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Tribological Aspects of Numerical Simulation of Deep-Drawing Process

Jozef Vyboch, Emil Evin, Jozef Kmec

Abstract

In this contribution the results obtained by FEM simulation and experiments are compared. Values of friction coefficients were experimentally obtained by cup test at change of blankholder pressure and size of blank.

Keywords: formability, FEM simulation, cup test, friction coefficient 1 Introduction

Formability of steel sheets (produceability of stamped part) depends on material properties (mechanical properties, microgeometry of contact surfaces), geometry of die and microgeometry of its contact surfaces, pressure of blank-holder, used lubricant, etc. By changing material properties the change of formability approx. 10-15 % can be obtained, by changing die geometry about 30-35 %, by changing friction ratios approx. about 35 %, and other effects can be obtained by changing sheet thickness, strain speed, etc. 1. Accurate determination of influence of single parameters on technological characteristics is problematic, because single parameters are changed from one case to another and also their share on formability is changed. To predict the influ-ence of material properties, geometry of die, stamping con-ditions on sheet formability is possible by simulation met-hods which enable us to optimise the utilisation of material properties under concrete conditions. The result of simula-tion depends on: - used material model, - accuracy and completness of simulation software, - accuracy and completness of material database, - accuracy and completness of tribological data etc. (e.g. restricting conditions).

Specialized CAE softwares for simulation of sheet metal forming processes use the explicit formulation of FEM for solution of motion equation of equilibrium they consider non-linear deformation history of sheet and for description of material behaviour the Hills condition of plasticity is used : f

1.

..1.2....

090

21209045

22211090

2220

21190

rr

rrrrrrr (1)

where: r0, r90, r45 are the values of normal anisotropy coefficients due to rolling direction.

Hardening of material is described by the Swift-Krupkowskys relation. Understanding the deformation his-tory enables us to include the criteria of material damage (thinning, curve of limiting deformation), creation of wrin-kling, pressure on contact surfaces, drawig forces, etc. into calculation.

By changing friction ratios of material couple sheet stamping die, the change of material flow can be expes-sively influenced in such range that the sheet which on the basis of values of mechanical properties shows unsuitability to production of concrete stamped part, at application of suitable lubricant shows required formability in some cases

i.e. it is suitable for production of concrete stamped part. And on the contrary, the material with excellent forming properties and unsuitable surface microgeometry at appli-cation of unsuitable lubricant may be in some cases unsuitable for production of given stamped part (it shows lower formability). At formability prediction it is important to define the friction ratios in die value of friction coef-ficient. Requirement for completness of information on friction ratios has arisen from the moment when for prediction of formability the simulation methods, new high strength materials, materials with various surface treatment started to be used. Tribological properties of these materials are different from those classical intended for deep drawing. It means, that what is suitable for classical steel sheets need not be suitable for sheets with applicated surface treatment- fig.1.

Fig. 1 C-E analysis of the tribological processes

Lubricants for deep drawing are selected according to combination of materials of friction couples, according to surface microgeometry of contact surfaces, size of stressing of contact surfaces and not at last measure according to influence on working environment and possibilities of their application and degreasing. Requirements on function of lubricants applied at stamping are contrary in many cases, however in the greater amount of cases the aim is decree-asing the friction, providing the quality of surface of both the formed part and die and influencing the flow of material by friction.

Database of lubricants for deep drawing should contain information on friction coefficients for various combina-tions of material couples, stressing, and drawing speed. In stamping processes the mixed friction occurs the most fre-quently. To restrict the rise of dry friction the lubricants with surface active substances (polar effective substances, high-pressure substances - EP-additives) are used which then provide adsorption and chemisorption. At incre-asing the pressure on contact surfaces in consequence of acting of

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additives the value of friction coefficient is constant or in some cases the decrease of friction coefficient values occurs.

