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REGENERATIVE CHATTER VIBRATIONS
CONTROL IN THE TANDEM
COLD ROLLING MILLS
P.V. Krot, I.Y. Pryhodko
Iron and Steel Institute NAS of Ukraine, Dnepropetrovsk, Ukraine
paul_krot@mail.ru, pryhodko@mail.ru
P.P. Chernov
JSC Novolipetsk Metallurgical Combine (NLMC), Lipetsk, Russia
chernov_pp@nlmk.ru
Chatter vibrations were investigated for the high speed 5 stand 4-h tandem
cold rolling mill 2030 of the NLMC. Real-time chatter vibration monitoring
and diagnostics system was developed and supplied for that mill. The tension
forces oscillations and the chatter regeneration due to strip thickness varia-
tion is discussed. The new methods of the 3rd octave chatter early diagnostics
were developed and model based mill control improved. Methods are based
on stands synchronization control and the tandem mill resonance avoiding
due to a speed and other rolling parameters variation of small amplitude.
Work rolls hydraulic bending system influence on the bearings vibration and
chatter modes is discussed. Methods and devices for chatter damping are rep-
resented briefly.
Keywords: chatter vibrations, control, regenerative effect, damping
Introduction
Since 1970th chatter vibration in the high speed cold rolling and temper mills is a
phenomena still intensively investigated because it significantly (20-30%) re-
duces annual plant productivity and strip quality. The most advanced tendencies
in this domain of research were discussed in Ref. [1] and other papers. But some
aspects, namely, regenerative chatter and its control was not reported. Stands
interaction by the strip tension was analyzed but not from the view point of mill
control. Also stands synchronization due to roughness and thickness variation in
the tandem mills was not investigated as an explicit cause of chatter amplifica-
tion. Chatter research in the tandem (5 stands) cold rolling mill 2030 of the
NLMC allowed us supplying an automatic system. This work is devoted to
minimizing impacts and new chatter control methods development.
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1 Chatter Studies
The high speed tandem cold rolling and temper mills are complicated machines
with the Many-Input-Many-Output (MIMO) structure. Modern strategies of its
control based on adaptive models including fuzzy logic algorithms, neural nets
for parameters prediction to meet customer’s very high demands on steel strips
flatness, roughness and thickness tolerance (±5 µm). Conventional Automatic
Gauge Control (AGC) system sensors and actuators are not able to control high
frequency chatter vibrations because its effective pass band is less than 10 Hz
(hydraulic AGC). Therefore in practice the only effective way to control chatter
is speed fast drop by the vibration signals being monitored in special purpose
systems. But the frequent speed drops reduce mill productivity and strip quality.
Monitoring the speed related (kinematical) sources is a usual approach to the
vibration problem solving in any rotating machines and in the rolling mills too.
Resonances appear when the natural frequencies coincide with the speed related
disturbance. Parametric resonances are also included to that area of research
(tooth couplings, roll bearings etc.). Methods of such vibrations control assume
avoiding resonance ranges during plant operation. But for tandem mills the num-
ber of possible sources of vibration is very big and different elements may have
more or less importance in a short period of time (work rolls changes every 3-4
hours). Beside it a large variation of mill natural frequencies and modes exits
under the working conditions. Therefore such approach is rather useful for rotat-
ing equipment diagnostics off-line than for real-time mill automatic control.
Nevertheless many cases of chatter elimination reported based on mill mainte-
nance improving.
Lubricant degradation as a vibration source under the high duty conditions has
been investigated by many authors. Narrow contacts (10-15)×(1000-2000) mm
of strip and both work rolls (WR) are the only places where the biggest part of
power (up to 10 MW) from electric motors is being transferring by the friction to
metal for its elasto-plastic deformation in every stand. Therefore even smallest
disturbance in contact friction conditions under the high loads in stands (10-
15 MN) may produce impulsive impacts with the wide band spectrum. Conse-
quently it excites all natural frequencies of the mill stands in the range of 1000-
1500 Hz for the high rolling speeds 18-25 m/s (in the last stand). The obvious
methods were reported for emulsion concentration control (increasing) by the
vibration signals in the stands. Beside the emulsion very high cost, mill cooling
system could not able to vary concentration quickly (time of response 20-40 min)
so it can not be used for fast chatter control. Nevertheless mills show sensitivity
(less robustness) to that parameter and stands cooling system set-up before roll-
ing may be optimized. In Ref. [2] it has been shown by simulation and experi-
ment that in tandem mill for the 2 neighboring stands exists optimal friction fac-
tor (not low and not high) for minimal mill susceptibility to chatter.
