Micro Electrical Discharge Machining Deposition in Air for Fabrication of Micro Spiral Structures

Micro electrical discharge machining（EDM） deposition process is a new micro machining method for fabrication of metal micro structures. In this process, the high level of tool electrode wear is used to achieve the metal material deposition. Up to now, the studies of micro EDM deposition process focused mainly on the researches of deposition process, namely the effects of discharge parameters in deposition process on the deposition rate or deposition quality. The research of the formation of micro structures with different discharge energy density still lacks. With proper conditions and only by the z-axis feeding in vertical direction, a novel shape of micro spiral structure can be deposited, with 0.11 mm in wire diameter, 0.20 mm in outside diameter, and 3.78 mm in height. Then some new deposition strategies including angular deposition and against the gravity deposition were also successful. In order to find the forming mechanism of the spiral structures, the numerical simulation of the transient temperature distribution on the discharge point was conducted by using the finite-element method（FEM）. The results show that there are two major factors lead to the forming of the spiral structures. One is the different material removal form of tool electrode according with the discharge energy density, the other is the influenced degree of the movement of the removed material particles in the discharge gap. The more the energy density in single discharge is, the smaller the mass of the removed material particles is, and the easier the movements of which will be changed to form an order tendency. The fine texture characteristics of the deposited micro spiral structures were analyzed by the energy spectrum analysis and the metallographic analysis. It shows that the components of the deposited material are almost the same as those of the tool electrode. Moreover the deposited material has the brass metallic luster in the longitudinal profile and has compact bonding with the base material. This research is useful to understand the micro-process of micro EDM deposition better and helpful to increase the controllability of the new EDM method for fabrication of micro structures.

Simulation algorithm for spiral case structure in hydropower station

In this study, the damage-plasticity model for concrete that was verified by the model experiment was used to calculate the damage to a spiral case structure based on the damage mechanics theory. The concrete structure surrounding the spiral case was simulated with a three-dimensional finite element model. Then, the distribution and evolution of the structural damage were studied. Based on investigation of the change of gap openings between the steel liner and concrete structure, the impact of the non-uniform variation of gaps on the load-beating ratio between the steel liner and concrete structure was analyzed. The comparison of calculated results of the simplified and simulation algorithms shows that the simulation algorithm is a feasible option for the calculation of spiral case structures. In addition, the shell-spring model was introduced for optimization analysis, and the results were reasonable.

ANALYTIC STUDY ON POTENTIAL INSTABILITY AND SPIRAL STRUCTURE OF RAIN CLUSTERS

This paper presents a study on potential instability and spiral structure of unstable rain clusters.First,we develop a linearized non-axisymmetrical mathematic model for rain clusters in circular cylindrical coordinates and acquire its analytic solution.Second,we discuss the potential instability of non-axisymmetrical rain clusters.Finally,we conclude that spiral structures can exist in rain clusters.Our analysis indicates that potential instability occurs when humid stratification coefficient is less than zero.Unstable growth rate increases with the increase of the absolute value for humid stratification coefficient.The simpler the vertical structure of perturbation,the thicker the inversion layer;additionally,the smaller the radius of the rain clusters,the larger the unstable growth rate.Simulation results agree well with those from observation and forecast.The spiral structure simulated by our model is similar to a radar echo,suggesting that rain clusters with spiral structures can occur in the atmosphere.In addition,they are generally close to the model solution in this work.

Homoclinic （Heteroclinic） Orbit of Complex Dynamical System and Spiral Structure

Starting from iterated systems, it is shown that the homoclinic (heteroclinic) orbit is a kind of spiral structure. The emphasis is laid to show that there are homoclinic or heteroclinic orbits in complex discrete and continuous systems, and these homoclinic or heteroclinic orbits are some kind of spiral structure.

Three-dimensional spiral structure of tropical cyclone under four-force balance

The steady axis-symmetrical atmosphere dynamical equations are used for describing spiral structure of tropical cyclones under four-force （pressure gradient force, Coriolis force, centrifugal force, and friction force） balance, and the dynamical systems of three-dimensional （3D） velocity field are introduced. The qualitative analysis of the dynamical system shows that there are down 3D spiral structures in eye of tropical cyclone and tropical cyclone is 3D counterclockwise up spiral structure. These results are consistent with the observed tropical cyclone on the weather map.

The bar and spiral arms in the Milky Way: structure and kinematics

The Milky Way is a spiral galaxy with the Schechter characteristic luminosity L*,thus an important anchor point of the Hubble sequence of all spiral galaxies.Yet the true appearance of the Milky Way has remained elusive for centuries.We review the current best understanding of the structure and kinematics of our home galaxy,and present an updated scientifically accurate visualization of the Milky Way structure with almost all components of the spiral arms,along with the COBE image in the solar perspective.The Milky Way contains a strong bar,four major spiral arms,and an additional arm segment(the Local arm)that may be longer than previously thought.The Galactic boxy bulge that we observe is mostly the peanut-shaped central bar viewed nearly end-on with a bar angle of^25°-30°from the SunGalactic center line.The bar transitions smoothly from a central peanut-shaped structure to an extended thin part that ends around R^5 kpc.The Galactic bulge/bar contains^30%-40%of the total stellar mass in the Galaxy.Dynamical modelling of both the stellar and gas kinematics yields a bar pattern rotation speed of^35-40 km s-1 kpc-1,corresponding to a bar rotation period of^160-180 Myr.From a galaxy formation point of view,our Milky Way is probably a pure-disk galaxy with little room for a significant merger-made,"classical"spheroidal bulge,and we give a number of reasons why this is the case.

