Concave Spherical Surface Research Articles

Key Factors in Fiber Point Diffraction Interference Technology for Measuring Surface

The point diffraction interferometer (PDI), which generates the nearly ideal spherical wavefront with the pinhole method, is realized the absolute interferometric measurement without the use of reference surface. But it is hard to detect the diameter of the pinhole and hard for use of phase shifting interferometers in PDI. However the advanced fiber point diffraction interferometer (FPDI) not only replaces the pinhole with the fiber, but also makes it possible to implement phase shifting and maintain advantage of traditional PDI. In this paper, the different methods of measuring surface are proposed according to different experimental conditions and different targets (such as concave spherical surface, convex spherical surface, flat surface) with the fiber point diffraction interferometer built in the laboratory. Base on these experiments, there are several key factors in the measurement process such as measurement configuration, laser source, polarization beamsplitter, optical fiber. And these factors, affecting the experiment accuracy, were analyzed seriously.

Seismic behaviour of isolated multi-span continuous bridge to nonstationary random seismic excitation

This paper concentrates on the results of responses of a multi-span continuous bridge isolated with double concave friction pendulum bearings subjected to non-stationary random seismic excitation characterized by the incoherence, the wave-passage, and the site-response effects. The earthquake excitation is modelled as a non-stationary random process as uniformly modulated broad-band excitation. To perform the seismic isolation procedure, the double concave friction pendulum bearings which are sliding devices that utilize two spherical concave surfaces are placed at each of the six support points of the deck. The non-stationary response of the isolated bridge is compared with the corresponding stationary response in order to study the effects of non-stationary characteristics of the earthquake input motion. Solutions obtained from the stationary and non-stationary stochastic analyses for the isolated bridge to spatially varying earthquake ground motions are compared for the special cases of the earthquake ground motion model. The spatially varying earthquake ground motions are described stochastically based on an empirical coherency loss function and a filtered power spectral density function. The site effect is considered by a transfer function derived from one dimensional wave propagation theory. It is observed that the stationary assumption is reasonable for the considered ground motion duration.

The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressure

The generalization of Derjaguin–Frumkin approach for the description of wettability of curved interfaces is given. The equations for the calculations of the contact angle on concave and convex cylindrical and spherical surfaces based on the isotherms of the disjoining pressure are derived. Analysis performed has shown that for the radius of curvature comparable to the range of surface forces action increasing the surface curvature for convex surfaces results in the contact angle increasing, whereas for concave surfaces the wetting improves. It is shown that curving the substrate surface may cause philic/phobic or phobic/philic wettability transition.

Van der Waals interaction of a neutral atom with the surface of a metal or dielectric nanosphere

We analyse the van der Waals interaction of a neutral atom with the internal and external surfaces of either a metal or dielectric nanosphere. We derive closed analytical equations for the van der Waals interaction energy using an electrostatic approximation and show that the energy increases or decreases as a function of the atom's distance from the surface, depending on the surface curvature. For concave spherical surfaces, the van der Waals energy can increase by up to a factor of 6, while for convex surfaces it decreases by as much as a factor of 2, when compared to that obtained for a flat surface. The derived analytical equations are very simple and can be used for a comparison between theory and experimental measurements of the van der Waals constant, C3.

Two-spherical-wave ultraviolet interferometer for making an antireflective subwavelength periodic pattern on a curved surface

An ultraviolet two-spherical-wave interferometer was developed in order to make a subwavelength structured surface on a curved surface. The change in fringe period on the curved surface was significantly suppressed compared with the two-plane-wave interferometer. The optical setup method for suppressing the change in fringe period is described. The effect of the two-spherical-wave interferometer was investigated by numerical simulations. In an experimental demonstration for a concave spherical surface with 11.1 mm radius of curvature and 10 mm diameter, the change in period of the photoresist pattern was reduced to 12 nm for the target period of 250 nm.

