Flexible joints are widely used in ‘soft’ touching and holding, and they represent the main component of ultra-short radius drilling tools. The analysis of contact and motion characteristics is an essential issue in the design and development stage of flexible joints. In this study, a collision dynamics model of a ball cage flexible joint (BCFJ), which is suitable for the characteristics of small clearance and large load, is established. The model contains a nonlinear stiffness coefficient and can describe the contact force between the ball key and the raceways. Moreover, the computational procedure for the dynamic analysis of BCFJ with clearance is established, and the dynamic simulation for collision and contact between ball, cage, outer race, and inner race was carried out. By numerical calculation, the variation of contact force on the five contact points of the ball key and ball cage is discussed, and the influence of ball cage clearance on contact force between ball key, ball seat, and ball cage is obtained. The results indicate that the effects of the ball cage clearance on the contact force cannot be ignored, which is the main cause for the vibration of the flexible joint system, and the amplitude of the contact force will gradually increase with the increase of the clearance. The proposed model and procedure can analyze the dynamic behavior of flexible joints with small clearance and large load, providing a basis for further research on wear prediction and safety evaluation of the BCFJ with clearance.

The flexible joint is an important part in ultra-short-radius drilling tools, and its structural parameters and motion characteristics are key factors affecting the success of drilling. In this work, a new type of ball cage flexible joint, which is applied in 5″ and 5.5″ cased wells, was proposed based on the working principle of the ball cage universal joint. A structural parameter design method for the ball cage flexible joint was established according to the geometric coordination relation and material strength theory. Using this new method, the length, diameter, and window size of the ball cage flexible joint were analyzed. The multi-body motion process was further analyzed using a multi-body dynamics method, and then the motion characteristics, such as impact contact force, isokinetic characteristics, transfer efficiency, deflection torque and so on, were studied. Based on the above analyses, the structural parameters of the designed joint were optimized by means of the orthogonal test method. Results demonstrate that the experimental ball cage flexible joint has excellent isokinetic transmission characteristic, which can effectively suppress vibration and shock caused by changes in rotational speed. The transmission efficiency of the structure was 89.8%, while the power loss rate was 0.102%. According to the orthogonal test analysis, the optimal structure of the flexible joint has a ball seat diameter of 80 mm, a ball head diameter of 62 mm, and a ball key diameter of 16 mm. It is important to note that the ball key diameter was the most influential factor on the flexible joint internal contact force. The ball key contact force varied periodically, and there was a significant phase difference between the contact forces of different balls. On the other hand, with an increase in the flexible joint working angle, the deflection torque increased gradually, and the vibration amplitude of the torque increased. This work can provide reference for the parameter optimization design of the new flexible joint.

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

It is of practical interest to investigate the mechanical behaviors of a sidetracking tool system and to describe the sidetracking tool’s vibration mechanical response, as this can provide an important basis for evaluating and optimizing the tool structure and effectively controlling the profile of the sidetracking window. In this article, three nonlinear dynamic models with ten, six, and two degrees of freedom, respectively, are established using the Lagrange method to characterize the behavior of the sidetracking tool. It should be noted that in these models, the axial, lateral, and torsional vibration of the tool system are fully coupled. The process of the sidetracking tool mills in the casing-pipe wall is divide into three typical stages, i.e., the window mill, pilot mill, and watermelon mill grinding the casing, respectively. The dynamic response of the three stages is studied to more effectively analyze the influence of the sidetracking tool vibration deformation on the window width. The Runge–Kutta method, which is easy to implement, is applied to solve the supposed nonlinear dynamic model, and some useful findings are as follows. The effects of sidetracking tool vibrations at different stages on window widening size are illustrated quantitatively. The vibration trajectory pattern of the sidetracking tool is different from that of the conventional drilling tool due to the influence of the whipstock, which changes from the general whirling motion pattern to the X reciprocating pattern, and the vibration amplitude decreases. Due to the influence of the tool’s lateral amplitude, the window profile is widened. The widened window size of the window mill and the pilot mill are 3.30 mm and 2.74 mm, respectively, and the extended window size of the watermelon mill is 0.07 mm, while the maximum window width formed by the sidetracking tool is 374.34 mm. This work proposes, for the first time, the coupled vibration model of the sidetracking tool system, which is helpful to better understand the nonlinear dynamic effects of the sidetracking tool, laying the foundation for the optimization of the sidetracking parameters.