Convex Spherical Surface Research Articles

Multi-parametric optimization of convex spherical surface drilling of Ti6Al4V using finite element model and Taguchi coupled desirability function analysis

Multi-parametric optimization of convex spherical surface drilling of Ti6Al4V using finite element model and Taguchi coupled desirability function analysis

A modified dynamic contact angle model applied to double droplet impact curved surface

The microscopic processes involving droplet impact and interaction on spatially curved surfaces remain unclear. In this study, we implement a dynamic contact angle model with adjusted upper and lower limits into a simulation of droplet motion, constructing a three-dimensional numerical model to depict the dynamics and heat transfer characteristics of symmetric double droplets impacting plane, concave, and convex cylindrical, and concave and convex spherical surfaces. The processes of droplet spreading, retraction, rebound, splitting, and heat transfer are elaborated, revealing the role of surface curvature during impact. Our results show that different curvatures significantly affect the flow morphology of the flow dividing line. For the two main curvatures of the surface, the curvature in the direction of droplet arrangement predominates. Positive curvature promotes spreading and repels the liquid phase, while negative curvature promotes agglomeration and attracts the liquid phase. Extreme situations arise when both positive and negative curvatures occur simultaneously. Regarding heat transfer, the overall heat transfer rate is mainly determined by the spread area, and the heat transfer performance of convex surfaces is better than that of plane or concave surfaces. Residual bubbles increase heat transfer inhomogeneity, but different surfaces do not show significant variability. Additionally, the heat flow intensity in the central interaction region has the following relationship with its rebound height and is independent of the overall heat transfer intensity.

Self-Debonding of Adhesive Thin Films on Convex Cylindrical Surfaces and Spherical Surfaces

Abstract The emerging skin-integrated devices have been embedded with various functions, whose ideal implementation typically relies on intact bonding to curved substrates. However, the predeformation, which originates from the attachment of a thin film to a curved substrate, attempts to peel the film (i.e., self-debonding). It calls for strong enough interfacial adhesion in applications. On the other hand, too strong adhesion can destroy the surfaces of devices and substrates when the devices are peeled off after service. Therefore, seeking critical conditions becomes essential. Herein, we study the self-debonding of an adhesive thin film on a convex cylindrical surface. Taking Dugdale’s constant-stress law to describe the interfacial traction–separation relationship, we analytically unveil that the self-debonding behaviors are not solely determined by the interfacial energy. Instead, both the interfacial strength and critical interfacial separation are decisive. We thus obtain a phase diagram consisting of two critical conditions correspondingly. Similar results appear in the finite element analysis with the trapezoidal cohesive law, quantitatively showing the evolution of deflection and interfacial detachment force. Furthermore, we find that the circular film, symmetrically adhering to a spherical surface with small deflection, can still share similar self-debonding behavior. Our results provide guidance on how to stick a thin film on a convex cylindrical or spherical surface well with proper interfacial adhesion.

On Finding Determinantal Equations Involving the Coordinates of the Object Point, Point of Incidence, Point of Observation and the Image Point in Cases of Reflection and Refraction

This paper is concerned with the procedure of finding determinantal equations, each of which involves the coordinates of the object point, point of incidence, point of observation, and the image point in cases of reflection and refraction of light. An algorithm has been presented for the said purpose and it has been subsequently employed for the generation of relevant determinantal equations by considering some particular cases of reflection and refraction, based on which the readers will be able to reach the desired goal for all other remaining cases of reflection and refraction. Overall, two sets of such determinantal equations have been found to prevail in the present study. One resulted from handling the following cases: (i) Reflection at a plane reflecting surface, (ii) Refraction at a plane surface of discontinuity regardless of whether light moves from a rarer medium to a denser medium or from a denser medium to a rarer medium. The second one has been found while going through the following cases: (i) Reflection at a concave spherical reflecting surface, (ii) Reflection at a convex spherical reflecting surface, (iii) Refraction at a concave spherical surface of discontinuity regardless of whether light passes from a rarer medium to a denser medium or from a denser medium to a rarer medium, (iv) Refraction at a convex spherical surface of discontinuity regardless of whether light moves from a rarer medium to a denser medium or from a denser medium to a rarer medium

