Development of process control in sheet metal forming

Abstract

In sheet metal forming processes, the blank holder force controls the material flow into the die cavity, which is critical to producing a good part. Process control can be used to adjust the blank holder force in-process based on tracking a reference punch force trajectory to improve part quality and consistency. Key issues in process control include process controller and reference punch force trajectory design. The purpose of this paper is to present a systematic approach to the design and implementation of a suitable process controller and an optimal reference punch force trajectory. The approach includes modeling of the sheet metal forming process, design of the process controller, and determination of the optimal punch force trajectory. Experimental results from U-channel forming show that a suitable process controller can be designed through simulation and an optimal reference punch force trajectory can be synthesized through experiments. The proposed development should be useful in designing and implementing process control in sheet metal forming processes.

Full text

Development of process control in sheet metal forming
C.-W. Hsu
a,*
, A.G. Ulsoy
b,1
, M.Y. Demeri
c,2
a
TAC Automotive Group on Site at Ford Motor Company, Dearborn, MI 48121, USA
b
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109, USA
c
Ford Research Laboratories, Ford Motor Company, Dearborn, MI 48121, USA
Received 8 May 2002; accepted 13 May 2002
Abstract
In sheet metal forming processes, the blank holder force controls the material ¯ow into the die cavity, which is critical to producing a good
part. Process control can be used to adjust the blank holder force in-process based on tracking a reference punch force trajectory to improve
part quality and consistency. Key issues in process control include process controller and reference punch force trajectory design. The purpose
of this paper is to present a systematic approach to the design and implementation of a suitable process controller and an optimal reference
punch force trajectory. The approach includes modeling of the sheet metal forming process, design of the process controller, and
determination of the optimal punch force trajectory. Experimental results from U-channel forming show that a suitable process controller
can be designed through simulation and an optimal reference punch force trajectory can be synthesized through experiments. The proposed
development should be useful in designing and implementing process control in sheet metal forming processes.
#2002 Elsevier Science B.V. All rights reserved.
Keywords: Sheet metal forming; Process control; Optimization
1. Introduction
Sheet metal stamping is one of the primary manufacturing
processes because of its high speed and low cost for high
volume production. For example, parts such as body panels,
torque converter impeller blades, and fuel tanks are all
produced by this method. A simpli®ed stamping process
is shown in Fig. 1. The basic components are a punch, and a
set of blank holders which may, or may not, include draw-
beads. The punch draws the blank to form the shape while
the blank holder controls the ¯ow of metal into the die
cavity.
The quality of stamped parts is critical in avoiding
problems in assembly and in the ®nal product performance.
Two main considerations regarding the quality of stamped
parts are formability (e.g., wrinkling caused by excessive
compression and tearing caused by excessive tension) and
dimensional accuracy (e.g., springback caused by elastic
recovery). Main problems in sheet metal forming are shown
in Fig. 2. In addition, consistency (e.g., dimensional varia-
tions caused by lubrication or thickness variations) in the
stamping process signi®cantly affects subsequent assembly
in mass production.
New challenges emerge from the use of new materials.
For example, to reduce automobile weight (to improve fuel
economy) manufacturing companies must use lighter mate-
rials (e.g., aluminum) or thin gage high strength steel instead
of mild steel. However, such materials are not as formable as
mild steel and produce more springback [1].
The control of material ¯ow into the die cavity is crucial
to good part quality and consistency, and the blank holder is
used to control the material ¯ow. Previous research has
shown that varying the blank holder force during forming
can improve part quality [1±3] and consistency [1].Itis
worth pointing out that mechanical presses are being retro-
®tted with hydraulic multi-point cushion system to provide
more control of the forming process [4]. Such press tech-
nologies will facilitate the implementation of the process
control ideas presented in this paper.
One strategy for controlling sheet metal forming pro-
cesses through the application of variable blank holder force
is process control (see Fig. 3). In this strategy, a measurable
process variable (e.g., punch force) is controlled by
following a predetermined (e.g., punch force±displacement)
Journal of Materials Processing Technology 127 (2002) 361±368
*
Corresponding author. Tel.: 1-313-845-4646.
E-mail addresses: chsu1@ford.com (C.-W. Hsu), ulsoy@umich.edu (A.G.
Ulsoy), mdemeri@ford.com (M.Y. Demeri).
1
Tel.: 1-734-764-8464; fax: 1-734-647-3170.
2
Tel.: 1-313-845-6092; fax: 1-313-390-0514.
0924-0136/02/$ ± see front matter #2002 Elsevier Science B.V. All rights reserved.
PII: S 0924-0136(02)00321-7

