j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375

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Prediction of 3-D temperature field of TP2 copper tubes inthree-roll planetary rolling process

B. Lia, S.H. Zhanga,∗, G.L. Zhanga, H.Q. Zhangb

a Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, PR Chinab Shenyang University, Shenyang 110044, PR China

a r t i c l e i n f o

Article history:

Received 11 June 2005

Received in revised form

4 January 2007

Accepted 22 November 2007

a b s t r a c t

The calculation method and three-dimensional thermo-mechanical coupling model were

established for the planetary rolling process of TP2 copper tubes. The distribution rules of

temperature field of TP2 copper tubes were obtained by simulation analysis. The tempera-

ture of the TP2 copper tubes increases from room temperature to about 700 ◦C in three-roll

planetary rolling, which would reduce the rolling force, and improve the performance of the

rolled copper tubes. The temperature of TP2 copper tubes during rolling was in good agree-

ment with the measured results, which indicates that the finite-element method would

supply important reference merit for 3-D thermo-mechanical simulation of TP2 copper tubes

Keywords:

TP2 copper tube

Three-roll planetary rolling

Thermo-mechanical coupling

Temperature field

in the three-roll planetary rolling process.

© 2007 Elsevier B.V. All rights reserved.

by finite-element field. Li et al. (2002) simulated the temper-

Plastic deformation heat

1. Introduction

The planetary rolling of TP2 (ASTM: C12200) copper tubesis a large plastic deformation process in one rolling pass.The chemical compositions of TP2 copper tubes include: P0.015–0.040%; S 0.004%; Cu 99.90% (mass fraction). The large-deformation occurs in the copper tubes during the three-rollplanetary rolling process, in which the tube wall changessharply from 20 mm to 2 mm. Due to the heat energy gen-erating from the intense friction between the roller andthe copper tubes, plus the vast thermal effect result fromthe plastic deformation, the temperature of the rolled cop-per tubes increases rapidly. The highest temperature byestimation was higher than the recrystallization tempera-

ture of the TP2 copper, so it is important to find out thetemperature distribution of TP2 copper tubes in three-rollplanetary rolling in order to increase the precision, homog-

∗ Corresponding author. Fax: +86 24 2390 6831.E-mail address: shzhang@imr.ac.cn (S.H. Zhang).

0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2007.11.213

enize the quality and enhance the competitiveness of theproducts.

Some researches have addressed the three-roll planetaryrolling process. Sieke (1990) analyzed the mechanism andapplication of three-roll planetary rolling mill. Wu et al. (2002)discussed the bar rolling process by means of the three-rollplanetary mill. Shih et al. (2001) did much research work forplanetary rolling, including simulating the deformation of thesteel during rolling, obtaining the rolling deformation and theresulting stress and strain (Shih et al., 2002), and seeking thecharacteristic of the steel three-roll planetary rolling processwith theories and experiments (Shih and Hung, 2003). Thetemperature field for rolling process has been widely analyzed

ature field of 50CrV4 automobile gear bar steel in continuousrolling by FEM and obtained the temperature variations of thebar. Song et al. (2003) simulated the deformation, tempera-

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T

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t

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j o u r n a l o f m a t e r i a l s p r o c e s s i n g

ure field, thermal stress of 3-D plastics thermalforming andlow molding. Komori and Suzuki (2005) proposed a methodf analyzing deformation and temperature in press roll pierc-

ng based on finite-element method, and he also analyzed theeformation and temperature of a material during multi-passhree-roll rolling (Komori, 1999; Komori, 2003). The distribu-ion of equivalent strain, temperature and the stress in theoll gap and lateral profile are discussed for hot rolling pro-ess (Duan and Sheppard, 2002). Chen et al. (1992) obtainedhe temperature distribution in the roll gap during hot flatolling. However, there are few studies about the three-rolllanetary rolling of the copper, so it is especially difficult tobtain the temperature distribution in the three-roll planetaryolling of copper tubes. Therefore, it is of great significanceo seek the deformation and temperature distribution rulesf copper tubes in three-roll planetary rolling process by thenite-element method (FEM). Through simulating the temper-ture distribution, the rules of metal deformation resistancean be obtained and the forming performance of the prod-ct can be further predicted. The authors have studied thestablishment of planetary rolling FE model of copper tubesnd the deformation condition of TP2 copper tubes (Yang etl., 2003), and have also simulated the three-roll planetaryolling process of copper tube by large-deformation elastic-lastic finite-element method (Li et al., 2005). In this paper,ased on the finite-element software MSC.Marc, the thermo-echanical coupling simulation model was established which

ocus on predicting the temperature distribution of TP2 copperubes under the stable deformation stage in three-roll plane-ary rolling process.

