EuroWire November 2019

Technical Article

After ten passes of rolling, the temperature of the copper rod decreases greatly, and columnar crystal copper slab becomes equiaxed crystal copper rod. Continuous non-twist rolling greatly improves the production efficiency of copper rod. The copper rod hot rolling process is in the state of large deformation, high temperature and high strain rate, which belongs to a highly coupled thermal-mechanical non-linear problem. Considering the variation of the temperature field, stress-strain field and the law of interaction between temperature field and stress-strain field, the deformation process of copper rod during continuous rolling can be described more accurately. The Johnson-Cook model is used to describe the deformation behaviour of copper rod under large deformation, high strain rate and high temperature rolling [6] . where σ , ε are flow stress and equivalent strain; , are strain rate and reference strain rate; A, B, C are yield strength at strain rate, power pre-exponential coefficient and strain rate sensitivity coefficient; m, n are temperature sensitivity coefficient and work hardening coefficient; and T, T r , T m are reference temperature and melting point of copper rod. Mises yield criterion is used to describe the deformation behaviour of copper rod under thermo-mechanical coupling with the help of the Lagrange deformation displacement formula. The stress-strain field and temperature field of deformation are regarded as independent systems [7] . ! ε ! ε 0 ▲ ▲ Equation 3 σ = A + B ε n ( ) 1 + CLn ! ε ! ε 0 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 1 − ⎡ ⎣ ⎢ ⎢ T − T r T M - T r ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟ m ⎤ ⎦ ⎥ ⎥

Copper billet

Tundish

Idler wheel

Casting wheel

Pressing wheel Copper strip heater

Tension wheel

Tension adjusting mechanism

▲ ▲ Figure 1 : The structure diagram of a five-wheel casting machine system for SCR

Roughing

Finish rolling

Copper rod 50.27mm 2

Copper billet 3,800mm 2

▲ ▲ Figure 2 : Structural chart of hot continuous rolling mill

of convection during the constant speed rotation of the crystallisation wheel to form high temperature copper billet. The crystallisation wheel is induced by a demoulding device and subsequent bridge guide wheel. After edge cutting, the crystallisation wheel enters the rolling mill system. Thus the continuous casting of ‘casting-cooling-demoulding’ can be realised. In the solidification and crystallisation process of hot continuous casting copper liquid, casting temperature, casting speed, casting angle and heat transfer coefficient are important parameters affecting the crystallisation quality of slab. The theoretical model of slab forming is established considering the influence of process parameters. Differential equation of heat conduction in crystal cavity [5] :

There are momentum convection, inter- dendritic flow and flow with the mould in the solidification process of copper liquid. The differential equation of turbulent kinetic energy of copper liquid is established.

⎤ ⎦ ⎥ ⎥

⎡ ⎣ ⎢ ⎢

⎞ ⎠ ⎟⎟

⎛ ⎝ ⎜⎜

∂ ( ρ u i

k )

∂ k

∂ ( ρ k )

µ i σ k

µ i

∂ ∂ x

+ G

− ρε + D +

k

∂ t +

=

µ i

+

k

∂ x

K

∂ x

i

i

i

p

▲ ▲ Equation 2

Where k and ɛ are turbulent kinetic energy and turbulent dissipation rate; µ i and f i are viscosity and turbulence parameters; C i , σ k , σ ε , c µ are K – ε model constant. 2.2 Deformation analysis of copper rod in hot continuous rolling The hot tandem rolling mill adopts ten Morgan two-high cantilever tandem rolling mills arranged alternately (Figure 2 ); each stand drives independently and the rolling speed is automatically controlled by the signal provided by the caster. The copper billet is bitten automatically after entering the rolling mill, and ϕ 8 mm copper rod is formed after rolling through the roll system of each stand, controlled by ellipse-circular pass system ( Table 1 ).

⎧ ⎨ ⎪ ⎪

M T ( ) ∂ 2 U ∂ t 2

+ D T ( ) ∂ U

∂ t + K T ( ) U = F

C T ( ) ∂ T

⎩ ⎪ ⎪ ▲ ▲ Equation 4

∂ t + H T ( ) T = Q + ʹ Q

∂ T

( λ ∂ T ∂ x

( λ ∂ T ∂ y

∂ ∂ t

∂ ∂ y

ρ c

)+ Q

) +

∂ t =

Through and analysis of billet forming and deformation mechanism of hot continuous rolling copper rod in the continuous casting and rolling process, its technological principle was discussed, and this laid a foundation for numerical simulation. theoretical modelling

p

▲ ▲ Equation 1

Where c p and λ are specific heat capacity at constant pressure and thermal conducti- vity.

▼ ▼ Table 1 : Analysis of relevant parameters of hot continuous rolling

1H

2V

3H

4V

5H

6V

7H

8V

9H

10V

D k /mm 295.89 282.00 197.69 196.59 206.75 204.34 208.74 205.43 206.86 206.78 n /r·min -1 22.11 44.06 101.99 169.19 257.56 401.19 611.11 819.17 1,189.95 1,574.51 Z/% 34.21 47.20 39.39 40.00 37.50 35.00 35.90 24.00 31.58 22.66 δ 1.52 1.89 1.65 1.67 1.60 1.54 1.56 1.32 1.46 1.29

* Dk – Working diameter, n – Roll speed; Z – Section shrinkage; δ – Elongation coefficient

52

www.read-eurowire.com

November 2019