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Usually there are six stands for the finishing tandem mill, the first three stand are used

call beginnings stand and the last three ones as finishing stand; these mills have four

rolls, two of them are the work rolls and are in direct contact with the strip; being the

steel within a range of 1000 ºC at the mill entry and 800 ºC at the mill exit, and twobackup rolls, these ones having contact with the work rolls.

Pressure applied by the rolls on the slab results in a reduction of 203.2 mm and up to

1.8 mm, according to the customer specification. However, this process is one of the

most expensive ones for the steelmaking industry due to the elements this process

consist on [Ohkomori, 1988].

Hot rolling campaigns of the backup rolls are very long. The wear produced by the

mechanical contact with the work roll, and the temperature and the pressure exerted on

the roll work body as well.

1.1 Wear on rolls for hot strip rolling

Rolls are subjected to a large work volumes, and extreme temperatures as well, and

obviously they require a great strength against cracks and flaws [J.A Schey, 1983].

Considering that the rolls are the most expensive input in the rolling process, it is

important to define what is causing the roll wear, and taking into account the

aforementioned, it becomes relevant to be specific answering the following question, How the

wear of the rolls is generated in the Hot Rolling process? [Chausevich, 1983].

Mechanical properties required by the hot rolling rolls vary, depending on the process

stage in the rolling line; while at the beginning usually the dominant variables are the

high temperature strength and the toughness of the material, at the downstream stages

the abrasion wear strength becomes the most important wear factor; the yield is not

well defined yet, because there are several influence factors, such as mass or hot

rolled strip length produced per millimeters of material used or total of processed

product tons per roll kit per rolling schedule [S. Spuzic, 1994].

1.2 Types of wear on the rolls

Experience has demonstrated that the wear increases quickly after producing a specific

amount of rolled steel; therefore roll change shall be done after some specific

production in order to prevent a catastrophic wear [S. Spuzic, 1994], for that reason it is

needed to identify the processes which are wearing out these elements, which are

cited below:Abrasion: This element is one of the governing components; it is included in the total

of the wear during the process [Ginzburg, 1989]. Having a presence as scales of high

hardness oxide and low elasticity on the hot steel surface, we can usually think of

abrasion as two or three wear bodies [S.E Lundberg, 1993] [Gahr, 1987]. We may

expect that the roll deterioration be important, because micro-cuts, micro-fatigue and

micro-cracks are formed, which will damage the rolled steel quality [Ginzburg, 1989],

and this wear depends on the shape and hardness of the abrasive particles, producing

deformations, originated by a micro-cut or elasticity on the surface and in the inside

layers of the roll by the contact, resulting as a consequence, the formation of cracks

[Jahanmir, 1981].

2



Figure 1. Chart showing the rolling loads and the fundamental principle of the rolling

process.

Continuous rotation of the rolls makes that a compression force acts in a repeated way

on the contact surfaces between the work rolls and the backup rolls. This causes that a

contact fatigue occurs, which after a certain work period produces deformations on the

roll surface zones [Nakagawa, 1975].

In the case of the work rolls, fatigue does not represent a problem, because the surface

wear caused by the reducing high loads and the direct contact with the high

temperature metal slabs make that the mill schedule be relatively short. Normally, a

rolling schedule for these rolls varies from 6 to 10 working hours, depending on the

rolling variables at each particular mill.

The surface of the backup rolls are not in direct contact with the slab, however, thedirect contact with the work roll generates a wear which is relatively small compared

with the one caused on the work roll. Because of this the campaigns of the backup rolls

are longer than the ones of the work rolls, being able to be in a stand up to 28 days,

having only short mill shutdowns for a surface inspection.

When there is no wear control, the mechanical fatigue of the backup roll can generate

small micro-cracks which could cause a severe damage. In this case, it is necessary to

remove the defect, applying a surface machining (grounding), however this process

reduces considerably its useful life and affects its performance. This is particularly a

serious matter when you have in mind that the costs associated with the rolling rolls are

among the main expenses in a steelmaking facility, because they are componentsmanufactured with forged steel and its structure has high alloy content [Ohkomori,

1988].

