Research Article The Effects of Forming Parameters on

Research ArticleThe Effects of Forming Parameters onConical Ring Rolling Process

Wen Meng Guoqun Zhao and Yanjin Guan

Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education)Shandong University Jinan Shandong 250061 China

Correspondence should be addressed to Guoqun Zhao zhaogqsdueducn

Received 24 April 2014 Revised 28 June 2014 Accepted 29 June 2014 Published 17 August 2014

Academic Editor Huamin Zhou

Copyright copy 2014 Wen Meng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The plastic penetration condition and biting-in condition of a radial conical ring rolling process with a closed die structure onthe top and bottom of driven roll simplified as RCRRCDS were established The reasonable value range of mandrel feed rate inrolling process was deduced A coupled thermomechanical 3D FE model of RCRRCDS process was establishedThe changing lawsof equivalent plastic strain (PEEQ) and temperature distributions with rolling time were investigated The effects of ringrsquos outerradius growth rate and rolls sizes on the uniformities of PEEQ and temperature distributions average rolling force and averagerolling moment were studied The results indicate that the PEEQ at the inner layer and outer layer of rolled ring are larger thanthat at the middle layer of ring the temperatures at the ldquoobtuse angle zonerdquo of ringrsquos cross-section are higher than those at ldquoacuteangle zonerdquo the temperature at the central part of ring is higher than that at the middle part of ringrsquos outer surfaces As the ringrsquosouter radius growth rate increases at its reasonable value ranges the uniformities of PEEQ and temperature distributions increaseFinally the optimal values of the ringrsquos outer radius growth rate and rolls sizes were obtained

1 Introduction

The radial conical ring rolling process with a closed diestructure on the top and bottom of driven roll simplifiedas RCRRCDS is an advanced plastic forming technologyIt has dominant advantages in saving material and costand improving production efficiency Since the die structureconsisting of the driven roll and mandrel is closed inRCRRCDS process the deformation of conical ring alongthe axial direction suffers from the restrictions of the topand bottom parts of driven roll The fishtail defects usuallyoccurring in radial-axial conical ring rolling process can beeffectively avoided and rolled rings have good dimensionsand mechanical properties Therefore it is widely used in thefields of mechanical industry wind power aerospace and soforth The most typical conical products are nozzle supportsflanges [1] aeroengine accessory the main part of nuclearreactor shell [2] and aluminum alloy conical ring with innersteps [3]

Recently scholars mainly studied ring rolling processesby using simulation method including the feeding strategies

of reducing power consumption [4] reducing the maximumload [5] realizing a steady forming process [6] and the mod-eling of radial-axial ring rolling process [7]Many researchersinvestigated the changing laws of equivalent plastic strain(PEEQ) temperature grain size and microstructure evolu-tion of rolled rings in hot ring rolling or radial-axial ringrolling processes Wang et al [8] established a strain rate-temperature-microstructure-dependent constitutive modelof Ti-6Al-4V alloy by the userrsquos subroutine VUMAT ofABAQUSExplicit software analyzed the microstructureevolution laws in hot ring rolling of titanium alloy andclaimed that the uniformity of distribution grain size andvolume fraction of 120573 phase increase with the decrease ofdriven rollrsquos rotational speed or the increase of the mandrelfeed rate and the initial temperature of ring blank Qianand Pan [9] established a coupled macro-microscopic finiteelement model for combining blank-forging and rollingprocess and obtained the evolution and distribution lawsof strain temperature grains sizes and dynamic recrystal-lization from the ingot to rolled ring They declared thatthe higher temperature and larger strain are helpful for

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 235656 18 pageshttpdxdoiorg1011552014235656

2 The Scientific World Journal

the improvement of dynamic recrystallization fraction Zhuet al [10] simulated a hot ring rolling process of titaniumalloy by an internal state variable microstructure model forTA15 titanium alloy and pointed out that with the increaseof deformation degree or the initial rolling temperature theprimary 120572 grain size distribution becomes more uniformZhichao et al [11] analyzed the effects of rolling parametersof a hot ring rolling process on microstructure evolution ofrolled ring based on amicrostructure evolutionmodel ofAISI5140 steel

Zhou et al [12] investigated the effects of rolling param-eters on PEEQ and temperature distributions in radial-axialring rolling process and declared that with the increase ofthe mandrel feed rate and the initial temperature of ringblank the PEEQ and temperature distributions of rolled ringbecomemore uniform Anjami and Basti [13] and Zhou et al[14] studied the effects of rolls sizes on the PEEQ andtemperature distributions rolling force and rolling momentin hot ring rolling and radial-axial ring rolling processesrespectively They obtained the optimal rolls sizes for moreuniform PEEQ and temperature distributions of rolled ringsbut did not give out the reasonable mandrel feeding strategy

As the need for profiled rings increases in industries thestudies about profiled ring rolling processes become a hotissue However reports about the PEEQ and temperature dis-tributions in profiled ring rolling processes were insufficientespecially those about conical ring rolling process Qian et al[16] developed a combined ring rolling process based on theminimum resistance principle of metal plastic forming inorder to manufacture a thick-wall and deep-groove ring Intheir study they analyzed the metal flow laws in rolling pro-cess and obtained the PEEQ and temperature distributionslaws of rolled ring by finite elementmethodTheir simulationresults were in accordance with experimental ones Seitz etal [1] simulated and manufactured a dish-shaped ring witha thicker ring wall and lower ring height on radial-axial ringrolling mills and pointed out that a larger height reduction ofthe ring can result in dishing and ring climbing Han et al [3]optimally designed a prorolled ring blank in the aluminumalloy hot rolling process of a conical ring with inner steps bysimulation and experimental methods Yuan [17] optimallydesigned a conical ring blank with inner steps of steel bysimulation and experimental methods Gong and Yang [18]simulated and analyzed the effects of mandrel feed rate onthe PEEQ distribution in rolling process of a conical ringwith outer steps by using the feeding strategy with a constantmandrel feed rate and pointed out that the bigger mandrelfeed rate and lower driven rollrsquos rotational speed can improvethe mechanical property of rolled rings However all of themneither gave out the reasonable mandrel feeding strategy norstudied the effects of key forming parameters such as rollssizes on conical ring rolling processes

Therefore it is significantly necessary to set up the FEmodel of conical ring rolling process establish the plasticpenetration condition and biting-in condition in rollingprocess deduce a reasonable mandrel feeding strategy andinvestigate the effects of key forming parameters on the PEEQand temperature distributions of rolled rings average rollingforce and average rolling moment

H

21

Y

X 3

rt

120579

bt

l

(1) Driven roll (2) Mandrel (3) Conical ring

R998400D R

998400t

R998400M

RMRD Rt

r998400t

Figure 1 The schematic diagram of RCRRCDS process at 119905 time

This paper established the plastic penetration conditionand biting-in condition in RCRRCDS process set up areasonable mandrel feeding strategy with a constant ringrsquosouter radius growth rate and deduced the reasonable valuerange of mandrel feed rate in rolling process The coupledthermomechanical 3D FE model of RCRRCDS process wasestablished based on ABAQUS software The steady conicalring rolling process was realized by numerical simulationThe effects of ringrsquos outer radius growth rate and the sizes ofrolls on the uniformity of PEEQ and temperature distribu-tions of rolled rings average rolling force and average rollingmoment were analyzed

2 The Mathematical Model ofRCRRCDS Process

In RCRRCDS process the radii of driven roll andmandrel aswell as the inner and outer radii of conical ring are variablealong axial direction so at a certain time the plastic pene-tration condition and biting-in condition at different layer-heights are different However the values of feed amount perrevolution at different layer-heights are the same That is tosay an unreasonable mandrel feeding strategy (ie a smallmandrel feed rate)may result in a certain part (ie the bottompart) of conical ring being forged penetrated while the otherpart (ie the top part) of conical ring not being completelyforged penetrated In this situation ringrsquos top radius cannotgrow up successfully and the rolling process is unstableSimilarly a bigger mandrel feed rate may make a certain part(ie the bottom part) of conical ring successfully be bit-in theroll gap between the driven roll and the mandrel while theother part (ie the top part) of conical ring hardly be bit-inTherefore in order tomake the conical ring completely forgedpenetrated and simultaneously bit into the roll gap betweenthe driven roll and the mandrel the plastic penetrationand biting-in conditions at different layer-heights must besatisfied in the whole RCRRCDS process

21 The Plastic Penetration Condition and Biting-In Conditionin RCRRCDS Process Figure 1 shows the schematic diagramof RCRRCDS process at 119905 time In Figure 1 119877

119863is the bottom-

radius of driven roll 119877119872

is the bottom-radius of mandrel119877119905is the ringrsquos bottom outer radius at 119905 time 119903

119905is the ringrsquos

bottom inner radius at 119905 time 119887119905is the thickness of ring wall at

The Scientific World Journal 3

Z

X

L1

O1

r998400t

D

A B

CGH

EF

L2O2

O3

1

2 3

Flow inFlow out


R998400D

R998400t

R998400M

ΔhD(l t)

ΔhM(l t)

Figure 2 The schematic diagram of RCRRCDS process at 119897 layer-height and 119905 time

119905 time119867 is the height of conical ring 120579 is the included anglebetween ring wall and 119883 axis 1198771015840

119863is the driven rollrsquos radius

at 119897 layer-height 1198771015840119872

is mandrelrsquos radius at 119897 layer-height 1198771015840119905

is the ringrsquos outer-radius at 119897 layer-height and at 119905 time 1199031015840119905is

the ringrsquos inner-radius at 119897 layer-height and at 119905 time 119905 is therolling time 119897 is the layer-height of conical ring The valueranges of 119897 119905 and 119867 are (0 le 119897 le 119867) (0 le 119905 le 119879total) and(0 lt 119867 le 119877

119872tan 120579) respectively 119879total is the total rolling

timeFigure 2 shows the schematic diagram of RCRRCDS

process at 119897 layer-height and at 119905 time 1198741 1198742 and 119874

3are

the centers of driven roll mandrel and deforming ringrespectively Δℎ

119863(119897 119905) and Δℎ

119872(119897 119905) are the feed amount per

revolution of the driven roll andmandrel at 119897 layer-height andat 119905 time respectively 119871

1is the projected length of the contact

circular arc 119860119861 between conical ring and driven roll on 119911-axis 119871