reference trajectory through manipulating the blank holder
force [1]. This strategy could produce cups with ``optimal''
height regardless of initial blank holder force and friction
conditions [5]. Other measurable process variables (e.g.,
draw-in and friction force) have also been reported [6±8].
To systematically design a suitable process controller, the
process model in Fig. 3 must be identi®ed ®rst. Most sheet
metal forming models are based on ®nite element analysis,
which are very complex and, therefore, are not suitable for
controller design [9]. A piecewise linear model for controller
design has been developed [9]. However, this model cannot
be used in closed-loop simulation, because it cannot capture
the characteristic nonlinear behavior of a sheet metal form-
ing process. Therefore, issues in modeling for control of
sheet metal forming have not been adequately addressed,
especially from a control point of view, although methods of
system identi®cation have been well developed [10].
The most popular structure for the process controller is a
proportional plus integral controller [5,6,8]. However, con-
troller parameters are typically determined by trial and error
[11]. Although design of process controller has been well
developed [12], its application to sheet metal forming is still
not well investigated.
The reference trajectory in process control is important to
ensure good part quality in sheet metal forming [13]. It has
been determined experimentally or numerically [5,8].How-
ever, optimization of the reference trajectory has not been
well addressed.
Key issues regarding the application of process control to
sheet metal forming include design of an appropriate process
controller and design of an optimal reference trajectory. The
purpose of this paper is to address these two key issues to
systematically design and implement process control in
sheet metal forming.
2. Process control in sheet metal forming
2.1. Experimental facility
Process control experiments were conducted on a double
action hydraulic forming simulator equipped with a PID
digital controller (see Fig. 4). The press load capacity is
680 kN for the punch and 700 kN for the binder. The digital
controller allows the blank holder force to track a prede-
termined trajectory, which is the realization of the ``machine
controller'' block in Fig. 3.
2.2. Implementation of process control
Implementation of process control on this forming simu-
lator is shown in Fig. 5 [13]. The additional component is the
``DAQ'' block that is a data acquisition board. It acquires
data from the digital controller (the realization of the outer
feedback path in Fig. 3) and feeds the calculated blank
holder force command into the digital controller (the reali-
zation of the output of the ``process controller'' block in
Fig. 3). The ``program'' block with the ``DAQ'' block is the
realization of the ``process controller'' block in Fig. 3. The
``WSCI'' block is the original workstation communication
interface.
2.3. Influence of process control on sheet metal forming
2.3.1. Part consistency via process control
Recently, a comparison of machine and process control
for U-channel forming demonstrated the superiority of
process control to machine control [13].Fig. 6 shows
relative tracking errors for machine and process control
under dry and lubricated conditions. The results show that
Fig. 1. Schematic representation of a stamping process.
Fig. 2. Problems in sheet metal forming.
362 C.-W. Hsu et al./ Journal of Materials Processing Technology 127 (2002) 361±368

process control can maintain the same punch force trajec-
tories under different lubrication conditions but machine
control cannot. Table 1 shows average measured channel
heights for the cases shown in Fig. 6. The measurements
show that process control improves consistency in channel
height, despite change in lubrication. Therefore, consistency
in channel height can be related to consistency in punch
force trajectories.
2.3.2. Importance of process reference trajectories
The importance of the reference punch force can be
shown by comparing measured channel heights for different
reference trajectories [13].Fig. 7 shows two experimental
reference punch force trajectories. Table 2 shows measured
channel heights for these two trajectories. Trajectory (b)
produces better parts because the measured channel heights
are closer to the desired channel height (50 mm).
2.4. Design of process control in sheet metal forming
Based on the above experimental results, two important
considerations emerge:
Fig. 3. Process control of sheet metal forming.
Fig. 4. Forming simulator.
Fig. 5. Implementation of process control.
Table 1
Average measured channel heights (mm) for machine and process controls
under different lubrications
Control type Dry MP-404
Machine 47.600 46.211
Process 47.557 47.659
C.-W. Hsu et al./ Journal of Materials Processing Technology 127 (2002) 361±368 363

Evaluation of the tracking performance of the process
controller.
Selection of the reference punch force trajectory.
These two considerations will be addressed in the follow-
ing sections.
3. Sheet metal forming process modeling
Modeling a sheet metal forming process involving
hydraulically controlled single cylinder binder for process
controller design, which is a single-input±single-output
Fig. 6. Relative tracking errors.
Fig. 7. Experimental reference punch force trajectories.
Table 2
Measured channel heights (mm) for the reference punch force trajectories
in Fig. 7
Trajectory
(a) (b)
Test number
1 47.447 49.251
2 47.396 49.327
3 47.828 49.276
Mean 47.557 49.285
364 C.-W. Hsu et al./ Journal of Materials Processing Technology 127 (2002) 361±368