. Calculation of heat generation and the FEodel

.1. Thermo-mechanical coupling equation

he temperature of the copper tubes increases from roomemperature to an elevated temperature in three-roll plane-ary rolling. The heat energy mainly results from the plasticeformation and the friction. The updated Lagrange descrip-ion was selected in the simulation, which described thencremental strain expression for the temperature field cou-ling the large elastic-plastic deformation. The equation ofhe plastic deformation work transforming to the volume heatow is as follows

∂S

∂t= Mp

∂Wp

∂t(1)

here S is the surface on the boundary; ∂Wp/∂t is the plasticeformation work; and Mp is the heat coefficient of plasticeformation work.

The friction work transforms to the heat flow of surface inhe simulation

= M FfrV (2)

fr f r

here Ffr is friction force of contact surface; Vr is relative slid-ng speed of contact surface; and Mf is converting coefficientf friction work. In this paper, supposing the friction heat flow

h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375 371

between the roller and copper tubes was distributed on thecontacting surface equally.

For three-roll planetary rolling deformation of the coppertubes, the thermo-mechanical coupling energy conservationequation is as follows:

∫V

g�QdV −∫

S

gHdS =∫

V

g�DcT

DtdV +

∫V

∂g

∂Xikij

∂T

∂XjdV (3)

where Q is the specified volume heat flow; g is Galerkin func-tion; D is deformation rate; c is specific heat of copper; and His heat flow intensity of unit area on the boundary S.

2.2. The heat boundary conditions

In three-roll planetary rolling of the copper tubes, the heatboundary conditions contain not only the convective and radi-ant heat transfer between the copper tubes surface and theenvironment, but also the contact heat exchanges betweenthe copper tubes and the rollers. Both of the two boundaryconditions are the third boundary condition in the thermo-dynamics, in which the coefficient of heat transfer ˛ betweenthe copper tube and the environment, and the environmentaltemperature t∞ are given previously. The formula is as follows

q = −�

(∂t

∂n

)= ˛(t − t∞) (4)

where t – the temperature of the copper tubes surface (◦C); t∞ –the environmental temperature (◦C); � – the coefficient of heattransfer.

The coefficient of heat transfer ˛ includes the convectiveheat-transfer coefficient hc and the radiant heat-transfer coef-ficient hr as in Eq. (4). The value of convective heat-transfercoefficient hc can be influenced by the cooling condition.According to the radiation law, the radiant heat-transfer coef-ficient hr is gained.

hr = �ε(t + t∞)(t2 + t∞2) (5)

where � – radiation constant of black body; ε – emissivity. Itcan be obtained that the radiation coefficient hr is relative tothe temperature, so the heat boundary condition is nonlinear.

The contact heat conductivity between the copper tubeand the rollers is related to temperature, pressure and con-tact surface, and the coefficient of contact heat conductivityhJ was usually used to reflect the contact heat conductivity(Li and Sellars, 1998). At the beginning of three-roll plane-tary rolling, the temperature of the TP2 copper tube and therollers are both in room temperature state. With the develop-ment of rolling, the temperature of the copper tube increasesto above the recrystallization temperature by heat accumu-lated from the large-deformation and friction work. According

to the above boundary conditions and the initial temperaturecondition, the three-roll planetary rolling of TP2 copper tubeswas analyzed by the method of thermo-mechanical couplingsimulation.