2is the projected length of the contact circular arc 119862119863

between the conical ring and mandrel on 119911-axisIn RCRRCDS process since the ring suffers from the

rolling forces of the driven roll and mandrel and theresistances of the top and bottom part of driven roll theconical ringrsquos radius continuously increases while its height isinvariable Therefore it is reasonable to use the plastic pene-tration and biting-in conditions for plain ring rolling processpresented by Hua et al [19] as the beginning conditions todeduce the plastic penetration and biting-in conditions forRCRRCDS process It must be noticed that under the plasticpenetration and biting-in conditions for plain ring rollingprocess the radii of the driven roll and mandrel are bothtreated as constants and the inner and outer radii of ring areboth treated as the function of rolling time 119905 However underthe plastic penetration and biting-in conditions at 119905 time andat 119897 layer-height in RCRRCDS process the radii of drivenroll and mandrel are both treated as the functions of layer-height 119897 and the inner and outer radii of ring are treated asthe functions of both rolling time 119905 and layer-height 119897 In thisway the plastic penetration and biting-in conditions at 119905 time

and at 119897 layer-height in RCRRCDS process can be establishedas follows

Δℎmin (119897 119905)

= 655 times 10minus3(1198771015840119905minus 1199031015840119905)2

(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(1)

Δℎmax (119897 119905)

=21205732

(11198771015840119863+ 11198771015840

119872)2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(2)

Δℎmin (119897 119905)

le Δℎ (119897 119905) le Δℎmax (119897 119905) (3)

where Δℎ(119897 119905) is the feed amount per revolution at 119897 layer-height and at 119905 time and Δℎmin(119897 119905) and Δℎmax(119897 119905) are thepermitted minimum and maximum of Δℎ(119897 119905) respectively120573 is the friction angle between the conical ring and rolls And1198771015840119863= 119877119863+ 119897cot120579 1198771015840

119872= 119877119872minus 119897cot120579 1198771015840

119905= 119877119905minus 119897cot120579 and

1199031015840119905= 119903119905minus 119897cot120579

The RCRRCDS process is a problem with three-dimensional geometry and one-dimensional time In orderto make the conical ring completely forged penetrated andsimultaneously bit into the roll gap between the driven rolland the mandrel according to (1)ndash(3) the feed amount perrevolution at 119897 layer-height and at 119905 time Δℎ(119897 119905) shouldsatisfy the following equation

[Δℎmin (119897 119905)]max le Δℎ (119897 119905) le [Δℎmax (119897 119905)]min (4)

where [Δℎmin(119897 119905)]max is the maximum of Δℎmin(119897 119905) at 119905 timeand [Δℎmax(119897 119905)]min is theminimumofΔℎmax(119897 119905) at 119905 time Byignoring the smaller term 11198771015840

119905minus11199031015840119905in (2) and (3) according

to the monotonicity of functions Δℎmin(119897 119905) and Δℎmax(119897 119905)the maximum of function Δℎmin(119897 119905) and the minimum offunction Δℎmax(119897 119905) can both be obtained at 119897 = 119867 as follows

[Δℎmin (119897 119905)]max = Δℎmin (119897 = 119867 119905)

[Δℎmax (119897 119905)]min = Δℎmax (119897 = 119867 119905) (5)

In Figure 2 according to [13] and by assuming 1198711= 1198712=

119871 we can get

Δℎ (119897 119905) =1198712

2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

) (6)

119871 = radic2Δℎ (119897 119905)

11198771015840119863+ 11198771015840

119872+ 11198771015840

119905minus 11199031015840119905

(7)

In (7) when Δℎ(119897 119905) changes with the increase of 1198771015840119863or

1198771015840119872 both 119871 and the contact areas between the conical ring

and rolls increase Thus the conical ring can be more easilyforged penetrated

For convenience of statement we represent the innerradius surface layer of rolled conical ring by using IL theouter radius surface layer by using OL and the middle layer


by using ML respectively The deformation degrees at IL andOL are connected with Δℎ

119872(119897 119905) and Δℎ

119863(119897 119905) respectively

The bigger the Δℎ119872(119897 119905) is the bigger the deformation at IL

of the rolled ring is the bigger the Δℎ119863(119897 119905) is the bigger

the deformation at OL of the rolled ring is According togeometrical features of RCRRCDS process at 119897 layer-heightand at 119905 time shown in Figure 2 the following equations canbe obtained

Δℎ119863 (119897 119905) =

1198712

2(1

1198771015840119863

+1

1198771015840119905

) (8)

Δℎ119872 (119897 119905) =

1198712

2(

1

1198771015840119872

minus1

1199031015840119905

) (9)

In order to compare the deformation at IL with OL ofthe rolled ring at 119905 time the difference value 120593(119897 119905) betweenΔℎ119863(119897 119905) and Δℎ

119872(119897 119905) is adopted

120593 (119897 119905) = Δℎ119863 (119897 119905) minus Δℎ119872 (119897 119905)

=1198712

2(1

1198771015840119863

minus1

1198771015840119872

+1

1198771015840119905

+1

1199031015840119905

) (10)

In (10) the effect of 11198771015840119905+ 11199031015840119905in (10) can be neglected

because 11198771015840119905+ 11199031015840119905is much smaller than 11198771015840

119863minus 11198771015840

119872and

gradually decreases with the increase of rolling timeThus wecan get

120593 (119897 119905) =1198712

2(1

1198771015840119863

minus1

1198771015840119872

) (11)

In (11) if 120593(119897 119905) gt 0 it indicates that the deformationdegree at OL of rolled ring is bigger than that at IL of rolledring at 119905 time and at 119897 layer-height and vice versa

22 The Reasonable Value Range of Mandrel Feed RateDetermining a reasonable feeding strategy is the preconditionof realizing a steady rolling process To realize a steady andfeasible radial-axial ring rolling process the feeding strategythat can achieve a constant ringrsquos outer radius growth rate wasadopted by Guo and Yang [6] Pan [20] and Kim et al [21]respectively However the mandrel feeding strategy deducedby them can only be used in radial-axial rectangular ringrolling processes but cannot be directly used in conical ringrolling process For this reason this paper deduced the rea-sonable value range ofmandrel feed rate by adopting the feed-ing strategy with a constant ringrsquos outer radius growth rate

In this section by assuming that the ringrsquos outer radiusgrows up at a constant rate the instantaneous mandrel feedrate is deduced Thus when mandrel rolls the conical ring bythe deduced feed rate it is thought that the conical ringrsquos outerradius grows up at a constant rate The deviation process ofthe instantaneous mandrel feed rate is as follows

In RCRRCDS process the driven roll rotates at a constantperipheral speed V

119863 When the constant ringrsquos outer radius

grows up at a constant rate V1015840119877 the ringrsquos outer radius at 119897 layer-

height and at 119905 time 1198771015840119905 can be expressed as follows

1198771015840119905= 1198770minus 119897 sdot cot120579 + V1015840

119877119905 (12)

where 1198770is the initial ringrsquos bottom outer radius

After heating upsetting and punching the ingot isproduced into a conical ring blank at first Then the conicalring blank is rolled into a needed conical ring on ring rollingmills According to the principle of volume constancy inRCRRCDSprocess the ringrsquos outer radius at 119897 layer-height andat 119905 time can be also expressed as

1198771015840119905=1198871015840119905

2+1198870(1198770+ 1199030minus 119867cot120579)

21198871015840119905

+119867cot1205792

(13)

where 1198871015840119905is the thickness of ring wall at 119897 layer-height and at

119905 time and 1199030and 1198870are the initial inner radius and thickness

of conical ring respectivelyBecause the derivative of 1198771015840

119905with respect to time 119905 is

V1015840119877 taking the derivative of (13) with respect to time 119905 the

following equations can be obtained

V1015840119877=1198891198771015840119905

119889119905=V1015840119905

2[(1198770+ 1199030minus 119867cot120579) 119887

0

11988710158402119905

minus 1] (14)

V1015840119905=

2V1015840119877

(1198770+ 1199030minus 119867cot120579) 119887

011988710158402119905minus 1

(15)

where V1015840119905is themandrel feed rate at 119897 layer-height and at 119905 time

The mandrel feed rate at 119897 layer-height and at 119905 time V1015840119905

can be also approximately expressed by the average mandrelfeed rate when the ring just right-rotates one revolution at 119905time

V1015840119905asympΔℎ (119897 119905)

Δ119905 (16)

where Δ119905 is the time when the ring just right-rotates onerevolution at 119905 time

By neglecting the sliding motion between the rolls andring in RCRRCDS process at 119905 time of the rolling processthe length that the ringrsquos bottom outer radius rotates onerevolution equals the length that the radius of the driven rollrotates Therefore we have

21205871198771015840119905= 1198991198631198771015840119863Δ119905 (17)

where 119899119863is the angular velocity of the driven roll

According to (15) (16) and (17) it can be obtained that

Δℎ (119897 119905) =4120587V1015840119877(11987710158400+ V1015840119877119905)

1198991198631198771015840119863

sdot11988710158402119905

(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905

(18)


1198991198631198771015840119863

21205871198771015840119905

[Δℎmin (119897 119905)]max le V1015840119905le1198991198631198771015840119863

21205871198771015840119905

[Δℎmax (119897 119905)]min (19)


X

Y

Z

MandrelFore guide roll

Driven roll Back guide roll Conical ring

Figure 3 The FE model of RCRRCDS process

According to (14) and (19) the reasonable value range ofV1015840119877can be obtained

119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmin (119897 119905)]max

le V1015840119877

le119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmax (119897 119905)]min

(20)

To sumup in order to realize a steady RCRRCDS processthe instantaneous mandrel feed rate V1015840

119905can be obtained by

(15) while the reasonable value ranges of V1015840119905and V1015840

119877can be

obtained by (19) and (20) respectively

3 The FE Modeling of RCRRCDS Process

According to the mandrel feeding strategy established inSection 2 the FE model of RCRRCDS process was set upbased on ABAQUSExplicit software as shown in Figure 3The key FE modeling techniques are expressed as follows indetail

