Analysis of roll stack deflection in a hot strip mill
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Analysis of roll stack deﬂection in a hot strip mill
Article in Journal of the Brazilian Society of Mechanical Sciences and Engineering · July 2007
DOI: 10.1590/S167858782007000300008
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Sudipta Sikdar et al
Sudipta Sikdar
[email protected]
R & D, Tata Steel, India
Shylu John
[email protected]
R & D, Tata Steel, India
Ashwin Pandit
[email protected]
R & D, Tata Steel, India
Analysis of Roll Stack Deflection in a
Hot Strip Mill
Predictive models are required to provide the bending set point for bending for the flatness
control devices at rolling stands of finishing mill of Hot Strip Mill (HSM). A simple model
for roll stack deflection at the finishing mill has been illustrated where a modified
Misaka’s equation has been used to obtain mean flowstress. Investigation has been
performed to understand the effect of width of roll on roll stack deflection. The bending on
the deflection has been found to have a positive effect to reduce the amount of the stack
deflection. The results from the sensitivity analysis of the roll width on roll deflection are
also described.
Keywords: hot strip mill (HSM), finishing stands, mean flow stress (MFS), continuously
variable crown (CVC), shear stress, bending.
Raju Dasu
[email protected]
R & D, Tata Steel, India
Introduction
1
Predictive models are required to provide the bending set point
for bending for the flatness control devices at rolling stands of
finishing mill of Hot Strip Mill (HSM). A simple model for roll
stack deflection at the finishing mill has been illustrated where a
modified Misaka’s equation has been used to obtain mean flowstress. Investigation has been performed to understand the effect of
width of roll on roll stack deflection. The bending on the deflection
has been found to have a positive effect to reduce the amount of the
stack deflection. The results from the sensitivity analysis of the roll
width on roll deflection are also described.
Nomenclature
A = Area of cross section of roll, m2
C = Carbon concentration in wt %
D = Roll diameter at center, mm
E = Young’s Modulus, N/m2
F = Bending force, Newton
I = Moment of Inertia, m4
G = Shear modulus, N/m2
H = Entry thickness, mm
h = Exit thickness, mm
K = A constant (= 4/3)
k = Constant in equation (9)
L = Contact length between work roll and backup roll, m
L’ = Moment arm for bending force, metre.
M = Bending Moment, Nm.
MFS = Mean flow stress, MPa
Mn = Manganese concentration in wt %
Nb = Niobium concentration in wt %
P’(x) = Force on work roll due to strip, Newton
q(x) = Force on work roll due to backup roll, Newton
Q = Geometrical factor
R = Roll radius, mm
r = Reduction at each pass, %
S = Shearing force, Newton
Srbur = Shearing force due to back up roll, Newton
Srstrip = Shearing force due to strip, Newton
T = Temperature, oK
Paper accepted March, 2007. Technical Editor: Anselmo E. Diniz.
284 / Vol. XXIX, No. 3, JulySeptember 2007
Ti = Titanium concentration in wt %
w = Width, mm
X = Softening fraction
x = Segmented length with reference to center, mm
Y = Thickness of roll gap at neutral point, mm
t = Tube thickness, m
U = Overall heat transfer coefficient, W/(m2 K)
Greek Symbols
Φ = Neutral angle, radian
•
ε
ε
σ
δ
= Strain rate, s1
= Strain
= Stress, MPa
= Deflection, mm
Subscripts
b
Bending
dyn Dynamic recrystallization
Reference to Misaka’s equation
M
ss Steady state
s
Shear
Scope and Policy
Today’s steel market is guided by the fulfillment of customer
demand to meet the stringent requirement of strip quality. Out of
various qualities required for the hot rolled product from steel
producer, the most important one is the flatness on the strip
produced from a Hot Strip Mill (HSM). In a typical HSM, shown in
Fig.1, the strip from the roughing mill is passed through the
finishing mill via intermediate coilbox. In general, the various
contributing factors in the finishing mill of a hot strip mill such as,
(i) The thermal crown (ii) The deflection of the work roll and back
up roll (iii) The wear in the work roll, leads to the final shape of the
strip produced. The final roll gap between the work roll is the
cumulative effect of these three factors, which dictates the profile of
the strip produced. The roll shifting and bending moment are
applied in the rolls of the finishing mills to maintain the required
crown and flatness in the strip produced.
