A database oriented process control design algorithmfor improving deep-drawing performance

Hiroshi Koyamaa,*, Ken-ichi Manabea, Syoichiro Yoshiharab

aDepartment of Mechanical Engineering, Tokyo Metropolitan University, Tokyo, JapanbDepartment of Mechanical Engineering, Tokyo National College of Technology, Tokyo, Japan

Abstract

A new process control design algorithm for sheet stamping operations using a database was developed in order to provide design engineers

with an easy and suitable method of designing the process control rules. Utilizing the database, which consists of process information, the

algorithm enables the design of the process without the need for experts who are skilled and experienced in the forming processes. In this

study, the algorithm was applied to fuzzy adaptive control of the blank holding force (BHF) in the circular-cup deep-drawing process in order

to improve the limit drawing ratio (LDR), which is a typical industrial requirement. In the fuzzy adaptive controlled variable BHF deep-

drawing test with an aluminum alloy sheet, 2.4% improvement of the LDR was achieved. The result confirmed the efficiency of the developed

algorithm for LDR improvement, and an appropriate BHF path for improving the LDR was demonstrated.

# 2003 Elsevier Science B.V. All rights reserved.

Keywords: Database; Deep-drawing; LDR; BHF; Fuzzy adaptive control

1. Introduction

In a production system, the design of the forming process

is one of the paramount issues of carrying out the process

successfully. The optimum process design provides much

benefits, such as the improvement of formability and product

accuracy, and reduction of the running cost. Several studies

on the optimization of the process design have been per-

formed considering the development and investigation of

process control rules. In sheet stamping processes, the blank

holding force (BHF) technique, which is recognized as one

of the technical issues that affects the stamping performance,

has been the target of the process control. The authors

confirmed that the product accuracy and formability can be

enhanced by applying the optimal BHF via an appropriate

path [1,2]. Much effort focusing on BHF control techniques

has been made for improving the deep-drawing performance,

and a fuzzy adaptive controlled variable BHF deep-drawing

system has been developed to cope with the change of forming

condition during the process [3,4]. The process control system

indicated a high possibility of deep-drawing performance

improvement. The system, however, requires much time

and labor for the design and development of the process.

Above all, the engineer who develops the system should be a

knowledge expert as well as being skilled and experienced

with the forming process. Despite their need, the number of

experts has been gradually decreasing year by year.

In recent years, the product design period has been

drastically shortened due to the application and the evolution

of information technology, consequently the process design

phases should also be facilitated and shortened. Hence, a

new process control design algorithm which is free from the

dependency on experts and can be operated easily without

their assistance is required.

In order to meet such industrial requirements, a database

oriented process control design algorithm which can facil-

itate and shorten the design procedure of process control

is proposed. In the study, the algorithm is applied to an

adaptive control technique of BHF in a circular-cup deep-

drawing process for improving the limit drawing ratio

(LDR), which is an important technical issue in deep-

drawing operations. The purpose of this study is to construct

a fuzzy adaptive controlled variable BHF circular-cup deep-

drawing system with a database and to demonstrate the

applicability of the algorithm through system execution.

2. Database oriented process design algorithm

In order to enable freedom from the dependency on

engineering experts in the design phases of process planning

Journal of Materials Processing Technology 138 (2003) 343–348

* Corresponding author.

E-mail address: koyoma@ynu.ac.jp (H. Koyama).

0924-0136/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0924-0136(03)00096-7

and process control, a concept of database oriented process

control design for various deep-drawing operations without

the aid of a knowledge expert, was proposed [5]. Fig. 1

shows the outline of a system architecture based on the

concept. It can be broadly divided into two parts. One is a

processor and the other is a forming cell and system. The

forming cell has several sensors for supplying process

information to the processor, and also has actuators to

implement the commands from the processor. The proces-

sor, which consists of a database and an analyzer, is capable

of not only designing the process control rules using the

database, but also of identifying the deformation character-

istics of the workpiece, such as material properties, and

controlling the actuators based on the resultant process

control value. Since the database governs the performance

of the system, it should contain appropriate process infor-

mation under several tool conditions, lubrication conditions,

ambient conditions, and material properties in order to

design the process of forming target shapes. The processor

can also store the sensing information from a forming cell

during the forming process, which is similar to the experi-

ence of an expert. In other words, it can learn by acquiring

experience in the same manner as an expert. Hence, our

system is able to automatically optimize the process and can

be operated without any assistance from an expert, and can

handle a variety of workpieces as well as the change of

workpiece material, tool conditions and lubrication condi-

tions, by utilizing the database.

