Initial Radius Of Curvature Research Articles

Study on the construction of twisted cosine partially coherent beams and their propagation characteristics

We propose a novel Schell model source for generating twisted partially coherent beams with an initial radius of curvature, which is called a twisted flat-topped cosine Gaussian Schell-model (TFCGSM) source. The TFCGSM beam comprises a wavefront phase and a flat-top structure, with the source degree of coherence determined by two cosine functions. Based on the Huygens–Fresnel principle, the general analytical expression of the cross-spectral density function of the TFCGSM beam propagating through the paraxial ABCD optical system is derived, and then its propagation properties are studied. The results show that the conversion of the array of the beam and the non-uniform structure can be realized by adjusting the parameters in the source plane. As the propagation distance of the TFCGSM beam increases, it rotates around the axis and increases the intensity of the array distribution. Surprisingly, the initial radius of curvature can cause the beam to rotate. The unique shape and properties of the TFCGSM beam create new possibilities for optical communication and enhanced optical functions.

Forming process and evaluation of chip in machining of high-strength steel by an independent-developed microgroove turning tool.

Chip morphology is one of the evaluation indexes of cutting performance of cutting tools, and chip forming process has a direct and important influence on chip morphology. High-strength steel 40CrMnMo is one of typical oil country tubular goods (OCTG) and difficult-to-cut materials, and its chip morphology represents the machining quality of OCTG. The chip forming process of a new independent-developed microgroove turning tool for turning oil country tubular goods 40CrMnMo is researched, combining machining experiments with theoretical analysis. Research results show that with the increase of cutting speed, the initial radius of curvature of the chip fluctuates slightly, but the overall trend is upward. However, the ultimate radius of curvature decreases and the chip's radius ratio also decreases. The relative ideal chip can be obtained if the proper cutting velocity and feed rate are given. Chip morphology results from the comprehensive effect of the two processes: The fracture and separation process of the workpiece during passing through the shear deformation zone and the process of curling and breaking away of the chip after passing through the rake face of the tool. The research results have a certain guiding significance for controlling the cutting process of machining the other material with similar performance.

Propagation of Shock Waves of Varying Curvature

When a shock wave having variable concave curvature propagates, it can develop a kink followed by the development of a reflected shock. A typical example is a plane incident shock encountering a surface with concave curvature, the part of the shock adjacent to the surface curves forward and subsequently develops into a Mach reflection with a Mach stem, shear layer and reflected shock. The physical mechanisms associated with the evolution of the shock profile was evaluated for shock waves with initial profiles comprising a cylindrical arc, placed in-between two straight segments, propagating in a converging channel. The temporal variation of the pressure distribution immediately behind the shock wave was studied using CFD. This revealed a pressure imbalance in the region where the curved (which was initially cylindrical) and straight shock segments meet. This imbalance occurs due to the difference in the propagation behaviour of curved and planar shock waves, and results in the development of reflected shocks on the shock front. The angle at which the channel walls converge, the initial curvature radius, and the shock Mach number, was varied between 40 and 60 degrees, 130 and 190 mm and 1.1 to 1.4, respectively. The variation with time of the pressure-gradient distribution and the maximum pressure gradient behind theshock wave was evaluated. From this, the trajectory angle of the triple points, and the rate at which the reflected shocks develop, was deduced. It was found that when shock waves with larger curvature radii propagate in channels with lower wall angles, the reflected shocks develop at a slower rate, and the triple points follow a steeper trajectory. Consequently, the likelihood of reflected shocks emerging on the shock front, within the duration of the shock propagation, is reduced. This is due to the triple points intersecting the walls, before reflected shocks can fully develop. Similarly, when the shock Mach number is higher, the trajectory angle of the triple points is greater, and they intersect the walls before the reflected shocks can emerge.

Mechanical Properties of Thin and Thick Coatings Applied to Various Substrates

In this work, theoretical and experimental studies have been carried out to determine the Young's modulus of materials for coatings applied to substrates. It is shown that residual stresses are generated inside thin and thick coatings deposited on a substrate. As a result of these stresses, the strip of the two-layer material is assumed to have some curvature. With the help of bending theory, it was substantiated that the bending stiffness of two-layer materials is a function of the initial radius of curvature generated by residual stresses, the mechanical radius of curvature arising during bending tests, mechanical (Young's modulus) and geometric (width and thickness) characteristics of two-layer systems. The corresponding expression was converted to a second or third order equation to calculate the Young's modulus of the coating undergoing residual stresses.

