Model-based parameter optimization for arc welding process simulation

This paper presents a model-based parameter optimization for simulating a metal-inert gas welding process. The computational model used in this study is based on computational fluid dynamics methods and implemented using the finite volume approach on a 3D computational domain. The wire electrode, the arc plasma and the workpiece are treated as a self-consistent system. Important welding parameters, including arc current, wire feed rate, workpiece thickness, welding speed and geometry, as well as the metal alloy types used for the wire and workpiece, were implemented as adjustable parameters. By tuning these parameters, the performance of the arc welding can be predicted, and different settings can be compared to optimize welding performance.A benchmarking study of the arc model against experimental measurements is presented to demonstrate the model's capabilities in the prediction of the weld pool changes and thermal dynamics involved in the welding process. Two numerical case studies are presented to demonstrate the use of the model-based optimization to quantify welding pool variations with the change in welding parameters. The first case study is the determination of the optimal arc current and welding speed settings for different workpiece thicknesses. The optimization process shows that the predictions are not only in agreement with established experimental welding experience on the direct relationship between workpiece thickness and arc current, but more importantly quantify this relationship for a given workpiece thickness. The second case study focuses on the welding parameters optimization for different metal alloys. The comparison suggests that the welding parameters suitable for some aluminium alloys are less likely to be successful in welding magnesium alloys. A further model validation of Mg alloy AZ31 welding shows an agreement with experimental measurements. The work presented shows the potential of model-based parameter optimization to assist process engineers in the practical improvement of the welding process.     

On dispersive stability of Hamiltonian systems on lattices

We study the long-time dynamics of oscillations in lattices of infinitely many particles interacting via certain non-linear potentials. The aim is to proof dispersive stability of such Hamiltonian systems analogously to results known for PDEs. To do so we first recapitulate the dynamics of linear Hamiltonian systems on an infinite chain and give optimal decay rates based on the dispersion relation. Based on this we proof that if the non-linearity is weak enough, the non-linear system shows a similar behaviour like its linearization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.     

Three-dimensional periodic boundary layers

The method of successive approximations used by Eichelbrenner and A?kovíc¹ for the study of unsteady three-dimensional boundary layer flow has been extended to analyse the periodic boundary layers in three dimensions. The analysis, which is valid for oscillations of small amplitude, shows some special features such as “steady streaming” flow in the first-order cross-flow similar to the one that has been predicted and observed by Schlichting for two-dimensional periodic boundary layers.     

Direct and inverse multichannel scattering problems

We consider small oscillations of a system of pairwise interacting particles in an external field near a stable equilibrium. The system is assumed to consist of finitely many channels, i.e., semi-infinite linear chains of particles, attached to a scatterer, which is a finite system of interacting particles. Direct and inverse scattering problems are considered. In particular, an algorithm finding characteristics of the channels on the basis of scattering data is given.     

Stability analysis of the continuous ethanol fermentation process with a delayed product inhibition

In the paper, we propose and analyze a mathematical model of the continuous ethanol fermentation process to study the mechanisms of the self-sustained oscillations of ethanol concentration. The model is based on the assumption that microorganism cells response to the inhibitory effect of product (ethanol) concentration with a delay. From the local stability analysis of the system, we show that the delay time is one of the crucial factors for the occurrence of oscillations and for a critical delay time the fermentation process undergoes a Hopf bifurcation. Further analysis shows that the operating variables and kinetic parameters have also a significant effect on the dynamical behavior of the fermentation system. A proper manipulation of the operating variables allow us to eliminate the oscillatory behavior.     

Oscillation-Generating Mechanisms in Stochastic and Deterministic Models of a Catalytic Reaction

The article examines consistent mathematical micro- and macro-level models of CO oxidation on platinum-group metals. New mechanisms responsible for the excitation of oscillations are studied in detail by simulation. Micro-level oscillations may arise in parameter-space regions where the corresponding macro model has a limiting cycle, a bistability, or a unique stable steady-state solution. In the latter case, necessary conditions for the excitation of oscillations include fluctuations in the concentration of adsorbed particles, which are characteristic of micro models of small-volume systems, and a special arrangement of the macro-model trajectories on the phase plane producing sensitivity to small perturbations or excitability of the medium.     

Das Gleichgewicht eines Wasserringes mit freier Oberfläche in einem rotierenden Hohlkörper

Summary The problem of the critical speed of revolution of a hollow rotor which has a water ring revolving inside and with it, is investigated and it is found to be identical with the critical speed of revolution of a rotor completely filled with water. As the calculation of the oscillations of the water ring itself shows, dangerous resonances with the rotor oscillations need not be expected.      

A thermomechanical analysis of interfaces between the mating parts in ultrasonic wire bonding

Ultrasonic welding (USW) is an alternative solution for the bonding process especially in automotive industry. Ultrasonic welding of metals is a joining technique as a combination of applying pressure and frictional vibrations within the range of ultrasonic frequencies. In automotive industry, ultrasonic welding is often used for wired connections. As an alternative for crimping technology of multi-strand aluminum cables in wire bonding, ultrasonic welding is used. This work presents a thermomechanical analysis of the interface between two mating parts in USW. For this reason, the temperature distribution at bonding locations inside a wire bundle due to frictional vibrations and pressure is investigated using the finite element method (FEM). The obvious difference in microsections from different welding samples, which originates from different local temperature rises, was the motivation for this study to further investigate the thermomechanical aspects of the USW by use of finite element simulations. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical modeling of chatter stability using multi-dimensional approach

