Phase space analysis of friction stir weld quality

A plot of the y feedback parameter values versus its derivative defines a trajectory for a dynamical system that appears to be an indicator of weld quality. The ideal trajectory for the dynamical system is defined by the spindle frequency and is characterized by repeated orbits in an elliptical shape. The number of points in each orbit is also defined by the spindle frequency, and each orbit, or sequence of orbits, can be analyzed to determine the stability of the system during a weld. The orbits in phase space of welds without metallurgical defects tend to remain within a neighborhood surrounding the ideal trajectory while welds containing defects produced more variable orbits. Calculation of Lyapunov exponents for the dynamical system and analysis of the Poincare map generated by successive orbits were evaluated for their ability to accurately predict weld quality from the phase space trajectories. The Lyapunov exponent shows promise as an indicator of weld quality in certain situations, but the Poincare map approach appears to provide a more flexible, and more computationally efficient, method for predicting the presence of metallurgical defects.