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Research Papers

Dynamic Analysis of Cold-Rolling Process Using the Finite-Element Method

[+] Author and Article Information
Sajan Kapil

Mechanical Engineering Department,
Indian Institute of Technology,
Bombay, Mumbai 400076, India
e-mail: kapil.sajan17@gmail.com

Peter Eberhard

Institute of Engineering and
Computational Mechanics,
University of Stuttgart,
Pfaffenwaldring 9,
Stuttgart 70569, Germany
e-mail: peter.eberhard@itm.uni-stuttgart.de

Santosha K. Dwivedy

Mechanical Engineering Department,
Indian Institute of Technology,
Guwahati, Guwahati 781039, India
e-mail: dwivedy@iitg.ernet.in

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received December 25, 2014; final manuscript received July 30, 2015; published online October 27, 2015. Assoc. Editor: Brad L. Kinsey.

J. Manuf. Sci. Eng 138(4), 041002 (Oct 27, 2015) (10 pages) Paper No: MANU-14-1715; doi: 10.1115/1.4031280 History: Received December 25, 2014; Revised July 30, 2015

In this work, the finite-element method (FEM) is used to develop the governing equation of motion of the working roll of a four-high rolling mill and to study its vibration due to different process parameters. The working roll is modeled as an Euler Bernoulli beam by taking beam elements with vertical displacement and slope as the nodal degrees-of-freedom in the finite-element formulation. The bearings at the ends of the working rolls are modeled using spring elements. To calculate the forces acting on the working roll, the interaction between the working roll and the backup roll is modeled by using the work roll submodel, and the interaction between the working roll and the sheet is modeled by using the roll bite submodel (Lin et al., 2003, “On Characteristics and Mechanism of Rolling Instability and Chatter,” ASME J. Manuf. Sci. Eng., 125(4), pp. 778–786). Nodal displacements and velocities are obtained by using the Newmark Beta method after solving the governing equation of motion of the working roll. The transient and steady-state variation of roll gap, exit thickness profile, exit stress, and sheet force along the length of the strip have been found for different bearing stiffnesses and widths of the strip. By using this model, one can predict the shape of the outcoming strip profile and exit stress variation which will be useful to avoid many defects, such as edge buckling or center buckling in rolling processes.

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References

Figures

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Fig. 1

(a) Schematic diagram of a four-high rolling mill and (b) modeling of the upper half of the four-high rolling mill

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Fig. 2

Two-node beam element with four degrees-of-freedom

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Fig. 3

Force acting on the beam at the boundary

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Fig. 4

Free-body diagram of the working roll

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Fig. 5

Roll bite model of a rolling process, see Ref. [18]

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Fig. 6

Flow chart for the simulation of the rolling mill

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Fig. 9

Distribution of sheet force over the working roll length for kw=5×1010 N/m and L2=0.508 m: (a) both transient and steady state and (b) steady state

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Fig. 8

Time response of different nodes on the working roll for kw=5×1010 N/m and L2=0.508 m

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Fig. 7

Node selection in different zones

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Fig. 16

Exit thickness distribution of sheet over the length of working roll for kw=5×109 N/m and L2=0.508 m: (a) both transient and steady state and (b) steady state

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Fig. 15

Distribution of sheet force over the working roll length for kw = 5×109 N/m and L2 = 0.508 m: (a) both transient and steady state and (b) steady state

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Fig. 14

Time response of nodes A, B, and C on the working roll for kw=5×109 N/m and L2=0.508 m

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Fig. 13

(a) Exit stress distribution over the length of the working roll in both transient and steady state, (b) exit stress distribution over the length of the working roll in steady state, and (c) variation in average exit stress with time, kw=5×1010 N/m and L2=0.508 m

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Fig. 12

(a) Variation in average entry velocity with time and (b) variation in average exit velocity with time, kw=5×1010 N/m and L2=0.508 m

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Fig. 11

(a) Distribution of entry velocity of strip over the length of working roll, (b) distribution of the ratio of entry velocity of strip and working roll velocity in steady state, (c) distribution of exit velocity of strip over the length of working roll, and (d) distribution of the ratio of entry velocity of strip and working roll velocity in steady state, kw=5×1010 N/m and L2=0.508 m

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Fig. 10

Exit thickness distribution of sheet over the length of working roll for kw=5×1010 N/m and L2=0.508 m: (a) both transient and steady state and (b) steady state

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Fig. 17

Time response of different nodes on the working roll, for kw=5×1010 N/m and L2=0.9 m

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