Machining is one of the most common manufacturing processes in industry due to its high flexibility and ability to produce parts which excellent quality. Chatter, a type of self excited vibrations arising in metal cutting operations, is a major limitation in machining resulting in poor quality and reduced productivity. Under certain conditions, the cutting process may become unstable yielding oscillations with high amplitudes and cutting forces. Stability analysis of the dynamic cutting process can be used to determine chatter-free machining conditions with high material removal rate. Usually, one dimensional models are used for stability analysis of machining. However, based on the geometry of the actual machining process, multi-directions would have to be used for accurate modeling of the process dynamics and the stability. In this presentation, multi directional models for turning and milling processes are presented. The effects of multi directional process mechanics on the stability are demonstrated by applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enhancement of particle trapping in the wave-particle interaction

The saturated dynamics of a Single-Pass Free Electron Laser is considered within a simplified mean-field approach. A method is proposed to increase the size of the macro-particle, which is responsible for the oscillations of the intensity of the wave. This approach is based on the reconstruction of invariant tori of the dynamics of test particles. To this aim a dedicated control term is derived, the latter acting as a small apt perturbation of the system dynamics. Implications of these findings are discussed in relation to the optimization of the laser source.     

A finite element analysis of effects of ultrasonic welding parameters on the temperature distribution in wire bonding

Wire bonding is an essential process in the automotive industry. Multi-strand flexible aluminium cables are used for connection of different electronic components and electrical centres in cars. As an alternative for crimping technology in wire bonding, ultrasonic welding (USW) is applied, which is a rapid manufacturing process used to create solid joints between mating materials at low energy consumption compared to the known welding processes, such as oxy-fuel welding and arc welding. An ultrasonic welding machine consists of different parts, such as pneumatic cylinder, piezoelectric converter, booster, welding sonotrode and anvil. Despite of the simplicity of the USW process, choosing the right machine and process parameters, like pressure of the pneumatic cylinder, welding time as well as vibration amplitude of the piezo-converter, is a tricky and complicated task for obtaining an adequate bond. Experimental investigations done in this area are extremely time-consuming and require a lot of effort. Therefore, some new approaches must be developed to understand the process in more detail. The present study focuses on the influence of the ultrasonic welding parameters, such as sonotrode pressure and vibration amplitude, on the temperature distribution at interfaces of two mating pieces in wire bonding [1,2]. Investigations are done by means of FEM simulations as well as by experiments. The results are then extended to thermo-mechanical analysis of multi-strand models. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal Expansion Planning for an Electric Distribution Network with the NLP Solver WORHP

This paper shows how an electrical distribution network can be modeled as constraints of a continuous nonlinear optimization problem. The objective is to minimize the deviation from a given nominal voltage. We explain how this setup can be used to optimize wire diameters within the network. Thus we find the optimal expansion of the network by identifying wires which should be enforced. The results are shown by applying the functionality to a real world example. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical description of material diffusion during an ultrasonic wire bonding process

The volume diffusion during an ultrasonic wire bonding process leads to a material transport between the wire and the material of the substrate and thus creates an intermetallic phase between them. In order to investigate this process, the thermal and mechanical mechanisms occurring during wire bonding should be studied. For this purpose, finite element simulations based on coupled thermo-mechanical equations are performed to study the temperature and stress distribution in and around the interface. The final objective of the model is to develop a growth law for the intermetallic phases by considering the mechanical work applied to the wire in addition to the temperature increase at the interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Passive aerodynamics control of plasma instabilities

The possibility of using a smart-damping scheme to modify the dynamic responses of plasma oscillations governed by a two-fluid model is considered. The passive aerodynamics control strategy is used to address this issue. The control efficiency is found by analyzing the conditions satisfied by the control gain parameters for which, the amplitude of oscillations is reduced both in the harmonic and chaotic states. In the regular state, the analytical stability analysis uses for linear oscillations the Routh-Hurwitz criterion while the Whittaker method and Floquet theory are utilized for nonlinear harmonic oscillations. The stability boundaries in the control gain parameter space is derived. The agreement between the analytical and numerical results is good. In the chaotic states, numerical simulations are used to perform quenching of chaotic oscillations for an appropriate set of control parameters.     

Application of Multi-Parametric Quadratic Programming to Simulation of Deflected Wires in a Wire Saw

In the wire sawing process, a silicon brick is fed into a moving wire web, thus deflecting the wires. By considering static deflections only, the wire displacement and the contact forces between wire and brick may be computed by minimizing the potential energy of the wire, which introduces a constrained quadratic optimization problem. In a time-domain simulation, the continuously changing contour inside the kerf requires the optimization problem to be solved recurringly. This work aims at reducing the optimization-related computational effort by applying multi-parametric quadratic programming. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Virtual modeling of residual stress in drawn wire due to the skin pass effect

The wire drawing technological process is wide use in industry. The effect of skin‐pass is apply for reduction of residual stress in final product. The finite element method is applied to simulate the effect of skin‐pass in wire drawing process. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Peculiarities of relativistic particle evolution in classical scalar field theory

The interaction of particles in the model of a scalar field linearly coupled with the source is demonstrated to have the following peculiarities. First, the particles are attracted to one another at large interparticle distances and are repelled at small. Second, in the process of evolution of the system of particles, its components gain the maximum possible velocity, the velocity of light. Third, after the head-on collision of two identical particles, the pumping effect may probably arise. This effect consists of the fact that after experiencing a few oscillations between the walls of a squeezing potential well, the particles fly out of the finite motion region to the region of infinite motion. Fourth, on the trajectory of the interacting particles, a plateau region of motion with a high and relatively constant velocity appears.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 464–473, December, 1996.     

Analysis of a collocation method for integrating rapidly oscillatory functions

A collocation method for approximating integrals of rapidly oscillatory functions is analyzed. The method is efficient for integrals involving Bessel functions J_v(rx) with a large oscillation frequency parameter r, as well as for many other one- and multi-dimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases.