Analysis and optimization of cooling channels performances for industrial extrusion dies

Riccardo Pelaccia. DISMIDepartment of Sciences of Methods for Engineering, University of Modena and Reggio Emilia, Reggio Emilia, Italy. Corresponding author: Riccardo Pelaccia. E-mail address: riccardo.pelaccia@unimore.it Marco Negozio. DINDepartment of Industrial Engineering, University of Bologna, Bologna, Italy Barbara Reggiani. DISMIDepartment of Sciences of Methods for Engineering, University of Modena and Reggio Emilia, Reggio Emilia, Italy Lorenzo Donati. DINDepartment of Industrial Engineering, University of Bologna, Bologna, Italy Luca Tomesani. DINDepartment of Industrial Engineering, University of Bologna, Bologna, Italy


Intr Introduction oduction
The thermal control of the hot extrusion process is a mandatory activity in order to obtain sound products, while preserving the production rate in relation to the high temperatures developed for friction and deformation [1,2].
Indeed, an excessive increase of temperatures nearby the bearing zones, where the profile gets its final shape, can lead to surface defects and then to a final product waste. In addition, steep thermal gradients can reduce the service life of tools due to excessive wear and thermal fatigue [3][4]. In this context, the liquid nitrogen cooling of the extrusion die is a widely adopted industrial practice to remove heat in the areas where the highest temperatures are reached as well as to reduce the exit profile temperature [5][6].
The cooling channels are milled in the third plate (backer) surface in contact with the die, while the exit channels are drilled in the die to convey the nitrogen flow to the exit profile surface. Liquid nitrogen removes heat from the tooling set while gaseous nitrogen, at the exit of the channel, covers the profile of an inert atmosphere reducing the oxidation and, to a small extent, the profile temperature.
Even if capabilities of liquid nitrogen systems to significantly increase the production rate in extrusion have been established [7], channel design is still often based on die-makers experience and the performances strongly dependent on many geometrical, thermal and fluid dynamics parameters [8].
If the experimental assessment of the cooling performances is a time and cost-consuming activity, numerical models allow evaluating different design solutions in a relatively short time without the costs of manufacturing. The finite element modelling (FEM) of hot aluminum extrusion process is a yet well-consolidated practice to predict the main output parameters in terms of thermal gradient, extrusion load and potential profile and tool defects [9][10][11][12]; however, only few works deal with the modelling of cooling. In this context, aim of this work is further assessing the potentiality of a 3D numerical model of the extrusion process integrated with a 1D model of the cooling channel, proposed by the authors in a previous work [13], against a more complex industrial case study. The capabilities of the numerical re-design of the channel are also shown with the aim to obtain during the die design stage an optimal cooling solution in terms of balanced thermal field and nitrogen consuming.

Experimental Campaign Experimental Campaign
The industrial profile showed in Fig. 1 was selected for the experimental campaign. The mandrel, the die and the backer compose the tooling set (Fig. 2). The planar cooling channel with a rectangular cross section of 6,1x2 mm (wide x depth) surrounds the profile exit, while eleven transferring holes with 5 mm of diameter convey the nitrogen from the cooling channel to the profile surface. The channel is made in the backer on the face in contact with the die and positioned at 37 mm far from the bearing zones, while the transferring holes are drilled in the die supporting a gas nitrogen cooling of the profile surface and protection against oxidation.   In the uncooled process, the exit profile temperature reached a value of 560°C, while thermocouples T1, T3 and T5 in the die recorded a peak temperature of 518°C, 520°C and 510°C, respectively, lower than that of the exit profile due to the distance of thermocouples of about 15 mm from the bearing zones in the extrusion direction. In the proximity of the welding chamber, thermocouples T2 and T4 registered a maximum temperature of 517°C and 525°C, respectively.
In terms of process load, a peak of 19.1 MN was recorded in the uncooled process without significantly differences from billet 4 to billet 6.
During the extrusion process of billet 8 with 100 % of nitrogen flow rate, the exit profile temperature decreased of 20°C (from 560°C to 540°C), in relation to the effect of the cooling in the die and the small contribution of the gas atmosphere at the profile way out. In this experimental campaign, the liquid nitrogen cooling showed its potentiality in terms of heat removal rate with only a slightly increase of extrusion load. On the other hand, the data acquired by the thermocouples highlighted the limit of the this channel design in terms of balancing of the thermal gradient in the bearing zones. Indeed, the three thermocouples in the die recorded about the same temperature during the uncooled process, while great differences were detected with nitrogen cooling (Fig. 4). In addition, the selected design showed a significantly reduced cooling effectiveness with valve opened lower than 100 %, thus limiting the handling of the nitrogen consuming. The use of FEM for the design of the cooling channel could provide a support to obtain an optimal cooling solution, thus limiting analyses such as thermo-fluid dynamics and thermo-structural problems [14]. In the present work, the code has been used to perform a 3D thermo-fluid dynamics study of the extrusion process integrated with a 1D analysis of the die nitrogen cooling. The 1D modelling of the cooling channel reduces the calculation of the thermal and fluid dynamics variables to the middle line of the cooling path but allows to set the geometric characteristic of the channel section as well as the concentrated pressure drop within the channel. In addition, the heat transfer coefficient is not considered constant along the cooling path [13][14] thus suggesting a reliable evaluation of the cooling efficiency of the channel design combined with a substantial reducing of computational time. In Fig. 5, the generated FE model is shown with the tooling set combined into a single tool to reduce the mesh elements and the billet in the already-extruded configuration according to the pure Eulerian numerical approach. The latter allows to replace the container and the ram by equivalent boundary conditions in terms of thermal and load contributions, thus reducing the number of elements composing the mesh and the computational time. Within the tooling set, the 1D cooling channel was integrated, as showed in Fig. 5b.
For the validation of the numerical model, the experimental stationary data of the sixth billet, for the uncooled condition, and of the eighth billet for the cooled one, were selected. Specifically, in Table 1 are reported the numerical input parameters in terms of initial temperatures and boundary conditions set accordingly to the experimental data. In this model, the hot aluminium was treated as a fluid with high viscosity depended on the share rate and temperature, while the flow stress was modelled with the Sellars-Tegart inverse sine hyperbolic law [15]. In the contact areas between the billet and the tooling set, a sticking friction condition was generally imposed, while in the bearing zones the slip friction condition was used. The thermal properties of the nitrogen were set as a function of pressure and temperature [16], using a high heat transfer coefficient around the boiling point in order to account for the heat removal during the phase change. However, in terms of density, the nitrogen was considered as liquid within the channel.  and in the die, respectively. In the process modelled without cooling ( Fig. 6a and 7a), a slight overestimation of the die temperature (T1, T3 and T5) was observed, while a general underestimation of mandrel temperature (T2 and T4) was found. However, the results reported in details in Table 2 return errors below 3 %, confirming the goodness of the numerical predictions. In terms of extrusion load, the underestimation of 6 % is considerably acceptable. T Table 2. Experimental-Numerical comparison in t able 2. Experimental-Numerical comparison in terms of t erms of temper emperatur ature and load e e and load ev valuation (Billet 6 and Billet 8). aluation (Billet 6 and Billet 8).
In Fig. 8 and Table 3 are reported the numerical results with the 20 % of nitrogen flow rate, that showed an ineffective cooling as emerged by the experimental campaign.
T Table 3.    It can be then concluded that the proposed 1D numerical model allows achieving a solution in a reasonable computational time and the adjustments in channel geometry and process variables can be easily iterated to find an optimal design within the pre-processing stages, perfectly matching with the requirement of supporting the die design phase in an industrial framework.