc = 0.67h,which named as conventional duct in the work). In addition to this, the combined effect of both rounded corner and dimple-shaped intrusion has also been studied on flow of air and heat transfer and for this purpose; the relative streamwise distance (z/e) is varied from 6 to 14 with constant relative transverse distance (x/e) that is10. Steady-state, turbulent flow heat transfer under thermal boundary conditions is analyzed for Reynolds number from 5600 to 17,700. ANSYS (Fluent) 12.1 software is used to perform numerical simulations and good match has been observed between the simulated and experimental results. Due to rounded corner and dimple intrusions, velocity near the corner region has higher value in comparison to the conventional duct. The uniform temperature distribution is seen in the case of dimple intruded duct as compared to conventional and rounded corner duct (with Rc value of 0.33h). In comparison to conventional duct, the heat transfer increased about 21–25%, 13–20%, and 5–8%, for the Rc value of 0.33h, 0.49h, and 0.57h, respectively, but the combination of rounded corner and dimple-shaped intrusion augments heat transfer by 46–94%, 75–127%, 60–110%, for the z/e value of 6, 10, and 14, respectively, with the Reynolds number increase from 5600 to 17,700.

Output offset in silicon Hall effect based magnetic field sensors

In this paper we present simulation and measurements for output offset in integrated silicon Hall sensors. Using FEM simulations of various sensor structures, sources of output offset and methods to mitigate this are identified. The simulation results indicate that using cross-shaped sensors exhibit 75% higher variance than octagon shaped sensors as well as sensors shaped as a square with rounded corners. It is determined that restricting the direct current flow path would yield larger offset variances. Additionally the measurements indicate that there are proximity effects that also impact the offset in addition to the geometry. Sensors surrounded by other structures do exhibit the variation relations observed in the simulations. The sensors located on the edges exhibit additional sensor offset variation. The measured sensor offsets vary between 5 mV–20 mV including proximity effects. If we can reduce proximity effects the variation is measured from 5 mV to 10 mV. Therefore reducing the Hall sensor output voltage offset variance involves using dummy devices as avoidance of restrictions on the current flow.

An efficient evolutionary structural optimization method with smooth edges based on the game of building blocks

ABSTRACTAlthough bi-directional evolutionary structural optimization (BESO) has the advantages of a simple concept and clear-cut solutions, the edges of the optimal solution are normally non-smooth. This article proposes an approach that directly represents the smooth structure using finite elements. The pseudo-auxiliary line is introduced to make the staggered boundary approach a smooth one, and a rule is presented to make the boundary element deformable to describe the structure’s edges. To improve the efficiency, the game of building blocks is incorporated into the classical BESO algorithm. A set of basic blocks is predefined and is positioned in a suitable location to assemble the optimal structure. In this way, the optimal structure has better mechanical performance and smooth edges with acceptable computational cost. The roundness of corners is easily controlled by adjusting the configuration of the basic blocks. Several two- and three-dimensional numerical examples investigate the effects of the parameters of auxiliary lines and the shape of basic blocks on the boundary smoothness and optimization performance. The efficiency of the proposed method is justified through these examples.

Constrained Finite Strip Method with Rigid Corner Element for the Buckling Analysis of Thin-Walled Members with Rounded Corners

In this paper modal decomposition of the deformations of thin-walled structural members are discussed. Modal decomposition is a process which separates the characteristic behavior modes. If applied in buckling analysis, modal decomposition makes it possible to analyze pure global or pure distortional buckling or pure local-plate buckling. Ability to calculate critical loads to a pure buckling mode is highly useful in the design of thin-walled structural members, such as cold-formed steel beams or columns. Cold-formed steel profiles are always produced with rounded corners, and earlier studies showed that the now-used modal decomposition techniques of the constrained finite element method and generalized beam theory fail to lead to reasonable results if the rounded corners are directly modelled in the analysis. An extension to the constrained finite strip method is proposed and discussed. The proposal introduces rigid corner elements, which make it possible to perform the modal decomposition by the same process used for members with sharp corners, even if the rounded corners are directly modelled. The formulation of the proposal is summarized, then the rigid-corner approach is studied by an extended parametric study.

