Roll Pass Design strategy

A Contribution to Rolling Mill Technology
_
Roll Pass Design Strategy for
Symmetrical Sections
by Sead Spuzic and Kazem Abhary
University of South Australia
School of Engineering
2

Keywords

• roll pass design (RPD)
• statistical analysis
• roll wear
• generic function
• optimisation

3

Intro

• Depreciations caused by large-scale industrial
processes call for technological improvements.

• Hot steel rolling mills belong to this class of industry.
• Here, a key for further optimisation must be sought in
the roll pass design (RPD), a principal factor that
delimits process efficiency, product quality and
resource consumption.
4

Intro

• Scientists and engineers search for statistical patterns
hidden within the growing databases.

• A prerequisite for understanding the patterns of rolling
passes is to intelligently translate the process
parameters into appropriate mathematical forms.

• Presently, a variety of RPD algorithms offer differing
predictions, and the practice of RPD continues to
outstrip our theoretical understanding of it.
5

Intro

• Even when the process is developed to a stage when
it delivers acceptable products, roll wear still can
undermine the rationality of full scale industrial runs.

• Rolling substantially depends on the geometry of the
deformation zone, which, in turn, depends on the
geometries of subsequent grooves.

• The whole spectrum of methods (stochastic models,
FEM, slip-line-fields, genetic algorithms etc.) relate
to some mathematical definition of rolling passes. 6

Intro
• This discussion presents examples of generic functions
used to define roll grooves, and the applications of these
analytical forms in RPD for symmetrical long products.

7

Allow me to start by listing a few
well known aspects.

8

Problem specification

• Roll pass design is defined by the pass geometry and a
range of chemo-physical parameters such as roll speed,
bar temperature, chemical composition, cooling rate…

• At the start of the rolling sequence, grooves are
newly dressed and each point along the groove contour
has nearly identical attributes.

• As the series of bars continue to be rolled through, the
grooves wear unevenly and this causes the changes in
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pressure and plastic flow distribution.

• Ideally, hot steel should flow plastically through a

sequence of passes and wear the grooves in a way
that results in optimised productivity, quality, and
yield at minimised costs.

• Any RPD (typically
developed after several
corrections) can
be further improved.

• Two mills roll the same
product using RPD’s
that differ at various
ranges.
10

• The gradual wear of grooves leads to an increasing
frequency of adjustments along the rolling line (i.e. the
production delays) in order to keep the final product
within the tolerances. Ultimately, the rolls are replaced.

11


• Given other the same, grooves can be cut in the rolls
in several ways, without increasing the roll cutting costs.

• In addition, the nowadays capabilities allow for
improving both precision and tolerances in
manufacturing the rolls.

• Previously, RPD was restricted by a motivation to
rationalise the numeric results - round them to less
decimal places and avoid complex curves.
12


• This is in obvious contrast with the modern tertiary
industry standards, where for example the strict
requirements are posed on manufacturing components
such as the mass of rear mirrors on passenger cars.

• In order to extract knowledge from large RPD data
bases (which includes the records addressing the
performance), the roll passes should be translated into
some convenient mathematical form.
13


• As a first approach, a number of candidate functions
were analysed to select a generic function that satisfies
very wide range of simple symmetrical grooves.

• A focus on the cases that have at least two mutually
perpendicular planes of symmetry allows for reducing
the groove meridian to the first quadrant of the
Cartesian coordinate system.
14


• There is a number of possible solutions to this problem,
and a suitable option depends on the type of analysed
rolling series and the purpose of investigation.

• Such generic functions are convenient for a range of
mathematical & computerised analyses, e.g. the
function parameters can be treated as vectors where the
components are extendible to include further parameters
of the rolling process (bar velocity, roll hardness, chem.
compositions, mechanical attributes etc).
15

An example of generic function

a, b, c, d, and e, are parameters.
With regard to the pass geometry, at least three additional
parameters are needed. Often is convenient to define such
parameters as x coordinate of the separation point between
the exit profile and the groove contour, inverse roll radius
at the groove centre, etc.
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17


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a = 77.21749
b = -129.14861
c = 83.19560
d = -22.04599
e = 1.81063; f = 2.8837; g = 5.9255; p = 0.125; ∆y < 0.03 mm
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a = 6.8
b = 0.05626
c = -0.99264
d = 0.08189
e = 0.00792; f = 0.326; g = 9.823; p = 2; ∆y < 0.03 mm
20

Examples of application

The following is a demonstration of how generic function
Eq. (1) can be used to approach RPD tasks related to hot
rolling a square bar with nominal side of 19 mm.
Various simplifications are possible depending on the
purpose of analysis and the observed RPD system.
21


In this case, since the heating furnace, the rolling mill,
and the rolled material grades are identical for the
whole series, the parameters Ki9 to Ki13 can be excluded.
This analysis is restricted to data related to two finishing
grooves used in the same type of rolling mills for rolling
squares of sides between 10 and 20 mm.
22

Analysis is focused on
“diamond” groove
(example shown in
Figure) and “square”
groove.
The quality control
requires obtaining
more sharp edges.
It has been concluded to make a modification in the leader pass
since the finishing “square” groove is deemed to be satisfactory.
23

Roll pass designers
have decided to
introduce curved sides
in the diamond
groove, similar to the
arc of radius 38.5 mm
shown in Figure.