372 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375

etary

Fig. 1 – FEM model of three-roll plan

2.3. Model of three-roll planetary rolling mill

The three-roll planetary mill mainly contains three conicalrollers, the external ring and the mandrel. The rollers have acertain inclined angle ˇ and an offset angle ˛, which make thecopper tubes generate plastic deformation and move forwardas the rollers rotate. The main purpose of the external ring is tocounteract the twisting deformation of the copper tubes dur-ing rolling. Influenced by the incline angle and offset angle, thedirection vector of the roller axe will change with the revolu-tion of rollers. Thus, the kinematic and contact relationshipsof the three-roll planetary rolling are very complicated andwill lead to huge computational time for FE simulation. So itis reasonable to simplify the simulation model. If the axes ofthe rollers are fixed and the orbital revolution of the rollers isignored, the external ring can be ignored from the model. Theorbital motion provided by the external ring can be substitutedby the relative motion of the copper tubes with free rotationaldegree of freedom. Thus, the key points in the analysis of thesimplified model contain only the rotation of the rollers andcontact conditions between the rollers and the copper tubes,and those between the copper tubes and the mandrel.

The finite-element meshes were plotted by the hexahedralelement with six faces and eight nodes, and the length of thecopper tube was 160 mm. The copper tube was divided into12,960 elements and 15,986 nodes. Through the coordinateconversion, the model of the rolling process, as shown in Fig. 1,

was established, which considered not only inclined angle ˇ

but also offset angle ˛ of the three rollers.In the calculation, the problems of 3-D large-deformation

were resolved by the updated Lagrange arithmetic, the

Table 1 – Parameters of three-roll planetary rolling

Material Copper tubeexternal diameter

ϕC (mm)

Copper tubethickness t

(mm)

Inclinedangle ˇ (◦) an

TP2 80 20 50

rolling: (a) side view; (b) front view.

Prandtl-Reuss flow equation and the von Mises yield criteria.The parameters of the TP2 copper tubes in three-roll planetaryrolling are shown in Table 1.

Based on the above model and boundary conditions, thetemperature field of the TP2 copper tubes was obtained forthree-roll planetary rolling.

3. Results and discussion

3.1. FE results

Fig. 2 shows the temperature distribution of the copper tubesin three-roll planetary rolling. Along the rolling axis direction,the temperature of the copper tubes ascends quickly from theinitial temperature 20 ◦C to above 200 ◦C. With the temperatureincreasing, the highest temperature in the roller gap positionof the concentrative deformation area could arrive at about700 ◦C. When the copper tube was separating from the roller,the temperature of the rolled copper tube slowly decreases tothe room temperature. Due to the cumulation of heat gen-eration and the local concentrative large-deformation, thetemperature of the concentrative deforming zone under theroller gap position arrives at the highest; thus in this zone thetemperature of the deformation copper tube increases abovethe recrystallization temperature of the TP2 copper tube. Sothe FE simulation analysis is useful to obtain the temperature

distribution for rolling different sizes of copper tubes. Due tothe generation of the friction heat between the copper tubesand the rollers and the heat of plastic deformation, the tem-perature of the contact area was relatively higher along the

Offsetgle ˛ (◦)

Roller rotationalspeed ωRoller (rpm)

Pusher speedVP (mm/s)

MandreldiameterϕM (mm)

8 180 20 36

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375 373

cttt

tofgtsptadw

raihtaf

F

Fig. 4 – Transverse temperature field of TP2 copper tube.

Fig. 5 – Circumferential temperature curves of the tube

Fig. 2 – Temperature distribution of TP2 copper tube.

ircumferential direction of the workpiece. When the copperube was apart from the rollers, the temperature of copperubes along the circumferential direction decreased slowly ashe heat exchange with the surrounding environment.

The curve of temperature change of one point in the copperube is shown in Fig. 3. The curve reflects the fluctuant trendf the rolled copper temperature as the rolling process goingorward. The temperature of the rolled copper tubes increasesradually in the whole process from the initial biting stage tohe final one. Due to the copper tubes going forward along apiral track in three-roll planetary rolling, the point in the cop-er tubes would contact with the three rollers in turn. Whenhe point contacting with the roller, its temperature wouldscend. Once separating from the roller, its temperature wouldecrease. Then contacting with the next roller, its temperatureould ascend again.

