Concave Sphere Research Articles

Non-contact method of thickness measurement for thin-walled rotary shell parts based on chromatic confocal sensor

In this paper, a non-contact method of thickness measurement for thin-walled rotary shell parts based on chromatic confocal sensor is presented. To obtain thickness, a flip method is applied to acquire surface profiles from both sides of the workpiece. The decentration and tilt errors of the workpiece are measured by a centering system consisting of a laser interferometer and a collimated tube. By establishing a unified reference coordinate system, the external and internal surface profiles are reconstructed and the thickness is calculated. A measurement experiment for a sapphire spherical shell workpiece was conducted on a four-axis measurement system and the result is 2.99341 mm. A wavelength-tuning interferometer and a dynamic interferometer were utilized to measure the sapphire spherical shell and an aluminum concave sphere and the results show in good agreement.

Impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic spheres at low Weber numbers

While the previous studies discussed the impact and freezing coupling processes of supercooled water droplets on cold superhydrophobic convex spheres at medium or high Weber numbers (We > 10), the cases on convex and concave spheres at low Weber numbers (We ≤ 10) are numerically studied. A numerical model using the VOF (Volume of Fluid) method and solidification-melting model is established and validated by comparing the calculated results with the experimental data in reference. The influences of the Weber number, supercooling degree, and sphere diameter (characterized by the sphere-to-droplet diameter ratio) on the dynamic behaviors, including the droplet profile, the spreading area and arc angle, and the final outcomes, are explored. As the Weber number increases and the supercooling degree decreases, the impact droplet yields a higher retraction speed and tends to rebound from the cold spheres more easily. The influence of the diameter ratio at low Weber numbers is distinct from that at medium Weber numbers. With the increase of the diameter ratio, the maximum spreading area factor on the convex sphere increases while that on the concave sphere decreases. The final droplet outcome transits from adhesion to rebound when the surface shape continuously changes from concave to convex. The rebound-adhesion morphology maps in terms of the Weber number and diameter ratio are obtained at various supercooling degrees. The rebound region of the convex sphere in the morphology map is wider than that of the concave sphere, and the adhesion region of the morphology map expands with a greater supercooling degree. A smaller diameter ratio yields a smaller critical Weber number between rebound and adhesion regions on the convex sphere but a greater one on the concave sphere. The innovation and optimization of the anti-icing surface may obtain theoretical reference and guidance from the above findings.

ELID Mirror Surface Grinding for Concave Molds by Conductive Elastic Wheel Containing Carbon Black

Elastic grinding wheels have previously been adopted for the development of the mirror surface finishing method for concave spheres. In this study, new conductive elastic grinding wheels, to which electrolytic in-process dressing (ELID) can be applied, are developed; the aim of the study is to address the challenge of maintaining a constant removal rate for rubber bond wheels. When ELID grinding is performed using a non-diene (isobutane isoprene rubber, IIR)-based wheel, a larger removal amount is achieved, and a higher-quality surface is also achieved compared to a diene (acrylonitrile-butadiene rubber, NBR)-based wheel. In addition, to investigate the effect of grinding wheel bond hardness on the removal amount and ground shape accuracy, grinding wheels with various levels of hardness are prepared by controlling the amount of carbon black contained in them, and grinding experiments are conducted. Thus, a larger removal amount is achieved using a harder grinding wheel, but the roughness of the ground surfaces deteriorates. Therefore, in practice, it is necessary to select an appropriate grinding wheel that can achieve both productivity and surface quality. Finally, to obtain a high-quality mirror finish on a concave spherical surface, ELID grinding is performed on the workpieces as is done for spherical lens molds. Thus, high-quality mirror surfaces with roughness Ra < 10 nm were generated. When the work pieces are ground using a grinding wheel of the same radius, excessive removal occurs at the edge of the concave spherical profile, decreasing the form accuracy. Numerical simulation demonstrates that chamfering of the grinding wheel is effective for improving the shape accuracy. The results of this study are expected to contribute to automation and cost reduction in the mirror-finishing process for concave molds.