Lubricity can be non-directly evaluated on the basis of dynamic and kinematic viscosity. For instance, the Burns equation describes the dependance of dynamic viscosity on pressure and temperature as follows:

Tpe ..0 . (2)

where: 0 - reference dynamic viscosity determined at reference temperature, - coefficient in dependance on pressure, - coefficient in dependance on temperature, p - pressure on contact surfaces, T - difference between working and reference temperatures.

Despite the great amount of various research works, for the state of mixed friction, the dependance of friction coef-ficient on lubricant properties and stamping conditions has not been physically described yet. For determination of friction coefficient for various lubricants and surfaces the model equipment is used simulators or technological tests that simulate the stressing of material in real stamping pro-cess.

2 Used methods and obtained results In the framework of national projects VEGA and

international project ENFORM the research for determi-nation of friction coefficient by various methods was carried out. For verification of the programme file PAM-STAMP applied for simulation of sheet metal forming processes the drawing force was used as a criterion because it sensitively reacts on the change of friction ratios at deep drawing. Dra-wing forces determined by simulation were compared with results obtained in deep-drawing process of cylindrical cups made of deep-drawable steel sheet B (type DC05) and zinc-coated sheet E Tab. 1. Used lubricant FERROCOAT A 6130 is the mixture of mineral oils, synthetic esters and additives with kinematic viscosity 26 mm2 /s at temperature 40o C.

Tab. 1 Material properties of tested materials

Mat

eria

l

Rol

ling

dire

ctio

n

Rp0

,2

[MPa

]

Rm

[M

Pa]

C

[MPa

]

n

R

0 164 299 505 0,23 1,9 45 172 309 531 0,219 1,5

A

90 166 296 511 0,221 2,2 X 168 303 531

0,006

0,228

0 170 292 492 0,208 1,98 45 180 304 503 0,203 1,04

B

90 184 297 487 0,215 1,59 X 182 300 497

0,008

0,207

X mean value For determination of friction coefficient the tester with

parallel jaws and drawing die for cylindrical cups were used.

On the basis of obtained results by tester the dependan-

ces of friction coefficient on pressure of jaws were descry-bed by following regression models:

material B lubricant FERROCOAT 2,0

0 . paf BB (3)

material E lubricant FERROCOAT 192,0

0 . paf EE (4)

Pressure of jaws was modeled in the range 1,5 MPa to 10 MPa.

For instance at pressure of jaws p = 2 MPa value of fric-tion coefficient at material B was fB = 0,131 and at material E was fE= 0,146.

Drawing conditions for cylindrical cup are given in Tab. 2. Friction coefficient in this case was determined by:

a) methodics based on the change of blankholder pres-sure at constant blank diameter (Fig. 2):

Fig. 2 Dependence of drawing force on blankholding force

).(2 1212

pp

tt

FFFFf

(5)

This relation was determined from condition of equili-brium of forces acting in deep drawing process and also at the assumption that friction coefficient on contact surfaces between sheet, blankholder and die is not changed (f1 = f2 = f3), angle of wrap of the die drawing edge in the moment of drawing force maximum is equal = /2. Measured va-lues of friction coefficients are given in Fig. 2 and Tab. 3.

Tab. 2 Conditions of experiment

Material of die

19 732 die steel according to Slovak Standard

Material of blankholder 12 061 Material of punch 19 732 Diameter of punch with flat bottom 32,85 mm

Radius of die edge of punch with flat bottom 4,5 mm

Radius of die edge of die 4,5 mm Clearance - flat bottom 1,57 mm Sheet metal thickness 0,8 mm Roughness of punch with flat bottom Ra = 0.8 m

Roughness of die Ra = 0.4 m Amount of lubricant 7g/m2

Tab. 3 Calculated values of friction coefficients

Drawing force [kN]

Blankholding force [kN] Mate-

rial Ft1 Ft2 Fp1 Fp2

Friction coefficient f

B 22,4 24 2 10 0,104 E 20,5 22,5 2 10 0,127

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b) methodics based on comparing the drawing force deter-mined at utilisation of reference lubricant Ftrto drawing force Ftij determined at utilisation of tested lubricant [1]:

trj

ijij F

F (6)

