Transcript Finite Element Simulation Of Profile Rolling Of Wire

Finite Element Simulation Of
Profile Rolling Of Wire
Author: R. Iankov
Presenter: Patrick Lewis
Date: September 15, 2008
Introduction
• Investigate profile rolling of wire using 2 finite
element model approaches.
– 3D
– 2D
• Compare model results to experimental data.
• Determine applicability to Profile Rolling
Industry
Introduction - Cont.
•
References
– W. Daves, F.D. Fischer, Drawing of a curved wire, in: Shen, Dawson (Eds.), Simulation of
Materials Processing: Theory, Methods and Applications, NUMIFORM’95, A.A. Balkema,
1995, pp. 693–698.
– W. Boris, A. Mihelic, Optimal design of the die shape using nonlinear finite element analysis,
in: Shen, Dawson (Eds.), Simulation of Materials Processing: Theory, Methods and
Applications, NUMIFORM’95, A.A. Balkema, 1995, pp. 625–630.
– A. Skolyszewski, J. Luksza and M. Pasko, Some problems of multi-stage fine wire drawing of
high-alloy steels and special alloys. J. Mater. Process. Technol. 60 (1996), pp. 155–160.
– T.H. Kim, B.M. Kim and J.C. Choi, Prediction of die wear in the wire-drawing process. J.
Mater. Process. Technol. 65 (1997), pp. 11–17.
– MSC.MARC2000, User Manual 2000, MSC.Software Corporation.
– Jan WINTERS Experimentele studie en alasto-plastische eindige-elementen-simulatie van de
materiaalvloei bij het platwalzen van staaldraad, Kuleuven, 1989–1990
– M.A. Grisfield, Non-linear Finite Element Analysis of Solids and Structures, vols. 1 and 2,
Wiley, New York.
Models & Design Principles
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Rolling is a metal forming process
where the work piece is placed
between opposing rollers.
Advantages over drawing:
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Little motion between rollers
High production speeds
No coating needed to improve
application of lubricant
Improved measurement and control of
the final product
No traction forces – no risk of a wire
break
No slippage between drawing disks =
no surface damage
Models & Design Principles Cont.
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Advantages of the Cold Rolling Process
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Higher productivity due to continuous rolling process
Tighter tolerances are attainable
Immediate detection of shape defects.
Driven rolling machines automatically pull the material
Finished wires can either be spooled or cut to length
with flying shears
Purposeful hardening of materials that can’t be
achieved through other processes.
Models & Design Principles Cont.
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Finite Element Model
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Used to predict the force parameters, as well as to
control and optimize many other parameters.
Advantages of the Finite Element approach:
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Elimination of physical modeling, as well as material and
energy costs of physical prototypes.
Optimization of the technological parameter of the forming
process.
“Choice of suitable material and predict the stress and strain
fields during the process, residual stresses in a final product,
damage evolution, strain localization, spreingback effect and
so on.”
Models & Design Principles Cont.
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Model Assumptions:
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Wire material is a continuum
Material is isotropic
Anisotropic effect due to high plastic
deformation is ignored
Quasi-static loading condition
Inertial effects are ignored
Material is elastic-plastic with hardening
Models & Design Principles Cont.
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The Mathematics
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Cauchy stress tensor (σ), Domain (Ω)
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Deformation gradient tensor (F)
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Dp = 3έpσ / (2 σy)
Friction Force (Ft), Coulomb friction coefficient (μ), Normal reaction force (Fn), Relative Sliding Velocity (vr),
Tangent unit vector (t)
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f = σ2 – σy2
Flow Rule, plastic strain rate (έp)
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D = De + Dp
σJ = C4 : (D – Dp)
Von Mises yield function (f), von Mises stress (σ), Yield stress (σy)
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ρcpT’ - λ∇2T = Qfσ : Dp + qf
Elastic (De) and Plastic (Dp) deformation rate tensor
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B = F * Fc
Thermal heat transfer equation
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L = D + Ω, D = .5(L + Lc), Ω = .5(L – Lc)
Cauchy Green strain Tensor (B)
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L = (∇0v)c = F’ * F-1
Deformation rate tensor (D), Spin tensor(Ω)
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F = (∇0x)c
Velocity gradient tensor (L)
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∇σ = 0,σ = σc
Ft = -μFn(2/π)arctan(vr/C)t
t = vr / |vr|, C = constant
Heat flux generated due to friction (qf)
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qf = Ft vr
Models & Design Principles Cont.
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Numerical Simulation
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3D Model
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Quarter of wire and two rolls are modeled by eight nodes isotropic finite element.
Rolls are assumed to be rigid bodies with prescribed rotating speed.
Each roll reduces the height/radius by 20%.
Wire length is 10x the radius.
Simulation performed one roll at a time.
2D Model
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Generalized Plain Strain (GPS) approach using 4 node finite element analysis.
Deformation zone lies between two bounding plates (move as rigid bodies).
Element is allowed to grow in the z-direction.
Simulation done with profile rolling of wire.
Material is elastic plastic with nonlinear hardening.
Each roll reduces the cross-sectional area by 12-15%.
Models & Design Principles Cont.
Results
Results Cont.
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3D Model
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Technique allows investigation
of the influence of roll
diameter, rotating speed, and
tension force on final lateral
spread of wire.
 Lateral spread of the crosssection can be predicted.
 Residual stress, equivalent
strain, strain rate and
equivalent stress distribution
are obtained.
 Fracture criteria can be
incorporated during the rolling
process.
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2D Model
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Equivalent plastic strain, total
strain and stress can be
obtained.
 Spread of material as a
function of the roll shape can
be controlled
Conclusions
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3D Model
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Application to a multi-pass profile leads to very
long computational time.
High accuracy is attainable
2D Model
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Shorter computing time and less computer
memory are required.
Useful when several passes are required
May reduce the number of industrial trials.
Conclusions Cont.
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No technical advancement
is created.
Study simply verifies that
the 2D FE approach is less
time intensive then the 3D
FE approach.
Study does not investigate
other programs, but does
show that it is possible to
predict the
behavior/outcome when
dealing with complicated
profiles.