Filters

2006 - 2009122010 - 201817

More filters

201929
Reset filters

Settings

Author: Hömberg, Dietmar × End date: 2019 × Has files: Yes × Type: Text ×

Search Results

Now showing 1 - 10 of 29
  • Thumbnail Image
    Item
    Discretisation and error analysis for a mathematical model of milling processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hömberg, Dietmar; Rott, Oliver; Sturm, Kevin
    We investigate a mathematical model for milling where the cutting tool dynamics is considered together with an elastic workpiece model. Both are coupled by the cutting forces consisting of two dynamic components representing vibrations of the tool and of the workpiece, respectively, at the present and previous tooth periods. We develop a numerical solution algorithm and derive error estimates both for the semi-discrete and the fully discrete numerical scheme. Numerical computations in the last section support the analytically derived error estimates.
  • Thumbnail Image
    Item
    Optimal control of a cooling line for production of hot rolled dual phase steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bleck, Wolfgang; Hömberg, Dietmar; Prahl, Ulrich; Suwanpinij, Piyada; Togobytska, Nataliya
    In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.
  • Thumbnail Image
    Item
    Task assignment, sequencing and path-planning in robotic welding cells
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Landry, Chantal; Welz, Wolfgang; Henrion, René; Hömberg, Dietmar; Skutella, Martin
    A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently
  • Thumbnail Image
    Item
    Identification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hömberg, Dietmar; Liu, Jujun; Togobytska, Nataliya
    We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning numerical simulation play an important role. To this end a crucial problem is to identify the thermal growth kinetics of the coagulated zone. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. The solution to this inverse problem is defined as the minimizer of a nonconvex cost functional. The existence of the minimizer is proven. We derive the Gateaux derivative of the cost functional, which is based on the adjoint system, and use it for a numerical approximation of the optimal coefficient.
  • Thumbnail Image
    Item
    Optimal control for the thermistor problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hömberg, Dietmar; Meyer, Christian; Rehberg, Joachim; Ring, Wolfgang
    This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem.
  • Thumbnail Image
    Item
    Development of a stability prediction tool for the identification of stable milling processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hömberg, Dietmar; Uhlmann, Eckart; Rott, Oliver; Rasper, Patrick
    This paper deals with a new mathematical model to characterise the interaction between machine and work piece in a milling process. The model consists of a multi-body system representing the milling machine and a linear thermo-elastic work piece model. An extensive experimental analysis supported the development of the governing model equations. A numerical solution strategy is outlined and complemented by simulations of stable and unstable milling processes including work piece effects. The last part covers the development of a new algorithm for the stability analysis of large milling systems.
  • Thumbnail Image
    Item
    Simulationsbasierte Regelung der Laserhärtung von Stahl
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Alder, Holger; Hömberg, Dietmar; Weiss, Wolf
    Bei der Oberflaechenhärtung mit Hilfe von Laserstrahlen ist eine konstante Einhärtetiefe erwünscht, wobei gleichzeitig Anschmelzungen vermieden werden sollen. Um Anschmelzungen zu verhindern, kann die Temperatur im Auftreffpunkt des Lasers gemessen werden und die Laserleistung entsprechend geregelt werden. Eine konstante Temperatur fährt bei geometrisch komplizierten Bauteilen jedoch nicht zu einer konstanten Einhärtetiefe. In dieser Arbeit wird ein Verfahren aufgezeigt, wobei durch numerische Simulationen eine nichtkonstante Oberflächentemperatur berechnet wird, die eine konstante Einhärtetiefe liefert. Die berechnete Oberflächentemperatur kann als Solltemperatur im realen Prozess benutzt werden.
  • Thumbnail Image
    Item
    Optimal control of robot guided laser material treatment
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Hömberg, Dietmar; Steinbrecher, Andreas; Stykel, Tatjana
    In this article we will consider the optimal control of robot guided laser material treatments, where the discrete multibody system model of a robot is coupled with a PDE model of the laser treatment. We will present and discuss several optimization approaches of such optimal control problems and its properties in view of a robust and suitable numerical solution. We will illustrate the approaches in an application to the surface hardening of steel.
  • Thumbnail Image
    Item
    A comparison of analytical cutting force models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Rott, Oliver; Hömberg, Dietmar; Mense, Carsten
    The modeling of dynamic processes in milling and the determination of stable cutting conditions have become increasingly important for the optimization of manufacturing processes. Analytic approaches and time domain simulations based on simplified dynamic systems are used to identify chatter-free machining conditions. Stresses applied to the system are generally estimated by cutting force models. The goal of this paper is to compare the influence of the cutting force models on the stability limits. Numerical simulations of a simplified, generic milling machine model are therefore performed, while varying the cutting force approach. In order to distinguish stable from unstable cutting conditions a numerical stability criterion is used. The resulting stability charts are then investigated and analyzed to show the effect of the different cutting force models.
  • Thumbnail Image
    Item
    Shape optimization for a sharp interface model of distortion compensation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Sturm, Kevin; Hintermüller, Michael; Hömberg, Dietmar
    We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.