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Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

* 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

Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

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.

213

2

12110 **** PPPPS

(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.

Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

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 (β, with exception of the

Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

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)

Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

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

Forming Technology Forum 2017

October 12 & 13, 2017, Enschede, The Netherlands

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.