Non-circular Shape Research Articles

Synchronous multipass spinning of oblique-bottom shape

Recently, various methods for the metal spinning of noncircular shapes have been proposed to overcome the limitation of its application range. In this study, a metal spinning method for noncircular shapes with oblique bottoms is proposed. This method is a combination of synchronous spinning and multipass spinning, in which the roller is synchronized with the mandrel rotation to track a noncircular cross section while the workpiece is gradually deformed without much thinning through some paths of the roller. The roller trajectory is calculated by linear interpolation in the radial direction and axial direction between the inclined blank shape and the inclined cross section of the product. A circular cup and square cup with an oblique bottom and vertical side walls are successfully spun using this method. As the wall thickness locally increases at the side edges of the square cup, the thickness distribution is equalized by using an intermediate circular shape. This method interpolates the roller trajectory between the blank shape and intermediate shape and between the intermediate shape and the product. The difference in the wall thickness is reduced since the square shape is formed via a cylindrical shape. In addition, the effect of the process parameters on the forming results is experimentally investigated.

No difference in the graft shift between a round and a rounded rectangular femoral tunnel for anterior cruciate ligament reconstruction: an experimental study.

We developed a novel technique of creating a rounded rectangular femoral bone tunnel for anatomical, single-bundle, autologous hamstring tendon anterior cruciate ligament (ACL) reconstruction. Although this tunnel has many advantages, its non-circular shape has raised concerns regarding excessive graft shift within the bone tunnel. This study aimed to compare the graft shift between round and rounded rectangular tunnels using a graft diameter tester for simulating the femoral bone tunnel. Seven semitendinosus tendon grafts harvested from fresh-frozen cadavers were prepared by removing all excess soft tissue. The two ends of a double-fold hamstring tendon were sutured using a baseball stitch and then looped over a TightRope (Arthrex Co., Ltd., Naples, Florida, USA) to make a fourfold graft. The diameter of the graft was standardized to 8mm using a round graft diameter tester. A round and an original rounded rectangular graft diameter tester were used for simulating the respective femoral bone tunnels. The graft was inserted into the tunnel, with the TightRope positioned on the outside of the tunnel. The distal end of the graft was tensioned to 40N at an angle of 75° to reproduce the most severe graft bending angle. Digital photographs of the tunnel aperture taken at each simulated tunnel and the range of graft shift in the simulated tunnel were analyzed by ImageJ software. Statistical analyses were performed using the Tukey test. P < 0.05 was considered to be significant. There were no significant differences between the round and the rounded rectangular tunnel groups (P > 0.05) in terms of graft shift, gap area, and graft shift ratio. In a simulated ACL reconstruction, there is no difference in the graft shift between a round and a rounded rectangular bone tunnel.

Sintering forces acting among particles during sintering by grain‐boundary/surface diffusion

AbstractThe microstructural evolution during sintering involves the formation and pinch‐off of pore channels. The sintering of 3 particles in 3 dimensions is a simple model for studying the pinch‐off of a pore channel. We simulate the solid‐state sintering of 3 particles by using Brakke's Surface Evolver program, which incorporates coupled grain‐boundary diffusion and surface diffusion. The pinch‐off of pore channel divides the sintering process into 2 stages; the initial stage and the later stage. The contact area has a noncircular shape bounded by both surface triple junction and triple junction in the later stage. A general method is presented to determine the sintering force acting on the noncircular contact. The mechanical approach of densification, where the relative motion of particles is driven by both sintering force and applied force, is applicable not only for the initial stage, but also for the later stage.