31 CAE Modeling The conical ring blank is defined as a 3Ddeformable body all rolls are defined as rigid bodies Thecoupled thermodisplacement element with eight nodes andsix faces (C3D8RT) was adopted to mesh the conical ringblankThe number of finite element meshes is approximately8000 Four pairs of contact relationships between the conicalring and the driven roll mandrel fore guide roll and backguide roll were defined respectivelyThe frictional conditionsand thermal conditions such as thermal conduction thermalconvection and thermal radiation were considered in theFE model In order to prevent the conical ring from beingblocked in the gap between the driven roll and the mandrelthe glass lubricant is usually used on the interfaces betweenthe conical ring and the top and bottom part of driven rollAccording to [22] the friction factor on these interfaces isdefined as 01 The friction factor on the interface between

the conical ring and the side face of driven roll is definedas 05 [23] The friction factors on the interfaces betweenthe conical ring with the mandrel and guide rolls are alsodefined as 05 The temperatures of driven roll and guiderolls are 100∘C The temperature of mandrel is 200∘C Theinitial temperature of conical blank is 900∘C The coefficientof thermal convection is 002Nsminus1mmminus1∘C the thermalemissivity is 06Nsminus1mmminus1∘Cminus4 [24] In order to reduce thesimulation time the mass scaling technology and dynamicexplicit algorithm are employed The mass scaling factor isselected as 50 Reduction integration and ALE remeshingtechnology are also adopted to avoid the nonconvergence offinite element numerical solution caused by severely distortedmeshes Hourglass control is employed to avoid zero energymodes

32 TheMotions Control of Rolls The FEmodel is assembledunder the global coordinate system Each of the rolls is setto its own reference point In the numerical simulation ofRCRRCDS process the rotational and translational motionsof rolls can be controlled by setting the motion conditionsof their own corresponding reference points The driven rollrotates about its own fixed center by a constant peripheralspeed Suffering from the friction force of the conical ringthe mandrel and guide rolls can rotate about their own corre-sponding centers respectively The mandrel moves along theminus119909-axis The 119883 coordinate of mandrel at 119905 time 119909

119905 can be

obtained according to (15) 119909119905= 1199090minusint V1015840119905119889119905 where 119909

0is the119883

coordinate ofmandrel at the initial timeThe guide rollsmovein 119883119874119885 plane and the movement locus (displacement-timerelationship curves) of guide rolls can be obtained accordingto [25]

33 Material Constitutive Model The material of the conicalring is selected as Ti-6Al-4V Its destiny andPoissonrsquos ratio are4430 kgm3 and 03 respectively Its temperature-dependentphysical properties such as thermal conductivity specificheat and Youngrsquos modulus are from [24] Its constitutivemodel within the forging temperature range 800∘Csim950∘C isfrom [26]

120590 = 119896119885119898120582119899 (1 minus 119890minus120573120576)

120582 = 1205820119885119902 + (1 minus 120582

0119885119902) 119890minus120572120576

119885 = 120576119890119876defm119877119879

(21)

where 120590 is the flow stress 119885 is the Zener-Hollomon param-eter 120582 is an internal state variable 120576 is the plastic strain 120576is the strain rate 119876defm is the deformation activation energyfor Ti-6Al-4V 119877 is the universal gas constant 119879 is theabsolute temperature 119896 is a scaling constant 119898 is the strainrate sensitivity 119899 is the structure-stress exponent 120573 is anexponential damping constant relating strain and stress 120582

0

is a scaling constant related to the steady-state stress 119902 isthe rate sensitivity of structure 120572 is an exponential dampingconstant relating strain and structureThe values of the abovecoefficients are shown in Table 1


Table 1 Constitutive data for Ti-6Al-4V

Coefficient Value119896 469 times 10minus4

119898 03119899 1120573 66731205820

6424119902 minus517 times 10minus2

120572 607119876defm119877 50668 times 104

Table 2 Forming parameters in RCRRCDS process

Parameters ValueBottom radius of guide roll (mm) 40Initial bottom outer radius of ring (mm) 300Initial bottom inner radius of ring (mm) 150Initial height of ring (mm) 865Angle between ring and horizontal plane (∘) 60Total feed amount (mm) 70The peripheral speed of driven roll (mms) 1000

4 Validation of the FE Model ofRCRRCDS Process

41 Theoretical Validation Here the energy balance ruleis adopted to theoretically validate the reliability of theestablished FEmodel Generally if the ratio of the FEmodelrsquoskinetic energy (ALLKE) to its internal energy (ALLIE) issmaller than 5ndash10 in rolling process and the changingcurves of ALLKE and ALLIE with rolling time are smooththe established FE model is theoretically reliable In RCR-RCDS process studied in Section 51 of this paper the bottomradii of the driven roll and mandrel are 200mm and 100mmrespectivelyThe ringrsquos outer radius growth rate V1015840

119877is 6mms

Other forming parameters are shown in Table 2 Accordingto (20) the reasonable value range of V1015840

119877is 1215mms lt

V1015840119877lt 665mms Thus the plastic penetration and biting-in

conditions in the entire RCRRCDS process can be satisfiedFigure 3 shows the established FE model of RCRRCDSprocess

Figure 4 shows the changing curves of ALLKE andALLIEand the ratio of the FE modelrsquos kinetic energy to its internalenergy (ALLKEALLIE) with rolling time It can be seenthat the ratio of the FE modelrsquos kinetic energy to its internalenergy is smaller than 5ndash10 in the main rolling processTherefore the established FE model of RCRRCDS process istheoretically reliable

42 Experimental Validation The established RCRRCDSprocess is similar to the conical ring rolling experimentsin [15] In order to experimentally validate the reliability ofthe established RCRRCDS process this paper established thecorresponding FE model of RCRRCDS process accordingto the experimental situation and the parameters in [15]The RCRRCDS experiments were carried out on D51-160A

0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400

ALLKEALLIEALLKEALLIE

Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25

Figure 4 The changing curves of the kinetic and internal energiesof the FE model with rolling time

hot ring rolling mill The experimental forming parametersare shown in Table 3 The material of conical ring blank islead Its density Youngrsquos modulus and Poissonrsquos ratio are11340 kgm3 16 GPa and 03 respectively Its constitutivemodel is 120590 = 25061205760241 [15] In the validated model inthis paper the friction factor between conical ring blank androlls is 05 The mass scaling factor is 50 Table 4 shows thecomparison of simulation and experimental results wherethe numerical error between simulation results and experi-mental ones is defined as (simulation value minus experimentalvalue)experimental value

It can be seen from Table 4 that the simulation valuesare close to experimental onesThemaximum andminimumnumerical errors are 62 and 07 respectively This indi-cates that the FE model of RCRRCDS process established inthis paper is reliable

5 Results and Discussion

This section simulated and analyzed the effects of key formingparameters on RCRRCES process based on the FE model ofRCRRCDS process established in Section 3 In accordancewith different research objectives the numerical simulationexperiments are made up of the following four cases

Case 1 Investigate the changing laws of the PEEQ andtemperature distributions with rolling time Select 119877

119863=

200mm 119877119872= 100mm V1015840

119877= 6mms while other parameters

are listed in Table 2 and keep invariable

Case 2 Investigate the effects of ringrsquos outer radius growthrate on the PEEQ and temperature distributions in RCR-RCDS process Select 119877

119863= 200mm 119877

119872= 100mm V1015840

119877=

3mms 4mms 5mms 6mms while other parameters arelisted in Table 2 and keep invariable


Table 3 Experimental parameters of RCRRCDS process in [15]

Parameters ValuesDiameters of driven rollrsquos big and small ends (mm) 34000 29960Diameters of mandrelrsquos big and small ends (mm) 4452 500Diameters of guide rollrsquos big and small ends (mm) 10000 2950Outer and inner diameters of initial conical ring blankrsquos big ends (mm) 10060 6440Outer and inner diameters of initial conical ring blankrsquos small ends (mm) 6020 2400Heights of driven roll mandrel and guide roll (mm) 8000Height of initial conical ring blank (mm) 8000Rotational speed of driven roll (rmin) 122Mandrel feed rate (mm) 200

Table 4 Experimental and simulation values of rolled ring

Outer diameterof small end (mm)

Inner diameterof small end (mm)

Outer diameterof big end (mm)

Inner diameterof big end (mm)

Height(mm)

Taper angle(∘)

Experimental values [15] 115 94 167 145 76 711Simulation values 114 93 175 154 765 683Numerical error minus087 minus11 48 62 07 minus39

Case 3 Investigate the effects of driven roll radius on thePEEQ and temperature distributions in RCRRCDS processSelect 119877

119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm

400mm 600mm 800mm In order to maintain the drivenroll rotating at a constant peripheral speed the angular veloc-ities of the driven roll are accordingly selected as 10 rads5 rads 25 rads 167 rads and 125 rads respectively whileother parameters are listed in Table 2 and keep invariable

Case 4 Investigate the effects of mandrel radius on the PEEQand temperature distributions in RCRRCDS process Select119877119863= 200mm V1015840

119877= 4mms Since 119877

119872should be smaller

than the initial bottom inner radius of the conical ringblank (150mm) and bigger than 50mm by considering that1198771015840119872

decreases along axial direction according to geometricalfeatures in Figure 1 therefore the values of 119877

119872are respec-

tively selected as 119877119872

= 70mm 80mm 90mm 100mm110mm while other parameters are listed in Table 2 and keepinvariable

Here the standard deviation of equivalent plastic strain(SDP) and the standard deviation of temperature (SDT) areemployed to evaluate the uniformity of PEEQ and tempera-ture distributions of rolled conical rings respectively

SDP = radicsum119873

119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894

SDT = radicsum119873

119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)

where PEEQ119886is the average value of PEEQ PEEQ

119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ

119894is the PEEQ of element 119894 119881

119894

is the volume of element 119894119873 is the total number of elementsof the conical ring 119879

119886is the average value of temperature

119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873

119894=1119881119894 119879119894is the temperature of element

119894 The lower the SDP is the more uniform the PEEQdistribution is The lower the SDT is the more uniform thetemperature distribution is

