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Journal of Materials Processing Technology 213 (2013) 2015– 2032

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

jou rn al hom epage: www.elsev ier .com/ locate / jmatprotec

umerical modelling of powder metallurgical coatings oning-shaped parts integrated with ring rolling

. Kebriaeia,∗, J. Frischkorna, S. Reesea, T. Husmannb, H. Meierb, H. Moll c, W. Theisenc

RWTH Aachen University, Institute of Applied Mechanics, Mies-van-der-Rohe-Str. 1, D-52074 Aachen, GermanyRuhr-Universität Bochum, Chair of Production Systems, Universitätsstraße 150, D-44780 Bochum, GermanyRuhr-Universität Bochum, Chair of Material Technologies, Universitätsstraße 150, D-44780 Bochum, Germany

r t i c l e i n f o

rticle history:eceived 2 August 2012eceived in revised form 23 May 2013ccepted 27 May 2013vailable online 11 June 2013

eywords:inite element simulationing rolling

a b s t r a c t

Today’s demands for flexible and economic production of ring-shaped work pieces coated by functionallayers can only be met by new manufacturing techniques. These are suitably based on precise processmodelling and high-performance control systems. The process-integrated powder coating by radial axialrolling of rings introduces a new hybrid production technique. It takes advantage of the high tempera-tures and high forces of the ring rolling process. This is not only to increase the ring’s diameter, but alsoto integrate powder metallurgical multi-functional coatings within the same process. To improve thefeasibility assessment of the proposed geometries and material combinations as well as to investigateimportant quantities such as the stress state in the rolling gaps and the residual porosity of the powder

owder coatingontrol mechanismunctional layer

metallurgically produced layer, the versatile application of the finite element method (FEM) is crucial.Therefore, parameterized two-dimensional and three-dimensional finite element (FE) models are cre-ated. It will be shown that the implementation of a new control mechanism based on Apollonian mutuallyorthogonal circles and bipolar coordinates allows an efficient stabilization of the proposed systems. Thepaper is concluded by a detailed description of the process simulation and a comparison of its resultswith experimental data.

. Introduction

Ring rolling represents an incremental forming process which issed to manufacture precisely dimensioned seamless rings. Its firstcientific developments were made in the 20th century (Harbordnd Hall, 1923; Weber, 1959). Typical applications can be foundn aerospace, automotive and railroad industries (Johnson et al.,968), e.g. rings for railway wheels and tires (Tiedemann et al.,007). Additionally, the potential of a novel incremental ring rollingrocess which allows a flexible near-net-shape forming of both hotnd cold rings is presented by Allwood et al. (2007).

In many applications, it is advantageous to equip the rolled ringith a wear resistant smart functional layer (German, 2005; Moll

t al., 2007). Examples are the rolls in crushing and briquetting millssed in mineral industries. There are several techniques availableo manufacture these coatings. One example is thermal spraying

tudied, e.g. by Haefer (1987) and Kuroda et al. (2008). This coatingrocess has several variations such as plasma spraying proposed byach et al. (2004), flame spraying presented by Bach et al. (2000)

∗ Corresponding author. Tel.: +49 241 80 25012; fax: +49 241 80 22001.E-mail addresses: reza.kebriaei@rwth-aachen.de, rezakebriaei@gmail.com

R. Kebriaei).

924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.jmatprotec.2013.05.023

© 2013 Elsevier B.V. All rights reserved.

and detonation spraying investigated and utilized by Haefer (1987),in which melted materials are sprayed onto the proposed surface.However, the created coatings are not thick enough to be applied inbriquetting machines used in mining and mineral industries. Addi-tionally, long process times and high process cost are disadvantagesof these methods (Berns et al., 1993).

Another famous technique related to wear resistant coatingis hot isostatic pressing (HIP) which is performed by Helle et al.(1985). This manufacturing process is used to produce near-net-shape devices from metal powder that exhibit almost no residualporosity (Tanaka et al., 1989). In comparison to cold compaction ofmetal powder, which is usually followed by pressureless sintering,the risk of cracks caused by residual stresses is much lower withinthe HIP process. However, the size of available HIP plants can onlyhouse rings with a diameter up to 1.6 m and a height up to 2.5 m(German, 2005). Due to the poor availability of large HIP plants, longprocess times and high logistic costs have to be taken into account.

Hence, there is a need for a novel and innovative productiontechnique to overcome these disadvantages. Kopp et al. (2004a)study the joining of functional steel parts with a steel component

during thixoforming in one process step. In another paper, Koppet al. (2004b) propose forming of metals in the semi-solid state andinvestigate the mechanical properties for three groups of materialsas, e.g. thin film deposited by physical vapor deposition, plasma

2 cessing Technology 213 (2013) 2015– 2032

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016 R. Kebriaei et al. / Journal of Materials Pro

ssisted chemical vapour deposition and bulk ceramic materials.ollowing these ideas, a new ring rolling technology is developedy Meier et al. (2007) and Theisen et al. (2007).

In this new process, the integration of the compaction processnto the rolling stage is thought to break the limitations that comelong with the mentioned coating processes. The created prod-cts can have a diameter up to 12 m and a height up to 2.8 m.lthough this novel process is reasonably efficient with respect

o energy, process time and costs, there exists some difficulties.he encapsulation has to maintain vacuum conditions and con-entional rolling strategies are not applicable. Furthermore, theeometrical design (influence of chamber’s design on the rollingnd compaction behavior), constructional aspects (type and posi-ion of welding seams to ensure the required mechanical strengthnd stability under load and filling solution) and processing aspectssurface processing parameters, cleanliness of all surfaces and qual-ty of the welding seams) are additional difficulties which have toe overcome.

To support the design of this new process and to predict thenfluence of several geometry and process parameters on the resid-al porosity in the layer, parameterized FE models are developed.igh computational run time is a well known problem in the sim-lation of the ring rolling process (Davey and Ward, 2002a). Toeduce the computational effort, Hu and Liu (1992) study the con-equences of working with a 2D plane strain model. Additionally,he use of hybrid meshes (Hellmann et al., 2000) in combinationith arbitrary Lagrangian–Eulerian (ALE) techniques are investi-

ated by Davey and Ward (2000) and Davey and Ward (2002b).y applying the ALE formulation the mesh distortion is indepen-ent of the material flow. In this way, a fine mesh needs to be onlyaintained in the rolling gap.An important issue of ring rolling research is concerned with

ystem stabilization. An analysis of the guide roll forces is presentedy Johnson and Needham (1968). Kopp et al. (1984) introduce a con-rol algorithm based on geometrical and kinematical relations ofolls and the ring in the process. This control mechanism is appliedxperimentally. The kinematical relations between the deforma-ion and the ring’s geometry in order to control the process withespect to the feed speed of the rolls are presented by Koppers andopp (1992). A comprehensive overview of applicable strategies

or controlling the ring rolling process is demonstrated by Allwoodt al. (2005). Additionally, there are several studies which are pub-ished by Guo et al. (2004), Hawkyard et al. (2007) and Li et al.2008) related to the control of the guide roll movement.

