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Advanced feasible forming condition for reducing ring spreads in radial–axial ring rolling
International Journal of Mechanical Sciences 76 (2013) 21–32
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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
Advanced feasible forming condition for reducing ring spreads in radial–axial ring rolling Kyung-Hun Lee a, Byung-Min Kim b,n a b
PNU-IFAM JRC, Pusan National University, Busan 609-735, South Korea School of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 11 June 2013 Received in revised form 31 July 2013 Accepted 19 August 2013 Available online 30 August 2013
In this study, we derive an advanced feasible forming condition for reducing ring spreads and maintaining process stability during radial–axial ring rolling (RARR) process. First, the plastic penetrating condition was determined using the mean thickness-to-length ratio of the plastic zone. This calculation was based on the plane strain indentation theory considering Coulomb friction at the ring blank– mandrel interface. Second, a mathematical model for the RARR process was developed assuming constant volume of ring blanks and constant growth velocity condition (CGVC) of the ring outer diameter. Finally, the advanced feasible forming condition was determined from the mathematical correlations among the main roll, mandrel and axial roll sets, and reasonable range of extreme growth velocities. To verify the proposed condition, we carried out FE-simulations by developing reliable three-dimensional finite element (3D-FE) models using Forge, a commercial finite-element software package. The simulation results show that the designed process results in relatively uniform deformation behavior and reduces ring spreads. Predicted rolled ring spreads were compared with the experimental results. The ring growth velocity, which is a median value of its reasonable range determined using the advanced feasible forming condition, is recommended for the forming process design considering the reduced ring spreads and uniform plastic deformation. Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
Keywords: Radial–axial ring rolling Constant growth velocity conditions Plain strain indentation theory Advanced feasible forming condition Finite element simulation Ring spreads
1. Introduction Ring rolling is a versatile metal-forming process for manufacturing seamless annular products with circumferential grain flow and accurate dimensions. Ring rolling usually requires less input material than alternative forging methods, and it can be used for mass production in any quantity. The most commonly used modern ring rolling mill is the radial–axial ring rolling (RARR) machine; it consists of a radial and an axial set of rolls, as shown in Fig. 1. Ring blanks are placed on the rolling table. Two sets of rolls are arranged diametrically opposite relative to the ring center, where a main roll and the mandrel are arranged horizontally and an upper and a lower axial roll are arranged vertically. The main roll rotates at a constant, predetermined speed. The ring begins to rotate as the mandrel squeezes the ring wall. This, in turn, rotates the mandrel [1]. The roll geometries and comparatively small reductions in ring height and ring wall thickness per rolling pass result in ring spreads bulged at the four corners of the ring cross section. This inhomogeneous deformation is called a “fishtail.” During ring rolling, any
n
Corresponding author. Tel.: þ 82 515102319; fax: +82 515813075. E-mail address: [email protected] (B.-M. Kim).
spread in the radial gap is rolled off into the axial gap and vice versa. This alternating bulge deformation results in the concentration of strain- and forming energies at the corners of the ring cross section, leading to severe microstructural damage as well as forming defects [2]. Thus far, there have been a few studies on the effect of mandrel feed rate on ring spreads during ring rolling. Johnson and Needham [3] ascribed diametric reduction to the formation of a plastic hinge at a point on the ring that is diametrically opposite to the point of indentation; they arrived at this conclusion while attempting to arrive at an upper-bound estimate of the necessary rolling load. Hawkyard et al. [4] presented the spread and flow patterns in plane and profile ring rolling. Ring spreads are irregular and nonrectangular with fishtailing in each case, and the feed rate has a marked effect on the ring spreads because the spreads become more regular as the feed rate increases. Lugora and Bramley [5] investigated the spread in plain ring rolling using Hill′s general method of analysis. Fast and slow mandrel feeding may cause the ring blank to stop rotating and expanding, respectively; these situations represent two extremum draft conditions. The theoretical extremum feeding speeds that should be satisfied for achieving pure radial ring rolling (PRRR) were first suggested by Hua and Zhao [6]. Yan et al. proposed the method of planning the feed rate based on the growth rate of the ring outer diameter in cold ring rolling [7].
0020-7403/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmecsci.2013.08.007
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
Fig. 1. Schematic illustration of radial–axial ring rolling machine.
To ensure that the ring grows uniformly and stably, growth rate of the outer diameter must be constant and feed speed must decrease gradually as ring thickness decreases. However, compared with PRRR, RARR is a complex dynamic forming system caused by adding a pair of axially conical rolls that are mounted diametrically opposite to the radial pass. It is difficult but critical to determine reasonable ranges of the key RARR process variables. In past studies, process design was mainly based on experience or by trial, and the obtained ranges of steady forming conditions were wide; therefore, a convenient and practicable method for establishing the RARR process was not arrived at. Lately, a few numerical-simulation-based studies on RARR have been reported; these include finite-element-based studies of RARR. Davey and Ward [8,9] presented an arbitrary Lagrangian–Eulerian (ALE) approach for finite element ring-rolling simulation to save computational cost. Based on a finite-element method, Kang and Kobayashi [10] and Joun et al. [11] studied preform design in ring rolling using the backward tracing scheme and an axisymmetric forging approach, respectively. FE-modeling and numerical simulation have been proven to be both powerful and accurate for studying plastic deformation behaviors of materials under various complicated metal forming processes [12–14] and can be used for conducting more comprehensive, profound, and detailed investigations compared to the analytical and experimental methods. Recently, a few studies on the numerical simulation of the RARR process have been reported. For example, Wang et al. [15] developed a virtual RARR process for guiding process design and optimization using LS-DYNA FE code with the mass-scaling function. Design Language program was developed for controlling complex movements of the guide and axial rolls. Guo and Yang [16] presented some key technologies, i.e., technologies for the flexible control of the motions of guide and axial rolls, for the 3D-FE modeling of the RARR process using an elastic–plastic dynamic explicit procedure in the ABAQUS environment. Hua et al. [17] established a ring stiffness condition in RARR; this condition was validated using numerical simulation. The ring stiffness condition is related to the ring blank′s dimensions and rolling ratio, position angle of guide roll, roll dimensions, axial roll positions, radial and axial feed rates, and friction condition. Yeom et al. [18] investigated the RARR design of a large-scale ring product composed of Ti–6Al–4V alloy using a calculation method and FEM analysis. Hua et al. [19] proposed the stable forming conditions for RARR process and investigated the effect of key parameters on the uniformity of the deformation and temperature distribution of alloy steel large ring. The effects of roll size on uniformity of strain and temperature distributions of the rolled ring are investigated to provide valuable guidelines for the roll design by Zhou et al. [20]. Hua et al. [21] developed the motion
control method of axial rolls to increase the uniformity of STD and SDP. Qian and Pan [22] presented the combined simulation for blank forging and ring rolling process to investigate the effect of blank forging on ring deformation behaviors. However, in the abovementioned studies, RARR process design was based mainly on experience or trial and error, and, hence, these studies do not present a simple and convenient method for establishing the process and maintaining its stability. Therefore, it is necessary to derive an advanced feasible forming condition for reducing ring spreads, fishtail defects, and maintaining process stability during RARR. The purpose of this study is to develop a mathematical model of the aforementioned advanced feasible forming condition by determining the mathematical correlations among the rolls, reasonable ranges of ring-growth velocity based on the mean thickness-to-length ratio of the plastic deformation zone, and constant growth velocity condition (CGVC). To verity the proposed condition, we carried out FE simulations by developing reliable 3D-FE models using Forge, a commercially available finiteelement platform. The analytical results of ring spreads and deformation behavior of large rings were validated against the results of RARR experiments performed using an AISI 1035 alloy steel ring with an initial outer diameter of 600 mm. 2. Slip-line field analysis for ring rolling 2.1. Interfacial Coulomb friction In ring rolling, rotation of the deformed ring relies greatly on the friction between the ring and the rolls, i.e., the main roll and the set of axial rolls. The ring be drawn successively into the gap and be rotated continuously only if the gripping condition is satisfied. A model for the gripping condition is shown in Fig. 2 [23]. The following equations can be obtained through force analysis: ∑F x ¼ T 1 cos ðξ1 α1 ÞP 1 sin ðξ1 α1 ÞP 2 sin ðξ2 α2 Þ Z 0
ð1Þ
∑F y ¼ T 1 sin ðξ1 α1 ÞP 1 cos ðξ1 α1 Þ þ P 2 cos ðξ2 α2 Þ ¼ 0
ð2Þ
where P1 and T1 are the normal force and tangential friction, respectively, between the main roll and the ring. The mandrel and
Fig. 2. Gripping condition for ring rolling [23].
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
the two centering rolls are driven, and should therefore have minimal friction moments; for simplicity, we assume ring-mandrel and – centering roll friction to be zero. P2 represents the normal force of the mandrel on the ring. ξ1α1 and ξ2α2 represent the angles of P1 and P2 with respect to the y-axis, respectively, where ξ1, ξ2 A(0, 1) are dimensionless coefficients. According to the Coulomb friction condition, T1 ¼ μP1, where μ is the friction coefficient. Thus, the gripping condition can be obtained as follows:
μ Z tan ðξ1 α1 þ ξ2 α2 Þ
ð3Þ
From the given geometric conditions, the projected length L of the contact patch between the ring and the rolls is given as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðS0 SÞ L¼ ð4Þ 1=Rmain þ 1=Rmandrel þ 1=R 1=r where Rmain and Rmandrel are the radii of the main roll and the mandrel, respectively, and R and r are the radii of the outer and inner surfaces of the ring workpiece. From Ref. [7], we consider the following geometrical relationships:
α1
L ; Rmain
α2
L Rmandrel
ð5Þ
For the given dimensions of the rolls, initial ring workpiece, and rolled ring, the minimum friction coefficient can be calculated using Eqs. (3)–(5). The needed input parameters for the calculation are listed in Table 1 and the determined friction coefficient is 0.178. Let the normal compressive stress at the interface between tools and a ring workpiece due to the tool pressure be q. Then, the Table 1 Input parameters required for RARR process verification. Parameter
Value
Ring material Outer diameter of ring blank Wall thickness of ring blank Height of ring blank Outer diameter of rolled ring Wall thickness of rolled ring Height of rolled ring Initial temperature of ring blank Radius of main roll Radius of mandrel Cone angle of axial rolls Tool temperature Friction coefficient Rotational speed of main roll Ambient temperature
AISI 1035 600 mm 100 mm 95 mm 976 mm 68 mm 77 mm 1250 1C 425 mm 65 mm 401 200 1C 0.178 28 rpm 20 1C
23
resultant shear stress tangential to the interface considering Coulomb friction is τxy ¼ μq. The resultant shear force exerted on any element of the interface is balanced by the resolved components of the forces acting on the slip lines. One slip line will, therefore, intersect the interface at some angle ϕ o π/4. If the forces exerted on the element are resolved in a direction tangential to the interface and equated to zero for equilibrium, then it will be found that [24] μq =2 ð6Þ ϕ ¼ cos 1 k Substituting μ ¼0.178 into Eq. (6), the angle mined as 0.36287 rad (¼361).
