Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 3, No. 2, 2022 

 

18 

Kinematic	Characteristics	of	Vertical	Runner	and	
Numerical	Simulation	Analysis	of	Rock	Breaking	
Jirui Li1, a, Yingxin Yang1, b, * 

1School of Southwest Petroleum University, Chengdu, Sichuan 610500, China 
a674872490@qq.com, byangyx36@qq.com 
Corresponding author: Yingxin Yang 

 

Abstract: In order to solve the problems of PDC teeth easy to collapse and fail in hard, hard and soft interlaced formations 
and gravel bearing formations, low mechanical speed, and difficult orientation caused by high torque response of pdc bits in 
directional drilling, this paper proposes a new type of composite bit with vertical wheels on the blade. Through theoretical 
analysis, the rotating conditions of the vertical wheel are obtained, that is, the contact angle of the cutting teeth of the vertical 
wheel must be greater than the center angle of its two adjacent teeth. At the same time, the cutting tracks generated by the 
previous vertical wheel unit experiments are analyzed, and the causes of different cutting tracks are obtained. Finally, the rock 
breaking of the PDC teeth under the pre damage of the vertical wheel is numerically simulated and analyzed, and it is concluded 
that the force on the PDC teeth is closely related to the relative height between the cutting teeth of the vertical wheel, It increases 
with the increase of relative height. When the relative height is 2mm, the tangential force on the PDC tooth is 4.78 times that 
when the relative height is 0mm, and the axial force is 2.47 times that when the relative height is 0mm. At the same time, the 
relationship between the force on the PDC teeth and the normal deflection angle and the rake angle of the vertical roller is not 
obvious. 

Keywords: PDC cutting teeth, Vertical wheel, Rotating conditions, Cutting track, Relative height. 
 

1. Introduction 
The focus of oil and gas exploration and development in 

China has shifted to deep/deep water/unconventional oil and 
gas (including shale gas).[1] The technical innovation of bit 
is one of the most promising efforts to improve the drilling 
speed in deep formation. [2]The most widely used bit in oil 
and gas drilling is polycrystalline diamond composite bit, that 
is, PDC (Polycrystalline Diamond Compact) bit. This bit has 
the advantages of high rock breaking efficiency, high 
penetration rate and long working life in medium hard 
formations.[3] However, its drilling speed is slow, its service 
life is low, and its stability is poor when drilling into deep and 
hard to drill formations such as strong plasticity, gravel and 
interlayer.[4] In view of this situation, the bit laboratory of 
Southwest Petroleum University proposed a vertical wheel 
PDC bit. Its structure is shown in Figure 1. It combines the 
runner and bearing and applies them to the PDC bit, forming 
a new technology of vertical wheel PDC bit. The theoretical 
analysis and experimental test results show that the setting of 
the vertical runner has the functions of auxiliary cutting, 
partial pressure buffering and torque stabilizing, which can 
significantly improve the working stability of the PDC bit and 
reduce the wear rate of the bit cutting teeth.[5] However, the 
precondition for the vertical roller PDC bit to achieve the 
above functions is that the vertical roller can rotate smoothly 
when working at the bottom of the well. Therefore, the 
rotating conditions of the vertical roller are very important for 
the design of the vertical roller PDC bit. The vertical wheel 
PDC bit introduces a vertical runner on the conventional fixed 
cutting bit. Compared with the conventional PDC bit, the 
runner structure is placed on the PDC main blade, which 
works with the PDC fixed blade. The pre breaking of the 
runner on the rock will greatly reduce the difficulty of PDC 
cutting teeth in cutting the rock and improve the performance 

of the bit. In order to quantitatively study the rock breaking 
effect of the combined action of the cutting teeth and PDC 
teeth of the runner and conduct numerical simulation, the 
main position parameters of the runner are analyzed, 
including the normal angle of the runner α、 Front inclination 
γ And the influence of the relative the PDC tooth on the stress 
of the PDC tooth 