These mechanisms work well for the systems including a soliding. However, they are not well applicable for rings coated byulti-functional surfaces with non-isochoric plastic deformation.

he basic ideas related to the analysis of the guide roll forces forhe rings coated with porous materials are presented by Kebriaeit al. (2013). In that study only a 2D plane strain model is inves-igated. Therefore, this control mechanism is now improved to bepplicable to 3D simulations and practical investigations. In con-rast to the previously mentioned authors our control algorithms combined with a FE model. Additionally, we introduce a specialechnique to control and to stabilize the process based on informa-ion of the current stroke of the hydraulic cylinders that actuate theuide rolls.

In the paper we study different models including a large vari-ty of geometries for the simulation of the ring rolling process.e demonstrate the influences of the layer material as well as

arious roll geometries and well-defined ring relocations on theompaction behavior.

The paper is structured as follows. In Section 2 the principlesf the process-integrated powder coating are discussed. After thatn Section 3, the material model which describes the sintering andompaction of the metal powder will be introduced. In Section 4,

Fig. 1. Principle of ring rolling.

the setup of the FE model is discussed. Section 5 is devoted to thedevelopment of a novel control mechanism for the guide roll move-ment in order to reach a stable ring position throughout the process.The significant effect of the applied control mechanism on the ringroundness and the ring rolling stability is then subject of the firstpart of Section 6. This is followed by an investigation which meshdensity is required to obtain converged results. Additionally, westudy the influence of working with the assumption of plane straininstead of a fully three-dimensional model. Moreover, the effect ofdifferent ring and roll geometries as well as the well-defined relo-cation of the ring on the residual porosity in the layer is presentedin this section. The paper closes with some concluding remarks.

2. Process-integrated powder coating

The principle of the rolling process is sketched in Fig. 1. Themandrel pushes the ring towards the main roll which is driven byan angular velocity. Friction between the ring and the main rollas well as between the ring and the mandrel lead to a rotation ofthe ring. By decreasing the radial rolling gap the ring growths intangential and in axial direction. In the opposing axial rolling gapthe height of the ring is controlled and reduced by the axial rolls.

In the new process, a sheet metal is welded circumferentiallyaround the outside of an unrolled ring blank. Powder layer mate-rial (metal matrix composite, MMC) is placed inside the resultingchamber (see Kebriaei et al., 2013). The powder chamber is exposedto nitrogen atmosphere and is evacuated afterwards. Then the ringis heated up to approximately 1150 ◦C. This temperature is main-tained for 4–6 h in order to perform sintering of the metal powder.In this way the powder particles are connected to each other bysinter bridges. Next, the rolling of the ring is performed. This startsat temperatures of about 1100 ◦C. The encapsulation has to main-tain the vacuum conditions until the compaction of the layer hasreached the point of closed porosity, i.e. that the pores are sepa-rated from each other. Otherwise oxidation of the layer materialmay occur.

3. Constitutive modelling of metal powder

3.1. A pressure sensitive model of viscoplasticity

The model used to describe the compressible layer material isbased on a finite strain elasto-plastic material formulation. Sincethe process takes place at high temperatures rate dependence hasto be taken into account. The kinematic framework is based on themultiplicative split of the deformation gradient F into elastic ( Fe)and plastic ( Fp) parts. The free energy per mass is additivelydecomposed into the two parts s and p. The energy stored in thesolid skeleton is considered by s while p accounts for the free

surface energy due to the porosity of the material. The presenceof p is important to model sintering effects, i.e. a temperaturedriven densification under the absence of an external load. Specificforms of p are introduced, e.g. by Mähler and Runesson (2000) and

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2017

l at d

Msdts

�

Itm(msdcc

wttdss

�

wj

�

Fig. 2. Yield curves of the substrate (encapsulation) materia

ähler and Runesson (2003) by making an assumption about thehape of the pores. The specific free energy part, p is assumed toepend on the relative density �r. To define �r we further introducehe so-called average density � of the mixture including the solidkeleton and the gas filled pores:

= ns�s + np�p ≈ ns�s (1)

n the latter relation �s is the current density of the solid skele-on. The current density of the gas inside the pores �p is in general

uch smaller than �s. Therefore, we can neglect the term np�p in1). The volume fractions of the solid skeleton and the pores at a

aterial point are given by ns and np, respectively. Additionally, theaturation condition ns + np = 1 holds. The relative density �r is thenefined as the ratio between the average density in the deformedonfiguration to the density of the metal powder in the undeformedonfiguration �r = �/�s0.

The free energy per mass is finally defined as

= s + p(�r) (2)

here s = e( be) + i(�). e represents the elastic strain energyhat is defined in terms of the elastic part of the left Cauchy-Greenensor be = Fe FTe . The inelastic energy due to isotropic hardening iepends on the accumulated plastic strain �. Besides the standardtress quantities like the Kirchhoff stress tensor � and the dragtress R

= 2�0∂ e∂be

be, R = −�0∂ i∂�, (3)

e find the so-called sintering stress �s as thermodynamically con-

ugate to the relative density.

s = −�0∂ p∂�r

�r (4)

ifferent strain rates: (a) 900 ◦C, (b) 1000 ◦C, and (c) 1100 ◦C.

Defining � by � = � − �s I leads to the reduced form of the internaldissipation inequality

� ·(

−12L�be b−1

e

)+ R � ≥ 0 (5)

from which the corresponding evolution equations for the internalvariables are deduced:

−12L�be b−1

e = �∂�∂�, � = �

∂�∂R, � = 1

v

⟨�

�0

⟩mv

(6)

The Lie derivative Lvbe is a short hand notation for the product

Lvbe = F C−1p FT . The internal variables are the plastic right Cauchy-

Green tensor Cp = FTpFp and the accumulated plastic strain �. In thelimit case of rate independent plasticity, i.e. zero viscosity v, thevariable � plays the role of a Lagrange multiplier defined by theKarush-Kuhn-Tucker conditions � ≥ 0, � ≤ 0, �� = 0. Exploitingthe balance of mass and neglecting elastic volume changes (whichare usually very small in case of metal plasticity) the current relativedensity can be approximated by �r ≈ �r0/detFp. To have an effecton the relative density during plastic deformation we introduce apressure sensitive yield function:

� = ı�

(�y0

�y0 − R

)232

‖�′‖2 + �

13

〈 − tr �〉2 − �2y0, ı�

= 1 + ıf (1 − �r)ıe , � = f (1 − �r)e (7)

Herein, �y0 denotes the initial uniaxial Kirchhoff yield stress. Thefunctions ı� and � that weight the deviatoric and the hydrostaticstress states are chosen such that the influence of hydrostatic stress

states vanishes if the relative density approaches 1. Hence, in caseof full compaction, the yield function approaches the standard vonMises form. The described material model is implemented intoAbaqus via a user material subroutine VUMAT. A comprehensive

2018 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

Table 1Material parameters for the substrate (encapsulation).

