Iterative process control and sensor evaluation for deep drawingtools with integrated piezoelectric actuators

Tobias Bäume1,*, Wolfgang Zorn3, Welf-Guntram Drossel3, and Gerd Rupp2

1 Technology Development Tool Shop and Press Shop, Volkswagen AG, 38440 Wolfsburg, Germany2 Head of Tool Shop of the Volkswagen Brand, Volkswagen AG, 38440 Wolfsburg, Germany3 Fraunhofer Institute for Machine Tools and Forming Technology (IWU), 09126 Chemnitz, Germany

Received 30 October 2015 / Accepted 2 January 2016

Abstract – Due to the design-driven increase in complexity of forming car body parts, it becomes more difficult toensure a stable forming process. Piezoelectric actuators can influence the material flow of stamping parts effectively.In this article the implementation of piezoelectric actuators in a large scale sheet metal forming tool of a car man-ufacturer is described. Additionally, it is shown that part quality can be assessed with the help of triangulation lasersensors, which are mounted on the blankholder. The resulting flange draw-in signals were processed and used to adoptthe applying actuator force iteratively to reduce the occurrence of cracks. It was shown that process control helped toimprove the quality of the stamping parts significantly.

Key words: Closed-loop control, Deep drawing, Process control, Piezo actuators, Production engineering, Sensortechnology

1. Introduction

In sheet metal forming several parameters influence thequality of a part. If stable production conditions cannot beassured an open- or closed-loop feedback control can help toreduce rejected parts. Several feedback control approacheshave been investigated to reduce the quantity of rejected partswhich are caused by the adjusted process parameters.

As [1] showed it is possible to control a metal forming pro-cess if the material flow is monitored and a PID-controller var-ies the blank holder force. In this case a segmented blankholderis used to improve the quality of a square cup under laboratoryconditions. Reference curves have been generated from sensorsignals where the part quality was sufficient. Furthermore [2]designed another feedback control where master curves havebeen generated and unidirectional material flow sensors wererecorded to monitor the process conditions. Adjustable nitro-gen cylinders were controlled to regulate the blank holder forcedistribution of a modified wheel house liner tool. In reference[3] also used the material flow as sensor signal to control theblankholder force. Here a fuzzy control has been developedwhich simplifies the modelling due to a less accurate modelwhich is adequate enough. In reference [4] examined anotherspecially adopted tool where the active area of the blank holder

is mounted on piezoelectric sensors to measure the dynamicforce which is due to the sliding sheet metal between dieand blankholder. The measured force signal can be convertedinto dynamic friction coefficients. Four embedded cavities,which vary blank holder force regions locally, are used byEndelt and Dankert [5] to control a sheet metal forming pro-cess. A cascade control was designed. The inner loop is usedto minimize a linear-quadratic regulator (LQR) cost function(LQR optimal control). The outer loop reduces long term dis-turbances with the help of a linear learning algorithm. Due tothe modified tool the concept is hardly implementable intoserial production tools. For all of these concepts, a speciallydesigned tool is needed in order to enable a local alternationof the blank holder force distribution.

This work will show an additional approach where piezo-electric actuators. The approach was derived from the refer-ence [14]. Here, multiple arranged piezoelectric actuatorswhere used to influence the material flow. An experimental toolwas used to verify the effectiveness of this concept. A coverplate protects the actuators and will transfer the applied force.The followed working principle can be seen in Figure 1. Thisconcept was taken and the actuators where embedded into thedie of a large scale sheet metal forming tool. Additionally theactuators were controlled to vary the blankholder force distri-bution, which have not been investigated before. Different*Corresponding author: tobias.baeume@volkswagen.de

Manufacturing Rev. 2016, 3, 3� T. Bäume et al., Published by EDP Sciences, 2016DOI: 10.1051/mfreview/2016002

Available online at:http://mfr.edp-open.org

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

OPEN ACCESSRESEARCH ARTICLE

sensors were analysed in advance to obtain an optimized con-trol variable for the presented closed loop control approach.