An experimental measurement research on impact load of high speed water jet acting on a rigid target by a Hopkinson pressure bar

A high speed water jet generation device based on explosion in a cylindrical cavity is introduced, which can eject a well-characterized water jet with a velocity around 100 m/s. The evolution characteristics and impact phenomenon of water jet act on a rigid target are observed by a high speed camera and the impact load is measured by a Hopkinson pressure bar. The top shape of water jet develops from a convex spherical surface to a flat plane as the stand-off increases under the influence of air resistance. When the top of water jet contacts the target plate, a transient high-pressure zone appears at the liquid-solid interface. A horizontal annular splashing jet generates and the velocity of splashing jet is much higher than that of incident jet as the result of high-pressure zone. The impact load is measured by the Hopkinson pressure bar, including transient “water hummer” pressure and subsequent hydrodynamic load. The “water hummer” pressure of water jet with a flat top is twice that with a convex spherical top, while the subsequent hydrodynamic pressure is equivalent at a comparable transient impact velocity. The measurement results by a Hopkinson pressure bar are in good agreement with the theory formulas in terms of both “water hummer” pressure and hydrodynamic pressure. It is certified that the Hopkinson pressure bar has a credible measuring capacity for both transient and steady-state pressure. By controlling cavity depth, charge amount and stand-off distance, the different top shape and velocity of water jet can be obtained.

光ファイバーを用いた圧力測定におけるプローブ先端形状の検討

Fiber-optic probes have advantages such as high time resolution on the order of GHz, high spatial resolution on the order of hundreds of microns, corrosion resistance, heat resistance, and pressure resistance. Due to these advantages, application to fluid pressure measurement has been studied. This is useful in the medical field for the development of ultrasonic therapy equipment. However, the signal change of the fiber-optic probe is small concerning the pressure change of the liquid, and it is difficult to measure with high sensitivity. Here, we focused on the tip shape of the fiber-optic probe and investigated the effect on the sensitivity. This study prepared the types of cleave, convex sphere, cone, and truncated cone. We experimented on each shape by immersing it in 6 different concentrations of glycerin-water solutions. We found that the cleave and the convex spherical surface polished with a roughness of 0.02 μm have good sensitivity. Moreover, the cone showed a sensitivity exceeding the theoretical line. From there, the surface roughness and shape of the probe should be selected correctly in pressure measurement.

Forced-based tool deviation induced form error identification in single-point diamond turning of optical spherical surfaces

In the single-point diamond turning (SPDT) of optical spherical/aspheric surface, tool deviating from the spindle rotation center significantly deteriorates the form accuracy of the spherical/aspherical surface and its optical performance. In this study, the influence of tool deviation on the form accuracy of a convex spherical surface and the cutting force forms during the turning process were studied first, following which a force-based tool deviation model was derived to identify the tool deviation using cutting force. Finally, by analyzing the influence of tool deviation on the three-dimensional (3D) form of residual structures at the center of the convex spherical surface, the 3D form of the convex spherical surface was predicted online. Results indicate the existence of a mapping relation between the tool deviation and the cutting force form, which could be further used to online predict the 3D form of the machined convex spherical surface in SPDT through the established geometric model.

Direct FEM-Domain Decomposition Using Convex-to-Concave Spherical Ports for Space Applications

This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on the analytical manipulation of the generalized scattering matrix obtained from the finite-element method, when concave and convex spherical surfaces are defined as ports. The technique combines: the power of full-wave resolution, the flexibility and speed of the direct domain decomposition techniques and the application of analytical rotations and translations from the addition theorems for spherical vector waves, while keeping the same accuracy as a complete full-wave method since no model simplifications are considered.

Interferometric grazing incidence test of rough steep convex spherical and aspherical surfaces: first simulations and experimental proof of principle.