In general, the changing trend of the temperature of theolled copper tube increases gradually with rolling time. Whilerriving at the roller gap position of the concentrative deform-ng zone, the temperature of rolled copper tube reached the

eight of about 700 ◦C. After being apart from the rollers, theemperature of rolled copper declines gradually. The temper-ture distribution of the rolled copper tubes could be obtainedor three-roll planetary rolling deformation process.

ig. 3 – Temperature curve of a point in the TP2 copper tube.

sections.

The section temperature field of the copper tubes in three-roll planetary rolling is indicated in Fig. 4. It shows that thedeformation rule of three-roll planetary rolling is from a roundsection A to a round-triangle section B under the concentra-tive deforming zone, finally to a round section C by the rollers.In section A, the temperature of the outer surface is higherthan that of the internal, and the temperature gradient islarger than section B; the temperature almost does not changealong section C, which is good for forming the uniform qual-ity of the copper tubes. Therefore, the rules of the temperatureand the deformation of section shape in three-roll planetaryrolling can be obtained. Moreover, the structure and propertymechanism for three-roll planetary rolling deformation can befurther investigated.

The curves of temperature change of exterior surface ofsections A, B and C along the circumferential direction areshown in Fig. 5. The curve of section A shows that the tempera-ture of exterior surface is relative lower. Because section A is inthe temperature ascending stage, the temperature fluctuation

is the largest. As the copper billet contacts with the rollers, itstemperature increases quickly. Once separating from rollers,its temperature decreases gradually. The temperature fluctu-ation of the section B is larger due to the heat accumulation in

374 j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375

Table 2 – Measured temperature of the mandrel

Copper tube number 1 2 3Mandrel temperature (◦C) 608 612 616 6

Fig. 6 – Longitudinal temperature field of the copper tube.

the rolling process, and the temperature change of the exte-rior surface is about 50 ◦C, which is good for the equality ofthe whole section deformation. Because the rolled materialhas already separated from the roller, the temperature fluctu-ation of section C is the lowest, which benefits to the equalityof the rolled copper tubes.

The temperature distribution of the copper tubes alongthe longitudinal direction is exhibited in Fig. 6. The anglesbetween the rollers are 120◦ in the space, thus the upper-halfpart of copper tubes in Fig. 6 is the temperature distribu-tion contacting with the roller, and the lower-half part is thetemperature distribution separating with the roller. Accord-ing to the simulation results, the temperature of copper tube

ascends gradually in the rolling and the highest temperaturecould arrive at about 700 ◦C.

Fig. 7 – Microstructure of TP2 copper tube section.

4 5 6 7 8 921 628 632 639 648 652

Fig. 7 shows the microstructures of the section of the TP2copper tube in three-roll planetary rolling. The grain of theexterior surface area contacting with the rollers is refined,indicating the higher temperature and the more deformationoccurred in this area, which is similar to the temperature dis-tribution of copper tube in Fig. 6. The grain of the roller gapdeforming focus area is the thinnest, indicating that when thetemperature is the highest the deformation reaches the max-imum in this area, which also agrees with Fig. 6. So by themethod of the FE simulation, the rules of the temperature dis-tribution in three-roll planetary rolling could be obtained, andthe microstructure evolution would be predicted.

3.2. Comparison of the FE simulation with themeasured temperature

To verify the reliability of the FE results, the temperature of thecopper tubes in three-roll planetary rolling has been measuredby experiments. Because the temperature of the copper tubewas similar to the mandrel temperature in the stable rollingstage, the mandrel temperature was measured. The measuredresults are presented in Table 2.

In Table 2, the mandrel temperature ascended gradually asthe number of the copper tubes increases, due to the mandreltemperature increasing gradually during the rolling progressand finally reaching the steady state. Considering that themandrel temperature will be influenced by the surroundingenvironment and reduced about 50–60 ◦C, the rolling temper-ature of the copper tubes in three-roll planetary rolling will be650–700 ◦C. The measured results verified the FE simulationresults, which indicate the accuracy of the thermo-mechanicalcoupling simulation analysis and the value of predicting theeffects of the temperature of the rolled copper tubes in thethree-roll planetary rolling process.

