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.

References

References
1.
Yarita
,
I.
,
Furukawa
,
K.
,
Seino
,
Y.
,
Takimoto
,
T.
,
Nakazato
,
Y.
,
Nakagawa
,
K.
, and
Fukunaga
,
I.
,
1978
, “
An Analysis of Chattering in Cold Rolling of Ultrathin Gauge Steel Strip
,”
Trans. Iron Steel Inst. Jpn.
,
18
(
1
), pp.
1
10
.
2.
Tlusty
,
J.
,
Chandra
,
G.
,
Critchel
,
S.
, and
Paton
,
D.
,
1982
, “
Chatter in Cold Rolling
,”
Ann. CIRP
,
31
(
1
), pp.
195
199
.10.1016/S0007-8506(07)63296-X
3.
Johnson
,
R. E.
, and
Quan
,
Q.
,
1993
, “
Chatter Dynamics in Sheet Rolling
,”
Int. J. Mech. Sci.
,
36
(
7
), pp.
617
630
.10.1016/0020-7403(94)90017-5
4.
Johnson
,
R. E.
,
1994
, “
The Effect of Friction and Inelastic Deformation on Chatter in Sheet Rolling
,”
Proc. R. Soc. London, Ser. A
,
445
, pp.
479
499
.10.1098/rspa.1994.0073
5.
Yun
,
I. S.
,
Wilson
,
W. R. D.
, and
Ehmann
,
K. F.
,
1998
, “
Chatter in Strip Rolling Process—Part I: Dynamic Rolling Modelling
,”
ASME J. Manuf. Sci. Eng.
,
120
(
2
), pp.
330
336
.10.1115/1.2830131
6.
Yun
,
I. S.
,
Wilson
,
W. R. D.
, and
Ehmann
,
K. F.
,
1998
, “
Chatter in Strip Rolling Process—Part II: Dynamic Rolling Experiments
,”
ASME J. Manuf. Sci. Eng.
,
120
(
2
), pp.
337
342
.10.1115/1.2830132
7.
Yun
,
I. S.
,
Wilson
,
W. R. D.
, and
Ehmann
,
K. F.
,
1998
, “
Chatter in Strip Rolling Process—Part III: Chatter Model
,”
ASME J. Manuf. Sci. Eng.
,
120
(
2
), pp.
343
348
.10.1115/1.2830133
8.
Yun
,
I. S.
,
Wilson
,
W. R. D.
, and
Ehmann
,
K. F.
,
1998
, “
Review of Chatter Studies in Cold Rolling
,”
Int. J. Mach. Tools Manuf.
,
38
, pp.
1499
1530
.10.1016/S0890-6955(97)00133-8
9.
Hu
,
P.
, and
Ehmann
,
K. F.
,
1999
, “
A Dynamic Model of Rolling Process. Part I: Homogenous Model
,”
Int. J. Mach. Tools Manuf.
,
40
, pp.
1
19
.10.1016/S0890-6955(99)00049-8
10.
Hu
,
P.
, and
Ehmann
,
K. F.
,
1999
, “
A Dynamic Model of Rolling Process. Part II: Inhomogeneous Model
,”
Int. J. Mach. Tools Manuf.
,
40
, pp.
21
31
.10.1016/S0890-6955(99)00050-4
11.
Swiatoniowski
,
A.
, and
Bar
,
A.
,
2003
, “
Parametrical Excitement Vibration in Tandem Mills-Mathematical Model and Its Analysis
,”
J. Mater. Process. Technol.
,
134
, pp.
214
224
.10.1016/S0924-0136(02)01037-3
12.
Lin
,
Y. J.
,
Suh
,
C. S.
,
Langari
,
R.
, and
Naoh
,
S. T.
,
2003
, “
On Characteristics and Mechanism of Rolling Instability and Chatter
,”
ASME J. Manuf. Sci. Eng.
,
125
, pp.
778
786
.10.1115/1.1617981
13.
Sun
,
J.
,
Peng
,
Y.
,
Liu
,
H.
, and
Jiang
,
G.
,
2010
, “
Vibration of Moving Strip With Distributed Stress in Rolling Process
,”
J. Iron Steel Res.
,
17
(
4
), pp.
24
30
.10.1016/S1006-706X(10)60081-7
14.
Sun
,
J.
,
Peng
,
Y.
, and
Liu
,
H.
,
2010
, “
Non-Linear Vibration and Stability of Moving Strip With Time-Dependent Tension in Rolling Process
,”
J. Iron Steel Res.
,
17
(
6
), pp.
11
15
.10.1016/S1006-706X(10)60106-9
15.
Dwivedy
,
S. K.
,
Dhutekar
,
S. S.
, and
Eberhard
,
P.
,
2012
, “
Numerical Investigation of Chatter in Cold Rolling Mills
,”
Materials With Complex Behaviour II
, Vol.
16
,
Springer
,
Berlin
, pp.
213
227
.
16.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1979
,
Nonlinear Oscillations
,
Wiley-Interscience
,
New York
.
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