In the past, grazing incidence interferometry has been applied for rough plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, we demonstrate that also rough convex steep rotational symmetric spherical or aspherical surfaces can be measured along one meridian in a single step using diffractive beam splitters and phase-shifting techniques. The extension to the whole surface can be attained by successive meridional measurements of the surface under test by azimuthal adjustments. The principle of the method is given and for a spherical ball lens as an extremely curved surface simulated, and experimental data are presented. The features of the interferogram are discussed, and the experimental evaluation of a single meridian including the unwrapped phase data is shown.

Reconfigurable RCS Reduction from Curved Structures Using Plasma Based FSS

The radar cross section (RCS) reduction from curved surfaces using plasma based frequency selective surfaces (FSS) is investigated. A frequency reconfigurable plasma based FSS unit-cell element with target-shaped structure is proposed. The operating frequency of the FSS is governed by the plasma ionization degree (i.e. plasma frequency). zero crossing frequency of the FSS unit-cell has a tuning range extending from 9.6 GHz to 11.3 GHz with an average bandwidth of 1.1 GHz. Planar and curved metallic surfaces are investigated. The curves structures include cylindrical (convex and concave), and spherical (convex and concave) surfaces. Single ionization source is applied at the rare end of the plasma FSS array design is optimized to maintain uniform plasma flow over the metallic surfaces by applying a single ionization source at the rare end of the array. The plasma FSS arrangement with ωp = 9 × 1011 rad/Sec loading a planar sheet reduces the RCS by 23 dB at 10.2 GHz and the (− 5 dB) frequency band of 14.7% for planar plate compared with the unloaded plate case. Different hybrid arrangements are investigated for wideband RCS reduction of 36.4% by superimposing reduction bands of three different plasma frequencies. A 21.5 dB reduction is achieved at 9.8 GHz for FSS arrangements (III). The effect of changing the radii of curvature for convex and concave cylindrical and spherical metallic surfaces is studied at different plasma frequencies. A full-wave analysis of the loaded metallic plates with plasma FSS is used to calculate the backscattered and bistatic RCS for different surfaces.

Method for measuring the reflectance distribution over a spherical convex surface with large curvature

This paper presents a method for measuring the reflectance over the radial coordinates of the convex spherical surface of an optical component having a large curvature. The reflectance measurement results for both a clean surface and a surface with an antireflection coating are presented. Evaluation of the results obtained showed that the maximum relative error in the deviation of the reflectance from the theoretical calculation does not exceed 4.5%.

Theoretical analysis of bubbles nucleating on surfaces of convex spherical inclusions in molten steel during vacuum treatment

Based on the theory of classical solidification nucleation, a thermodynamic model of bubbles nucleating on surfaces of convex spherical inclusions in molten steel was established. The expression of bubble critical-nucleation radius was derived. The differences between bubbles nucleating on convex spherical surface and flat substrate were discussed. The results show that the radii of spherical inclusions determine the degree of deviation on the two types of nucleation under same conditions and bubbles are more easily generated by flat substrate nucleation. In addition, the degree of deviation between the two types of nucleation decreases with the decrease of melt depth. The results also show that bubbles are easier to nucleate on the surface of inclusions with large radius or poor wettability. For a determined bubble critical-nucleation radius, the radii of spherical inclusions, the contact angles of spherical inclusions and the pressure of vacuum treatment have little influence on the depth range of bubble nucleation, while the pretreatment pressure shows significant impact on that. The probability of bubble nucleation reduced with the increase of melt depth, which was verified by related experiments.

