Two-three degree of freedom model for Anti Stick-Slip Tool of Drill-string

The drill-string is exposed to strong vibration due to its long length and the dynamic forces caused by the bit-rock interactions. The Anti Stick-Slip Tool which is located at the end of the drill-string and inside the bottom hole assembly prevents occurrence of the stick-slip. In this research, a new model for investigation of this tool is presented, which covers the limitations of previous models for analyses of the drill-string along with Anti Stick-Slip Tool. The system is modelled with two degrees-of-freedom in non-activated state and behaves like a rigid body. By activation of the tool, a degree-of-freedom is added to the system based on kinematic constraint of the tool and the system becomes three degrees-of-freedom. Based on the proposed model and determined conditions, the tool switches between the non-activated state with two degrees-of-freedom and the active state with three-degrees-of-freedom. The results obtained by simulating the dynamics of the tool represent a sensible behavior of the tool in presence of the external forces and torques on two parts of the tool. The proposed model precisely demonstrates the effect of weight on bit and weight on hook on the activation of the tool. The non-linear behavior of the tool caused by the switch between two set of linear equations has been discussed by using the presented model in a certain operational condition.