4. Conclusions

(1) Calculation methods were established for predicting theheat generation of the copper tubes in three-roll planetaryrolling. FE simulation was carried out by using the abovemethods. The analyses from many aspects such as exte-rior surface, lateral section and longitudinal section of thecopper tubes were conducted for gaining the temperaturefield of TP2 copper tubes.

(2) The temperature distribution was predicted for the rollingof copper tubes. All the analytic results show that thetemperature of the TP2 copper tubes increases from roomtemperature to about 700 ◦C in three-roll planetary rolling,which would reduce the rolling force, and improve themicrostructure and performance of the rolled copper

tubes.

(3) The deformation temperature of TP2 copper tubes by thesimulation is close to the measured temperature, whichverifies that the FE simulation of thermo-mechanical cou-

t e c

A

TtCc

r

C

D

K

K

K

j o u r n a l o f m a t e r i a l s p r o c e s s i n g

pling in this paper has great reference and predictionvalues.

cknowledgements

he authors would like to thank the Natural Science Founda-ion of China (No. 50474059) and the National Key Projects ofhina (No. 2002BA327C) for their support in the area of theasting and rolling of copper tubes.

e f e r e n c e s

hen, B.K., Thomon, P.F., Choi, S.K., 1992. Temperaturedistribution in the roll gap during hot flat rolling. J. Mater.Process. Technol. 30, 115–130.

uan, X., Sheppard, T., 2002. Three dimensional thermalmechanical coupled simulation during hot rolling ofaluminum alloy 3003. Int. J. Mech. Sci. 44, 2155–2172.

omori, K., 1999. Simulation of deformation and temperature inmulti-pass three-roll rolling. J. Mater. Process. Technol. 92-93,450–457.

omori, K., 2003. Simulation of deformation and temperature in

multi-pass caliber rolling: effect of finite-element mesh incross-section. J. Mater. Process. Technol. 143–144, 367–372.

omori, K., Suzuki, M., 2005. Simulation of deformation andtemperature in press roll piercing. J. Mater. Process. Technol.169, 249–257.

h n o l o g y 2 0 5 ( 2 0 0 8 ) 370–375 375

Li, Y.H., Sellars, C.M., 1998. Comparative investigations ofinterfacial heat transfer behaviour during hot forging androlling of steel with oxide scale formation. J. Mater. Process.Technol. 80-81, 282–286.

Li, C.S., Liu, X.H., Wang, G.D., 2002. Simulation on temperaturefield of 50CrV4 automobile gear bar steel in continuous rollingby FEM. J. Mater. Process. Technol. 120, 26–29.

Li, B., Yang, Z., Liu, H.M., Zhang, S.H., Zhang, J.L., 2005. Computersimulation on the movement and deformation rules ofthree-roll planetary rolling process of copper tube. J. Plastic.Eng. 5 (12), 70–73 (in Chinese).

Shih, C.K., Hung, C., 2003. Experimental and numerical analyseson three-roll planetary rolling process. J. Mater. Process.Technol. 142, 702–709.

Shih, C.K., Hung, C., Hsu, R.Q., 2001. The finite element analysison planetary rolling process. J. Mater. Process. Technol. 113,115–123.

Shih, C.K., Hsu, R.Q., Hung, C.H., 2002. A study on seamless tubein the planetary rolling process. J. Mater. Process. Technol.121, 273–284.

Sieke, T., 1990. Investigation on tubes rolling of three-rollplanetary mill (PSW). Steel Tubes 5, 50–55 (in Chinese).

Song, Y.H., Zhang, K.F., Wang, Z.R., Diao, F.X., 2003. 3-D FEManalysis of the temperature field and the thermal stress forplastics thermalforming. J. Mater. Process. Technol. 97, 35–43.

Wu, S.J., Hwang, Y.M., Chang, M.H., 2002. A three-dimensional

finite element analysis of the three-roll planetary mill. J.Mater. Process. Technol. 123, 336–345.

Yang, Z., Zhang, S.H., Xu, Y., 2003. Models of finite elementsimulation on three-roll planetary rolling process of castcopper tubes. J. Plastic. Eng. 10 (6), 70–73 (in Chinese).