A lead-framed glass mirror from a Roman woman's grave in Padua/Patavium (north-eastern Italy) – investigating its function and production with a multidisciplinary approach

Abstract A small Roman mirror, made up of a square lead frame and a convex reflective glass surface, was recently recovered in Padua in a grave dating back to the second half of the 2nd century AD. It was investigated with a multidisciplinary approach. During restoration, the artefact was dismantled, its individual components cleaned, consolidated and then reassembled. Chemical and isotopic analyses were carried out on microscopic fragments from both the glass and the lead components to identify their origin and production technologies. Structured-light 3D scanning was used both to produce a model of the artefact and to reconstruct its optical properties. Archaeometric results show that the 200 μm thick reflective glass surface, coated with a thin lead film, belongs to the Sb-colourless group. The lead frame is now totally oxidised. The lead isotope ratios of both the glass coating and the frame show a common composition, statistically close to some Romanian ores. These data suggest a multistep production process, most likely carried out in the same workshop. The distribution of similar finds mainly between the Northern-Adriatic basin and the Danube could indicate that these products were manufactured in the central-eastern provinces of the Roman Empire, presumably in the Southern Carpathian area, close to the local lead ore deposits. The typology is well defined thanks to the 3D model that is an important tool for morphometric investigations. The optical properties of the mirror, given by its convex spherical surface with a 9 cm radius, suggest the object was actually used as a makeup tool. In conclusion, this multidisciplinary approach reveals that despite its non-precious materials, the mirror can be considered a product of superior technological and scientific skills.

Study on Analysis of Cutting Mechanism of Ball End Mill for Concave and Convex Spherical Surface Using 3D-CAD

In this paper, cutting mechanism and cutting performance of ball end mill for spherical surface with contour path method is investigated. Ball end mills are used to produce molds, dies and so on. However, the edge shape is complex, so cutting process is not clear. Then, it is not clear effectively using method of the tool based on good cutting performance. Therefore, in this study, the purpose is proposal of high efficient and high accurate cutting method is using 5-axis control machine tool. At first, cutting model assembled by a ball end mill (R8 mm) and a workpiece with convex or concave spherical surface (Workpiece radius 20 mm) is carried out using 3D-CAD (SolidWorks). The pick feed direction which is from bottom to top is defined “Stepped up”, the one which is inverse direction is defined “Stepped down”. In addition, both cutting methods include up milling and down milling, then there are four cutting modes. The radius of tool path for contour path are varied from 14.0 mm to 19.4 mm for convex spherical surface, from 6.5 to 9.2 mm for concave spherical surface. The lead angle of the tool is defined the plus sign when the tool is inclined to the tool feed direction and varied from-45° to 45°. Secondly, the cutting cross-sectional area is calculated by the interference of a rake surface of the tool and an uncut chip volume which can be removed by one cutting operation. Thirdly, cutting experiments are done in order to measure cutting force. Finally, analytical and experimental results are discussed, and then the cutting conditions which are expected good cutting performance are considered.

Fast conical surfaces evaluation with null-screens and randomized algorithms

A method for the evaluation of the shape of fast conical surfaces based on the null-screen method is presented. The proposed method is based on randomized algorithms, where instead of integration as is usually performed, the shape of the surface is recovered in a direct and random way. This is done by proposing a new test surface; the surface parameters are randomly generated and the calculated null-screen is compared against the originally designed one. The coefficients that generate the null-screen closest to the reference null-screen are taken as the final values that describe the surface under test. The algorithm validation was done in the theoretical and experimental way. For the theoretical way, a convex parabolic surface with 21.36 mm radius of curvature and f/0.178 was simulated and analyzed; in the experimental way, a convex spherical surface f/0.33 and a concave ellipsoidal mirror f/0.2381 were evaluated. The results obtained with our algorithm in the evaluation of the ellipsoidal surface were compared against the results obtained with traditional methods. We found that the radius of curvature, conic constant, and the decentering coefficients that were used to generate each surface were retrieved in a good manner with our algorithm. The results show that these parameters can be recovered with a percent error smaller than 1% in the case of simulations, and smaller than 2% in the two experimental cases.

Dendron and Hyperbranched Polymer Brushes in Good and Poor Solvents.

We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self-consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes.

Laser differential confocal ultra-large radius measurement for convex spherical surface.