51 The Changing Laws of PEEQ and Temperature Distribu-tions of Rolled Ring with Rolling Time The whole RCRRCDSprocess is made up of four rolling stages initial biting-insteady forming final rolling and finishing rolling roundstages The initial biting-in stage is from the time when themandrel starts to roll the ring to the time when the ringjust right-rotates the first one revolution The steady formingstage is from the end of the initial biting-in stage to the timewhen the mandrel stops feed movement The final rollingstage is from the end of the steady forming stage to the timethat the mandrel goes on rolling ring another one revolutionThe finishing rolling round stage is from the end of the finalrolling stage to the time that the mandrel goes on rollingring two additional revolutions According to the simulationconditions of Case 1 the durable time of the initial biting-instage is calculated as 377 s the time of the steady formingstage is 2183 s the time of the final rolling stage is 277 s thetime of the finishing rolling round stage is 553 s and the totalrolling time is 339 s

Figure 5 shows the PEEQ distributions of the deformingring at different rolling times It can be seen that thedeformation of the rolled ring mainly concentrated on theinner radius surface layer (IL) and outer radius surface layer(OL) the usually seen fishtail defects do not appear at the topand bottom part of conical ring Generally speaking if theinitial billet geometry has sharp edges the singularity issuessuch asmeshes distortionsmay occur at the ringrsquos sharp edgespositions However for the RCRRCDS process studied in thispaper the singularity issues do not appear The main reasonmay be that on the one hand the closed die structure shapeof driven roll reasonable mandrel feed rate and the usage


PEEQ

Outer radius surface layer

Inner radius surface layerMiddle layer

+8804e minus 01+8079e minus 01+7354e minus 01+6628e minus 01+5903e minus 01

+4452e minus 01+3727e minus 01+3002e minus 01+2277e minus 01+1551e minus 01+8259e minus 02+1006e minus 02

+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00

+9505e minus 01+6820e minus 01+4134e minus 01

(Avg 75)

(c) 119905 = 20 s

PEEQ

+5124e + 00+4744e + 00+4364e + 00+3984e + 00+3604e + 00+3224e + 00+2844e + 00+2464e + 00+2084e + 00+1704e + 00+1324e + 00+9436e minus 01+5635e minus 01

(Avg 75)

(d) 119905 = 339 s

Figure 5 The PEEQ distributions of deforming ring at different rolling times

of reduction integration and ALE remeshing technology caneffectively avoid the singularity issues on the other handaccording to [15] the bigger the ratio of the initial conicalring blankrsquos height to its diameter is the more serious thedistortion of rolled ring along the radial direction is and viceversa In this paper the ratio of the initial conical ring blankrsquosheight to its diameter is so small (only approximately 0144)that the distortion of the rolled ring is too tinyTherefore thesingularity issues do not appear

In Figure 5 with the increase of rolling time the maxi-mum PEEQ appears at the top and bottom part of IL Thereason is that themetal at the top and bottompart of IL suffers

from the resistances of the top and bottom part of driven rolland can only be seriously deformed along the circumferentialdirectionThese positions are the potential areaswhere cracksmay occur due to their large and severe deformation

Figure 6(a) shows the conical ring blank and the rolledconical ring Since the PEEQ and temperature distributionsof the conical ring are axis-symmetric about its center acertain cross-section of rolled conical ring ldquoS-Srdquo is selectedto investigate the PEEQ and temperature distributions at 119905 =339 s as shown in Figures 6(b) and 6(c) In Figure 6(b) thePEEQ at IL and OL are bigger than that at the middle layer(ML) The reason can be explained as follows On the one


Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H

IOuter radius Inner radius


(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)

Figure 6 (a) Conical ring blank and rolled conical ring (b) the PEEQdistribution at the cross-section ldquoS-Srdquo of rolled conical ring at 119905 = 339 s(c) the temperature distribution at the cross-section ldquoS-Srdquo of rolled conical ring at 119905 = 339 s

hand since the conical ring suffers from the rolling forcesof driven roll and mandrel along radial direction and thetangential stress along the circumferential direction there area contracted metal flow tendency along the radial directionand expanded tendency along the axial and circumferentialdirections On the other hand since the conical ring suffersfrom the restrictions of the top and bottom part of thedriven roll the metal flow tendency along the axial directionis restricted In this situation the ring radius continuouslyincreases the thickness of ring wall gradually decreases andthe height of the ring is invariable The large deformationmainly concentrates on IL and OL of the rolled ring It alsocan be seen that the PEEQ at 119897 layer-height of IL is larger thanthat of OL The reason is that 120593(119897 119905) lt 0 according to theconditions of Case 1 and (11)Thismeans that the feed amountof the driven roll at 119897 layer-height is smaller than that of themandrel and the larger deformation locates at IL of the rolledring

Nine tracking points AndashI at the cross-section ldquoS-Srdquo ofthe rolled ring are selected to investigate the PEEQ andtemperature distributions with rolling time as shown inFigures 6(b) and 6(c) Figure 7(a) shows the changing curvesof the PEEQ of points AndashI with rolling time

It can be seen from Figures 5 and 7(a) that at the initialbiting-in stage and steady forming stage the PEEQ of pointsBndashI basically increase linearly while the PEEQ of point A

increases fast at first and then slower At the final rollingand finishing rolling round stage the PEEQ of points AndashIare invariable This indicates that with the increase of therolling time the uniformity of PEEQ distribution graduallydecreases at the initial biting-in stage and steady formingstage and then keeps unchanged at the final rolling stage andfinishing rolling round stage

Figures 7(b) and 7(c) show the changing curves of PEEQat the cross-section ldquoS-Srdquo of the rolled ring along the axialand radial directions at 119905 = 339 s respectively It can be seenfrom Figures 6(b) and 7(b) that the PEEQ at IL (line-IHG)OL (line-CBA) and ML (line-FED) of the rolled ring reducein turn Along the axial direction from the ringrsquos bottom toringrsquos top the PEEQ at the ML (line-FED) of the conical ringis basically unchanged the PEEQ at IL (line-IHG) decreasesat first and then increases and finally keeps unchanged thePEEQ at OL (line-CBA) increases slowly at first and then fastThis indicates that the larger PEEQ appears at the top andbottom of IL and the top of OL The reason is that the metalat points A G and I suffers from the restriction of the topand bottom part of the driven roll and can only flow alongthe circumferential direction with a larger resistance whichleads to serious deformation at these positions It also can beseen that the PEEQ at point C is smaller than those at pointsA G and I The reason may be that the conical ring radiusat point C is larger than those at points A G and I and thus


0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F

Point GPoint HPoint I

Trac

e poi

nts P

EEQ

Rolling time (s)

Point APoint BPoint C

Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ

Distance from bottom point to top point (m)

Line CBALine FEDLine IHG

(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ

Distance from inner point to outer point (m)

Line IFCLine HEBLine GDA

(c)

Figure 7 (a) The changing curves of the PEEQ of points AndashI with rolling time (b) the changing curves of PEEQ along the axial direction at119905 = 339 s (c) the changing curves of PEEQ along the radial direction at 119905 = 339 s

theremay exist a larger geometric space along circumferentialdirection for the deformed metal flow which can reduce thePEEQ at point C to some extent

It can be seen from Figures 6(b) and 7(c) that alongthe radial direction from the inner radius to outer radiusthe PEEQ of the bottom layer (BL line-IFC) top layer (TLline-GDA) and middle layer (ML line-HEB) of the rolledring decrease at first and then keep unchanged and finallyincrease The PEEQ of rolled ring significantly changes alongradial direction This may be because the metal at IL and OLof conical ring is more easily forged penetrated than that at

ML of conical ring It can be deduced that the grain sizes atthe positions with large PEEQ (points A G and I) are fineand the mechanical properties at these positions are betterHowever these positions are the potential areas where cracksmay occur due to their large and severe deformation

Figure 8 shows the temperature distributions of thedeforming ring at different rolling times It can be seen fromFigures 8(a)ndash8(d) that at the beginning of RCRRCDS processthe temperatures at the top and bottom part of IL and the toppart ofOL are higher than those at other positions as shown inFigures 8(a) and 8(b) while at the end of RCRRCDS process


NT11Obtuse angle zones

Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s

NT11+1127e + 03+1107e + 03+1086e + 03+1065e + 03+1044e + 03+1024e + 03+1003e + 03+9819e + 02+9611e + 02+9403e + 02+9195e + 02+8987e + 02+8779e + 02

(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s

Figure 8 The temperature distributions of deforming ring at different rolling times

the temperatures at the bottom part of IL and the top partof OL are higher than those at other positions as shown inFigures 8(c) and 8(d)

Figure 9(a) shows the changing curves of the temperatureof points AndashI with rolling time It can be seen from Figures 8and 9(a) that at the initial biting-in stage the temperaturesof points A and I rapidly increase due to the deformationheat At the steady forming stage the temperatures of pointsA and I basically keep unchanged because the deformationheat approximately balances the heat loss At the final rollingstage and finishing rolling round stage the temperaturesof points A and I gradually decrease because there are notdeformation heat while the heat loss still exists At the initialbiting-in stage the temperatures of points C and G gradually

increase due to larger deformation heat At the steady formingstage final rolling stage and finishing rolling round stage thetemperatures of points C and G obviously decrease becausethe heat loss at these positions is larger than the deformationheatThe temperatures of points B C E F andH change a bitat the temperature range between 875∘C and 900∘C It can beconcluded that the uniformities of temperature distributionsat the corners of conical ringrsquos cross-section become worsewhich may be caused by both uneven deformation andinhomogeneous heat loss

Figures 9(b) and 9(c) show the changing curves oftemperatures at cross-section ldquoS-Srdquo of rolled ring along theaxial and radial directions respectively Figures 5(c) and 8(b)show that along the axial direction from the ringrsquos bottom


0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150


Point DPoint EPoint F


Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)

Figure 9 (a)The changing curves of the temperature of points AndashI with rolling time (b) the changing curves of temperatures along the axialdirection at 119905 = 339 s (c) the changing curves of temperatures along the radial direction at 119905 = 339 s

to ringrsquos top the temperature at OL (line-CBA) increasesslowly at first and then fast the temperature atML (line-FED)increases slowly at first then keeps unchanged and finallydecreases the temperature at IL (line-IHG) decreases sharplyat first and then gradually increases

It can be seen from Figures 6(c) and 9(c) that alongradial direction from the ringrsquos inner radius to ringrsquos outerradius the temperature at BL (line-IFC) decreases sharplyat first then keeps unchanged and finally decreases againthe temperature at ML (line-HEB) slightly increases at firstthen keeps unchanged and finally decreases a little thetemperature at TL (line-GDA) decreases slowly at first andthen increases sharply