The combined effect of wrinkles and noncircular shape of fibers on wetting behavior of electrospun cellulose acetate membranes

ABSTRACTRoughness‐induced hydrophobicity is an area of rapid growth which can be achieved through surface texture or surface porosity. Characterizing the effect of surface roughness on wetting behavior of surfaces with irregular shapes has always been a challenging problem. In this work, changing the environmental conditions during electrospinning of hydrophilic cellulose acetate solutions produced highly porous ribbon like fibers, differed widely in their surface morphologies. All samples showed apparent hydrophobicity with water contact angles between 121° and 146°. The specific surface area was introduced for the first time, as a comprehensive parameter to predict contact angles of noncircular fibers. Statistical modeling revealed that the log‐linear models would better fit the data in comparison with the other linear forms. These results confirmed that the specific surface area could be an appropriate single variable for predicting the contact angles of multiscale porous and wrinkled structures of electrospun fibers. Moreover, the membrane produced at 20 °C temperature and the relative humidity of 60% revealed surprisingly high specific surface area (276.63 m2/g) that seems very promising for industrial applications such as separation technologies. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 1012–1020

Numerical analysis of slug flow boiling in square microchannels

Boiling heat transfer in micro-geometries has been studied extensively in the recent years as an efficient heat removal mechanism. Numerical simulations have been traditionally employed to resolve the small spatial and temporal scales of the flow, thus accessing many details of the flow unattainable experimentally. However, existing fundamental analyses mainly have focused on circular channels that could be modeled with 2D axisymmetric geometries, while flows in more complex cross-sections are still seldom explored. Since geometries for microfluidic applications have typically non-circular shapes with sharp corners, this constitutes an important gap in the literature. Built on this consideration, the present work presents a fundamental investigation of the fluid flow and heat transfer features associated with slug flow boiling in a square microchannel. Numerical simulations are conducted with the open-source finite-volume solver OpenFOAM 2.3.1. The built-in VOF method is adopted to capture the interface dynamics, while phase change has been introduced through external subroutines. Flow configurations that differ in terms of geometry of the channel cross-section (circular and square) and liquid flow rate are analyzed. It is observed that the bubble dynamics and heat transfer change considerably depending on the channel geometry. In the square channel, the bubble always travels faster compared to the circular tube, while the liquid film thickness reaches values which are one order of magnitude smaller given the same capillary and Reynolds numbers due to the thickening at the corners and thinning on the faces. The flow configuration in the square channel undergoes a substantial transition as the capillary number is reduced, as the bubble shape becomes non-axisymmetric, the interface curvature changes sign along the sides of the cross-section, and the liquid film thickness varies considerably along the perimeter of the cross-section. This has a profound impact on the heat transfer performance, with extremely high values of the heat transfer coefficient along the faces while the corners of the square cross-section give a negligible contribution to heat removal. Importantly, draining flows which are transversal to the main stream direction make the liquid film thinner as the bubble rear is approached, so that in a square channel the liquid film will always eventually dry out when the bubble becomes sufficiently long.

Onset of detachment in adhesive contact of an elastic half-space and flat-ended punches with non-circular shape: analytic estimates and comparison with numeric analysis

A recent paper by Popov, Pohrt and Li (PPL) in Friction investigated adhesive contacts of flat indenters in unusual shapes using numerical, analytical and experimental methods. Based on that paper, we analyze some special cases for which analytical solutions are known. As in the PPL paper, we consider adhesive contact in the Johnson–Kendall–Roberts approximation. Depending on the energy balance, different upper and lower estimates are obtained in terms of certain integral characteristics of the contact area. The special cases of an elliptical punch as well as a system of two circular punches are considered. Theoretical estimations for the first critical force (force at which the detachment process begins) are confirmed by numerical simulations using the adhesive boundary element method. It is shown that simpler approximations for the pull-off force, based both on the Holm radius of contact and the contact area, substantially overestimate the maximum adhesive force.

Optimum design of fiber angle and hole orientation of an orthotropic plate

With the goal of decreasing the stress concentration along the hole boundary in an orthotropic plate under inequi-biaxial loadings, an optimum design of the fiber angle and hole orientation is presented. The maximum absolute tangential stress along the hole boundary is taken as the objective function, and the fiber orientation angle and the hole orientation angle are considered as design variables. The conformal transformation method of a complex function and the Differential Evolution (DE) algorithm are used. Two non-circular shapes, ellipse and hexagon are taken as examples to analyze the problem. Based on the results, we can conclude that the major axis of elliptical holes should be designed in the direction of the maximum external loading for a perforated structure in an orthotropic plate. However, the principal direction that has the larger Young’s modulus should be inclined to the direction of the minimum loading, especially for a significantly orthotropic plate.