Design of Ultrasonic Levitation Control System Based on FPGA

As a method to achieve containerless processing, the object levitation technique has a broad application prospect in vital research fields. However, the levitation distance of Electromagnetic levitation, near-field acoustic levitation is not far enough to complete cantainerless processing, and the stability of ultrasonic levitation that use single emitter or single transductor array is still needed to be improved. Therefore, this paper proposes a new embedding electronic system based on FPGA controller to drive a construction of transducer arrays that perpendicularly formed by uniaxial concave sphere and uniaxial biplane. A phase delay algorithm is used on this system to change the position of the stand wave points to move the object smoothly. Furthermore, through experimental validation, this system has a stable signal output to reach the goal of levitation and control.

Effect of asymmetric structural characteristics of multi-hole marine diesel injectors on internal cavitation patterns and flow characteristics: A numerical study

Cavitating flow potentially emerging in diesel injector nozzles plays a prominent role influencing the subsequent process of spray atomization and combustion reaction. A computational study is conducted to investigate influences of asymmetric structural characteristics on interior nozzle flow in a multi-hole marine low-speed diesel injector. The simulation results illustrate that both mass flow rates and flow discharge coefficients of two holes on both sides are larger than those of two holes in the middle with increasing hole entrance corner radius (R), hole diameter (D) and hole length. The concave sphere shapes connecting the injector body and the holes are beneficial to reduce the negative effect of eccentric holes and bring about different flow patterns. R/D has a significant effect on the flow discharge coefficient but little influence on the mass flow rate. Besides, the hole entrance corner radius of 0.10 mm is an appropriate option to ensure the consistency of injections. The increasing hole length is conducive to the development of geometry-induced cavitation and vortex-induced cavitation. The development trends of flow phenomena in all holes are different with various hole taper degrees. It suggests that multi-hole marine diesel injectors with Kfactor of 1 ~ 2.5 can be considered in the actual manufacture.

Dynamic behavior and maximum spreading of droplets impacting concave spheres

Droplet impact is omnipresent in nature and industry, and it is affected by the surface shape. Here, experiments, simulations, and theoretical analyses are conducted to explore the impact behaviors of water droplets on the concave spheres, especially the maximum spreading. The simulation model using the volume of fluid method is validated by comparing the temporal droplet profiles and spreading factors yielded by the simulation and experiment. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio on the maximum spreading are exhaustively investigated. The results indicate that both the maximum spreading factor and arc angle increase with the increase in the Weber number and the decrease in the contact angle. The maximum spreading factor and area on the concave sphere generally first increase slightly and then decrease with the reduction in the diameter ratio owing to the combined action of the gravity and the surface shape. As the diameter ratio decreases, the maximum spreading arc angle increases and the maximum diameter of the contact line decreases. For a fixed diameter ratio, the droplet generally spreads less on a concave surface than on a convex one. Based on the energy conservation, a theoretical model is further established to predict the changing trend of the maximum spreading factor with the Weber number, contact angle, and diameter ratio, which yields a ±15% deviation over 93% of all the data points. This work may deepen our understanding of the mechanism of droplet impact on concave spheres and contribute to the associated applications.

Reducing edge error based on further analyzing the stability of edge TIF and correcting the post-edge algorithm in MRF process

A precise and efficient edge-controlled method is of importance to ensure the final performance of the optical system. The authors put forward a novel method to reduce the edge effect in the magnetorheological finishing (MRF) process through further analyzing the stability of the MRF edge tool influence function (TIF) and correcting the post-edge algorithm of dwell time. To demonstrate the feasibility and advantage of this edge-controlled theory, two mirror substrates are taken as the experimental samples. The Φ 200 mm, R-200 mm concave sphere mirror (fused silica) is removed about 3 μm uniformly and the experimental results indicate that the edge error region can be effectively suppressed below 1.5 mm. Another Φ 610 mm, R-2100, K-1 lightweighting parabolic mirror is verified about the actual practicability. The residual error reaches RMS 6.5 nm from original RMS 182 nm after two run iterations; meanwhile, the edge effect is well controlled to a large extent. The simulations of edge error coincide well with the corresponding experimental results, which strongly verify the feasibility of the edge-suppressing theory presented in this paper.