NUMERICAL ANALYSIS OF DISPLACEMENTS IN SPATIAL MECHANISMS WITH SPHERICAL JOINTS UTILIZING AN EXTENDED D-H NOTATION

Spherical joints consist of a pair of concave and convex spherical surfaces engaged in such a way as to prevent translational motion of the ball and socket whilst simultaneously allowing three degrees of rotational freedom. The kinematics of spatial mechanisms comprising links and joints are commonly analyzed using the Denavit-Hartenberg (D-H) notation. However, whilst this method allows the kinematics of mechanisms containing prismatic, revolute, helical and cylindrical joints to be explicitly defined, it cannot be directly applied to mechanical systems containing spherical pairs. Accordingly, this paper proposes an extended D-H notation which allows the independent parameters of any spatial mechanism, including one with spherical pairs, to be derived for analysis and synthesis purposes. The validity of the proposed notation is demonstrated via its application to the analysis of mechanisms containing revolute (R), spherical (S), cylindrical (C) and prismatic (P) joints. The results confirm the viability of the extended D-H notation as a means of analyzing the displacements of mechanical systems containing kinematic chains such as RSCR, RSCP, CSSR and CSSP.

Sound Reflections from Concave Spherical Surfaces. Part I: Wave Field Approximation

Focussing arising from reflections at concave surfaces is a well-known problem in room acoustics. Focussing can cause high sound pressure levels, colouration or an echo. Although the problem is known, the amplification in the focal point and the sound field around the focal point are not. This paper provides some mathematical formulations for sound reflections from concave spherical surfaces. The formulation is based on a wave extrapolation method. The approximations given can be used to calculate the sound field in and around the focal point. The calculation method is verified with an experiment. In the focal point the pressure depends on the wavelength. The width of the peak pressure is also related to the wavelength. For small wavelengths the amplification is high but the area is small, while for lower frequencies the amplification is less, but the area is larger. In a second part of this paper [1] geometrical and engineering methods will be discussed for describing the focussing effect.

Sound Reflections from Concave Spherical Surfaces. Part II: Geometrical Acoustics and Engineering Approach

Focussing arising from concave surfaces has long been a well-known problem in room acoustics. The focussing can cause high sound pressure levels, colouration or an echo. Part I of this paper [1] provides a mathematical approximation based on wave extrapolation of the sound field in and around the focal point due to reflections by a spherical surface. This second part of the paper provides some practical methods for calculating the sound field. A geometrical approach is presented, the limitations of image source methods are described and an engineering method is presented. Computer models based on image source methods are not capable of describing the pressure in or out of the focal. The sound field outside the focal area can be calculated within reasonable accuracy with a geometrical approach. The results show that for a small wavelength the focussing effect is fairly strong. Generally the possible reduction of the focussing effect by absorbers or diffusers is not enough to eliminate the focussing effect by spherical surfaces.

Experimental Study on Ultra-Precision ELID Grinding for Concave Spherical Surface of Carbide

This paper describes the current situation of spherical grinding for carbide material. The experiment of Concave spherical ELID grinding of generating method for carbide is conducted. Because dressing electrode can’t be installed in limited space due to the small space of concave spherical surfaces and carbide material has good conductivity, the workpiece material was used as dressing electrode in the ELID grinding experiment. According to negative effect of spark discharge in the process of grinding to surface roughness, two methods "ELIDⅡ" and "ELID Ⅲ" were designed. Comparing and analyzing the experimental results, it is confirmed preliminary that the spherical error and surface roughness of the workpiece after "ELIDⅡ" grinding were better than those after the "ELID Ⅲ" grinding. The ELID grinding method using micro diamond powder wheel and using carbide workpiece as dressing electrode is an effective way for spherical ultra-precision grinding for carbide.

Earthquake response of isolated cable-stayed bridges under spatially varying ground motions

A comprehensive investigation of the stochastic response of an isolated cable-stayed bridge subjected to spatially varying earthquake ground motion is performed. In this study, the Jindo Bridge built in South Korea is chosen as a numerical example. The bridge deck is assumed to be continuous from one end to the other end. The vertical movement of the stiffening girder is restrained and freedom of rotational movement on the transverse axis is provided for all piers and abutments. The longitudinal restraint is provided at the mainland pier. The A-frame towers are fixed at the base. To implement the base isolation procedure, the double concave friction pendulum bearings are placed at each of the four support points of the deck. Thus, the deck of the cable-stayed bridge is isolated from the towers using the double concave friction pendulum bearings which are sliding devices that utilize two spherical concave surfaces. The spatially varying earthquake ground motion is characterized by the incoherence and wave-passage effects. Mean of maximum response values obtained from the spatially varying earthquake ground motion case are compared for the isolated and non-isolated bridge models. It is pointed out that the base isolation of the considered cable-stayed bridge model subjected to the spatially varying earthquake ground motion significantly underestimates the deck and the tower responses.

