modeling of machine and tool elasticity in coupled … in der umformtechnik modeling of machine and...

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Modeling of Machine and Tool Elasticity in Coupled Forging Simulation M. Tannert, C. Brecher, S. Bäumler, K. Bakarinow Laboratory for Machine Tools and Production Engineering (WZL), RWTH Aachen University, Aachen Abstract

This paper presents an approach for a holistic simulation of forging processes considering

the interactions between forging press, tooling system and forging process. It can be used in

coupled simulations and will enable industrial users in forging industry to do simulation-aided

tool optimizations in the design stage of newly developed forging dies. The final aim is to

reduce the time-consuming experimental optimization process of these dies on the

production machine which nowadays leads to high overall costs.

In forging simulations today the simulated workpiece dimensions significantly deviate from

the real forged workpiece geometry. These deviations are the consequence of relative

displacements between the upper and the lower die which occur in the forging press and

tooling system due to process loads. Customary forging simulation systems do not, however,

offer adequate ways of modeling these interactions, especially in the case of multi-stage

processes.

In order to take the machine-tool-process interactions into account a method was developed

and implemented in a software tool that allows the coupling of forging simulation systems

with external simulation models of the forging press and tooling system. The

parameterization of the external models can be done by results from measurements or

simulation. The method makes it possible to investigate the development of forging errors

caused by the elasticity of press and tooling system for single- and multi-stage processes.

This allows simulation-aided optimization of new forging dies as well as the individual

adaptation to a particular production press prior to first forging tests.

1. Introduction

High dimensional accuracy of the final workpiece is one of the most important targets in

forging. In addition, a long tool life is aspired, which is the basis for cost-effective and highly

productive forging processes that are often performed as multi-stage operations

simultaneously on one press. In many cases, newly developed processes need to undergo

Scient if ic Workshop


an experimental time-consuming optimization process on the production press until the

geometrical accuracy of the final part is reached. This optimization implies a deep and

comprehensive knowledge of the manufacturing technology and leads often to reworking of

dies and tooling system [1-3]. Such problems do not result from the incorrect planning of the

processes, but rather from additional effects that can only be explained by the machine-tool-

process interactions (Figure 1). So the dimensions of forged parts are directly influenced by

the elastic deformations of the forging dies on the one hand and by the displacements in the

die holders and tooling systems as well as in the press on the other hand. Simulation

systems available today not offer adequate ways of modeling and considering the

aforementioned interactions taking place between the workpiece and the tooling system or

press. They provide no possibility, therefore, of achieving simulation-aided tool optimization

in order to minimize the efforts and costs involved in trial-and-error optimization processes.

Figure 1: Machine-tool-process interactions

The example in Figure 2 illustrates the interactions taking place in press and tooling system

by a single-stage cold ring upsetting test under various simulation conditions compared to a

forging test [4, 5]. The ring manufactured from steel St52-3 was upset from 50 mm to 34 mm

height using a crank press. The ring's initial outer diameter is 90 mm, its inner diameter is

45 mm and the forging position in the press was -125 mm eccentrically in x-direction. The

high flow stress of the workpiece material causes loads on the press and the tooling system,

resulting in considerable deflections of these components. This, in turn, influences the

workpiece dimensions.

contact conditions

guidances (stiffness,

clearance)

deflection

tilting

horiz. offset

kinematics

process force

material behavior

friction

heat transfer

elastic deformations

in dies and die holders

Press Forging Process

Dies and Tooling System

Interactions

with influence on

forging result



Figure 2: Measured and simulated results of ring upsetting [4]

The investigations with this simple example show, that the results of conventional customary

simulation systems with ideal-rigid or linear-elastic press models do not match well with the

results of the forging test. Better results can be achieved using coupled simulations with

nonlinear-elastic press models, which are able to calculate the influence of press deflection

and tilting on the dimensions of the forged workpiece. In this example an analytical press

model parameterized with measured stiffness and clearance values was used. In addition the

significance of modeling the elastic behavior of dies and die holder systems can be seen as

the workpiece thickness of the upsetting test can only be computed correctly using elastic

models.

In case of multi-stage forging processes with two or more stages in tool contact at any point

in time, the interactions between the forging processes and the machine are considerably

more complex due to the individual tool stages are influencing each other, too. As all process

stages in a multi-stage die contribute to the overall load on the press, alterations to just one

stage is enough to cause the press load and thus press deflection response to change,

thereby influencing all present stages of the process.