3. New process control system with database

3.1. Algorithm for LDR improvement

3.1.1. BHF path for improving LDR

Considering the effect of the BHF history on formability

in the deep-drawing process [6], the BHF in the early stage

of the process should be kept as low as possible in order to

prevent local thinning. However, in a constant BHF deep-

drawing operation, excessive BHF must be applied even in

the early stage of the process in order to avoid wrinkling at

the flange, which occurs in the middle to the last stage of the

process, as shown in Fig. 2. Contrarily, in a variable BHF

deep-drawing operation, it was confirmed that wrinkles,

which occurred in the early stage of the process, can be

eliminated by applying higher BHF in the middle to the last

stages of the process [7]. Therefore, LDR improvement can

be achieved by applying the minimum BHF above the

wrinkle limit; this condition can maintain the punch load

minimum and prevent fracture at the punch shoulder. To

obtain such a minimum BHF condition, the process control

rule should be designed to control the BHF to be as low as

possible to prevent the local thinning which leads to fracture,

and increase the BHF to avoid and eliminate wrinkles if they

occur.

3.1.2. Features and advantages of the system

This minimum possible BHF condition is available not

only for the LDR improvement but also for energy saving

due to the decrease of forming energy. In addition, low

viscosity and water-washable lubricants can be used under

this BHF condition. Hence, the process control algorithm for

LDR improvement has great advantages from the environ-

mental aspect.

Fig. 1. System architecture of an intelligent metal forming cell with a database.

Fig. 2. Minimum BHF limit under constant BHF condition.

344 H. Koyama et al. / Journal of Materials Processing Technology 138 (2003) 343–348

3.2. Evaluation functions

In order to realize the above mentioned minimum possible

BHF condition, the BHF should be controlled to be as low as

possible. If wrinkling occurs, the BHF should be increased

for preventing the wrinkles. To accomplish such process

control, the evaluation functions should accurately indicate

the risk of wrinkling and be independent of blank materials,

tool conditions, environmental conditions and other factors.

Although clarifying the whole deformation behavior of the

deformed blank provides ideal information for wrinkle

prediction, it is impossible to obtain such process informa-

tion during the process. Therefore, in this work, the max-

imum apparent thickness of the blank was employed as the

evaluation function c for wrinkle prediction, as shown in

Fig. 3. The thickness can be obtained by measuring the

displacement of the blank holder. The evaluation function ccan be increased by applying less BHF and can be decreased

with higher BHF, as presented in Fig. 4. Hence, when the

evaluation function c indicates a high value, the risk of

wrinkling is high and the BHF should be increased in order

to prevent wrinkling. In addition, the differential coefficient

of c determined from the flange reduction ratio (DDR�), c0

is also applied as one of the evaluation functions for

enhancing the reliability of prediction. The DDR� indicates

the progress of the process and can be obtained from the

flange end displacement of the blank as

DDR� ¼ s

rp

(1)

where rp is the punch radius and s is the flange end

displacement. By using the combination of the two evalua-

tion functions c and c0, proper wrinkle estimation can be

performed.

3.3. Database requirement in the system

The database in this work consists of four kinds of process

variables, punch stroke, ideal curve, maximum apparent

thickness of blank and DDR�, under constant BHF deep-

drawing tests, as shown in Fig. 5. These process data are

utilized in order to design the process control rules, so they

must be accumulated under various process conditions

(material property, tooling condition, lubrication condition,

ambient condition, etc.) and should be labeled by the

forming conditions for speedy reference. The data related

to punch stroke and ideal curve are used for designing the

process control rules for cup height improvement and thus

are not utilized or described in this paper. In the present

paper, only the maximum apparent blank thickness and

DDR� relation curve is used in order to design the process

control rules for LDR improvement. Therefore, these pro-

cess data must be obtained under the constant BHF condition

which leads to wrinkling.

3.4. Fuzzy inference

In order to determine the process control value, the

increment of BHF (DBHF), a fuzzy inference is adopted

as the AI tool for process control. The fuzzy model used in

the system consists of three elements.

Two sets of membership functions for the antecedent

of ‘If-then’ rules shown in Fig. 6 can be designed by the

Fig. 3. Representation of wrinkling behavior due to blank holder

displacement.

Fig. 4. Evaluation function c for wrinkling estimation.

Fig. 5. Essential items stored in database.

H. Koyama et al. / Journal of Materials Processing Technology 138 (2003) 343–348 345

processor by utilizing the database. These sets of member-

ship functions are used for wrinkle estimation. For accurate

wrinkle estimation, four values in the sets of input member-

ship functions (ca, cb, ca0, cb

0) should be defined precisely.

In the present system, these values can be obtained auto-

matically from the results of constant BHF circular-cup

deep-drawing experiments stored in the database. cb is

the maximum value of c obtained from the constant

BHF deep-drawing test. In other words, cb should corre-

spond to the state of wrinkling. cb0 is the maximum value of

c0 in the database. ca and cb can be determined by sub-

stituting the minimum values of c and c0 in the database,

respectively.

Fig. 7 indicates a set of membership functions for the

consequent of the ‘If-then’ rules. In our previous work,

this part was decided with the assistance of the expert.

The expert must determine all the output values through

trial and error, so that much time and labor were required for

the determination. However, in this study, the simplified set

of membership functions eliminate the need for engineers to

be skilled and experienced. The operator of the system has to

provide only a multiplier to the system output value (DBHF)

corresponding to the characteristics of the forming cell used.

In this work, the scale factor applied to the system output

was decided as 0.3.