Experimental Study on Five-Axis Machining Parameter for NAK80 Die Steel

The surface quality and contouring accuracy of die cavities directly influences the surface roughness of the products. Different types of complex surfaces of products have become popular in product design in recent years and consequently 5-axis machining techniques become a mainstream in the manufacturing of the die and moulds used in products mentioned above, because of their features and flexibility. This research applies Taguchi method to find out a set of optimal machining parameters in five-axis milling process. The table rotating-tilting type five-axis machine is used to perform the experimental cutting. The cavity of die is modeled as convex half spherical surface, and the material of die is NAK 80 die steel. The four parameters studied are cutting speed, feed rate, tool paths, and contact points, and each of these factors has three levels. The target of this study is the feature of smaller-the-better that is minimization of the surface roughness. The experimental results show that the optimal parameters are moderate cutting speed and contact points, higher feed rate, five-axis tool path. ANOVA analysis indicates that the tool path influences the surface roughness most, which accounts for about 86%. Using optimal parameters to machine a roughly machined concave spherical surface can reach its roughness to 0.234μm, and the roundness error about 0.0314mm. It is believed that the results and method presented in the paper give a good reference for industry applied.

Fundamental Study on Diamond Spherical Shell Film for Polishing of Concave Spherical Surface

In this paper, a new polishing technique was proposed to polish concave spherical surface by diamond spherical shell deposited by DC-Plasma Jet CVD(chemical vapor deposition), and preparation was studied from both experiment and theory. The deposited films were investigated by some techniques including: scanning electron microscopy (SEM), atom force microscopy (AFM), Raman spectroscopy, and roughness-profile-meter, which were used to analyze surface phase, microstructure, internal quality and surface roughness. The results show that the deposited diamond spherical shell film has some remarkable properties, such as high surface density, high hardness. Compared to traditional polishing techniques, it will have some potential advantages as convenient, flexible, efficient and precious. To adjust some important parameters as methane concentration, depositing time, and it can deposit the different size grain diamond spherical shell films, which are used to polish different precision degree concave spherical surfaces. Meantime, to change curvature of diamond spherical shell, it can adapt to polish various curvature radius concave spherical surfaces.

Precision Grinding of Concave Spherical Surface of High-Alumina

The performances of high-alumina ceramic are analyzed such as physical and mechanical property. In consideration of its brittleness-ductility change, the critical cutting depth agc of high-alumina ceramic is 3μm. When the cutting depth of single grain is less than the critical cutting depth of alumina ceramic in precision manufacturing, the material is wiped off with ductility. So the cutting depth of single grain agm should be selected within 0.1~2.5μm.Grinding wheel sharp edge is utilized for the spherical surface generation cutting. The ceramic-bonded fine grain diamond wheel is selected after considering manufacturing technology, machining parameters, its making and mending. The granularity of grinding wheel is M1~M5 and the consistence is 125%. The method of spherical surface generation cutting and the effect of high-alumina ceramic ductile machining were verified by the experiment of high-alumina ceramic precision grinding using precision grinding machine MGK1420. The result shows that the surface quality is very high and achieves the requirements.

Air bearing kinematic couplings

Abstract The “kinematic coupling” is a well-known device used to achieve highly repeatable positioning of one machine or instrument element relative to another. Normally, it consists of three precision balls attached to one machine element in a triangular pattern. These balls mate with three V-grooves in the surface of the mating element, creating ball/flat point contacts at six locations on each body. Friction forces at the contacts limit the repeatability and accuracy of the coupling, and can result in wear over time. This paper describes a novel coupling design where we replace the ball/flat contacts with an intermediate element consisting of a double-sided porous carbon air bearing with one planar surface and one concave spherical surface. These air bearings ride on corresponding surfaces on the two bodies to be mated, thus restricting motion along a single line in space while introducing essentially zero friction in the other directions. With six such elements appropriately placed, all 6 d.f. of relative motion between the two bodies can be restrained. Experimental measurement of coupling repeatability shows that the air bearing kinematic coupling (ABKC) outperforms traditional ball/groove couplings both in positioning repeatability and load carrying capacity.

