Conference PaperPDF Available

APPROACHES FOR CONTROL IN DEEP DRAWING

Authors:
  • Franke Water Systems AG KWC

Abstract

In small to medium batch production, the number of scrap parts has a significant impact on production cost. While aiming for zero failure production, different observable and unobservable influences determine the part quality. The main influences in series production are material fluctuations throughout a coil and between different coils, as well as the tool temperature rising during the production lot as the material properties stainless steel used in kitchen sink production are highly temperature dependent, likewise the friction. In the presented paper different control approaches are shown and virtually tested for their robustness against modelling errors as well as measuring errors. The control approaches are relying on eddy current measurements for the material properties for the application in feed forward control, while optical draw-in measurements are used for feedback loops. The adjustable parameters in the production line are blank holder forces and blank position. Finally, the different approaches are evaluated.
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* Corresponding author: ETH Zürich Institut für virtuelle Produktion Technoparkstrasse 1 CH-8005 Zürich, +41 44 633
78 10, fischer@ivp.mavt.ethz.ch
APPROACHES FOR CONTROL IN DEEP DRAWING
P. Fischer1*, D. Harsch2, J. Heingärtner2, Y. Renkci3 and P. Hora1
1Institute of Virtual Manufacturing, ETH Zurich, Switzerland
2Inspire-ivp, Switzerland
3Franke Technology and Trademark Ltd, Switzerland
ABSTRACT: In small to medium batch production, the number of scrap parts has a significant impact on
production cost. While aiming for zero failure production, different observable and unobservable influences
determine the part quality. The main influences in series production are material fluctuations throughout a coil
and between different coils, as well as the tool temperature rising during the production lot as the material
properties stainless steel used in kitchen sink production are highly temperature dependent, likewise the fric-
tion. In the presented paper different control approaches are shown and virtually tested for their robustness
against modelling errors as well as measuring errors. The control approaches are relying on eddy current
measurements for the material properties for the application in feed forward control, while optical draw-in
measurements are used for feedback loops. The adjustable parameters in the production line are blank holder
forces and blank position. Finally, the different approaches are evaluated.
KEYWORDS: control, deep drawing, modelling
1 INTRODUCTION
After the optimisation of the tools for robust pro-
cesses [1], the next step in aiming for a zero failure
production is the introduction of process control.
Process control is needed as different influences can
lead to shifts in the process window. With rising de-
sign aspects, the process cannot be designed to ac-
count for all influences like scattering material prop-
erties or changing temperatures and therefore inline
adaptions of the process parameters like blankpos-
tion and blankholder forces is needed. For the indus-
trial application, the process control needs to fulfil
certain robustness criteria. The presented paper tries
to answer some questions which arise when the con-
troller design is done by the utilisation of finite-ele-
ment-model simulations for the design of the control
algorithm.
2 PROCESS MODEL
For designing a control algorithm, an appropriate
model of the process is needed. The process can be
modelled either by using measurement data or by
using FEM simulations. In the following, the pro-
cess design by FEM simulations is described.
2.1 FEM VARIATIONS
The used part in the study is a stainless steel kitchen
sink with the already in IDDRG 2016 [2] described
material parameters. For the generation of the pro-
cess model, a Sigma run in AutoForm is done with
the parameter range given in table 1. The total draw-
ing depth is about 175mm. As the risk of splits in
the corner can be reduced significantly by reducing
the blankholder forces after a certain drawing depth,
the force until 80mm is varied separately from the
force from 100mm on. The transition between the
forces is done by a linear interpolation. The yield
stress is varied coupled with the tensile strength and
therefore the UTS is not shown in the table. rm rep-
resents a variation of the Lankford coefficients. The
friction has a nominal value of 0.07, while the wide
variation range is needed to cover potential friction
changes at different temperatures. Besides the blank
holder forces, the positon of the blank in material
flow direction can be influenced. Based on a latin
hypercube design 128 simulations were performed
in AutoForm R7.