Investigation and modeling of the interactions between forging process, press and tools in

simulation was thus the object of numerous research activities in bulk and also sheet metal

forming over recent years. An overview is given in [6] and [7].

2. Approaches for modeling machine and tool elasticity in forging simulation

In order to consider the occurring deformations in tools and press, the FE simulation has to

be able to predict them. In [8] the possible deformations are differentiated between local and

global elastic deformations which result from different reasons. There are local deformations

Example Forging Mean thickness of forged

workpiece mm

Forging test 34.9

Simulation Rigid diesElastic dies/

die holders

Conventional

simulation

Ideal-rigid press model33.1

( = -1.8)

33.6

( = -1.3)

Linear-elastic press

model

34.1

( = -0.8)

34.5

( = -0.4)

Coupled

simulation

Nonlinear-elastic

analytical press model

34.6

( = -0.3)

34.9

( = 0.0) 35.1

34.8

35.0 34.8

33.1

33.1

33.133.1

Forging test

Simulation



of the dies, global deflections of the die holders or tooling systems and global dislocations as

an influence of the press.

Commercial, special-purpose Finite Element (FE) forging simulation systems, e.g.

Simufact.forming®, FORGE®, DEFORM® or AutoForm®, are mainly used in forging industry

today to observe material flow and capture defects or to calculate the press forces and die

stresses [9]. These systems offer capabilities to simulate local deformations of the dies by

using volume elements and linear-elastic material models. However, in case of large tool

models, e.g. die holder systems or multi-stage processes, this leads to unacceptable

preprocessing effort and computational times for industrial applications [10].

In almost all cases, local deformations are small compared to global tool deflections and tool

dislocations. Of course, global tool deflections or dislocations can also be modeled as elastic

bodies for tooling system and press within the FE simulation but with the aforementioned

problems of large models. Therefore, different approaches for coupling FE workpiece models

and press or tooling system models were developed. Basic coupling concepts are presented

in [11] and [12]. Figure 3 shows three general coupling principles which are classified

according to their method of integration in offline-coupling, model integration and co-

simulation.

Figure 3: Approaches to consider process-machine/tooling system interactions [11, 12]

In offline-coupling the process simulation and the machine simulation are calculated

separately. The process force progressions of the entire forming process are computed with

Offline-Coupling

iterative between various

simulation environments

without active interaction

convergence between the

simulations is critical

Processsimulation

Machinesimulation

Load

Processmodel

Response

Machinemodel

Model Integration

in a cycle within one

simulation environment and

direct interaction

enhancement of either the

process or the machine

model and integration of the

(simplified) other model

Enhanced process ormachine simulation

Processmodel

Load ResponseLoad Response

Machinemodel

Co-Simulation

in a synchronized cycle

between various simulation

environments

active process manipulation,

controlled subsystems

(drives, compensation,

hydraulics)

Synchronization

Machinemodel

Processsimulation

Machine simulation

Processmodel

ResponseLoad



the workpiece model in a first step. These process force progressions are transferred to the

machine simulation, where the press behavior is computed. Subsequently, the adjusted ram

movement, as a result of the machine simulation serves as a boundary condition for the FE

simulation, if a new calculation by the two models is performed by means of an iterative loop.

The cycle can be repeated until convergence of the simulations is reached. The most

important advantage of offline coupled simulations is that both simulations are implemented

in their common software environment and benefit from the tools, which are available in the

typical software environment. The disadvantage of this approach is the fact, that no dynamic

interaction can be simulated and that the calculation time increases due to repeated

calculations, because one simulation typically uses the complete results from an entire run of

the other one. Examples for offline-coupling are presented in [13] and [14].

The approach named model integration uses one simulation environment to model the press

elasticity and the forming process. Usually, the workpiece model within the FE simulation is

extended by a simplified press model. The tilt and the vertical deflection of the press ram can

be taken into consideration by means of discrete spring and damping elements. General-

purpose simulation systems, such as MARC®, ABAQUS® or LS-DYNA®, provide the

prerequisite for using this approach but these systems are complex and therefore not very

often used in industry.