ϕ can be deter-
2.2. Plane strain indentation considering interfacial Coulomb friction In ring rolling, the radius of curvature of the smaller roll, i.e. mandrel, is also generally large in relation to the contact lengths, the proportions being investigated the effect of key parameters on the uniformity of the deformation and temperature distribution of ASLR that a reasonable approximation to the rolling situation is provided by the analysis for the indentation of a lock by opposed flat indenters of equal width [25]. Fig. 3 shows a slip-line field for plane-strain indentation and the right-hand half of this field with a changing stress state, as indicated. CBAO′ is a α-line, while radial lines such as OB and OA are β-lines. When moving clockwise from B to A along an α-line through an angle Δϕa ¼ 1:7279 rad, the Hencky equations yields s2A ¼ k þ 2kð1:7279Þ ¼ 4:4558k
ð7Þ
This is also the value of s2 throughout AOO′ because this region is composed of straight lines only and is acted upon by compressive stresses along all principal directions. To determine tool pressure, P ? , which is sy ¼ s3 , P ? ¼ s3OO0 ¼ s2A k sin ð2ϕÞ ¼ 5:407k Thus, the pressure factor
ð8Þ
γ is
γ ¼ P ? =2k ¼ 2:7035
ð9Þ
2.3. Indentation as a function of ring blank geometry As the mean thickness-to-length ratio S/L becomes larger than one, a different field must be used for satisfying field requirements. This is illustrated in Fig. 4, which is a net with 301 angular increments. Moving along an α-line to (0, 1) and back along a β-line to (1, 1), sxð1;1Þ ¼ P ? þ k sin ð2ϕÞ þ k þ 2kðΔϕα Δϕβ Þ
Fig. 3. Slip-line field for plane-strain indentation of semi-infinite slab [26].
ð10Þ
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and mandrel, respectively. Raxial and α are the radius and half cone angle of axial conical rolls, respectively. Nmain is the rotational speed of the main roll; dD/dt is the constant growth velocity of the ring. The subscripts i and n are the actual number of revolution and all revolutions, respectively. (ii) The volume of ring blank is constant in plastic deformation, neglecting the mass decrease by oxidized scales and maintaining the ring circularity and rectangular cross section shape. Let c0 and ci are the initial and instantaneous volume, respectively. C 0 ¼ π ðDi Si ÞSi H i ¼ C i
ð13Þ
(iii) Let Si, Hi, and Di denote the instantaneous wall thickness, height, and outer diameter of the ring, respectively, assuming that the wall thickness and height reductions are equal in each revolution. Thus, for i¼1, 2, …, n, we have the following equations: Si ¼ Si1 þ ðSf S0 Þ=n
ð14Þ
H i ¼ H i1 þðH f H 0 Þ=n
ð15Þ
Di ¼ C i =π ðSi H i Þ þ Si
ð16Þ
(iv) Let ti be an instant of time during the process. According to the CGVC, we have the following: t i ¼ t i1 þ ðDi Di1 Þ=ðdD=dt i Þ Fig. 4. Slip-line field for two centered fans showing x and y as functions of Δϕ using a 301 net
At any point (n, n), Δϕα ¼ nπ =6, Δϕβ ¼ nπ =6, so sxðn;nÞ ¼ P ? þ 1:9517k þ 2k Δϕ
ð11Þ
If the slab is unconstrained in the x-direction, an appropriate boundary condition is F x ¼ 0. The net force, F x in the x-direction is equal to the integral of sx along the centerline. Z 4k S=2 2Δϕ dy ð12Þ P ? ¼ 1:9517k þ S 0 Values of Δϕ as a function of y are given in Fig. 4 for a 301 net. Using the results shown in Fig. 4, Eq. (12) can be integrated graphically by first plotting 2Δϕ versus Y-axis. At values of the mean thickness-to-length ratio of the plastic zone S/L 47.08, P ? =2k for this field exceeds 2.7035, which is the threshold value for non-penetrating indentation. Physically, this means that nonpenetrating deformation should be expected when S/L 47.08 and penetrating deformation for smaller values of S/L.
3. Advanced feasible forming condition 3.1. Mathematical modeling for RARR The mathematical model was developed based on the constant volume condition of a ring and CGVC for the concerns related to uncooperative roll motions and RARR process stability. The modeling process is summarized as follows: (i) The initial set of parameter values was determined. D0, H0, and S0 are the outer diameter of the ring blanks, height, and wall thickness, respectively. Df, Hf, and Sf are the final outer diameter of the rolled rings, height, and wall thickness, respectively. Rmain and Rmandrel are the radius of the main roll
ð17Þ
(v) The instantaneous ring geometry and time evolve feed rates of the mandrel and the upper axial roll, according to the central difference method, are as follows:
1 Si þ 1 Si S S V mandrel;i ¼ þ i i1 ð18Þ 2 t i þ 1 t i t i t i1 V axial;i ¼
1 2
H i þ 1 H i H i H i1 þ t i þ 1 t i t i t i1
ð19Þ
(vi) The relative contact positions between the axial rolls and the outer surface of the rings, such as point C shown in Fig. 1, should remain unchanged as far as possible. The rotational speed Naxial of the axial rolls can be calculated using Di as follows: 2π Rmain N main ¼ π Di N ring ¼ 2π Raxial N axial
ð20Þ
(vii) The withdrawal speed of the axial roll frame Vframe should be as consistent with the ring growth velocity as possible to maintain the minimum relative slip between the axial rolls and the end faces of the ring, i.e., the relative contact positions between the axial rolls and the ring should remain unchanged as far as possible [27]. V f rame ¼
1 dD 2 dt
ð21Þ
3.2. Advanced feasible forming condition for PRRR The plastic deformation zone of ring blanks is related directly to the draft of mandrel ΔS. For reducing ring spreads and ensuring stable expansion of the ring blank in ring-rolling, the draft ΔS must exceed the minimum draft ΔSmin needed to penetrate through the thickness. For satisfying this condition, it would be necessary to roll at a sufficiently high feed rate so as to ensure that
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
S/L is less than 7.08. Substituting Eq. (4) in the limited value of S/L and rearranging, the minimum draft ΔSmin per revolution is obtained, as follows: 1 1 1 1 ΔSmin ¼ 1 102 ðRi r i Þ2 þ þ ð22Þ Rmain Rmandrel Ri r i where Ri and ri are the instantaneous radii of the outer and inner surfaces of the ring blank, respectively. If ΔS increases to exceed the maximum draft ΔSmax corresponding to the gripping condition, the ring blank will not be drawn into the roll gap; therefore, ΔS cannot exceed ΔSmax. Substituting Eqs. (4) and (5) into Eq. (3) and re-arranging, ΔSmax is obtained as follows: 2ðarctan μÞ2 Rmain 1 1 1 1 ð23Þ ΔSmax ¼ þ þ ð1 þ Rmain =Rmandrel Þ Rmain Rmandrel Ri r i Assuming no slip between the main roll and the ring blank, the circumference of the outer ring in one rotation is equal to the perimeter of the main roll; therefore:
ΔS ¼ V mandrel Δt; Δt ¼ Ri =ðN main Rmain Þ
ð24Þ
Based on the extremum draft for PRRR process and Eq. (24), a reasonable range of extremum mandrel feed rates can be calculated as follows: V min r V mandrel r V max V min ¼ 1 10
V max ¼
2
R 1 1 1 1 N main main ðRi r i Þ2 þ þ Rmain Rmandrel Ri r i Ri
2ðarctan μÞ2 N main R2main R R R 1 þ main þ main main Ri ð1 þRmain =Rmandrel Þ Rmandrel Ri ri
ð25Þ ð26Þ
ð27Þ
3.3. Advanced feasible forming condition for RARR The RARR process is an extremely complex dynamic forming system. There are complex and severe dynamic contacts and collisions between the ring and the rolls that may result in severe process instability. However, these severe dynamic contacts and collisions can be alleviated greatly by maintaining a constant ring growth velocity because growth acceleration of the ring at the contact points with all rolls is zero under a constant ring growth velocity. That is to say, a constant ring growth velocity would considerably improve process stability [27]. Based on this consideration, we propose that maintaining a constant ring growth velocity is a key design objective in RARR process design. This is referred to as the constant growth velocity condition (CGVC) of the ring in this study. When the ring grows with a constant velocity during the RARR process, the outer diameter of the ring can be expressed as a linear function of the rolling time: D ¼ D0 þ ðDf D0 Þt=T
ð28Þ
dD ¼ ðDf D0 Þ=T dt
ð29Þ
where D is the instantaneous outer diameter of the ring and t is the rolling time. When t equals zero, D equals the initial outer diameter D0 of the ring blank. When t equals T, i.e., the rolling time needed to complete one operation, and D equals the final outer diameter Df of the rolled ring, dD/dt is the growth velocity of the outer diameter of the ring. Let ΔStotal denote the total amount of reduction of the ring wall; then we have
ΔStotal ¼ S0 Sf
ð30Þ
25
Therefore, total time T can be calculated as follows: T ¼ ΔStotal =V mandrel
ð31Þ
Finally, we obtain a range of dD/dt of the ring using the proposed CGVC and Eqs. (26) and (27): dD=dt min r dD=dt r dD=dt max
ð32Þ
V min ðDf D0 Þ Δsmin Rmain N main ðDf D0 Þ dD ¼ ¼ dt min R0 Δstotal Δstotal
ð33Þ
V max ðDf D0 Þ Δsmax Rmain N main ðDf D0 Þ dD ¼ ¼ dt max Rf Δstotal Δstotal
ð34Þ
For given Nmain, μ, and geometries of the rolls, initial ring blank, and deformed ring, the ranges of dD/dt, Vmandrel, and Vaxial can be calculated using Eqs. (22)–(34). Eq. (32) implies that dD/dt of the ring should be controlled to be within dD/dt A (dD/dtmin, dD/dtmax) for successfully establishing a RARR process considering the plastic deformation behavior of the ring material.
