Adaptivity in the context of high speed cutting

The purpose of this short work is the thermomechanical modeling of shear band and chip formation during high-speed cutting. Shear bands develop in areas of maximal mechanical dissipation in which temperature-dependent softening dominates strainand strain-rate-dependent hardening. In the simulations, the well-known problem of the mesh-dependence of the shear-band development is addressed, involving both mesh size and mesh orientation. An example simulation is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Features of an adaptive remeshing strategy in the context of deformation localization and high speed cutting

The purpose of this work is the modeling and simulation of shear banding and chip formation during high–speed cutting. Here, the use of error estimation and adaptive remeshing is of special interest. The current work investigates the application of different refinement strategies on the problem of adiabatic shear banding. As a result the authors will present a combination of a recovery based error estimation and a refinement indicator. Simulation results for the high speed cutting process will be presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the role of energy in chip formation

The implicit code ABAQUS/Standard is used to simulate the formation of continuous and segmented chips. Using the described model, the idealized process of friction‐less machining of an elastic ideally‐plastic material is studied. It is shown that Merchant's classical shear angle relation does not hold, as chip formation does not minimize the energy as assumed by Merchant. The model is also used to study segmented chip formation using a realistic material law for the Titanium alloy Ti6Al4V at high cutting speeds.     

Modeling, simulation and optimization in logistics

This text summarizes the PhD thesis defended by the author in March 2009 under the supervision of Pasquale Legato at the University of Calabria, Italy. The thesis is written in English and is available for download at the following URL: . It aims to explore friendly Operations Research tools for modeling and simulation of logistics processes, with particular interest for mathematical programming models combined with stochastic simulation tools. In particular key assignment and scheduling problems that arise in maritime container terminals are explored. Initially it is presented a study on different modeling paradigms devoted to the representation of logistical processes and the formalization of problems with complex scheduling/assignment constraints. Successively an IP model for managing the assignment of a pool of rail-mounted gantry cranes to berthed vessels is proposed. Then, according to a functional integration approach, a second model centered on the intra-ship scheduling of vessel container bulks to the assigned cranes is further formulated. Finally a simulation-based optimization approach is investigated and the effectiveness of recent search methods is evaluated by comparison with a commercial solver.     

Modeling and simulation of pollutants transport in rivers

This paper is devoted to mathematical modeling and computer simulation of diffusion and transport of chemicals in rivers. We present one-, two-, and three-dimensional models in terms of time-dependent convection–diffusion–reaction differential equations, further we give the finite difference approximation and appropriate numerical algorithms for these models, and finally we discuss briefly the computer implementation of this methodology in a user friendly software package. To verify the model and the computer code we have used it to study the diffusion and transport of chemicals, in this case NO₃ and PO₄, in two rivers in Western Georgia flowing into the Black Sea. Namely, we considered the river Khobistskali subject to pollution sources Ochkhomuri and Chanistskali river Choga polluted with NO₃.     

Modeling the impact of discretizing rotor angular position on computation of field-oriented current components in high speed electric drives

Modern drives consist of alternating current electric motors, and the field-oriented control (FOC) of such motors enables fast, precise, and robust regulation of a drive's mechanical variables such as torque, speed, and position. The control algorithm, implemented in a microprocessor, requires feedback from motor currents, and the quality of this feedback is essential to a drive's control properties. Motor phase currents are sampled and processed in order to extract their mean over a digital control interval. Afterwards, the mean phase currents are transformed into a rotating field-oriented reference frame to enable controlling the mechanical variables. The field-oriented frame rotates continuously, but in practice the transformation is carried out using a discrete angular position. This paper investigates how the discretization impacts the computed field-oriented currents in high speed drives, where the rotor displacement during a control interval is substantial. A continuous-time model of field-oriented currents is indicated as a reference to quantify errors. An original approach to normalize variables and to solve the model analytically is proposed in order to investigate how the errors related to rotor position discretization are influenced by drive operating conditions. The analytical solution is validated by computer simulation. The results show that the currently applied methodology of computing field-oriented current components, due to an invalid assumption, introduces errors of a few percent when a drive operates at high speed. These errors can be compensated using the presented solution.     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.     

