Available online at ScienceDirect. Procedia Engineering 150 (2016 )

Procedia Engineering 150 ( 2016 ) 667 – 673

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICIE 2016 doi: 10.1016/j.proeng.2016.07.075

ScienceDirect

International Conference on Industrial Engineering, ICIE 2016

Simulation and Calculation of Temperature Distribution in Roll Fittings’ Guides in Contact with the Rolled Strip

N.Sh. Tyuteryakov ^a, *, R.R. Dema ^a , S.P. Nefed'ev ^a

a

Nosov Magnitogorsk State Technical University, 38 Lenin Avenue, Magnitogorsk, 455000, Chelyabinsk Region, Russia

Abstract

The article deals with the heat exchange model of roll fittings’ guides, the rolled strip and cooling water.

The heat model allows determination of the guides’ temperature both in their volume and on the working surfaces to study the wear process and to develop ways of the roll fittings’ guide wear resistance increase.

To solve the predetermined task, the three-dimensional heat conductivity equation has been derived, as well as the border conditions taking into account the heat exchange peculiarities between the rolled hot strip and the working surface of the guide’s front part, the contact surfaces roughness of the strip and the guide and also water cooling of guide’s non – working surfaces have been determined. The heat conductivity equation was solved using the method of final differentials.

The analysis of calculation results shows that the deviation of calculated temperature values does not exceed 30°ɋ in comparison with those received during the industrial research which indicates quite a high accuracy of temperature calculations with the use of the developed model both at the stage of transient heat transfer in the guide fittings and during the steady process.

© 2016 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the organizing committee of ICIE 2016.

Keywords: guides; rolled strip; heat model; temperature; cooling water

When designing the roll fittings of section mills, conducting of strength calculations, predicting of change parts wear it is necessary to consider the temperature both in their volume, and on the working surfaces. The temperature conditions value of the roll fittings employment permits reasonably to assign methods and intensity of cooling, determine the rational design parameters and wear parts materials. This problem is especially important in the design of the roll fittings for the billets groove-less rolling [1-12]. The guides’ front parts of such roll fittings (Fig. 1)

*

Corresponding author. Tel.: +79049410710 E-mail address: [email protected]

© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of ICIE 2016

are in the gaps between the rolls. Uneven wear of the guides working surfaces leads to distortions of rolls sections, which complicates their further rolling.

Fig. 1. The roll fittings guide for groove-less rolling. 1 - The guide’s front part; 2 - The guide’s reception part.

In order to study the wear process and the development of ways of improving the guide’s wear resistance, a mathematical model of heat exchange between the guide, the rolled strip and the cooling water has been created [8, 10, 13]. In the development of the thermal model it was assumed that the guide front part of the roll fittings is a pyramid with a base size of H0 and H1 (Fig. 2) [9-17]. The length of the guide front part L is equal to the length of the deformation zone l. We placed the onset point in the coordinate axis O lying on the central axis line of the guide’s front part (Fig. 2).

Fig. 2. Geometry of the guide front part of roll fittings.

The initial condition has the following form

( , , )

t x y z t (1)

Then the thermal state of the guide front part can be described by the heat conductivity equation in the Cartesian

coordinate system [2]

2 2 2

2 2 2

( )

ɥ ɥ ɥ ɥ

t t t t a x y z W

w w w w

 

w w w w , (2)

where t

- the temperature of the guide front part (°C); x, y, z - coordinate; a c

O

U - thermal diffusivity (m

/h); Ȝ - coefficient of thermal conductivity of the guide material(W/m · degrees)); c - the specific heat of the guide material (J/kg · degrees); ȡ - density of the guide material (kg / m

).

The boundary condition on the surface CC’B’B (see Fig. 2) in the direction OX:

t 0 x w

w (3)

On the surface DD’A’A, the boundary condition of the 3rd kind, due to washing by cooling water:

' '

( )

g ɫ g

DD A A

t t t

O ^w x D

 

w . (4)

On the surface A’B’C’D’, the boundary condition of the 3rd kind:

' ' ' '

( )

g ɫ g

A B C D

t t t

O ^w y D

 

w . (5)

On the surfaces AA’B’B and DD’C’C:

' '' '

( )sin( )

AA B B g ɫ g

DD C C

t t t

O ^w x D I

 

w ; (6)

' '' '

( ) cos( )

AA B B g ɫ g

DD C C

t t t

O ^w z D I

 

w . (7)

Preliminary calculations showed that the friction between the strip and the guide leads to a slight (6 - 7 °C) increase in temperature of the working surface [15]. Therefore, in the simulation we did not take into account the heat flow resulting from friction.

