Blanking as a process-system

Blanking as a process-system

Citation for published version (APA):

Veenstra, P. C., & Ramaekers, J. A. H. (1977). Blanking as a process-system. (TH Eindhoven. Afd.

Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0411). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1977 Document Version:

Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.

• The final author version and the galley proof are versions of the publication after peer review.

• The final published version features the final layout of the paper including the volume, issue and page numbers.

Link to publication

General rights

Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

• You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:

www.tue.nl/taverne

Take down policy

If you believe that this document breaches copyright please contact us at:

openaccess@tue.nl

providing details and we will investigate your claim.

81

WPR

bsw

Fig. 1.

1

j

.~ __ ANKING AS A PROCESS-SYSTEM (Lecture INDIA 1977) 1. Introduction WT-Rapport 411

P.C. Veenstra ~ J.A.H. Ramaekers

August 1977

Usually metal working processes are being studied by analyzing and . investigating a particular aspect of it, whereas in Industry lithe

process" is only part of a manufacturing system. For instance in cutting research a lot of work is done with respect to the shear-angle relationship, the cutting forces, the dynamic cutting

coefficients, the kinematics of chip flow, the wear behaviour of the tool, and so forth.

However the industry is interested in the optimum setting of cutting parameters for a given tool, a given machine tool, a given material and given cost of the operation per unit time. In other words:

industry is interested in the optimum path through the "system cutting". In the laboratory for production engineering of Eindhoven University of Technology the solution to this problem is well under way; however,

today I will not discuss this issue, as the results are to be published before long by my collegues.

In the present lecture I hope the elucidate the "system blankingl l , as

blanking in the mass-production of metal parts and components is one of the most important processes in a great variety of industries.

When looking at the aspects involved in cold forging or cold forming of metals in general and hence also in blanking, we may list at least six items, as done in fig. 1.

In this figure it is tried to evaluate roughly the amount of knowledge or know-how available with respect to every item, both in industry and

in research laboratories.

Obviously the researchers know a lot about plasticity mechanics and analysis of metal forming processes - anyhow far more than is commonly

known in industry.

On the other hand practical know-how of the choice of lubricants is mainiy to be found in industry, since classical tribology does not apply to

lubrication problems !~nder the conditions of extreme high pressures as

Fig. 2.

Analogous remarks can be made to the other items listed, and although the knowledge appears to be more or less defective at some places, it

must be well worth trying integration in a manufacturing system. 2. The blanking process

In practice commonly the relationship

(2.1)

is used to calculate the maximum force in blanking, where according to fig. 2.1 is the length of the cut, h the thickness of the blank

o

and Tsh the average shear stress.

The latter is often related to the tensile strength of the material by applying

Tsh'" fsh °B (2.2)

where fsh is the shearing factor, an experimental constant relevant for a particular blanking operation. Its value can be taken from several handbooks.

These data, being purely experimental, have no prognostic value if materials are to be worked the factory is not used to. For this

reason and in order to get closer to optimum process control, the shearing factor must be related to more "fundamental" material properties.

As to this it is assumed that the material behaves plastically according to the van Mises' law and that strain-hardening is described by the extended Nadal relation

- - - n

o ... C (€ + € )

o

(2.3)

where 0 is the effective stress, C the specific stress (a materialls

constant), € the effective strain, € the initial strain and n the

strain-o

hardening exponent.

When watching a blanking process closely and by studying micro-photographs of the shearing zone it appears that different types of deformation playa role in blanking.

1. the blank is subjected to bending, whilst apart from this in the shearing zone compression can be observed.

Both these deformations have a substantial influence on the initiation of crack formation as well as on the geometrical accuracy of the product.

2. the main deformation process in blanking is simple shearing. When neglecting for the moment the contributions of the secondary deformations, the path of the punch is according to fig. 2 given by

where h is the instantaneous height of the shear zone or the "remaining thickness" of the blank.

(2.4)

Performing a blanking process in successive incremental steps, the

effective strain in the shearing zone can be determined as a function of the value h by means of micro-hardness measurements.