4. FE—Analysis for verifying advanced feasible forming condition 4.1. 3D-FE modeling for RARR To verify the proposed advanced feasible forming condition, we developed a 3D-coupled thermo-mechanical FE model for the RARR process using FORGE-3D, as shown in Fig. 5. Ring rolling simulations were carried out using an ALE approach and a coupled thermo-mechanical tetrahedron element with 4 nodes. In the FORGE platform, the centering option triggers a specific algorithm that maintains the ring centered position to stabilize the process [28]. In real ring rolling mills, this function is performed by centering rolls. The ring material used is AISI 1035 carbon steel alloy and its elastic modulus and Poisson′s ratio are 200 GPa and 0.3, respectively. The result of hot compression tests under different temperatures and strain rates are used for determining the material′s stress–strain curves, as shown in Fig. 6. The friction coefficient at the ring–main roll interface is 0.178. The mandrel and axial rolls are assumed as smooth surfaces; therefore, the friction coefficients between these surfaces and the ring blank are zero. The temperature-dependent physical properties (thermal conductivity specific heat, etc.) of the alloy used here were obtained from Metal Suppliers Online of
Axial roll Ringblank
Mandrel
Main roll
Fig. 5. 3D-FE model of RARR process.
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130
90
120 110
Effective stress [MPa]
Effective stress [MPa]
80 900 °C
70 60
1000 °C
50
1100 °C
40 30
1200 °C
900 °C
100 90 80
1000 °C
70 60
1100 °C
50
1200 °C
40 30
20
20
10 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0
0.2
0.4
Effective strain
0.6
0.8
1.0
1.2
1.4
1.6
Effective strain
180
Effective stress [MPa]
160 900 °C
140 120
1000 °C
100 80
1100 °C
60
1200 °C
40 20 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Effective strain
Fig. 6. Effective stress–strain curves of AISI 1035 carbon steel alloy under different temperatures and strain rates: (a) 0.1 s 1; (b) 1 s 1; and (c) 10 s 1.
1.4
dD/dt= 6 mm/s dD/dt= 8 mm/s dD/dt=12 mm/s dD/dt=14 mm/s dD/dt=16 mm/s
2.0
Feed rate of axial roll(mm/s)
Feed rate of mandrel(mm/s)
2.5
1.5
1.0
0.5
dD/dt= 6 mm/s dD/dt= 8 mm/s dD/dt=12 mm/s dD/dt=14 mm/s dD/dt=16 mm/s
1.2 1.0 0.8 0.6 0.4 0.2
65
70
75
80
85
90
95
100
105
Wall thickness of rolled ring (mm)
76
78
80
82
84
86
88
90
92
94
96
Height of rolled ring (mm)
Fig. 7. Variation curves of feed rate in RARR process: (a) Vmandrel and (b) Vaxial.
America: specific heat 778 J kg 1 1C 1, conductivity 35.5 W m 1 C 1, and emissivity 0.88. All rolls were treated as rigid bodies, and the general conditions are listed in Table 1. Initial process parameters for modeling: radius of main roll and mandrel were 425 and 65 mm, respectively. Initial parameters of ring blank: outer radius, thickness, and height were 500, 100, and 80 mm, respectively. Additionally, the rotational speed Nmain of the main roll is 28 rpm. The variation curves of Vmandrel with the thickness S of the ring and time T can be plotted for a series of dD/dt values from within the proposed range of dD/dt A (6.002, 16.287 mm/s) and equal to 6, 8, 12, 14, and 16 mm/s. Case 1: dD/dt1 ¼6 mm/s, arbitrarily minimum ring growth velocity. Case 2: dD/dt2 ¼ 8 mm/s, minimum ring growth velocity proposed by Guo and Yang [27].
Case 3: dD/dt3 ¼12 mm/s, minimum ring growth velocity investigated by Lee in this study (¼ dD/dtmin). Case 4: dD/dt4 ¼14 mm/s, arbitrary medium ring growth velocity. Case 5: dD/dt5 ¼16 mm/s, maximum ring growth velocity. ( ¼dD/dtmax). From Fig. 7, it can be concluded that Vmandrel and Vaxial should decrease gradually to ensure a constant ring growth velocity, and that the larger dD/dt, the larger is Vmandrel. Fig. 7 presents the feasible region for the design of Vmandrel and Vaxial whereby the RARR process can realize stable forming. 4.2. Results and discussion of FEA for RARR The deformed ring shapes for various dD/dt are shown in Fig. 8. The rolled ring was distorted for dD/dt1 of 6 mm/s. The ring was
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
27
Fig. 8. Shape of deformed rings under different dD/dt in RARR process: (a) 6 mm/s; (b) 8 mm/s; (c) 12 mm/s; (d) 14 mm/s; and (e) 16 mm/s.
Fig. 9. Fishtail coefficient with different dD/dt in RARR process.
compressed within the gaps for dD/dt5 of 16 mm/s; therefore, the ring could be drawn into the roll gap and showed little diameter growth. This indicates that the RARR process cannot be established successfully when dD/dt ¼6 mm/s or 16 mm/s. At the minimum growth velocity proposed by Guo and Yang [27] dD/dt2 ( ¼8 mm/s), the one dD/dt3 ( ¼12 mm/s) proposed in this paper, and the medium value of limit ranges dD/dt4 (¼ 14 mm/s), the RARR process achieved stable forming with good ring circularity. Especially for dD/dt5 ¼ 16 mm/s, a severe cavity defect occurred on the outer surface of the ring after axial rolling. Therefore, the ring could not be nipped into the radial roll gap and showed little growth in diameter. The effect of dD/dt on ring spreads is evident from Fig. 9 in that, within the defined scope, with increasing dD/dt, the fishtail coefficient ζh ¼(Hmax Hmin)/Hmin; ζs ¼(Smax Smin)/Smin decreases in the range determined using the advanced feasible forming condition. That is to say, ring deformation becomes uniform and ring spreads decrease as dD/dt increases. Fig. 10 shows the effect of dD/dt on the cross-section configurations and contours of effective strain in the RARR process. Average effective strain on the upper surface of the rolled ring along the radial direction is shown in Fig. 11. From Figs. 10 and 11, when dD/dt increases, the values of average effective strain on the surface region (SR) and the central region (CR) of the ring
decrease. However, the extent of this decrease is larger for the SR than for the CR. Therefore, deformation of the rolled ring is uniform. The reasons underlying this uniform deformation are as follows: as shown in Fig. 7, (a) Vaxial increases according to the CGVC with increasing Vmandrel, (b) the radial and axial feed amounts per revolution increase, (c) the value of mean thickness-to-length ratio is considerably smaller than 7.08, and (d) the plastic deformation zones can penetrate the ring form the SR to CR more easily. Fig. 12 shows the effect of dD/dt on cross-section configurations and temperature distribution during the RARR process. Fig. 13 shows the average temperature distribution on the upper surface of the rolled ring along the radial direction. It has similar characteristics as deformation at different ring growth velocities. With increasing dD/dt, the average temperatures of both the SR and the CR of the ring increase, and temperature distribution in ring becomes more homogeneous, except in the case of dD/dt5. The reasons for this are as follows: the larger the dD/dt, greater is the heat generated, shorter is the rolling time, and lower is the heat loss from the SR[thermo-mechanical, FE analysis of coupled]. Thus, overall ring temperature increases and the average SR temperature decreases slightly. From Fig. 12(d), when dD/dt equals 16 mm/s, severe heat generation occurs on the outer surface of the ring after radial rolling owing to excessive local deformation.
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
EQ_STRAIN
EQ_STRAIN 4.76995
4.32370
4.35826
3.95466
3.94657
3.58561
3.53488
3.21657
3.12320
2.84753
2.71151
2.47849
2.29982
2.10944 1.74040
1.88813
Max. 4.7699
1.47644
1.37136
Min. 0.6531
1.06475
1.00231
0.65307
0.63327
EQ_STRAIN
EQ_STRAIN
3.96573
1.12772
3.63071
1.02971
3.29569
0.93171
2.96067
0.83371
2.62565
0.73571
2.29062
0.63770
1.95560
0.53970
Max. 4.3237 Min. 0.6333
0.44169
1.62058
Max. 3.9657
1.28556
0.34369
Min. 0.6155
0.95064
0.24569
Max. 1.1277 Min. 0.1477
0.14769
0.61552
Average effective strain
Fig. 10. Effective strain distribution of deformed ring in RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
8 mm/s 12 mm/s 14 mm/s 16 mm/s
4
3
2
1
Inside surface
0 0
10
20
Outside surface 30
40
50
60
70
Distance along the thickness direction from inside to outside surfaces of the ring [mm] Fig. 11. Average effective strain on upper surface of deformed ring under different dD/dt.