Some typical forging simulation systems also allow modeling of press elasticity by model

integration. Using the simulation system FORGE®, for example, it is possible to define linear-

elastic stiffness behavior of the press in 6 dimensions, which means translation in x-, y-, and

z-direction and rotation around these axes [15]. The computation “conventional simulation/

linear elastic press model” in Figure 2 was performed using this feature. The simulation

system Simufact.forming® even provides the opportunity to model non-linear elastic press

behavior [16]. Figure 4 shows the approach that uses translatory and rotational springs,

which can be defined by a parameter input tables. In this way clearance and different

elasticity behavior depending on the axis direction can be considered. Simulation results of

the ring upsetting from Figure 2 with Simufact.forming® in [16] coincide with the results in [4,

5] using coupled simulation (co-simulation approach).

The advantage of an integrated model of the press in the forging process simulation is the

direct interaction accompanied by high numerical stability with stable contact situations. This

improves the accuracy of the forming simulation and makes the computation less time

consuming than other approaches.



Figure 4: Simulation model regarding press elasticity (a) and Simulation model of ring

upsetting process (b) in Simufact.forming 10.1 [16]

So the computational cost of the Simufact.forming® model is increased only by 2% if the

translations and rotations due to the machine elasticity are considered.

However, the method reaches its limits if the press properties shall be examined or multi-

stage processes are the object of simulation, because this leads to elaborate models. More

examples using the approach of model integration are explained in [17-21].

Using the third approach named co-simulation, both simulations run simultaneously in

different independent simulation environments and communicate in synchronized cycles after

each iteration step. Thus it is possible to consider dynamic influences within the simulation,

which occur during the forming process. In co-simulation, press models with different

degrees of detail can be used, e.g. analytical models or even multi-body simulation models,

and are coupled with one or more FE workpiece simulation models [4, 5, 22]. The

synchronization of the simulations and the exchange of simulation data is both carried out by

a special coupling tool. With the co-simulation approach it is also possible to simulate multi-

stage processes without increasing the complexity of the several FE simulation models. The

method developed by WZL and described in the following is based on a co-simulation

approach. Furthermore in [23, 24] co-simulation approaches of forming processes are

presented.

3. Coupled simulation of machine and forging process by co-simulation

When coupling process and machine simulation with a co-simulation approach, it are first the

process loads on the dies that are transferred from the forging simulation system to the

machine simulation. Based on the forging load that arises, the displacements within the

press are calculated before then being transferred back to the forging simulation. By altering

Ram (rigid, press driven)

Bed plate (rigid)

Die (elastic)

Die (elastic)

Rotational springTranslatory springs

Workpiece

a) b)



the finite element mesh of the tools in the forging simulation in accordance with the

displacement and tilting behavior of the press, machine behavior is completely taken into

account during the simulation of the forging process. The complex interaction between tool

displacement, the change in material flow which results from this, and the altered press load

can be calculated in comprehensive detail.

The coupling is achieved in each case between two simulation time increments of the forging

simulation and controlled by a software tool called “GekoSim”. As commercially available

forging simulation systems do not supply the necessary data interface for coupled

simulations, system FORGE® was first provided with the necessary functionality to develop

the method. Current research work focuses the coupling with DEFORM®, AutoForm® and

Simufact.forming®.

GekoSim can be used for coupled simulation of single- or multi-stage processes. Figure 5

shows the necessary information flow for the coupled simulation of a three-stage process.

Each stage is calculated using an individual forging simulation. So models of conventional

FE simulations of the forging process can be used.

Figure 5: Coupled simulation of multi-stage processes

In addition, machine parameters in the form of axial and tilting stiffnesses as well as the

associated initial displacements and clearances are necessary for modeling the press with

the analytical machine model which is implemented in the software. This nonlinear-elastic

machine model, programmed in a high-level language (Matlab®), is sufficient for the

Simulation control and handling of data traffic (“GekoSim”)

Press simulation

(e.g. analytical)

Process simulation

stage 1

Process simulation

stage 2

Process simulation

stage 3

process load (stage)

total process load

(press)

press behavior

die displacement

Machine model:

Process models:

axial stiffness

tilting stiffness

clearances

e.g. results of measurement

conventional FE

simulation models of

each stage

adaptation of model

coordinate systems



simulation of the machine behavior of most forging presses. The required machine

parameters may be determined by means of measurement, for example.

Detailed information about the method of coupled simulation, the software “GekoSim” and

the available machine models can be found in [22] for single-stage and [5, 23] for multi-stage

processes.