From the equilibrium condition of forces it is possible to express the increment of friction due to reference lubricant:

kf ijij

16,11

(7)

where: k = Fpij / Ftij Fpij blankholding force, Ftij drawing force, Ftrj drawing force at application of reference lubricant, i lubricant, j material. Then the final friction coefficient is:

ijrjij fff (8) Drawing forces were determined at drawing of

cylindrical cup with blank diameter D01=60, D02=65 and D03=70 mm. Course of drawing force determined by simulation of cylindrical cup made of material B and blank D01=60 mm is given in Fig. 2. Calculated and measured values od drawing forces at drawing of cups made of materials B, E are given in Tab. 4.

From Fig. 3 and Fig.5 result that dependances determi-ned on the basis of experimental results and obtained by simulation show a very good correlation of tendencies of dependances (slopes).

Fig. 3 Course of drawing force versus time - material B,

blank diameter D01 = 60 mm Difference between measured and calculated values can

be due to the fact that material properties were obtained at strain speed 0,0008 s-1 and drawing was carried out at strain speed 0,3 s-1. According to 2 if influence of deformation

speed at materials type DC 05 can be described by depen-dance of real stress on deformation speed by equation

0695,0. C , then at the speed change from 0,0008 s-1 to 0,3 s-1 the increase of strengthness about approx. 40 60 MPa occurs. Programme product PAM-STAMP enables us to include into calculation the influence of deformation speed. Taking into account the influence of deformation speed the differences between measured and calculated values approx. 5 % may be expected.

Fig. 4 Dependance of drawing force on blank diameter

EN-measured values, ES-calculated values

Fig. 5 Dependance of drawing force on blank diameter

EN-measured values, ES-calculated values

3 Summary From measured results there can be stated: 1. Difference between measured and calculated values of

drawing forces is approx. 20 % without including the influence of deformation speed. Measured values of dra-wing forces in comparison to values obtained by simu-lation were higher.

2. Obtained results show that programme product PAM-STAMP enables us to simulate the influence of parame-ters of deep drawing process with acceptable accuracy, however it is required countinuously to make more ac-curate the input material and technological data.

3. Obtained results show also the fact that by combination of both the simple tester tests and technological tests the values of friction coefficients for various combinations of stamping conditions can be determined, however it is necessary to define the accurate conditions of experi-ment.

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4. PAM-STAMP enables us to predict the pressure on contact surfaces between die and sheet and by this the optimisation of experiment conditions may be carried out, and also the selection of suitable lubricant for concrete technological process.

Acknowledgement This article was created by implementation of the pro-

ject "Centre for Management Research technical, environ-mental and human risks for sustainable production and pro-ducts in engineering" (ITMS: 26220120060), by supporting operational program Research and development program financed from the European Regional Development Fund. The authors the work gratefully acknowledge for the financial support of the Scientific Grant Agency of the Slovak Republic (VEGA 10890/09).

Vyboch Jozef, M.Sc., Faculty of Mechanical Engineering

of the Technical University of Kosice, Msiarsk 74, 040 01 Kosice,

Slovak Republic E-mail: jozef.vyboch@tuke.sk

Prof. Evin Emil, M.Sc., PhD., Faculty of Mechanical Engineering

of the Technical University of Kosice, Msiarsk 74, 040 01 Kosice,

Slovak Republic E-mail: emil.evin@tuke.sk

Kmec Jozef, RNDr., PhD., Faculty of Manufacturing Technologies of the

Technical University of Kosice with a seat in Presov, Bayerova 1, 080 01 Presov,

Slovak Republic E-mail: jozef.kmec@tuke.sk

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Continued from page 37 Acknowledgement

Presented results have been obtained within research project, realized in years 2009-2011, financially supported by Polish Ministry of Science.

Prof. Zbala Wojciech, M.Sc., Dr hab.,

Cracow University of Technology, Faculty of Mechanical Engineering,

Production Engineering Institute, Department of Machining and Processes,

al. Jana Pawa II 37, 31-864 Krakw, Poland,

zebala@mech.pk.edu.pl,