feasible forming condition. The specifications of this ring mill include a maximum external diameter of 3000 mm and a maximum rolling force of around 800 t (see Fig. 14). General experimental conditions are the same as those listed in Table 1. The test material was AISI 1035 in an “as cast” condition. The cut slab was deformed into a pancake by several passes of open die forging and then fabricated into a pierced blank by upsetting and piercing. The pierced blank is turned into a plain ring during the RARR process. In this study, the dimensions (DfHfSf) of the desired ring are taken as 976 77 68 mm. The radii of the main roll and mandrel are designed as 425 and 65 mm, respectively. The half of con angle θ of the axial rolls is designed as 201. Then, the rotational speed Nmain can be selected from within the allowable range for the radial–axial ring mill, 28 rpm in this study. Experimental processes were aborted immediately after having reached the desired coordinates of the mandrel and the upper axial roll. Thereafter, each ring specimen was cut using a wire EDM machine and the cross-sections of the rolled rings were measured. Ring spreads measurements were taken at two positions after having passed through the gaps between the rolls and ring. 5.2. Result of ring rolling experiments
5. RARR process experiments 5.1. Experimental procedures The plain ring rolling experiments were conducted on a RARR mill from Kaltek Co., Ltd., in Korea, to validate the advanced
Fig. 15 represents the plain ring rolling experiment carried out using an industrial ring-rolling machine. Deformed ring shapes under different dD/dt in the RARR experiments are shown in Fig. 16. When dD/dt¼6 and 16 mm/s, the rolled rings were distorted. For other dD/dt values such as 8, 12, and 14 mm/s, the RARR process
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
Temp. (˚C)
29
Temp. (˚C)
1248.03
1250.90
1240.04
1245.24
1232.05
1239.57
1224.05
1233.90
1216.06
1228.23
1208.07
1222.56
1200.08
1216.89
1192.09
1211.22
Min. 1168
1184.10 1176.57
1205.56 1199.89
Max. 1248
Min. 1194 Max. 1251
1194.2
1168.11
Temp. (˚C)
Temp. (˚C)
1252.75
1302.01
1248.73
1291.18
1244.70
1280.35
1240.67
1269.53
1236.65
1258.70
1232.62
1247.87
1228.59
1237.04
1224.57
1226.22
Min. 1217
1220.54 1216.51
1215.39 1204.56
Max. 1253
1212.48
Min. 1194 Max. 1302
1193.73
Fig. 12. Temperature distribution of deformed ring in RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
Average temperature [˚C]
1260 1240 1220 1200 8 mm/s 12 mm/s 14 mm/s 16 mm/s
1180 1160 Inside surface
1140 0
10
20
Outside surface 30
40
50
60
70
Distance along the thickness direction from inside to outside surfaces of the ring [mm] Fig. 13. Average temperature on upper surface of deformed ring under different dD/dt.
achieved stable forming with good ring circularity. From Fig. 17, when dD/dt¼6 mm/s, severe inhomogeneous deformation occurs in the ring, resulting in ring climbing, tilting, and process failure. This indicates that the RARR process cannot be established successfully. Therefore, dD/dt should be greater than dD/dt1 and less than dD/dt5 for establishing a successful RARR process.
The cross-sectional shapes of the plain ring after passing through the radial and axial roll gaps under different dD/dt are shown in Fig. 18. In general, the maximum and the minimum spreads occur close to the SR of the ring and in the CR, respectively. When dD/dt close to the median of its limit range of dD/dt (¼dD/dt3, dD/dt4), the ring spreads slightly decreased. The reasons for this are that: the value of mean thickness-to-length ratio is considerably smaller than 7.08, and the plastic deformation zone can penetrate the ring from the SR to CR more easily with increasing the radial and axial feed amounts per revolution. When dD/dt ¼8, 12, and 14 mm/s, the simulated and experimental results for the fishtail coefficient are shown in Fig. 19. These results indicated that the fishtail coefficient decreased significantly with increasing dD/dt. The reducing tendency of experimental values are in good agreement with that of simulation data. However, the simulative values after passing through radial roll gap is higher than the experimental data. The discrepancy may be attributable to the errors arising from mesh sizes, thermomechanical properties, ring cross section, etc. In real ring rolling process, the heated ingot is forged as an initial ring blank by the hydraulic press firstly. Then, the bulged ring blank is rolled on the ring rolling mill. On the other hand, the cross section of initial ring blank is rectangle in FE-simulation. Considering the effective strain, temperature distribution, and geometry of the rolled ring, the ring growth velocity of 14 mm/s, i.e., dD/dtmin o dD/dt4 odD/dtmax, is our suggested value for RARR process design.
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Feed rate of mandrel(mm/s)
2.5 dD/dt = 16 mm/s
dD/dt = 14 mm/s
dD/dt = 12 mm/s
2.0
1.5 dD/dt = 8 mm/s
1.0 dD/dt = 6 mm/s
0.5 65
70
75 80 85 90 95 100 Wall thickness of rolled ring (mm)
105
Fig. 16. Experimental results with different dD/dt in RARR process.
Axial roll Centering roll
6. Conclusions Main roll
TR
Mandrel
Fig. 14. Radial–axial ring rolling machine used in this study.
Mandrel
Upper Axial roll
Centering roll Ring blank
Upper Axial roll
Fig. 15. Radial–axial ring rolling experiment.
In this paper, an advanced feasible forming condition for the RARR process was determined for reducing ring spreads and maintaining process stability. Using 3D coupled thermo-mechanical FE-model and analysis, we investigated the effect of the advanced feasible forming condition on the fishtail coefficient and deformation distribution characteristics of the plain ring. Furthermore, the proposed condition was validated through experimental results obtained by performing ring rolling experiments using AISI 1035 alloy steel. The main conclusions are as follows: (1) Penetrating plastic deformation should be expected when the mean thickness-to-length ratio of the plastic zone is smaller than 7.08, which is determined using the plane strain indentation theory with considering Coulomb friction at the ring blank–mandrel interface. The minimum draft ΔSmin per revolution is expressed using Eq. (22) for reducing ring spreads. (2) The advanced feasible forming condition is exposed based on the plastic penetration, gripping conditions, CGVC and mathematical modeling for the RARR process, which is expressed by Eqs. (32)–(34), respectively. (3) The deformation of the ring becomes uniform and the fishtail coefficient, ζ, decreases as the growth velocity of the ring outer diameter dD/dt increases within the proposed range of the advanced feasible forming condition. (4) With increasing dD/dt, the mean thickness-to-length ratio becomes smaller than 7.08 and the plastic deformation zone can be penetrated from the SR to CR more easily. Therefore, the effective strain of both the SR and the CR of the rolled ring decrease and the ring becomes more homogeneous. (5) With increasing dD/dt, average temperatures of both the SR and the CR of the ring increase and their distribution on the upper surface of the rolled ring along the radial direction becomes uniform except in the case of dD/dt5. (6) Through the plain ring rolling experiment using AISI 1035 alloy steel, the proposed advanced feasible forming condition for RARR was evaluated in terms of the shape and geometry of the rolled ring. The median of its limit range of dD/dt(¼dD/dt3, dD/dt4) led to stable forming with reduced ring spreads and good circularity due to the reasonable value of S/L and the sufficiently high feed amounts per revolution for the mandrel and upper axial roll. The fishtail coefficient decreased significantly with increasing dD/dt, and these reducing tendency of
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
31
Fig. 17. Experimental results with dD/dt of 6 mm/s in RARR process.
67.89
77.87
78.22
77.58
69.08
68.69
78.89
78.54
80.05
71.41
70.52
Cross section after passing the mandrel
Cross section after passing the axialroll
Cross section after passing the axial roll
73.17
68.05
71.41
76.5
78.36
69.16
79.96
77.61
77.87
78.14
Cross section after passing the mandrel
68.51
73.48
68.66
Cross section after passing the mandrel
Cross section after passing the axial roll
Cross section after passing the mandrel
Cross section after passing the axial roll
Fig. 18. Cross section of a ring rolled using RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
0.06
0.06 FE-Simulations Experiments Fishtail coefficient,
Fishtail coefficient,
FE-Simulations Experiments 0.04
0.02
0.00
0.04
0.02
0.00
8.126
12.375 dD/dt (mm/s)
14.331
8.126
12.375
14.331
dD/dt (mm/s)
Fig. 19. Comparison of FEA and experimental results for fishtail coefficient under different dD/dt in RARR process: (a) after passing through radial roll gap and (b) after passing through axial roll gap.
32
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
experimental values are in agreement with that of simulation data. (7) Considering the effective strain, temperature distribution, and geometry of the rolled ring, dD/dt of 14 mm/s, dD/dtmin odD/dt4 o dD/dtmax, is our suggested value for RARR process design.
Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (nos. 2012R1A5A1048294) and PNU-IFAM JRC. References [1] Semiatin SL. ASM handbook, vol. 14A. Metal working: bulk forming. Ohio: ASM International; 2005. [2] Kluge A, Lee YH, Wiegels H, Kopp R. Control of strain and temperature distribution in ring rolling process. Journal of Materials Processing Technology 1994;45:137–41. [3] Johnson W, Needham G. Plastic hinges in ring indentation in relation to ring rolling. International Journal of Mechanical Sciences 1968;10:487–90. [4] Mamalis AG, Hawkyard JB, Johnson W. Spread and flow patterns in ring rolling. International Journal of Mechanical Sciences 1976;18:11–6. [5] Lugora CF, Bramley AN. Analysis of spread in ring rolling. International Journal of Mechanical Sciences 1987;29:149–57. [6] Hua L, Zhao ZZ. The extremum parameters in ring rolling. Journal of Materials Processing Technology 1997;69:273–6. [7] Yan FL, Hua L, Wu YQ. Planning feed speed in cold ring rolling. International Journal of Machine Tools & Manufacture 2007;47:1695–701. [8] Davey K, Ward MJ. A practical method for finite element ring rolling simulation using the ALE flow formulation. International Journal of Mechanical Sciences 2002;44:165–90. [9] Davey K, Ward MJ. An ALE approach for finite element ring–rolling simulation of profiled rings. Journal of Materials Processing Technology 2003;139: 559–66. [10] Kang BS, Kobayashi S. Preform design in ring rolling processes by the threedimensional finite element method. International Journal of Machine Tools and Manufacture 1991;31:139–51.
