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Research Papers

Stability Analysis of Chatter in Tandem Rolling Mills—Part 2: The Regenerative Effect

[+] Author and Article Information
Huyue Zhao

High Energy Physics Division,
Argonne National Laboratory,
9700 S. Cass Avenue,
Argonne, IL 60439
e-mail: hzhao@anl.gov

Kornel F. Ehmann

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60201
e-mail: k-ehmann@northwestern.edu

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received August 30, 2008; final manuscript received December 27, 2012; published online May 29, 2013. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 135(3), 031002 (May 29, 2013) (11 pages) Paper No: MANU-08-1240; doi: 10.1115/1.4024033 History: Received August 30, 2008; Revised December 27, 2012

Using the multi-stand chatter models derived in Part 1, a stability analysis, based on the integral criterion of stability for delay differential equations, will be carried out for the regenerative mechanism to better understand the effects of rolling parameters on regenerative instability. It will be shown that the interactions between consecutive stands through the time delay effect of the strip thickness variations consistently boost the tendency of each stand to chatter and, therefore, reduce the stability of the rolling process. Simulations will demonstrate stable and unstable behaviors of multi-stand rolling mills and aid in verifying stability charts created through stability analysis based on analytical models. They will be instrumental in identifying the critical vibration propagation paths of the regenerative mechanism in multi-stand mills through strip thickness and instant inter-stand tension variations. The critical vibration propagation paths of the regenerative mechanism will explain the modulation frequency observed in tandem mills that, as it will be shown, is inversely proportional to the shortest time delay during strip transport from the upstream stands to the downstream stands.

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References

Figures

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Fig. 3

Integral of the logarithmic derivative versus rolling speed, vr

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Fig. 2

Integral of the logarithmic derivative versus ω

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Fig. 1

Three mill stands connected by the strip

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Fig. 4

Stability chart of μ2 versus vr

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Fig. 5

Comparison of stability charts for μ2

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Fig. 6

Comparison of stability charts for μ1

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Fig. 7

Comparison of stability charts of σ1,2

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Fig. 8

Comparison of stability charts for σ2,2

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Fig. 12

Comparison of stability charts for w

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Fig. 9

Comparison of stability charts for L2

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Fig. 10

Comparison of stability charts for L3

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Fig. 11

Comparison of stability charts for E

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Fig. 17

Regenerative chatter—case #1: rolling force variations

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Fig. 18

Regenerative chatter—case #2: vr = 25 m/s, μ = 0.015

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Fig. 19

Regenerative chatter—case #3: vr = 28 m/s, μ = 0.015

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Fig. 20

Regenerative stability chart comparison

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Fig. 13

Regenerative chatter—case #1: vr = 26.5 m/s, μ = 0.015

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Fig. 14

Vibration flow path of the regenerative effect

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Fig. 15

Regenerative chatter—case #1: tension variations

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Fig. 16

Regenerative chatter—case #1: entry and exit velocity variations

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Fig. 25

Comparison of the two-Stand and five-Stand regenerative effect

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Fig. 21

Regenerative chatter—case #4: vr = 23 m/s, μ = 0.015

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Fig. 22

Regenerative chatter—case #4: rolling force variations

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Fig. 23

Regenerative chatter—case #4: inter-Stand tension variations

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Fig. 24

Regenerative chatter—case #5: vr = 25 m/s, μ = 0.015

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