Table 1: Variation parameters
Parameter
Min
Max
Thickness
0.775
0.825
Force until 80mm
1600kN
2400kN
Force from 100mm
450kN
1050kN
Friction m
0.05
0.1
Rp0.2
239
289
rm
0.9751
1.192
Blank position x
-5
15
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2.2 MODELLING OF PROCESS
As the control algorithms in the following section
are based on draw-in measurements, the draw-in at
the points shown in figure 1 has to be modelled
based on the simulation results.
Fig. 1 Positioning of Sensors
For the purpose of modelling, all four sensors are
modelled by quadratic response surfaces, also the
interaction between different inputs is modelled (see
equation 1). The correlations between the quality
criteria, like thinning and maximum failure in the
edges of the base, and the sensor values are between
mainly over 0.5 and therefore the sensors can mon-
itor the part quality. The calculation of the sensitiv-
ities of the sensor models shows that the sensor val-
ues are highly influenced by the actuators (blank
holder and blank position) and therefore the process
is observable and controllable. Based on the models,
the next step is the design of a control algorithm.
(1)
3 INTRODUCTION OF CONTROL
ALGORITHMS
In general two different types of control are know,
feedforward and feedback control. The first pro-
posed algorithm consists of a proportional feedback
loop with an additional feedforward control, while
the second control algorithm combines both types of
control. While feedback control needs an already
produced part and tries to minimise the difference
between the last part and the reference, feedforward
control utilises already gained knowledge. For both
control algorithms, it is assumed that the yield stress
is known through eddy current measurement.
3.1 PROPORTIONAL CONTROL
The first feedback control algorithm simply relies
on linear relations between the draw-in error and the
actuators. As the values for Sensor S01 and S02 are
highly depended on the blank position, they are used
to control the blank position as described in equation
2. With K being a linear constant and ΔS0x the ref-
erence draw-in subtracted from the current draw-in.
The minus sign in the equation results from S01 and
S02 having opposing trends on a blank shift.
02*01*SKSKx xx
(2)
With S03 and S04 not being disturbed by the blank
position, they are used for the correction of the blank
holder. As the reaction of S03 and S04 is the same
on a changed blank holder force. The equation (3)
for the correction of the blank holder forces is the
following:
)0403(*
80 SSKF F
(3)
To simplify the problem, the ratio between F80
(Force until 80mm) and F100 is fixed to 2.66 as in the
currently used nominal press settings.
The feedforward control for the yield stress on the
other hand uses the gradient of the model of S03 at
the nominal working point and therefore results in
the non-ideal control reaction shown in equation 4,
as the relation between F80 and F100 is not ideally im-
plemented, as well as the interactions in the deriva-
tives are neglected.
)
03
66.2103
(
03
*
10080
80
dF
dS
dF
dS d
dS
F
(4)
The behaviour of the control algorithm on a shifted
starting point as well as a jump in the yield stress is
shown in figure 3.
3.2 OPTIMIZATION BASED ALGORITHM
In contrast to the proportional control, the optimiza-
tion based control approaches evaluates the simula-
tion based meta models directly. To account for in-
accuracies in the meta model, the first step in the op-
timizer based algorithm is the calculation of virtual
draw-in values with the given settings and the given
material parameters. The values calculated in step 1
can be distinguished by an added v in the name. As
a next step, the current deviations between the ref-
erence and the current draw-in is added to the virtual
draw-ins as shown in equation 5.
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010101 SvSS t
(5)
Based on these target draw-ins, the new forces can
be calculated with an optimizer. The cost function
for the optimiser is the squared difference between
the target value and the value of the optimization re-
sult at the current step. The formulation for the cost
function can be seen in equation 6.
T
opttopttSSSS )(*)(
(6)
For the optimization the blank position and the force
F80 can be varied, while F100 is still coupled with F80.