[11] Joun MS, Chung JH, Shivpuri R. An axisymmetric forging approach to preform design in ring rolling using a rigid-viscoplastic finite element method. International Journal of Machine Tools and Manufacture 1998;38:1183–91. [12] Guo LG, Yang H, Zhan M. Research on plastic deformation behaviour in cold ring rolling by FEM numerical simulation. Modelling and Simulation in Materials Science and Engineering 2005;13:1029–46. [13] Wang M, Yang H, Sun ZC, Guo LG. Analysis of coupled mechanical and thermal behaviors in hot rolling of large rings of titanium alloy using 3D dynamic explicit FEM. Journal of Materials Processing Technology 2009;209:3384–95. [14] Yang H, Zhan M, Lu YL, Xian FJ, Sun ZC, Lin Y, et al. Some advanced plastic processing technologies and their numerical simulation. Journal of Materials Processing Technology 2004;151:63–9. [15] Wang ZW, Zeng SQ, Yang XH, Cheng C. The key technology and realization of virtual ring rolling. Journal of Materials Processing Technology 2007;182: 374–81. [16] Guo LG, Yang H. Key technologies for 3D-FE modeling of radial–axial ring rolling process. Materials Science Forum 2008;575–78:367–72. [17] Hua L, Pan LB, Lan J. Research on the ring stiffness condition in radial–axial ring rolling. Journal of Materials Processing Technology 2009;209:2570–5. [18] Yeom JT, Kim JH, Park NK, Choi SS, Lee CS. Ring–rolling design for a large–scale ring product of Ti–6Al–4V alloy. Journal of Materials Processing Technology 2007;187-88:747–51. [19] Zhou G, Hua L, Lan J, Qian DS. FE analysis of coupled thermo-mechanical behaviors in radial–axial ring rolling of alloy steel large ring. Computational Materials Science 2010;50:65–76. [20] Zhou G, Hua L, Qian DS. 3D coupled thermo-mechanical FE analysis of roll size effects on the radial–axial ring rolling process. Computational Materials Science 2011;50:911–24. [21] Zhou G, Hua L, Qian DS, Shi DF, Li HX. Effects of axial rolls motions on radial– axial rolling process for large–scale alloy steel ring with 3D coupled thermomechanical FEA. International Journal of Mechanical Sciences 2012;59:1–7. [22] Qian DS, Pan Y. 3D coupled macro-microscopic finite element modelling and simulation for combined blank-forging and rolling process of alloy steel large ring. Computational Materials Science 2013;70:24–36. [23] Xu W, Yang X, Gong X, Zhou J. A new mathematical model for predicting the diameter expansion of flat ring in radial–axial ring rolling. International Journal of Advanced Manufacturing Technology 2011;60:913–21. [24] Slater RAC. Engineering plasticity: theory and application to metal forming processes. London: The Macmillan Press; 1977. [25] Hill R. The mathematical theory of plasticity. Oxford: Oxford University Press; 1950. [26] Hosford WF, Caddell RM. Metal forming: mechanics and metallurgy. New Jersey: Prentice-Hall; 1983. [27] Guo L, Yang H. Towards a steady forming condition for radial–axial ring rolling. International Journal of Mechanical Sciences 2011;53:286–99. [28] Forge 2009 Online Help. Version 3.2En. November 2009.
Contents lists available at ScienceDirect
International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
Advanced feasible forming condition for reducing ring spreads in radial–axial ring rolling Kyung-Hun Lee a, Byung-Min Kim b,n a b
PNU-IFAM JRC, Pusan National University, Busan 609-735, South Korea School of Mechanical Engineering, Pusan National University, Busan 609-735, South Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 11 June 2013 Received in revised form 31 July 2013 Accepted 19 August 2013 Available online 30 August 2013
In this study, we derive an advanced feasible forming condition for reducing ring spreads and maintaining process stability during radial–axial ring rolling (RARR) process. First, the plastic penetrating condition was determined using the mean thickness-to-length ratio of the plastic zone. This calculation was based on the plane strain indentation theory considering Coulomb friction at the ring blank– mandrel interface. Second, a mathematical model for the RARR process was developed assuming constant volume of ring blanks and constant growth velocity condition (CGVC) of the ring outer diameter. Finally, the advanced feasible forming condition was determined from the mathematical correlations among the main roll, mandrel and axial roll sets, and reasonable range of extreme growth velocities. To verify the proposed condition, we carried out FE-simulations by developing reliable three-dimensional finite element (3D-FE) models using Forge, a commercial finite-element software package. The simulation results show that the designed process results in relatively uniform deformation behavior and reduces ring spreads. Predicted rolled ring spreads were compared with the experimental results. The ring growth velocity, which is a median value of its reasonable range determined using the advanced feasible forming condition, is recommended for the forming process design considering the reduced ring spreads and uniform plastic deformation. Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
Keywords: Radial–axial ring rolling Constant growth velocity conditions Plain strain indentation theory Advanced feasible forming condition Finite element simulation Ring spreads
1. Introduction Ring rolling is a versatile metal-forming process for manufacturing seamless annular products with circumferential grain flow and accurate dimensions. Ring rolling usually requires less input material than alternative forging methods, and it can be used for mass production in any quantity. The most commonly used modern ring rolling mill is the radial–axial ring rolling (RARR) machine; it consists of a radial and an axial set of rolls, as shown in Fig. 1. Ring blanks are placed on the rolling table. Two sets of rolls are arranged diametrically opposite relative to the ring center, where a main roll and the mandrel are arranged horizontally and an upper and a lower axial roll are arranged vertically. The main roll rotates at a constant, predetermined speed. The ring begins to rotate as the mandrel squeezes the ring wall. This, in turn, rotates the mandrel [1]. The roll geometries and comparatively small reductions in ring height and ring wall thickness per rolling pass result in ring spreads bulged at the four corners of the ring cross section. This inhomogeneous deformation is called a “fishtail.” During ring rolling, any
n
Corresponding author. Tel.: þ 82 515102319; fax: +82 515813075. E-mail address: [email protected] (B.-M. Kim).
spread in the radial gap is rolled off into the axial gap and vice versa. This alternating bulge deformation results in the concentration of strain- and forming energies at the corners of the ring cross section, leading to severe microstructural damage as well as forming defects [2]. Thus far, there have been a few studies on the effect of mandrel feed rate on ring spreads during ring rolling. Johnson and Needham [3] ascribed diametric reduction to the formation of a plastic hinge at a point on the ring that is diametrically opposite to the point of indentation; they arrived at this conclusion while attempting to arrive at an upper-bound estimate of the necessary rolling load. Hawkyard et al. [4] presented the spread and flow patterns in plane and profile ring rolling. Ring spreads are irregular and nonrectangular with fishtailing in each case, and the feed rate has a marked effect on the ring spreads because the spreads become more regular as the feed rate increases. Lugora and Bramley [5] investigated the spread in plain ring rolling using Hill′s general method of analysis. Fast and slow mandrel feeding may cause the ring blank to stop rotating and expanding, respectively; these situations represent two extremum draft conditions. The theoretical extremum feeding speeds that should be satisfied for achieving pure radial ring rolling (PRRR) were first suggested by Hua and Zhao [6]. Yan et al. proposed the method of planning the feed rate based on the growth rate of the ring outer diameter in cold ring rolling [7].
0020-7403/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijmecsci.2013.08.007
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
Fig. 1. Schematic illustration of radial–axial ring rolling machine.
To ensure that the ring grows uniformly and stably, growth rate of the outer diameter must be constant and feed speed must decrease gradually as ring thickness decreases. However, compared with PRRR, RARR is a complex dynamic forming system caused by adding a pair of axially conical rolls that are mounted diametrically opposite to the radial pass. It is difficult but critical to determine reasonable ranges of the key RARR process variables. In past studies, process design was mainly based on experience or by trial, and the obtained ranges of steady forming conditions were wide; therefore, a convenient and practicable method for establishing the RARR process was not arrived at. Lately, a few numerical-simulation-based studies on RARR have been reported; these include finite-element-based studies of RARR. Davey and Ward [8,9] presented an arbitrary Lagrangian–Eulerian (ALE) approach for finite element ring-rolling simulation to save computational cost. Based on a finite-element method, Kang and Kobayashi [10] and Joun et al. [11] studied preform design in ring rolling using the backward tracing scheme and an axisymmetric forging approach, respectively. FE-modeling and numerical simulation have been proven to be both powerful and accurate for studying plastic deformation behaviors of materials under various complicated metal forming processes [12–14] and can be used for conducting more comprehensive, profound, and detailed investigations compared to the analytical and experimental methods. Recently, a few studies on the numerical simulation of the RARR process have been reported. For example, Wang et al. [15] developed a virtual RARR process for guiding process design and optimization using LS-DYNA FE code with the mass-scaling function. Design Language program was developed for controlling complex movements of the guide and axial rolls. Guo and Yang [16] presented some key technologies, i.e., technologies for the flexible control of the motions of guide and axial rolls, for the 3D-FE modeling of the RARR process using an elastic–plastic dynamic explicit procedure in the ABAQUS environment. Hua et al. [17] established a ring stiffness condition in RARR; this condition was validated using numerical simulation. The ring stiffness condition is related to the ring blank′s dimensions and rolling ratio, position angle of guide roll, roll dimensions, axial roll positions, radial and axial feed rates, and friction condition. Yeom et al. [18] investigated the RARR design of a large-scale ring product composed of Ti–6Al–4V alloy using a calculation method and FEM analysis. Hua et al. [19] proposed the stable forming conditions for RARR process and investigated the effect of key parameters on the uniformity of the deformation and temperature distribution of alloy steel large ring. The effects of roll size on uniformity of strain and temperature distributions of the rolled ring are investigated to provide valuable guidelines for the roll design by Zhou et al. [20]. Hua et al. [21] developed the motion
control method of axial rolls to increase the uniformity of STD and SDP. Qian and Pan [22] presented the combined simulation for blank forging and ring rolling process to investigate the effect of blank forging on ring deformation behaviors. However, in the abovementioned studies, RARR process design was based mainly on experience or trial and error, and, hence, these studies do not present a simple and convenient method for establishing the process and maintaining its stability. Therefore, it is necessary to derive an advanced feasible forming condition for reducing ring spreads, fishtail defects, and maintaining process stability during RARR. The purpose of this study is to develop a mathematical model of the aforementioned advanced feasible forming condition by determining the mathematical correlations among the rolls, reasonable ranges of ring-growth velocity based on the mean thickness-to-length ratio of the plastic deformation zone, and constant growth velocity condition (CGVC). To verity the proposed condition, we carried out FE simulations by developing reliable 3D-FE models using Forge, a commercially available finiteelement platform. The analytical results of ring spreads and deformation behavior of large rings were validated against the results of RARR experiments performed using an AISI 1035 alloy steel ring with an initial outer diameter of 600 mm. 2. Slip-line field analysis for ring rolling 2.1. Interfacial Coulomb friction In ring rolling, rotation of the deformed ring relies greatly on the friction between the ring and the rolls, i.e., the main roll and the set of axial rolls. The ring be drawn successively into the gap and be rotated continuously only if the gripping condition is satisfied. A model for the gripping condition is shown in Fig. 2 [23]. The following equations can be obtained through force analysis: ∑F x ¼ T 1 cos ðξ1 α1 ÞP 1 sin ðξ1 α1 ÞP 2 sin ðξ2 α2 Þ Z 0
ð1Þ
∑F y ¼ T 1 sin ðξ1 α1 ÞP 1 cos ðξ1 α1 Þ þ P 2 cos ðξ2 α2 Þ ¼ 0
ð2Þ
where P1 and T1 are the normal force and tangential friction, respectively, between the main roll and the ring. The mandrel and
Fig. 2. Gripping condition for ring rolling [23].
