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.
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