In a fourhigh hot strip mill, the finishing mill of the hot strip
mill is equipped with two workrolls and two backup rolls and is
shown in Fig. 2. During the passage of the strip between the two
work rolls, a large amount of roll separating force is developed. This
changes the initial set value of roll gap between the work rolls
ABCM
Analysis of Roll Stack Deflection in a Hot Strip Mill
(Wilms et al. (1985)). Flatness is dependent on the roll gap or
clearance between the working rolls during the process of rolling.
Strip profile and flatness can be influenced by the mill features like
work roll bending and CVC (Continuous Variable Crown) shifting.
Backup
Roll
Roughing Mill
Coil Box
Coil
Runout Table
Finishing
Mill

Down
Coiler
Work
Roll
Figure 1. Layout of a typical Hot Strip Mill.
Hence, the knowledge of the contribution of the effect from
work roll bending is essential to the people associated with the
improvement of profile and flatness. In general, the roll separating
force acting between the strip and the work rolls has a parabolic
profile. In order to predict flatness and thickness of roll strips, it
becomes indispensable to analyze the amount of roll.
Strip Profile and Shape
Profile and flatness in the rolling of strip are related to each
other in rolling operation. Achieving the flatness requirements in
rolling thinner gauge sheets has always been greater challenge as we
encounter fewer flatness problems in rolling of thicker gauge sheets.
Crown is the difference in thickness between the centre and at a
point 40 mm from the edge of the strip (taken average of both
sides). Flatness or Shape is defined by the degree to which a flat
rolled product is planar, when not subjected to external constraining
forces.
The deflection of the work rolls results in a widthwise
distribution of strip thickness in the form of a convex crown, in
which the thickness is greater at the center of the width and smaller
at the edges. This widthwise difference in thickness is known as the
strip crown. To reduce the convex shape, in general, a bending force
is applied in the opposite direction. The work roll bending forces are
applied to the work roll chocks that are located at the roll ends.
When roll bending forces are applied in the direction of opening the
roll gap, this is known as positive or crownin roll bending.
Inversely, when the roll bending forces are applied in the direction
of closing the roll gap, this type of bending is termed negative or
crownout roll bending. Positive roll bending causes the strip profile
to be concave whereas negative roll bending causes the strip profile
to be convex.
Backup roll
q (x)
Mill Configuration
p (x)
Bending Force
strip
Work
roll
Backup roll
Figure 2. Schematic diagram of forces acting during rolling conditions.
A vast literature with different techniques fills the subject of the
roll stack deflection. Out of various simple models, the roll
deflection has been obtained from the beam theory in the model of
Stone and Gray (1965) where the rolls are presented as a simple
beam. Later on this has been adopted by many workers. Another roll
deflection model based on the beam theory for the evaluation of the
roll deflection in plate rolling was used by Ohe et al. (1994), where
they assumed the pressure distribution between the rolled plate and
the work roll as well as between the backup roll and the work roll to
be a polynomial of fourth degree. Many other workers have also
worked to determine the roll stack deflection for reducing the profile
and flatness error. Steel producers can achieve improvement in the
productivity and quality by improving the profile and flatness and
for this reason; it is of utmost importance to analyze the effect of
various parameters in improving the quality such as work roll
deflection, backup roll deflection.
This article describes a mathematical model based on simple
deflection equations for each stand of six finishing mills in a hot
strip mill and this describes the effect for a whole schedule of
rolling. This simple model is an easy resort to estimate the roll
deflection instead of several complex models described in the
literature. The purpose of this work is to find out the effect of
different parameters on roll deflection. For six stands, the overall
roll deflection values are evaluated. The effects of the size of the
strip width and roll bending values have also been studied.
J. of the Braz. Soc. of Mech. Sci. & Eng.
In the hot strip mill under study, the slabs from the slab caster
are rolled into strips by reducing their thickness from 210 mm to a
value ranging from 1.6 mm to 12 mm, with the width of the strip
ranging from 860 to 1540 mm. The slabs are heated and soaked in a
Walking Beam typereheating furnace up to a temperature of almost
1250oC. At fourhigh reversing roughing stand, the heated slabs are
reduced to a thickness of 30 mm with seven passes. Finally, the
required thickness is achieved in a fourhigh sixstand tandem
finishing mill (F1 to F6) at a finish rolling temperature of 870 900oC, depending on the grades. Centrifugally cast high chrome
rolls are used for the purpose of work rolls of six finishing mill
having a barrel length of 2000 mm and a diameter ranging from 660
mm to 710 mm. With the objective to achieve required metallurgical
properties at different coiling temperature, the strip from finishing
stands are cooled in the Run Out Table (ROT), where it is water
cooled and coiled finally in the down coiler.
