Research On The Aluminum Alloy Profile Extrusion Simulation By Using Finite Volume Method

With the fast development of national economy, aluminum profile products are getting wider employment in various fields. For the aluminum profiles' variant specifications and extrusion dies' fierce working condition due to complex material flow status and the large deformation, the product development and the mould design are more and more important. The traditional product pattern relying on experience design and trial-correct courses can't satisfy the fast development of the aluminum alloy profile product. Under the economic entironment where the efficiency and the quality are the most important factors, the enterprises think much of the improvement of the efficiency of the die design and machining. Reliable and effective numerical simulation methods are required. They can predict the metal flow pattern, including the distribution and the development of the physical fields, such as velocity, stress, strain and pressure, etc. and then forecast the defect that possibly appears, evaluate if the process and mould conductive parameter are rational and if not. These parameters will be amended, and the trial-correct courses wasting time, manpower and money will be avoided on some degree. And then the process and die design will be completed rapidly and rationally, shortening the product cycle. The most popular numerical simulation method in the metal plastic deformation fields is the finite element method based on Lagrangian mesh. But if the Lagrangian based finite element method is used to simulate the extrusion processes with severely large deformations, serious mesh distort and frequent remeshing will happen. The remeshing will bring the waste of the CPU time, volume loss, the distortion of the results and serious error, etc. When the Reduction ratio in area is pretty large, the simulation can't continue because of the severe mesh distortion and calculation error.Compared with Laglanrian based finite element method, Eulerian based finite volume method can avoid mesh distort and remeshing for its Euler mesh, and shows its advantages in simulating bulking forming with large deformations. Commercial software Msc/SuperForge is the only tool based on finite volume method to simulate bulking metal forming processes. But SuperForge is not a software that specially aims at aluminum alloy profile extrusion. Many researchers in the world simulate the aluminum alloy profile extrusion with SuperForge. It was found that the SuperForge has many advantages in simulating process with large deformation such as extrusion over finite element softwares, but the balance of the calculation accuracy and the simulation effective is the bottleneck of the SuperForge software. SuperForge uses triangular facets encapsulating the FVM grid to track the free surface and the wall boundary of the deforming body. When the FVM mesh is pretty sparse, the simulation speed is relative high, at the same time, the simulation results are very coarse, and the serious burr brought by the triangular facets is serious. A thick mesh is required if the improvement of the simulated surface finish is needed. But because the Eulerian background mesh is unit and can't be locally refined at the interested place, improvement of the surface property will bring the increase of the mesh number in cubic way, decreasing the simulation effective.According to aluminum alloy extrusion with large deformation, based on the character of the aluminum alloy during the hot extrusion, this paper aims to study the key technologies of the aluminum alloy profile extrusion simulation by finite volume method, to find suitable and effective methods to build aluminum alloy profile extrusion simulation model by using finite volume method, and introduce the finite volume method and the Euler mesh suitable for large deformation simulation to the aluminum alloy profile extrusion simulation, supplying a simple and effective academic instruct tool to the real aluminum alloy extrusion product.In this paper, the characteristics of the material in aluminum alloy profile extrusion processes are studied carefully, especially the constitutive equation of the metal. The elastic deformation of the processes is ignored and then the material is assumed to be rigid-plastic or visco-plastic material. Isotropic material properties are assumed. The dynamic viscosity is prominently influenced by the equivalent strain-rate and temperature, for the aluminum alloy profile extrusion processes always takes place above the recrystal temperature. So hot aluminum alloy material is described as a non-linear Newtonian fluid material, and the SIMPLE algorithm can be used to iteratively calculate the velocity, pressure fields, and then the temperature is calculated by the energy equation. After that, the dynamic viscosity is updated based on the constitutive equation using the calculated temperature and effective strain-rate.Aluminum profile extrusion includes steady extrusion and unsteady extrusion. The actual extrusion processes is also divided into steady stage and unsteady stage. Because in the industrial production, aluminum profile product is always a continuous processes. The valid extrudate takes shape in the steady stage, further more, when the ratio of the height and the radius is large, the proportion of the steady stage is