Atomistic Modeling of Grain Boundary Migration in Nickel

Herein, the molecular dynamics (MD) simulations of pure Ni crystallites are performed to show the influence of the grain boundary (GB) geometry on the values of the activation energy of GB migration. The considered systems are bicrystal with Σ5[010] tilt plane boundary, spherical grain with initial curvature radius 5 nm, and polycrystalline 30 nm × 30 nm × 30 nm block. The motion of three types of GBs (flat, spherical, and polycrystalline) at constant temperatures and no applied forces is studied. The obtained values of activation energy are 0.45, 0.11, and 0.57 eV for flat, spherical, and polycrystalline types of GBs, respectively. These values are smaller than those that are reported in experimental works, which is a common issue for atomistic simulations of GB migration. Possible sources of such disagreement and ways to overcome it are discussed. The particular part of this work is devoted to the development of the automated analysis of polycrystalline structure. This analysis provides detailed information on grain size distribution and its evolution in time.

Investigation of curing deformation behavior of curved fiber metal laminates

To keep the size and shape accuracy of fiber metal laminates (FMLs) with an initial curvature during manufacturing, curing deformation behavior is investigated by using analytical, numerical and experimental methods. Based on Eckstein’s theory, an analytical model considering slippage effect between metal layer and fiber layer is developed to study the warping deformation modes of curved FMLs after curing process. The warping displacements of the curved FMLs predicted by the analytical method are in good agreement with the finite element results and experimental data. The final equilibrium configurations of the curved FMLs can be captured by using the analytical method, which can guide the size and shape control for FMLs. The effect of the side length, initial curvature radius and stacking sequence on the curing deformation characteristics of curved FMLs is studied. The curing deformation mechanisms of the curved FMLs with [Al/0/90/Al] and [Al/90/0/Al] stacking sequences are also illustrated from the perspectives of force and total strain energy.

Thin-disk laser resonator design: The dioptric power variation of thin-disk and the beam quality factor

This paper investigates the general limitations of thin-disk laser (TDL) resonators due to the dioptric power variation of thin-disk (TD) crystal to attain the good beam quality. For this reason, the generalized formulation of TDL resonator in geometric optics theory is analytically derived. The analytical model is developed by considering two general configurations of stable resonators based on the position of the TD crystal inside the resonator; end-disk and fold-disk resonators. The calculation results reveal best M2 factor at operation pump power (OPP) from a specified disk is proportional to the variation interval of the dioptric power of the TD and it depends on the general configuration of resonator. For each configuration, the initial radius of curvature of the TD determines the resonator shape to attain the minimum acceptable M2 factor.

Focusing and sorting of multiple-sized beads and cells using low-aspect-ratio spiral microchannels

A separation of Polystyrene micro-beads (PMBs) and natural Mast-cell tumor cells (MCTCs) of about 10–25 μm diameter was performed using a microfluidic spiral microchannel. In this study, five-turned spiral microchannels were 500 μm high and 130 μm wide with an initial radius of curvature of 5.5 mm. Sorting efficacy of targeted PMB or MCTC samples of each size by focusing them into a single stream depended on the size of the samples and the flow rate. Flow cytometric analysis revealed that almost 90 % of PMBs and MCTCs of 15–25 μm diameter could be successfully sorted from a mixture of smaller beads or cells at a flow rate of 1.0 mL/min.

Carbon-fiber-reinforced polymer variable-curvature mirror used for optical zoom imaging: prototype design and experimental demonstration

In recent years, optical zoom imaging without moving elements has received much attention. The key to realizing this technique lies in the design of the variable-curvature mirror (VCM). To obtain enough optical magnification, the VCM should be able to change its radius of curvature over a wide range. In other words, the VCM must be able to provide a large sagittal variation, which requires the mirror material to be robust during curvature variation, require little force to deform, and have high ultimate strength. Carbon-fiber-reinforced polymer (CFRP) satisfies all these requirements and is suitable for fabricating such a VCM. Therefore, in this research, a CFRP prototype VCM has been designed, fabricated, and tested. With a diameter of 100 mm, a thickness of 2 mm, and an initial radius of curvature of 1740 mm, this VCM can provide a maximum 23-μm sagittal variation and a minimum and maximum radius of curvature of 1705 and 1760 mm.