A large number of slabs are rolled in a schedule of rolling by the
work rolls of finishing stands until work rolls are replaced at the end
of the schedule. A whole schedule contains the mixture of the slabs
of different grades of steels of different width and different target
thickness in the hot strip mill. In general the number of strips
produced from a schedule varies from 4560 depending on the
requirement and availability of slabs. A coffin schedule is followed
in hot strip rolling to arrange the width of the slabs to be rolled. In
this arrangement, slabs with lower width are placed at the beginning
of the rolling and the width of slabs are gradually increased up to a
maximum value and after that the width is reduced to close the
starting values of slab width. In nutshell, the slabs arranged in this
way looks like the shape of a coffin.
Shapes of work roll
As the length of the work roll and back up roll are equal, the
effect of roll bending is not prominent to reduce the crown. To
obviate this problem, the use of tapered crown work rolls in a
Japanese steel plant, as mentioned in the paper by Kitahama et al.
(1987), was introduced, where shifting of the work roll was made to
compensate for crown developed. Later on many plants use CVC
Copyright 2007 by ABCM
JulySeptember 2007, Vol. XXIX, No. 3 / 285
Sudipta Sikdar et al
(Continuously Variable Crown) developed by SMS (SchloemannSiemag ) where the shifting the work rolls in the opposite directions
reduces the roll separating force. The finishing mill is equipped with
Continuous Variable Crown (CVC) technology with a maximum
biaxial shifting of ±150 mm for stands F2 to F6 and roll bending (F1
to F6) for shape control. The work rolls in stand 1 are cylindrical. In
CVC system, two axially rolls have a shape of “S” and deviate from
a cylindrical shape by a dimension of range of microns. The
opposite shifting enables the operator to achieve symmetrical
thickness profile. The movement of the both rolls in pair in the
opposite direction acts like the conventional cylindrical rolls to
produce a crown. A smaller or bigger size of crown can be achieved
by the mode of the direction of the shifting. The workroll shifting
type aims to make the strip thickness uniform and improve the
flatness over a wide range of strip widths by shifting CVC rolls.
A linear relationship exists between the effective roll crown and
the CVC shifting. The range of crown adjustment depends on the
shifting distance and the difference between the maximum and
minimum diameter of the Sshaped roll.
Deflection by Bending,
E .I .
d 2δ b
dx
=M
2
(1)
Deflection by shear stress,
GA d δ
.
K
dx
s
= S
(2)
where, E: Young’s Modulus, I: Moment of inertia, S: Shearing
force, A: Area of cross section of roll, M: bending Moment, G:
Modulus of rigidity, K: 4/3. For the determination of bending
moment, the roll force is required. In this model the roll force is
calculated first. The flow diagram of roll stack deflection model is
shown in Fig. 4.
Entry & Exit Thickness
Roll Diameter
Mathematical Model
In this section, we describe the method of development of the
deflection model, based on short beam deflection theory, to predict
the deflection of the work roll at different positions along the length
of the roll at the finishing stands of the Hot Strip Mill. This model
takes into account the following assumptions:
(i) The work roll is considered to be cylindrical instead of CVC
roll.
(ii) No work roll shifting is considered.
Chemical composition
Width of Coil
Roll Force
Model
Roll force
Stack Deflection Model
S r_bur
q(x)dx
WR
WR
WR
WR
P’(x)dx
X
F/2
Deflection at each position along Barrel length
Figure 4. Flow diagram for the development of stack deflection model for
a number of coils in a schedule.
S r_strip
X
w/2
L/2
L’
L’/2
Figure 3. Free body diagram of work roll.
To develop a simple deflection model the deflection of the
workroll and backup roll are considered. For the calculation of
the roll deflection, the theory uses the roll as simply supported
overhanging beam. The backup roll is considered as a simply
supported beam. The elastic roll deformation is determined by
superimposition of deflection due to bending ( δ b ) and deflection
due to shear ( δ s ) on the roll.