Friction factor nonlinear dependence on relative speed of contacting bodies slip-
ping is a well known mechanism of instability in mechanics. Usually it is con-
sidered that for the real rolling conditions and lubricants parameters a minimum
value of friction factor is about 5 m/s speed and hence could not cause instability
at higher speeds.
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During mill operation backup rolls (BUR) and WR with the unavoidable local
defects (e.g. spalling) may produce the same wide band impacts as the slips in
contact. If the frequency of some source of vibration at the certain speed accords
to roll circumference length the periodic defects (chatter marks) may appear on
the BUR (Figure 1a). It is well known fact that to the end of BUR service time
(7-10 days) when the surface defects accumulated the probability of chatter in-
creases significantly. It should be divided the chatter marks from rolling and
grinding processes. The chatter marks after grinding almost invisible on roll
(Figure 1b) and could be cleared up only by chock test.
a) b)
Figure 1: Chatter marks on the backup rolls after rolling (a) and grinding (b)
Such roll being installed in the mill behaves like speed related source and excites
chatter at certain frequency. Vibration diagnostics allows to reduce structural
resonances in the grinding machines but reliable device (preferably optical) is
required for hidden chatter marks recognition (∆Ra = 1-3 µm) and grinding
process control. The tuned vibration absorbers (designed by the AMTRI Com-
pany, UK) are also effective means to avoid grinding chatter marks.
2 Chatter Control Problems
Because of chatter amplitude arises enough quickly (0.3-0.5 s) mill operators try
to set vibration monitoring alarm levels as close to normal level as it possible.
But it frequently cause wrong alarm signals as the rolls and strip size change
from coil to coil. As it follows from the known publications and patents there are
no systems which provide chatter early diagnostics (5-8 s before chatter on-set)
and vibration amplitude forecasting in the tandem rolling mills. The main ques-
tions for chatter control are as following (motivation of research):
- How to detect chatter earlier (by 5-8 s) than it comes to visible amplitudes?
- How to control chatter with the stands interaction in the tandem mill?
- How to damp chatter by the impacts of small amplitude (1-2%)?
- How to feed and where to mount actuators with respect to mill design?
Taking into account all above mentioned the following problems are discussed.
1) Natural frequencies and modes deviation in a multi-body roll stack.
2) Friction factor and rolling speed nonlinear relation.
3) Feedback loops and stands synchronization in the tandem mill.
4) Chatter regeneration due to thickness variation.
5) Vibration passive damping devices and active control methods.
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2.1 Natural frequencies and modes deviation of mill stack
In papers some divergence exists in roll stack spring-mass models schemes for
chatter simulation. It depends not only on the stands different design: 4-h, 6-h,
20-h (cluster mills), but on the chocks and rolls assigning as lamped masses and
springs. The only feature that accurate models have to exhibit is the symmetry
modes of upper and lower sets of rolls at the main frequencies of 3rd and 5th oc-
tave chatter for certain mill (Figure 2a). Chatter in 3rd octave appears only for
thin strips when the upper and lower pairs of rolls move symmetrical about the
strip plane. Symmetrical modes were discussed by many authors but the strip
properties and WR bending system influence on modes deviation has not been
enough studied. Calculations have shown that modes frequencies may vary sig-
nificantly (Figure 2b).
a) b)
Figure 2: Chatter vibrations modes (a) and WR bending influence (b)
Vibration measurements in tandem mill 2030 have been carried out with the ac-
celerometers being mounted on every of WR and BUR chocks. Thin (0.6 mm)
and thick (1.0 mm) strips have different modes of stack movement. Thin strip
rolling corresponds to main node in the roll bite but thick strip stiffness shifts
node out of rolls and strip contact. Such result may be obtained by simulation
only if to suppose not symmetrical stack model (upper housing included as
lamped mass). Thick strip stable rolling was available at the high speed without
chatter. Mill had the same technical condition and almost the same rolling pa-
rameters (steel type, width, rolls, loads, specific tensions, coolant amount etc.).
There are some reasons for such behavior.
1) Even with a little output thickness deviation (∆h=0.4 mm) strip mechanical
properties (hardening and yield stress) varies significantly (20-30%). It influ-
ences on damping properties of steel strip in the roll bite. Harder strip corre-
sponds to less damping.