Parameter �[kg/m3] E [MPa] �

900 ◦C 7330 85,000 0.3301000 ◦C 7300 50,000 0.3361100 ◦C 7260 12,000 0.340

Fpt

dasJAag

3

tmIswssmtcmt(hahd

Tsrs

Table 3Identified material parameters that control the densification behavior.

Material ıf ıe f e

TC

ig. 3. Principle of the closed die compression test. A porous cylindrical specimen islaced inside a cylinder. This casing suppresses the transversal material flow duringhe compression.

escription of the above material model can be found in Frischkornnd Reese (2012). Additionally, for the substrate and the encap-ulation (sheet metal) the same material model is used. It is a2-plasticity model with isotropic hardening which is offered bybaqus. The corresponding yield curves at different strain ratesre given in Fig. 2. Moreover, elasticity and density parameters areiven in Table 1. Further details can be found in Meier et al. (2008).

.2. Material model validation – closed die experiments

Closed die experiments on pre-sintered specimens made ofhe powder layer material are utilized in order to validate the

aterial model and to find appropriate material parameters.n this test a cylindrical specimen is put into a cylinder thaterves as casing. The specimen is then compressed by two dieshile the casing suppresses any bulging of the specimen. Fig. 3

ketches the experimental setup. In this way large hydrostatictress states can evolve and a considerable densification of theaterial is reached. The process takes place at elevated tempera-

ures. Therefore, it is carried out inside a dilatometer under vacuumonditions in order to avoid an oxidation of the porous layeraterial. Experiments are performed at three different tempera-

ures (900, 1000, and 1100 ◦C) and at four different die velocities0.01, 1.0, 5.0, and 10.0 mm/s), respectively. The specimen itselfas a length of 3 mm and a diameter of 2.5 mm. In order tochieve homogeneous warming of the specimen the temperatureas been hold constant for about 5 min before the specimen iseformed.

In addition, two different powder materials are investigated.

hese are a hot work tool steel X40CrMoV5-1 and a cold work toolteel X220CrVMo13-4. While the cold work tool steel is the mate-ial of choice with regard to the wear properties, the hot work toolteel has become attractive from the process development point

able 2hemical combination of the applied materials.

Material Chemical composition

C Cr Ni Mo

56NiCrMoV7 0.55 1.10 1.70 0.50

X40CrMoV5-1 0.39 5.15 – 1.35

X220CrVMo13-4 2.30 12.50 – 1.10

1.2380 1.177 3.914 15.140 0.9201.2344 1.000 22.010 23.070 0.290

of view. This is because its forming resistance lies between that ofthe substrate, which is made of another hot work tool steel 56NiCr-MoV7, and the cold work tool steel. Details on these materials aregiven in Table 2. The cylindrical specimens are produced by sinter-ing of the corresponding powder material for 4 h at 1150 ◦C. Therelative density of the sintered specimen is approximately �r = 0.7(Moll, 2009).

The resulting response curves (true stress over stretch) are usedto identify the parameters of the material model. In the simula-tion of the closed die experiment, to model the experiments in away as simple as possible, we neglect the friction between the cas-ing and the specimen. This allows us to consider a homogeneousdeformation of the specimen given by the deformation gradient.The deformation gradient F can then be specified as shown in

F =

⎡⎢⎢⎢⎢⎣

L0 − u

L00 0

0 1 0

0 0 1

⎤⎥⎥⎥⎥⎦ (8)

Herein, L0 is the undeformed length of the specimen and u theapplied die displacement. This has the advantage that we donot need the finite element method to compute the responseof the model. An optimization procedure offered by the numeri-cal computing software MATLAB is applied to identify the modelparameters and to match the experimental response curve. Herewe only consider the experiments at a die velocity of 1 mm/s.Fig. 4 shows the resulting values for the yield stress, the harden-ing modulus and the viscosity in dependence of the temperature.The parameters ıf, ıe, f and e are assumed to be temperatureindependent. Their values are given in Table 3.

A comparison of the experimental response curves and theresults of the simulation based on the identified parameters is givenin Fig. 5 for both layer materials at three temperatures, respec-tively. The ordinate shows the true stress in axial direction andthe abscissa the stretch in this direction. The symbols representthe experimental values. The simulation results are given as lines.The relative density at the end of the compaction lies above 95%in the experiment as well as in the simulation for all investigatedmaterials and temperatures.

The model overestimates the slope of the response curves at theend of the compaction process. This might be a result of neglectingthe friction in the simulation. Looking at the simulation results for1100 ◦C one can observe a little overshoot in the beginning of thesimulation. This is possibly due to increased rate dependence at

this temperature. The maximum relative difference between theexperiment and the model is 7.9% for the cold work steel and 2.8%for the hot work steel. Altogether, the material model matches theexperimental material response quite well.

Material number

V Mn Si

0.10 0.75 0.25 1.27141.00 0.38 1.00 1.23444.00 0.40 0.40 1.2380

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2019

ateria

4

c

Fh

Fig. 4. Temperature dependence of material parameters for the layer m

. Finite element model

The finite element simulations of the ring rolling process arearried out on the basis of two- and three-dimensional finite

ig. 5. Compression test, experiment (e.) vs. simulation (s.): (a) cold work steel, (b)ot work steel.

ls: (a) initial Kirchhoff yield stress, (b) hardening modulus, (c) viscosity.

element (FE) discretizations. The FE geometries are parameterizedwith respect to geometry and discretization. The reason for usinga two-dimensional discretization is to save run time especiallywhen parameter variations are performed. The overall change inthe height of the ring is very small in the first half of the timeperiod of the experimental process. In this time period the powdercompaction takes place. Therefore, the plane strain assumption isapplied in the whole time period. Clearly, in the real process thereis first an increase of the ring’s height within the radial rollinggap before the height is decreased again in the axial rolling pass.Consequently the stress and deformation states computed in theplane strain model will differ from those of the three-dimensionalmodel. To evaluate whether the two-dimensional model is ableto predict the influences of, e.g. the geometry parameters onthe resulting stress and strain as well as residual porosity, com-parative simulations using the two- and three-dimensional FEdiscretization are carried out (see Section 6.3).

Fig. 6 shows the two-dimensional model. All rolls are repre-sented as rigid bodies. The corresponding masses, inertias andboundary conditions are defined at the reference points locatedin the center of the rolls. The motion of the guide rolls is controlledby the center arms. Each center arm is defined by two rigid links(length l1 and l2, fixed angle ı) and is simply supported at C andG, respectively. The guide rolls can freely rotate. On the right handside the center arms are connected to ground through dashpots. Anangular velocity ˝mr is applied at the main roll and the horizontaldisplacement of the mandrel uma is prescribed. The ring itself showsa discretization of the substrate, the layer and the encapsulation.Its position is defined by means of the relocation angle which iszero at the start of the analysis. In the two-dimensional model theposition of the ring can be influenced through the guide rolls byspecifying appropriate forces FB and FF at B and F, respectively.The determination of appropriate forces will be treated in Section 5.