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
the two centering rolls are driven, and should therefore have minimal friction moments; for simplicity, we assume ring-mandrel and – centering roll friction to be zero. P2 represents the normal force of the mandrel on the ring. ξ1α1 and ξ2α2 represent the angles of P1 and P2 with respect to the y-axis, respectively, where ξ1, ξ2 A(0, 1) are dimensionless coefficients. According to the Coulomb friction condition, T1 ¼ μP1, where μ is the friction coefficient. Thus, the gripping condition can be obtained as follows:
μ Z tan ðξ1 α1 þ ξ2 α2 Þ
ð3Þ
From the given geometric conditions, the projected length L of the contact patch between the ring and the rolls is given as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðS0 SÞ L¼ ð4Þ 1=Rmain þ 1=Rmandrel þ 1=R 1=r where Rmain and Rmandrel are the radii of the main roll and the mandrel, respectively, and R and r are the radii of the outer and inner surfaces of the ring workpiece. From Ref. [7], we consider the following geometrical relationships:
α1
L ; Rmain
α2
L Rmandrel
ð5Þ
For the given dimensions of the rolls, initial ring workpiece, and rolled ring, the minimum friction coefficient can be calculated using Eqs. (3)–(5). The needed input parameters for the calculation are listed in Table 1 and the determined friction coefficient is 0.178. Let the normal compressive stress at the interface between tools and a ring workpiece due to the tool pressure be q. Then, the Table 1 Input parameters required for RARR process verification. Parameter
Value
Ring material Outer diameter of ring blank Wall thickness of ring blank Height of ring blank Outer diameter of rolled ring Wall thickness of rolled ring Height of rolled ring Initial temperature of ring blank Radius of main roll Radius of mandrel Cone angle of axial rolls Tool temperature Friction coefficient Rotational speed of main roll Ambient temperature
AISI 1035 600 mm 100 mm 95 mm 976 mm 68 mm 77 mm 1250 1C 425 mm 65 mm 401 200 1C 0.178 28 rpm 20 1C
23
resultant shear stress tangential to the interface considering Coulomb friction is τxy ¼ μq. The resultant shear force exerted on any element of the interface is balanced by the resolved components of the forces acting on the slip lines. One slip line will, therefore, intersect the interface at some angle ϕ o π/4. If the forces exerted on the element are resolved in a direction tangential to the interface and equated to zero for equilibrium, then it will be found that [24] μq =2 ð6Þ ϕ ¼ cos 1 k Substituting μ ¼0.178 into Eq. (6), the angle mined as 0.36287 rad (¼361).
ϕ can be deter-
2.2. Plane strain indentation considering interfacial Coulomb friction In ring rolling, the radius of curvature of the smaller roll, i.e. mandrel, is also generally large in relation to the contact lengths, the proportions being investigated the effect of key parameters on the uniformity of the deformation and temperature distribution of ASLR that a reasonable approximation to the rolling situation is provided by the analysis for the indentation of a lock by opposed flat indenters of equal width [25]. Fig. 3 shows a slip-line field for plane-strain indentation and the right-hand half of this field with a changing stress state, as indicated. CBAO′ is a α-line, while radial lines such as OB and OA are β-lines. When moving clockwise from B to A along an α-line through an angle Δϕa ¼ 1:7279 rad, the Hencky equations yields s2A ¼ k þ 2kð1:7279Þ ¼ 4:4558k
ð7Þ
This is also the value of s2 throughout AOO′ because this region is composed of straight lines only and is acted upon by compressive stresses along all principal directions. To determine tool pressure, P ? , which is sy ¼ s3 , P ? ¼ s3OO0 ¼ s2A k sin ð2ϕÞ ¼ 5:407k Thus, the pressure factor
ð8Þ
γ is
γ ¼ P ? =2k ¼ 2:7035
ð9Þ
2.3. Indentation as a function of ring blank geometry As the mean thickness-to-length ratio S/L becomes larger than one, a different field must be used for satisfying field requirements. This is illustrated in Fig. 4, which is a net with 301 angular increments. Moving along an α-line to (0, 1) and back along a β-line to (1, 1), sxð1;1Þ ¼ P ? þ k sin ð2ϕÞ þ k þ 2kðΔϕα Δϕβ Þ
Fig. 3. Slip-line field for plane-strain indentation of semi-infinite slab [26].
ð10Þ
24
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and mandrel, respectively. Raxial and α are the radius and half cone angle of axial conical rolls, respectively. Nmain is the rotational speed of the main roll; dD/dt is the constant growth velocity of the ring. The subscripts i and n are the actual number of revolution and all revolutions, respectively. (ii) The volume of ring blank is constant in plastic deformation, neglecting the mass decrease by oxidized scales and maintaining the ring circularity and rectangular cross section shape. Let c0 and ci are the initial and instantaneous volume, respectively. C 0 ¼ π ðDi Si ÞSi H i ¼ C i
ð13Þ
(iii) Let Si, Hi, and Di denote the instantaneous wall thickness, height, and outer diameter of the ring, respectively, assuming that the wall thickness and height reductions are equal in each revolution. Thus, for i¼1, 2, …, n, we have the following equations: Si ¼ Si1 þ ðSf S0 Þ=n
ð14Þ
H i ¼ H i1 þðH f H 0 Þ=n
ð15Þ
Di ¼ C i =π ðSi H i Þ þ Si
ð16Þ
(iv) Let ti be an instant of time during the process. According to the CGVC, we have the following: t i ¼ t i1 þ ðDi Di1 Þ=ðdD=dt i Þ Fig. 4. Slip-line field for two centered fans showing x and y as functions of Δϕ using a 301 net
At any point (n, n), Δϕα ¼ nπ =6, Δϕβ ¼ nπ =6, so sxðn;nÞ ¼ P ? þ 1:9517k þ 2k Δϕ
ð11Þ
If the slab is unconstrained in the x-direction, an appropriate boundary condition is F x ¼ 0. The net force, F x in the x-direction is equal to the integral of sx along the centerline. Z 4k S=2 2Δϕ dy ð12Þ P ? ¼ 1:9517k þ S 0 Values of Δϕ as a function of y are given in Fig. 4 for a 301 net. Using the results shown in Fig. 4, Eq. (12) can be integrated graphically by first plotting 2Δϕ versus Y-axis. At values of the mean thickness-to-length ratio of the plastic zone S/L 47.08, P ? =2k for this field exceeds 2.7035, which is the threshold value for non-penetrating indentation. Physically, this means that nonpenetrating deformation should be expected when S/L 47.08 and penetrating deformation for smaller values of S/L.
3. Advanced feasible forming condition 3.1. Mathematical modeling for RARR The mathematical model was developed based on the constant volume condition of a ring and CGVC for the concerns related to uncooperative roll motions and RARR process stability. The modeling process is summarized as follows: (i) The initial set of parameter values was determined. D0, H0, and S0 are the outer diameter of the ring blanks, height, and wall thickness, respectively. Df, Hf, and Sf are the final outer diameter of the rolled rings, height, and wall thickness, respectively. Rmain and Rmandrel are the radius of the main roll
ð17Þ
(v) The instantaneous ring geometry and time evolve feed rates of the mandrel and the upper axial roll, according to the central difference method, are as follows:
1 Si þ 1 Si S S V mandrel;i ¼ þ i i1 ð18Þ 2 t i þ 1 t i t i t i1 V axial;i ¼
1 2
H i þ 1 H i H i H i1 þ t i þ 1 t i t i t i1
ð19Þ
(vi) The relative contact positions between the axial rolls and the outer surface of the rings, such as point C shown in Fig. 1, should remain unchanged as far as possible. The rotational speed Naxial of the axial rolls can be calculated using Di as follows: 2π Rmain N main ¼ π Di N ring ¼ 2π Raxial N axial
ð20Þ
(vii) The withdrawal speed of the axial roll frame Vframe should be as consistent with the ring growth velocity as possible to maintain the minimum relative slip between the axial rolls and the end faces of the ring, i.e., the relative contact positions between the axial rolls and the ring should remain unchanged as far as possible [27]. V f rame ¼
1 dD 2 dt
ð21Þ
3.2. Advanced feasible forming condition for PRRR The plastic deformation zone of ring blanks is related directly to the draft of mandrel ΔS. For reducing ring spreads and ensuring stable expansion of the ring blank in ring-rolling, the draft ΔS must exceed the minimum draft ΔSmin needed to penetrate through the thickness. For satisfying this condition, it would be necessary to roll at a sufficiently high feed rate so as to ensure that
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
S/L is less than 7.08. Substituting Eq. (4) in the limited value of S/L and rearranging, the minimum draft ΔSmin per revolution is obtained, as follows: 1 1 1 1 ΔSmin ¼ 1 102 ðRi r i Þ2 þ þ ð22Þ Rmain Rmandrel Ri r i where Ri and ri are the instantaneous radii of the outer and inner surfaces of the ring blank, respectively. If ΔS increases to exceed the maximum draft ΔSmax corresponding to the gripping condition, the ring blank will not be drawn into the roll gap; therefore, ΔS cannot exceed ΔSmax. Substituting Eqs. (4) and (5) into Eq. (3) and re-arranging, ΔSmax is obtained as follows: 2ðarctan μÞ2 Rmain 1 1 1 1 ð23Þ ΔSmax ¼ þ þ ð1 þ Rmain =Rmandrel Þ Rmain Rmandrel Ri r i Assuming no slip between the main roll and the ring blank, the circumference of the outer ring in one rotation is equal to the perimeter of the main roll; therefore:
ΔS ¼ V mandrel Δt; Δt ¼ Ri =ðN main Rmain Þ
ð24Þ
Based on the extremum draft for PRRR process and Eq. (24), a reasonable range of extremum mandrel feed rates can be calculated as follows: V min r V mandrel r V max V min ¼ 1 10
V max ¼
2
R 1 1 1 1 N main main ðRi r i Þ2 þ þ Rmain Rmandrel Ri r i Ri
2ðarctan μÞ2 N main R2main R R R 1 þ main þ main main Ri ð1 þRmain =Rmandrel Þ Rmandrel Ri ri
ð25Þ ð26Þ
ð27Þ
3.3. Advanced feasible forming condition for RARR The RARR process is an extremely complex dynamic forming system. There are complex and severe dynamic contacts and collisions between the ring and the rolls that may result in severe process instability. However, these severe dynamic contacts and collisions can be alleviated greatly by maintaining a constant ring growth velocity because growth acceleration of the ring at the contact points with all rolls is zero under a constant ring growth velocity. That is to say, a constant ring growth velocity would considerably improve process stability [27]. Based on this consideration, we propose that maintaining a constant ring growth velocity is a key design objective in RARR process design. This is referred to as the constant growth velocity condition (CGVC) of the ring in this study. When the ring grows with a constant velocity during the RARR process, the outer diameter of the ring can be expressed as a linear function of the rolling time: D ¼ D0 þ ðDf D0 Þt=T
ð28Þ
dD ¼ ðDf D0 Þ=T dt
ð29Þ
where D is the instantaneous outer diameter of the ring and t is the rolling time. When t equals zero, D equals the initial outer diameter D0 of the ring blank. When t equals T, i.e., the rolling time needed to complete one operation, and D equals the final outer diameter Df of the rolled ring, dD/dt is the growth velocity of the outer diameter of the ring. Let ΔStotal denote the total amount of reduction of the ring wall; then we have
ΔStotal ¼ S0 Sf
ð30Þ
25
Therefore, total time T can be calculated as follows: T ¼ ΔStotal =V mandrel
ð31Þ
Finally, we obtain a range of dD/dt of the ring using the proposed CGVC and Eqs. (26) and (27): dD=dt min r dD=dt r dD=dt max
ð32Þ
V min ðDf D0 Þ Δsmin Rmain N main ðDf D0 Þ dD ¼ ¼ dt min R0 Δstotal Δstotal
ð33Þ
V max ðDf D0 Þ Δsmax Rmain N main ðDf D0 Þ dD ¼ ¼ dt max Rf Δstotal Δstotal
ð34Þ
For given Nmain, μ, and geometries of the rolls, initial ring blank, and deformed ring, the ranges of dD/dt, Vmandrel, and Vaxial can be calculated using Eqs. (22)–(34). Eq. (32) implies that dD/dt of the ring should be controlled to be within dD/dt A (dD/dtmin, dD/dtmax) for successfully establishing a RARR process considering the plastic deformation behavior of the ring material.