higher. So the steady flow pattern of the aluminum alloy profile extrusion is studied and simulated by the finite volume method. Combined with the material characters and the constitutive equation, the key technologies of the aluminum profile steady extrusion processes simulation by finite volume method are studied. The three-dimensional discretised forms of the momentum conservation equation, continuity equation and energy conservation equation are obtained. The three dimensional equations and the flow program of the SIMPLE algorithm are given. The method to update the dynamic viscosity of the material in the aluminum alloy profile extrusion is yielded. The convergence criterion is also discussed. Local refinement of the mesh is realized improving the simulation effective, and at the same time, insuring the simulation quality. On the base of above, the code is programmed on Virual C++ plat, and the steady aluminum alloy profile extrusion simulation model using finite volume method is built. Some steady cases are simulated by the model, and the results are compared with those simulated by FEM software DEF0RM-3D and CASFORM, FVM software SuperForge. The comparisons prove the accuracy and the effectiveness of the steady aluminum alloy profile extrusion simulation model using finite volume method.The starting unsteady process before the extrusion reaches its steady state can influence the steady flow and decide the forehead shape and the accumulation of the strain etc., which are the important factors determining if the defects such as bend and craze will happen. To make the simulation model match the real processes of the aluminum extrusion, and reinforce the instruct function of the software to the actual extrusion product, it is necessary to study the change of the physical fields versus the time. On the base of the research of the steady-state flow, the three-dimensional discretised forms of the momentum conservation, continuity equation and energy conservation equation for unsteady-stat aluminum alloy profile extrusion are obtained. The equations and the flow chart of the three-dimensional unsteady SIMPLE algorithm are also got. According to the unsteady flow of the metal, the VOF method which is widely used in the Computational Fluid Dynamics is induced into the catch of the metal free surface. The flowing trend of the metal free surface is simulated factually and good surface finish is obtained. Based on the VOF method, the flowing fields are calculated by a 'part calculation method', that is, the variables on the elements full of metal fluid are calculated by the government equation, the dynamic and kinematic boundary conditions are implemented on the free surface elements, and the air elements are skipped. This 'part calculation method' can improve the calculation efficiency. The 'Moving grid system' is advised to locally used, which can not only solute the calculation domain changing problem rising by the moving of the punch, but also avoid the time waste if all the mesh is changed. The auto-control of the time step is put forward to improve the efficiency of the calculation, based on the stability command of the calculation. On the base of the key technology above, three-dimensional unsteady aluminum alloy profile extrusion finite volume method simulation model is built, and the software is programmed. Several unsteady extrusion cases are simulated to prove the accuracy and the efficiency of the aluminum alloy profile extrusion simulation model by finite volume method.All the above steady and the unsteady extrusion models are build under Cartesian orthogonal grid which can adapted to flow caluculation with all kinds of boundaryes. But when the mesh is corse, the "Stepwise approximation" will introduce error and make the boundary condition treatment difficulty. To make the boundary of the numerical grid match the flowing domain for the convenience of the implement of the boundary condition, fitting the calculation to the actual extrusion process, the body-fitted mesh generation technology is researched, on the base of which, the influence of the grids' non-orthogonal to the conductive term and the diffusion term etc. is studied, the three dimensional discretised forms of the governing equations on body-fitted grid are built. On the base of the VOF method and the moving grid system, combining the influence of the grid's non-orthogonal, the VOF method and the moving grid system technology on the non-orthogonal grid system are built, too. Shear friction model are used on the boundary, and then the velocity boundary condition implement method is brought forward. By these key technologies, the aluminum alloy profile extrusion model by finite volume method on the body-fitted mesh system is built, and the according software is coded, too. Typical steady and unsteady extrusion cases are used to prove the efficiency of the model.Experiment is the most powerful tool improving the accuracy of the simulation. So to prove the accuracy of the aluminum alloy profile extrusion finite volume method model, a set of extrusion dies for aα-shaped extrudate are designed on the base of the extrusion arts and the dies. The experiment is done successfully and the comparing between the experiment results and the simulation ones proves that the aluminum alloy profile extrusion finite volume method model built in this paper is accurate again.