Theoretical and Finite Element Analysis of Residual Stress Field for Different Geometrical Features After Abrasive Waterjet Peening

Abrasive waterjet (AWJ) peening can be used for metal surface strengthening by introducing near-surface plastic strain and compressive residual stress. The present studies seldom focus on residual stress by AWJ peening of targets with different geometrical features. In fact, those targets usually exist on some machine parts including gear roots, shaft shoulders, and stress concentration areas. According to Hertz theory of contact and Miao's theoretical model for predicting residual stress of flat surface, this paper developed a theoretical model for investigating residual stress of targets with different geometrical features including concave arc surface, concave sphere surface, convex arc surface, and sphere surface. AWJ peening of targets with different geometrical features and different radii of Gaussian curved surface was simulated by abaqus. Theoretical results were consistent with numerical simulation results and published experimental results (H. Y. Miao, S. Larose, et al., 2010, “An analytical approach to relate shot peening parameters to Almen intensity,” Surf. Coat. Technol., 205, pp. 2055–2066; Cao et al., 1995, “Correlation of Almen arc height with residual stresses in shot peening process”, Mater. Sci. Technol. 11, pp. 967–973.), which will be helpful for predicting residual stress of gear roots, shaft shoulders, and stress concentration areas after AWJ peening. The research results showed that under the same peening parameters, σmax, σtop, dmax, and dbottom in concave surface (including concave arc surface and concave sphere surface) were the maximum; σmax, σtop, dmax, and dbottom in convex surface (including convex arc surface and sphere surface) were the minimum; for concave surface, σtop, σmax, dbottom, and dmax decreased, respectively, with target radius; for convex surface, σtop, σmax, dbottom, and dmax increased, respectively, with target radius.

Temperature‐Induced Stacking to Create Cu2O Concave Sphere for Light Trapping Capable of Ultrasensitive Single‐Particle Surface‐Enhanced Raman Scattering

AbstractThe fabrication of bowl or concave particles with “asymmetric centers” has drawn considerable attentions, in which multiple scattering occurs inside the particles and the ability of light scattering is distinctly enhanced. However, the limited variety of templates, the uncontrollable dimensions such as the size of concavity and the complex growth process have posed serious limitations to the reproducible construction of concave particles with desired geometries and their light‐trapping properties. Herein, a “temperature‐induced stacking” strategy is proposed to create controllable concavity Cu2O spheres for the first time. Different sizes of F68 micelles can be formed through aggregation under different reaction temperatures, which can serve as soft template to tailor concave geometries of Cu2O spheres. The as‐prepared Cu2O concave sphere (CS) can serve as single‐particle (SP) surface‐enhanced Raman scattering (SERS) substrate for highly repeatable and consistent Raman spectra. The unique cavity of Cu2O CS entraps light effectively, which also enhances the scattering length owing to multiple light scattering. Combined with slightly increased surface area and charge‐transfer process, Cu2O CS exhibits remarkable single‐particle SERS performance, with an ultralow low detection limit (2 × 10−8 mol L−1) and metal comparable enhancement factor (2.8 × 105).

High-precision spherical subaperture stitching interferometry based on digital holography

A novel subaperture stitching interferometry is proposed to measure the high-numerical-aperture sphericity for workshop testing, which combined digital holographic technology, subaperture stitching algorithm and systemic aberration calibration. Each subaperture is fleetly measured by the digital off-axis holography with a single shot so that the influence of measurement environment can be effectively reduced. The high-precision full aperture shape is obtained by stitching these subapertures, meanwhile, the subaperture alignment errors and the systemic aberration can be correctly compensated by the method of least-squares with the Zernike polynomial fitting. The approach is verified by testing three spherical surfaces, including a concave sphere, a convex sphere, and a hemisphere, in general environment. Moreover, the measurement results are compared with full aperture results by using a large aperture interferometer of Zygo and stitching result by using a subaperture stitching interferometer of QED. The results based on the proposed approach are consistent with the commercial interferometers. Specifically, the relative deviations of RMS are 0.009 λ and 0.02 λ for testing a concave and a convex spheres, and that is 0.011 λ for testing a hemisphere. Our method not only has the comparable measurement accuracy with the commercial interferometers but also is more robust, feasibility and inexpensive than other subaperture stitching interferometry. We provide an anti-interference way to test spherical surfaces in workshop environment.