2) WR bending influences only on high frequency modes No. 5…7 (Figure 2b)
therefore thin strip periodic thickness or surface roughness could cause stands
interaction and tandem mill excitation. Strip variable stiffness in the roll bite may
be considered as a parametric excitation in the stands. Some papers published on
this theme. Experiments with the mill drives rotation under the working loads
and speeds without strip in stands have shown that vibration signals exhibit an-
other patterns. But during rolling as strip come from previous slow stands to
faster further ones the main parametric resonance condition (frequency of excita-
tion twice more than natural one) is impossible to be fulfilled.
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2.2 Friction factor and rolling speed nonlinear relation
Dynamic model for chatter research includes parameters of technology and lu-
bricant: tMAX - ultimate temperature of oil flash, KT – roll surface temperature by
speed relation factor, ν50 – initial viscosity (at 50°C), Ra – WR surface rough-
ness, ε – strip relative reduction, kS – type of oil factor (synthetic or natural), tR –
current temperature of roll surface. Calculations have shown that only roll sur-
face temperature (tR
) may shift minimum of friction factor toward the higher
speeds (up to 15 m/s). But all other parameters variation cause only up and down
shift of friction factor minimum value. This particularity was not reported before.
During the long coils rolling time (4-5 min) of thin strips (0.3-0.8 mm) when
chatter mostly occurs the rolls temperature may exceeds the limit of oil degrada-
tion (150-200°C) and causes instability in most loaded last stands of mill. There-
fore as the WR temperature being varied has influence on friction factor and in-
stability it may be considered as bifurcation parameter. The rolls coolant amount
varying and lubricants parameters optimization is one of the methods to control
chatter. Work rolls temperature on-line control by pyrometers is not reliable so
heat transfer model based observers are required for mill control. As a rule vibra-
tion is initiated in stands No.3-4 where the high loads and speeds lead to the
most duty lubrication conditions.
In order to identify contact friction instability and strip stiffness (hardening) the
vibrations spectrums in the different stands shown in Figure 3. There are three
different patterns in every stand.
0 1000 Hz
Figure 3: Chatter vibrations spectrums in the stands No.3-5
Friction tangential forces and deformation normal forces determine strip stressed
condition and its nonlinear stiffness as an elasto-plastic element in the roll stack.
Type of nonlinearity in the roll bite and its nature may be determined by the
harmonics of main frequency. It is known that cubic nonlinearity give odd har-
monics (stand No.3) and quadratic relation causes even harmonics (stands No.4-
5). Odd harmonics are rather related with the strip hardening (like cubic curve)
and friction nonlinearity rather shows even harmonics (curve with minimum). So
that to separate nonlinearities the two or three axis sensors should be used in the
mill. Horizontal axis corresponds to friction forces.
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2.3 Feedback loop and stands synchronization in the tandem mill
Some approaches to chatter research came from the other treating operations
(grinding, milling cutting etc.) studies. See detailed overview in Ref. [3].
Feedback loop mechanism in the tandem mills appears because rolling load in-
teracts with strip tension. Tension forces in elastic strip are determined as:
∫−
−
⋅
=dtVV
L
SE
Tiiii )/( 1
ξ, (1)
where T – strip tension, N; E – modulus of elasticity, MPa; V – strip speed, m/s;
ξ - strip elongation factor; L – strip length (distance between the stands), m; S –
strip section, m2; i - stand number; t – time, s. Tension is proportional to the inte-
gral of speeds difference and may be explained as a low-pass filter. Hence 90°
phase shift between the input and output should appear which is not depends on
frequency. Roll stack main mode movements (strip gauge) give additional 90°
phase shift so entry and exit tension always oscillate with the 180° phase shift.
It can be shown on the basis of continuity of mass flow through the mill stand
during rolling that a change of exit thickness will produce a change in strip
speed, assuming entry gauge and exit speed remain constant. Feedback loop gain
depends on rolling speed. Thus beyond the speed threshold chatter will appear.
In Ref. [4] using Routh’s stability criterion for mill stack linear model, the criti-
cal strip speeds at which 3rd octave chatter occurs were obtained. Stability de-
pends on tension response time constant and partial derivative of load by tension.
Also mill internal damping is present in criterion. Some authors suggested other
stability criterions based on linear models too. Analysis of criterions has shown
that it can be used rather for qualitative estimation than for real-time mill control.
We consider that tandem mill chatter should be described in terms of chain of
coupled oscillators and synchronization conditions. Chatter vibration in the
stands No.2-5 of tandem mill is shown in Figure 4a. In Figure 4b main chatter
period has shown (about 120 Hz). Stands No.2-4 are synchronous within both
low and high frequency but stand No.5 is always out of phase with the other
stands because it works in “infinite stiffness” mode of control.
a) b)
Figure 4: Chatter vibrations in stands No. 2-5
Nonlinear friction and strip stiffness in the contact zone make it difficult whole
system analytical analysis. System is described by the parametric differential
equations with varying time-delay.