It turns out to hold

{f

h

- 0

€ - -_n I n -_h

uniformly distributed over the cylindrical surface r - D/2.

Since in simple shear the plasticity condition reduces to

(1

=

-it follows through eqs.

2.3

and

2.5

for the shear stress

C

(ff

h

)n

T = - - ln~+~

rz

13

n h 0

also uniformly distributed over the shearing surface.

(2.5)

(2.6)

When neglecting the effects of friction, as will be discussed later, it follows for the instantaneous blanking force

F

=

...L

₁₃

1 • h •

("n-

_;V

_n

1 n hho + ; ) n

In a reduced form with and lit S can be written Flit

= ...!...

(l-sllt)

(13

In

--L

+

~

)n

13

n 1-sllt 0 (2.8)

(2.9)

(2.10)

By differentiating this equation with respect to slit it is found for the maximum value of the reduced blanking force

1

= - (2.11)

13

which value is achieved for

(2.12)

with the condition

-if

€ _o ~ _{. n} - (2.1) In the case of highly strain-hardened or b,rittle material, since it then holds

the tool path to reach the maximum force is virtually zero and consequently

1

=--

(2.14)

13

From elementary analysis of the tensile test it follows that the tensile strength, defined as the tensile force per unit area of the initial cross-section of the specimen, can be written either as

O'B

=

C

(~)n

e EO (2. 15) if E ~ n 0 or as C - n O'B

=

E 0 (2.16) if E > n 0

Now, through the eqs. 2.1, 2.2 and 2.8 the shearing factor can be wri tten as

(2. 17)

From this and the eqs. 2.11, 2.14, 2.15 and 2.16 the shearing factor now can be expressed in terms of both the strain hardening properties of the material and the amount of initial deformation. It follows

fsh =

~({f)n

(2.18) if E = 0 0 fsh ₌

~

(fr)"

exp

[~o (V~

-

~

]

(2.19) if

o

< _EO < n fsh

-

~

(0

(~

)"

exp

[~o

f]

(2.20) if n < E <

Ifr1

0 fsh = -1

13

_(2.21) if EO ~

I3i1

Fig. 3.

Fig. 4.

A graphical representation is shown in fig.

3.

It is remarked that

these theoretical values are in fair agreement with practical data. Up to now the influence of friction on the blanking force is

neglected.

When assuming the model of the constant friction factor, the frictional shear stress along the tool surface can be written as

T_f

=

m L _max

o

~ m ~

(2.22)

and next through eq. 2. it is found for the reduced frictional force

2 -m s·

f

(3

lIT" In - 1 + - ) £ n

13

0

V

n

1-s. 0

(2.23) From literature it may be concluded that ususally the influence of friction is minor, corresponding to a value m ~ 0.05 - as confirmed by own experiments. In our opinion frictional effects are of the same order of magnitude as the effects of the scatter in material's properties,

including the blank thickness.

However, in blanking austenitic stainless steels, which often offers

difficulties, matters are different. These kinds of steel are characterised by extreme values of the material's constants, for instance C

=

1500 N/mm2 and n

=

0.5, whereas the thermal conductivity is low. According to eq. 2.7 the blanking force is high and consequently the energy dissipation in the shearing zone. In combination with the thermal constants of the material a high temperature develops.

In the present model, as formulated in the eqs. 2.10 and 2.23 these

effects can be accounted for by a friction factor m ranging in 0.2 to 0.3. Conclusion: The formulae 2.10 and 2.23 describe a mechanical model of

the blanking process. This model, in which only the materials' constants C, ~ and n are used, and the more

o

or less arbitrary friction factor m, proves to be sufficiently accurate to give a basic understanding of the process.

Fig. 5.

By applying the present model a number of questions in daily manufacturing practice can readily be answered.

Today I will deal with the by far most important one, being the critical wear of blanking tools in the context of the life-time of die-sets. The cost of die-sets, designed and build for mass-production, ranges in several thousands of guilders to a couple of hundred-thousand.

From the design of the tool it is known how many times it can be ground before it is finally worn out. Thus, for a wanted volume of production - a lot-size of several millions being very common - it is important to know which is the average life-time of a tool between grindings,expressed

in terms of number of products made, based on a given criterion of critical tool wear.