Models for Prediction of Surface Roughness in a Face Milling Process Using Triangular Inserts

Research was carried out to develop a mathematical model based on the cutting tool surface profile geometry to predict surface roughness in face milling. Previous models were derived using either the simple assumption of a perfectly round tool nose or statistical analysis based on a large number of experiments. In this research, three milling cases were defined based on the magnitude of the feed rate using a triangular insert with a round corner. In case 1, the machine marks only consisted of a series of arcs. In case 2, the machine marks included a series of an arc and one straight line. In case 3, the machine marks consisted of a series of an arc and two straight lines. Three different equations for surface roughness prediction were obtained based on each of the three cases. Experiments were done to validate the models, and the results showed that the mathematical models had good correlation with experimental results.

Aeroacoustics of Rounded Forward-Facing Steps: Far-Field Behavior

Measurements and predictions of far-field sound radiated by rounded forward-facing steps immersed in an incompressible turbulent boundary were performed. Four different corner rounding radii equal to 0%, 6.25%, 12.5%, and 25% of the step height were considered. The step height was 26.2% of the incoming boundary-layer thickness and the Reynolds number based on step height ranged between 35,000 and 104,000. Measurements of the spanwise averaged unsteady pressure show that the pressure on the downstream surface is a function of rounding due to change in the size and strength of the separation bubble, whereas on vertical face it remains independent of corner rounding. The pressure on either surface scales on the step height and free-stream velocity. Rounding the step corner leads to a consistent reduction in noise without changing the overall shape of the sound spectrum significantly. The sound from each rounded step exhibits the effects of step noncompactness, which prevents spectral scaling. The predictions of sound from an unrounded forward-facing step were made by combining a theoretical formulation with surface pressure measurements. The predictions describe the overall shape of the sound spectrum including the effects of step noncompactness accurately.

Effect of post-processing on the dimensional accuracy of small plastic additive manufactured parts

PurposeThis paper aims to investigate the effect of post-processing techniques on dimensional accuracy of laser sintering (LS) of Nylon and Alumide®and fused deposition modelling (FDM) of acrylonitrile butadiene styrene (ABS) materials.Design/methodology/approachAdditive manufacturing (AM) of test pieces using LS of Nylon and Alumide®powders, as well as the FDM of ABS materials, were first conducted. Next, post-processing of the test pieces involved tumbling, shot peening, hand finishing, spray painting, CNC machining and chemical treatment. Touch probe scanning of the test pieces was undertaken to assess the dimensional deviation, followed by statistical analysis using Chi-square and Z-tests.FindingsThe deviation ranges of the original built parts with those being subjected to tumbling, shot peening, hand finishing, spray painting, CNC machining or chemical treatment were found to be different. Despite the rounding of sharp corners and the removal of small protrusions, the dimensional accuracy of relatively wide surfaces of Nylon or Alumide®test pieces were not significantly affected by the tumbling or shot peening processes. The immersion of ABS test pieces into an acetone bath produced excellent dimensional accuracy.Research limitations/implicationsOnly Nylon PA2200 and Alumide®processed through LS and ABS P400 processed through FDM were investigated. Future work could also examine other materials and using parts produced with other AM processes.Practical implicationsThe service bureaus that produce prototypes and end-use functional parts through AM will be able to apply the findings of this investigation.Originality/valueThis research has outlined the differences of post-processing techniques such as tumbling, shot peening, hand finishing, spray painting, CNC machining and chemical treatment. The paper discusses the advantages and disadvantages of each of those methods and suggests that the immersion of ABS test pieces into an acetone bath produced excellent dimensional accuracy.