Figure 3 shows the freebody diagram depicting different forces
acting on the work roll of a finishing stand. From the freebody
diagram (Fig. 3) of the workroll:
286 / Vol. XXIX, No. 3, JulySeptember 2007
The deflection of backup roll axis is calculated in a similar
manner. To determine the work roll deflection along with the
deflection of backup roll, the roll force between work roll and back
up roll is necessary. The roll force is determined with roll force
model, described in the following sections.
This roll force is used in determining the bending and the shear
force in Eq.(1) & Eq.(2). The roll diameter and related thickness of
the strip for the chosen schedule of rolling are given in the Table 1.
The area of cross section of work roll can be determined from the
data of the table.
Table 1. Dimension of work roll and thickness of strip at finishing stands
of the selected schedule for analysis.
Finishing stand
No.
Roll diameter
(mm)
1
2
3
4
5
6
719
706
672
689
675
712
Strip thickness at the
exit of individual stand
(mm)
20.61
14.49
10.46
8.08
6.59
5.55
ABCM
Analysis of Roll Stack Deflection in a Hot Strip Mill
Specific force between the rolls (interroll specific force) has
been calculated from the roll force model. This model uses the mean
flow stress (MFS) of the material to calculate the rolling load.
Several phenomena such as recrystallization, strain accumulation
and phase transformation can be evaluated with the MFS behavior
during rolling. The roll force for each stand was calculated using
the Sims (1954) approach. Essentially, this calculation requires the
strip thickness, width and MFS of the material for each pass. The
Sims equation used for the calculation is as follows:
1
2
. MFS . w . (R . (H − h )) 2 . Q
P =
3
(3)
due to short interpass time, and dynamic recrystallisation (DRX)
followed by metadynamic recrystallisation (MDRX) occurs. The
evolution of MFS as a function of inverse absolute temperature is
350
300
H −h
H
50
0.74
0.76
0.78
1
(5)
Y = 2 R (1 − cos Φ ) + h
(6)
The flow stress is governed by the repeated recrystallization
which can be either static or dynamic. It depends on the interpass
time, strain, strain rate and temperature. Misaka’s equation from
Misaka and Yoshimoto (1967) has been used to specify the MFS for
CMn steels during hot strip rolling and the equation is given by:
(
)
•
MFSM = 9.81exp 0.126 − 1.75[C ] − 0.594[C ]2 + ε 0.21 ε
2851 + 2968[C ] − 1120[C ]2 0.21 •
ε
ε
+ 9.81exp
T
0.86
Figure 5. Comparison of MFS as a function of the inverse absolute
temperature.
depicted in Fig. 5 by comparison of the data from the work of
Sicliano (2004).
Validation
The comparison between the predicted and the measured
(actual) roll force for a selected schedule at the finishing stand no. 2
of the hot strip mill is shown in Fig. 6. The average of measured
Roll Force in Stand No. 2
(7)
20
15
10
Actual
Predicted
5
(8)
(9)
here a constant factor of k = 1.14 is introduced to convert the stress
to mean flow stress. The MFS during rolling at each stand, as
calculated by Eq. (9), was used in Eq. (3) for the calculation of roll
force.
The mean flow stress, determined from Eq.(7) is similar to the
nature of the graphs of Pankaj et al. (2004) for plain CMn grade
and microalloyed grade steel:
(10)
where T=Temperature
In case of Nb microalloyed steels, the presence of Nb in solid
solution causes the retardation of static recrystallisation (SRX).
During finishing stages of strip rolling, strain accumulation occurs
J. of the Braz. Soc. of Mech. Sci. & Eng.
0.84
25
0.13
= MFS M (0 .768 + 0 .51[Nb ] + 0 .137 [Mn ] + 4 .217 [Ti ])
MFS = f (1 / T )
0.82
1
0.13
where , MFS M is the modified Misaka’s equation for MFS in MPa
and [C] is the carbon concentration in weight %, T =Temperature,
in oK Later on, Siciliano et al. (1996) modified equation (7) to
incorporate the effect of different alloying elements such as Mn, Nb,
Ti etc. and the softening due to dynamic recrystallization, if any.