From the figures obtained, the management has to decide whether one, two or more tools must be ordered in order to warrant a continuous production. Ordering one tool to much means waste of money, iT there is a tool short production will fall to a stand-still.

For the very reason that this high volume component manufacture is always an integral part of a much bigger production system, as for instance the making of television sets, the effects of a wrong decision with respect to the tools are desastrous.

3.

A criterion for critical tool wear

In order to enter the problem of wear of tools the phenomena of the very first stage of the blanking process must be studied more closely.

As remarked before, the process is always accompanied by bending of the blank. In the initial stage, when the punch just hits the blank, the bending is due to a uniform load, according to membrane theory.

This means that immediately after the impact of the punch, in the center the contact between punch and blank is lost and finally the load is concentrated at a narrow ring at the periphery of the punch.

In practice this ring can easily be recognized by its shining appearance, indicating that the material has been plastically deformed.

When assuming now that the pressure ring fully develops to its width b at

the moment of maximum load F , because of equilibrium it must hold

Fig. 6. 0/2 2TI

f

on r dr

=

Fmax

o

- - b ₂

(3.1)

where cr is the average normal pressure on the ring, whereas F is

n max

known from the model of the blanking process.

Next, from theory of the bending of thin plates due to closely

neighbouring opposite forces - as is the case in blanking - the vertical displacement W(r) at any place can be calculated.

Now from eq. 3.1 it becomes clear that as soon as a model is available for the distribution of the normal load over the pressure ring, the

w.idth b of the ring can be expressed in terms of materials 'constants only. Hence the distance a of the resultant force to the edge of the punch is known and consequently - for a given clearance u - the distance between the resultant force and its reaction force exerted by the die.

Thus the local displacement of the blank W(r) can be found, which as a matter of fact describes the bending shape of the blank.

During the blanking operation the punch as well as the die, will wear; the former mainly at it periphery.

As a hypothesis it is proposed now that thJs wear develops· gradually until the moment that the worn surface of the tool matches the bending shape of the blank. As soon as this is the case the wear develops rapidly and the products made show increasing burr. This means that it is supposed that the critical flank wear in terms of vertical displacement of th.e blank amounts to

b_s

=

IW(r=D/2) - W(r=D/2-b)I (3.2)

In order to quantify this, first, as remarked before, the pressure

distribution over the pressure zone must be known. This can be calculated according to the theory of compression between flat dies, in the case of Coulomb friction as well as plastic friction. However, for the sake of Simplicity it is assumed that the pressure distribution is linear. Since the maximum load occurs when the blanking process has developed up to, say 30%, it is next assumed that the average pressure in the pressure zone equals the average of the yield stress of the material as received

.

and the yield stress in the shear zone at the moment of maximum force, and thus

Fig. 7.

Fig. 8.

if the material shows the initial deformation t and the definition

o

of the 0.2% strain yield limit is applied. From the eqs.

2.8, 2.11, 3.1

and

3.3

it follows

exp [eo

Vf-

nJ

().4)

As shown in fig. 7 this reduced width of the pressure zone is not very strongly dependent on materials' properties. In particular, If some initial deformation is present, the reduced width of the pressure zone becomes virtually a constant. Because of its shining appearance this width can easily be measured. The average of

28

measurements on samples of different thickness proved to be b-

=

0.57

t

0.07,

which

is in excellent agreement with eq.

3.4.

When substituting eq.

3.4

in Prescott's formula for bending of a thin

plate under the particular loading condition of blanking and applying eq.

3.2

it is obtained for the reduced critical flank wear of the tool

(1-~ _{2 C} ) - exp

1-

€

'If

-E

0 3

C3

.5)

where C/E is the ratio of specific stress and the elasticity modulus,

~ is Poisson's constant and u-

=

~ is the reduced clearance.

o

This formula is visualized in fig. 8, which again shows the relatively

great influence of initial deformation.

However, since technical materials as applied in blanking practically always have a few percent of initial deformation and moreover the technically relevant value of the strain-hardening exponent ranges in

o

to 0.6, it may be concluded that eq.