4. FE—Analysis for verifying advanced feasible forming condition 4.1. 3D-FE modeling for RARR To verify the proposed advanced feasible forming condition, we developed a 3D-coupled thermo-mechanical FE model for the RARR process using FORGE-3D, as shown in Fig. 5. Ring rolling simulations were carried out using an ALE approach and a coupled thermo-mechanical tetrahedron element with 4 nodes. In the FORGE platform, the centering option triggers a specific algorithm that maintains the ring centered position to stabilize the process [28]. In real ring rolling mills, this function is performed by centering rolls. The ring material used is AISI 1035 carbon steel alloy and its elastic modulus and Poisson′s ratio are 200 GPa and 0.3, respectively. The result of hot compression tests under different temperatures and strain rates are used for determining the material′s stress–strain curves, as shown in Fig. 6. The friction coefficient at the ring–main roll interface is 0.178. The mandrel and axial rolls are assumed as smooth surfaces; therefore, the friction coefficients between these surfaces and the ring blank are zero. The temperature-dependent physical properties (thermal conductivity specific heat, etc.) of the alloy used here were obtained from Metal Suppliers Online of
Axial roll Ringblank
Mandrel
Main roll
Fig. 5. 3D-FE model of RARR process.
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130
90
120 110
Effective stress [MPa]
Effective stress [MPa]
80 900 °C
70 60
1000 °C
50
1100 °C
40 30
1200 °C
900 °C
100 90 80
1000 °C
70 60
1100 °C
50
1200 °C
40 30
20
20
10 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.0
0.2
0.4
Effective strain
0.6
0.8
1.0
1.2
1.4
1.6
Effective strain
180
Effective stress [MPa]
160 900 °C
140 120
1000 °C
100 80
1100 °C
60
1200 °C
40 20 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Effective strain
Fig. 6. Effective stress–strain curves of AISI 1035 carbon steel alloy under different temperatures and strain rates: (a) 0.1 s 1; (b) 1 s 1; and (c) 10 s 1.
1.4
dD/dt= 6 mm/s dD/dt= 8 mm/s dD/dt=12 mm/s dD/dt=14 mm/s dD/dt=16 mm/s
2.0
Feed rate of axial roll(mm/s)
Feed rate of mandrel(mm/s)
2.5
1.5
1.0
0.5
dD/dt= 6 mm/s dD/dt= 8 mm/s dD/dt=12 mm/s dD/dt=14 mm/s dD/dt=16 mm/s
1.2 1.0 0.8 0.6 0.4 0.2
65
70
75
80
85
90
95
100
105
Wall thickness of rolled ring (mm)
76
78
80
82
84
86
88
90
92
94
96
Height of rolled ring (mm)
Fig. 7. Variation curves of feed rate in RARR process: (a) Vmandrel and (b) Vaxial.
America: specific heat 778 J kg 1 1C 1, conductivity 35.5 W m 1 C 1, and emissivity 0.88. All rolls were treated as rigid bodies, and the general conditions are listed in Table 1. Initial process parameters for modeling: radius of main roll and mandrel were 425 and 65 mm, respectively. Initial parameters of ring blank: outer radius, thickness, and height were 500, 100, and 80 mm, respectively. Additionally, the rotational speed Nmain of the main roll is 28 rpm. The variation curves of Vmandrel with the thickness S of the ring and time T can be plotted for a series of dD/dt values from within the proposed range of dD/dt A (6.002, 16.287 mm/s) and equal to 6, 8, 12, 14, and 16 mm/s. Case 1: dD/dt1 ¼6 mm/s, arbitrarily minimum ring growth velocity. Case 2: dD/dt2 ¼ 8 mm/s, minimum ring growth velocity proposed by Guo and Yang [27].
Case 3: dD/dt3 ¼12 mm/s, minimum ring growth velocity investigated by Lee in this study (¼ dD/dtmin). Case 4: dD/dt4 ¼14 mm/s, arbitrary medium ring growth velocity. Case 5: dD/dt5 ¼16 mm/s, maximum ring growth velocity. ( ¼dD/dtmax). From Fig. 7, it can be concluded that Vmandrel and Vaxial should decrease gradually to ensure a constant ring growth velocity, and that the larger dD/dt, the larger is Vmandrel. Fig. 7 presents the feasible region for the design of Vmandrel and Vaxial whereby the RARR process can realize stable forming. 4.2. Results and discussion of FEA for RARR The deformed ring shapes for various dD/dt are shown in Fig. 8. The rolled ring was distorted for dD/dt1 of 6 mm/s. The ring was
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
27
Fig. 8. Shape of deformed rings under different dD/dt in RARR process: (a) 6 mm/s; (b) 8 mm/s; (c) 12 mm/s; (d) 14 mm/s; and (e) 16 mm/s.
Fig. 9. Fishtail coefficient with different dD/dt in RARR process.
compressed within the gaps for dD/dt5 of 16 mm/s; therefore, the ring could be drawn into the roll gap and showed little diameter growth. This indicates that the RARR process cannot be established successfully when dD/dt ¼6 mm/s or 16 mm/s. At the minimum growth velocity proposed by Guo and Yang [27] dD/dt2 ( ¼8 mm/s), the one dD/dt3 ( ¼12 mm/s) proposed in this paper, and the medium value of limit ranges dD/dt4 (¼ 14 mm/s), the RARR process achieved stable forming with good ring circularity. Especially for dD/dt5 ¼ 16 mm/s, a severe cavity defect occurred on the outer surface of the ring after axial rolling. Therefore, the ring could not be nipped into the radial roll gap and showed little growth in diameter. The effect of dD/dt on ring spreads is evident from Fig. 9 in that, within the defined scope, with increasing dD/dt, the fishtail coefficient ζh ¼(Hmax Hmin)/Hmin; ζs ¼(Smax Smin)/Smin decreases in the range determined using the advanced feasible forming condition. That is to say, ring deformation becomes uniform and ring spreads decrease as dD/dt increases. Fig. 10 shows the effect of dD/dt on the cross-section configurations and contours of effective strain in the RARR process. Average effective strain on the upper surface of the rolled ring along the radial direction is shown in Fig. 11. From Figs. 10 and 11, when dD/dt increases, the values of average effective strain on the surface region (SR) and the central region (CR) of the ring
decrease. However, the extent of this decrease is larger for the SR than for the CR. Therefore, deformation of the rolled ring is uniform. The reasons underlying this uniform deformation are as follows: as shown in Fig. 7, (a) Vaxial increases according to the CGVC with increasing Vmandrel, (b) the radial and axial feed amounts per revolution increase, (c) the value of mean thickness-to-length ratio is considerably smaller than 7.08, and (d) the plastic deformation zones can penetrate the ring form the SR to CR more easily. Fig. 12 shows the effect of dD/dt on cross-section configurations and temperature distribution during the RARR process. Fig. 13 shows the average temperature distribution on the upper surface of the rolled ring along the radial direction. It has similar characteristics as deformation at different ring growth velocities. With increasing dD/dt, the average temperatures of both the SR and the CR of the ring increase, and temperature distribution in ring becomes more homogeneous, except in the case of dD/dt5. The reasons for this are as follows: the larger the dD/dt, greater is the heat generated, shorter is the rolling time, and lower is the heat loss from the SR[thermo-mechanical, FE analysis of coupled]. Thus, overall ring temperature increases and the average SR temperature decreases slightly. From Fig. 12(d), when dD/dt equals 16 mm/s, severe heat generation occurs on the outer surface of the ring after radial rolling owing to excessive local deformation.