Coupled simulation provides the user with the opportunity of achieving a targeted simulation-

aided optimization of forging process and dies. By evaluating the calculation results of the

coupled simulation in the post-processor of the forging simulation, e.g. workpiece geometry

(Figure 6) or tool stresses, as well as in the post-processor of GekoSim (machine load,

displacements and tilting – Figure 6, left), sufficient information is available for carrying out

optimization measures.

Figure 6: Results of a coupled simulation - machine behavior (left) and workpiece geometry

Optimization criterion may be for instance the workpiece geometry at the end of the forging

process, the resultant force and torque on the press or the stress generated in the dies.

In the case of an optimization concerning the workpiece geometry the simulation-aided

optimization of the dies with coupled simulation is just like the procedure of an optimization

on the basis of forging tests. After one computation the geometrical errors of the final

workpiece are measured and compared with allowed values. Then the simulation set up is

modified according to the detected deviations and the procedure repeats until the requested

forming results are reached. In this way the experimental optimization effort of forging

processes is reduced and the efficiency increases.

X

Z

X

Z

workpiece geometry computed with coupled simulation and

difference to conventional simulation (ideal machine)

mean height: 24.841 mm

diff. to ideal machine: +1.176 mm

left / right: +0.048 mm

forging position in press:

x = -400 mm, y = 0 mm

machine parameters:

axial/ tilting stiffness:

- cz = 3,500 kN/mm

- cy = 900 kNm/(mm/m)

axial/ tilting clearance:

- vaz = 0.4 mm

- vaz = 0.6 mm/m-5.32

-5.26z-displacement

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4 5 6 7

pre

ss

de

fle

cti

on

(z)

[mm

] a

nd

tilt

ing

of

ram

(y)

[mm

/m]_

remaining stroke [mm]

deflection

tilting



4. Enhanced coupled simulation considering interactions of the tooling system

The presented approach of coupled simulation with GekoSim allows the consideration of

global dislocations of the dies within the forging simulation as an influence of the press

behavior. To consider additional deflections of the dies resulting by interactions of the die

holders or tooling systems in general two approaches are available (Figure 7).

Figure 7: Coupled simulation approaches considering workpiece-tool-press interactions

The one hand a combined model of the forging process and the tooling system can be used.

This is possible for single-stage processes or multi-stage processes, too, if all forging stages

are integrated in one comprehensive FE forging simulation model. However, the

disadvantages of that approach are the already mentioned increase of CPU time and

preprocessing effort. One the other hand a model of the tooling system can be combined

with the existing analytical machine model of the coupled simulation. For this purpose, the

software tool “GekoSim” was extended by reduced analytical models of the die and tool

holder system.

Figure 8 shows a simplified example of that approach for the elasticity of the die holder in the

direction of ram movement (z). The picture on the left shows the FE process model of an

upsetting with elastic modeling of the upper die holder and a coupled simulation of the

forging press (indicated as spring). In the picture on the right the same process model

without elastic die holder in the FE simulation but with an additional analytical model for the

holder within the coupled simulation (spring for tooling system) can be seen. The simulation

results for the final workpiece geometry are nearly the same with both models. An important

difference can be seen in the computation time (table in Figure 8). Due to the additional

modeling of the die holder in the FE model the computation time for the coupled simulation

Press ram

Press bedPress bed

Press ram

Press bed

Press ram

1. Workpiece and dies 2. Tooling system 3. Press

Combined model of forging

process and tooling systemCombined model of press

and tooling system



with the press increases by over 50% compared to a rigid tooling system. The consideration

of the die holder as additional elasticity within GekoSim, on the other hand, does not

influence the computation time significantly. At this point it is important to mention, that the

total computation time for the coupled simulation of this simple upsetting process seems to

be very long. In this example the total computation time is determined by the time for

coupling and data transfer between the simulations. Due to the simple FE model the

computation time for one time increment of the forging simulation is very short compared to

this coupling time. In case of complex FE simulation models this relation would look quite

different and the total time for simulation would be determined by the forging process.

Figure 8: Combined model of press and tooling system in coupled simulation

Another advantage of the approach with GekoSim is, that the analytical models for die or tool

holder systems only once have to be parameterized. Afterwards they can be used for

coupled simulations of any process which works with the same tooling system. This is often

the case in closed-die forging.

The parameterization of the models can be done by using measurement or simulation

results. In case of the example shown in Figure 8, the FE simulation of the elastic die holder

was used to deduce the elasticity behavior and hence the stiffness for GekoSim.