Cutting Characteristics of Direct Milling of Cemented Tungsten Carbides Using Diamond-Coated Carbide End Mills with Untreated and Treated Cutting Edge

This study investigates the cutting characteristics of direct milling of cemented tungsten carbides performed using a diamond-coated carbide end mill. The diamond-coated carbide end mills have cutting edges that are both treated and untreated, and the sharp cutting edge can be developed at the ridgeline of the diamond coating on the flank face via treatment of the cutting edge. Two types of cemented tungsten carbide were used as workpiece materials, i.e., TAS VM-40 and VC-70. The influence of the cutting length on the cutting characteristics was also studied. In the case of cutting of the VM-40, the cutting force of the treated tool was significantly lower than that of the untreated tool. The cutting forces of both tools were observed to be similar after the diamond coating on the rake face of the untreated tool was flaked. The cutting edge at the ridgeline of the diamond coating on the flank face of both tools was retreated during the cutting progress, and the thickness of the diamond coating of the untreated tool was also decreased. The finished surface integrity was drastically altered owing to the flaking of the diamond coating on the rake face of the untreated tool and the irregularity of the cutting edge of both tools. The accuracy of the machined shape obtained by using the treated tool was better than that obtained using the untreated tool, and the tendency was significantly observed as the cutting progressed. In the case of cutting of VC-70, flaking of the diamond coating of untreated tool did not occur, and the cutting force of the treated tool was significantly lower than that of the untreated one. The cutting edge of the treated tool was maintained sharp up to a groove length of 500 mm, although the workpiece material was clearly observed to be adhering to the round corner of the cutting edge of the untreated tool. Moreover, the accuracy of the shape of the machined groove obtained using the treated tool was better than that obtained using the untreated tool.

Phase behavior of two-dimensional Brownian systems of corner-rounded hexagons

Investigations into the phase behavior of Brownian systems of nonspherical colloids have received considerable attention because these systems can exhibit very rich self-assembled structures, some of which have potential for applications. In this work, we explore the phase behavior of corner-rounded hexagons in two dimensions, both through experiments and Monte Carlo (MC) simulations. Our experiments, using lithographically shape-designed hexagons, which have corner-rounded vertices and nearly hard in-plane interactions, reveal three different solid phases for increasing particle area fraction ${\ensuremath{\phi}}_{\mathrm{A}}$: hexagonal rotator crystal (RX), hexagonal crystal (HX), and frustrated hexagonal crystal (FHX). In the RX phase, hexagons form a hexagonal lattice, but they are randomly oriented and their rotations are ergodic. In the HX phase, hexagons orient uniformly on average, but their rotations are still ergodic via slower hopping motion. In the FHX phase, all hexagons are uniformly oriented, but their rotations are highly bound and nonergodic. MC simulation results on matching rounded hexagons confirm this experimentally observed sequence of phases. Using simulations, we increase the corner roundness and show that the molecular-orientational order decreases at fixed ${\ensuremath{\phi}}_{\mathrm{A}}$. Our results provide insights into controlling the large-scale self-assembly of spatially and orientationally ordered two-dimensional arrays of colloids through particle shape design and crowding conditions.

Path Planning for Robotic Grinding on a Large Forged Workpiece

In this paper a robotic grinding system which can produce a finished workpiece that respects some product geometric specifications is proposed. It is composed of a 1 DoF active compliance actuator fixed between the grinder and the robot. The 1 DoF actuator associated to the tool can be mounted at existing robotic installations which make this solution very flexible and easy to use by the industrials. The grinding system composed of the robot and the actuator is able to apply a constant contact force between the workpiece and the grinding tool. A path planning method is also presented in this article. Using analytical calculations, the robot path is determined for grinding a rounded corner on a parallelepiped workpiece with a given precision of the surface shape.

Formability analysis of bearing ring produced by short-flow warm extrusion processing

Bearing rings are the most common used machine parts. It is of great significance to reduce the processing flow of bearing rings for saving energy and material, increasing productivity. In this work, one step warm extrusion processing using ring blank as preform was proposed to form bearing ring which possesses upper and lower rings. The upper and lower rings are formed by materials reverse and forward flow during warm extrusion, respectively, and the ratio of materials reverse flow amount to forward flow amount (RRFA) determines the formability of bearing rings. In order to process bearing rings at optimum RRFA at which the upper and lower rings can be simultaneously formed, finite element models for the warm extrusion processing were established based on DEFORM-3D software. The effect of extrusion ratio, round corner radius of extrusion die, extrusion temperature, friction coefficient on the flow rules of materials was analyzed by the developed finite element models. The results show that small extrusion ratio (i.e. small outer diameter of ring blank) and large round corner radius of extrusion die enhance the material flowing into lower ring and facilitate the forming of lower ring. Extrusion temperature and friction coefficient have little effect on RRFA. Comprehensively considering the flow rules of materials, the well-formed bearing rings can be obtained when extrusion ratio is 2.33, round corner radius of extrusion die is 1.5, extrusion temperature is 700-800 °C.