The modified equation is restructured as follows:
MFS = MFS * (1 − X dyn ) + k σ SS X dyn
0.8
1000/T ( K )
Roll Force, MN
1
1
*
150
(4)
2
π
1 1 − r 2 −1 r 2 R 2 Y
Q =
− ln (1 − r ) −
tan
4
r − 1 h h
2 r
MFS
200
100
where, MFS = Mean flow stress, w=width, R=Work roll radius,
H=Entry thickness, h=Exit thickness and, Q= Geometric constant.
r=
For Nb grade steel ( Pankaj et al.)
For CMn (base) grade steel ( Pankaj et al.)
Siciliano's Model
250
MFS, MPa
Roll Force Model
10
20
30
40
50
60
Coil No.
Figure 6. A comparison of predicted vs. actual roll force for stand no. 2 in
a complete schedule of rolling.
force (in MN, MegaNewton) for each coil is taken from the hot strip
mill (HSM). For the whole schedule, average values of actual force
for each coil are captured by levelII automation in HSM with the
help of load cell located in the finishing mill housing. The predicted
and the actual roll forces are found to be in good agreement. The
deviations of the average of actual roll force for 80% of the coils are
found to be with in 78%. In some cases, the prediction matches
with the actual value of the average roll force. Similar results are
found to be true for all the other stands.
Copyright 2007 by ABCM
JulySeptember 2007, Vol. XXIX, No. 3 / 287
Sudipta Sikdar et al
The results encompass the analysis of the model simulation with
the data of strip rolled and the work rolls of the finishing stands of a
complete schedule. The roll diameter, entry and exit thickness for
each stand as well as chemical composition and width for each coil
of the schedule have been used as input for the roll deflection
model.
Figure 7 displays the variation of deflection with the width for
different finishing stands simulated by the model. For any stand of
the finishing mill, the amount of deflection increases with the
increase of the width of the work roll and after a particular value of
width the deflection again starts drooping down. This result implies
that the maximum deflection can be obtained for a particular width
of the strip, which is about 5560% of work roll length. A similar
observation has been made in the reference literature by Ginzburg
(1995) also. It is noticed from the simulation study that the strip
width has a significant effect on the roll deflection. The strip
transmits the rolling load between the work rolls, which are
generally greater in length than the strip width. The work roll
deflection increases with an increase in strip width, whereas for
wider widths deflection decreases with an increase in strip width,
reaching its maximum value of 5560% of the barrel length. This
Deflection, microns
Width, mm
800
50
900
1000
1100
1200
1300
1400
1500
1600
The effect of work roll bending at different stands of the
finishing mill is illustrated in Fig. 8. The effect of bending and
without bending creates two parallel curves. The relative profile at
different stands with bending remains constant, as can be seen by
the curves, which are parallel. Thus, the roll bending force is
designed in such a way so as to maintain a uniform relative profile
at different stands to avoid flatness error. Here, the roll force is
decreasing with subsequent stands, thereby reducing the deflection.
The difference of the deflection value with and without bending for
the particular process parameter lies between 5060 microns. The
table in the inset shows the parameters of roll force and bending
force considered for the analysis. The inset in the Fig. 7 also shows
the roll force and bending force values considered for the analysis.
Barrel Length, mm
200
400
600
800 1000 1200 1400 1600 1800 2000
50
Deflection, microns
Results
100
150
400 kN
450 kN
200
500 kN
550 kN
100
Stand No.1
150
250
600 kN
Stand No.2
200
Stand No.3
250
Stand No.4
Figure 9. Effect of roll bending on roll deflection of stand 1 (Roll Force:
14.07 MN, Strip Width: 900 mm, Entry Thickness: 29.27 mm, Exit
thickness: 2.02 mm).
Stand No.5
Stand No.6
Figure 7. Effect of strip width on roll deflection at different stands (#).
trend is basically due to the effect of strip width on the roll force i.e.
with the increase in width, the roll force increases up to a value of
width and then decreases.
Figure 9 portrays the result of the variation in deflection along
the barrel length of stand 1 for increasing bending forces, keeping
the roll force and strip width constant. Significant point to be
observed is the decreasing trend of the amount of deflection with the
increase in bending force up to a particular barrel ( roll) length.