 
Figure 1. Structural Diagram of Vertical Wheel PDC Bit 

2. Rotating Conditions of Vertical 
Runner Rotating Conditions of 
Vertical Runner 

As shown in Fig. 1 (a), it represents the position diagram 
of A tooth and B tooth when the runner rotates clockwise and 
A tooth just contacts the rock. At this time, the vertical height 
of B tooth from the rock surface is m. Figure 1 (b, The 
adjacent subsequent cutting teeth can eat into the rock. Figure 
1 (c) shows the height L of the B tooth descending 
perpendicular to the rock surface during the process of A tooth 
contacting the rock at the beginning and leaving the rock. 
According to the above critical rotating conditions of the 



 

19 

runner, the rotating conditions of the runner are: 

 

𝐿 𝑚                  (1) 

 

 
Figure 2. Schematic Diagram of Rotating Conditions of 

Runner 

2.1. Find the Value of m 

 
(a)                 (b)                      (c) 

Figure 3. Diagram of relationship between m value and 
normal deflection angle and front inclination angle 

 
Figure 3 (a) shows the schematic diagram of the runner 

without normal deflection angle and rake angle. At this time, 
the vertical height of B tooth from the rock is 0. Figure 3 (b) 
shows that the normal inclination of the runner is α The 
vertical height of tooth B from the rock is e. Figure 3 (c) 
shows that the normal deflection angle of the runner is α,It 
also has a front inclination angle β The vertical height of tooth 
B from rock decreases from e to m. 

As shown in Figure 3 (b) and Figure 4:  

𝑒 2𝑟𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝛼                (2) 

 

Where R is the radius of the top circle of the runner cutting 
tooth, θ Is the center angle between A and B teeth, α Is the 
normal deflection angle. 

 

 

Figure 4. Schematic diagram of e value 

 

Figure 5. Schematic diagram of m value 

As shown in Figure 2 (c) and Figure 5: 

𝑚 𝑒 𝑛              (3) 
 

𝑛 𝑅 𝐻 cos 𝜑 𝛽 cos 𝜑      (4) 
 

𝑚  2𝑟𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝛼 𝑅 𝐻 cos 𝜑 𝛽 cos 𝜑  (5) 
 

Where R is the contour radius of the runner tooth surface, 
and H is the exposed height of the cutting teeth 

 

(a) 

 

(b) 

Figure 6. Schematic diagram of L value and A gear 
rotation angle 



 

20 

2.2. Finding the Value of L 
Figure 6 (a) shows that the cutting tooth starts to contact 

the rock at A ′ position, and when it reaches A position, the 
cutting tooth leaves the rock. In this process, the rotation 
angle of the cutting tooth A is Ф. Then the cutting tooth B 
turns at an angle of φ. In this process, the height L of B tooth 
descending in the direction perpendicular to the rock: 

 

𝐿  2𝑟𝑠𝑖𝑛Ф𝑠𝑖𝑛𝛼 𝑅 𝐻 cos 𝜑 𝛽 cos 𝜑  (6) 
 

 

The calculation process is the same as the above principle. 
Since its rotation condition is L ≥ m 

 

2𝑟𝑠𝑖𝑛Ф𝑠𝑖𝑛𝛼 𝑅 𝐻 cos 𝜑 𝛽 cos 𝜑  
2𝑟𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝛼 𝑅 𝐻 cos 𝜑 𝛽 cos 𝜑    (7) 

Get: 
 

Ф 𝜃                      (8) 
 
Therefore, the condition for the runner to rotate is that the 

contact angle of the cutting teeth of the runner must be greater 
than the center angle of the two adjacent teeth. 
2.3.1 Find Contact Angle Ф Value of When Only Normal 

Deflection Angle Exists 

 
(a)   

 
(b) 

 
(c) 

Figure 7. seek Ф Schematic Diagram of Value Location 

As shown in Fig.7 (a), J represents the tooth tip circular 
plane of the runner cutting teeth. We assume that the tooth tip 
feature point of each cutting tooth is prior to the rock contact. 
When the tooth penetration depth is C, the sketch map of the 
intersection between the tooth top circle plane and the rock 
plane is shown in Figure 7 (c), where K represents the rock 
plane, and the line segment LC represents the projection 
length of the part of the tooth top circle intersecting the rock 
in the cutting direction. Its length in the top view of the runner 
is shown in Figure7 (b), so it can be seen from Figure 7 (c) 
that: 

𝐿                 (9) 

 

From Figure 7 (b): 

Ф 2 cos 1          (10) 

 

Therefore, under ideal conditions, as long as 

2 cos 1 𝜃, The wheel can turn. 