2. Set-up

To design a process control sensors are necessary to distin-guish the parameters which correlate with part quality. Severalsensors for different mode of failures have been investigated insheet metal forming. The lower boundary of the forming pro-cess can be analysed with sensors tested by Griesbach [1],

Blaich and Liewald [6] and Straube [7]. If the sensor signalsalter from the reference signals then wrinkling will arise andthe blankholder force has to be increased. The upper processlimit is where necking, tearing or cracking occurs. Kergenand Jodogne [8] shows that strain gauges are feasible to detectthose mentioned failures. Beside inductive displacementsensors [9] for detecting the change of material propertiesthe contact-less measurement of the flange draw-in viatriangulation lasers are a suitable alternative for process qualityevaluation [10].

Figure 2. Preliminary analysis of a triangulation laser (a), blankholder strain gauge (b) and punch strain gauge (c) sensor to evaluate thetechnical suitability as control.

Figure 1. Working principle and set-up of piezoelectric actuators in metal forming tools [14].

2 T. Bäume et al.: Manufacturing Rev. 2016, 3, 3

These aforesaid measurement methods have been analysedwith regards to their ability to be implemented into the iterativeprocess for control strategies. Therefore different types of sen-sors have been integrated into a forming tool, as suggested byWaltl [12] (see Figure 2). For each sensor the correspondingexemplarily signals are illustrated in Figure 2. Sensor (b) and(c) where implemented as suggested by Kergen and Jodogne[8] and represent the strain of the affected tool areas causedby the acting blankholder/process force. Sensor (a) was usedto measure the flange draw-in as [10] proposed. The signalpath of a good and one rejected part were chosen exemplarilyto amplify and clarify the difference in signal characteristics.The area of crack occurrence can be seen in Figures 2 and11. Wrinkling has not been considered.

Due to the die cushion, which applies the blankholder forceto the blankholder, Sensor (b) represents the compression/strain in that region. Process variation will influence the signalqualitatively as Figure 2b shows. Here, the acting force willremain in the localised area where the crack occurs. Thusthe sensor is suitable to detect process variations. Additionallyit is possible to sense exceed process limits only if the sensor ismounted close to the area of failure.

During the forming process the blank will be stretched overthe punch. Moderate process changes will not affect the signalcharacteristics reliably. If a crack occurs the acting force can-not be transferred anymore, which causes an abrupt signaldrop. Hence, mostly the signal paths in Figure 1c are congruentuntil a crack occurs at approximately 85% of the process time.Consequently this sensor represents a binary signal character-istic. Closer proximity to the crack initialization increases thesignal sensitivity. Therefore the sensor is useful to recognizematerial failure locally.

The flange draw-in represents the material flow during thestroke. As Figure 2a illustrates, sensor signals weakly start todiverge when small process fluctuations appear. Furthermore,the signal starts to differ when the load/strain limits of thematerial are exceeded and tearing begins. The material flowwill differ significantly when a crack occurs which reducesthe total draw-in (see Figure 2a at approximately 85% of theprocess time). The large process variation can cause an earlydiverge of the signals. In both cases the total flange draw-inwill differ from signals of normal process behaviour. As a

result, the flange draw-in was identified as parameter whichstrongly correlates with part quality [11]. In contrast to wrin-kling and crack detecting sensors flange draw-in sensors allowto estimate the part quality without exceeding the process lim-its. Regarding the requirements to fulfil the large scale produc-tion conditions, the triangulation laser was used for furtherinvestigation.

Due to the small dimensions the laser can be flexiblymounted on the outer regions of the blank holder as Figure 3illustrates. That allows replacing the sensor if the errorpattern, which was predicted from sheet metal formingsimulation, differs from reality. Finally the triangulation laserprovides reliable measure signals with an accuracy of lessthan 0.1 mm.

