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2010-01-0270

Finite Element Simulation of Ring Rolling Process

Srinivasan Vimalnathan Clemson University Dept. of Mechanical Engineering

Laine Mears Clemson University – International Center for Automotive Research

Copyright © 2010 SAE International

ABSTRACT

Three-dimensional simulation has become an indispensable approach to develop improved understanding of ring rolling technology, with validity as the basic requirement of the ring rolling simulation. Cold ring rolling is simple conceptually, however complex to analyze as the metal forming process is subject to coupled effects with multiple influencing factors such as sizes of rolls and ring blank, form geometry, material, process parameters, and frictional effects. Investigating the coupled thermal and plastic deformation behavior (the plastic deformation state and its development) in the deformation zone during the process is significant for predicting metal flow in order to control the geometric and tensile residual stress quality of deformed rings, and to provide for cycle time optimization of the cold ring rolling process. In this work, we present derivation of a 2-D analytical description governing ring rolling under the plane strain assumption, then perform finite element analysis of the same process from a surrogate flat rolling condition, extended to 3-D ring rolling. The analytic model reduction is shown to be acceptable for rough process parameter setting, and the finite element analysis can be used to tune the manufacturing process for cycle time optimization.

INTRODUCTION

Rolling is continuous forming of metal between a set of rotating rolls whose shape or height is incrementally reduced to produce desired section through imposing high pressures for plastic deformation. It is the process of reducing thickness, increasing length without increasing the width markedly. The ring rolling process can be performed with the material at a high temperature (hot) or initially at ambient temperature (cold). Ring rolling is an advanced technique to manufacture seamless rings with flexible cross-sectional shape, improved grain structure, and minimal scrap. The ring is formed from an initial blank, incrementally from a small diameter and thick section to large diameter and thin section by local continuum rolling method as shown in Figure 1. The research and development of ring rolling techniques with rings complicated in shape or large in dimensions or with high precision has become an important subject in metal plastic processing field [1]. Due to the complexity and high nonlinearity of the process, it is difficult to accurately describe the process purely by analytical methods. Though empirical descriptions are valid for the process on which they are developed, it is difficult to accurately extrapolate results. Therefore, the finite-element method to investigate and develop the advanced ring rolling technologies is motivated. Developing a reasonable 3D-FE ring rolling model has become an urgent issue, and the issue of how to control the guide rolls reasonably is one of the key problems to obtain a successful 3D-FE ring rolling simulation, especially for the rings complicated in shape or large in dimensions or with high precision.

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Figure 1: Ring rolling process [1]

RING ROLLING PROCESS

There are two types ring-rolling process based on the temperature effect. Cold rolling has the effect of increasing the yield strength of steel by cold working significantly into the strain-hardening range. These increases are predominant in high-strain zones of the cross-sectional shape. The effect of cold working is thus to enhance the mean yield stress by 15% - 30% on average. For purposes of design, the yield stress may be regarded as having been enhanced by a minimum of 15%. Some of the main advantages of cold rolled sections, as compared with their hot-rolled counterparts are as follows:

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Figure 2: Hot Rolling Process [2]

• Cross sectional shapes are formed to close tolerances and these can be consistently repeated for as long as required.

• Cold rolling can be employed to produce almost any desired shape to any desired length. • Pre-galvanised or pre-coated metals can be formed, so that high resistance to corrosion as well as an

attractive surface finish can be achieved.

Figure 2 shows the grain structure in the hot rolling process. Before entering the rollers the grains are larger and more homogeneous when compared to the exit grain size. The equipment can be quite large and expensive, so a high investment is required for the hot rolling process. Figure 3 shows examples of the different options for roller configuration, and the instance of ring rolling is shown in Figure 4.

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Figure 3: Flat Roller Configurations [2]

Figure 4: Ring rolling [2]

Flat rolling is typically the first process used after casting an ingot. Cast ingots are rolled to form slabs (flat plates, 40mm-100mm thick), billets (long thick rods with square, rectangular, or circular cross-sections), and blooms. Slabs are then rolled into sheets, plates, and welded pipes, and billets are rolled and drawn into bars, rods, pipes, and wires. Blooms are roll formed into structural shapes such as I-beams and rails [3] (see Figure 5). Achievable tolerances range from 1 to 2.5 percent of the dimension for hot rolling. Dimensional variations are greater than cold rolling due to non-uniformities in material properties such as hardness, roll deflection and surface conditions. Lubrication can be used for ferrous alloys (graphite) and non-ferrous alloys (oil emulsion) to optimize friction during rolling. Cold rolling can be performed with low viscosity lubricants such as paraffin or oil emulsion. Hot rolling requires the preparation of stock material to remove surface oxides before processing. Maintenance of rolling temperature in hot rolling dictates quality: too low and the material becomes difficult to deform, too high and the surface quality is reduced.

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Figure 5: Various shapes from rolling process [3]

ANALYTICAL DESCRIPTION OF RING ROLLING

The flat rolling analysis of Kalpakjian and Schmid [4] is extended to the ring rolling process. Process parameters are defined as in Figure 6.

