# Study on Mechanism of Stick-Slip Vibration Based on Torque Characteristics of PDC Bit
## 5 Mechanism of SV of PDC Bit in Drilling
### Mechanism and Law of SV of the Drill Bit  
When the bit rotates under the condition of dynamic balance, the bit resistance suddenly increases, which will lead to the situation of first a decrease and then an increase in the bit's rotational speed. As shown in Figure 13, when the simulation time is 22.1 s, this changes the original arrival time and the stabilization time is 2 s, and then decreases. The bit angular velocity decreasing rapidly from 8.37 rad/s in dynamic equilibrium to 4.2 rad/s indicates the presence of viscosity. Because the speed of the upper rotary table is constant, the drill string distorts and starts to accumulate energy while the drill bit still rotates. When the drill string energy is high enough, the drill bit speed suddenly increases to 13.1 rad/s, and then slippage occurs. Because the drill pipe is an elastic element, the drill bit still rotates at a variable speed after this, and it finally tends towards dynamic balance. Obviously, during the stage of bit slippage, its rotational speed is much higher than that in dynamic balance, which will inevitably cause the cutting teeth to suffer dynamic load impact. With the occurrence of SV, the cutting teeth become prone to premature failure.  
Under the same conditions, the torque changes of unit nodes 1, 50, 100, 150, 200, 250, and 300 at different positions of the drill string are shown in Figure 14. When the load changes suddenly, the torque borne by the drill string increases with the depth of the well, and it approaches from the bit to the bit. When dynamic balance is reached, the torque changes from the bottom hole. Therefore, when the drill bit penetration depth changes or the lithology abrupt changes lead to torque, the drill pipe will also bear greater torque, which will lead to SV, and the drill pipe will also bear cyclic variable stress.  
Figure 15 shows the rotational speed near the bit when the peak torque is 1.3 times, 1.5 times, 1.7 times and 1.9 times of the initial torque, respectively (corresponding peak torque is 5200 Nm, 6000 Nm, 6800 Nm and 7600 Nm, respectively). When the peak torque applied to the bit exceeds 6500 Nm, obvious viscosity occurs when the bit penetration rate is zero. When the peak torque is 7600 Nm, the rotational speed of the bit is close  
Figure 12: Torque distribution along dynamic loading drill string.  
Figure 16 shows the change in bit speed under different drill string lengths. Because the active load (4000 Nm) is applied at the bit, the bit speed fluctuates during the initial stage of drilling. When the drill string is 3000 m, the rigidity of the drill string is sufficient, and the bit does not stop after the initial fluctuation. With this length of the drill string, the rotating speed of the drill bit is far less than the wellhead rotating speed (8.37 rad/s) for a long time. This is the elastic energy storage stage of the drill string. When the drill string reaches 11,000 m, the drill string still stops for a long time after the active load fluctuation (after 5 s), and when the accumulated force of the drill string becomes sufficient, it begins to break. Therefore, even if the bit resistance is constant, the SS phenomenon can occur provided the drill string is long enough.