The forming tool was supplemented by five piezo actuatormodules, which are used to redistribute the pressure in theflange area of the blankholder, as suggested by Mainda [13].The actuator modules corresponding power amplifiers arearranged within the tool. The energy supply and the controlsignals are induced via an additional interface mounted onthe tool. This interface is also used for the sensor signals.The control processing was firstly realized on a rapid controlprototyping system, which was arranged outside of the formingmachine. This allows a convenient reconfiguration of the con-troller without stopping the process.

3. Control

3.1. Basics

An arbitrary process W, which connects an input vector xwith an output vector z is defined as

z ¼ W xð Þ ð1Þwhere x and z contain several single variables with thedimensions n and m respectively:

x ¼ x1; x2; . . . xnð Þ ð2Þ

z ¼ z1; z2; . . . zmð Þ ð3ÞFor each output variable zi a functional relation can be

defined. The type of initial function mainly depends on thenon-linearity of the process. If there is no information ofthe process, a polynomial approach should be a feasiblepossibility of reflecting the process. Within the scope ofthe presented examinations a second-order polynomial wasapplied:

zi ¼ ai;0 þ ai;10 � x1 þ ai;20 � x2 þ . . .þ ai;12 � x1 � x2

þ ai;11 � x21 þ ai;22 � x2

2 þ . . . ð4ÞThe coefficients ai,j are calculated with a regression anal-

ysis of the results, derived from simulations or metrologicalexaminations (see section 0). Using Eqs. (1) and (4) an ana-lytical description of the deep drawing process with specifiedinput and output parameters could be obtained.

In Figure 4 a schematic representation of the target area oferror-free parts depending on the output parameters zi is given.

Figure 3. Mounted triangulation laser L2 and working principle.

T. Bäume et al.: Manufacturing Rev. 2016, 3, 3 3

zact and zref represent the actual output values of an arbitraryproduction step and the given reference values respectively.

To help ensure a stable process the output values shouldcoincidence with the reference values. Due to systematicand statistic errors there is a difference between the actualand the reference values. The reasons for this are notcovered by the regression model in any case. To minimizethe gap a Taylor expansion in the topical operating point �xcan be done for z.

�z1 ¼ @z1@x1

���x¼�x��x1

h i

þ @z1@x2

���x¼�x��x2

h i

þ . . . @z1@xn

���x¼�x��xn

h i

�z2 ¼ @z2@x1

���x¼�x��x1

h i

þ @z2@x2

���x¼�x��x2

h i

þ . . . @z2@xn

���x¼�x��xn

h i

..

.

�zm ¼ @zm@x1

���x¼�x��x1

h i

þ @zm@x2

���x¼�x��x2

h i

þ . . . @zm@xn

���x¼�x��xn

h i

ð5Þ

This linear system of equations can be expressed by

�z ¼ JA ��x ð6ÞThe difference Dz between actual and reference values is

known from the process, the matrix JA with its coefficientscan be derived from the process model. By transforming ofequation (6) the necessary modification Dx of the operatingpoint can be calculated:

�x ¼ J�1A ��z ð7Þ

In general the number of input parameters does not corre-late with the number of output parameters. Thus, JA is a non-square matrix in most cases, which requires a pseudoinverseto calculate Dx. This allows programming a controller, whichuses the current operating point and the analytical model.The corresponding scheme of the closed loop control isshown in Figure 5.

To illustrate this approach two scenarios were applied. Inthe first scenario the convergence behaviour was examinedby assuming a random-parametrized model with two dimen-sions. Due to the non-linear process model the calculated Dz

does not necessarily match the output Dz. This requires anadditional damping factor and several steps to approach thereference point. The second scenario provides a disturbedprocess. The controller tries to keep the output variable atthe stable point, while an increasing offset manipulates the pro-cess. Figures 6a and 6b show corresponding simulation resultsfor both scenarios.

