Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: (a) Schematic diagram of a four high rolling mill, (b) coordinate system, and (c) equivalent spring-mass system

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Roll bite geometry information as in Ref. [9]

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: (a) Horizontal and vertical forces acting on the work roll and (b) equivalent spring-mass-damper system representing the four high roll mill

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Time response curve of work roll (a) inlet velocity 12.7 m/s and (b) inlet velocity 25.4 m/s

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Transition curves for damping ratio ζ = 0.103 and μ = 0

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Time response curve for ζ = 0.103, p = 2.95 × 1010 N/m2, and (a) σ = − 300 rad/s, (b) σ = 0 rad/s, and (c) σ = 300 rad/s

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Transition curves for damping ratio ζ = 0.222 and μ = 0

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Time response curves for ζ = 0.222, σ = 0, and (a) p = 6.22 × 1010 N/m2 and (b) p = 6.18 × 1010 N/m2

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Frequency-response curves for p = 2.9 × 1010 N/m2, ζ = 0.103, and (a) μ = 0.1 and (b) μ = 0.2

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Frequency-response curves for p = 3 × 1010 N/m2, ζ = 0.103, and (a) μ = 0.03 and (b) μ = 0.02

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Frequency-response curves for μ = 0.2, p = 2.5 × 1010  N/m2, and ζ = 0.103

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Frequency-response curves for μ = 0.2, ζ = 0.103 and (a) ω0 τ = π and (b) ω0 τ = π4

Date of download: 11/8/2017 Copyright © ASME. All rights reserved. From: Nonlinear Dynamic Analysis of a Parametrically Excited Cold Rolling Mill J. Manuf. Sci. Eng. 2014;136(4):041012-041012-10. doi:10.1115/1.4026961 Figure Legend: Parametric instability regions in the σ ∼ τ plane for ζ = 0.103, p = 3 × 1010 N/m2, a = 1.8 × 10 − 3 m, and (a) μ = 0.01, (b) μ = 0.035, and (c) μ = 0.1