Simulation of sound field in a tissue medium generated by a concave spherically annular transducer

The concave spherically annular transducer is regarded as a negative and a positive concave spherical transducer, and the spheroidal beam equation is used to simulate the linear and nonlinear sound field in a tissue medium generated by this transducer. It is found that the acoustic focus of the ring does not coincide with the acoustic focus of its central part. If the width of the ring increases, its acoustic focus will move toward the geometric focus and the amplitudes of nonlinear harmonics will increase obviously. If there are several coaxial rings placed on the concave spherical surface, more than one peak will appear along the axial direction for the fundamental, and high harmonics focus better. The distribution of sound field will change with the number and the excited signals of rings, so it maybe is a potential approach to treat locally big tumors.

Ultraprecision grinding of tungsten carbide for spherical mirrors

This paper reports the ultraprecision grinding of tungsten carbide for spherical mirrors with nanometre surface roughness and submicron form accuracy. Spherical grinding was conducted with a computer numerical control grinding machine using a metal-bond diamond tool with grit size of 15 μm. Form accuracy and surface roughness were investigated as functions of the grinding conditions. Ground tungsten carbide with concave and convex spherical surfaces was obtained with form accuracy in terms of peak-to-valley values of 0.13-0.165 wave (83-104nm) and surface roughness values smaller than Ra = 5 nm. These surfaces were also characterized with fracture-free morphology. The analyses of microscopic topography of the applied diamond tool showed that self-sharpening of diamond abrasives occurred in grinding. The results show that ultraprecision grinding can be applied to the direct fabrication of spherical mirrors made of tungsten carbide without additional lapping and polishing processes.

Focus retrocollimated interferometry for long-radius-of-curvature measurement

Focus retrocollimated interferometry is described for measuring long radius of curvature (>/=1 m), and achievable accuracy is discussed. It is shown that this method can be applied to both concave and convex spherical surfaces and can provide measurement to accuracy of 0.01-0.1%.

THEORETICAL STUDY OF THE THERMAL EFFECT IN BIOLOGICAL MEDIUM GENERATED BY FOCUSED ULTRASOUND SOURCE

The steady state temperature field in human body generated by concave spherical surface focused ultrasound transducer for hyperthermia has been studied through solving bioheat conduction equation by the difference method in this paper.The influence of parameters of the transducer and biological tissue properties on the effective treated area has been analyzed through introducing the heat focal distance and isotherms, and characteristics of the sound field and temperature field are studied thoroughly.

Numerical analysis of displacements in spatial mechanisms with ball joints

The ball joint, often referred to as a spherical or ‘S’ joint is modeled using dual-number coordinate-transformation matrices. The joint consists of concave and convex spherical surfaces engaged to prevent translations but allowing three degrees of freedom, all of which are rotations. Derivative-operator matrices to be used in the Fischer–Paul adaptation of the Uicker–Denavit–Hartenberg numerical scheme for displacement analysis of spatial mechanisms are developed. The generalized slider-crank (CSSP) mechanism is presented as an example featuring ball joints where coordinate-transformation matrices modeling links with ball joints are used in a concatenation with analogous matrices modeling links with revolute, prismatic or cylindrical joints to analyze the displacements.

Wafer chuck for magnification correction in x-ray lithography

Magnification correction has emerged as a critical issue in x-ray lithography for very large scale integrated circuits. We have developed a simple and robust method to correct the magnification, which is suitable for use in a collimated x-ray beam from a storage ring. In our technique the wafer is bent to conform to a chuck whose surface is a portion of a sphere of adjustable radius. Both increases and decreases in the pattern size may be accommodated by using convex and concave spherical surfaces, respectively. The radius of the chuck can be set to achieve desired corrections of up to several parts per million. The maximum attainable correction is determined by the permissible out of plane distortion which accompanies the wafer bending, and is dependent upon the wafer thickness and the field size. The change in the wafer pattern is expected to be very nearly an isotropic magnification; however a limited one-dimensional magnification correction may also be added by differentially scanning the mask and wafer.