Question is: which value should be selected for this radius?
24

Bearing in mind the sharp edge requirement, the
parameter f can be taken to be approximately equal to
zero, while the parameter p can be excluded from this
analysis.
The fillet radius at the roll collar (at the point g) is
calculated as 0.2W , where W = theoretical width at
the level of roll gap (at y = 0).

25

Although the handbook reference suggests that no
curvature is applied to the diamond groove sides when
rolling squares above 18 mm, an extrapolation of a
generic rule implies that a radius 3.5k = 67.2 mm could
help improving the edge sharpness.
However, we can approach this problem by analysing the
data base obtained by translating the series of relevant
grooves into the parameters of the equation (1).
26

The following data are collected for analogous RPD cases:

27

k = square side at temperatures of the finishing pass, mm
Wn = nominal width (a diagonal) of the finishing square
groove, mm
Wcal = actual width of the square groove at the point of
transition into the roll collar, mm
gk = x coordinate of the point g for the square groove, mm
sk = roll gap (clearance between the top roll and bottom
roll collar), mm
28


29

Hnomr = nominal height of the diamond groove, mm
Wnomr = nominal width of the diamond groove, mm
Wcalr = actual width of the diamond groove at the point
of transition into the roll collar, mm
sr = roll gap, mm
xc = x coordinate of the centre of the circle describing the
arc that forms the diamond groove side curvature, mm
yc = y coordinate of the centre of that circle, mm
R = radius of the diamond groove side curvature, mm
gr = x coordinate of the point g, mm

30

A simple correlation with the square side k, based on the
regression analysis of the data in Table 1
R = regression function (k),
confirms the value of 67.2 mm, the same as suggested
by the generic rule
R = 3.5k = 3.5 ·19.2 = 67.2 mm.
However, the data in Table 1 indicate that for k = 19 mm
the curvature of the diamond groove side disappears.
31

Moreover, the actual values of R depart from the rule
R = 3.5k
with a tendency to grow following a power curve, rather
than the above linear function. So from this observation,
we could expect that the value of R for diamond groove
will be larger than 67.2 mm.
We shall make an estimate for R based on the trends of
the parameters a, b, c, d, and e from the generic function

32


These parameters will be correlated to value k (finishing
square side at temperatures of the finishing pass, mm).
In addition, the intragroup correlations between the
diamond groove parameters will be observed as well.
The parameters Kij for i = N-1 and j > 5 are deemed to
have no effect on R, and are known a priory. These
simplifications are made, because in this demonstration
the sample size is quite small.
33

The above rule R = 3.5k does not take in account the
interaction of R and remaining features of the diamond
groove.
Similarly, most of the features of the diamond groove
are traditionally analysed in an isolation; each feature is
designed with regard to a single counterpart.
On the contrary, in this proposal, a more complete pattern
of groove interrelations is revealed when regression
analysis includes the parameters of Eq. (1).
35


Let us start with observing how of these parameters
change with increasing values of square groove side k:

The parameters b and c are approximately constant:
baverage = 0.06; (standard deviation = 0.008);
caverage = -1.0; (standard deviation = 0.004);

36


a = 0.6247k = 12 ………….……(2)

The coefficient of determination is 0.988, and the F and t
statistics are satisfactory at alpha risk of less than 1%. The
standard error for the a estimate is less than 0.2.
With the larger sample size, a Canonical Variate Analysis
would allow for straightforward capturing relations for the
whole set of variables. In our case, the above choice of
parameters a, b and c will allow for Multiple Regression to
determine the values of the remaining parameters.
37


d = 0.1229-0.024919k+0.03449a = 0.0583 ……….. (3)
The coefficient of determination is 0.88, the F and t test are
satisfactory at risk of less than 1%. The standard error for
the d estimate is about 0.004.
e = 0.0253- 0.0052a0.5- 0.0471d = 0.0045 …..…..… (4)
The coefficient of determination is 0.99, the F and t test are
satisfactory at a risk of less than 1%. The standard error for
38
the e estimate is about 0.0001.