A Study on the Variation of Wind Velocity between Buildings with the Change of Building Corner Modification

Building Integrated Wind Power (BIWP), the installation of wind power generators on buildings to generate energy, is being attempted in various ways. The advantage of BIWP is that it does not require a support fixture for positioning a wind turbine at a desired height. Furthermore, it allows the energy generated by a turbine to be used directly within the building. Utilizing computational fluid dynamics (CFD), this study examines the variations in wind velocity and turbulence intensity occurring as a result of changes in the morphology of a building’s corners to increase the efficiency of wind power generators that are installed between buildings. Results of this study show that buildings with round corners experienced an increase in wind velocity of up to 13%, as compared to regular corners, while corner cuts increased wind velocity by 15%. The morphology of the corners will have less of an impact on the location where wind velocity is highest where the distance between buildings is greater. However, if the distance between the buildings is shorter and the corners are long enough, wind velocity increases and turbulence intensity decreases.

Increased mechanical robustness of piezoelectric magnetoelastic vibrational energy harvesters

This work presents a cantilever based broadband piezoelectric magnetoelastic vibration energy harvester with increased mechanical robustness. The energy harvester is fabricated using KOH etching to define the cantilever and the proof mass is made using micromachined Fe foils which together with a pair of miniature magnets provides the magnetoelastic properties. KOH etching leads to very sharp corners at the anchoring point of the cantilever which makes the cantilever fragile. The mechanical robustness of the energy harvesters is increased using a lithography-free two-step fabrication process where a thermal oxidation is used for corner rounding. The corner rounding at the anchoring point lowers the stress concentration and thereby increases the robustness of the device. The radius of curvature for the corner depends linearly on the thickness of the oxide. Both enhanced and non-enhanced beams are excited at increasing frame accelerations. The conventional beams break at frame accelerations of around 3 g while the enhanced break at almost twice as much, 5.7 g. The devices are characterized electrically by impedance measurements in both their linear and non linear regime. The magnetoelastic behaviour can be adjusted by varying the beam-magnet distance which allows for both spring softening and spring hardening.

Zircon U-Pb ages and REE composition constraints on the provenance of the continental slope-parallel submarine fan, western Qiongdongnan Basin, northern margin of the South China Sea

Abstract The Ledong Submarine Fan in the western Qiongdongnan Basin runs parallel to the continental slope, with an area of over 10,000 km2 and maximum thickness of greater than 2000 m. Using bulk rare earth element (REE) compositions of the sediments and detrital zircon U-Pb age data, we analysed the provenance of the Ledong Submarine Fan and its regional tectonic implications. The zircon grains in the Ledong Submarine Fan show a wide range of shapes, from prismatic crystals to oval grains with mostly rounded corners, indicating the long transport distance of these zircon grains prior to deposition. The zircon ages have a wide range from 27 to 3006 Ma, with five major age peaks at ca. 27 Ma, 88 Ma, 256 Ma, 415 Ma and 785 Ma, along with a number of subordinate age peaks at ca. 1024 Ma, 1376 Ma, 1879 Ma and 2374 Ma. These age distribution patterns are similar to those from the Red River at Yen Bai. The total REE content range is between 87.72 and 210.38 mg/g in the Ledong Submarine Fan. The chondrite-normalized REE patterns show light REE (LREE) enrichment and weakly negative Eu anomalies, which are similar to those in the Red River at Hanoi. The evidence from zircon U-Pb ages and REE geochemistry indicates that the provenance of the Ledong Submarine Fan is the Red River System. The development of the Ledong Submarine Fan indicates that a rapid subsidence occurred in the western Qiongdongnan Basin during the late Miocene, and the strike slip reversal of the Red River Fault from sinistral to dextral motion was the key factor that induced gravity flow to form the Ledong Submarine Fan.