Modeling and simulation with operator scaling

Self-similar processes are useful models for natural systems that exhibit scaling. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulation. A simulation method is developed for operator scaling Lévy processes, based on a series representation, along with a Gaussian approximation of the small jumps. Several examples are given to illustrate the range of practical applications. A complete characterization of symmetries in two dimensions is given, for any exponent and spectral measure, to inform the choice of these model parameters. The paper concludes with some extensions to general operator self-similar processes.     

Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.     

Modeling and simulation of population balances in particulate systems

This article focuses on the modeling and simulation of population balance equations (PBEs) for simultaneous growth, nucleation and aggregation processes. Two numerical method are proposed for this purpose. The first method combines the method of characteristics (MOC) for growth process with a finite volume scheme (FVS) for aggregation process. The second method uses a high resolution finite volume scheme to solve the resulting PBEs. The numerical results show that both methods give accurate results. However, the first method is more efficient and accurate as compared to the second method. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of extrusion of aluminum alloys

The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion, cooling and metal forming processes. In particular, the alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg) are relevant here. Under the corresponding conditions, their behavior is controlled mainly by dynamic recovery during the extrusion and static recrystallization during cooling. The current material model is based on the role of the energy stored in the material during extrusion as the driving force for microstructural evolution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of cutting force prediction in machining high-volume SiCp/Al composites

Variations in cutting forces significantly influence the tool wear and part quality in machining high-volume SiC-particle-reinforced aluminum matrix (SiCp/Al) composites. Properties of the reinforcement SiC particles, such as size and volume fraction, contribute to the change in the cutting forces. This paper presents a cutting force model based on the geometrical and mechanical nature of the tool and workpiece, considering the effect of the SiC reinforcement particles. The cutting force is predicted as three components (F_z, F_x, and F_y) and the resultant cutting force F_τs. The cutting force was considered to generate three deformed zones: (a) shear deformed zone, (b) friction deformed zone on the chip–tool interface, (c) plow deformed zone. The effect of SiC reinforcement particles on friction deformed zone is analyzed emphatically. The friction force from friction deformed zone was obtained by calculating the sliding friction force and rolling friction force. To verify the feasibility and validity of the predicted model of cutting force, cutting experiments were performed with different combinations of cutting speed, feed rate, depth of cut, and tool nose radius. The predicted cutting force values demonstrate good agreement with the measured experimental cutting force values in most cutting conditions. The average percentages of the prediction error were 1.93%, 6.20%, and 10.48% for the F_z, F_x, and F_y components, respectively, thus proving the validity and accuracy of the predicted model of cutting forces.     

Modeling of MIG/MAG welding with experimental validation using an active contour algorithm applied on high speed movies

This paper investigates some issues in physical modeling of metal inert gas/metal active gas (MIG/MAG) welding process in the short arc mode. In this mode, a metal supply is molten in the arc state and then transferred to the weld pool during the short-circuit state. A hybrid model having two distinct continuous states whose switchings are controlled by two guard conditions is proposed. Due to the complexity of the physical phenomena involved in the welding process, simplifications are used to obtain a model accounting for the main physical contributions but simple enough to yield an efficient, fast and numerically tractable simulator which can be used intensively for evaluating different control strategies. In an attempt to validate the proposed model, different measurements have been made including supply voltage and current sampled synchronously with high speed digital video. In order to extract some relevant quantities representative of the metal transfer from image sequences, an active contour algorithm is developed and tested. The effectiveness of the proposed model in the prediction of major tendencies of a welding process, especially in the arc state, is shown using experimental data. Some limitations of the model during the metal transfer are also stressed and possible remedies are then proposed.     

Modeling and simulation of the CLS cryogenic system

This paper presents results pertaining to the numerical modeling of the cryogenic system at the Canadian Light Source. The cryogenic system consists of a cryostat that houses a Radio Frequency (RF) cavity used for boosting the energy of an electron beam. For consistent operation of the RF cavity, it must be kept immersed in liquid helium at a constant level with the pressure in the gas space maintained to an accuracy of ±1 mbar. An improvement to the cryostat model suggested in [3] using control volumes is described. The model and numerical method developed for the liquid helium supply and gaseous helium return lines are validated using two different cases, viz., the liquid helium flow rate from the liquid helium transfer line and the gaseous helium flow rate from the cryostat for various heater power input settings. The numerical method described here is significantly more accurate, efficient, and flexible than that used in [1] based on an iterative bisection method.     

