Polycrystalline diamond compact bit directional drilling technology has proven to be an important means to effectively improve drilling efficiency and save drilling costs. Under the directional drilling condition of PDC bit, due to the existence of screw angle or offset mechanism, the center axis of the bit deviates from the center of the borehole, and the cutting teeth of the bit do complex alternating trajectory cutting motion at the bottomhole and the trajectory lines of the cutting teeth themselves intersect in space. (1) The kinematics analysis of directional drilling PDC bit under different working conditions was carried out, including motion analysis at the stage of sliding steering deflection and motion analysis at the stage of composite steering drilling. The kinematics equation of PDC bit under sliding steering deflection and motion space equation of PDC bit cutters at the stage of composite steering drilling were deduced respectively. (2) By establishing the calculation model of cross Angle of cutters under directional drilling conditions, the influences of transmission ratio, tooth placement, offset and deflection Angle on the cross angle are analyzed. The movement law of PDC cutters and the bottom hole morphology formed by bit are studied under directional drilling conditions. (3) Based on the digital simulation system of PDC bit rock breaking, the cutting load under the state of alternating trajectory was studied. On this basis, the cutting mechanics model of PDC bit cutters in directional drilling was established. At the same time, the accuracy of simulation analysis was verified by laboratory unit experiments. It is considered that PDC cutters can form alternate cutting path in directional drilling, which can easily invade rock and improve mechanical efficiency. The larger the intersecting angle of the cutting teeth, the more likely the rock is to form a through crack and then be broken. When the intersecting angle is 90°, the average energy consumption of rock breaking in cross cutting is reduced by about 32.9% compared with parallel cutting. The research results have improved the understanding of the rock breaking mechanism of PDC bit directional drilling, provided a new technical means for bit performance analysis and have also provided a reference for the design of new personalized bits under the discussed working conditions. • The establishment of the function model of the intersection angle between the current circle motion trajectory of each cutting tooth of the PDC drill bit and the motion trajectory of the front and back two circles in the time step. According to the principle of mechanics and using the vector method, the calculation formula of the cutting tooth trajectory crossing angle in different steering systems under the condition of PDC bit directional drilling was deduced, and the corresponding mathematical model was established. The most important performance of the movement path of PDC bit cutters is the change of the cross Angle between the current movement path and the front and back movement paths of each cutter in the time step. The cross angle produced by the variable has an important influence on the crushing specific work and the main cutting force. • The cutting tooth motion trajectory is studied under different parameters. Analyze the influence of the four factors of PDC bit in the directional drilling conditions of speed ratio, positioning radius, deflection angle and offset on the single-tooth motion trajectory and the impact on the bottom hole coverage of the cutting tooth motion trajectory. The survey found that in previous studies, the difference in the intersection angle formed by the single-tooth cutting motion trajectory under different factors was not studied, and the influence of different factors on the bottom hole coverage of the cutting tooth motion trajectory was also not studied. The following conclusions are drawn: as the speed ratio increases, the corresponding cutting tooth movement track is longer. When the rotation ratio is a non-integer, the problem of the track line being fixed in the same area can be avoided, so the speed ratio is set to a larger value or A non-integer value is appropriate; with the increase of the positioning radius, the change range of the cross angle of the cutting tooth motion trajectory is significantly reduced. The core teeth of the inner cone of the positioning radius are prone to directional "rotation", while the other areas of the drill bit The cutting teeth will not have this kind of phenomenon. Therefore, when designing the PDC drill bit layout, attention should be paid to the problem of the reverse force on the heart teeth; as the bit offset continues to increase, the cutting teeth are between the front and rear trajectories The crossing angle of the tooth is obviously increased; with the increase of the deflection angle, the radial fluctuation area and the axial fluctuation range of its trajectory increase, and the movement cutting trajectory formed by each tooth is longer, which is more conducive to the realization of cutting The full coverage of the trajectory of the teeth at the bottom of the well improves the rock breaking efficiency of the drill bit. • The change of the intersection angle between the current circle motion trajectory and the motion trajectory of the two circles before and after each cutting tooth of the PDC drill bit in a time step, and the effect of the resulting cross angle variable on the crushing power and main cutting force. When other parameters remain unchanged, compared with parallel cutting, with the increase of the cross angle (maximum 90°), the axial main cutting force and crushing work of the cutting teeth in the cross cutting mode show a gradient decline and are both lower than Main cutting force and crushing specific work in parallel cutting mode. When the cross angle is 90°, the main cutting force and crushing specific work of the cutting teeth in the cross cutting state reach the lowest value. Therefore, when the drill bit is working, forming a rock breaking method with a cross angle is more labor-saving than parallel cutting, and the greater the cross angle (maximum 90°), the more labor-saving. Therefore, the PDC bit design should ensure that the cutting teeth can form a cross at the bottom of the hole The cutting feature facilitates cross-cutting of the rugged ridge topography formed at the bottom of the well, making it easier for the PDC bit to improve the efficiency of rock breaking and save drilling costs. [ABSTRACT FROM AUTHOR]