The rolls are in contact with the ring. The friction force at thecontact zones has two main components which are in the nor-mal and the tangential directions (Bay and Wanheim, 1976). UsingCoulomb’s friction law with a penalty formulation lets us to define

2020 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

Table 4Anchor points of the rolling plant.

point A [mm] C [mm] E [mm] G [mm] I [mm]

(x/y) (800/400) (300/200) (800/−400) (300/−200) (0/0)

Table 5Parameters that define the rolling plant of the two-dimensional model.

Parameter l1 [mm] l2 [mm] ı [◦] rmr [mm] rma [mm] rgr [mm]

Value 200 700 75 225 65 100

Table 6Parameters that define the ring geometry of the two-dimensional model.

Parameter rri [mm] tsu [mm] tla [mm] tec [mm] nc nrsu nrla nrec

Value 122.5 47.5 14 3 300 10 3 1

nsion

tldT

sTe

Fig. 6. The two-dime

hese two components appropriately. Moreover, Coulomb’s frictionaw is well suitable for the modelling of stress states developinguring the localized shear at the rolling gaps (Marone et al., 1992).he frictional contact coefficient between the ring and the rolls isf = 0.3.

The anchor points of the rolling plant are given in Table 4. Table 5ummarizes the remaining parameters that define the rolling plant.he ring geometry and its discretization is controlled by the param-ters given in Table 6. In particular these are the inner radius of

Fig. 7. Experimental ring (a) and three-d

al ring rolling model.

the ring (rri), the thickness of the substrate (tsu), the layer (tla)and the encapsulation (tec). The FE discretization is specified bymeans of the number of elements in circumferential direction (nc)as well as the number of elements in radial direction for the sub-strate (nrsu), the layer (nrla) and the encapsulation (nrec). Fig. 7(a)

illustrates the different parts of the experimental ring. Based onthe experimental setup the FE model is established. Fig. 7(b)shows the three-dimensional FE discretization of the ring rollingmodel.

imensional ring rolling model (b).

cessing Technology 213 (2013) 2015– 2032 2021

cerftdHac

TAu

5

5

lsotmfts

tFttvf

aobtvtToblodnb

cdthmem

nhiptsfi

analytically and does not need to be treated within the blackbox of the control unit. Moreover, the guide roll forces will belimited in order to avoid a deformation of the ring (Allwood et al.,

R. Kebriaei et al. / Journal of Materials Pro

In the experimental tests using the ring rolling machine, theharacteristics of the upper and the bottom cone rolls as, e.g. geom-try and velocities are assumed to be the same. It means that theeal system is symmetric from the mechanical point of view. There-ore, to reduce the number of degrees-of-freedom, only a half ofhe ring’s height is discretized. Further symmetry conditions in y-irection are used at the midplane of the ring in 3D simulations.owever, the effects of the gravity force are neglected here. Inddition the cone roll that defines the axial rolling pass is alsoonsidered.

Both models were built up using the FE program system Abaqus.he computations are carried out using the dynamic explicit codebaqus/Explicit. Herein the ALE method provided by the code issed in order to reduce the mesh distortion throughout the analysis.

. Control mechanism

.1. Motivation

As it is already mentioned in Section 1, there are several pub-ications which are related to the control of guide roll forces andystem stability. Johnson and Needham (1968) study the rollingf different rings with various speeds. Using the information abouthe rolls’ force and torque (Johnson et al., 1968) create a ring rolling

achine in which the guide rolls are controllable. Afterwards, theundamental systematic design and kinematical relations betweenhe deformation and the ring’s geometry with respect to the feedpeed of the rolls are presented by Kopp et al. (1984).

Recently, the problem of defining appropriate guide roll forces isreated for solid rings by Li et al. (2008) within a three-dimensionalE simulation. They relate the mass flow rate m of the fluid insidehe hydraulic ram to the guide roll movement. However, they needo perform a number of process simulations to find appropriatealues for m. Additionally, the obtained m is not necessarily validor different configurations.

In summary, the suggested control techniques in the literaturere based on kinematical relations which connect the displacementf the mandrel and the angular velocity of the main roll. This isased on the assumption of volume constancy of the ring. Usinghese informations the position of the guide rolls and the angularelocity of the axial roll can be determined. However, this assump-ion is not valid for a compound ring with a compressible layer.he first part of the rolling process is governed by the compactionf the layer material. Thereby even a decrease of the ring radius cane observed. During the compaction the forming resistance of the

ayer material increases. At the point when the forming resistancef substrate and layer are on the same level an increased substrateeformation takes place and significant ring growth sets in. Hence,ew control mechanisms are needed to incorporate the differentehavior in this new process.

More recent studies are related to online measurement of theurrent shape and position of the ring using optical measurementevices (Kneissler, 2009; Meier and Briselat, 2010). On the one handhe protection of the image optical processing hardware againsteat and steam is not easy. On the other hand, the precision of theeasurement results due to missing data for detecting the process

rrors or unwanted ring deformations is lower than in conventionaleasurement systems.Therefore, in this paper we introduce a new control mecha-

ism which only needs information about the current stroke of theydraulic cylinders that actuate the guide rolls. This information

s easy to gather compared to optical measurements of the ring’s

osition which makes it also attractive for experimental applica-ion. Here, the control mechanism is used in conjunction with FEimulations of the ring rolling process. To our knowledge this is therst approach to provide FE-based ring rolling simulation which

Fig. 8. Relation of Apollonian circle to the ring rolling system.

includes a fully integrated control mechanism to guarantee thestability of the system.

5.2. Working principle

The control mechanism is based on the determination of thecurrent ring center xK (point K in Fig. 6) and the outer ring radiusrro. The current values of xK and rro can be efficiently determinedusing the theory of Apollonian circles if the current guide roll posi-tion at the inlet xD and at the outlet xH is known. The precision ofthe method depends on two conditions. First, the guide rolls haveto maintain contact with the ring and secondly, the ring must beideally circular in shape. These conditions are usually fulfilled atthe beginning of the rolling analysis. Hence, as long as the con-trol mechanism works with sufficient accuracy, the validity of thedetermination of xK and rro is given.

The sensors in Fig. 6 provide the current positions of the centerarm hinges xB and xF, where the forces of the hydraulic units areinduced. With that the position of the guide rolls is easily computedby considering the kinematics of the center arms. Next, the currentring center and ring radius can be determined providing the activerelocation angle ˛. In the next step the desired guide roll positionsx′D and x′

H that yield the prescribed relocation angle � can be com-puted which finally yield the desired values x′

B and x′F at the center

arm hinges.Now, we calculate appropriate values for FB and FF by means

of a proportional–integral–derivative control unit (PID) in order tominimize the errors eB(t) = x′

B(t) − xB(t) and eF (t) = x′F (t) − xF (t)

(cf. Fig. 9). The geometrically nonlinear kinematics is considered

Fig. 9. The configurations of the rolling plant with respect to the current ring posi-tion (solid lines) and the desired ring position (dashed lines).