On the skin friction due to turbulence in ducts of various shapes

We consider fully developed turbulence in straight ducts of non-circular cross-sectional shape, for instance a square. A global friction velocity $\overline{u}_{\unicode[STIX]{x1D70F}}$ is defined from the streamwise pressure gradient $|\text{d}p/\text{d}x|$ and a single characteristic length $h$, half the hydraulic diameter (shapes with disparate length scales, due to high aspect ratio, are excluded). We reason that as the Reynolds number $Re$ reaches high values, outside the viscous region the streamwise velocity differences and the secondary motion scale with $\overline{u}_{\unicode[STIX]{x1D70F}}$ and the Reynolds stresses with $\overline{u}_{\unicode[STIX]{x1D70F}}^{2}$. This extends the classical defect-law argument, associated with Townsend and many others, and is successful in channel and pipe flows. We then posit matched asymptotic expansions with overlap of the law of the wall and the behaviour we assumed in the core region. The wall may be smooth, or have a Nikuradse roughness $k_{S}$ (such that it is fully rough, with $k_{S}^{+}\gg 1$). The consequences include the familiar logarithmic behaviour of the velocity profile, but also the surprising prediction that the skin friction tends to uniformity all around the duct, except near possible corners, asymptotically as $Re\rightarrow \infty$ or $k_{S}/h\rightarrow 0$. This is confirmed by numerical solutions for a square and two ellipses, using a conventional turbulence model, albeit the trend with Reynolds number is slow. The magnitude of the secondary motion also scales as expected, and the skin-friction coefficient follows the logarithm of the appropriate Reynolds number. This is a validation of the mathematical reasoning, but is by no means independent physical evidence, because the turbulence models embody the same assumptions as the theory. The uniformity of the skin friction appears to be a new and falsifiable deduction from turbulence theory, and a candidate for high-Reynolds-number experiments.

NONCIRCULAR CFRP BICYCLE'S CHAINRING, PART II: FINITE ELEMENT ANALYSIS

In this paper, numerical simulation is developed in order to analyze the failure of a noncircular composite chainring, and teeth damage is especially detailed. Simulation consists of the chainring and a part of the metallic chain. To reduce the size of the numerical model only the first 11 rollers are simulated. In order to validate the numerical simulation, the force–displacement curve is compared with the experimental results obtained on the same specimens used in the simulation. Then, the effect of the noncircular shape is studied through three different loading positions, and a damage scenario is proposed. Moreover, the effect of composite lay-up is investigated through different lay-ups. The results show that the loading position has no influence on the chainring behavior, while the damage scenario depends on it. The damage consists of matrix cracking located on the teeth surface. Finally, the thickness can be reduced to 9 plies lay-up and even if the damage is larger, it is always located on the teeth surface.

Stiffness of frictional contact of dissimilar elastic solids

The classic Sneddon relationship between the normal contact stiffness and the contact size is valid for axisymmetric, frictionless contact, in which the two contacting solids are approximated by elastic half-spaces. Deviation from this result critically affects the accuracy of the load and displacement sensing nanoindentation techniques. This paper gives a thorough numerical and analytical investigation of corrections needed to the Sneddon solution when finite Coulomb friction exists between an elastic half-space and a flat-ended rigid punch with circular or noncircular shape. Because of linearity of the Coulomb friction, the correction factor is found to be a function of the friction coefficient, Poisson's ratio, and the contact shape, but independent of the contact size. Two issues are of primary concern in the finite element simulations – adequacy of the mesh near the contact edge and the friction implementation methodology. Although the stick or slip zone sizes are quite different from the penalty or Lagrangian methods, the calculated contact stiffnesses are almost the same and may be considerably larger than those in Sneddon's solution. For circular punch contact, the numerical solutions agree remarkably well with a previous analytical solution. For non-circular punch contact, the results can be represented using the equivalence between the contact problem and bi-material fracture mechanics. The correction factor is found to be a product of that for the circular contact and a multiplicative factor that depends only on the shape of the punch but not on the friction coefficient or Poisson's ratio.

