Nonlinear modeling for adaptive suppression of axial drilling vibration

Vibrations developed during drilling present challenges in an array of industries including mechanical, medical, structural, and oil extraction. Velocity weakening, intracranial vibrations, large amplitude standing pressure waves in material cavities, and failure of drill strings are prominent issues among these fields. Stick-slip (torsional) and bit-bounce (axial) vibrations have been found to be particularly problematic in precision drilling jobs such as machining to tight tolerances, dismantling vibration-sensitive devices, and surgical work. Current technologies to detect and suppress systematic vibrations have several shortcomings including malfunctioning, complete failure, complexity, and high power consumption. This paper proposes a method to suppress vibrations of drilling material surfaces using adaptive positive position feedback (APPF) control for efficient tunable damping. An experiment-based parametric study has been conducted to determine the relationship of force, rotational velocity, and acceleration on both drill vibrations and drilling material surface vibrations. Results of a parametric study and Rational Polynomial Fraction method are used to estimate fundamental behaviors of the drilling system to create a refined numerical model for simulating the drilling process. An APPF controller together with the model provided a method to evaluate new actuator designs for vibration suppression and has shown a 69.8 % reduction of displacement vibrations