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2.4 Strip Thickness Variation and Chatter Regeneration
The modern isotopic gauge meters are too slow (response time about 0.1 s) and
are not able to measure high frequency strip thickness variation (waviness peri-
ods 20-140 mm) in the tandem mill at the high rolling speeds. In Ref. [5,6] re-
generative effects due to strip thickness and roughness variation in the tandem
mills has been studied in the dynamic models.
In cutting and other operations Spindle Speed Variation Method is used for chat-
ter avoiding due to regeneration from the previous passes waviness. Tandem
rolling mill can not be controlled in such way due to big drives torques transient
oscillations (in 2-3 s). Slow mill speed variation will make dynamic situation
even worse because of torsional vibration at the low natural frequencies
(9-12 Hz) which lay in AGC system pass band.
One of remarkable chatter features noted in every research. During rolling under
the normal conditions vibration signals in every stand are always accompanied
by the more or less modulations of low (2-3 Hz) frequency (Figure 4). Some
authors explained this feature as frequency beating between neighboring stands
which have the same design. Other authors explain it as a BUR eccentricity in-
fluence, another ones considered it as a tension frequency.
Another explanation may be given of modulation effect. Calculation with the
dynamic model has shown (Figure 5) that if to disturb stand by series of periodic
impulses (chatter marks on the strip) it will exhibit modulation and after certain
threshold will become unstable. Although the twice difference of speeds in
stands No.2 and No.5 (Figure 4a) we see the same phases of low frequency
modulation. It is impossible to explain this fact if to consider the BUR eccen-
tricities influence as a source of modulation. But it appears possible if to assume
modulation as a result of thickness periodic defects accumulation which is not
directly speed related and depends on phases of previous stand and current stand
vibration. Such nature of resonance vibrations called «regenerative» chatter in
publications. BUR abnormal eccentricity will increase mill sensitivity. Therefore
even when very high vibration levels occur in the last stand No.5 of tandem mill
2030 NLMC it never causes mill chatter (there is no back action).
a) b)
Figure 5: Vibration modulation (a) and thickness variation (b)
During the occasional strip breaks it may be calculated stand’s real internal
damping by the decrement of transient oscillations. Time of attenuation about
0.3 s is obtained for different stands. For the rolling speed 15 m/s the distance
between stands in 4.75 m will be passed in 4.75/15 = 0.3167 s and for 20 m/s in
4.75/20 = 0.2375 s. So the previous stand is stable and last stand is unstable. Af-
ter speed limit 4.75/0.3 = 15.83 m/s it will not be able to dissipate periodical im-
pacts and vibration amplitude will rise in time even at constant speed.
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3 Chatter Control
As the mill speed drop during chatter control reduces productivity the two ways
are to solve problem: to control other rolling parameters (tension, reductions) or
minimize speed drop value. Experiments proved that specific tension decreasing
by 5 N/mm2 between the stands No.4-5 allows speed increasing by 0.7-0.8 m/s.
Relative reduction increasing in stands No.1-2 and it decreasing in the stands
No.3-4 allows to bring up mill speed by 0.3 m/s for every 1% of relative
reduction decreasing. The second way to improve control is to recognize chatter
amplification earlier than it comes to large amplitudes in the stands and thus to
minimize speed drops because less vibration requires less control signals.
For the first stage of research “black box” approach has been applied. Cross-
correlation matrices of all available for measurement mill parameters (loads,
tensions, torques, drive speeds, vibrations) were calculated as time functions and
most related parameters were chosen for chatter prediction and mill speed con-
trol. For the second stage some additional factors (so called “chatter index”)
were tested in order to improve the reliability of automatic mill speed control.
Coefficient of harmonics (nonlinear distortion), modulation factor and some
other indexes were tested on-line in the automatic monitoring system. Band-pass
filtering used to improve signals in the desired frequency ranges. Data analysis
has shown that vibration signals are more sensible than loads, tensions etc. and
most suitable signal for chatter control. Speed impacts reduced from 100 m/min
(10%) to 10 m/min (1%) (Figure 6). Notations: 1, 4, 8 – spectrum and indexes
alarm levels, 2 - chatter frequency, 3 – amplitude, 5, 6, 7 – chatter new indexes.
a) b)
Figure 6: Chatter control by the known (a) and new methods (b)
System has been working since June 2006. Patent is pending on method and sys-
tem for chatter vibrations early diagnostics and tandem mill control.