GBT deformation modes for thin-walled cross-sections with circular rounded corners

This paper addresses an improved cross-section analysis approach for calculating the deformation modes of thin-walled cross-sections with circular rounded corners in the framework of generalized beam theory (GBT). In the cross-section discretization, in contrast to the classic GBT one, the circular rounded corners are treated as independent circular walls, and deflection functions of the corresponding circular arches, which play the role of basis functions, are used to approximate the in-plane displacements of any points on the corner mid-line. Because the geometries of the circular corners are accurately modelled by curved elements, the proposed procedure is more efficient than those based on the polygonal approximation of the corner mid-lines. Illustrative cases concerning the employment of the procedure to four cold-formed cross-sections are presented to show its validity and potential. Through comparisons of the proposed procedure against that based on the polygonal approximation, it is shown that it yields accurate results with much coarser cross-section discretization.

Aeroacoustics of Rounded Forward-Facing Steps: Near-Field Behavior

Measurements of wall pressure fluctuations induced by forward-facing steps with rounded corners immersed in a turbulent boundary layer were performed. Four different roundings of the step corner () equal to 0, 6.25, 12.5, and 25% of the step height () were considered. The step height was 26.2% of the undisturbed boundary-layer thickness, and the Reynolds number based on step height ranged between 35,000 and 104,000. The results show that both mean and fluctuating pressure upstream of the step remain independent of the corner rounding, whereas they are a strong function of rounding on the downstream surface. The latter was found to be due to a reduction in the spatial extent of the separation bubble with increasing rounding. The fluctuating pressure on the vertical face of the steps was found to increase with increasing corner rounding. For , the pressure spectra within the downstream separation bubble, and sufficiently away from the salient corner, were found to scale on the reattachment length and free-stream velocity. Downstream of the separation bubble, the spectra evolve differently and a separate scaling, one which suggests that the pressure fluctuations evolve independently of the incoming boundary layer, is shown to collapse the spectra.

On the Influence of the Entrance Section on the Rotordynamic Performance of a Pump Seal With Uniform Clearance: A Sharp Edge Versus A Round Inlet

Secondary flows through annular seals in pumps must be minimized to improve their mechanical efficiency. Annular seals, in particular balance piston seals, also produce rotordynamic force coefficients, which easily control the placement of rotor critical speeds and determine system stability. A uniform clearance annular seal produces a direct (centering) static stiffness as a result of the sudden entrance pressure drop at its inlet plane when the fluid flow accelerates from an upstream (stagnant) flow region into a narrow film land. This so-called Lomakin effect equates the entrance pressure drop to the dynamic flow head through an empirical entrance pressure loss coefficient. Most seal designs regard the inlet as a sharp edge or square corner. In actuality, a customary manufacturing process could produce a rounded corner at the seal inlet. Furthermore, after a long period of operation, a sharp corner may wear out into a round section. Notice that to this date, bulk-flow model (BFM) analyses rely on a hitherto unknown entrance pressure coefficient to deliver accurate predictions for seal force coefficients. This paper establishes the ground to quantify the influence of an inlet round corner on the performance of a water lubricated seal reproducing a configuration tested by Marquette et al. (1997). The smooth surface seal has clearance Cr = 0.11 mm, length L = 35 mm, and diameter D = 76 mm (L/D = 0.46). The test case considers design operation at 10.2 krpm and 6.9 MPa pressure drop. Computational fluid dynamics (CFD) simulations apply to a seal with either a sharp edge or an inlet section with curvature rc varying from ¼Cr to 5Cr. Note the largest radius (rc) is just 1.6% of the overall seal length L. Going from a sharp edge inlet plane to one with a small curvature rc = ¼Cr produces a ∼20% decrease on the inlet pressure loss coefficient (ξ). A further reduction occurs with a larger circular corner; ξ drops from 0.43 to 0.17. That is, the entrance pressure loss will be lesser in a seal with a curved inlet. This can occur easily if the inlet edge wears due to solid particles eroding the seal inlet section. Further CFD simulations show that operating conditions in rotor speed and pressure drop do not affect the inlet loss coefficient, while the inlet circumferential swirl velocity does. In addition, further CFD results for a shorter (half) length seal produce a very similar entrance loss coefficient, whereas an enlarged (double) clearance seal leads to an increase in the entrance pressure loss parameter as the inlet section becomes less round. CFD predictions for most rotordynamic coefficients are within 10% relative to published test data, except for the direct damping coefficient C. For the seal with a rounded edge (rc = 5 Cr) at the inlet plane, both the direct stiffness K and direct damping C decrease about 10% compared against the coefficients for the seal with a sharp inlet edge. The other force coefficients, namely cross-coupled stiffness and added mass, are unaffected by the inlet edge geometry. The same result holds for seal leakage, as expected. A BFM incorporates the CFD derived entrance pressure loss coefficients and produces rotordynamic coefficients for the same operating conditions. The CFD and BFM predictions are in good agreement, though there is still ∼10% discrepancy for the direct stiffnesses delivered by the two methods. In the end, the analysis of the CFD results quantifies the pressure loss coefficient as a function of the inlet geometry for ready use in engineering BFM tools.

