CHINESE JOURNAL OF MECHANICAL ENGINEERING
Vol.16,0No.2,n2003
Shu Xuedao
Department of Mechanical Engineering,
University of Science and
Technology Beijing,
Beijing 100083, China
Shen Guangxian
Department of Mechanical Engineering,
Yanshan University,
Qinhuangdao 066004, China
Ren Fujun
181
ANALYSIS OF ROLL SYSTEM STABILITY ABOUT ALUMINUM FOIL MILLS∗
Abstract:To improve roll system stability of aluminum foil mills, roll system stability of 2200 highspeed aluminum foil mill is analyzed with energy stable method. Two different restrictive conditions
which gaps between chock of work roll and window of stand whether exist or not, are studied respectively. A new concept of roll system with open /closed compound pair comes up with as well for renewably synthesizing restrictive mechanism of aluminum foil mills’ chock. Through these studies, the
conflict, whether reserving the gap for the roller replacement or eliminating the gap for roller’s normal
work, is successfully settled. This concept and analyzed result give the actual mechanism with
open/closed compound restriction and the method of realizing high-speed rolling and prolonging
longevity of end thrust bearing on work roll. It has important theoretical meaning and engineering
value for modern technical reform of aluminum foil mills and plate strip mills.
Key words: Aluminum foil mills Stability Open /closed compound pair
0 INTRODUCTION∗
At present, for large-sized and high-efficient aluminum foil
mills that are served in the world, their roll systems are pair systems with gap. These gaps enter running of mill and affect roll
system stability. Work roll and chock system inside stand depend on
geometry restriction of pressure screw and pressure plate fixing
their position along vertical and axial direction, and depend on force
balance restriction which is generated by eccentricity distance e
between work roll and back roll fixing their position along level
direction. Hence, roll system is 2-D restrictive state with gap along
level and axial direction. Because of dynamic disturb at the level
direction, the unstable behaviorof the chock in roll system not only
generates cross between work roll and back roll but also leads chock
level vibration. In addition, it also makes wear extent of sideslip
plate increase and gap between window of stand enlarge, generates
abnormal axial force because of cross between work roll and back
roll, aggravates mill’s level vibration. These factors lead end thrust
bearings on work roll burn and shorten longevity for seriously
overload, shape of strip become bad and accident of broken strip
occur, mill have to work at lower speed (below 1 000 m/min) finally.
Therefore, the analysis of roll system stability about aluminum foil
mills has important realistic meaning for increasing bearing
longevity and product precision, realizing high-speed rolling. It is
also an advancing edge subject to be studied urgently at present.
In this paper, with energy stable method, through the analysis
of roll system stability with gap about aluminum foil mill, a new
concept of roll system with open/closed compound pair is put forward. In contrast, the stability of roll system without gap is analyzed
too. Through these studies, the conflict, whether reserving the gap
for the roller replacement or eliminating the gap for roller’s normal
running, is successfully solved. These studied results provide theoretical and practical proof for studying method of preventing burnt
and prolonging longevity about end thrust bearing on mill, improving product precision and realizing high-speed rolling.
between chock on work roll and window of stand in order that roll
and chock can expediently enter window of stand for roller replacement. This kind of restriction with gap is called open restriction or open pair. The chock’s restriction of 2200 aluminum foil
mill shown in Fig.1 is open restriction. Because of the existence
of gap in open pair, dynamic characteristic of mechanism is deteriorated. As a result, mechanism works at an unstable state. Especially, the influence will be much larger for high speed, high precision and high efficiency mechanism. Hence, it is necessary not
to separate pair components under working condition for improving mechanism dynamic characteristic. In order to solve the disadvantage for open restriction, a new concept of restriction, open/
closed compound restriction is put forward in this paper. It means
that mechanism can ensure different restrictive demand under two
kinds of state. In other words, under open restrictive condition, the
gap must be reserved for mechanism’s replacement or assemble,
and under closed restrictive condition, the gap must be eliminated
for mechanism’s normal running. Its sketch is shown in Fig.2.
Under assembled or taken down condition, mechanism is open
,
is separestriction because δ gap exists and components
rated, and under working condition, mechanism is closed restric,
are betion because δ gap is eliminated and components
coming a whole body. Therefore, when roll system mechanism of
aluminum foil mill is renewably synthesized with open /closed
compound restriction, the conflict which troubled aluminum foil
mills for many years, either reserving the gap for meeting the need
of assemble or eliminating the gap for ensuring to work in stable
state, has been successfully overcome.
1 ROLL SYSTEM MECHANISM WITH OPEN/
CLOSED COMPOUND RESTRICTION
As a usual mechanism, its pair restriction can be expressed
with a determined equation of coordinates. There is not gap between pairs. This kind of restriction is called closed restriction.
However, for aluminum foil mill, it is necessary to reserve the gap
* This project is supported by National Natural Science Foundation of China
(No.50075075). Received November 23, 2001; received in revised form December 25, 2002; accepted January 24, 2003
Fig.1 Open restriction of chock of 2200 aluminum foil mill
1. Baffle plate at axial direction 2. Top chock
3. Bend roll cylinder 4. Balance cylinder
5. Side slip plate 6. Stand 7. Bottom chock
182
CShu Xuedao, et al: Analysis of roll system stability about aluminum foil mills
Fig.2 Schematic open /enclosed compound pair
2
ANALYSIS OF ROLL SYSTEM STABILITY
ABOUT 2200 ALUMINUM FOIL MILL
For stability analysis, two kinds of usual methods are Floquet
theory method[1,2] and energy stable method[3]. Both of them can
be used to analyze dynamic stability of mill’s roll system with gap
or not. Energy stable method becomes simple and is adopted in
this paper because it combines numerical integral. The restrictions
shown in Fig.1 are open restrictions, and pairs between chock on
work roll and window of stand are open pairs too. The mechanical
system model of chock on work roll is shown in Fig.3. Where, the
number of freedom is 1 and generalized coordinates is x.
x > 0.1
 x − 0.1