3.2. Design of experiments and process model

As already stated the process model of the deep-drawing-process is represented by the analytic equations for the flangedraw-in depending on the control parameters of the piezoactuators. Each equation satisfies the structure given inequation (4). To determine the parameters ai,j a regressionanalysis was used with the usage of a statistical design ofexperiments. As variable parameters the amplitude of the actu-ation voltage of each piezo actuator was chosen. To reduce therange of the design a time variant voltage was not taken intoconsideration. The design of experiments (DOE) was achievedwith computational assistance using the commercial softwareCornerstone. For each of the five input parameters three cate-gories (low, mean, high) were given. As a result of the DOE atotal number of 26 input vectors were suggested as grid pointsfor deriving the process model using the multi-dimensionalregression analysis. For clarification, Figure 7 reduces the men-tioned principle to a one-dimensional plot with reference to theconsideration of the x-values as n-dimensional values. Theregression curves for all three flange draw-ins provide the coef-ficients ai,j (see Eq. (4)), which were obtained using the before-mentioned software Cornerstone.

It was established that conventional industrial deep draw-ing simulations have some limitations. The models with rigidtool surfaces and Coulomb friction models cannot reproducethe interaction between actuators and the reaction of theforced-controlled drawing cushion/cushion bead. Thereforeinvestigated FEM-based models differ significantly from theanalysed empirical ones. Further investigations with refinedsimulation models could improve the quality of the processmodel. A volumetric mesh of the full tool is advised to con-sider the operating principle of the actuators with respect tothe effects on the stiffness of the blankholder [11, 13]). Con-sidering this the empirical models have been used for furtheranalysis.

For the first experimental set-up a forming press withmulti-point die/drawing cushion has been implemented. Heresixteen hydraulic cushion pins were distributed evenly on the

Figure 5. Control loop.

Figure 4. Target area of error-free parts.

4 T. Bäume et al.: Manufacturing Rev. 2016, 3, 3

inner area of the blankholder to apply the force homoge-neously. The analysis of the calculated parameters ai,j haveshown several effects of cross correlation. Thus, a single actu-ator does not just affect the peripheral area, but also a flangedraw-in in other sectors of the blank (see Table 1). One reasonfor such occurrence could be the inner elastic and plastic bond-ing of the forming material. This will cause changes in actuatorforces and in certain active areas it will affect the material flowof the surrounded area as well.

To clarify the cross correlation, the process model has beenvisualized in Figure 8. Actuator P1 and P3 are plotted toillustrate the aforementioned effects. All other actuators areturned off. The initial draw-in plane shows the zero level ofthe flange draw-in from laser 2 when all actuators aredeactivated.

As Figure 8 indicates, actuator P1 will affect the materialflow of the distant area from laser 2. Paraphrased, P3 inhibitsthe material flow which causes a reduced draw-in. P1 induces

a contrary effect. Furthermore, due to reciprocal effects, thisretarding impact will be reinforced if both actuators worksimultaneously. This will allow combining several actuatorsto maximize the efficiency.

A try-out press with eight-point drawing cushion was usedto obtain a second empirical process model. The determinedparameters ai,j are comparable in their qualitative appearance.Divergences of the interacting actuators can be explained bythe elasticity of the forming tool and the use of a die cushion,where one pressure cylinder acts on more than one barrels ofthe tool. This leads to a decrease in the contact pressure ofthe implied peripheral areas. Therefore the affected areasdepend on the selected die cushion. In addition, quantitativeresults of the model-based flange draw-in are not able tobe compared due to different total blankholder forces and thementioned deviating amount of cross correlation. Furthermore,the obtained draw-in values of both experimental set-upscannot be compared because of a gradient-based controller.Relative deviations of the flange draw-in are used to calculatethe relative response of the actuator force. Due to similarmodel characteristics no additional analysis is presented.

