Journal of MOHAPATRA Scientific & Industrial et : NUMERICAL Research SIMULATION OF ALUMINUM BAR CASTING FOR WIRE ROD PRODUCTION Vol. 69, December 2010, pp. 913-918 913 Numerical simulation of aluminum bar casting for wire rod production S P Mohapatra 1, S K Sahoo 2 *, S Nanda 1, P Hembram 1, A Palchaudhary 1 and S C Patnaik 3 1 Research and Development Department, Smelter Plant, NALCO, Angul 759 145, India 2 Department of Mechanical Engineering, NIT, Rourkela, 769 008, India 3 Department of Metallurgical & Materials Engineering, IGIT, Sarang 759 146, India Received 09 March 2010; revised 13 October 2010; accepted 15 October 2010 In a continuous casting of wire rod production, a cast bar, which is formed in a rotating wheel mould, is subsequently rolled by a set of rolls to form wire rod. To improve fundamental understanding of wheel-belt continuous bar casting process, a two dimensional transient thermal model has been formulated based on finite element method. Temperature of cast bar predicted by model has been verified by actual temperature measurement during casting at different operating conditions. Simulation results show the influence of various operating parameters on temperature distribution of cast bar. Keywords: Continuous casting; Finite elements method, Simulation, Solidification, Temperature distribution Introduction Production of aluminum and steel billets, bars, and slabs by continuous casting is receiving increasing attention, due to its significance in processing of steels (high productivity, good quality and low cost). Efforts have been made to achieve a better understanding of transporting and solidifying processes of liquid metal pool in a continuous casting mould 1-3. In a Properzi or Southwire process of casting (Fig. 1), a copper mould of trapezoidal or rectangular cross section is mounted on a rotating wheel, into which liquid metal is poured. Berg & Fredriksson 4 demonstrated an experimental measurement method for heat transfer coefficients for pure copper wire casting in Southwire process. Lindholm et al 5 measured temperature in rotating wheel and found appropriate boundary conditions. Liu et al 6 presented temperature profile of belt and wheel for dendrite arm spacing, but bar temperature has not been measured. Ju et al 7 determined temperature profile of non-ferrous metal wire rods during continuous casting of stationary mould. Shi & Guo 8 simulated casting geometry and processing parameters to study solidification pattern of wire rod. This study presents a mathematical model to calculate temperature field in bar, wheel and belt using thermal transient analysis with phase change for continuous casting of bar. *Author for correspondence E-mail: sks@nitrkl.ac.in Experimental Section Model Development Cross section of copper mould (shape, trapezoidal; top width, 70 mm; bottom width, 35 mm; height, 55 mm; and corner radius, 10 mm) with belt and metal has been considered with following assumptions: i) System is in steady state; ii) There is negligible change in density with change in phase (For numerical purposes, density was assumed to be same in both phases); iii) Materials were considered to be isotropic; iv) Heat is removed predominantly in transverse direction and conduction along axis is negligible; v) Finite slice of melt, mold and belt move along periphery at same speed as casting rate.; and vi) Radiation effect had been neglected. 2-D time dependent heat conduction equation for heat transfer in a rectangular Cartesian coordinate system can be expressed as T T T ρ ( T ) c( T ) = k ( T ) + k ( T ) + Q t x x y y (1) where x = strand width, y = strand thickness,?(t) = density (kg/m 3 ), k(t) = thermal conductivity (W/mK), c(t) = specific heat (J/kgK), Q = Latent heat source (J/ m 3 ), T = temperature (K) and t = time (s). Latent heat, generated during phase change between liquids and solids temperature, is expressed as