x ≤ 0.1
where f ( x) = 0

x
x
0
.
1
+
< −0.1

Through energy stable method[3], energy equation can be attained
(5)
E& = x&q sin t
When combining dynamic Eq.(4) and energy Eq.(5), first order
differential equations set is attained as follows
 y&1 = y2

2
(6)
 y& 2 = −ω n f ( x) + q sin t
 y& = y q sin t
2
 3
 y1 = x

 y 2 = x&
y = E
T
 3
ET
Energy variety of total system during a cycle T
The parameters of system of work roll and chock about 2200
aluminum foil mill in Fig.3 is shown in Table. Assumed initial
condition is
 y 1 ( 0) = 0

 y 2 ( 0) = 0
 y ( 0) = 0
 3
where
Table Computing parameters of chock
Fig.3 Mechanical system model of work roll chock about
2200 aluminum foil mill
Supposed power force of the system is
f (t ) = q0 sin ωt
(1)
Amplitude value of power force
ω
Frequency of power force
Through contact force model, the following dynamic
mechanic equation of system can be attained
m&x& + kf ( x) = q0 sin ωt
(2)
where q0
where
x − r

f ( x) = 0

x + r
Contact rigid
k/(N mm )
ω/(rad s–1)
Amplitude value of
power force
q0 /kN
650
1.05×106
120
50
–1
With numerical integral method[5]of four-step Runge-Kutta of
given step, in three kinds of gap cases which r is respectively
equal to 0.0 mm, 0.5 mm, 1.0 mm, bearing force of chock and
energy variation of chock system are respectively calculated, as
follows Fig.4 and Fig.5.
x>r
x ≤r
x < −r
Mass of chock
m
k
Contact rigid
r
Valve of gap
Dealing with Eq.(2) by no dimensional method [4]
l 0 = 10 r
ω 0 = ω , m0 = m
x = x l0
&x& = ω &x& l 0
*
Frequency of
power force
Mass of
chock
m /kg
2
*
assuming that
t = tω 0
*
k / m = ω 0ω
Fig.4 Varying chart of chock compact force
*
n
q 0 = ω 02 q * l 0 m 0
then Eq.(2) is rewritten as follows
2
&x&* + ω n* f ( x * ) = q * sin t *
(3)
 x * − 0.1
x * > 0. 1