High-accuracy process based on the corrective calibration of removal function in the magnetorheological finishing

The corrective calibration of the removal function plays an important role in the magnetorheological finishing (MRF) high-accuracy process. This paper mainly investigates the asymmetrical characteristic of the MRF removal function shape and further analyzes its influence on the surface residual error by means of an iteration algorithm and simulations. By comparing the ripple errors and convergence ratios based on the ideal MRF tool function and the deflected tool function, the mathematical models for calibrating the deviation of horizontal and flowing directions are presented. Meanwhile, revised mathematical models for the coordinate transformation of an MRF machine is also established. Furthermore, a O140-mm fused silica plane and a O196 mm, f/1∶1, fused silica concave sphere samples are taken as the experiments. After two runs, the plane mirror final surface error reaches PV 17.7 nm, RMS 1.75 nm, and the polishing time is 16 min in total; after three runs, the sphere mirror final surfer error reaches RMS 2.7 nm and the polishing time is 70 min in total. The convergence ratios are 96.2% and 93.5%, respectively. The spherical simulation error and the polishing result are almost consistent, which fully validate the efficiency and feasibility of the calibration method of MRF removal function error using for the high-accuracy subaperture optical manufacturing.

Astral Ascent in the Occult Revival

The occult revival of the later 19th century inherited Neoplatonic and Hermetic ideas of astral ascent and commerce with the planetary spirits, but felt obliged to square these with contemporary discoveries in astronomy. In the 1850s, Andrew Jackson Davis adapted Swedenborgian ideas into a semi-scientific cosmology that served as the norm for spiritualists. In the 1870s, occultism separated from spiritualism and made its own pact with science, with results visible in the works of Emma Hardinge Britten, H. P. Blavatsky, and the Hermetic Brotherhood of Luxor. Outside these well-known movements, Cyrus Teed, known as Koresh, taught that the earth is a concave sphere with the heavenly bodies at the center. His system revived the themes of astral immortality through ascesis and an alchemical relation of humans to a closed cosmos. It was the basis for one of America's more successful utopian communities, which outlasted Teed for more than 50 years.

Radius measurement by laser confocal technology.

A laser confocal radius measurement (LCRM) method is proposed for high-accuracy measurement of the radius of curvature (ROC). The LCRM uses the peak points of confocal response curves to identify the cat eye and confocal positions precisely. It then accurately measures the distance between these two positions to determine the ROC. The LCRM also uses conic fitting, which significantly enhances measurement accuracy by restraining the influences of environmental disturbance and system noise on the measurement results. The experimental results indicate that LCRM has a relative expanded uncertainty of less than 10 ppm for both convex and concave spheres. Thus, LCRM is a feasible method for ROC measurements with high accuracy and concise structures.

Simulation and Experiment for the Position of Standing Wave Levitation

It is important to find the proper levitated positions in the standing wave levitator. Using ANSYS and MATLAB, the standing wave field and the time average potential are simulated with the levitator whose radiating surface and reflecting surface are concave spheres. The simulation results show that the position close to reflecting surface deviates from the central axis, the others in the central axis. Levitation experiments for the light specimens are carried out with the standing wave levitator, which conforms to the simulation results.

Performance study of standing wave levitation with emitting and reflecting surface of concave sphere structure

In order to improve levitation capability and stability of ultrasonic standing wave, a novel levitation device was presented, which adopted concave spherical surface on the emitter and the reflector. Using ANSYS software, the acoustic field generated by the concave spherical emitting surface was analyzed and the formation of ultrasonic standing wave was simulated. Based on the simulation result, the distribution and maximum acoustic pressure under different radius of concave spherical surface on the emitter and the reflector were ascertained. Through the MATLAB simulation, the optimal structural parameter and levitation position were predicted. Based on the optimization result, the prototype of standing wave levitation device was designed and manufactured. In the laboratory, the radiation force was tested and levitation experiments were also carried out and the actual levitation position was in accordance with the simulation results. When the distance between the emitter and the reflector equaled to about 34.9 mm, three steel balls of 3 mm diameter could be levitated at the same time in three disparate nodes position, the levitation capability and stability were demonstrated to be enhanced largely.

