Heat Conduction in a body resulting from a moving heat source is of great technical importance and has broad applications in the fields of arc welding, surface hardening, continuous casting and recently in the stir welding under rotating pins and metal softening (FSW). The FSW generates a three dimensional temperature flow field with heat source and the establishment of the heat-conduction equation in differential form is most advantageous even if difficult to be solved in an analytical fashion. There are commercial codes widely used that approximate the differential equation in a finite difference approach or finite elements modelling and solve the temperature flow field under tentative first guess of temperature initial values. The codes are user friendly designed but are also quite general and difficult to use by not trained engineers. A simple analytical solution in the Cartesian coordinate system is presented to solve the energy equation under not steady conditions, in the hypothesis that stir welding proceeds along a fixed direction in space, and heat generation in the point of welding is mainly transmitted by conduction along the metal and it is larger than heat convection to air. If the properties of the material are considered a weak function of temperature and therefore constant, a quantity of heat at a rate Wi is supplied by a point source moving along the x axis with a velocity U. Therefore a moving coordinate system of which the heat point source is the center will appear in reference to the fixed system and the transformation from the variables of the stationary coordinates system to the moving one will generate a quasi-steady form of the heat equation. A simple PC or palmar calculator are then able to solve the equation with Math codes. In this paper, the simple analytical solution is compared with more complex Finite Volume analysis in 3-dimension. The numerical code allows the implementation of the correct boundary conditions. The theoretical and numerical models were validated by means an experimental tests on Al2198 T3 Aluminum sheets, largely employed in aeronautical applications.
Validazione di un modello di simulazione del flusso termico in una giunzione Friction Stir Welded
BUONADONNA, PASQUALE;CAMBULI, FRANCESCO;DIONORO, GENNARO;FLORIS, FRANCESCO;TRONCI, AURELIO
2010-01-01
Abstract
Heat Conduction in a body resulting from a moving heat source is of great technical importance and has broad applications in the fields of arc welding, surface hardening, continuous casting and recently in the stir welding under rotating pins and metal softening (FSW). The FSW generates a three dimensional temperature flow field with heat source and the establishment of the heat-conduction equation in differential form is most advantageous even if difficult to be solved in an analytical fashion. There are commercial codes widely used that approximate the differential equation in a finite difference approach or finite elements modelling and solve the temperature flow field under tentative first guess of temperature initial values. The codes are user friendly designed but are also quite general and difficult to use by not trained engineers. A simple analytical solution in the Cartesian coordinate system is presented to solve the energy equation under not steady conditions, in the hypothesis that stir welding proceeds along a fixed direction in space, and heat generation in the point of welding is mainly transmitted by conduction along the metal and it is larger than heat convection to air. If the properties of the material are considered a weak function of temperature and therefore constant, a quantity of heat at a rate Wi is supplied by a point source moving along the x axis with a velocity U. Therefore a moving coordinate system of which the heat point source is the center will appear in reference to the fixed system and the transformation from the variables of the stationary coordinates system to the moving one will generate a quasi-steady form of the heat equation. A simple PC or palmar calculator are then able to solve the equation with Math codes. In this paper, the simple analytical solution is compared with more complex Finite Volume analysis in 3-dimension. The numerical code allows the implementation of the correct boundary conditions. The theoretical and numerical models were validated by means an experimental tests on Al2198 T3 Aluminum sheets, largely employed in aeronautical applications.
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