In this approach the change in the yield stress can be
directly implemented by using the yield stress of the
given part in the first step and using the new yield
stress in the optimization. For all calculations based
on the meta models, the unknown inputs are kept at
their nominal level.
3.3 NOMINAL CONTROLLER
BEHAVIOUR
The ideal reaction of the control algorithm can be
determined in a virtual test environment where the
same models are used as process as they are used for
the design or implementation of the algorithms. For
the ideal response, neither measuring noise nor
modelling errors are introduced. The test scenario
consists of two step functions. The first step func-
tion is the shift to a wrong starting point for the al-
gorithm, while the second step function is a sudden
change of the yield stress (shown in figure 2).
Fig. 2 Step in yield stress
The virtual reference draw-in is calculated for a
blank with the yield stress of 260 MPa and the press
settings F80=2000 kN, F100=750 kN with the blank
centered (0 mm). The feedback part of the control
algorithm is tested by starting from F80=2400 kN,
F100=900 kN and the blank position shifted to -
15mm.
The response of the proportional controller with the
gradient based feedforward control in figure 3
shows that the controller needs about five parts to
bring the draw-in back to normal, but afterwards
they stay close to the reference values (+-0.2 mm).
The jump in the draw-in through the sudden change
in the yield stress cannot be completely compen-
sated, but after a few parts it is back to the reference.
Fig. 3 Response of proportional control
Fig. 4 Response of optimization based control
In the ideal case that the simulation based process
model matches the reality perfectly, the optimiza-
tion based control algorithm can compensate the er-
ror in one step (figure 4), while the change in the
yield stress cannot be recognized, as it is perfectly
compensated. All in all, both control algorithms ful-
fil their purpose.
4 INFLUENCE OF MODELLING
ERRORS
With the control algorithms based on finite element
simulations, two different types of modelling errors
seem likely. The first error would be a wrong pre-
diction of the gradient of the model, while the sec-
ond would be an offset between model and reality.
In reality a combination of both errors might occur,
but for testing purposes the influences are looked at
separately.
4.1 DIFFERENT GRADIENT
With the finite element model usually calculating
the right direction of trends, the gradients in the
model usually do not match then reality perfectly.
Therefore a deviation of minus 30% and plus 30%
of all model parameters , with exception of the
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constant β0) is assumed and the control reactions
checked again.
Fig. 5 Response of proportional control (+30%)
Fig. 6 Response of proportional control (-30%)
Figure five shows that an underestimation of the in-
fluence of the draw-in can result in a faster conver-
gence for a conservative controller design, while the
overestimation (figure 6) slows down the controller
drastically. But on the other hand, the acceleration
through the underestimation might lead to over-
shoots.
Fig. 7 Response of optimization based control
(+30%)
Fig. 8 Response of optimization based control (-
30%)
In the case of the optimization based control algo-
rithm, the underestimation of the influences leads to
significant overshoots as seen in S01 (figure 7)
which may again result in defect parts. The overes-
timation on the other hand leads to a response which
is comparable with the calibrated proportional con-
trol algorithm.
Summarized, the one step correction of the optimi-
zation based controller is highly depending on the
modelling accuracy, while the proportional control-
ler is more insensitive.
4.2 MODELLING OFFSET
Another modelling error that might occur is an off-
set between the model and the reality. This can be
checked by scaling β0 in the process model by 30%.
The model offset does neither influence the propor-
tional controller nor the optimization based control-
ler as it can be seen in figure 9 and 10. The propor-
tional controller is insensitive because it only uses
the difference between reference value and current
value. The optimization based controller on the
other hand always stays inside its own reference en-
vironment which is only influenced by the differ-
ences and not the absolute values.
Fig. 9 Response of proportional control (offset)
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Fig. 10 Response of optimization based control
(offset)
5 INFLUENCE OF SENSOR NOISE
As the whole study is based on virtual models, it is
possible to distinguish between “measured” draw-in
results and the directly calculated values. In this sec-
tion, the directly calculated ones are always plotted
as they show the real state of the part. As measured
values are used for the feedback control as well as
for the feedforward control, the influence of noise in
the yield stress measurement as well as the draw-in
measurement will be shown.
