Fig. 4 — Schematic of the pentagonal probe. Fig. 5 — Schematic of the hexagonal probe. Fig. 6 — A — Model geometry for FSW; B — temperaturedependent 0.2% offset yield strength for AA 2014T6. Modeling offers great prospects in the future for reducing experimental efforts in the development of welding parameters, tool and machine designs, clamping systems, and many other areas. Also, with the large effort currently being made in modeling, it is reasonable to expect a significant return on this investment (Ref. 19). Because of the nature of this approach, the proposed analytical model relies on three major elements — analytic algebra, numerical calculations, and experimental data. The analytic algebra is based on existing research and results but includes some improvements. The algebra is developed for a complete welding tool, involves more dominant parameters in the calculations than in previous models, recognizes more dependencies between parameters, neglects fewer parameters, and has a shorter calculation time (Ref. 19). The numerical method can solve complicated functions that are difficult to be solved by the analytical method. However, a numerical solution is discrete. On the other hand, the analytical method can solve relatively easy functions. Its solution is given by a formula that clearly shows the relationship between independent and dependent variables (Ref. 25). In this paper, a combined approach of both methods is considered. In the first part, an approximate analytical equation for heat generation is developed for different pin profiles. In WELDING RESEARCH the next part, the effect of the different process parameters on the temperature history is shown. In the present work, analytical modeling of different tool geometries such as TR, SQ, PEN, and HEX (all regular polygons) are developed. The next section is divided into four subsections; the first four sections show proposed analytical models for heat generation for the FSW process on different tool pin geometries, then thermal modeling of different pin geometries using Comsol is presented. Later, comparison of all tool geometries in terms of total heat generation and peak temperature generated is presented. The FSW process consists of a rotating tool pin penetrating into the two butt joint positioned plates to be joined and transverse motion to the tool. The shoulder surface heats the plate surface due to tool rotation whereas the pin mixes the material from the front of the pin to the back of the pin due to tool rotation and translation. The following underlying assumptions are made for analytical modeling: • The analytical estimation based on a general assumption of uniform contact shear stress contact is considered. • Weld cycle excludes plunging; first, second dwell, and retract cycles. • Tool inclination angle was not considered. APRIL 2015 / WELDING JOURNAL 117-s A B
Welding Journal | April 2015
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