In vivo characterization of the murine venous system before and during dobutamine stimulation: implications for preclinical models of venous disease

Although widely used as a preclinical model for studying venous diseases, there is a scarcity of in vivo characterizations of the naïve murine venous system. Additionally, previous studies on naïve veins (ex vivo) have not included the influence of surrounding structures and biomechanical forces. Using MRI, we noninvasively quantified the cross-sectional area, cyclic strain, and circularity of the venous system in young and old, male and female C57BL/6 mice. We investigated the most common venous locations used to perform venous disease research: the common jugular vein, suprarenal inferior vena cava (IVC), infrarenal IVC, common iliac vein, and common femoral vein. Our results elucidate age-dependent changes in venous cross-sectional area, which varied by location. Maximum cyclic strain, a parameter of lumen expansion, showed 10% change across the cardiac cycle, approximately half the magnitude of arteries. Veins demonstrated noncircular shapes, particularly in the core vasculature. The cardiovascular stressor dobutamine had only a small impact on the venous system. Also, our data demonstrate that the peripheral veins tend to decrease in cross-sectional area and circularity with age. Conversely, the IVC tends to increase in size and circularity with age, with males exhibiting larger variability in response to dobutamine compared to females. This work provides a foundation for drawing age and sex comparisons in disease models, and represents the first in vivo characterization of the murine venous system at rest and during the application of a pharmacological exercise surrogate.

An automated procedure for the generation and conformal discretization of 3D woven composites RVEs

A generation tool is developed for complex three dimensional textile reinforced composites Representative Volume Elements (RVEs). This integrated methodology takes into account contact conditions between yarns with polygonal convex cross sections by means of an iterative geometry generation scheme. The tensioning of the yarns is applied in an implicit geometrical manner resulting in their movement leading to contacts between them. The non-circular shape of their cross sections requires the use of a rotational degree of freedom to describe their movement. This rotational degree of freedom is managed during the contact solving procedure. A level set-based post-processing is then used at the end of RVE the generation to automatically supress any residual interpenetration, that further enables controlling the volume fraction (Vyarn) of each family of yarns in the RVE. A thin clearance can also be inserted between yarns during the post processing phase in order to ease the subsequent conforming mesh generation. An implicit geometry-based meshing procedure is subsequently used to produce a high quality discretization of the obtained RVEs. This integrated procedure is used for various woven and 3D RVEs to illustrate its versatility, showing that the discretized RVEs can be used for parametric studies based on computational homogenisation.

Heat transfer and pressure drop during condensation of low-GWP refrigerants inside bar-and-plate heat exchangers

This paper presents new experimental results of heat transfer coefficient and pressure drop measured during condensation of R1234ze(E) and R32 in a brazed aluminum multichannels test section with 1.6mm hydraulic diameter at 40°C saturation temperature, mass velocity from 55 to 275kgm−2s−1, heat flux up to 35kWm−2 and a complete range of vapor quality. The test section displays parallel channels obtained through the bar-and-plate technology using perforated turbulators brazed to the aluminum plates. These are the first data of condensation in a similar geometry presented in the open literature.The measured heat transfer coefficients suggest that the condensation process is strongly affected by the surface tension effects in the whole range of operating conditions, while the effect of mass flux is very limited. This is related to the non-circular shape of the parallel minichannels. Condensation heat transfer has also been studied during flow of superheated vapor. The experimental data have been compared against prediction methods available in the literature. Fourteen models have been applied for the heat transfer coefficient, ten models have been applied for the pressure drop. Relevant suggestions are given for the design of condensers using such a technology.