From Figures 6(c) 9(b) and 9(c) it can be seen thatthe temperature distribution at the central part of the cross-section of rolled ring is uniform while the temperaturedistributions at the edges and corners of rolled ring differquite a lot The temperatures at the ldquoobtuse angle zonerdquo (asshown as points A and I in Figure 6(c)) of the conical ringrsquoscross-section are higher while the temperatures at the ldquoacuteangle zonerdquo (as shown as points C and G in Figure 6(c)) ofthe conical ringrsquos cross-section and at the middle part of theringrsquos surfaces are lower This phenomenon can be explainedby the following two aspects On the one hand the largerdeformation concentrated on IL and OL of the conical ringresults in the larger deformation heat at these positions On


3 4 5 60

1

2

3

4

5

6

7

8

Maximum PEEQAverage PEEQ

Outer radius growth rate of conical ring (mms)

PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP

Figure 10 The changing curves of the maximum minimum andaverage PEEQ and SDP with ringrsquos outer radius growth rate

the other hand since the specific surface areas at points Aand I are smaller than those at points C and G the heat lossesat points A and I are less than those at points C and G Tosum up though the larger deformations at points A C Iand G occur the temperatures at the ldquoobtuse angle zonerdquo (asshown as points A and I) are larger than those at the ldquoacuteangle zonerdquo (as shown as points C and G) which may lead tothe residual heat tensile stress The metal at the ldquoobtuse anglezonerdquo has a relatively large damaging potential

52 The Effects of Ringrsquos Outer Radius Growth Rate on PEEQandTemperatureDistributions Figure 10 shows the changingcurves of the maximum minimum and average PEEQ andSDP with ringrsquos outer radius growth rate In Figure 10 withthe increase of the ringrsquos outer radius growth rate themaximum PEEQ and SDP decrease the minimum PEEQincreases the average PEEQ slightly decreases The reasonis analyzed as follows Firstly according to (18) when theperipheral speed of the driven roll is unchanged the feedamount per revolution increases and the ring is more easilyforged penetrated with the increase of the ringrsquos outer radiusgrowth rate This phenomenon improves the uniformityof PEEQ distribution Secondly according to (7) with theincrease of the feed amount per revolution the length of thecontact circular arc and the contact area between the conicalring and rolls increases This phenomenon makes the metalmore easily forged penetrated

Figure 11 shows the changing curves of the maximumminimum and average temperatures and SDT with ringrsquosouter radius growth rate In Figure 11 with the increase ofthe ringrsquos outer radius growth rate theminimum temperaturegradually increases This is because when the total feedamount of the mandrel is unchanged with the increase ofthe ringrsquos outer radius growth rate the rolling time decreasesThus the heat loss caused by convection and radiation

850

900

950

1000

1050

1100

1150

1200

Maximum temperatureAverage temperature


Tem

pera

ture

(∘C)

34

35

36

37

38

39

40

Minimum temperatureSDT

SDT

(∘C)

3 4 5 6

Figure 11 The changing curves of the maximum minimum andaverage temperatures and SDT with ringrsquos outer radius growth rate

decreases but the minimum temperature increases It alsocan be seen that with the increase of the ringrsquos outer radiusgrowth rate the maximum temperature gradually decreasesThis is because according to (18) and with the increase ofthe ringrsquos outer radius growth rate the feed amount perrevolution increases The ring becomes more easily forgedpenetrated and thus the deformation heat decreases

In Figures 10 and 11 with the increase of the ringrsquos outerradius growth rate SDP gradually decreases from 14 to 095SDT increases from 355 to 385 at first and then decreases totheminimum value 347This indicates that with the increaseof the ringrsquos outer radius growth rate the uniformities ofPEEQ and temperature distributions increase When theringrsquos outer radius growth rate is 6mms the PEEQ andtemperature distributions of the rolled conical ring are themost uniform simultaneously

53 The Effects of Driven Rollrsquos Bottom Radius on PEEQandTemperatureDistributions Figure 12 shows the changingcurves of the maximum minimum and average PEEQ andSDP with driven rollrsquos bottom radius In Figure 12 with theincrease of the driven rollrsquos bottom radius the minimumPEEQ is basically unchanged the maximum and average ofPEEQ slightly decrease at first and then keep unchangedSDP decreases rapidly at first and then increases slowly Basedon the conditions of Case 2 and (18) when the peripheralspeed of the driven roll and ringrsquos outer radius growth rateare unchanged the feed amount per revolution is invariableAccording to (7) when the feed amount per revolutionis invariable with the increase of the driven rollrsquos bottomradius from 100mm to 600mm the length of the contactcircular arc and the contact areas between the conical ringand the driven roll increase which results in the ring beingmore easily forged penetrated Moreover with the increaseof the driven rollrsquos bottom radius from 600mm to 800mm


0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6

Maximum PEEQAverage PEEQMinimum PEEQSDP

Driven rollrsquos bottom radius (mm)

PEEQ

110

115

120

125

SDP

Figure 12 The changing curves of the maximum minimum andaverage PEEQ and SDP with driven rollrsquos bottom radius

0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)

Maximum temperatureAverage temperatureMinimum temperature

Figure 13 The changing curves of the maximum minimum andaverage temperatures and SDT with driven rollrsquos bottom radius

the contact areas between the conical ring and driven rollfurther increase and thus the heat loss between the conicalring and rolls increases which leads to the increase of mate-rial yield strength and the decrease of the forged penetratedability of the ring

Figure 13 shows the changing curves of the maximumminimum and average temperatures and SDT with thedriven rollrsquos bottom radius In Figure 13 with the increase ofthe driven rollrsquos bottom radius the maximum temperaturehas a small fluctuation between 1150∘C and 1200∘C theminimum temperature gradually decreases the average tem-perature is basically invariable and SDT slightly decreases

70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP

Mandrelrsquos bottom radius (mm)

PEEQ

08

10

12

14

16

18

SDP

Maximum PEEQAverage PEEQMinimum PEEQ

Figure 14 The changing curves of the maximum minimum andaverage PEEQ and SDP with mandrelrsquos bottom radius

at first and then gradually increases The reason may bethat with the increase of the driven rollrsquos bottom radius thecontact area between the conical ring and rolls increasesthe heat loss of the rolled ring increases the minimum tem-perature decreases and thus the uniformity of temperaturedistribution gets worse

In Figures 12 and 13 with the increase of the driven rollrsquosbottom radius SDP decreases from 124 to the minimumvalue 107 at first and then increases to 112 SDT slightlydecreases from 395 to 385 at first and then graduallyincreases to 44This indicates that the PEEQ and temperaturedistributions become uniform at first and then nonuniformHowever the minimum values of SDP and SDT are obtainedat different driven rollrsquos bottom radius respectively Whenthe driven rollrsquos bottom radius is 200mm SDT obtains itsminimum value SDP obtains its relatively minimum value(approximately 113) and thus the temperature distributionof rolled conical ring is most homogeneous and the PEEQdistribution of the rolled conical ring is relatively uniform

54The Effects ofMandrelrsquos BottomRadius on PEEQ and Tem-perature Distributions Figure 14 shows the changing curvesof themaximumminimum and average PEEQand SDPwithmandrelrsquos bottom radius In Figure 14 with the increase ofmandrelrsquos bottom radius the maximum and average of PEEQand SDP gradually decrease while the minimum of PEEQ isbasically unchanged This indicates that with the increase ofmandrelrsquos bottom radius the PEEQ distribution of the rolledring becomes uniform The reason is that according to theconditions of Case 3 and (18) when both the peripheral speedof the driven roll and the ringrsquos outer radius growth rateare constants the feed amount per revolution is invariableAccording to (8) when the feed amount per revolution isinvariable with the increase of mandrelrsquos bottom radius thelength of the contact circular arc and the contact area between


70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)


Figure 15 The changing curves of the maximum minimum andaverage temperatures and SDT with mandrelrsquos bottom radius

the conical ring and mandrel increase and thus the conicalring becomes more easily forged penetrated

Figure 15 shows the changing curves of the maximumminimum and average temperatures and SDTwithmandrelrsquosbottom radius In Figure 15 with the increase of mandrelrsquosbottom radius the minimum and average temperaturesare invariable the maximum temperature has a fluctuationbetween 1170∘C and 1220∘C the SDT fluctuates between 365and 39 This indicates that the effect of mandrelrsquos bottomradius on the temperature distribution of the rolled ring isnot obvious

In Figures 14 and 15 with the increase of mandrelrsquosbottom radius SDP gradually decreases from 175 to theminimum 10 and SDT decreases from 39 to the minimum365 at first then increases and finally decreases to 375This indicates that as mandrelrsquos bottom radius increasesthe PEEQ distribution becomes more uniform while theuniformity of temperature distributionhas a small fluctuationbetween 365 and 39 However the minimum values of SDPand SDT are obtained at different mandrelrsquos bottom radiusrespectively When mandrelrsquos bottom radius is 110mm thePEEQ distribution of rolled conical ring is most uniformand the temperature distribution of the rolled conical ring isrelatively uniform

55 The Effects of Key Forming Parameters on AverageRolling Force and Rolling Moment Figure 16(a) shows thechanging curves of the average rolling force and averagerolling moment with the ringrsquos outer radius growth rateIn Figure 16(a) with the increase of the ringrsquos outer radiusgrowth rate the average rolling force decreases to theminimum 248 kN at first then increases and finally keepsunchanged The reason is that with the increase of the ringrsquosouter radius growth rate the feed amount per revolutionis basically unchanged and thus the rolling force changes

a little It also can be seen that with the increase of theringrsquos outer radius growth rate the average rolling momentis basically unchanged approximately 30 kNmThe reason isthat with the increase of the ringrsquos outer radius growth ratethe force arm is unchanged while the rolling force changes alittle and thus the rolling moment is basically invariable

Figure 16(b) shows the changing curves of the averagerolling force and average rolling moment with the drivenrollrsquos bottom radius In Figure 16(b) with the increase of thedriven rollrsquos bottom radius the average rolling force increasesfrom 240 kN to 263 kN at first and finally slightly decreasesto 261 kN The reason is that with the increase of the drivenrollrsquos bottom radius the contact area between the conicalring and rolls increases more metal participates in the plasticdeformation and thus the average rolling force increases Italso can be seen that with the increase of the driven rollrsquosbottom radius the average rollingmoment basically increaseslinearly from 20 kNm to 85 kNmThe reason is that with theincrease of the driven rollrsquos bottom radius both the rollingforce and force arm increase and thus the average rollingmoment increases