2 cessin

2Eltroi

5

wtleWtFah

(

(

(

so

a

a

w

a

a

d

d

S

x

Pv

e

e

f

f

f

− 2 g3(g1 xK + g2 yK ) − g23 }. (36)

022 R. Kebriaei et al. / Journal of Materials Pro

005). The determination of the maximum forces is based on theuler–Bernoulli beam theory. This is not an appropriate but ateast a conservative assumption at the start of the rolling wherehe wall thickness of the ring is relatively large compared to theadius. The assumption becomes more appropriate in the coursef the process since the wall thickness reduces and the radiusncreases.

.3. Current ring center and ring radius – Apollonian circles

In order to determine the current center and radius of the ringe search for a circle that touches the main roll and the guide rolls

angentially. In mathematics this problem is known as the prob-em of Apollonius (Grinberg and Yiu, 2002). In general there existight possible solutions to the problem (see Kebriaei et al., 2013).ithin the problem at hand we are only interested in the solu-

ion where the desired circle lies inside the given three circles (seeig. 8). Mathematically spoken, the distance between the center of

given circle (black) and the center of the unknown circle (blue)as to be equal to the sum of their radii:

xK − xI)2 + (yK − yI)

2 − (rro + rmr)2 = 0 (9)

xK − xD)2 + (yK − yD)2 − (rro + rgr)2 = 0 (10)

xK − xH)2 + (yK − yH)2 − (rro + rgr)2 = 0 (11)

Now, by subtracting (10) from (9) and (11) from (10), it is pos-ible to transform the nonlinear system of equations into a linearne

1xK + b1 yK = d1 − c1 rro (12)

2 xK + b2 yK = d2 − c2 rro (13)

hereby the following abbreviations have been used:

1 = 2(xD − xI), b1 = 2(yD − yI), c1 = 2(rgr − rmr) (14)

2 = 2(xH − xD), b2 = 2(yH − yD), c2 = 0 (15)

1 = x2D − x2

I + y2D − y2

I + r2mr + r2gr (16)

2 = x2H − x2

D + y2H − y2

D + 2 r2gr (17)

olving the linear system of equations for xK and yK yields

K = b1d2 − b2d1 + b1c2rro − b2c1rroa1b2 − b1a2

,

yK = −a1d2 + a2d1 − a1c2rro + a2c1rroa1b2 − b1a2

(18)

lugging xK and yK back into, e.g. (9) and using the following abbre-iations

1 = b1 d2 − b2 d1, e2 = b1 c2 − b2 c1, e3 = a1 d2 − a2 d1

(19)

4 = a1 c2 − a2 c1, e5 = a1 b2 − a2 b1 (20)

1 = e1 e2 + e3 e4 − e25 rrm − e2 e5 xI − e4 e5 yI (21)

2 = e21 + e2

3 − e25(r2mr − x2

I − y2I ) − 2 e1 e5 xI − 2 e3 e5 yI (22)

3 = e22 + e2

3 − e25 (23)

g Technology 213 (2013) 2015– 2032

we find the current ring radius given by

rro = −f1 +√f 21 − f3 f4f3

(24)The current guide roll positions have to be computed using theinformation of the position sensors located at B and F, respectively:

xD = xC + Rı+ (xB − xC )l2l1, xH = xG + Rı− (xF − xG)

l2l1

(25)

Rı+ and Rı− are rotation matrices in order to perform a rotationabout the z-axis with the angles +ı and −ı, respectively.

5.4. Relocation of the ring

After the current center and radius of the ring have been deter-mined we need to compute the new positions of the ring and theguide rolls in order to satisfy the desired ring relocation angle � (cf.Fig. 9). By assuming that the ring radius stays constant throughoutthe relocation we find the new ring center given as

xK ′ = (rmr + rro) sin ϕ, yK ′ = (rmr + rro) cos ϕ (26)

The relation between the prescribed angle � and the angle ϕ, thatis needed to determine the new ring center position, leads to thefollowing equation

tan � = yK ′

||xK ′ || − ||xI || − rmr= (rmr + rro) sinϕ

(rmr + rro) sinϕ − ||xI || − rmr(27)

Eq. 27 can be solved for ϕ which yields

ϕ = arcsin

(− 1

2 tan�+

√1 − ||xI || + rmr

rmr + rro+ 1

4 tan2�

)(28)

Next, we need to find the corresponding new center positions ofthe guide rolls. Again, we set up the equations that describe thedistance between the ring center and each guide roll center:

(xK ′ − xD′ )2 + (yK ′ − yD′ )2 − (rro + rgr)2 = 0 (29)

(xK ′ − xH′ )2 + (yK ′ − yH′ )2 − (rro + rgr)2 = 0 (30)

Since the guide rolls can only move on the orbits given by the radiusl2 and the center points C and G, we have the following additionalconditions available:

(xD′ − xC ′ )2 + (yD′ − yC ′ )2 = l22, (xH′ − xG′ )2 + (yH′ − yG′ )2 = l22

(31)

With that the new center positions of the guide rolls become

xD′/H′ = h1 −√h3

h4, yD′/H′ =

h1 + a1a2

√h3

h4(32)

In the latter equations the abbreviations

g1 = 2(xC − xK ), g2 = 2(yC − yK ),

g3 = 122 − (rgr + rro)2 + x2

K + y2K − x2

C − y2C (33)

h1 = g22 xK − g1 g2 yK − g1 g3, (34)

h2 = g21 yK − g1 g2 xK − g2 g3 (35)

h3 = g22 {g2

1[(rgr + rro)2 − x2

K ] + g22[(rgr + rro)

2 − y2K ] − 2 g1 g2 xK yK

h4 = g21 + g2

2 (37)

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2023

elocit

ho

x

5

pxfait

httdanrcrmc

w

F

Tfi

tive of the error are computed. Additionally, the time integral ofthe error is updated which implies the use of history variables.Finally, the values of FPID

x B/F(t) for the current time step are com-

puted.

Table 7

Fig. 10. Time functions: (a) the mandrel displacement, (b) angular v

ave been used whereby the index C has to be replaced by G inrder to obtain the solution for xH′ .

The new positions of B′ and F′ can then be computed by

B′ = xC + Rı− (xD′ − xC )l1l2, xF ′ = xG + Rı+ (xH′ − xG)

l1l2

(38)

.5. Definition of appropriate guide roll forces - PID controller

Now, knowing the current positions B and F as well as the desiredositions B′ and F′ we can compute the error measures eB(t) =′B(t) − xB(t) and eF (t) = x′

F (t) − xF (t). The definition of appropriateorces at B and F in order to minimize the error measures is based on

proportional–integral–derivative controller (PID). We only spec-fy forces in x-direction which is why the error is defined solely byhe deviation in x-direction.

