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°and is suggested to range from 53°to 70°. 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.

Due to friction characteristics of clutch, the driveline is prone to cause a judder during vehicle starting, and then to cause the vehicle body to vibrate, which affects driving quality. In order to analyze the judder phenomenon, a nonlinear numerical friction model based on the Gaussian friction model is established in this paper. For the driveline of a front-wheel-drive vehicle, a five-degree-of-freedom (5DOF) lumped parameter model including a nonlinear friction element is established. The complex mode of the driveline during the clutch in slip condition is calculated. The key parameters affecting the driveline stability are analyzed. The self-excited judder and pressure-induced judder of the driveline are numerically simulated, and the corresponding causes are analyzed. The nonlinear friction torque of the clutch is also calculated. Furthermore, the effects of the key parameters such as the torsional stiffness and damping of the clutch and drive shaft suppressing the self-excited judder and pressure-induced judder are numerically studied respectively. Compared with the widely used Karnopp friction model, the nonlinear numerical friction model established in this paper comprehensively includes the stribeck effect in slip and the friction torque characteristics in stick. The phenomena of the judder and stick-slip of the driveline during vehicle starting are more accurately simulated. The simulation results are in good agreement with the experimental results, which verify the accuracy and effectiveness of the dynamic model including the nonlinear friction element established in this paper.