Figure 16(c) shows the changing curve of the averagerolling force and average rolling moment with mandrelrsquosbottom radius In Figure 16(c) with the increase of mandrelrsquosbottom radius the average rolling force gradually increasesfrom236 kN to 256 kNThe reason is that with the increase ofmandrelrsquos bottom radius the contact area between the conicalring and rolls increases more metal participates in the plasticdeformation and thus the average rolling force increasesIt also can be seen that with the increase of mandrelrsquosbottom radius the rolling moment is basically unchangedapproximately 30 kNm

To sum up the radii of the driven roll and mandrel havesignificant effects on the average rolling force the driven rollrsquosradius has significant influences on average rolling momentbut the ringrsquos outer radius growth rate slightly affects theaverage rolling force and average rolling moment

6 Conclusions

This paper established a mathematical model of RCRRCDSprocess deduced the plastic penetration condition andbiting-in condition and determined the reasonable valuerange of the mandrel feed rate in the entire rolling processThe effects of the ringrsquos outer radius growth rate and theradii of the driven roll and mandrel on the PEEQ andtemperature distributions average rolling force and averagerolling moment were investigated The main conclusions aredrawn as follows

(1) The PEEQ at IL and OL of rolled ring are largerthan that at ML of the rolled ring Temperatures atthe ldquoobtuse angle zonerdquo of the ringrsquos cross-sectionare higher than those at ldquoacute angle zonerdquo Thetemperature at the central part of the conical ring ismore uniform while the temperatures at the cornersof ringrsquos cross-section change significantly

(2) With the increase of the ringrsquos outer radius growthrate at its reasonable value range the uniformities


3 4 5 6230

235

240

245

250

255

260

265

Average rolling forceAverage rolling moment


Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)

Figure 16 (a) The changing curves of average rolling fore and average rolling moment with ringrsquos outer radius growth rate (b) the changingcurves of average rolling fore and average rolling moment with driven rollrsquos bottom radius (c) the changing curve of average rolling fore andaverage rolling moment with mandrelrsquos bottom radius

of PEEQ and temperature distributions increase theaverage rolling force fluctuates between 253 kN and257 kN and the average rollingmoment is unchangedbasically When the conical ringrsquos outer radius growthrate equals 6mms the PEEQ and temperature dis-tributions of the rolled conical ring are most uniformsimultaneously

(3) With the increase of the driven rollrsquos bottom radiusthe PEEQ and temperature distributions becomemore uniform at first and then nonuniform boththe average rolling force and average rolling momentincrease gradually However the minimum values of

SDP and SDT are obtained at different driven rollrsquosbottom radius respectively When the driven rollrsquosbottom radius is 200mm the temperature distri-bution of the rolled conical ring is most uniformthe PEEQ distribution of the rolled conical ringis relatively more uniform and both the averagerolling force and average rollingmoment are relativelysmaller

(4) With the increase ofmandrelrsquos bottom radius the uni-formity of PEEQdistribution increases while the uni-formity of temperature distribution changes a little


and the temperature fluctuation range is only 365ndash39∘C With the increase of mandrelrsquos bottom radiusthe average rolling force gradually increases whilethe average rolling moment is basically unchangedHowever the minimum values of SDP and SDTare obtained at different mandrelrsquos bottom radiusrespectively When mandrelrsquos bottom radius equals110mm the PEEQ distribution of the rolled conicalring is most uniform the temperature distributionof the rolled conical ring is more uniform and thecorresponding rolling force is 255 kN

(5) The optimal combinations of forming parameters thatcan obtain more uniform PEEQ and temperaturedistributions of this kind ofmiddle size titanium alloyconical rings are as follows the conical ringrsquos outerradius growth rate is 6mms the driven rollrsquos bottomradius is 200mm and mandrelrsquos bottom radius is110mmThe results of this study can provide guidancefor the selection of ringrsquos outer radius growth rate androlls sizes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work is supported by the Program for ChangJiang Scholars and Innovative Research Team in Universityof Ministry of Education of China (no IRT0931)

References

[1] J Seitz V Jenkouk and G Hirt ldquoManufacturing dish shapedrings on radial-axial ring rolling millsrdquo Production Engineeringvol 6 pp 1ndash8 2013

[2] Z W Wang S Q Zeng X H Yang and C Cheng ldquoThe keytechnology and realization of virtual ring rollingrdquo Journal ofMaterials Processing Technology vol 182 no 1ndash3 pp 374ndash3812007

[3] X Han L Hua J Lan Z Zuo G Jia and L Huang ldquoSimulationand experimental study of hot rolling of LD10 conical ring withinner stepsrdquo Journal of Wuhan University of Technology vol 29no 11 pp 7ndash10 2007

[4] L Giorleo E Ceretti and C Giardini ldquoEnergy consumptionreduction in Ring Rolling processes a FEM analysisrdquo Interna-tional Journal of Mechanical Sciences vol 74 pp 55ndash64 2013

[5] N Kim H Kim and K Jin ldquoOptimal design to reduce themaximum load in ring rolling processrdquo International Journalof Precision Engineering and Manufacturing vol 13 no 10 pp1821ndash1828 2012

[6] L Guo and H Yang ldquoTowards a steady forming condition forradial-axial ring rollingrdquo International Journal of MechanicalSciences vol 53 no 4 pp 286ndash299 2011

[7] W Xu X Yang X Gong and J Zhou ldquoA new mathematicalmodel for predicting the diameter expansion of flat ring inradial-axial ring rollingrdquo International Journal of AdvancedManufacturing Technology vol 60 no 9ndash12 pp 913ndash921 2012

[8] MWang H Yang C Zhang and L Guo ldquoMicrostructure evo-lution modeling of titanium alloy large ring in hot ring rollingrdquoInternational Journal of Advanced Manufacturing Technologyvol 66 no 9ndash12 pp 1427ndash1437 2013

[9] D Qian and Y Pan ldquo3D coupled macro-microscopic finiteelement modelling and simulation for combined blank-forgingand rolling process of alloy steel large ringrdquo ComputationalMaterials Science vol 70 pp 24ndash36 2013

[10] S Zhu H Yang L G Guo and R J Gu ldquoInvestigation of defor-mation degree and initial forming temperature dependences ofmicrostructure in hot ring rolling of TA15 titanium alloy bymulti-scale simulationsrdquo Computational Materials Science vol65 pp 221ndash229 2012

[11] S Zhichao Y He and O Xinzhe ldquoEffects of process parameterson microstructural evolution during hot ring rolling of AISI5140 steelrdquo Computational Materials Science vol 49 no 1 pp134ndash142 2010

[12] G Zhou L Hua J Lan and D S Qian ldquoFE analysis of coupledthermo-mechanical behaviors in radial-axial rolling of alloysteel large ringrdquo Computational Materials Science vol 50 no1 pp 65ndash76 2010

[13] N Anjami andA Basti ldquoInvestigation of rolls size effects on hotring rolling process by coupled thermo-mechanical 3D-FEArdquoJournal of Materials Processing Technology vol 210 no 10 pp1364ndash1377 2010

[14] G Zhou L Hua and D S Qian ldquo3D coupled thermo-mechanical FE analysis of roll size effects on the radial-axial ringrolling processrdquo Computational Materials Science vol 50 no 3pp 911ndash924 2011

[15] X H Han The Mastersrsquo Dissertation for Wuhan University ofTechnology Wuhan China 2006

[16] D Qian Z Zhang and L Hua ldquoAn advanced manufacturingmethod for thick-wall and deep-groove ringmdashcombined ringrollingrdquo Journal of Materials Processing Technology vol 213 no8 pp 1258ndash1267 2013

[17] H L Yuan The optimal design for the dimensions of profiledring blank and the numerical simulation for ring rolling process[PhD thesis] Huazhong University of Science and TechnologyWuhan China 2006

[18] X Gong and F Yang ldquoResearch of PEEQ for conical ring withouter steps ring rollingrdquo Physics Procedia vol 25 pp 257ndash2612012

[19] L Hua X G Huang and C D Zhu Theory and Technology ofRing Rolling Mechanical Industry Press Beijing China 2001

[20] L B PanThemetal deformation laws in radial-axial ring rollingprocess and the study on CAPP system [Doctoral dissertation]Wuhan University of Technology Wuhan China 2007 httpcdmdcnkicomcnArticleCDMD-10497-2008046182htm

[21] B Kim H Moon E Kim M Choi and M Joun ldquoA dual-mesh approach to ring-rolling simulations with emphasis onremeshingrdquo Journal ofManufacturing Processes vol 15 pp 635ndash643 2013

[22] K Shiro O Soo-ik andA TaylanMetal Forming and the Finite-Element Method Oxford University Press New York NY USA1989

[23] M Wang H Yang Z C Sun and L G Guo ldquoAnalysis ofcoupled mechanical and thermal behaviors in hot rolling oflarge rings of titanium alloy using 3D dynamic explicit FEMrdquoJournal of Materials Processing Technology vol 209 no 7 pp3384ndash3395 2009


[24] R S Lee and H C Lin ldquoProcess design based on the deforma-tion mechanism for the non-isothermal forging of Ti-6Al-4Valloyrdquo Journal of Materials Processing Technology vol 79 no 1ndash3 pp 224ndash235 1998

[25] V Jenkouk G Hirt M Franzke and T Zhang ldquoFinite elementanalysis of the ring rolling process with integrated closed-loopcontrolrdquo CIRP AnnalsmdashManufacturing Technology vol 61 no1 pp 267ndash270 2012

[26] ZMHu JW Brooks andT ADean ldquoExperimental and theo-retical analysis of deformation andmicrostructural evolution inthe hot-die forging of titanium alloy aerofoil sectionsrdquo Journalof Materials Processing Technology vol 88 no 1 pp 251ndash2651999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


the improvement of dynamic recrystallization fraction Zhuet al [10] simulated a hot ring rolling process of titaniumalloy by an internal state variable microstructure model forTA15 titanium alloy and pointed out that with the increaseof deformation degree or the initial rolling temperature theprimary 120572 grain size distribution becomes more uniformZhichao et al [11] analyzed the effects of rolling parametersof a hot ring rolling process on microstructure evolution ofrolled ring based on amicrostructure evolutionmodel ofAISI5140 steel