凹面または凸面へのレーザ加熱で生じる変形に及ぼす入熱量と初期曲率半径の影響

凹面または凸面へのレーザ加熱で生じる変形に及ぼす入熱量と初期曲率半径の影響

Analysis of Variable Section Piezoelectric Harvester

This paper first presents an analytical model for investigating the vibration performance of a thin curved laminated piezoelectric beam with variable curvatures and transverse sections. This kind of beam is widely used for the MEMS piezoelectric vibration energy harvester. The curved thin beam theory with bisymmetric section, here rectangular section used, is employed to explore the bending and twisting coupling vibration characteristics. In order to study the vibration properties with concentrated load, the effects of the tip proof mass isnt used. The paper also shows that the adoption of ANSYS software to carry out the MEMS piezoelectric vibration energy harvesters numerical simulation can improve the efficiency of the harvester designing and manufacturing consumedly. The results showed that the maximum voltage at the resonant point was increasing while the initial curvature radius increasing. On the other hand, the voltage difference of the inner edge and the outer edge was very small because the matrix layer was PDMS with very small stiffness and density.

Energy Conversion Efficiency of Rainbow Shape Piezoelectric Transducer

With the aim to enhance the energy conversion efficiency of the rainbow shape piezoelectric transducer, an analysis model of energy conversion efficiency is established based on the elastic mechanics theory and piezoelectricity theory. It can be found that the energy conversion efficiency of the rainbow shape piezoelectric transducer mainly depends on its shape parameters and material properties from the analysis model. Simulation results show that there is an optimal length ratio to generate maximum energy conversion efficiency and the optimal length ratios and energy conversion efficiencies of beryllium bronze substrate transducer and steel substrate transducer are (0.65, 2.21%) and (0.65, 1.64%) respectively. The optimal thickness ratios and energy conversion efficiencies of beryllium bronze substrate transducer and steel substrate transducer are (1.16, 2.56%) and (1.49, 1.57%) respectively. With the increase of width ratio and initial curvature radius, both the energy conversion efficiencies decrease. Moreover, beryllium bronze flexible substrate transducer is superior to the steel flexible substrate transducer.

回転矯正および温間引張り矯正を用いた極細線の高真直化

Higher straightness of superfine wires of 0.1 mm or less in diameter is in demand for recent development of electronic devices.A rotational blade straightener is effective for straightening superfine wires. It is particularly effective for straightening coiled wires because the straightener can bend wires along the longitudinal and circumferential directions. We found that a higher rotational speed of blades, lower feeding velocity, and gradual decrease in curvature ratio during straightening were very effective in producing excellent straightness in rotational blade straightening.Tension annealing is also one of the popular methods to straighten superfine wires. The tension annealing has a higher level of straightening effect without surface damage. The phosphor bronze and the tungsten superfine wires are used in this study. We observe that the initial radius of curvature, roundness and work hardening exponent are very important factors to make excellent straightness in tension annealing.

レーザー加熱を用いた薄板鞍形成形時の収縮量に及ぼす初期曲率半径の影響

To form curved surface, in-plane strain is introduced into a plate by using several methods such as line heating, press working and laser heating in shipbuilding and sheet metal working in forming nose shape for the shinkan-sen. Laser forming could be a potential useful method for sheet metal forming as well as press working.Curved surface is classified based on its features of primary curvature radius into two typical shapes, so called bowl and saddle. So, when we research some technique to form curved surface, at least two types of bowl and saddle shapes should be investigated. For the bowl shape, some researchers reported that initial curvature radius has no effect on the in-plane strain induced by laser heating.In this report, the effect of initial curvature on the in-plane strain induced by laser heating is investigated for the saddle shape. As a result, shrinkage distributions caused by in-plane strain were varied with different initial curvatures. In this phenomenon, bending moment acts a key role in both heating and cooling processes.

Shapes of Submerged Funicular Arches

In this paper, the analytical forms of the shapes of submerged funicular arches are expressed in terms of elliptic integrals. The initial radius of curvature at the apex is related to the water depth at the apex and the axial compressive force. The shape of the submerged funicular arches depends on the ratio between this initial radius of curvature and the water depth at the apex. Using the analytical expressions, the maximum span and height of the submerged funicular arches can be determined explicitly. Besides, the analytical expressions are useful in determining the design parameters for the submerged funicular arches accurately.