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Figure 6: Ring Rolling Process Description

The parameters used in the analysis are

i

o

r

m

r

o

a

d inner diameterd outer diameterd roll diameterd mandrel diametern roller rotational speedn ring rotational speedv advancevelocity of mandrel

≡

≡

≡≡

≡≡

≡ (1)

The first relationship to be established is the dependence between cross-sectional thickness and diameter through volume conservation. In this case, plan strain is assumed, so there is no strain in the width direction.

( ) ( )

( )

0

2 2 2 2,0 ,0

2 2 2,0 ,0

4 4o i o i

i o o i

V V

d d w d d w

d d d d

π π=

− = −

= − − (2)

The inner diameter is therefore dependent on the outer diameter and original blank volume as calculated from original diametral dimensions.

The next step in analysis is to provide equivalence to the flat rolling process through equating contact lengths between the material and roll or mandrel. This analysis targets defining the equivalent diameter of a flat rolling process roll to represent the more complex curvilinear ring roll. A result for the forming roll which undergoes convex-convex contact is

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( ),

,0

,0

21r

r eqr

o o

r

o

o

dd dd d

d roll diameterd initial outer diameterd ring outer diameter

=+

+

≡≡

≡ (3)

The equivalent flat rolling diameter (convex-flat contact) is therefore smaller than the true diameter of the larger form roll undergoing convex-convex contact. Similarly for the mandrel (inner surface roll):

( ),

,0

,0

21

mm eq

m

i i

m

i

i

dd dd d

d mandrel diameterd initial inner diameterd ring inner diameter

=−

+

≡

≡

≡ (4)

The equivalent flat roll diameter is larger due to translation of the convex-concave contact of mandrel to inner ring surface to convex-flat contact of flat rolling.

Now that the ring rolling process has been translated to flat rolling, the issue of draft must be addressed. The draft is defined as the height reduction in rolling. For flat rolling, the initial and final heights are independent outside of the rolling process itself. However, for ring rolling, the entrance and exit heights are coupled as the exit height in one rotation becomes the entrance height for the next rotation. This coupling effect can be described in terms of the mandrel advance velocity and the rotational speed of the system. If we take the instantaneous advance velocity to be

a

dhvdt

= (5)

and assume constant velocity over the mandrel travel, we can represent the height change in a single rotation as a finite difference of the form

1 2

arotation

h hvt−

= (6)

The time for a single rotation is derived from the rotational velocity and diameter of the ring and roll:

[ ] [ ]

[ ]

,1 1

0 0

60 60sec

120 6060sec2

rotationo

rotationroll r r r r

dtn rpm v

d ddtv d n d n

π

πππ

= =

≈ = = (7)

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Therefore, the height change can be described as

0

1 260 a

r r

d vh hd n

− = (8)

Note that h1 and h2 represent the heights into and out of the rolling zone, not the initial and final ring thicknesses, and the strain undergone by the ring section is relative to the original sectional dimensions, as there is no annealing operation between rotations.

If we take the maximum draft condition to be the point where frictional and normal forces balance in the rolling direction, a maximum angle of acceptance can be defined for flat rolling. This situation is represented in Figure 7, where nF represents the normal force against the workpiece and fF the frictional force tangential to the roll.

Figure 7: Force Balance at Critical Rolling Height

In order to pull the material into the process, the following force component constraint must be respected:

cos sin

tantan

f n

f n

n n

F F

F F

F F

α α

μ

μ αμ α

>

=

>

> (9)

If we assume the roll radius much greater than the height change (large roll assumption),

2

max

tan sin hR

h R

α α

μ

Δ≈ ≈

Δ = (10)

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This analysis is summarized in [4]. Setting this maximum draft condition equal to (8) results in the following relationship:

20 ,max

max

2 2

,max0

602

120

ar

r r

r ra

d vdhd n

d nvd

μ

μ

Δ = =

= (11)

Therefore, an upper limit on the prescribed mandrel advance velocity is established in order to maintain rotation of the ring during rolling.

FINITE SIMULATION OF FLAT ROLLING

Two individual studies on the rolling process are done using the finite element analysis (FEA) simulation package ABAQUS V6.8. First, a billet is compress between two rollers. In this case the roller is not rotated as bulk deformation of the billet is accomplished, so as to simulate material flow through the rolling die without dynamic effects. The main assumption made in case of this process is that the roller does not rotate, so that the tool-work interaction effects are isolated. The solid model of the roller cross-section is shown in Figure 8.

Figure 8: Solid Model of Rollers

The 3D FEA simulation of this process is a challenge due to the complex and coupled constraints; therefore, some simplifying assumptions are employed. The rollers shown in Figure 8 are assumed as rigid bodies, meaning that the forming roll and mandrel will not undergo any deformation. The work piece is taken to be ASTM 52100 bearing steel, and its height reduced by compressing between the two rollers. The forming roll (top rigid roller) is constrained in the forming direction, while the mandrel (bottom rigid roller) is allowed to move upwards in order to reduce the cross-section, and rotation of the rollers is restricted. Figure 9 shows the mesh on the roller and the work piece. C3D10 elements are used for the analysis, and a displacement imparted

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to the bottom roller. The bottom roller is moved upwards 4 mm at 0.8mm/sec. The analysis was run for 20 seconds simulation time in ABAQUS explicit. So the work piece height is reduced by 4 mm.

