Feedback control of chaotic circular point sets with arbitrary velocity profile

To simulate general particle motion on the cross-section of a particle laden jetflow by using fractal point sets, a feedback control process is developed to ensure the validity of nonlinear mapping techniques that transform an original fractal point set into the point set with any desired velocity profile. The points are utilized to represent quantitatively functional abrasive particles in abrasive waterjets which are capable of penetrating hard-to-machine materials such as titanium and advanced ceramics. The theoretical framework constitutes one of the most important parts in three-dimensional modeling of particle jetflow machining. Experimental results from cutting titanium and aluminum verify that the model has very good accuracy.