Fourier Transforms of Tubular Objects with Spiral Structures

Crystal structures of several naturally occurring minerals are known to contain various deformities such as cones, cylinders, and tapered hollow cylinders with different apex angles, which have been described as solid and hollow cones, “cups”, “lampshades” as well as rolled cylindrical planes. The present study was undertaken to determine how these different shapes within a crystal structure can be explained. Since the usual method of observing them is by either X-ray and electron diffraction or electron microscopy, we investigated Fourier transforms of these forms, which were considered in terms of spirals with varying radii. Three types of spirals were considered, namely: 1) Archimedean spiral;2) Involute of a circle or power spiral and 3) Logarithmic spiral. Spiraling caused the radius r to be modified by a factor f(θ), so that r becomes rf(θ), where f(θ) = θ for Archimedean helix, θn for power helices like θ1/2 for Fermat’s helix, θ-1 for hyperbolic helix and eθ or e-θ for logarithmic helix, r and θ being co-ordinates of the map on which the helix has to be drawn, f(θ) is unaffected by the magnitude of r. Expressions have been derived that explain the diffraction of structures containing the distortions described above, and bring all of these phenomena under one “umbrella” of a comprehensive theory.

New estimates of scale heights and spiral structures for non-edge-on spiral galaxies

On the basis of Poisson＇s equation for the logarithmic perturbation of matter density, we provide improved estimates of scale heights and spiral structures for non-edge-on spiral galaxies by subtracting the surface brightness distributions from observed images. As examples, the non-edge-on spiral galaxies PGC 24996, which is face-on, and M31, which is inclined, are studied. The scale height, pitch angle and inclination angle of M31, our nearest neighbor, that are presented in this work, agree well with previous research.

Middle or low water pressure direct spiral double helix converging nozzle structure optimization and flow field analysis

In order to solve the problem of using middle or low water pressure to form fine water mist,a new nozzle is proposed in fire rescue robot.Existing water mist nozzles are basically used for high pressure and in large size,complex structure and poor low pressure atomization effect in comparison with requirement of snake-like fire rescue robots.On the basis of comprehensive typical spray nozzles,a direct spiral double helix converging nozzle(DSDHCN) is proposed,which has the advantages of small volume,light weight,simple structure,and convenient installation.To make the spray nozzle have good performance,and meet the requirements of more efficient fire extinguishing,a numerical study is carried out to analyze the internal and external full flow field of nozzle.A gas-liquid two-phase flow is applied to simulate the external full flow field of nozzle with VOF model in fluent software.The simulation results show the real situation of water flow out of the atomization nozzle and the water jet trajectory.Some simulations about middle or low water pressure direct spiral double helix converging optimized nozzle have been done in 30 bar pressure.The simulation results show that the optimized nozzle structure not only makes the spray droplets have a good cone angle,but also have a sufficient axial velocity,which proves the structure rationality of the proposed optimized nozzle.

Influence of spiral anchor composite foundation on seismic vulnerability of raw soil structure

A typical single-layer raw soil structure in villages and towns in China is taken as the research object.In the probabilistic seismic demand analysis,the seismic demand model is obtained by the incremental dynamic time history analysis method.The seismic vulnerability analysis is carried out for the raw soil structure of nonfoundation,strip foundation,and spiral anchor composite foundation,respectively.The spiral anchor composite foundation can reduce the seismic response and failure state of raw soil structure,and the performance level of the structure is significantly improved.Structural requirements sample data with the same ground motion intensity are analyzed by linear regression statistics.Compared with the probabilistic seismic demand model under various working conditions,the seismic demand increases gradually with the increase of intensity.The seismic vulnerability curve is summarized for comparative analysis.With the gradual deepening of the limit state,the reduction effect of spiral anchor composite foundation on the exceedance probability becomes more and more obvious,which can reduce the probability of structural failure to a certain extent.

Pinion Tooth Surface Generation Strategy of Spiral Bevel Gears

Aviation spiral bevel gears are often generated by spiral generated modified（SGM） roll method.In this style,pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances.For the optimal contact pattern and transmission error function,local synthesis is applied to obtain the machine-tool settings of pinion.For digitized machine,four tooth surface generation styles of pinion are proposed.For every style,tooth contact analysis（TCA） is applied to obtain contact pattern and transmission error function.For the difference between TCA transmission error function and design objective curve,the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established.Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function.The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers.The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair.This study is an expansion to generation strategy of spiral bevel gears,and offers new alternatives to computer numerical control（CNC） manufacture of spiral bevel gears.