Load sharing by tooth pairs in involute toothed harmonic drive with conventional wave generator cam

A harmonic drive is a two gear epicyclic drive with a gear set of circular ring gear (RG), a flex rimmed external toothed gear (FG) and an oval cam. FG, with oval cam inside, takes non-circular gear shape encounters improper teeth mating with RG, having only two teeth difference. Consequently, interferences occur at several tooth pairs even at no load. These are inherent and obvious. Overcoming such interferences and further with applied load estimation of load sharing by tooth pairs poses a complex problem. In solving it, first, tooth stiffness of internal gear and external gear are derived in the present investigation. A method of estimating the load shared by the multiple tooth pairs in contact is proposed. The load distribution pattern in proportion to the tooth deformation is considered. Load shared by contacting tooth pairs is estimated and stresses in FG cup are found out using FEM. Finally, such results are compared with experimental results, which have good agreement.

Safety factor assessment of a tunnel face reinforced by horizontal dowels

The use of dowels as a reinforcement technique has been successfully applied to improve the tunnel face stability during excavation, for the sake of safety and for the construction speed. The conventional tunneling, e.g. the New Austrian Tunneling Method, promotes the use of such techniques in design for a maximum optimization of the tunnel support. In this work, the kinematic approach in combination with the strength reduction technique is employed to evaluate the safety factor of a reinforced tunnel face. The discretization technique is extended to generate the failure mechanism for a realistic tunnel face shape (non-circular shape). An interaction zone with finite thickness is used to model the interaction between the soils and the dowels. The width of the interaction zone introduces a new parameter in the optimization process. In order to validate the implemented method, the results are compared with those of numerical analysis, which shows that the developed approach is an efficient design tool for the safety factor assessment of a reinforced tunnel face. Several charts are provided for parametric analysis to discuss the influence of the bolt length, the bolt density and the soil shear strength.

Acoustic source localization in an anisotropic plate without knowing its material properties – A new approach

Acoustic source localization (ASL) in a highly anisotropic plate is a challenging task. The basic assumption in many of the currently available techniques is that the wave propagates along a straight line from the source to the receiving sensor. However, waves in anisotropic solids propagate along curved lines and form non-circular wave fronts. As a result, for a highly anisotropic solid the acoustic source localization techniques that assume straight line propagation of waves from the source to the receiver are bound to produce a significant error.In this paper a new technique is introduced for acoustic source localization in an anisotropic plate by dealing with non-circular shape of wave fronts. Direction vectors of the wave fronts are computed from the Time-Difference-Of-Arrivals (TDOA) at three sensors placed in a cluster, then they are cast into a geometric vector analysis or an optimization process to accurately obtain the acoustic source location. Two common wave front shapes in highly anisotropic plates, rhombus and ellipse, are analyzed. Following this analysis, the acoustic source could be successfully localized without knowing the material properties of the plate.

Experimental and Computational Analysis of the Swirling Flow Generated by an Axial Counter-Rotating Swirler in a Rectangular Model Chamber Using Water Test Rig

This paper reports the particle image velocimetry (PIV) measurement of swirling flow in a confined rectangular-shaped model combustion chamber. Water is used as the working fluid, and the average profiles of axial, radial, and magnitudes of velocity are given. Flow behavior is investigated and a rebound angle term is defined to investigate the direct effects of the noncircular chamber shape. Flow behavior near the walls is discussed in detail, as are other important swirling flow features such as the appearance of corner and central toroidal recirculation zones. Additionally, experimental data are compared with simulation results. Analyses were performed via commercial software STAR-CCM+ version 9.0. The large eddy simulation (LES) dynamic Smagorinsky subgrid scale, realizable k–ε model, and k–ω shear-stress transport (SST) detached eddy version were used as simulation tools. Three different test filters of 1.0, 2.2, and 3.0 were applied to the LES to identify improvements in accuracy. The overall best turbulence model is compared to the experimental result and reliability of such model is evaluated. The ability of such model was profound within the upstream and to some extent unreliable in downstream.