914 J SCI IND RES VOL 69 DECEMBER 2010 metal entering the wheel Bar Mould Guess heat transfer coefficients at mould surface Numerically calculate temperature profiles in ansys 0 O 83 O Compare the calculated temperature with measured data Q bar leaving the wheel = ρ (T)sL fs t (2) where L = latest heat of fusion (J/kg), fs = solid fraction and?(t) s = density of solid (kg/m 3 ). For simplification of Eqs (1) & (2), enthalpy formulation 9 is used as H ( T ) t = C ( T ) ρ (T)s T ρ (T)sL t fs t (3) where H(T) is enthalpy (J/m 3 ). Finally, heat conduction can be written as H ( T ) t 227 O Fig.1 Schematic diagram of casting wheel T = k ( T ) x x 200 O T + k ( T ) y y (4) Boundary Conditions On mould surface, where mould contacts cooling water, T k ( T ) s = h eff ( T s T a ) n 150 O (5) where, h eff is effective value of heat transfer coefficient at mould surface, which is obtained from inverse method, by using measured temperature values of mould and bar at exit, T s and T a are mould surface and ambient temperatures, n is normal and s is surface for 0-227 of wheel rotation. As belt temperature could not be measured, heat transfer coefficient between belt and Are errors small No enough Yes Heat transfer coefficient at ingot surface Fig. 2 Flow chart of inverse calculation water was assumed to be a uniform value, 2000 W/m 2 C. A uniform effective heat transfer coefficient was selected so that temperature of bar after it has become homogeneous would be correctly predicted by the model. At t =0, T = T o, T o is initial metal(pouring) temperature. Numerical Simulation Ansys software based on Finite Element Analysis (FEA) is used to compute development of temperature field in bar, wheel, belt during casting and temperature profile of bar alone as it leaves mold and enters rolls. Model geometry moved along wheel at the speed of casting and experienced cooling along its path. Air gap due to shrinkage between mould & metal and between metal & belt are accounted by incorporating reduced thermal contact conductance coefficient 6. Effect of fluid flow has been accounted by means of an enhanced thermal conductivity value (700 W/mC) in liquid state 9,10. Inverse method of calculating boundary condition was adopted from an optimization program based on algorithm (Fig. 2). Similar use of inverse method has been repeated 11,12. Time taken by bar to reach roll entry point after exit of wheel at 1.96 rpm is 114.0 s. Heat loss is due to natural convection and heat transfer coefficient between bar and surrounding is chosen to be 25W/m 2 -C. Mould parameters and casting conditions used in simulation are as follows: pouring temperatures, 705 & 730 C; RPM of casting wheel, 1.96, 2.0 & 2.1 rpm; diameter of casting wheel, 1820 mm; thickness of steel belt, 1820 mm; thickness of steel belt, 3 mm; cooling water pressure,
MOHAPATRA et al : NUMERICAL SIMULATION OF ALUMINUM BAR CASTING FOR WIRE ROD PRODUCTION 915 Temp, o C a) Table 1 Material properties used in the model Temperature Enthalpy Thermal C 10 9 J/kg conductivity W/m C 0 0 206 100 int 206 300 int 201 500 int 194 634.5 1.68 250 658.5 2.76 700 695 int 700 700 int 700 1000 62.2 700 int: linear interpolation Temp, o C b) Fig. 3 Temperature profile at different rpm of: a) cast bar; and b) core 4 kg/cm 2 ; heat transfer coefficient, 2200 W/m 2 C; and ambient temperature, 32 C. On wheel of 1.96, 2.0 and 2.1 rpm, residence time of bar is 19.3, 19.0 and 18s respectively. Material used for analysis is conductor grade aluminium (Table 1). Total domain of interest was discretized into 2178 number of four different kinds of elements (surface, target, plane and contact elements). Elements could be able to represent whole domain accurately with no discontinuity. Convergence of solution was based on Newton-Raphson method with a tolerance of 1.0e-8. There were total 4793 nodes. Material property of belt and copper mould were kept constant. Minimum time step chosen for program is 0.01 s. Results and Discussion Simulation was carried out with varying process parameters to study effect on solidification profile. Temperature profile in cast bar (Fig. 3a) and core (Fig. 3b) depict a steady reduction in temperature along entire length of bar computed at different angle of wheel rotation. Varying slope of both curves is due to different cooling rate taking place on surface than inside the core. This is in agreement with reported 13 studies. Core metal temperature is