In the experimental setup the forces are applied by means of theydraulic pressure in the dashpots. The force directions are given byhe dashpot directions. The horizontal forces can be easily relatedo the corresponding pressure in the dashpots. To produce a nearlyense coating a self-developed ring rolling software has been usednd the control mechanism is implemented. This software onlyeeds a pre-set of the rolling forces and the final geometry of theing, which should be coated and rolled. Additionally, a shut-off-riterion was defined. In the rolling tests the final thickness of theing was defined as a criterion to end the rolling process. Further-ore, in the simulation the paths of the mandrel and axial roll are

oming from experimental measurements (see Fig. 10).The total force is split up into a constant preload force and a part

hich is defined by the PID controller:

x B/F (t) = FPREx B/F + FPID

x B/F (t) (39)

he force defined by the PID controller consists of three parts: therst part is proportional to the error itself, the second and the third

y of the main roll and (c) the vertical displacement of the axial roll.

part are proportional to the time integral and the time derivativeof the error, respectively:

FPIDx B/F (t) = Kpgr eB/F (t) + Kigr

∫ t

0

eB/F (�) d� + Kdgrd eB/F (t)

dt(40)

The three different contributions are weighted by means of theproportionality factors Kpgr , Kigr and Kdgr . In what follows we con-sider them as constants (see Table 7). Following the early workof Yun and Cho (1984), the determination of the parameters forthe PID controller is based on a frequency response test on thesystem. The system is subjected to a unit step input and a unitstep disturbance at different time intervals. Based on the responsetests the optimal PID gain parameters are defined (see Iwancyzk,1994). The proportional part as well as the integral part have a pos-itive effect on the rise time, i.e. the time needed to decrease theerror significantly. They may lead to an overshoot of the error onthe other hand. In addition, the integral part is needed to reducethe steady state errors essB(t) = lim

t→∞eB(t) and essA(t) = lim

t→∞eA(t),

respectively.The control unit is implemented via the Abaqus user interface

VUAMP. The routine is called every n time steps, whereby n hasto be specified by the user. Within the routine the current and thedesired positions B/F and B′/F′ are computed by means of the sen-sor information and the prescribed relocation angle � , respectively.Based on this information the current error and the time deriva-

Identification of the PID parameters.

Weighting factor Kpgr Kigr Kdgr

PID 348.90 296.73 48.56

2024 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

Fla

6

mtmdisa

CgTvrrMi

6

arfieeingcrrcflr“tcctc

p

Table 8Variation of the PID parameters.

Weighting factor Kpgr Kigr Kdgr

PID 1 348.90 296.73 48.56

pressible layer is considered. The geometry of the ring is defined bythe outer ring radius (rro = 145 mm) and the wall thickness of thering (tr = 70 mm). The number of elements is changed in radial aswell as in circumferential direction to keep the aspect ratio nearly

ig. 11. Evolution of the ring-shape at process times 0, 10, 20 and 33 s (from theeft to the right): (a)-(d) without control mechanism and (e)-(h) with control mech-nism.

. Results

In this section various numerical results of the ring rollingodel introduced above are presented. First we demonstrate

he functionality and the necessity of the implemented controlechanism. After that, the convergence with increasing mesh

ensity is investigated to ensure that an appropriate discretizations chosen for further investigations. The consequences of the planetrain assumption compared to the three-dimensional simulationre subject of Section 6.3.

To reduce the complexity, all the calculations are based on theartesian coordinate system. If it is not explicitly mentioned theeometric parameters of the rolling plant are the ones given inable 5. In what follows the mandrel displacement, the angularelocity of the main roll and the vertical displacement of the axialoll given in Fig. 10 are used. The excitation functions of the mainoll, the mandrel and the axial roll are taken from the experiments.oreover, the direct measurements of the machine after smooth-

ng by splines are used in our dynamic computations.

.1. Evaluation of the control mechanism

The motivation for establishing a control mechanism is to reach stable position of the ring and to preserve the roundness of theing throughout the rolling process. It is of course also possible tond appropriate force excitations of the guide rolls by trial andrror methods in order to reach that goal. However, we are inter-sted in performing variations of several geometry parameters tonvestigate this new process for different configurations. Unfortu-ately changing the ring’s geometry and working with the sameuide roll forces leads to unstable positions of the ring and the pro-ess finally breaks down. This is, e.g. shown for a two-dimensionalolling simulation based on a solid ring with an outer radius ofro = 141 mm and a wall thickness of tr = 60 mm. This simulationould be performed successfully after the appropriate guide rollorces had been determined by trial and error methods. The simu-ation in which the control mechanism is used shows also satisfyingesults. Next, the outer ring radius is changed to 250 mm and thetrial and error” guide roll forces from the previous simulation areaken. Fig. 11(a)–(d) shows the shape of the ring at different pro-ess times. An increasing deviation from the ideal circular shape islearly visible. The simulation of the larger ring in combination with

he proposed control mechanism shows again an almost ideallyircular shape of the ring throughout the process (Fig. 11(e)–(h)).

Additionally, we investigate the influence of different PID gainarameters on the system (see Table 8). Therefore we look at the

PID 2 348.90 350.0 48.56PID 3 400.0 296.73 48.56

current relocation angle ˛(t) for a prescribed relocation angle � = 0◦.Fig. 12 shows the current relocation angle with respect to theprocess time. The large effect of the PID parameters on the ringroundness which has a direct relation with the applied forces onthe guide rolls can be seen in this figure.

Finally we examine the capabilities of the control mechanism tosteer the ring’s position. Therefore we look at the current reloca-tion angle ˛(t) for two prescribed relocation angles � = 0◦ and � = 3◦

(cf. Fig. 9). Fig. 13 shows the current relocation angle with respectto the process time. The small deviation from the prescribed relo-cation angles demonstrates the precision of the proposed controlmechanism.

To conclude, apart from the stabilization of the system, the con-trol mechanism is utilized to set up a well-defined relocation ofthe ring during the rolling process. This influences the pass reduc-tion at the main roll and the mandrel with the aim to reach a highcompaction level of the layer material at an earlier stage. The relo-cation of the ring leads to a different bite of the main roll and themandrel. The improvement of the compaction behavior is discussedin Section 6.5. To our knowledge, the rate of the feed has a directeffect on the compaction behavior. The decrease of the ring temper-ature decreases the flow velocity of the powder material. Therefore,by increasing the speed of the feed a better compaction behaviorcan be seen. However, the measurement of the bite of the rolls,effects of the speed on the process and the relation between thefeed rate and the defects (e.g. roundness, fishtail, dishing) are underinvestigation.

6.2. Study of the mesh convergence

In order to work with an appropriate discretization, studiesof convergence are performed by means of the two-dimensionalmodel. Therefore we look at several different quantities as, e.g. vonMises stress for different meshes. Fig. 14 demonstrates the dis-tribution of the von Mises stress along a path which includes 16equidistant points (independent of the discretization) within theradial rolling gap (from the inner to the outer point of the ring’swall) at the end of the process.

This study is performed by means of a solid ring, i.e. no com-

Fig. 12. Influence of PID parameters on the system stability and the final ring-shape.

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2025

Fig. 13. Current relocation angle for two prescribe

cu

si

6

iozathotdexttsrt

TD

Fig. 14. Von Mises stress along the ring thickness in the radial rolling gap.

onstant. Table 9 shows the discretization of the meshes that aresed to investigate the mesh convergence.

Looking at the results plotted in Fig. 14 we can conclude that theolution is not altered significantly by using more than 18 elementsn radial and 450 elements in circumferential direction.