3 DESIGN METHODOLOGY

Work methodology for this research is shown in Figure 2, where variables which affect

the performance and wear of the backup rolls in a hot strip tandem mill are identified;

there is also a comparison with other research works and the basic concepts of the

theory of Hertz [K.L Johnson, 1985] and Archard [R.D Arnell, 1993] are used. As a

result, the following supported mathematical model is proposed.

4



Figure 2 – Methodology and technique of the design

3.1 Mathematical Modeling

Most of the existing wear models use a series of analyzed variables and empiricalcoefficients developed along years of experience, however, for this analysis the following

variables have been considered to be analyzed:

• Number of rolling passes

• Number of rolling stands

• Rolling loads

• Roll body width

• Total sheet length

• Contact area

• Work roll diameter

• Backup roll diameter

• Work roll mechanical properties (elasticity and hardness modulus)• Backup roll mechanical properties (elasticity and hardness modulus)

• Wear coefficients

Rolling roll hardness is the variable measured directly in the working place, the rest of

the variables consist on data logging in the facility, specifically in the rolling mills, process

control, quality control and grounding shop; other variables are not considered, such as

mechanical vibration and horizontal loads, because their impact on the mill roll wear are

not significant.

The elastic contact theory established the Hertz equations for non-conforming surfacesdue to the contact pressure between them [K.L. Johnson, 1985]. These equations are:

5



3

1

*4

3

=E

PRa (1)

3

1

23

2*

20

6

2

3

==

R

PE

a

P P

π π

(2)

where:

a = Contact arc length

P = Normal load

R = Relative curvature radius

*E = Effective elastic modulus

0P

= Maximum pressure

The Relative curvature radius, R, is defined by the following equation:

21

111

RRR+= (3)

Where R1 and R2 represent the radii of each one of the spheres or cylinders which are on

contact, as shown in Figure 3.

Effective elasticity modulus, *E , is defined by the following equation:

2

2

1

1

*

22

111

E E E

ν ν −+

−= (4)

In the abrasive wear equation, applying the theory of Archard [R.D. Arnell, 1993], the

following formula has been established:

H

LxK V abr = (5)

6

R2

R1

Figure 3. Contact area considering two surfaces

cilíndricas



where:

V = Removed material volume

abr K = Abrasive wear coefficient

L = Applied load

x = Traveled distance

H = Hardness ratio

If equation (5) is applied to the rolling process, removed material volume from the roll

is the worn material and it is equal to the contact area between both rolls times the

worn height, Ah . Applying this principle, and solving the formula for the worn

material height h , the formula shall be as follows:

HA

LxK h

abr =

(6)

Considering thatA

Lrepresents the pressure of a load on a given area, 0

P can be

replaced in the equation (6), considering that we are looking for the maximum contact

pressure; thus, equation (6) shall be as follows:

H

xP K h

abr 0=

(7)

Replacing equation (2) in equation (7), the formula shall be as follows:

H

xR

PE K

H

xR

PE K

h

abr abr

3

1

22

2*3

1

23

2*66

=

=π π π

(8)

Figure 4 illustrates the mechanical contact between the two rolling rolls, where we

can appreciate that the contact area is aW A = . Applying the elastic contact theory

of Hertz [K.L Jhonson, 1985], where the area establishes a relative curvature radius

R, and where the contact area is 2RA π = , and considering besides the contact

distance a , we can substitute in equation (8) by the contact area established

previously for the rolling process, resulting the following equation:

H

xaW

PE K

h

abr

3

1

2

2*6

=π

(9)

where: =W Roll body width and =a Contact arc

7

Figure 4.- Representation of the mechanical contact

aW



D

DL

aW

PE K

abr

13

1

2

2*6

π

Rolling process is a process where the higher hardness material is rotating and

the basic equation of wear was generated from a model where the hard material is

moving along a straight line but without turning, therefore, in order to develop the

model, equation (9) shall be multiplied times a factor that associates the contact arc

between the two cylinders, where D1 is the diameter for the work roll and D2 the

diameter for the backup roll, which is2

1

D

D, in such a way that the equation (9) shall

be as follows:

(10)

Considering that the total length of the strip identified as L is equivalent to the

traveled distance x , and applying, in the contact area of the two rolls, the same

criteria used to develop the equation in the contact area of the slab with the rolls, the

equation (10) shall be as follows:

(11)

Unit value of the height the rolling roll is worn per each processed slab can be

calculated with the equation (11), however, a rolling campaign consist on several

rolled slabs, changing according to the production program; so, the total value of the

wear per rolling campaign corresponds to a summation of values accumulating the

wears from the first slab and up to an indefinite number of slabs, n , therefore, the

final equation of the mathematical model would result as follows:

8

H

D

Dx

aW

PE K

h

abr

2

13

1

2

2*6

=π



(12)

where:

abr K = Abrasive wear coefficient

a = Length of the contact arc

P = Rolling load (Rolling force)*

E = Effective elastic modulus

L = Total length of the strip

H = Hardness ratio

=W Roll body width

=1

D Work roll diameter

=2

D Backup roll diameter

4 RESULTS

As a result of the research of this article, we were able to identify the different types of

wear in the Tandem Mill backup rolls at the hot rolling processes. Main variables that

have influence in the wear phenomenon (number of rolling passes, number of stands,

contact area, work roll diameter, backup roll diameter, mechanical properties of the

rolling rolls, wear coefficients and ratio of hardness between rolls) were detected, and

variables that do not have any impact or influence in this phenomenon due to their poor

relation or significance (vibration and horizontal rub or friction) were discarded.

The mill consists on 6 stands, using 2 backup rolls and 2 work rolls each. The workrolls from the stands 1 to 3 are called roughing rolls and they have the same

mechanical properties, while the work rolls from the stands 4 to 6 are referred as

finishing rolls and they have also the same properties. In the case of the backup rolls,

in the stand 1 the backup rolls are made of cast steel, while in the stands from 2 to 6

the material is still steel, but it follows a forge process. In Table 1 we can see clearly

this description of applications of the materials of the rolls, and their own mechanical

properties as well.

Material

Hot MillApplicati

on

YoungModul

us(Mpa)

Poisson

Modulus

F1 F2 F3 F4 F5 F6

CastSteel Back Up

Roll195 0.290

ForgedSteel 200 0.300High

Chromium

Work

Roll220 0.295

Indefinite Chill 180 0.280

Table 1 - Main alloys of the rolls used in hot rolling process, and their mechanical

properties as well.

9

∑

=n

n

abr

H

D

DL

aW

PE K

h

1

2

1

1

3

1

2

2*6

π



The methodology and the design technique for the making of the mathematical model

was a suitable one, because it enables us to verify the variables used in other

researches using the Archard theory [R.D Arnell, 1993] in order to apply it to the rolling

process, allowing us to understand the behavior of other models and the existing

solutions related to this subject of material removed by contact between materials and

wear.

In the making of the model, it was considered that during the rolling process, the harder

the material the higher the wear produced in the rest of the materials, this same

situation is found in relation with the contact arc between the rolls, that is why the ratio

of temperatures and the hardness of the rolls is taken in the field, in order to consider

the warm-up experienced by the rolling rolls due to the influence of the heat

transference provided by the slab.

The model establishes the total value of the wear during the whole rolling cycle or

schedule, considering the summing up of the accumulated values of the wears for thewhole number of used (rolled) slabs. This wear ratio during all the rolling process is

directly related to the mechanical fatigue of the backup rolls, which at a certain level of

overload may generate micro-cracks that affect the strip production process.