Behaviour of hollow curved steel struts subjected to compressive load

Experimental tests have been performed on hollow curved steel struts in order to investigate the stability and general behaviour of such struts. Two different manufactured types of tubes were used: electric resistance welded tube (ERW) with 60.4 mm outside diameter and 2.3 mm wall thickness, and hot finish seamless tube (HFS) with 60.4 mm outside diameter and 4 mm wall thickness. The strut tests were effectively pin-ended and had slenderness ratios, based on the straight length between ends, ranging from 37 to 147. Although the experimental results showed that the ultimate load capacity of curved steel struts decreased with decreasing initial radius of curvature due to increasing initial deflection at mid-height, as expected, the post-buckling behaviour of the seamless struts was significantly different from that of the ERW struts. It is seen that the ultimate load capacity of stress-relief-annealed (SRA) curved struts is significantly reduced in comparison with the equivalent as-received (AR) struts. Also, it is observed that the Bauschinger effect is not significant for the curved struts tested herein, although it has been seen to be significant for straight struts.

Non-linear inplane deformation and buckling of rings and high arches

A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduction of the geometrically non-linear 3-D elasticity under the assumptions of comparable magnitudes of initial radius of curvature and wavelength of deformation, small strain, and small ratio of cross-sectional diameter to initial radius of curvature ( h/R). The 1-D constitutive law contains an asymptotically correct refinement of O(h/R) beyond the usual stretching and bending strain energies which, for doubly symmetric cross sections, reduces to a stretch–bending elastic coupling term that depends on the initial radius of curvature and Poisson’s ratio. As illustrations, the theory is applied to inplane deformation and buckling of rings and high arches. In spite of a very simple final expression for the second variation of the total potential, it is shown that the only restriction on the validity of the buckling analysis is that the prebuckling strain remains small. Although the term added in the refined theory does not affect the buckling loads, it is shown that non-trivial prebuckling displacements, curvature, and bending moment of high arches are impossible to calculate accurately without this term.

Modification of the tip shape of a scanning probe microscope using ion sputtering

The process of ion sputtering of the tip of a scanning probe microscope is modeled to determine the conditions for the formation of protrusions at the apex of the tip. It is shown that for an isotropic sputtering process sharper protrusions form at the apex of a conical tip if the initial radius of curvature of the tip is not too large and the angular dependence of the sputtering coefficient has a fairly sharp peak at angles of incidence of 60–70°.

Mechanical properties of thin and thick coatings applied to various substrates. Part II. Young's modulus determination of coating materials*

To determine Young's modulus of coating materials when they are applied to substrates, theoretical and experimental analyses are performed. Significant residual stresses are generated within thin and thick coatings applied to substrates. As a result of these stresses, the bi-material strip assumes a certain curvature. The curved beam theory was used to establish the equivalent bending stiffness of bi-layer materials as functions of (a) the initial radius of curvature generated by residual stresses, (b) the mechanical radius of curvature during flexure testing, and (c) mechanical (Young's moduli) and geometrical (widths and thicknesses) characteristics of bi-layered systems. The relevant expression was transformed to a second- or third-order equation in order to calculate Young's modulus of the coating undergoing residual stresses (using models developed in Part I and by Stoney, Röll, and Inoue).

Effective beam parameters and the turbulent beam waist for convergent Gaussian beams

Expressions are developed for the location and the size of the beam waist for a convergent Gaussian beam in statistically homogeneous and isotropic atmospheric turbulence. Subsidiary expressions are presented that lead to the maximum distance from the transmitter at which the beam waist can be located under given optical turbulence conditions and the optimal initial radius of curvature required for placing the beam waist at a desired location. The free-space beam radius W of a Gaussian beam satisfies the relationship ∂W/∂z = - W/R, where z represents the path length and R is the phase-front radius of curvature at z. By enforcing this relation on the effective beam spot size in turbulence W(e), we can define an effective radius of curvature R(e). In addition to specifying the beam waist, R(e) leads to a pair of effective beam parameters θ(e) and Λ(e) that provide a natural extension to the complex amplitude plane. Within this context, general propagation characteristics may be described, including the coherence properties of a Gaussian beam in both weak and strong optical turbulence.