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Research Papers

Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill

[+] Author and Article Information
Sajan Kapil

Mechanical Engineering Department,
Indian Institute of Technology Guwahati,
Guwahati 781039, 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

Manuscript received September 22, 2013; final manuscript received February 24, 2014; published online May 21, 2014. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 136(4), 041012 (May 21, 2014) (10 pages) Paper No: MANU-13-1350; doi: 10.1115/1.4026961 History: Received September 22, 2013; Revised February 24, 2014

In this work, a four high cold rolling mill is modeled as a spring-mass-damper system considering horizontally and vertically applied time-dependent forces due to the interaction between the strip and the working rolls. The effect of vibration of the moving strip on the work roll vibration is also considered for developing the governing equation of motion of the system which is found to be that of a nonlinear parametrically excited system. The governing equation of motion is solved by using the method of multiple scales to find the instability regions and frequency-response curves of the system. The critical amplitude of horizontal load in roll bite is calculated and the frequency-response is studied in detail considering the effect of various process parameters, such as velocity, thickness of strip, time delay, amplitude, and frequency of horizontal load in roll bite. This work can find application in the design and development of high speed and chatter free rolling mills.

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References

Figures

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Fig. 3

(a) Horizontal and vertical forces acting on the work roll and (b) equivalent spring-mass-damper system representing the four high roll mill

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Fig. 2

Roll bite geometry information as in Ref. [9]

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Fig. 1

(a) Schematic diagram of a four high rolling mill, (b) coordinate system, and (c) equivalent spring-mass system

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Fig. 5

Transition curves for damping ratio ζ = 0.103 and μ = 0

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Fig. 6

Time response curve for ζ = 0.103, p = 2.95 × 1010N/m2, and (a) σ = − 300 rad/s, (b) σ = 0 rad/s, and (c) σ = 300 rad/s

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Fig. 4

Time response curve of work roll (a) inlet velocity 12.7 m/s and (b) inlet velocity 25.4 m/s

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Fig. 9

Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

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Fig. 10

Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

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Fig. 11

Frequency-response curves for p = 2.9 × 1010N/m2, ζ = 0.103, and (a) μ = 0.1 and (b) μ = 0.2

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Fig. 12

Frequency-response curves for p = 3 × 1010N/m2, ζ = 0.103, and (a) μ = 0.03 and (b) μ = 0.02

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Fig. 13

Frequency-response curves for μ = 0.2, p = 2.5 × 1010 N/m2, and ζ = 0.103

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Fig. 7

Transition curves for damping ratio ζ = 0.222 and μ = 0

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Fig. 8

Time response curves for ζ = 0.222, σ = 0, and (a) p = 6.22 × 1010N/m2 and (b) p = 6.18 × 1010N/m2

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Fig. 14

Frequency-response curves for μ = 0.2, ζ = 0.103 and (a) ω0 τ = π and (b) ω0 τ = π4

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Fig. 15

Parametric instability regions in the σ ∼ τ plane for ζ = 0.103, p = 3 × 1010N/m2, a = 1.8 × 10 3 m, and (a) μ = 0.01, (b) μ = 0.035, and (c) μ = 0.1

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