Port function based modeling and control of an autonomously variable spring to suppress self-excited vibrations while drilling

Self-excited vibrations are a major problem for rotary drilling. They may be mitigated by introducing adjustable compliance near the bottom of the drillstring, but it is challenging to identify the appropriate stiffness, particularly in situ and with limited available data on the rapidly-changing overall system dynamics. We describe an approach to modeling and simulating self-excited vibrations in drillstrings. Our approach uses impedance and admittance port functions to represent and systematically combine subsystems, and integrates established models for drillstring vibrations and rock / bit interactions. Simulations predict that intermediate stiffnesses provide better stability than either compliant or stiff extremes, which aligns with results from earlier work. Results also indicate that at least two different mechanisms limit stability in different stiffness regimes, producing significant differences in the relationship between vibration frequency and controlled module stiffness. This suggests a potential means of developing autonomous stiffness controllers that depend only on measurements taken at the variable stiffness module, without requiring a dynamic model of the rest of the drillstring.