| Summary: | A mathematical lumped model for horizontal operating three axes machine for Friction Stir Welding (FSW) of heat exchangers' tube to tubesheet, is formulated using Finite Element Analysis (FEM) in conjunction with Lagrange's equation formulations. The equations of motion are obtained in matrix form using Lagrange's equation. The system consists of 14 degrees of freedom. The structure's natural frequencies, together with the output motion at two main points, are obtained by solving the generalized eigenvalue problem resulting from the system matrices using both Solidworks (SW) and Matlab. Dynamic behavior is simulated by providing dynamic motion of the same points on the structure under cyclic forces/torques at different frequencies. These studies were performed with the spindle located at the center of the machine frame and enduring traverse loadings. Frequency predictions and displacement responses obtained from lumped model are compared with those provided by FEM and found in excellent agreement.
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