Figure 9: Mesh on the rollers and work piece

Figure 10: Deformation of the work piece

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Figure 11: Steps in Deformation of the Workpiece at (0, 5, 10, 15, and 20 seconds)

The deformation of the work piece takes places in step by step reduction in height. In the simulation about 20 steps used to reduce 4 mm height. Figure 11 shows the deformation at step 0, 5, 10, 15 & 20. The simulation done for cold rolling process. The hot rolling can be easily done by heating the work piece for the required time and apply load. Figure 12 shows the stress distribution on the workpiece.

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Figure 12: Stress Distribution on the Workpiece after Forming

A second simulation of the process is carried out to introduce the rolling effect. First, a linear estimation of the contact length is derived, where R is the roller radius and hΔ the reduction in height from 0h to fh :

22

0

22 2

2

22 4

f

hL R R

h h h

h hL R R R

L R h

Δ⎛ ⎞≈ − −⎜ ⎟⎝ ⎠

Δ = −

Δ Δ≈ − + −

≈ Δ (12)

The rolling study was originally setup as shown in Figure 13.

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Figure 13: 3D Modeling of Ring Rolling

The ring is placed between the two ring rollers (outer form roll and inner mandrel). The outer roller has a depression in the circumference and the inner roller a step on the circumference to simulate bearing race formation. The two guides are placed to support the ring. The 3D simulation proved too difficult to control the movement of ring, so a surrogate 2D flat rolling process is used.

In the rolling study a 2D plain stress analysis is carried out to quantify the frictional effect of the rolling process. Figure 14 shows the initial meshing of the rolling process created in ABAQUS.

Figure 14: Flat rolling process FEA Step up

At the beginning of rolling, material is pulled into the nip by friction and rolls are slipping past work. At the exit, material is moving more quickly and work is slipping past rolls. At some point in between, frictional forces equally oppose each other and the neutral point (point of no slip) occurs. A reduction of 2 mm is simulated. The geometric progression of flat rolling is shown in Figure 15.

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(a) (b)

(c) (d)

Figure 15: Steps in Flat rolling process (progression from a to d)

The stress distribution is graphically described in Figure 16.

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Figure 16: Stress Distribution in Flat Rolling

The study of flat rolling in plain strain provides a better numerical understanding of how the thickness of the plate is incrementally reduced. This stress profile will be applied to better understand deformation in cold ring rolling.

FINITE SIMULATION OF RING ROLLING

The flat rolling simulation is extended to finite curvature sections where the input to the deformation zone is a continuous function of the deformation zone output with a time delay dependent on the average surface velocity of the ring. This configuration is simulated using ABAQUS software, with results of von Mises stress given in Figure 17.

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Figure 17: Finite Element Simulation of Ring Rolling

The simulation was carried out using tetrahedral elements for the deformable body, with the constraint of plane strain deformation (no change in width of the deformed region). The element meshing is shown in Figure 18.

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Figure 18: Meshing of three-dimensional ring rolling structure.

The roll and mandrel are constrained as rigid. The roll is driven at constant rotational velocity of 60 rpm and the mandrel advanced at 1.5 mm/s. The resultant three-dimensional stress distribution is shown in Figure 19.

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Figure 19: Three-dimensional incremental deformation of ring structure

SUMMARY/CONCLUSIONS

Simplified governing equations for 2D ring rolling analysis are derived from the flat rolling process description, then a simulation study of the rolling process is presented. A 2D flat rolling analysis was completed, then extended to plane-strain three-dimensional rolling of ring structures. The paper discusses the complexity in simulating 3D ring rolling process and the various factors which influence the simulation. The plane strain study of flat rolling provides a clear understanding how the load acts and the deformation of the workpiece, and is extended to ring rolling analysis. Further study on the contact pressure of non-homogeneous deformation is planned.

REFERENCES

1. Lanyun Li, He Yang, Lianggang Guo and Zhichao Sun. “A control method of guide rolls in 3D-FE simulation of ring rolling”, Journal of Materials Processing Technology, Volume 205, Issues 1-3, 26 August 2008, Pages 99-110

2. Smith.E.H , Mechanical Engineers Reference Book, Elsevier Butterworth-Heinemann,1194-p,1998, ISBN-10: 0750642181

3. C. Poli, Design for Manufacturing, Butterworth-Heinemann, 2001, ISBN 0750673419, 9780750673419, 375 pages.

4. Kalpakjian, S. and Schmid, S, Manufacturing Processes for Engineering Materials, 5/e Prentice-Hall, 2008.

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CONTACT INFORMATION

Laine Mears

Clemson University - International Center for Automotive Research

864-283-7229

mears@clemson.edu