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3.1 Chatter Damping Methods and Devices
As the upper threshold of rolling speed depends on mill internal dissipation abil-
ity then chatter passive damping methods and devices were investigated. Some
companies produce polyamide removable liners and pads for rolling stands and
chocks. Also thin inflatable hydraulic cylinders used for pressing chocks to mill
housing. It allows preventing clearances opening and chocks horizontal vibration
when the tension oscillations amplitude is too high. Experiments have shown
that only 5-10% speed increasing may be achieved by passive dampers.
Active chatter suppression methods are quite popular now in the research papers
and patents. This method of damping includes the additional source of energy
(preferably hydraulics) and some devices which produce regulated periodic force
in the rolling mill stands. In Ref. [7] additional degree of freedom (DOF) has
been introduced for strip vibration phase shifting between stands and reserve of
stability increasing in the rolling mill. Some other patents give the same ideas.
Many kind of damping methods were proposed earlier (1985) for dynamics re-
duction in hydraulic system in the 2030 mill of NLMC and later (2005-2007) for
vibration damping. There are several ways for active chatter control.
1) Periodic force changing in AGC cylinders through the fast servo-valves. But it
is difficult to compensate rolls moving with the 120 Hz chatter main frequency
as the usual AGC pass band restricted by the 10-15 Hz.
2) Periodic force generation in the backup rolls balancing system. Usually it
works in the on-off mode. But the same problem appears with the low pass band
of servo-valves and big cylinders.
3) Periodic force generation in the work rolls bending cylinders. This method is
more effective as the acting force of small amplitude is implied close to contact.
4) One method includes safety valves installed in the hydraulic system close to
work rolls bending cylinders. It acts like a non linear element when vibration
amplitude overcomes certain limit. Safety valves may work separately or by the
signals from the vibration monitoring system (preferable). The tandem mill
stands hydraulic block and rolls shocks section are represented in Figure 7.
Figure 7: Rolling mill hydraulic system and polyamide damping pad
The main problem in active chatter damping is the absence of reliable high fre-
quency hydraulic valves for exact damping force phase regulation in every of 8
pistons of the stand. Even a little phase divergence under control may cause de-
fects of strip flatness and even worse situation in the mill than before. In any case
the vibration monitoring system is needed to produce valve control signals.
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Conclusion
- Kinematical sources monitoring is required but it is not effective for control.
- Mill natural frequencies and modes vary under the working conditions.
- Stability criterions based on linear models are not effective for control.
- Work rolls surface temperature is a bifurcation parameter for chatter on-set.
- Chatter frequency harmonics may be used for friction forces diagnostics.
- Chatter vibration modulation in the tandem mills has regenerative nature.
- Stands synchronization control is the most reliable method for chatter control.
- Chatter passive damping devices have no remarkable effect.
Acknowledgments
Authors would like to express its appreciation to the ECSC2008 organizing
Committee for the possibility to represent our common work in this paper.
References
[1] Pryhodko, I.Y., Krot, P.V., et al., Vibration monitoring system and the new
methods of chatter early diagnostics for tandem mill control, Proc. of Int.
Conf. “Vibration in rolling mills”, Inst. of Materials, Minerals and Mining,
London, UK, 9th November, pp. 87-106, 2006.
[2] Kimura, Y., Sodani, Y., Nishiura, N., Ikeuchi, N. and Mihara, Y., Analysis
of Chatter in Tandem Cold Rolling Mills, ISIJ International, Vol. 43, No. 1,
pp. 77–84, 2003.
[3] Wiercigroch, M., Budak, E., Sources of nonlinearities, chatter generation
and suppression in metal cutting, Phil. Trans. of the Royal Soc. of London,
Vol. 359, pp. 663-693, 2001.
[4] Farley, T.W.D., et al., Understanding mill vibration phenomena, Proc. of
Int. Conf. “Vibration in rolling mills”, Inst. of Materials, Minerals and Min-
ing, London, UK, 9 November, pp. 5-10, 2006.
[5] Hu, P.H., Ehmann, K.F., Regenerative effect in rolling chatter, Journal of
Manufacturing Process, Vol. 3, No. 2, pp. 82-93, 2001.
[6] Chen, Y., Liu, S., Shi, T., Yang, S., Liao, G., Stability analysis of the rolling
process and regenerative chatter on 2030 tandem mills, Proc. Inst. Mech.
Eng., Part C: J. Mech. Eng. Sci., Vol. 216, No. 12, pp. 1225-1235, 2002.
[7] Evans, P.R., Rolling mill vibration control, Patent WO 96/27454,
B21B 37/48, 07.03.1996.
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