3.5

provides a safe upper limit for tool wear, also in the case that the strain-hardening properties and the initial deformation are not exactly known.

It appears that the data thus obtained agree very well with the wear criteria as applied the shop, as established by long year's

4. The life time of die-sets

Having accepted a criterion for critical wear of tool, either by using

eq.

3.5

or by rejecting products manufactured because of burr or

some other technological reason, the life time of tools can be discussed.

As can be expected on forehand, the problem of life time is a statistical one, rather than being deterministic.

Case studies in the factory show, that the life time of tools - defined in terms of the number of products between grindings - does not follow a normal distribution.

Research reveals that the distribution function is Weibullian, which is (4.

n

being the probability that the tool fails after having made x products.

The quantities

a

and

n

are shape-factors of the distribution and prove

to be closely related to the type of manufacturing operation performed and thus to the type of tool.

The objective now is clearly to determine the characteristic quantities nand

B

for a given operation and to conclude from this on the average

1 ife time of a tool.

It is easy to prove that all functions F(x) intersect at the point x

=

n, where holds

F(x)

=

- - =

_e 1 0.632

(4.2)

This in fact is the definition of the characteristic number n, being the number of products made at the moment of 63,2% tool failure. Now in order to show that the life time of die-sets obeys a Weibull distribution, statistical sampling theory must be applied - since of course we have not the disposal of many tools of the same kind. Thus the behaviour of a tool between grindings is considered to be

representative for a large hypothetic family of identical tools. According to statistical routine each individual can be listed in a way corresponding to the number of products made between grindings and next be labeled by its "plotting positionll

S I ide

S I ide

i-O.3 F(x.)

= .

0

4

100%

I J+.

where j refers to the size of the family and too 1.

(4.3)

indicates a particular

An actual example is given in the table, where j

=

7 and = 1,2, ... 7.

(Report WI 0349 table I).

Next it follows from eq. 4.1 that

1

In In 1-F{x)

=

8(lnx - Inn) (4.4)

which is the basis of plotting observations in a Weibul1 probability chart; if the distribution is Weibullian the plot must be a straight line.

(Report WI 0349 fig. 1).

Now it can mathematically be proven that the plotting position, as

discussed before, equals the cumulative percentage failure for a particular tool of the family; in other words when studying the Weibull plot obtained, that particular tool shows a probability of 10% to fail after having made 150.000 products, whereas this probability has grown to 90% after some 700.000 products.

The Weibul1 chart permits to estimate the relevant distribution constants. For this particular case the characteristic number is about 450.000,

whereas appl ication of nomography enables the reading of 8

=

1.8.

However, when knowing that the distribution is Weibul1 ian, this figures can be obtained more precisely by numerical computation.

In this way a great number of tools were investigated and the results are 'shown in the next table.

(Report WT 0349 table I I).

Now in order to apply this in the factory's management, one must realise that so far nothing is known about the average I ife time of a tool. From the table of results it can only be seen which operation is a "difficult" one, corresponding to a low value of characteristic number, or which is an "easy" one.

Thus of course, there must be a relationship between characteric number and average life time.

In deriving this quite a bit of mathematics is involved, however, basicly the theorem is applied which states that the sum of an adequate number of stochastic quantities, all of them following the same distribution law, approaches a normal distribution.

In the present case, where a tool between grindings obeys a Weibull distribution, the overall behaviour of a number of those tools approaches to a normal distribution, and it can be proven to hold for the average life time between grindings (in terms of number of products)

where r represents the Eulerian gamma-function.

For the variance of average life time is derived

(4.5)

(4.6)

From eq. 4.5 it becomes clear that the characteristic number n and the average number of products made are different things.

Now jf a lot of N products is to be manufactured with an accepted uncertainty a, which means that the probability to make the real

lot Nt equals

P (Nt ~ N)

=

1 - a

(4.7)

it can be derived that the number of grindings to be performed to produce the lot N with the given uncertainty is

(4.8)

where a determines the surface area of a standard normal distribution corresponding to the uncertainty limit a as accepted.

