Mathematical Model for Metal Transfer Study in Additive Manufacturing with Electron Beam Oscillation

A computer model has been developed to investigate the processes of heat and mass transfer under the influence of concentrated energy sources on materials with specified thermophysical characteristics, including temperature-dependent ones. The model is based on the application of the volume of fluid (VOF) method and finite-difference approximation of the Navier–Stokes differential equations formulated for a viscous incompressible medium. The “predictor-corrector” method has been used for the coordinated determination of the pressure field which corresponds to the continuity condition and the velocity field. The modeling technique of the free liquid surface and boundary conditions has been described. The method of calculating surface tension forces and vapor recoil pressure has been presented. The algorithm structure is given, the individual modules of which are currently implemented in the Microsoft Visual Studio environment. The model can be applied for studying the metal transfer during the deposition processes, including the processes with electron beam spatial oscillation. The model was validated by comparing the results of computational experiments and images obtained by a high-speed camera.

INTERACTION OF SPATIAL OSCILLATION WITH ROUGHNESS OF SURFACE WORKED BY EXAMPLE OF TURNING

The work purpose is to determine the impact of cutter spatial oscillation upon parameters and values of worked surface roughness, in particular, the paper is dedicated to the definition of differences in roughness parameters depending on a projecting plane in which cutter oscillation is considered. There are considered the matters of the impact of cutter spatial oscillation upon roughness of the surface worked, and also cutting parameters influencing the intensity and frequency of oscillation of cutter point oscillation. The solution of the problems specified is carried out on the basis of the analysis of data published in scientific literature and experimental data obtained in the course of investigations. The novelty of the work: it is revealed that a dynamic state of the technological system for machining which depends upon a multitude of factors has an influence not only upon a value of surface roughness, but also upon its parameter. Conclusion: surface roughness depends upon relative oscillation processes of the part under machining and a tool cutting edge in the working space caused mainly by a process of chip formation.

Properties of a sweeping jet emitted from a fluidic oscillator

This experimental study investigates the flow field and properties of a sweeping jet emitted from a fluidic oscillator into a quiescent environment. The aspect ratio of the outlet throat is 1. Stereoscopic particle image velocimetry is employed to measure the velocity field plane-by-plane. Simultaneously acquired pressure measurements provide a reference for phase correlating the individual planes yielding three-dimensional, time-resolved velocity information. Lagrangian and Eulerian visualization techniques illustrate the phase-averaged flow field. Circular head vortices, similar to the starting vortex of a steady jet, are formed repetitively when the jet is at its maximum deflection. The quantitative jet properties are determined from instantaneous velocity data using a cylindrical coordinate system that takes into account the changing deflection angle of the jet. The jet properties vary throughout the oscillation cycle. The maximum jet velocity decays much faster than that of a comparable steady jet indicating a higher momentum transfer to the environment. The entrainment rate of the spatially oscillating jet is larger than for a steady jet by a factor of 4. Most of the mass flow is entrained from the direction normal to the oscillation plane, which is accompanied by a significant increase in jet depth compared to a steady jet. The high entrainment rate results from the enlarged contact area between jet and ambient fluid due to the spatial oscillation. The jet’s total force exceeds that of an idealized steady jet by up to 30 %. The results are independent of the investigated oscillation frequencies in the range from 5 to 20 Hz.

IMPROVEMENT OF VIBRATING FEEDERS-SCREENS FOR MINING AND METALLURGICAL INDUSTRY

The main scientific and practical results of the improvement of vibrating feeders-screens for mining and metallurgical industry are presented on the basis of dynamic calculation of the vibrating feederscreen with two differently directed self-balancing vibrators. Methods of theoretical generalizations are described using mathematical statistics, physical and mathematical modeling, computation and feasibility studies, laboratory and full-scale experimental studies, industrial tests in the conditions of operating enterprises using standard and new methods. Mathematical modeling and calculation of the parameters of a vibrating feeder of the PVG type are proposed. It is recommended when choosing dynamic parameters of the feeder, to use the vibration transmission coefficient, which is taken within the limits (1.5 – 3.5)g, and in heavy loading modes, is up to 5g. It is shown that during preparation of breeze coke in the crushing body, from 10 to 50 % of fine material is received from its bunker with a particle size of 0 – 3 mm, which is additionally re-milled, reducing the quality of coke. A vibrating feeder-screen with a spatial oscillation of the working element will increase the efficiency of screening of the material by 15 – 20 % and will improve the self-cleaning of the screen. The driving forces of the exciters are directed at different angles of 15 and 45° to the screening surfaceand are attached from each other at a distance equal to half width of the box, i.e. 600 mm. It is established that in the resonance mode at a constant amplitude with increasing frequency the coefficient of the vibro-displacement regime increases according to a quadratic dependence, at a working frequency of 100 rad/s it also increases from the loading edge of the feeder to the unloading and from one side to another, the value of which varies within 2.62 – 2.84.

Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer

Oscillatory morphodynamics provides necessary mechanical cues for many multicellular processes. Owing to their collective nature, these processes require robustly coordinated dynamics of individual cells, which are often separated too distantly to communicate with each other through biomaterial transportation. Although it is known that the mechanical balance generally plays a significant role in the systems’ morphologies, it remains elusive whether and how the mechanical components may contribute to the systems’ collective morphodynamics. Here, we study the collective oscillations in the Drosophila amnioserosa tissue to elucidate the regulatory roles of the mechanical components. We identify that the tensile stress is the key activator that switches the collective oscillations on and off. This regulatory role is shown analytically using the Hopf bifurcation theory. We find that the physical properties of the tissue boundary are directly responsible for synchronizing the oscillatory intensity and polarity of all inner cells and for orchestrating the spatial oscillation patterns inthe tissue.

A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales

We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.

A Strange Term in the Homogenization of Parabolic Equations with Two Spatial and Two Temporal Scales

We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficienta(x/ε,t/ε2)in the elliptic part and spatial oscillations in the coefficientρ(x/ε)that is multiplied with the time derivative∂tuε. We obtain a strange term in the local problem. This phenomenon appears as a consequence of the combination of the spatial oscillation inρ(x/ε)and the temporal oscillation ina(x/ε,t/ε2)and disappears if either of these oscillations is removed.