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
EQ_STRAIN
EQ_STRAIN 4.76995
4.32370
4.35826
3.95466
3.94657
3.58561
3.53488
3.21657
3.12320
2.84753
2.71151
2.47849
2.29982
2.10944 1.74040
1.88813
Max. 4.7699
1.47644
1.37136
Min. 0.6531
1.06475
1.00231
0.65307
0.63327
EQ_STRAIN
EQ_STRAIN
3.96573
1.12772
3.63071
1.02971
3.29569
0.93171
2.96067
0.83371
2.62565
0.73571
2.29062
0.63770
1.95560
0.53970
Max. 4.3237 Min. 0.6333
0.44169
1.62058
Max. 3.9657
1.28556
0.34369
Min. 0.6155
0.95064
0.24569
Max. 1.1277 Min. 0.1477
0.14769
0.61552
Average effective strain
Fig. 10. Effective strain distribution of deformed ring in RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
8 mm/s 12 mm/s 14 mm/s 16 mm/s
4
3
2
1
Inside surface
0 0
10
20
Outside surface 30
40
50
60
70
Distance along the thickness direction from inside to outside surfaces of the ring [mm] Fig. 11. Average effective strain on upper surface of deformed ring under different dD/dt.
feasible forming condition. The specifications of this ring mill include a maximum external diameter of 3000 mm and a maximum rolling force of around 800 t (see Fig. 14). General experimental conditions are the same as those listed in Table 1. The test material was AISI 1035 in an “as cast” condition. The cut slab was deformed into a pancake by several passes of open die forging and then fabricated into a pierced blank by upsetting and piercing. The pierced blank is turned into a plain ring during the RARR process. In this study, the dimensions (DfHfSf) of the desired ring are taken as 976 77 68 mm. The radii of the main roll and mandrel are designed as 425 and 65 mm, respectively. The half of con angle θ of the axial rolls is designed as 201. Then, the rotational speed Nmain can be selected from within the allowable range for the radial–axial ring mill, 28 rpm in this study. Experimental processes were aborted immediately after having reached the desired coordinates of the mandrel and the upper axial roll. Thereafter, each ring specimen was cut using a wire EDM machine and the cross-sections of the rolled rings were measured. Ring spreads measurements were taken at two positions after having passed through the gaps between the rolls and ring. 5.2. Result of ring rolling experiments
5. RARR process experiments 5.1. Experimental procedures The plain ring rolling experiments were conducted on a RARR mill from Kaltek Co., Ltd., in Korea, to validate the advanced
Fig. 15 represents the plain ring rolling experiment carried out using an industrial ring-rolling machine. Deformed ring shapes under different dD/dt in the RARR experiments are shown in Fig. 16. When dD/dt¼6 and 16 mm/s, the rolled rings were distorted. For other dD/dt values such as 8, 12, and 14 mm/s, the RARR process
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
Temp. (˚C)
29
Temp. (˚C)
1248.03
1250.90
1240.04
1245.24
1232.05
1239.57
1224.05
1233.90
1216.06
1228.23
1208.07
1222.56
1200.08
1216.89
1192.09
1211.22
Min. 1168
1184.10 1176.57
1205.56 1199.89
Max. 1248
Min. 1194 Max. 1251
1194.2
1168.11
Temp. (˚C)
Temp. (˚C)
1252.75
1302.01
1248.73
1291.18
1244.70
1280.35
1240.67
1269.53
1236.65
1258.70
1232.62
1247.87
1228.59
1237.04
1224.57
1226.22
Min. 1217
1220.54 1216.51
1215.39 1204.56
Max. 1253
1212.48
Min. 1194 Max. 1302
1193.73
Fig. 12. Temperature distribution of deformed ring in RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
Average temperature [˚C]
1260 1240 1220 1200 8 mm/s 12 mm/s 14 mm/s 16 mm/s
1180 1160 Inside surface
1140 0
10
20
Outside surface 30
40
50
60
70
Distance along the thickness direction from inside to outside surfaces of the ring [mm] Fig. 13. Average temperature on upper surface of deformed ring under different dD/dt.
achieved stable forming with good ring circularity. From Fig. 17, when dD/dt¼6 mm/s, severe inhomogeneous deformation occurs in the ring, resulting in ring climbing, tilting, and process failure. This indicates that the RARR process cannot be established successfully. Therefore, dD/dt should be greater than dD/dt1 and less than dD/dt5 for establishing a successful RARR process.
The cross-sectional shapes of the plain ring after passing through the radial and axial roll gaps under different dD/dt are shown in Fig. 18. In general, the maximum and the minimum spreads occur close to the SR of the ring and in the CR, respectively. When dD/dt close to the median of its limit range of dD/dt (¼dD/dt3, dD/dt4), the ring spreads slightly decreased. The reasons for this are that: the value of mean thickness-to-length ratio is considerably smaller than 7.08, and the plastic deformation zone can penetrate the ring from the SR to CR more easily with increasing the radial and axial feed amounts per revolution. When dD/dt ¼8, 12, and 14 mm/s, the simulated and experimental results for the fishtail coefficient are shown in Fig. 19. These results indicated that the fishtail coefficient decreased significantly with increasing dD/dt. The reducing tendency of experimental values are in good agreement with that of simulation data. However, the simulative values after passing through radial roll gap is higher than the experimental data. The discrepancy may be attributable to the errors arising from mesh sizes, thermomechanical properties, ring cross section, etc. In real ring rolling process, the heated ingot is forged as an initial ring blank by the hydraulic press firstly. Then, the bulged ring blank is rolled on the ring rolling mill. On the other hand, the cross section of initial ring blank is rectangle in FE-simulation. Considering the effective strain, temperature distribution, and geometry of the rolled ring, the ring growth velocity of 14 mm/s, i.e., dD/dtmin o dD/dt4 odD/dtmax, is our suggested value for RARR process design.
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
Feed rate of mandrel(mm/s)
2.5 dD/dt = 16 mm/s
dD/dt = 14 mm/s
dD/dt = 12 mm/s
2.0
1.5 dD/dt = 8 mm/s
1.0 dD/dt = 6 mm/s
0.5 65
70
75 80 85 90 95 100 Wall thickness of rolled ring (mm)
105
Fig. 16. Experimental results with different dD/dt in RARR process.
Axial roll Centering roll
6. Conclusions Main roll
TR
Mandrel
Fig. 14. Radial–axial ring rolling machine used in this study.
Mandrel
Upper Axial roll
Centering roll Ring blank
Upper Axial roll
Fig. 15. Radial–axial ring rolling experiment.
In this paper, an advanced feasible forming condition for the RARR process was determined for reducing ring spreads and maintaining process stability. Using 3D coupled thermo-mechanical FE-model and analysis, we investigated the effect of the advanced feasible forming condition on the fishtail coefficient and deformation distribution characteristics of the plain ring. Furthermore, the proposed condition was validated through experimental results obtained by performing ring rolling experiments using AISI 1035 alloy steel. The main conclusions are as follows: (1) Penetrating plastic deformation should be expected when the mean thickness-to-length ratio of the plastic zone is smaller than 7.08, which is determined using the plane strain indentation theory with considering Coulomb friction at the ring blank–mandrel interface. The minimum draft ΔSmin per revolution is expressed using Eq. (22) for reducing ring spreads. (2) The advanced feasible forming condition is exposed based on the plastic penetration, gripping conditions, CGVC and mathematical modeling for the RARR process, which is expressed by Eqs. (32)–(34), respectively. (3) The deformation of the ring becomes uniform and the fishtail coefficient, ζ, decreases as the growth velocity of the ring outer diameter dD/dt increases within the proposed range of the advanced feasible forming condition. (4) With increasing dD/dt, the mean thickness-to-length ratio becomes smaller than 7.08 and the plastic deformation zone can be penetrated from the SR to CR more easily. Therefore, the effective strain of both the SR and the CR of the rolled ring decrease and the ring becomes more homogeneous. (5) With increasing dD/dt, average temperatures of both the SR and the CR of the ring increase and their distribution on the upper surface of the rolled ring along the radial direction becomes uniform except in the case of dD/dt5. (6) Through the plain ring rolling experiment using AISI 1035 alloy steel, the proposed advanced feasible forming condition for RARR was evaluated in terms of the shape and geometry of the rolled ring. The median of its limit range of dD/dt(¼dD/dt3, dD/dt4) led to stable forming with reduced ring spreads and good circularity due to the reasonable value of S/L and the sufficiently high feed amounts per revolution for the mandrel and upper axial roll. The fishtail coefficient decreased significantly with increasing dD/dt, and these reducing tendency of
K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
31
Fig. 17. Experimental results with dD/dt of 6 mm/s in RARR process.
67.89
77.87
78.22
77.58
69.08
68.69
78.89
78.54
80.05
71.41
70.52
Cross section after passing the mandrel
Cross section after passing the axialroll
Cross section after passing the axial roll
73.17
68.05
71.41
76.5
78.36
69.16
79.96
77.61
77.87
78.14
Cross section after passing the mandrel
68.51
73.48
68.66
Cross section after passing the mandrel
Cross section after passing the axial roll
Cross section after passing the mandrel
Cross section after passing the axial roll
Fig. 18. Cross section of a ring rolled using RARR process: (a) 8 mm/s; (b) 12 mm/s; (c) 14 mm/s; and (d) 16 mm/s.
0.06
0.06 FE-Simulations Experiments Fishtail coefficient,
Fishtail coefficient,
FE-Simulations Experiments 0.04
0.02
0.00
0.04
0.02
0.00
8.126
12.375 dD/dt (mm/s)
14.331
8.126
12.375
14.331
dD/dt (mm/s)
Fig. 19. Comparison of FEA and experimental results for fishtail coefficient under different dD/dt in RARR process: (a) after passing through radial roll gap and (b) after passing through axial roll gap.
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K.-H. Lee, B.-M. Kim / International Journal of Mechanical Sciences 76 (2013) 21–32
experimental values are in agreement with that of simulation data. (7) Considering the effective strain, temperature distribution, and geometry of the rolled ring, dD/dt of 14 mm/s, dD/dtmin odD/dt4 o dD/dtmax, is our suggested value for RARR process design.
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