From the design of the tool the number of grindings is known when the tool is to be considered finally worn out, and hence the number of tools to manage the production of the lot N is known.

Based on this analysis a computer program has been developed. From the output it can be easily read how many grindings are to be performed for a given production volume N, whereas the uncertainty a is a parameter.

The method has been applied now for a couple of years and proved to be· of great value as a means for rational control of production cost.

Conclusion: In the present review it was shown that from basic understanding of a process in terms of a physical model and the corresponding mathematical formulation, conclusions can be drawn which are important for rational management of the factory.

In an analogous way, by combining the technological knowledge with analysis of the mechanical behaviour of presses and tools, directives can be given for optimum design of the tools.

---

---~---~

----.... -- ---...::..---

<i!---_Sl1\~NClW

_ ST",.

""a.

_ , ... eEQ

_LoAo

Q..

-

"\taD\OG~

~t''t."

",,''1.

El't

E,..,.et't£

ON

-r0&)\

' '?tt •

....-a."

_ TouI.

1)E.StQN _ ~'IUTtc

_ Taat.

"A1'1iJ\lA(

~\C'UO ..

_

1)\~TaRTlotrJ

_ lCOL

'Ie'lM:aIldBlIII

_ 1)O'fe,

_

1)n~to

..

Ti~

_

Wt4':11)oq

_

b~MA\"J~ ~ ActV\~

,T

wo","

c"GO~"tC'6

_

LtV!

T;

Itt.

oC\

NeT

_

"~"QA"aN

t'.. _

ACC".f\e~

o'F ~"tC\t~

, ••

?""NeT

"aa.~11l

•

life. .,' ...

_ A'ff'''..

of

,.au14

_ "ea..

"ft\09.,

AN

AL.Y,

U " ,

..

_

~OI

o...a

_to"'I"U\~

_

AM"OTn..,,\')~

..

~~ "r&D 0' . . . . QC.,,~

TOOL

•

_ 1e: ....

S1~.

-

, " . "

_.

.

_

eM"

'Pft\cti,

, , , , , a u ,

_

\0,.

t\'IE

_ AQ,""

...

1"aoL

_ c..4c..

_____ - ... ____

~

_____

....

1-C»\

"t~'t

L\'tt't\Y1e

O'P \)\

-e. •

~E1~

C

.\.1\:?

'~1"

,

,EN"tA'T\v1t

I

A~A~'\~

o'f

Co~t."\TuTINC

, f

'f',t. ...

0$

01=

\C-.MOW

L\t~1:.

IN CuLt:)

?utt.M'''''~

,

I?

A~..rr"Ct

\)1\.,

N

C.

A-r'ti!,~

\r

't.~1\~CJ..\OT

/

"",

\ ' S' , \,. "~-:-:-~-:--:-"":'+-:--::--~....,.---i\ ~. '

h"

_z

~

'!---,

.. _

-

---_._---Fig. 2. SIMPLIFIED DIAGRAM OF A BLANKING OPERATION.

0.1

tS\'

C.~ a~ o.{, o~8 1.0

f

Fig,

3.

The shear factor f_{sh '}

~

~

PT

,

...

a Q

...

.,,01 + 0 a

..

0 _tl + a.S

_s·

1 o~~=-~~X~

__

~~E-~-L~ ____ ~ __ ~~ () s Fig,

4.

The backpullforce F: as a function

It;

of the sheared length s5'

+ st 37 ; x C 45 ; • KMS 63 0 cu

STRESS DISTRIBUTION t IN PRESSURE ZONE a u

_b

OlE

F

Fig.

5.

PUNCH

FLANK WEAR BLANK

,,~. \ o.~

,

o.~ I o.~ I 0.:> I

(J.b

\

0.1

I u.c9

t.-0

,

•

0 .• 0,2 ~ I o.~

().'-t

0.-$

/' '10

=

o.Ot>

,

0.&

•

C l _ 1'Soo i''E -

-a •.

lO 4ft

~

=

0.3 ~lRn\NtiF\\lO'E.NiNC

.,

•

0.1

0.8 'Ex '?u ~~1'11'

0.,