A flat-foldable equiangular spiral folding pattern inspired by sunflowers for deployable structures

Flasher origami pattern has been widely utilized to improve the stowage efficiency of deployable structures.Nevertheless,flasher origami cannot be folded fully flat,and they still have great potential for optimization in terms of storage volume and folding creases.In this paper,a flat foldable equiangular spiral folding pattern inspired by the sunflower disk is introduced.Then,a parametric design method for this equiangular spiral crease diagram is introduced in detail.Subsequently,a kinematic model of the equiangular spiral folding pattern is established based on the kinematic equivalence between rigid origami and spherical linkages.A simulation of the developed model demonstrates that the equiangular spiral folding pattern can be folded flat.Using the folded ratio as an evaluation index,the calculated results and experiments show that the equiangular spiral crease pattern can yield fewer creases and improve stowage efficiency in comparison to flasher origami pattern.Equiangular spiral folding pattern can save a considerable amount of space and provide a new approach to spatially deployable structures.

The Dynamical Characteristics and Wave Structure of Typhoon Rananim (2004)

Typhoon Rananim （2004） was one of the severest typhoons landfalling the Chinese mainland from 1996 to 2004. It brought serious damage and induced prodigious economical loss. Using a new generation of mesoscale model, named the Weather Research and Forecasting （WRF） modeling system, with 1.667 km grid horizontal spacing on the finest nested mesh, Rananim was successfully simulated in terms of track, intensity, eye, eyewall, and spiral rainbands. We compared the structures of Rananim to those of hurricanes in previous studies and observations to assess the validity of simulation. The three-dimensional （3D） dynamic and thermal structures of eye and eyewall were studied based on the simulated results. The focus was investigation of the characteristics of the vortex Rossby waves in the inner-core region. We found that the Rossby vortex waves propagate azimuthally upwind against the azimuthal mean tangential flow around the eyewall, and their period was longer than that of an air parcel moving within the azimuthal mean tangential flow. They also propagated outward against the boundary layer inflow of the azimuthal mean vortex. Puthermore, we studied the connection between the spiral potential vorticity （PV） bands and spiral rainbands, and found that the vortex Rossby waves played an important role in the formation process of spiral rainbands.

Reverse Engineering of Machine-tool Settings with Modified Roll for Spiral Bevel Pinions

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.

The Structure and Bifurcation of Atmospheric Motions

The 3-D spiral structure resulting from the balance between the pressure gradient force, Coriolis force, and viscous force is a common atmospheric motion pattern. If the nonlinear advective terms are considered, this typical pattern can be bifurcated. It is shown that the surface low pressure with convergent cyclonic vorticity and surface high pressure with divergent anticyclonic vorticity are all stable under certain conditions. The anomalous structure with convergent anticyclonic vorticity is always unstable. But the anomalous weak high pressure structure with convergent cyclonic vorticity can exist, and this denotes the cyclone’s dying out.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Effect of static transmission error on dynamic responses of spiral bevel gears

The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.

Analysis and modeling of error of spiral bevel gear grinder based on multi-body system theory

Six-axis numerical control spiral bevel gear grinder was taken as the object, multi-body system theory and Denavit-Hartenberg homogeneous transformed matrix (HTM) were utilized to establish the grinder synthesis error model, and the validity of model was confirmed by the experiment. Additionally, in grinding wheel tool point coordinate system, the errors of six degrees of freedom were simulated when the grinding wheel revolving around C-axis, moving along X-axis and Y-axis. The influence of these six errors on teeth space, helix angle, pitch, teeth profile was discussed. The simulation results show that the angle error is in the range from -0.148 4 rad to -0.241 9 rad when grinding wheel moving along X, Y-axis; the translation error is in the range from 0.866 0 μm to 3.605 3 μm when grinding wheel moving along X-axis. These angle and translation errors have a great influence on the helix angle, pitch, teeth thickness and tooth socket.

Virtual System Solution of CNC Machine for Spiral Bevel and Hypoid Gears

A virtual computerized numerical control (CNC) processing system is built for spiral bevel and hypoid gears. The pre-designed process of the solution to locate the way of realization is investigated. A kind of combined programming method and principle of solid modeling are chosen. Multi-environmental programming thought and the inter-connected mechanisms between different environments are applied in the proposed system. The problems of data exchange and compatibility of modules are settled. Environment of the system is founded with object oriented programming thought. AutoCAD is located as the graphic environment. Matlab is used for editing the computation module. Virtual C++6.0 is the realization environment of the main module. Windows is the platform for realizing the multi-environmental method. Through establishing the virtual system based windows message handling mechanism and the component object model, the application of multi-environmental programming is realized in the manufacture system simulation. The virtual gear product can be achieved in the accomplished software.

Energy band structure in optical of spin-1 condensates lattices

The energy band structure of spin-1 condensates with repulsive spimindependent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional （1D） periodic optical lattices is discussed. Within the two-mode approximation, Bloch bands of spin-1 condensates are presented. The results show that the Bloch bands exhibit a complex structure as the atom density of mF = 0 hyperfine state increases： bands splitting, reversion, intersection and loop structure are excited subsequently. The complex band structure should be related to the tunneling and spin-mixing dynamics.