Zhou et al [12] investigated the effects of rolling param-eters on PEEQ and temperature distributions in radial-axialring rolling process and declared that with the increase ofthe mandrel feed rate and the initial temperature of ringblank the PEEQ and temperature distributions of rolled ringbecomemore uniform Anjami and Basti [13] and Zhou et al[14] studied the effects of rolls sizes on the PEEQ andtemperature distributions rolling force and rolling momentin hot ring rolling and radial-axial ring rolling processesrespectively They obtained the optimal rolls sizes for moreuniform PEEQ and temperature distributions of rolled ringsbut did not give out the reasonable mandrel feeding strategy

As the need for profiled rings increases in industries thestudies about profiled ring rolling processes become a hotissue However reports about the PEEQ and temperature dis-tributions in profiled ring rolling processes were insufficientespecially those about conical ring rolling process Qian et al[16] developed a combined ring rolling process based on theminimum resistance principle of metal plastic forming inorder to manufacture a thick-wall and deep-groove ring Intheir study they analyzed the metal flow laws in rolling pro-cess and obtained the PEEQ and temperature distributionslaws of rolled ring by finite elementmethodTheir simulationresults were in accordance with experimental ones Seitz etal [1] simulated and manufactured a dish-shaped ring witha thicker ring wall and lower ring height on radial-axial ringrolling mills and pointed out that a larger height reduction ofthe ring can result in dishing and ring climbing Han et al [3]optimally designed a prorolled ring blank in the aluminumalloy hot rolling process of a conical ring with inner steps bysimulation and experimental methods Yuan [17] optimallydesigned a conical ring blank with inner steps of steel bysimulation and experimental methods Gong and Yang [18]simulated and analyzed the effects of mandrel feed rate onthe PEEQ distribution in rolling process of a conical ringwith outer steps by using the feeding strategy with a constantmandrel feed rate and pointed out that the bigger mandrelfeed rate and lower driven rollrsquos rotational speed can improvethe mechanical property of rolled rings However all of themneither gave out the reasonable mandrel feeding strategy norstudied the effects of key forming parameters such as rollssizes on conical ring rolling processes

Therefore it is significantly necessary to set up the FEmodel of conical ring rolling process establish the plasticpenetration condition and biting-in condition in rollingprocess deduce a reasonable mandrel feeding strategy andinvestigate the effects of key forming parameters on the PEEQand temperature distributions of rolled rings average rollingforce and average rolling moment

H

21

Y

X 3

rt

120579

bt

l


R998400D R

998400t

R998400M

RMRD Rt

r998400t

Figure 1 The schematic diagram of RCRRCDS process at 119905 time

This paper established the plastic penetration conditionand biting-in condition in RCRRCDS process set up areasonable mandrel feeding strategy with a constant ringrsquosouter radius growth rate and deduced the reasonable valuerange of mandrel feed rate in rolling process The coupledthermomechanical 3D FE model of RCRRCDS process wasestablished based on ABAQUS software The steady conicalring rolling process was realized by numerical simulationThe effects of ringrsquos outer radius growth rate and the sizes ofrolls on the uniformity of PEEQ and temperature distribu-tions of rolled rings average rolling force and average rollingmoment were analyzed

2 The Mathematical Model ofRCRRCDS Process

In RCRRCDS process the radii of driven roll andmandrel aswell as the inner and outer radii of conical ring are variablealong axial direction so at a certain time the plastic pene-tration condition and biting-in condition at different layer-heights are different However the values of feed amount perrevolution at different layer-heights are the same That is tosay an unreasonable mandrel feeding strategy (ie a smallmandrel feed rate)may result in a certain part (ie the bottompart) of conical ring being forged penetrated while the otherpart (ie the top part) of conical ring not being completelyforged penetrated In this situation ringrsquos top radius cannotgrow up successfully and the rolling process is unstableSimilarly a bigger mandrel feed rate may make a certain part(ie the bottom part) of conical ring successfully be bit-in theroll gap between the driven roll and the mandrel while theother part (ie the top part) of conical ring hardly be bit-inTherefore in order tomake the conical ring completely forgedpenetrated and simultaneously bit into the roll gap betweenthe driven roll and the mandrel the plastic penetrationand biting-in conditions at different layer-heights must besatisfied in the whole RCRRCDS process

21 The Plastic Penetration Condition and Biting-In Conditionin RCRRCDS Process Figure 1 shows the schematic diagramof RCRRCDS process at 119905 time In Figure 1 119877

119863is the bottom-

radius of driven roll 119877119872

is the bottom-radius of mandrel119877119905is the ringrsquos bottom outer radius at 119905 time 119903

119905is the ringrsquos

bottom inner radius at 119905 time 119887119905is the thickness of ring wall at


Z

X

L1

O1

r998400t

D

A B

CGH

EF

L2O2

O3

1

2 3

Flow inFlow out


R998400D

R998400t

R998400M

ΔhD(l t)

ΔhM(l t)




at 119897 layer-height 1198771015840119872







3are


119863(119897 119905) and Δℎ









Δℎmin (119897 119905)


(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(1)

Δℎmax (119897 119905)

=21205732

(11198771015840119863+ 11198771015840

119872)2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(2)

Δℎmin (119897 119905)

le Δℎ (119897 119905) le Δℎmax (119897 119905) (3)


119872= 119877119872minus 119897cot120579 1198771015840

119905= 119877119905minus 119897cot120579 and

1199031015840119905= 119903119905minus 119897cot120579






[Δℎmin (119897 119905)]max = Δℎmin (119897 = 119867 119905)

[Δℎmax (119897 119905)]min = Δℎmax (119897 = 119867 119905) (5)


119871 we can get

Δℎ (119897 119905) =1198712

2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

) (6)

119871 = radic2Δℎ (119897 119905)

11198771015840119863+ 11198771015840

119872+ 11198771015840

119905minus 11199031015840119905

(7)







119872(119897 119905) and Δℎ

119863(119897 119905) respectively




Δℎ119863 (119897 119905) =

1198712

2(1

1198771015840119863

+1

1198771015840119905

) (8)

Δℎ119872 (119897 119905) =

1198712

2(

1

1198771015840119872

minus1

1199031015840119905

) (9)


119872(119897 119905) is adopted

120593 (119897 119905) = Δℎ119863 (119897 119905) minus Δℎ119872 (119897 119905)

=1198712

2(1

1198771015840119863

minus1

1198771015840119872

+1

1198771015840119905

+1

1199031015840119905

) (10)



119863minus 11198771015840

119872and


120593 (119897 119905) =1198712

2(1

1198771015840119863

minus1

1198771015840119872

) (11)








1198771015840119905= 1198770minus 119897 sdot cot120579 + V1015840

119877119905 (12)



1198771015840119905=1198871015840119905

2+1198870(1198770+ 1199030minus 119867cot120579)

21198871015840119905

+119867cot1205792

(13)







V1015840119877=1198891198771015840119905

119889119905=V1015840119905

2[(1198770+ 1199030minus 119867cot120579) 119887

0

11988710158402119905

minus 1] (14)

V1015840119905=

2V1015840119877

(1198770+ 1199030minus 119867cot120579) 119887

011988710158402119905minus 1

(15)




V1015840119905asympΔℎ (119897 119905)

Δ119905 (16)



21205871198771015840119905= 1198991198631198771015840119863Δ119905 (17)



Δℎ (119897 119905) =4120587V1015840119877(11987710158400+ V1015840119877119905)

1198991198631198771015840119863

sdot11988710158402119905

(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905

(18)


1198991198631198771015840119863

21205871198771015840119905

[Δℎmin (119897 119905)]max le V1015840119905le1198991198631198771015840119863

21205871198771015840119905

[Δℎmax (119897 119905)]min (19)


X

Y

Z





119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmin (119897 119905)]max

le V1015840119877

le119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmax (119897 119905)]min

(20)




119877can be







119905 can be


0is the119883



120590 = 119896119885119898120582119899 (1 minus 119890minus120573120576)

120582 = 1205820119885119902 + (1 minus 120582

0119885119902) 119890minus120572120576

119885 = 120576119890119876defm119877119879

(21)


0





119898 03119899 1120573 66731205820


120572 607119876defm119877 50668 times 104





119877is 6mms


119877is 1215mms lt





0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400


Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25







119863=

200mm 119877119872= 100mm V1015840




119863= 200mm 119877

119872= 100mm V1015840

119877=










Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Z

X

L1

O1

r998400t

D

A B

CGH

EF

L2O2

O3

1

2 3

Flow inFlow out


R998400D

R998400t

R998400M

ΔhD(l t)

ΔhM(l t)




at 119897 layer-height 1198771015840119872







3are


119863(119897 119905) and Δℎ









Δℎmin (119897 119905)


(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(1)

Δℎmax (119897 119905)

=21205732

(11198771015840119863+ 11198771015840

119872)2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

)(2)

Δℎmin (119897 119905)

le Δℎ (119897 119905) le Δℎmax (119897 119905) (3)


119872= 119877119872minus 119897cot120579 1198771015840

119905= 119877119905minus 119897cot120579 and

1199031015840119905= 119903119905minus 119897cot120579






[Δℎmin (119897 119905)]max = Δℎmin (119897 = 119867 119905)

[Δℎmax (119897 119905)]min = Δℎmax (119897 = 119867 119905) (5)


119871 we can get

Δℎ (119897 119905) =1198712

2(1

1198771015840119863

+1

1198771015840119872

+1

1198771015840119905

minus1

1199031015840119905

) (6)

119871 = radic2Δℎ (119897 119905)

11198771015840119863+ 11198771015840

119872+ 11198771015840

119905minus 11199031015840119905

(7)







119872(119897 119905) and Δℎ

119863(119897 119905) respectively




Δℎ119863 (119897 119905) =

1198712

2(1

1198771015840119863

+1

1198771015840119905

) (8)

Δℎ119872 (119897 119905) =

1198712

2(

1

1198771015840119872

minus1

1199031015840119905

) (9)