Considering the thermal resistance of the strip contact and the guide’s working surface with different roughness, radiance heat transfer and inter contact medium [3], the boundary condition in the contact zone of the strip line and the guide’s working surface of roll fittings has been obtained.

During the strip rolling

(

) (

)

k W  W d d W k W  W  W , (8) where k - is the number of the rolled strip k = 0,1,2 ... K

On the surface ABCD there is a boundary condition of kind 4

ɩ k

ABCD k

t t t R ^ O ^w y

w . (9)

During the pause,

(

)

( 1)(

)

k W  W  W   W k  W  W . (10) Upon cooling by water jets on the surface ABCD the boundary condition of the 3rd kind is

( )

ABCD g k g

t t t O ^w y D

 

w (11)

Solution of the heat equation (1) with the accepted boundary conditions was carried out by finite difference method [4, 5].

A rectangular grid was laid upon the three-dimensional workspace (Figure 3)

Fig. 3. The superposition of the grid on the computational domain.

x

˜ i ' x , y

˜ j ' y , z

˜ k ' z , (12) where i = 0, 1, 2 ... N – the number of the point along the x coordinate; j = 0, 1, 2 ... M – the number of the point in

the coordinate y; k = -k2 ... K2 - the number of the point in the coordinate z.

Calculation on one step in time when passing from the p-th time layer to (p+1) th was divided into separate segments. Cleavage diagram or the diagram of alternating directions, at which time step is divided into three parts, resulting in a system of three equations, each of which corresponds to an implicit scheme according to one of the coordinate directions [6]:

1 1 1 1

3 3 3 3

1 1

2 1 2 2 2

3 3 3 3 3

1 1

2

1 3 1 1 1

1 1

1 [ 2 ]

3

1 [ 2 ]

3

1 [ 2 ]

3

p p p p p

i i x i i i

p p p p p

j j y j j j

p p p p p

k k z k k k

T T Fo T T T T T Fo T T T T T Fo T T T

   

 

    

 

    

 

  

  

  

; (13)

where T = T (x; y; z) is the desired temperature function of the coordinates; Fo

^a

x 'W

' ,

a

Fo ɭ 'W

' ^,

Fo a z 'W ' . When solving any of the equations (2) we have a system of linear equations in the form of a tri - diagonal matrix

1 1 1

1 1

k k k

T i   A T  i  B T  i   C D , (14)

where A F

, B  1 2 F

, C F

, D  T

- are permanent

Since each of the equations of the system contains no more than three unknowns to be solved we use the pass method [6].

On the bases of the developed thermal model the program "Thermo guide" for the PC in the language of Visual basic in the Microsoft Excel environment. The program is registered in the State Coordinating Center of Information Technologies, Ministry of Education and Science of the Russian Federation under the number 50200500031 and was used later during the theoretical research and applied calculations [9, 14, 16].

To assess the adequacy of the developed thermal model to real processes of heat transfer in the guide front part of roll fittings the temperature calculation in the guide body at points corresponding to industrial research has been performed [7] (Figure 4). Operating conditions of the guide roll fittings have been simulated on cage ʋ2 of the rolling mill 150 at the JSC "Byeloretsk Metallurgical Plant".

Fig. 4. Calculated and experimental temperature values at the points 1,2,3,4 on the guide front part thickness.

Analysis of the graphs shows that the calculated temperature values differ slightly from the temperature values obtained by direct measurements in industrial research. The maximum deviation does not exceed 30°C, which indicates a high enough accuracy of temperature calculations with the use of the developed model both at the stage of transient heat transfer in the guide fittings, and in the steady process [18].

Using the developed thermal model it is possible to calculate the temperature on the working surface, as well as

in the body and on the guide outside during the steady rolling process at the strip exit and when cooling the guide

fittings by water spray (Fig. 5) [19-20].

Fig. 5. The temperature distribution. a – along the guide working surface; b - in the guide body; c – on the guide outer side.

The strip contact with the upper half of the guide front part is carried out [19].

References

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