Thus roll bending is a controllable parameter to modify the roll gap
and hence the crown and flatness of the strip rolled in the finishing
mill of the hot strip mill.
Conclusions
Deflection, microns
1
2
Stand No.
3
4
5
6
50
100
150
200
250
Without Bending
300
With Bending
350
Strip Width: 960mm
Roll stack deflection is an important issue in the determination
of profile and flatness of a strip rolled in hot strip mill. A simple roll
deflection model has been developed to predict the deflection of the
finishing stands of a hot strip mill. The roll deflection model
indicates the effect of width for deflection as well as the effect of
bending. The effect of work roll bending and the roll width has been
studied by this model. It has been observed that the increase of
width of work roll leads to the increase of roll deflection upto a
certain value following which it again decreases with the increase of
width of work roll.
The amount of deflection of rolls at different stands can be
changed by applying roll bending. The roll stack deflection
calculated in the above method can be used as an input for
determining the roll gap along the barrel length for flatness.
Figure 8. Comparison of bending and no bending on roll deflection (Entry
Thickness: 29.27 mm, Exit thickness: 2.02 mm ).
288 / Vol. XXIX, No. 3, JulySeptember 2007
ABCM
Analysis of Roll Stack Deflection in a Hot Strip Mill
Acknowledgement
The authors acknowledge the kind permission of the
management of Tata Steel, India for the publication of this paper.
References
Bald, W., Beiseman, G.., Feldmann, H. and Schultes, T., 1987,
“Continuous Variable Crown (CVC) Rolling”, AISE Year Book, pp. 127136.
Ginzburg, V.B., 1995, “Profile and Flatness of Flat Rolled Products”,
Rolling Mill Technology Series, Part II, International Rolling Mill
Consultants, Inc., Pittsburgh, PA, USA, pp.432.
Kitahama, M., Yarita, I., Abe, H. and Awazuhara, H., 1987, “Profile
Control of hot rolled strip by work roll shifting (KWRS) mill”, AISE Year
Book, pp. 474483.
Misaka, Y. & Yoshimoto, T., 1967, J. Jpn. Soc. Technol. Plast., Vol. 8,
pp.414.
Ohe, K., Morimoto, Y., Kajiura, S., Fujino, T. , Simada, S., Anarku, K.
and Mizuta, A., 1994, “Development of Shape Control in Plate Rolling”,
J. of the Braz. Soc. of Mech. Sci. & Eng.
View publication stats
METEC Congress 94 Proceedings, Vol. 2, 6th International Rolling
Conference, VDEh, Dusseldorf, Germany, pp. 7885.
Pankaj, Venugopalan, T., Mohapatra, S., Ravi, R. S. and Sadhu, M.C.,
2004, “New Product Development using the Hot Strip Mill as an
Experimental Tool”, Tata Search, Vol. 2, pp. 280283.
Pospiech, J., 2005, “Calculation method for deformation of stands and
rolls to obtain products with small dimension of tolerances”, Journal of
Materials Processing Technology, Vol. 166, pp. 417422.
Siciliano Jr, F., Minami, K., Maccagno , T.M. and Jonas, J.J., 1996,
“Mathematical Modeling of the Mean Flow Stress, Fractional Softening and
Grain Size during the Hot Strip Rolling of CMn Steels”, ISIJ International,
Vol. 36, pp.15001506.
Siciliano, F., 2004, “Modeling the Mean Flow Stress and Grain Sizes
During the Hot Rolling of Niobium Microalloyed Steels using Industrial
Data”, SimPro'04, International Conference on Thermomechanical
Simulations and Processing of Steels, Ranchi, Jharkhand, India, pp 217235.
Sims, R.B., 1954, “The calculation of roll force and torque in hot rolling
mills”, Proc. Inst. Mech. Eng., Vol. 168, pp.191200.
Stone, M.D. & Gray, R., 1965, “Theory and Practical Aspects in Crown
Control”, Iron and Steel Engineer Year Book, pp. 657674.
Wilms,W., Vogtmann, L., Klockner, J., Beisemann, G. and Rohde, W.,
1985, “Profile and Flatness Control in Hot Strip Mills”, Metallurgical Plant
and Technology, Vol. 8, pp. 7490.
Copyright 2007 by ABCM
JulySeptember 2007, Vol. XXIX, No. 3 / 289