Study on geometry and kinematics of spherical single-roller PDC bit

A spherical single-roller bit based on polycrystalline diamond compact (PDC) cutters is designed for the purposes of improving the adaptability of single-roller bit to the stratum with high hardness and abrasiveness. According to the characteristics of cutter shape, the distribution of cutter, as well as the mode of contact between cutter and rock, the methods of space analysis and coordination projection are used to establish the geometrical equation for the single-roller bit with PDC cutters and the velocity equation for the PDC cutters, to describe the change rules between the velocity and other parameters. It is concluded that the velocity is subject to high influence by the shaft inclination angle and the positions of PDC cutters, but is subject to low influence by the radius, lateral rotation angle, and front inclination angle of PDC cutters; the velocity of cutters can be affected by the rock stratum to some extent and is higher in soft rock than in hard rock; the velocity of PDC cutters varies at different positions on the roller, and the absolute velocity of the most cutters on the roller will become stable along with the increase in the shaft inclination angle, while great increase will be found in the velocity of the cutters near the top of roller, where the distribution of cutters is to be strengthened; the shaft inclination angle is to be designed larger than 53 degrees and is suggested to range from 53 degrees to 70 degrees. This study lays the foundation for the computer simulation research related to the single-roller PDC bits and the structural design optimization of cutter surfaces.