Influence of Blades’ Shape and Cutters’ Arrangement of PDC Drill Bit on Nonlinear Vibration of Deep Drilling System

In this paper, the surface morphology method is improved and the bit-rock interaction model between the rock and the PDC bit is studied, considering the influence of blades’ shape and the cutters’ arrangement. Based on this model, the dynamic model of the deep drilling system equipped with arbitrary shape PDC bit is established, and the stability prediction method is proposed. Based on the improved surface morphology method, the dynamic characteristics of the drilling system equipped with four different types of bit (an actual bit, a Tian bit, a Tian bit with blades, and a traditional bit) are studied, comparing with the Tian model based on polygon clipping. The results indicate that the influence of blades’ shape and cutters’ arrangement of PDC bit on the nonlinear vibration of the drilling system cannot be ignored. By applying the proposed method, the dynamic model of the drilling system equipped with an actual PDC bit presents excellent computational efficiency, accuracy, and avoids unreasonable behavior, which provides a reliable theory for the dynamic analysis of the drilling system. In addition, the proposed uncut volume error and repeated cutting volume error can be used to evaluate the shape design of the drill bit and the accuracy of the bit-rock interaction model.