where f ( x * ) = 0
x * ≤ 0. 1
 *
 x + 0.1
x * < −0 . 1
and, the function with * is no dimensional measure. When symbol
* is ignored Eq.(3) is rewritten as follows
2
&x& + ω n f ( x) = q sin t
(4)
Fig.5 Varying chart of chock energy
CHINESE JOURNAL OF MECHANICAL ENGINEERING
Known from Fig.4, impact force among pairs is rather lower
when eliminating gap between chock and sideslip plate, but it is
much larger when reserving it. The larger is value of gap, the
larger is impact force. The result with gap is that mill’s level
vibration is aggravated, bearing longevity and product quality is
directly effected.
Known from Fig.5, when gap between chock and sideslip
plate exists and chock is in open restrictive state, ET value of
energy variation of system is greater than zero, so system is unstable. And the larger is gap, the larger is ET value of energy
variation, the stronger is instability of system. When roll system
works in unstable condition, dynamic cross between work roll and
back roller must happen because of impact force. The result is that
abnormal and wave axial force is generated, and bearing longevity
and product quality is also directly affected. When gap r is equal
to zero and chock is in closed restrictive state, ET value is nearly
equal to zero, so system is stable. Hence it is unreasonable to
adopt open restriction for roll system of aluminum foil mill with
high precision, high speed and high efficiency. Open/ closed compound restriction can either meet the need of assembling demand
or ensure to work in a stable state without gap.
3 OPEN/CLOSED COMPOUND RESTRICTIVE
MECHANISM OF 2200 ALUMINUM FOIL
MILL AND TEST RESULT
183
between chock and adjusted block is becoming larger and larger,
so chock is in open restrict state. Because adjusted bolt and stand
is connected by sphere mat, load on chock is uniform. Under
open/closed compound restrictive state, test result of vibration
characteristic of chock is shown as Fig.8.
(a)
Open restriction
According to the actual mill’s structure, open/closed compound restrict mechanism of 2200 aluminum foil mill, is designed
follows as Fig.6 and Fig.7, which is made up of lead screw jacking apparatus to be installed between chock and stand bulge.
(b) Closed restriction
Fig.8 Test result of vibration characteristic of chock
Fig.6 Open/closed compound restrictive mechanism
of 2200 aluminum foil mill
1. Chock 2. Adjusted block 3. Square nut 4. Pressed block
5. Circle nut 6. Adjusted bolt 7. Sphere mat 8. Stand
Known from Fig.8, the ratio of amplitude of vibration in two
kinds of state is
Ac/Ao 0.872/1.419=61
(7)
where Ac
Amplitude of vibration under closed restrictive state
Ao
Amplitude of vibration under open restrictive state
Obviously, under closed restrictive state, value Ac of chock
vibration is lower and is 61% value Ao of open restrictive state.
Test result is nearly accordance with calculating result. And roller
system works in a stable state. About the stability of back roll’s
chock, it is similar to work roll’s chock except for larger inertia. It
may be studied if necessary.
4 CONCLUSIONS
Fig.7 Actual diagram of open/closed compound restrictive mechanism
In Fig.6, when rotating adjusted bolt, pressed block and adjusted block are pushed forward because square nut goes forward.
The gap between chock on work roll and window of stand is
eliminated because adjusted block drives work roll chock, so
chock is in closed restrict state. Per contra, when rotating adjusted
bolt at reverse direction, adjusted block is back off, and the gap
(1) Under open restrictive condition, system of work roll’s
chock of 2200 aluminum foil mill is unstable because energy
variation ET is greater than zero. The instability of system is a key
factor for shortening longevity of end thrust bearing on work roll
and being compelled to reduce mill’s working speed at present.
(2) The larger is gap between chock and window of stand, the
larger is value of energy variation and compact force, the stronger
is instability of roll system about 2200 aluminum foil mill.
(3) When chock is in closed restrictive state for controlling
gap to be equal to zero, compact force between pairs is smaller
and ET valve is nearly equal to zero, so system is stable. Therefore,
with open/closed compound restriction, the conflict, whether
reserving the gap for the roller replacement or eliminating the gap
for normal rolling about 2200 aluminum foil mill, is effectively
(Continued on page 189)