Analytical calculation of stress intensity factors for cracks emanating from a quasi-square hole in an infinite plane

A new conformal mapping is proposed in order to solve stress intensity factor (SIF) problem in an infinite plane containing a traction-free square hole with two unequal cracks, analytically. To this end, Schwarts-Christoffel integral is expanded as sum of finite term series through Newton’s binomial formula to approximate the square hole to a rounded corner square one, which is called quasi-square. Next, the mapping function of cracked hole is expanded to a series of fractional expressions to combine with Muskhelishvili formulation. Finally, SIFs are presented for the remote tensile loading and the effects of crack length and radius of corners on the SIF are studied. To ensure the accuracy, results are compared to the available literature and FEM. Contrary to the previous researches, it was shown that the hole-shape had a considerable effect on the SIF for the small cracks though for large length cracks it is negligible.

Crack defect of tailor rolled blank in deep drawing process

The deformation process of tailor rolled blank (TRB) is different from that of a monolithic blank as a result of the variable thickness in the rolling direction, and thus, the mechanism of the crack phenomenon needs to be further studied. The crack defect of TRB square box was studied by numerical simulation and stamping experiment. The stress state of TRB square box was elaborated. On this basis, the forming characteristics of TRB square box were summarized. The effects of blank size and blank holder force (BHF) on the thickness thinning of TRB were discussed. Finally, the mechanism of the crack defect for TRB square box was revealed. Results indicate that non-uniformity is the most prominent characteristic during forming of TRB square box. The larger the blank size and BHF on the thinner side are, the more inclined TRB is to crack. Excessive BHF or insufficient BHF on the thicker side can also lead to the occurrence of the crack defect. BHF on the thinner side slightly greater than that on the thicker side (40 kN on the thinner side and 20 kN on the thicker side) is advantageous to restrict the excessive thickness thinning of TRB and acquire a better formability. The location inclined to crack for TRB square box is the round corner of the wall on the thinner side.

Mohr-coulomb model for rectangular and square FRP-confined concrete

An analytical stress-strain model for fiber reinforced polymer (FRP) confined concrete is developed for predicting the compressive and dilation behavior of rectangular and square cross-sections with rounded corners. An iterative as well as a non-iterative two parameter Mohr-Coulomb yield criterion are introduced for analyzing the compressive behavior of FRP-confined concrete. A new diagonal Poisson’s ratio formulation is employed which describes the dilation behavior of FRP-confined concrete as a function of the mechanical properties of unconfined concrete, FRP jacket, section geometry, and internal damage of the confined concrete core. Equilibrium and strain compatibility are used to obtain the ultimate concrete compressive strength and strain as a function of the effective confining stiffness of the FRP jacket and transverse strains. Simplified expressions are derived for the FRP reinforcement ratio which precludes strain-softening in rectangular and square FRP-confined concrete sections.