Modeling of microstructural pattern formation in crystal plasticity

The mechanical behavior of most materials is dictated by a present or emergent underlying microstructure which is a direct result of different, even competing physical mechanisms occurring at lower length scales. In this work, energetic microstructure interaction via different non-convex contributions to the free energy in metals is modeled. For this purpose rate dependent gradient extended crystal plasticity models at the glide-system level are formulated. The non-convex energy serves as the driving force for the emergent microstructure. The competition between the kinetics and the relaxation of the free energy is an essential feature of the model. Non-convexity naturally arises in finite-deformation single-slip crystal plasticity and the results of the gradient model for this case are compared with an effective laminate model based on energy relaxation. Similarities as well as essential differences are observed and explained. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of ice formation in a reservoir

The one-dimensional formulation is considered of a two-phase Stefan problem of heat flow with an unknown phase transition temperature that depends on the concentration of impurity. A numerical method is described for implementing the constraints that the heat and mass conservation are given on the unknown nonstationary boundary between the liquid and solid phases. Some examples are included of simulations for the sodium chloride solutions of different concentrations.     

CDS simulation and pattern formation of phase separation

Several properties of the generation and evolution of phase separating patterns for binary material studied by CDS model are proposed. The main conclusions are (1) for alloys spinodal decomposition, the conceptions of “macro-pattern” and “micropattern” are posed by “black-and- white graph” and “gray-scale graph” respectively. We find that though the four forms of map f that represent the self-evolution of order parameter in a cell (lattice) are similar to each other in “macro-pattern”, there are evident differences in their micro-pattern, e.g., some different fine netted structures in the black domain and the white domain are found by the micro-pattern, so that distinct mechanical and physical behaviors shall be obtained. (2) If the two constitutions of block copolymers are not symmetric (i.e. r ≠ 0.5), a pattern called “grain-strip cross pattern” is discovered, in the 0.43 <r <0.45.     

Modeling and simulation of the microstructural behaviour in thermal sprayed coatings

The purpose of the current work is the investigation of the mechanical behavior of thermal sprayed coatings to predict the influence of the application of compaction on the coatings. Due to the porosity and the poor surface quality of thermal sprayed coatings, an additional process step is necessary to compact the coating and to increase the surface quality, though leading to a complex deformation behavior of the coating. In a first step the microstructural evolution is investigated. Due to the fact that the experimental determination of the mechanical properties of a coating is quite complicated and cost-intensive, a general procedure is developed which generates the desired quantities for different coating composites from microstructural images which are compared to analytical mean-field homogenization solutions for elastic material behavior. The discussed thermal sprayed coatings are multiphase systems consisting of a metal-matrix composite with pores. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling and simulation of nitrogen regulation in Corynebacterium glutamicum

Modeling the dynamic behaviour of biochemical systems at a molecular level aims at understanding and predicting the interactions of macromolecules inside the cell. Models of small subsystems based on differential equations not only prepare the way for the long-term goal of understanding a whole cell, but are inherently valuable due to their ability to predict the behaviour of the subsystem for varying external conditions or parameters. Nitrogen supply is essential for prokaryotes, thus the nitrogen uptake is an interesting target for model building. The goal is to provide new information about the interactions of the relevant proteins by performing various simulations.A model based on piecewise linear differential equations is formulated for the nitrogen uptake in Corynebacterium glutamicum. We theoretically derive a model for biochemical networks and introduce a general method for the parameter estimation which is also applicable in the case of very short time series. This approach is applied to a special system concerning the nitrogen uptake using Western blot experiments. The equations are set up for the main components of this system, the optimization problem for parameter estimation is formulated and solved, and simulations for the evaluation of the model as well as for predictions are carried out.We show that model building based on differential equations can also, when only a few measurements are performed, lead to a satisfactory model which provides valuable insights into the way it’s network components function. For example, we are able to make predictions about the maximal value of the time course as well as the steady-state level of the signal transduction protein GlnK in case of restricted activity of the proteases when considering the transition of nitrogen starvation to nitrogen excess or vice versa.