In order to achieve successful fuzzy inference, the sets of

membership functions for the antecedent and the consequent

should be properly related. The sets of membership func-

tions are connected according to the ‘If-then’ rules listed in

Table 1.

4. Experiment on LDR improvement

4.1. Experimental procedure

The first step in process control design is extracting

the required process information from the database. If the

database has no appropriate data for the target process,

sufficient process information should be obtained and

stocked in the database, as indicated in the left half of

Fig. 8. In the present system implementation, the process

information of the maximum apparent blank thickness and

the DDR� is essential for LDR improvement. Therefore, the

process information related to the wrinkle limit should be

captured for the database.

Fig. 6. Sets of input membership functions for fracture estimation.

Fig. 7. A set of output membership functions for DBHF decision.

Table 1

‘If-then’ rules of c, c0 and DBHF

If (c, c0) Then (DBHF)

c is small and c0 is small DBHF ¼ DBHFSS

c is small and c0 is large DBHF ¼ DBHFSL

c is large and c0 is small DBHF ¼ DBHFLS

c is large and c0 is large DBHF ¼ DBHFLL

Fig. 8. Process control design flow using the database.

346 H. Koyama et al. / Journal of Materials Processing Technology 138 (2003) 343–348

The fuzzy adaptive controlled variable BHF circular-cup

deep-drawing test is conducted after the four parameters for

the sets of input membership functions are generated by the

analyzer using the database, as in the right part of Fig. 8. In

this work, the parameters for the membership functions are

determined by using the process information stored in the

database, as listed in Table 2. The BHF can be automatically

controlled on the basis of the fuzzy rules obtained during

the process. In order to accomplish LDR improvement, the

BHF is basically controlled to be minimum while the

evaluation functions indicate a sufficiently low possibility

of wrinkling. When the evaluation functions indicate a

higher possibility of wrinkling, the BHF can increase for

preventing wrinkling.

4.2. Experimental apparatus

The experimental apparatus developed based on the con-

cept is equipped with several sensors for obtaining punch

stroke, punch load, BHF, flange end displacement measured

by the displacement transducer and blank holder dis-

placement, based on the database oriented process control

design concept. These sensors enable the processor to

identify the process status from the forming cell during

the process. The system also includes a hydraulic system

for applying the BHF which can be controlled adaptively by

the processor according to the process information from the

sensors.

4.3. Experimental conditions

In order to achieve successful process control, all experi-

ments are conducted with the constant punch speed of 5 mm/

min. Lubricating oil was applied only to the die side of the

blank. The range of variable BHF is defined as 0.5–5 kN

which is governed by the capacity of the experimental

apparatus. In this system implementation, an aluminum

alloy sheet metal (A5182-O) 1.0 mm thick was used. Tool

conditions and the material properties are given in Tables 3

and 4, respectively.

5. Results and discussion

Fig. 9 presents the experimental results for the BHF and

the punch load obtained in conventional constant BHF

condition and fuzzy adaptive controlled variable BHF tests.

The LDR in the case of conventional constant BHF is 2.09,

so the experiment with DR ¼ 2:10 results in failure. In the

case of variable BHF, the minimum BHF in the initial to the

middle stage of the process maintains the punch load lowest

and local thinning can be restrained. The BHF is increased

by the processor in the last phase of the process in order to

avoid and eliminate wrinkles. The LDR obtained under

constant- and variable-BHF conditions are shown in

Table 5. As a result, 2.4% improvement of the LDR was

achieved using the system developed based on the database

oriented process control design concept. Therefore, the

sufficiency of this system for LDR improvement was

confirmed and an appropriate BHF path for improving the

LDR was pointed out. Furthermore, the LDR can be further

improved, with thinner sheet metals or materials with a

lower strength coefficient, F value [8].

Table 2

Four parameters for membership functions

ca cb ca0 cb

0

0 0.400 0.196 3.84

Table 3

Tooling conditions

Part Radius (mm)

Punch shoulder 4

Punch 16.5

Die shoulder 3

Die cavity 18.25

Table 4

Material properties of blank used

Property Value

Yield stress, sS (N/mm2) 117

Tensile stress, sB (N/mm2) 264

F-value (N/mm2) 398

Breaking elongation (%) 30.1

n-Value 0.28

r-Value 0.6

Fig. 9. Comparison of experimental curves for LDR improvement.

Table 5

LDRs obtained under constant- and variable-BHF conditions

BHF condition LDR

Constant 2.09

Variable 2.14

H. Koyama et al. / Journal of Materials Processing Technology 138 (2003) 343–348 347

6. Conclusions

(1) A database oriented process control design algorithm

for the sheet stamping operation was developed. The

database consists of four types of process information

(punch stroke, blank holder displacement and flange

end displacement histories and ideal curve).

(2) The algorithm was applied to the fuzzy adaptive

control of BHF for LDR improvement, and a process

control algorithm for obtaining LDR improvement was

presented.

(3) The availability of the process control design algorithm

with a database was confirmed through the implemen-

tation of fuzzy adaptive controlled variable BHF tests

with the process control rules developed using the

algorithm.

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