With this enhanced functionalities of GekoSim it is possible to create holistic coupled

simulation models for single- or multi-stage forging process consisting of the several FE

Combined model of press

and tooling system (analytical)

Combined model of forging

process and tooling system (FE)

cpressram (rigid)

tooling system

(die holder)

die (elastic)

workpiece

rigid lower die reduced FE-model

ctooling_system

cpress

Kind of simulation/modeling of tooling system

Mean thickness workpiece [mm]

Computation time[min]

Coupled simulation

Rigid tooling system 37.11 21:30

Coupled simulation

Combined model of forgingprocess and tooling system (FE)

37.31 33:00

Coupled simulation

Combined model of pressand tooling system (analytical)

37.29 22:00

press model in coupled simulation:

cpress = 3,500 kN/mm;

clearance = 0.4 mm

forging simulation:

rigid press and lower die,

elastic upper die



forging process simulations and a combined analytical model of the press and the tooling

system.

5. Parameter investigation for models of machine and tooling system

The accuracy of a forming process is decisive defined by the deflection and tilting behavior of

the press and the tooling system under process load. To characterize the press in simulation,

the axial and tilting stiffness as well as the associated initial displacement and clearance is

used. For presses, the standardized measurement of these machine parameters is carried

out at the bottom dead centre position of the ram and with a static load according e.g. to

guideline DIN 55189 [24]. Furthermore, in [25] an approach for the dynamic measurement of

axial and tilting stiffness is given.

Knowledge of the press parameters for stiffness and clearance is not sufficient to draw direct

conclusions regarding machine behavior during the forming process. This is because, in

most cases, the press loads during the process are unknown. Measurements during the

forming process are therefore necessary. In [23] the fundamental suitability of a camera-

based, dynamic photogrammetry system for capturing the dynamic machine behavior as

displacement and tilting between the press ram and press bed was shown. In current

research works the measuring system MoveInspect® from the company Aicon 3D Systems

was enhanced by the more powerful camera system PCO.dimax with a resolution of 4

megapixels at 1.200 fps. The optical measurement setup and results for the ram tilting during

an industrial forging process on a 25.000 kN eccentric press are shown in Figure 9.

Figure 9: Measurement results and setup for investigation of press behavior during forging

x

z

yx



Besides the optical measurement a measurement with four tactile displacement transducers

was carried out. The calculation of the tilting between press ram and bed was done

according to DIN 55189 [24] with the displacement sensors on the one hand and the

photogrammetric measurement results on other hand. Using the high end cameras the

deviation between the two measurements is only up to 3% for vertical ram deflection and up

to 5% for tilting around y-axis.

Figure 10 shows the measurement setup for the investigation of the press behavior during an

extrusion process under laboratory conditions.

Figure 10: Measurement setup for investigation of model parameters

These measurements were also done with the MoveInspect® system and with different

cameras. The aim is to use the system for the measurement of the press behavior and

simultaneously for the measurement of deformations within the tooling system to deduce

also parameters for the models of the tool holder.

Besides the investigation of model parameters by direct measurements it is also possible to

use simulations, as mentioned in section 4, or to work with reverse engineering. The latter

means, for example, the measurement of a forged workpiece geometry and the optimization

of the machine model according to this measurement.

x

z

yx

press

ram

press bed

displacement sensors displacement sensors

markers for dynamic

photogrammetry

Aicon MoveInspect



6. Outlook for Simufact.forming®

For Simufact.forming® the direct integration of a press model with the functionalities of

GekoSim is planned for release 11.1. All functions will be integrated into the graphical user

interface of Simufact.forming®. The definition of the necessary elasticity parameters for the

press model, for example, will be done in a new tab within the existing object of the press.

The data will be saved in the database together with other press parameters, like press type

and kinematic. During pre-processing of a simulation which should be computed under

consideration of press behavior, besides the choice of the press object only the definition of a

rotational point for the rotational elasticity (tilting) has to be done and the simulation is ready

(Figure 11).

Figure 11: Integration of Press model in Simufact.forming®

In contrast to GekoSim the press elasticity is linked to the bed plate and not to the moved

ram, but this will not influence the computational results. One more difference to GekoSim is

that in Simufact.forming® multi-stage processes will be computed in one simulation model.

For the users of Simufact.forming® the direct integrations has some significant advantages.