119872(119897 119905) is adopted

120593 (119897 119905) = Δℎ119863 (119897 119905) minus Δℎ119872 (119897 119905)

=1198712

2(1

1198771015840119863

minus1

1198771015840119872

+1

1198771015840119905

+1

1199031015840119905

) (10)



119863minus 11198771015840

119872and


120593 (119897 119905) =1198712

2(1

1198771015840119863

minus1

1198771015840119872

) (11)








1198771015840119905= 1198770minus 119897 sdot cot120579 + V1015840

119877119905 (12)



1198771015840119905=1198871015840119905

2+1198870(1198770+ 1199030minus 119867cot120579)

21198871015840119905

+119867cot1205792

(13)







V1015840119877=1198891198771015840119905

119889119905=V1015840119905

2[(1198770+ 1199030minus 119867cot120579) 119887

0

11988710158402119905

minus 1] (14)

V1015840119905=

2V1015840119877

(1198770+ 1199030minus 119867cot120579) 119887

011988710158402119905minus 1

(15)




V1015840119905asympΔℎ (119897 119905)

Δ119905 (16)



21205871198771015840119905= 1198991198631198771015840119863Δ119905 (17)



Δℎ (119897 119905) =4120587V1015840119877(11987710158400+ V1015840119877119905)

1198991198631198771015840119863

sdot11988710158402119905

(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905

(18)


1198991198631198771015840119863

21205871198771015840119905

[Δℎmin (119897 119905)]max le V1015840119905le1198991198631198771015840119863

21205871198771015840119905

[Δℎmax (119897 119905)]min (19)


X

Y

Z





119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmin (119897 119905)]max

le V1015840119877

le119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmax (119897 119905)]min

(20)




119877can be







119905 can be


0is the119883



120590 = 119896119885119898120582119899 (1 minus 119890minus120573120576)

120582 = 1205820119885119902 + (1 minus 120582

0119885119902) 119890minus120572120576

119885 = 120576119890119876defm119877119879

(21)


0





119898 03119899 1120573 66731205820


120572 607119876defm119877 50668 times 104





119877is 6mms


119877is 1215mms lt





0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400


Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25







119863=

200mm 119877119872= 100mm V1015840




119863= 200mm 119877

119872= 100mm V1015840

119877=










Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





119872(119897 119905) and Δℎ

119863(119897 119905) respectively




Δℎ119863 (119897 119905) =

1198712

2(1

1198771015840119863

+1

1198771015840119905

) (8)

Δℎ119872 (119897 119905) =

1198712

2(

1

1198771015840119872

minus1

1199031015840119905

) (9)


119872(119897 119905) is adopted

120593 (119897 119905) = Δℎ119863 (119897 119905) minus Δℎ119872 (119897 119905)

=1198712

2(1

1198771015840119863

minus1

1198771015840119872

+1

1198771015840119905

+1

1199031015840119905

) (10)



119863minus 11198771015840

119872and


120593 (119897 119905) =1198712

2(1

1198771015840119863

minus1

1198771015840119872

) (11)








1198771015840119905= 1198770minus 119897 sdot cot120579 + V1015840

119877119905 (12)



1198771015840119905=1198871015840119905

2+1198870(1198770+ 1199030minus 119867cot120579)

21198871015840119905

+119867cot1205792

(13)







V1015840119877=1198891198771015840119905

119889119905=V1015840119905

2[(1198770+ 1199030minus 119867cot120579) 119887

0

11988710158402119905

minus 1] (14)

V1015840119905=

2V1015840119877

(1198770+ 1199030minus 119867cot120579) 119887

011988710158402119905minus 1

(15)




V1015840119905asympΔℎ (119897 119905)

Δ119905 (16)



21205871198771015840119905= 1198991198631198771015840119863Δ119905 (17)



Δℎ (119897 119905) =4120587V1015840119877(11987710158400+ V1015840119877119905)

1198991198631198771015840119863

sdot11988710158402119905

(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905

(18)


1198991198631198771015840119863

21205871198771015840119905

[Δℎmin (119897 119905)]max le V1015840119905le1198991198631198771015840119863

21205871198771015840119905

[Δℎmax (119897 119905)]min (19)


X

Y

Z





119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmin (119897 119905)]max

le V1015840119877

le119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmax (119897 119905)]min

(20)




119877can be







119905 can be


0is the119883



120590 = 119896119885119898120582119899 (1 minus 119890minus120573120576)

120582 = 1205820119885119902 + (1 minus 120582

0119885119902) 119890minus120572120576

119885 = 120576119890119876defm119877119879

(21)


0





119898 03119899 1120573 66731205820


120572 607119876defm119877 50668 times 104





119877is 6mms


119877is 1215mms lt





0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400


Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25







119863=

200mm 119877119872= 100mm V1015840




119863= 200mm 119877

119872= 100mm V1015840

119877=










Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




X

Y

Z





119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmin (119897 119905)]max

le V1015840119877

le119899119863119877119863[(1198770+ 1199030minus 119867cot120579) 119887

0minus 11988710158402119905]

4120587119877101584011990511988710158402119905

[Δℎmax (119897 119905)]min

(20)




119877can be







119905 can be


0is the119883



120590 = 119896119885119898120582119899 (1 minus 119890minus120573120576)

120582 = 1205820119885119902 + (1 minus 120582

0119885119902) 119890minus120572120576

119885 = 120576119890119876defm119877119879

(21)


0





119898 03119899 1120573 66731205820


120572 607119876defm119877 50668 times 104





119877is 6mms


119877is 1215mms lt





0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400


Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25







119863=

200mm 119877119872= 100mm V1015840




119863= 200mm 119877

119872= 100mm V1015840

119877=










Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






119898 03119899 1120573 66731205820


120572 607119876defm119877 50668 times 104





119877is 6mms


119877is 1215mms lt





0 5 10 15 20 25 30 35

0

200

400

600

800

1000

1200

1400


Rolling time (s)

Ener

gy o

f FE

mod

el (J

)

Ratio

of A

LLKE

to A

LLIE

()

times103

0

5

10

15

20

25







119863=

200mm 119877119872= 100mm V1015840




119863= 200mm 119877

119872= 100mm V1015840

119877=










Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials











Height(mm)

Taper angle(∘)



119872= 100mm V1015840

119877= 4mms 119877

119863= 100mm 200mm



119877= 4mms Since 119877




119872are respec-





119894=1(PEEQ

119894minus PEEQ

119886)2sdot 119881119894

sum119873

119894=1119881119894


119894=1(119879119894minus 119879119886)2sdot 119881119894

sum119873

119894=1119881119894

(22)


119886=

sum119873

119894=1(PEEQ

119894sdot 119881119894)sum119873

119894=1119881119894 PEEQ


119894



119879119886= sum119873

119894=1(119879119894sdot 119881119894)sum119873






PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




PEEQ





+5178e minus 01

(Avg 75)

(a) 119905 = 5 s

PEEQ

+1568e + 00+1441e + 00+1314e + 00


+1695e + 00

+1187e + 00+1060e + 00

(Avg 75)

(b) 119905 = 10 s

PEEQ

+3636e + 00+3368e + 00

+2830e + 00+2562e + 00+2293e + 00+2025e + 00+1756e + 00+1488e + 00+1219e + 00

+3099e + 00


(Avg 75)

(c) 119905 = 20 s

PEEQ


(Avg 75)

(d) 119905 = 339 s







Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Conical ring blank

Rolled conical ring

SS

(a)

PEEQA

B

C

D

E

F

G

H



(Avg 75)

(b)

NT11

F

HE

GA

B

C

D


+1146e + 03+1121e + 03+1097e + 03+1072e + 03+1048e + 03+1023e + 03+9987e + 02+9742e + 02+9496e + 02+9251e + 02+9006e + 02+8761e + 02+8516e + 02

(c)








0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 5 10 15 20 25 30 35

0

1

2

3

4

5

Point F


Trac

e poi

nts P

EEQ

Rolling time (s)


Point DPoint E

(a)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Axi

al d

istrib

utio

n PE

EQ



(b)

000 001 002 003 004 005 006 007 008 0090

1

2

3

4

5

Radi

al d

istrib

utio

n PE

EQ



(c)








Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





Acute angle zones

+1114e + 03+1095e + 03+1076e + 03+1057e + 03+1038e + 03+1019e + 03+1000e + 03+9812e + 02+9623e + 02+9433e + 02+9244e + 02+9055e + 02+8866e + 02

(a) 119905 = 5 s


(b) 119905 = 10 s


(c) 119905 = 20 s


(d) 119905 = 339 s







0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 5 10 15 20 25 30 35850

900

950

1000

1050

1100

1150




Trac

e poi

nts t

empe

ratu

re (∘

C)

Rolling time (s)

(a)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Axi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(b)

000 001 002 003 004 005 006 007 008 009850

875

900

925

950

975

1000

1025

1050

Radi

al d

istrib

utio

n te

mpe

ratu

re (∘

C)



(c)






3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




3 4 5 60

1

2

3

4

5

6

7

8



PEEQ

09

10

11

12

13

14

Minimum PEEQSD

PSDP





850

900

950

1000

1050

1100

1150

1200



Tem

pera

ture

(∘C)

34

35

36

37

38

39

40


SDT

(∘C)

3 4 5 6






0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6



PEEQ

110

115

120

125

SDP


0 100 200 300 400 500 600 700 800 900800

900

1000

1100

1200

SDT


Tem

pera

ture

(∘C)

38

39

40

41

42

43

44

45

46

SDT

(∘C)





70 80 90 100 1100

1

2

3

4

5

6

7

8

SDP


PEEQ

08

10

12

14

16

18

SDP







70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




70 80 90 100 110

850

900

950

1000

1050

1100

1150

1200

SDT


Tem

pera

ture

(∘C)

36

37

38

39

40

SDT

(∘C)











6 Conclusions





3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




3 4 5 6230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(a)

0 100 200 300 400 500 600 700 800 900230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103 times10

3

(b)

70 80 90 100 110230

235

240

245

250

255

260

265



Rolli

ng fo

rce (

N)

10

20

30

40

50

60

70

80

90

Rolli

ng m

omen

t (Nmiddotm

)

times103

times103

(c)











Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








Acknowledgment


References



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials














CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Documents

Research Article The Effects of Forming Parameters on