(SISO) system, has been investigated [14]. This is shown in
the block diagram in Fig. 8. The process model is a ®rst-
order nonlinear dynamic model. The disturbance, mainly
due to variations in lubrication, is also shown. This model
has been successfully used in modeling a U-channel forming
process. Fig. 9 shows comparison of simulation and experi-
mental results for different continuously variable blank
holder force trajectories.
4. Process controller design
Because of the empirical process model, systematic study
of process controller design can be conducted analytically
and numerically before implementation [13]. For the SISO
system, a proportional plus integral controller with feedfor-
ward action (PIF) has been investigated and successfully
implemented in the forming simulator [13]. The block
diagram of the controller is shown in Fig. 10. A ®rst-order
linear model can be used to design the controller gains. The
®rst-order linear model can be replaced with the ®rst-order
nonlinear model in Fig. 8 to evaluate the tracking perfor-
mance of the closed-loop system using the designed con-
troller gains.
Fig. 11 shows simulation results using the PIF process
controller and the ®rst-order nonlinear model. Fig. 11(a)
shows the blank holder force automatically generated by the
PIF process controller. Fig. 11(b) shows the reference punch
force trajectory, F
pd
, and the punch force trajectory, F
p
.
Good tracking performance is expected based on simulation
results.
Experimental results using the same PIF process con-
troller and the same reference punch force trajectory are
shown in Fig. 12. Although there was variation in the blank
holder force trajectories, the punch force trajectories were
similar. This indicates that the process controller works well.
Fig. 8. Process model of sheet metal forming.
Fig. 9. Experimental and predicted punch force trajectories for different variable blank holder force trajectories.
Fig. 10. Block diagram of the PIF control system.
C.-W. Hsu et al./ Journal of Materials Processing Technology 127 (2002) 361±368 365

5. Optimal punch force trajectory design
One method for obtaining an optimal reference punch
force trajectory is to use design optimization methods
[15,16]. With an ideal process controller, Fig. 3 can be
simpli®ed as shown in Fig. 13.
In this case, the stamped part shape, S, will be totally
determined by the reference punch force trajectory or
equivalently by the punch force trajectory, F
p
.
A mathematical expression can be used to describe the
relationship in Fig. 13:
SPFp(1)
The optimal punch force trajectory F
pfor a desired shape S
d
can be obtained by solving the following equation:
F
parg min
Fp2D
EPFp;Sd(2)
where F
pis the optimal punch force trajectory, Dthe safe
domain for F
p
without tearing and wrinkling, and Ethe cost
function to represent the difference between PFpand S
d
.
To ®nd F
pthrough optimization is still dif®cult. The
challenges are:
1. To find the operator P, which give a punch force
trajectory, yields the part shape.
2. To find the domain Dwhich defines safe punch force
trajectories.
Since current mathematical modeling of sheet metal forming
uses ®nite element methods [17,18], there is no simple
expression for Por D.
A procedure for solving Eq. (2) through parameterization
and design of experiments is as follows:
1. Parameterize F
p
and S. Parameters of F
p
are the design
variables and parameters of Sare the response variables.
2. Identify an empirical relationship between the design
and response variables.
3. Find the optimal design variables based on the empirical
relationship. The optimal punch force trajectory corre-
sponds to the optimal design variables.
Central composite design can be used for design of experi-
ments to ®t a second-order model [16]. Response surface
Fig. 11. Simulation results using the PIF process controller and the first-order nonlinear model.
Fig. 12. Experimental results using the same PIF process controller and reference punch force trajectory.
Fig. 13. Press with ideal process controller.
366 C.-W. Hsu et al./ Journal of Materials Processing Technology 127 (2002) 361±368

methodology can also be used to ®nd the optimal design
variables.
The in¯uence of the optimal punch force trajectory on
the process controller design is its smoothness. The
smoother the optimal punch force trajectory is, the easier
the process controller design is. Parameterization of F
p
and Sis realized by series expansion with orthogonal
functions (e.g., Chebyshev polynomials). The desired
smoothness of the optimal punch force trajectory can
be ensured by the smoothness of the orthogonal func-
tions.
The above procedure is a sequential one. The following
results are from the second application of the procedure to
U-channel forming. In this case, the response variable is the
channel height error, e
h
, which is de®ned as the desired
channel height minus the measured one. The punch force is
parameterized through
Fpa1f12:04f35:03f51:69f7(3)
where a
1
is the design variable and f
i
the ith order Cheby-
shev polynomial.
Coded design variables are usually used in design of
experiments. The coded design variable, x
1
,is
x1a1a10
la10
(4)
where a
10
is the center of the design domain and lis a scale
factor. In this case, a10 51:69 and l0:025.
Designed punch force trajectories corresponding to
x14, 2, 1, 0, 1, 2, and 4 for the experiments are
shown in Fig. 14(a). Channel height errors are shown in
Fig. 14(b). When tearing occurs, the channel height is
assumed to be the height at failure. The optimal F
p
in
Fig. 14(a) corresponds to the minimum (x
10:94) of
the ®tted response surface in Fig. 14(b).
From a physical point of view, the true optimum in this
case is a boundary optimum. Hence, the ®tted response
surface cannot predict the true optimum precisely. However,
the fact that it is a statistically good model and has a
minimum indicates the existence of a true minimum nearby.
Based on engineering judgement of safety and robustness of
the forming process, the optimal punch force trajectory is
determined as the one corresponding to x10.
6. Summary and conclusions
Process control has been shown to improve part quality
and consistency. Key issues such as process controller and
optimal punch force trajectory design have been addressed.
A systematic approach to the application of process control
to U-channel forming has been presented. A process con-
troller with good tracking performance and an optimal
punch force trajectory has been developed. Future work
includes the effect of high punch speed on process controller
design and application of the systematic approach to com-
plex parts where a ¯exible binder with hydraulically con-
trolled multi-cylinders may be involved.
Acknowledgements
The authors gratefully acknowledge the technical and
®nancial support provided by the Ford Motor Company.
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