5.1 NOISE IN EDDY-CURRENT
MEASUREMENT
For the evaluation of the influence a gaussian dis-
tributed noise with the standard deviation of 1MPa
can is added to the original defined yield stress pro-
gression. Resulting in the yield stress progression
seen in figure 11.
Fig. 11 Noisy step in yield stress
The influence of the sensor noise in the yield stress
can be evaluated in figure 12 and 13. The response
of the proportional control algorithm is little influ-
enced by the fluctuations, because the changes in the
yield stress are only compensated slowly in the
given design. The draw-in due to the control of the
intervention of the optimization based control algo-
rithm is significantly higher, as the controller tries
to compensate the none existing fluctuation in one
step. All in all an accurate measurement system is
needed to compensate for fluctuations in material
properties, as the control intervention might overre-
act in the cases of an insufficient accuracy.
Fig. 12 Response of proportional control (σy noisy)
Fig. 13 Response of optimization based control (σy
noisy)
5.2 NOISE IN DRAW-IN MEASUREMENT
Besides the disturbances on the process introduced
through the “correction” of material properties, also
disturbances can be introduced due to noise in the
draw-in measurement. As the draw-in of the part is
going to be measured by an optical system, several
influences might result in an inaccurate measure-
ment. Therefore, a gaussian distributed noise with
the standard deviation of 0.5mm is added to the
draw-in measurement resulting in a difference be-
tween real value and measured value as it can be
seen in figure 14.
Fig. 14 Influence of noise in draw-in measurement
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Fig. 15 Response of proportional control (S01-S04
noisy)
The response of the proportional control (figure 15)
at beginning of the control intervention looks com-
parable to the one without noise, as the noise is far
lower than the measurement inaccuracy, but begin-
ning at part 10 the control algorithm starts to oscil-
late around the reference value due to the measure-
ment noise, but stays inside a range of +- 0.5mm
which would still lead to parts with a good quality.
Fig. 16 Response of optimization based control
(S01-S04 noisy)
As it can be seen in figure 16, the measurement
noise gets amplified by the fast reaction of the opti-
mization based control algorithm, which results in a
significant high variation band of +-1 mm. Summa-
rized, the optimization based control algorithm is
more sensitive on measuring noise than the propor-
tional control algorithm due to its aimed elimination
of draw-in errors in one step.
6 CONCLUSIONS
The paper introduces different approaches for han-
dling feedback as well as feedforward control in
deep drawing. The evaluation of different cases
shows that the different approaches have their
strengths and weaknesses. The optimization based
algorithm works well, when the measuring accuracy
is high, as well as when the model is matching real-
ity. Therefore, the optimization based algorithm
needs a model calibration through measurement
data or even a model solely depending on measured
data. The more conservative reaction of the propor-
tional control algorithm on the other hand has its
weakness in the correction of larger deviations, as
the response time is significantly larger. The
strength of the algorithm on the other hand is the
lower sensitivity on measurement noise. All in all,
both algorithms can work well, while a combination
of both seems promising as the optimization based
approach handles the sudden jumps better, while the
proportional control works well for part to part var-
iations which are introduced through measurement
noise.
7 ACKNOWLEDGEMENT
The authors are grateful for the support of the CTI
(Commission for Technology and Innovation)
within the project 17366.1 PFIW-IW and also for
support of the additionally participating companies
(Franke, AutoForm and GOM).
REFERENCES
[1] M. H. A. Bonte, “Optimisation strategies for
metal forming processes,” Enschede, 2007.
[2] P. Fischer, D. Harsch, J. Heingärtner, Y.
Renkci, and P. Hora, “Inline feedback
control for deep drawing applications,” IOP
Conf. Ser. Mater. Sci. Eng., vol. 159, p.
12006, Nov. 2016.
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