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

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): doi: /
Figure Legend:
Roll bite geometry information as in Ref. [9]

3. 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): doi: /
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

4. 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): doi: /
Figure Legend:
Time response curve of work roll (a) inlet velocity 12.7 m/s and (b) inlet velocity 25.4 m/s

5. 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): doi: /
Figure Legend:
Transition curves for damping ratio ζ = 0.103 and μ = 0

6. 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): doi: /
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

7. 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): doi: /
Figure Legend:
Transition curves for damping ratio ζ = 0.222 and μ = 0

8. 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): doi: /
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

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): doi: /
Figure Legend:
Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

10. 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): doi: /
Figure Legend:
Transition curves for ζ = 0.103, and (a) μ = 0.01 and (b) μ = 0.1

11. 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): doi: /
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

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

13. 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): doi: /
Figure Legend:
Frequency-response curves for μ = 0.2, p = 2.5 × 1010  N/m2, and ζ = 0.103

14. 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): doi: /
Figure Legend:
Frequency-response curves for μ = 0.2, ζ = 0.103 and (a) ω0 τ = π and (b) ω0 τ = π4

15. 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): doi: /
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