The parameters a = 12.03, b = 0.0585, c = -1, d = 0.0583
and e = 0.0045 are translated into the dimensions of the
diamond groove shown in Figure below:
Note R ≈ 72 mm
instead ≈ 62 mm
g
●

39


The exact x coordinate of the point g is decided by
understanding the lateral spread. By following the backward
design, we analyse the correlation between the spread in the
diamond groove and the parameters of this groove:
Wdiamond - Wsquare = 0.02293(adiamond)2 +201.56ediamond … (5)
The coefficient of determination is 0.81, while F and t test
are satisfactory at a risk of less than 3%. The standard error
for the spread estimate is 0.25 mm.
40


Wdiamond - Wsquare = 0.02293(adiamond)2 +201.56ediamond …. (5)
The fillet radius at the roll collar (at the point g) is
calculated as 0.2W , where W is theoretical groove width
at the level of the roll gap. The smooth transition from 1st
quadrant into 4th quadrant occurs along an arc the center of
which is located at the x axis.

41

Checking for elongation has
revealed that the coefficient
of area reduction is decreased
from 1.2 to 1.1 with using the
new leader groove.

g

●

This means that the potential
adjustments are likely to be
made by increasing the roll
gap.
42

Also, since it should be anticipated that the wear in the
diamond groove is allowed to proceed faster than the wear
in the finishing square groove, the space is made available
for such increases in the diamond grove area.
Finally, if a groove geometry correction by grinding will
become inevitable, the space is made available for the
consequent increases in the diamond grove area.

43

As another example, let us consider a situation when a
manufacturer produces a whole series of square sections
shown in Table 1. In the industrial practice, the members of
the series rarely show mutually equal level of performance
indicators.
Frequently, one or several members are difficult to control
or otherwise show a poor performance.

44


45

In such situation it is rational to analyse whether some of
the groove vectors along the pass sequence stick out of
the trends indicated by the statistical analysis of the
whole assortment. The parameters corresponding to the
square 16 mm do not fit well with the trend lines
corresponding to the complete series.

46

Should the process of rolling this square 16 mm really
be defective, it is rational to attempt a RPD correction by
rectifying the above discrepancies in the groove vector
parameters.

47

The above case analyses provide supporting evidence in
favour of the proposed RPD strategy.
These analyses present the models, while finding the more
reliable estimates must be founded on a larger data base.
An approximate rule for the recommended count of
observations is shown in Eq. (6):
N ≥ 50 + 8z …….. (6)
N = the count of samples,
z = the count of the involved variables.
48

The groove vector statistical analyses can include data base
collected in several rolling mills, as long as all parameters
Kij are recorded.
These correlations are useful in orienting the propitious
boundaries for industrial trials.
The potentials of this strategy will be enhanced when the
roll maintenance data base is added to the sample space.

49


Procedure for RPD optimisation using generic functions

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Conclusions
• Reductions in the natural resource consumption require

technological changes in the large-scale industrial processes.
This prompts for application of knowledge based models to
improve systems such as hot steel rolling mills.

• Industrial and scholarly accumulated databases of rolling

pass schedules can be analysed statistically to extract useful
models.

• Roll pass design strategies can be improved by finding the
patterns in data sets accumulated by the product and tool
manufacturers and users.
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Conclusions
• Special generic functions can be used to enhance analysis
of a broad spectrum of pass geometries.

• Once the underlying knowledge about the RPD is

uncovered it can be used by rolling mill technologists to
calibrate promising trials at the commencement of new mills
and products, to optimise the existing schedules, to define
the emergency RPD routes, for urgent modifications to
compensate for system disturbances, etc.

52

Conclusions
• Anticipated benefits:
- the rolling process will become more stable (more
reliable); adjustments will become less frequent and faster,
- the overall life of tools (rolls) will increase, the depth of
necessary redressing of rolls will decrease,
- the resource consumption will decrease due to less
interruptions to the overall process,
- the productivity, yield and reliability will increase,
- the production costs will decrease,
- the ecological and ergonomic sustainability of the overall
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process will improve.

Conclusions
• The present results encourage hypothesizing that this

strategy can be extended to RPD for wide range of products.

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Conclusions
• An industrial application of the proposed strategy requires
collaboration of the academic and engineering systems with
other institutions responsible for recovering the sustainable
balance.

• Further research is recommended to explore the

possibility of a minimising the count of parameters of the
proposed generic functions and to explore the broader
potentials for RPD optimisations by using the parametric
models.
55

I shall be available at the booth in the foyer during the breaks.
Ich werde auf dem Stand im Foyer erhältlich in den Pausen.
Je serai disponible sur le stand dans le hall pendant les pauses.
Sarò a disposizione presso lo stand nel foyer durante le pause.
I deverão estar disponíveis no estande no foyer durante os intervalos.
Jag ska vara tillgänglig i montern i foajén under pauserna.
我将在休息大厅展位。

56

Thank you for your patience.
Questions please?

57

I shall be available at the booth in the foyer during the breaks.
Ich werde auf dem Stand im Foyer erhältlich in den Pausen.
Je serai disponible sur le stand dans le hall pendant les pauses.
Sarò a disposizione presso lo stand nel foyer durante le pause.
I deverão estar disponíveis no estande no foyer durante os intervalos.
Jag ska vara tillgänglig i montern i foajén under pauserna.
我将在休息大厅展位。

58

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