TY - THES
T1 - Mathematical Optimization of Industrial Sheet Metal Forming Processes
A1 - Rozgic,Marco
Y1 - 2018/08/21
N2 - In this work two methods for virtual process design in the context of coupled quasi-static
electromagnetic impulse sheet metal forming applications are introduced. The first half
of this thesis is concerned with solving the two main parameter identification problems
arising when simulating and designing such a forming process: The identification of
the employed material model and the identification of optimal process parameters.
For both problems a similar black box framework based on LS-DYNA FEM/BEM
simulations and IPOPT, an implementation of the inner point method is used.
A thermodynamically consistent material model developed by Vladimirov et al.
(2014), which is tailored for the efficient numerical treatment of anisotropic hyperelasticplastic materials is considered. This model is capable of representing rate dependent viscoplastic as well as rate independent elastoplastic materials. To account for material failure it is coupled to a scalar Lemaitre-type damage model. A framework for the
reliable identification of the model’s parameters for the simulation of the behavior
of the aluminum alloy EN AW-5083 at various strain rates based on uniaxial tensile
tests and a corresponding LS-DYNA simulation coupled to IPOPT is introduced. For
the comparison of data obtained by simulation and data coming from experiments
a distance measure based on the L2????distance of functions is used. To this end an
Akima spline developed by Akima (1970) is adapted to the experimental data. These
special splines have the advantage of producing smooth interpolates, that are just as
smooth as the according experimental curves, as long as no damage occurs. It is hence
possible to interpolate the experimental data at every point needed and thus compare it
efficiently to the data from simulation. It will be shown how a set of parameters suitable
for the modeling of the high-speed situation can be derived from data obtained by quasi-static experiments via a linear extrapolation of the damage threshold parameter.
The identified parameter set is suitable to represent a coupled forming process very
precisely, as is shown in Kiliclar et al. (2016).
The developed method for material parameter identification is adapted to perform a
process parameter identification in a coupled sheet metal forming process. The task is
to find a set of parameters describing a double exponential current pulse yielding a
sharp cup radius. Double exponential pulses are used as a prototype for general monodirectional pulses. The material’s behavior is simulated by the previously identified
material model, thus constraints for the damage can be employed efficiently. In contrast
to the usual optimal shape determination, an objective function completely independent
of the geometry parametrization is derived. It will turn out that a maximization of
the major strain in the area of question can be traced back to a lower cup radius,
thus yielding a sharper form. The subsequent application of electromagnetic forming
reduces the drawing radius by roughly 5mm, compared to quasi-static deep drawing
alone. The presented method can be seen as an extension to previous approaches by
Taebi et al. (2012), since it uses a unified simulation framework and exploits a material
model that incorporates damage.
The second part of this work is concerned with treating the identification of process
parameters as a PDE constrained optimization problems and deriving a fitting SAND
formulation. The solution of the PDE, modeling the physical behavior, is seen as a
state, and the parameters of the process are seen as controls. The first discretize, then
optimize approach, is pursued in this work. Regularization methods keeping the
controls in check can be avoided in this particular case, since the process parameters
are already represented as a real valued finite dimensional vector. A class of problems
mimicking a sheet metal forming problem in the linear elastic regime is introduced.
This simplification is picked, because the required FEM can easily be implemented but
the insights gained are useful for the development of a general optimization scheme
for those types of technologically relevant problems. In the course of this work an
efficient FEM solver for MATLAB, oFEM, was developed by Dudzinski et al. (2016) to
provide the necessary discretizations of the PDEs. With oFEM and IPOPT the family
of problems is thoroughly numerically analyzed. The derived SAND formulation is
compared to a black box optimization problem based on earlier works by Taebi et al.
(2012) and Rozgic et al. (2012). Compared to this so called NAND approach the SAND
approach shows a potential gain in efficiency by two orders of magnitude.
KW - Blech
CY - Hamburg
PB - Universitätsbibliothek der Helmut-Schmidt-Universität
AD - Holstenhofweg 85, 22043 Hamburg
L2 - http://edoc.sub.uni-hamburg.de/hsu/volltexte/2018/3204
ER -