The major one, of course, is the opportunity to consider the process-machine interactions in

process simulation. Also very important is the easy use within the already known software

environment and a complete support by Simufact. There is no need to use an additional



software package. For the simulation itself the direct integration has the advantage of high

numerical convergence with stable contact situations which leads high simulation stability.

7. Summary

An approach of coupled simulation was presented which considers the workpiece-tool-press

interactions in the FE simulation of forging processes. The method makes it possible to

reconstruct the development of forging errors caused by the press in single- and multi-stage

processes by simulation.

In addition to the workpiece-based interaction of the different forging stages in multi-stage

processes, where only one stage is in contact with the tools at any point in time, the

machine-based interaction is also taken into account by using coupled simulation software

GekoSim. It is these two interactions in particular that represent a challenge when optimizing

multi-stage processes with two or more active stages.

In present work the coupled simulation approach was enhanced to include the interactions

with the tooling system in the forging simulation in an easy way, too. Furthermore a direct

implementation of the GekoSim functionalities to Simufact.forming® is in progress.

Prediction of the mentioned interaction results through simulations represents a significant

improvement over the state of the art in forging simulations and can help to perform

simulation-aided process optimizations. Optimization criterion may be for instance the

workpiece geometry at the end of the forging process, the resultant force and torque on the

press or the stress generated in the dies. The procedure of such optimizations is just like the

experimental procedure on the basis of forging tests, but in a virtual way. So the

experimental optimization effort of forging processes can be reduced and the efficiency

increases.

Furthermore, in current research work a dynamic photogrammetry measuring system gets

enhanced by more powerful cameras and better measuring strategy with the aim to use the

system for measuring deflections and deformations within the press and the tooling system

simultaneously during the forging process. As in a feedback loop, the simulation results then

can be compared with observed experimental data. This enables the researcher and not at

least the simulation user in industry to gain a closer understanding of the details of process-

machine interactions in forging.




8. Acknowledgments

The authors would like to thank Stiftung Industrieforschung and Industrieverband

Massivumformung e.V. (German foundation for industry research and the federation of metal

forging companies) for supporting the research projects SI S 789 “Optimierung von

Mehrstufenwerkzeugen durch gekoppelte Simulation von Maschine und Prozess

(Optimization of multi-stage forging processes by coupled simulation of the machine and the

forging process)” and SI S 683 “Gekoppelte Simulation von Massivumformprozess und

Maschine (Coupled simulation of machine and process in forging)”. The final reports are

available in the German language at Forschungsgesellschaft Stahlverformung e.V., Goldene

Pforte 1, 58093 Hagen, Germany. The depicted IGF research project „Messtechnische und

simulative Quantifizierung des Werkzeugverhaltens in der Massivumformung (Metrological

and simulative quantification of tooling systems behavior in forging)“ (16707 N / 1) of

Forschungsgesellschaft Stahlverformung e.V., Goldene Pforte 1, 58093 Hagen, Germany is

supported via AiF by the German Federal Ministry of Economics and Technology on the

basis of a decision by the German Bundestag.

Furthermore, the authors would like to thank the industrial partners of the project working

groups for supporting the research works.

8. References

[1] Doege, E., Klawitter, G., 1999, Vom Lastenheft zum Schmiedewerkzeug, die CA-

Entwicklungskette in der Schmiedetechnologie. Umformtechnik 2000 Plus, Bamberg,

Meisenbach, 121-128.

[2] Slagter, W., Hambrecht, J., 2002, Schmiedesimulation: Umfrageergebnisse zur

Wirtschaftlichkeit, Schmiede-J., September 2002:14-16.

[3] Stalmann, A., Weigert, P., 2009, Werkzeugtechnik der Zukunft – Anforderungen und

Möglichkeiten, EFB Servopressen und Werkzeugsysteme zur Blechverarbeitung, 93-

106.

[4] Brecher, C., Schapp, L., 2007, Vorstoß in neue Dimensionen: Kopplung der

Umformsimulation mit nicht-linearen Pressenmodellen. VDI-Berichte Nr. 1993 Conf.

„Massivumformung: Produkte – Partner – Perspektiven“, Leonberg, Germany, VDI-

Verlag, 117-128.

[5] Brecher, C., Schapp, L., Tannert, M., 2008, Simulation-Aided Optimization of Multi-

Stage Dies – Coupled Simulation of Forging Processes with Non-Linear-Elastic

Machine Models. Proc. of 1st Int. Conf. on Process Machine Interactions (PMI),

Hannover, Germany, 167-174.

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