A new laser differential confocal ultra-large radius measurement (LDCRM) method is proposed for high-precision measurement of ultra-large radii. Based on the property that the zero point of a differential confocal axial intensity curve precisely corresponds to the focus points of focusing beam, LDCRM measures the vertex positions of the test lens and the last optical surface of objective lens to obtain position difference L1, and then measures the vertex positions of the reflector and the last optical surface of objective lens to obtain the position difference L2, finally uses the measured L1 and L2 to calculate the radius of test lens. This method does not require the identification of confocal position. Preliminary experimental results and theoretical analyses indicate that the relative uncertainty is 0.03% for a convex spherical lens with a radius of approximately 20 m. LDCRM provides a novel approach for high-precision ultra-large radius measurement.

Alignment and study of prototypes of the Offner hyperspectrometer

A prototype of the hyperspectrometer based on the Offner scheme has been tested. Drawings have been produced and the main mirror elements of the hyperspectrometer including diffraction grating on a convex spherical surface have been fabricated. The profile of the grating groove has been measured and light energy distribution in diffraction orders has been modeled as a function of wavelength. Optomechanical elements for the necessary alignments of the hyperspectrometer elements have been designed and manufactured. Adjustment of the optical prototyping scheme has been implemented and point images for three wavelengths of monochromatic radiation have been obtained. Distribution of light energy in diffraction orders and maxima positions are in an agreement with the simulation results. The spectrometer has also been tested on test images in polychromatic radiation under the control of the developed software.

A mobile sensing system for real-time 3D weld pool surface measurement in manual GTAW

An innovative mobile sensing system has been developed to non-intrusively monitor the manual pipe gas tungsten arc welding (GTAW) process. The system consists of a projective torch held by a welder, and a sensory helmet on the welder’s head. The three-dimensional (3D) weld pool surface is effectively measured in real-time as the welder performs the weld despite the movements of the torch and the helmet. In this study, the sensing system is first analyzed by numerical simulations in which the adjustment boundaries of the torch and helmet, i.e. their translation and orientation ranges, for effective sensing have been determined. Then, the sensing system is further evaluated using a simulation platform in which the movements of the helmet/welder’s head is mimicked by a tripod head with 6 degree-of-freedom (DOF), and a convex spherical mirror with a comparable size of a typical weld pool in a GTAW process is applied as a weld pool substitute. The effectiveness of the proposed system is validated by successfully capturing laser reflections from the mirror without great constraints on the welder’s movements of the torch and the helmet. Based on the analysis of the spatial relations among the torch, the helmet and the weld pool, an innovative real-time algorithm is proposed to reconstruct the 3D weld pool surface. The effectiveness and robustness of the algorithm have been verified by accurately reconstructing the convex spherical mirror surface despite the movements of the torch and the helmet in the simulation platform.

Path planning and parameter optimization of uniform removal in active feed polishing

A high-quality ultrasmooth surface is demanded in short-wave optical systems. However, the existing polishing methods have difficulties meeting the requirement on spherical or aspheric surfaces. As a new kind of small tool polishing method, active feed polishing (AFP) could attain a surface roughness of less than 0.3 nm (RMS) on spherical elements, although AFP may magnify the residual figure error or mid-frequency error. The purpose of this work is to propose an effective algorithm to realize uniform removal of the surface in the processing. At first, the principle of the AFP and the mechanism of the polishing machine are introduced. In order to maintain the processed figure error, a variable pitch spiral path planning algorithm and the dwell time-solving model are proposed. For suppressing the possible mid-frequency error, the uniformity of the synthesis tool path, which is generated by an arbitrary point at the polishing tool bottom, is analyzed and evaluated, and the angular velocity ratio of the tool spinning motion to the revolution motion is optimized. Finally, an experiment is conducted on a convex spherical surface and an ultrasmooth surface is finally acquired. In conclusion, a high-quality ultrasmooth surface can be successfully obtained with little degradation of the figure and mid-frequency errors by the algorithm.