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# EVALUATION OF THE GEOMETRY OF CURVES USED TO REPRESENT THE ISOTHERMS OF WELDED PLATE SURFACES

### Ferreira, Dario Magno Batista; Alves, Antonio do Nascimento Silva; Cruz Neto, Rubelmar Maia de Azevedo; Brandi, Sérgio Duarte;

##### Artigo Completo:

The heat transfer in welding is a phenomenon governed by Fourier equation, and occurs between the weld pool, its neighborhood and boundary conditions involved. It is characterized by high thermal gradients and high heating and cooling rates, which are observed by isothermal distribution and thermal cycles obtained. The isotherms are extremely important as they graphically describe the temperature gradients of heat transfer in all directions. An isotherm of particular interest is the melting temperature, for delimiting the contour of the weld pool, that is, separates the regions of liquid and solid metal. The models most commonly used in the literature allow describing temperature gradients in transient state. Among the models in literature, those developed by Rosenthal for heat transfer by conduction in welding processes in pseudo steady state is emphasized. The solutions of these models combine transcendental functions and special functions such as Bessel modified, depending on the boundary conditions and initial conditions for the model under study. They combine operational welding parameters, physical and geometrical properties of the plate to be welded. To obtain a graph of isotherms is necessary to use complex calculation using inverse functions of the solutions or by a process of calculating the roots of functions, for example. The mechanism will be adopted here. However, in numerical simulations of welding, authors have simplified one isotherm by a pair of ellipsoids. This brings the advantage of computational gain due to its simplicity compared to the Rosenthal model. In this sense, it is proposed to assess the extent of this gain to verify if this simplification is viable for different materials and welding operating conditions. This analysis was done to compare the geometry deviation of the ellipsoid with respect to the analytical solutions. The thermal diffusivity and welding speed were determinant in quantifying the error.

Palavras-chave: soldagem, simulação, isoterma, ciclo térmico, Elipsoide, welding, simulation, isotherm, thermal cycles, ellipsoid,

Palavras-chave: ,

DOI: 10.5151/mathpro-cnmai-0093

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##### Como citar:

Ferreira, Dario Magno Batista; Alves, Antonio do Nascimento Silva; Cruz Neto, Rubelmar Maia de Azevedo; Brandi, Sérgio Duarte; "AVALIAÇÃO DAS GEOMETRIAS DAS CURVAS UTILIZADAS PARA REPRESENTAR AS ISOTERMAS DAS SUPERFÍCIES DAS CHAPAS SOLDADAS", p. 525-534 . In: Anais do Congresso Nacional de Matemática Aplicada à Indústria [= Blucher Mathematical Proceedings, v.1, n.1]. São Paulo: Blucher, 2015.
ISSN em b-reve, DOI 10.5151/mathpro-cnmai-0093

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