critical as crack may develop in the bar of low ductility alloys at exit of wheel because of change of curvature. To verify feasibility of numerical simulation, computing results were compared with experimental measurements. Temperature of cast bar at exit of mould was measured at three different rpm (Fig. 4). Measured values compared well with computed values. Temperature of mould at 3 predefined points (150, 200 & 227 ) of wheel rotation was measured at 1.96, 2.0 & 2.1 rpm (Fig. 5). Temperature profile of bar at exit was also measured through thermography (Fig. 6). Higher initial temperature of metal will prolong solidification time of casting because of more heat to be removed. Entire thermal history of bar and metal core temperature till entry in to rolls at 1.96 rpm (Fig. 7) indicates that center of bar solidifies before wheel exit, which ensures safe operation. Operating beyond 1.96 rpm needs further adjustment of other operating parameters like cooling water pressure or temperature. Simulation with different casting speed and pouring temperature was done to find out influence of these parameters on cast bar temperature. Sensitivity of bar temperature is observed more pronounced for a change in casting speed (Fig. 8) than pouring temperature (Fig. 9). A linear regression model is formulated to predict bar temperature at different casting speeds and different pouring temperatures (at water pressure = 4 kg/cms and water temp. 24 C), at exit of wheel as well as at entry of rolls as
916 J SCI IND RES VOL 69 DECEMBER 2010 Fig. 6 Thermography result of cast bar at wheel exit Temp, o C Bar temperature, o C Surface temp, o C Mould temp, o C Fig. 4 Measured vs calculated cast bar temperature during wheel exit at different rpm Fig. 5 Measured vs calculated mould temperature during exit at different rpm Time, s Fig. 7 Thermal history of bar and metal core from pouring point to entry to rolls at 1.96 rpm Speed, rpm Fig. 8 Bar temp vs casting speed (pouring temperature, 705 C)
MOHAPATRA et al : NUMERICAL SIMULATION OF ALUMINUM BAR CASTING FOR WIRE ROD PRODUCTION 917 650 630 610 590 Surface temp, o C 570 550 530 510 490 470 450 1.9 2 2.1 2.2 2.3 2.4 RPM Fig. 10 Operating window for casting Bar temperature, o C 590 535 530 525 520 515 510 505 500 495 490 660 690 700 710 Pouring temperature, o C 720 Fig. 9 Bar temperature vs pouring temperature of metal (1.96 rpm) Bar temperature at wheel exit = 530+ 73.29 x (RPM- 1.96) + 0.431 x (Pouring temp. 705 C) Bar temperature at roll entry = 503+ 78 x (RPM- 1.96) + 0.5 x (Pouring temp. 705 C) Model has been validated by experimental measurement of cast bar temperature. A casting operator can instantly predict cast bar temperature for prevailing operating conditions without further simulation study. Machine is desired to run within a limiting temperature of 545 C at wheel exit and 515 C at roll entry in a spread of + 10 C for consistent product quality. An operating window for caster can be constructed (Fig. 10) to fine tune the operation for a desired temperature. It is evident from the graph that pouring temperature needs to be reduced to run machine beyond 2 rpm. Higher the speed of casting, higher is the mill entry temperature and effect is more pronounced beyond 2 rpm. Elongation can be increased by increasing casting speed or temperature of cast bar entering in to set of rolls. Casting speed, at which rolling is performed, is decreased to reduce temperature, which enhances ultimate tensile strength (UTS). Conductivity of wire rod mainly depends on metal chemistry; however, it is also influenced by mill entry temperature. Hence, quality of rod can only be obtained from an optimum casting speed at a particular set of operating conditions. Conclusions A transient thermal model based on FEA method is formulated to investigate heat transfer behaviour of continuous casting of cast bar for production of wire rods. Temperature profile of cast bar and mould measured during experiment compares well with calculated values. Model can be used to predict mill entry temperature for different alloys and at different operating recipes. Casting
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