Experimental study and analysis of a novel multi-media plate heat exchanger

The experimental study and analysis of a novel multi-media plate heat exchanger were performed in this paper. This novel multi-media plate heat exchanger was self-developed during the process of the investigation and design of the alpha magnetic spectrometer (AMS) thermal system. The plate of this kind of novel plate heat exchanger is formed by discontinuous structure wave consisting of convex sphere and concave sphere, its heat transfer performance is better than that of the BR1 chevron plate heat exchanger, and its resistance characteristics are superior to those of the normally used 60-degree plate heat exchanger. Furthermore, the mechanism analysis of heat transfer enhancement shows that the spherical wave structure can reduce the local field synergy angle, so as to improve the field synergy degree of velocity vector and temperature gradient vector.

Influence of the contact model on the dynamic response of the human knee joint

The goal of this work is to study the influence of the contact force model, contact geometry, and contact material properties on the dynamic response of a human knee joint model. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four non-linear spring elements that represent the main knee ligaments, is considered. The contact force models used were the Hertz, the Hunt–Crossley, and the Lankarani–Nikravesh approaches. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Since knee can exhibit conformal and non-conformal contact scenarios, three different geometrical configurations for femur–tibia contact are considered, that is convex–convex sphere contact, convex–concave sphere contact, and convex sphere–plane contact. The highest level of contact forces is obtained for the case of convex–convex sphere contact. As far as the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analysed and compared with three pathological and two artificial knee models. The obtained results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.

Basal plane bending of 6H-SiC single crystals observed by synchrotron radiation X-ray topography

Basal plane bending is a structural defect in SiC single crystals caused mainly by the thermal mismatch between seed and holder, which deteriorates the quality of the wafers and blocks their applications. In this paper, basal plane bending was detected by high-resolution X-ray diffractometry (HRXRD) and transmission synchrotron white-beam X-ray topography (SWBXT). HRXRD reveals that the (0001) Si face is a concave sphere and SWBXT shows that the shapes of the Laue spots are different from that of the cross section of the synchrotron radiation beam. On the basis of a spherical curvature model for a (0001) 6H-SiC single crystal, the shapes of the Laue spots were simulated. The results are in good agreement with the experimental observations. Thus, SWBXT is an effective method for detecting basal plane bending.

125 球面軸受とウォーム歯車の両機能を有した新しい関節駆動機構(OS14-2 応用・実用事例II)

For the robot hand of which the miniaturization is required, a new joint drive mechanism is proposed in this paper. This mechanism is composed of three members. The first member is a convex sphere with a spiral groove on the surface, and this member is the driving element of this mechanism. The second member is a concave sphere which wraps the convex sphere. At one place on the inside of this concave sphere, an internal tooth is buried. This tooth meshes with the spiral groove. This member is driven element of this mechanism, and it does the swinging motion. The third member is a spherical bearing which supports the rotating convex sphere. This spherical bearing is the fixed element of this mechanism, and it has the guide plane which decides the direction of the swinging motion. Here, the details of this mechanism are explained.

Contact Pressure Analysis in Conforming Problem

Concerning of non-conforming problem, various methods are proposed for calculating contact pressure between elastic two bodies. But about conforming problem, there are few papers for calculating method of contact pressure. Authors propose a new method applying Boussinesq solutions in conforming problem for calculating contact pressure between elastic arbitrary shape bodies. This method is of course effective in non-conforming problems. But, in this method, theoretical contradiction exists because of applying Boussinesq solutions, which is a solution of elastic half space, to conforming problem. For verification of this method, FEM calculations were performed in two cases. First is convex and concave sphere contact, and second is ball bearing innerrace and ball contact. The result of FEM was well corresponding to the result of authors' method in each case. The reason why this technique is corresponding to FEM, and why above contradiction is overcome are considered, in this paper. From the result of consideration, we thought that there is no problem on a practical side in applying this method to conforming problem, as long as two surfaces are adjacent and the basic surface can be set up.