The Effect of Non-Circular Bearing Shapes in Hydrodynamic Journal Bearings on the Vibration Behavior of Turbocharger Structures

Increasing quality demands of combustion engines require, amongst others, improvements of the engine’s acoustics and all (sub)components mounted to the latter. A significant impact to the audible tonal noise spectrum results from the vibratory motions of fast-rotating turbocharger rotor systems in multiple hydrodynamic bearings such as floating bearing rings. Particularly, the study of self-excited non-linear vibrations of the rotor-bearing systems is crucial for the understanding, prevention or reduction of the noise and, consequently, for a sustainable engine acoustics development. This work presents an efficient modeling approach for the investigation, optimization, and design improvement of complex turbocharger rotors in hydrodynamic journal bearings, including floating bearing rings with circular and non-circular bearing geometries. The capability of tonal non-synchronous vibration prevention using non-circular bearing shapes is demonstrated with dynamic run-up simulations of the presented model. These findings and the performance of our model are compared and validated with results of a classical Laval/Jeffcott rotor-bearing model and a specific turbocharger model found in the literature. It is shown that the presented simulation method yields fast and accurate results and furthermore, that non-circular bearing shapes are an effective measure to reduce or even prevent self-excited tonal noise.

Analysis of prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape by analytical and finite element methods

AbstractThis paper presents a methodology for designing prismatic springs of non-circular coil shape and non-prismatic springs of circular coil shape using analytical and numerical methods. To start with, simple analytical formulations for obtaining the axial deformation of the springs under axial load have been demonstrated. Next, the processes of obtaining CAD models of the springs and their subsequent finite element analysis (FEA) in commercial softwares have been outlined. In the third part, the different springs have been compared with a common cylindrical spring and their merits compared to a common spring have been demonstrated. Next, a fairly accurate analytical formulation (with maximum error of ∼7–8%) for obtaining the value and location of maximum shear stress for all the springs has been demonstrated. Next, two aspects of non-prismatic springs under dynamic loads, viz. damping introduced in a vibrating system and contribution of the spring to the equivalent mass in a one dimensional vibrating spring mass system due to shape of the spring have been discussed. The last part involves an analytical formulation for the linear elastic buckling of two springs with circular coil shapes. For the majority of the work, emphasis has been on obtaining and using closed form analytical expressions for different quantities while numerical techniques such as FEA have been used for validation of the same.Highlights Analytical formulations of axial deflection different springs under axial load. CAD modeling and FEA of prismatic and non prismatic springs of different coil shapes. Comparison of stress and deflection in mass-equivalent springs of different geometry. Approx. analytical formulation for the location and value of max. stress in springs. Effects of spring shape on damping, vibrational properties in 1D systems and buckling.

Concerning the Optimal Control of the Relative Positions of the Sections of a Center-Pivot Irrigation Machine for Processing of the Fields of Non-Circular Shapes

A center-pivot irrigation system is widely used all over the world. Its main drawback is its applicability only to the round fields. In order to avoid this limitation a possibility of changing the mutual arrangement of the sections of the center-pivot irrigation machine was proposed. So, the sections of the machine must be able to rotate one around the other. In order to achieve such a feature, the traditional wheeled vehicles must be replaced with the walking machines. The walking machines based on the rotary-orthogonal movers (for example, Orthonog walking robot developed in Volgograd State Technical University) have almost perfect maneuverability. This allows a machine to take the form of an arbitrary curved line. The optimality criterion was introduced, which was a minimal work of the drive motors during movement of the machine. The system of rigid sprinkling sections was replaced with a continuous curve, wherein each subsequent point was not closer to the center than the previous one. The optimal configuration of a sprinkler in a field plane was found by using the methods of calculus of variations. The resulting equation was solved by the numerical method. An analysis of the results was done in order to find the maximal range of the length change. The results are valid for the steady driving mode in the sector of constant radius. The proposed model can be improved by introduction of another optimality criterion and taking into account the errors arising from the replacement of a discrete system with a continuous curve. Thus, a possibility of the use of a center-pivot sprinkler for the fields of non-circular shape is substantiated.