For evaluating the sensor signal quality regarding the suit-ability for a closed-loop control the parts were individuallyexamined. Here, only the parts which were drawn on the presswith multi-point die cushion where taken into account. For sev-eral quality conditions (without errors, necking, cracks) therange of occurred draw-in-values was considered. Figure 9shows the corresponding box-plots for each laser sensor. Therewere overlaps of all considered quality conditions. The overlap

Figure 6. Simulation results for two convergence behaviour scenarios (a) and (b).

Figure 7. Principle of a regression analysis based on grid pointsderived from a statistical design of experiments.

Table 1. Extract of the coefficient table.

Term Laser 1 Laser 2 Laser 3

Umax,P1 – 0.005858 �0.02109Umax,P3 0.00627 �0.00486 0.00477Umax,P1 * Umax,P3 �0.00012633 �0.00014544 �0.00012679

T. Bäume et al.: Manufacturing Rev. 2016, 3, 3 5

Figure 9. Box-plot of the measured values.

Figure 10. Draw-in values (a) and actuator input (b) of a step-by-step control.

Figure 8. Visualized process model for actuator P1 and P3 over L2.

6 T. Bäume et al.: Manufacturing Rev. 2016, 3, 3

for laser 2 and laser 3 is rather huge significant, whereas theoverlap for laser 1 allows a quite good allocation of draw-invalues to the part quality. Hence, only the signal of laser 1 issuitable for a closed-loop control.

3.3. Results

To validate the functionality of this control approach sev-eral scenarios were investigated. Due to the aforementionedreasons these scenarios only consider laser 1 as input parame-ter. Figure 10 shows the results for a step-by-step control of thedraw-in of the blank. After an initial step the reference valuewas decreased. The controller calculated the new actuationforces of the five piezo actuators. Clearly visible is the step-wise convergence of the measured and actuating values. Thisseries was intended to investigate the principle control behav-iour of this approach. Assuming a larger range of operation thedifference between actual value and reference value shouldvanish.

In another scenario the tool was adjusted to produce a largecrack in the part front with no driven piezo actuators. To avoidthe crack the reference value of laser 1 was increased to resultin a more intensive flow of the material. As shown in Figure 11the controller takes three steps to minimize and eliminate thecrack.

4. Summary

Due to the design-driven increase in complexity of formingcar body parts, it becomes more difficult to ensure a stableforming process. Piezoelectric actuators can influence thematerial flow of stamping parts effectively by redistribute theforces in the tool. In this article the implementation of piezo-electric actuators in a large scale sheet metal forming tool of

a car manufacturer was described. Additionally, it was shownthat part quality can be assessed with the help of triangulationlaser sensors, which are mounted on the blankholder. Theresulting flange draw-in signals were used to reduce the occur-rence of cracking. An iterative process control was developedto minimize the current flange draw-in compared to a referencesignal. The applied piezoelectric actuator force will be adoptedafter each stroke to influence the blankholder force distribu-tion. The blankholder force of the die cushion was notmodified. If the reference flange draw-in will be set to theupper process boundaries wrinkling was minimized automati-cally. A resulting analytical process models from a multi-pointand eight-point die cushion press were derived. The origins areaccountable to the regression analysis based on an experimen-tal design. The obtained process models were comparable intheir qualitative characteristic. Deviations occur due to differ-ent operating behaviour and the resulting/caused changed crosscorrelation. Because of this further investigation regarding tothe interaction between actuators and die cushion is recom-mended. Finally, it was shown that process control helped toimprove the quality of the stamping parts significantly.

Disclaimer

The results, opinions or conclusions of this publication arenot necessarily those of the Volkswagen AG.

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Figure 11. Results of the step-by-step control.

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Cite this article as: Bäume T, Zorn W, Drossel W-G & Rupp G: Iterative process control and sensor evaluation for deep drawing tools withintegrated piezoelectric actuators. Manufacturing Rev. 2016, 3, 3.

8 T. Bäume et al.: Manufacturing Rev. 2016, 3, 3