.3. Applicability of the two-dimensional model

To evaluate the consequences of the plane strain assumptiondentical rolling simulations of a solid ring are performed by meansf the two-dimensional and the three-dimensional FE discreti-ation. Again, a ring geometry with an outer radius of rro = 141 mmnd a wall thickness of tr = 66 mm is used. The ring’s height in thehree dimensional model is hr = 90 mm whereby only the half of theeight is discretized. To assess the differences between the resultsf the two- and the three-dimensional mesh, we look at the con-ours of the logarithmic total strain in x- (Fig. 15) and in y- (Fig. 16)irection as well as at the von Mises stress (Fig. 17) at two differ-nt process stages (4 and 33 s). With regard to the total strain in- and y-direction we observe that they are underestimated in thewo-dimensional simulation. This is reasonable since the reduc-ion of the height in the three-dimenaional model leads to a higher

trains in the other two directions. In summary, the maximum erroreaches up to 27% at 4 s. However, the maximum error decreaseso about 6% at the end of the process.

able 9iscretizations that have been used to study the mesh convergence.

Number of elements Mesh 1 Mesh 2 Mesh 3 Mesh 4

Radial 12 18 24 50Circumferential 300 450 600 1250

d relocation angles �: (a) � = 0◦ and (b) � = 3◦ .

Considering the von Mises stress we see in general higher valuesin the three-dimensional model, although the difference is verysmall (see Fig. 17). An explanation can be found in the fact that thepresence of two rolling gaps in the three-dimensional model leadsto higher accumulated plastic strains since plastic straining occursin the radial rolling gap where the ring’s height is increased and itoccurs additionally in the axial rolling pass where the height of thering is decreased again.

To conclude, the quantitative error due to the plane strainassumption reaches up to 27% in the considered set-up. On theother hand the qualitative distribution of the examined quantitiesin the two-dimensional simulation are very similar to the ones inthe three-dimensional simulation. We conclude from this obser-vation that the two-dimensional model is applicable to investigateprinciple influences of several parameters as well as for basic stud-ies.

6.4. Hybrid mesh

Modelling the entire process using conventional Lagrangian FEmethods involves high mesh density and subsequently large com-putational time. The ALE method serves to exploit the advantagesof both Lagrangian and Eulerian methods since it allows the meshto move independently of the material (e.g. Donea et al., 2004).Two applications of the ALE method are distinguished in the fol-lowing. In the first one a homogeneous mesh is used and the ALEmethod is used to reduce mesh distortion with the aim to keepthe mesh homogeneous. The second method aims to work with afine discretization in the rolling gaps and a coarse discretizationin the remaining regions in order to work with a lower number ofelements. Therefore, it is necessary to keep the mesh fixed in cir-cumferential direction. This has been investigated in literature by,e.g. Davey and Ward (2003), Davey and Ward (2002a) and Lim et al.(1998). In this section we compare the two methods with respect tothe computational efficiency and the quality of the obtained results.

To simplify the problem, a ring rolling simulation of a solid ring(no layer) with a two-dimensional discretization is studied. Thering has an outer radius of 0.141 m and a wall thickness of 0.066 m.The homogeneous mesh consists of 13 elements in radial and 300elements in circumferential direction. The inhomogeneous meshalso uses 13 radial elements. Outside the radial rolling gap theelements of the inhonogeneous mesh have the same aspect ratio asthe elements of the homogeneous mesh. Inside the rolling gap themesh density in circumferential direction is approximately threetimes higher compared with the homogeneous mesh. Table 10

shows the comparison of run time for both discretizations. Thespeed up by using the inhomogeneous mesh is about 2.7.

To compare the simulation results we look at the contour plotof the von Mises stress in the region of the radial rolling gap at

2026 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

3D mo

trwtri

Fig. 15. Distribution of the logarithmic strain in x-direction for the

he end of the analysis given in Fig. 18. The values are in the sameange whereby the contours in the rolling gap look much smootherith the inhomogeneous mesh. Next, we look at the distribution of

he stress in radial direction along five different paths within theadial rolling gap. The angle with the paths are defined as shownn Fig. 19(a). The curves given in Fig. 19 show that the radial stress

Fig. 16. Distribution of the logarithmic strain in y-direction for the 3D mo

del (b and d) and 2D model (a and c) at 4 and 33 s (top to bottom).

predicted by the two simulations is very similar while the resultsof inhomogeneous mesh are smoother again.

In summary applying the ALE method in combination with an

inhomogeneous mesh offers considerable advantages with respectto the computational time while the quality of the results is accept-able.

del (b and d) and 2D model (a and c) at 4 and 33 s (top to bottom).

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2027

Fig. 17. Distribution of the von-Mises stresses for the 3D model (b and d) and 2D model (a and c) at 4 and 33 s (top to bottom).

Fig. 18. Distribution of von Mises stress: (a) normal mesh and (b) hybrid mesh.

Fig. 19. Radial stress along different paths: (a) normal mesh and (b) hybrid mesh.

2028 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

Table 10Run time of homogeneous and inhomogeneous ALE meshes.

Radial elements Normal mesh Hybrid mesh

8 34:25:17 12:18:11

6

rrdi

o2e

boppfiSvtd

a

TP

13 72:36:34 27:13:1718 102:27:40 38:25:15

.5. Densification of layer

To guarantee the functionality of the coating it is important toeach a high state of compaction inside the layer. To compare theelative density predicted by the two- and the three-dimensionaliscretization, comparative simulations with the parameters given

n Table 11 are performed.The experimental investigations emphasize that the maximum

btainable relative density after the sintering process is 0.7 (Moll,009). Therefore, an initial relative density of �r0 = 0.7 is consid-red.

To compare the predicted densification we look to the distri-ution of the relative density at two different process stages. Inrder to compare the experimental and simulation results morerecisely, points A and B given in Fig. 20 are chosen as measureoints. Fig. 21(a) and (b) shows the results for a process time of 4 sor the two- and three-dimensional discretizations, respectively. Ast is observed for the yield stress in the simulation for a solid ring inection 6.3, the three-dimensional approach yields slightly higheralues for the relative density. This could be expected, since both,

he evolution of the yield stress and the evolution of the relativeensity, are coupled to plastic deformations.

The presence of two rolling gaps in the three-dimensionalpproach consequently results in a larger amount of plastic

able 11arameters used in the FE simulation of compound rings.

parameter rri [mm] tsu [mm] tla [mm]

value 122.5 47.5 14

Fig. 21. Relative density of compacted layer by applying hot work steel in 2D

Fig. 20. Measure points for experimental and simulation results.

deformations. The same behavior holds for the results at a processtime of 15 s which are given in Fig. 21(c) and (d). It can also beobserved that a high state of compaction is already reached after4 s and that the relative density is not increased significantly bythe remaining rolling process.