5 DISCUSSION

Mathematical Model use is a fundamental tool in prediction making in production

processes. In this particular case of hot steel lamination where support rolls are

submited to strong workloads, consideration of all variables involved in its opreation

and wear is very important. This investigation only consider variables described in the

proposed mathematical model formulation at the begining of this text, which are ones

that impact support rolls wear process huge. It is relevant to consider accumulative

wear in each lamination campaign according to order production specifications.

6 CONCLUSIONS

Operational variables in the hot rolling process depend on the stand number, e.g. in the

roughing stands, strip reduction percentages are higher, requiring larger rolling forces,

even when the strip temperature is higher and there is higher plasticity. This variation

can also be observed in the calculation of the variables considered in the mathematical

model, therefore is coherent to think that the wear value obtained at the end of the

rolling schedule will have a variation among the different mill stands; this hypothesis

can be verified with the results obtained in Table 1.

The developed mathematical model allows to know and assess the performance of the

rolls at the mill, to make a prediction of the wear, and in this manner to make suitable

decisions for the right equipment operation, preventing finished product rework

because of the quality, or damaging the equipment and tooling, which are attributed to

accidents caused by excessive wear in the rolling rolls.

This mathematical model describes in precision support roll wear process behavior andoffers total amount in milimeters of wear at the end of a lamination campaign in each

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support roll. As we can see in table 2, changes in values of variables considered in this

model have effect in roll wear calculations.

By calculating wear amount suffered in support rolls, we are offering an alternative in

maximizing total life cicle of this rolls.

As a future work the authors pretend to use the model with computational algorithms to

calibrate and improve the precision of the results.

REFERENCES.

[1] R.D. Arnell, P.B Davies, J. Halling, T.L Whomes, Tribology, Principles and DesignApplications, [M] The Macmillan Press Ltd., Springer – Verlag Nueva York, EstadosUnidos de America, 1993, p. 54 and 71.[2] M. Chausevich, Rolling of Metallic Materials, [J] Veselin Maslesa, Sarajevo, 1983,30, p1-2.[3] R.B. Corbett, Rolls for the Metalworking Industries, [M] Iron and Steel Society,

Warrendale, PA, 1990, p. 273.[4] V.B. Ginzburg, Steel Rolling Technology, Theory and Practice, [M] Marcel Dekker,New York, 1989, p. 505.[5] S.Jahanmir, in N.P. suh (ed.). Fundamentals of tribology Proc. Int. Conf., [M] MITPress, London, United Kingdom, 1981, p. 455.[6] K.L Johnson. Contact Mechanics. [M] Cambridge University Press, Cambridge,United Kingdom, 1985, p.36-53.[7] S.E. Lundberg, The Influence of rolling temperature on roll wear, [J] Journal of Materials Processing Technology, Elsevier Amsterdam, Netherlands,1993, 36, p 273.[8] Nakagawa M.A, Consideration and decision of suitable regrinding amount of back-up roll for 4-High mills, [J] Hitachi Review, 1975, 33, p 467-472[9] Ohkomori, Cause end prevention of spalling of backup rolls for hot strip mill, [J]

Transactions of the ISIJ, 1988, v. 28, n. 1, p. 4[10] J.A Schey, Tribology in Metalworking – Friction, Lubrication and Wear, [M]American Society for Metals, Metals Park, OH, 1983, p.249 and 312.[11] A. Suarez, J. Velez, Study on wear proposed by Archard, [J] Redalyc, 2005, 72, P28[12] S. Spuzic, Wear of hot rolling mill rolls: an overview, [J] Elsevier, Amsterdam,Netherlands, 1994, 176, p 264.[13] R. V. Williams and G.M. Boxall, Deterioration in hot strip mills, [J] Journal of theIron & Steel Institute, 1965, 203, p 369–377[14] K- H Zum Gahr, Microstructure and Wear of Materials, [J] Elsevier, AmsterdamNetherlands, 1987, 90, P 253-261

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