Accordingly, in Fig. 22(a) and (b) the experimental results forthe relative density are compared with those predicted by the sim-ulation. In Fig. 22(a) the experimental data is based on experimentsthat were interrupted at 4 s. The measured relative density refersto point A (see Fig. 20). In this investigation, two tests for the coldwork steel and three tests for the hot work steel are studied. Itcan be observed that the prediction of the relative density by the

simulation has a good correlation with the experimental results.Moreover, it is observed that the hot work steel shows a highercompaction than the cold work tool steel which is also predictedby the simulation, respectively. Fig. 22(b) shows the relative density

tec [mm] nc nrsu nrla nrec

3 300 10 3 1

model (a and c) and 3D model (b and d) at 4 and 15 s (top to bottom).

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2029

Fig. 22. Comparing the experimental and simulation results: (a) hot and cold work steel and (b) hot work steel.

Fig. 23. Microstructure of ring cross-section at the measure points (see Fig. 20) after the rolling process: (a) hot work steel and (b) cold work steel.

Fig. 24. Relative density of compacted layer (hot work steel): (a) k = 1, (b) k = 2.7, (c) k = 3.5 and (d) k = 7.

2030 R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032

Fig. 25. Influence of geometrical parameters on relative density: (a) relative density with respect to k and (b) cross-section of the rolled ring for k = 2.7.

) diam

abwbd

hcns

t

Fig. 26. Difference of the solid and compound ring: (a

t the end of the rolling process. In this study, the simulation resultsased on two- and three-dimensional discretization are comparedith the experimental results. The density is slightly overestimated

y the three-dimensional, and slightly underestimated by the two-imenaional discretization.

Fig. 23 shows the corresponding microstructure for the cold andot work steel at points A and B. At point B the residual porosity islearly visible for both materials. In contrast to the cold work steel,

early no residual porosity is observable at point A for the hot workteel.

To evaluate the influence of different roll and ring radii onhe compaction of the layer, parameter studies are carried out.

Fig. 27. Reaction force of the mandrel for solid and compound ring.

eter increase and (b) reduction of the wall thickness.

Therefore, different radii for the main roll and the mandrel are cho-sen (see Table 12). The ratio of the main roll radius with respect tothe mandrel radius is defined as k.

Fig. 24(a)-(d) demonstrate the influence of k on the relative den-sity. It can be seen that the increase of k leads to a small decreaseof the relative density. This result can be observed in Fig. 25(a).It shows the predicted influence of k on the relative density atthe end of the rolling process. These results emphasize that withk = 1 the highest values for the relative density can be obtained.Working with k = 1 might not be realistic for a practical appli-cation. But it confirms the strategy to improve the compactionbehavior by increasing the pass reduction at the main roll. As anexample, the cross-section of the rolled ring for k = 2.7 is demon-strated in Fig. 25(b) and the compaction of the porous layer can beobserved.

The enlargement of the ring’s diameter and the reduction of

the ring’s wall thickness during the rolling process are illustratedin Fig. 26(a)-(b). During the rolling of a solid rings the diam-eter increases and the reduction of the wall thickness occurs

Table 12Variation of geometric parameters.

k Main roll Mandrel Ring

1 130 130 218.52.7 175 65 1413.5 350 100 2187 455 65 141

R. Kebriaei et al. / Journal of Materials Processing Technology 213 (2013) 2015– 2032 2031

Fig. 28. Decrease of the height of the solid and compound ring (a) and reduction of the volume of the compound ring (b).

lied co

sbDidrtFlts

chtroa

diteaeopbtidt

Fig. 29. Improvement of the compaction by app

imultaneously. Obviously the compound ring shows differentehavior than the solid ring, even already in the first rolling stage.epending on the powder material and chamber geometry applied

n the process, the ring shows a reduction of its outer diameteruring this stage of the rolling process. In the first stages of theolling process (about 10 s) the largest part of the applied deforma-ion forces is invested in the compaction of the layer material (seeig. 27). By increasing the relative density of the layer material, theayer material’s yield stress increases. Therefore, the stresses withinhe substrate material increase. This leads to a deformation of theubstrate material and thereby to a diameter increase of the ring.

The axial roll does not only prevent the increase of the ring’sross-section in axial direction, but also causes the reduction of theeight of the ring. This behavior can be observed in Fig. 28(a). Addi-ionally, the non-isochoric plastic deformation of the compounding is demonstrated in Fig. 28(b). Looking at this diagram, one canbserve a fast reduction of the ring’s volume due to the compactiont about 10 s.

Additionally, the control mechanism is utilized to set up a well-efined relocation of the ring during the rolling process in order to

nfluence the pass reduction at the main roll and the mandrel withhe aim to reach a high compaction level of the layer material at anarlier stage. The relocation of the ring leads to a different infeedt the main roll and the mandrel. This is an early result of (Mamalist al., 1976). In the present work, we show that the infeed behaviorf the rolls has a close relation with the densification behavior of theorous layer material. The effect on the densification of the layery relocating the ring with � = 8◦ can be seen in Fig. 29 at a process

ime of 4 and 12 s. The relative density along the path I shows anmprovement for a relocation angle of � = 8◦. To conclude, a well-efined relocation of the ring can reduce the residual porosity insidehe layer.

ntrol mechanism: (a) after 4 s and (b) after 12 s.

7. Conclusion

In the Federal Republic of Germany the annual cost caused byabrasive wear amount to about 65 billion euro. The manufacturingof functional surfaces represents a key point in functional surfacestechnology and is important for the development and the produc-tion of high technology products in the future.

The development of this new hybrid production process wasachieved by application of new simulation techniques in close col-laboration with new experimental manufacturing techniques. Theaccomplishment has led to successful applications such as differentmatrix powder coatings and control processes.

Additionally, the presently suggested combination of surfacefunctionalization with new manufacturing techniques has a sig-nificant effect on the decrease of the number of production steps. Itcan be concluded that this hybrid process introduces a new produc-tion technique for application of functional surfaces on ring-shapedwork pieces.

In this paper a parameterized FE ring rolling model was pre-sented that is applicable to the simulation of process-integratedpowder coating by radial axial rolling of rings. In addition, a mate-rial model that is able to describe the compaction of the powderlayer material was briefly introduced.

The FE model represents the basis to investigate the influenceof several geometry parameters on the ring deformation duringthe rolling and the residual porosity within the layer. Therefore,quantities such as the relative density are considered.

The stability of the system which leads to a round final ring-

shape is an important aim. For this purpose, we developed anovel type of control method which enables the ring to relocateby a given angle. Such a control system was programmed andimplemented via the user interface VUAMP. The new method

2 cessin

eb

isrt

A

twM

R

A

A

B

B

B

B

D

D

D

D

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nables us to increase the densification of the layer in one systemy applying different angles of relocation.

One of the most important studies which complete this researchs the integration of heat treatment of the rolled ring into the sub-equent cooling process. In another paper we discuss the resultsegarding the anomalously large expansion on heating and con-raction on cooling.

cknowledgement

The authors gratefully acknowledge the support of this work byhe Volkswagen Foundation under reference number I/81 247 Akithin the initiative ‘Innovative Methods for the Manufacturing ofultifunctional surfaces’.

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