2.3.2 When Normal Deflection Angle and Front 
Inclination Angle Exist Simultaneously 

As shown in Figure 8, The geometric coordinate system of 
the vertical wheel includes three rectangular coordinate 
systems with the spherical center of the runner tooth surface 
as the origin. They are respectively the position coordinate 
system 𝑂 𝑋 𝑌 𝑍  ; Normal declination coordinate 
system 𝑂 𝑋 𝑌 𝑍 ;  Tilt forward coordinate system or 
working coordinate system𝑂 𝑋 𝑌 𝑍 。 

Plane 𝑂 𝑋 𝑍  Center plane of runner, coordinate axis 
𝑂 𝑍  Perpendicular to the rock plane, 𝑂 𝑌  Axis pointing to 
𝑂  Speed direction at 1 point. Set 𝑂 𝑋 𝑌 𝑍  Coordinate 
system around 𝑂 𝑌   axis rotation α After the angle, 𝑂  is 
formed 𝑂 𝑋 𝑌 𝑍   Coordinate system. 
Set𝑂 𝑋 𝑌 𝑍 Coordinate system around𝑂 𝑋 -axis rotation- β 
After the angle, O is formed𝑂 𝑋 𝑌 𝑍 Coordinate system. 

When the normal deflection angle and the rake angle exist 
at the same time, the contact angle between the cutting teeth 
of the runner and the rock is required, which is actually the 
intersection point between the tooth tip circle of the cutting 
teeth of the runner and the rock plane. The contact angle is the 
center angle between the two intersection points. 

 
Figure 8. Coordinate system of vertical roller 

At𝑂 𝑋 𝑌 𝑍 , the equation of the addendum circle can be 



 

21 

expressed as: 

𝑥 𝑦 𝑅  
𝑍 𝐾            

(11) 
 

Where, R represents the radius of the addendum circle, 
and K represents the distance from the plane of the 
addendum circle to 𝑂  The height of 1 point.Through 
coordinate transformation, the equation of addendum 
circle can be obtained in coordinate system 𝑂 𝑋 𝑌 𝑍 The 
specific steps of the expression in 1 are as follows: 

Rotate around X axis β： 
 

𝑥 𝑥  
𝑦 𝑦 𝑐𝑜𝑠 𝛽 𝑍 sin 𝛽 
𝑧 𝑦 𝑠𝑖𝑛 𝛽 𝑧 𝑐𝑜𝑠 𝛽 

(12) 
                                                        

Rotate around y-axis- α 

 

𝑥 𝑧 𝑠𝑖𝑛 𝛼 𝑥 𝑐𝑜𝑠 𝛼 
𝑦 𝑦  

𝑧 𝑧 𝑐𝑜𝑠 𝑎 𝑥 𝑠𝑖𝑛 𝑎 
     (13) 

From the above formula, we can get:    

𝑥 𝑧 𝑠𝑖𝑛 𝛼 𝑥 𝑐𝑜𝑠 𝛼 
𝑦 𝑦 cos 𝛽 𝑧 cos 𝛼 𝑥 sin 𝛼  

𝑧  𝑦 sin 𝛽 𝑧 cos 𝛼 𝑥 sin 𝛼 cos 𝛽 
 (14) 

 
So the equation of the addendum circle is in the 

coordinate system 𝑂 𝑋 𝑌 𝑍 The expression in 1 is: 

𝑧 sin 𝛼 𝑥 cos 𝛼
𝑦 cos 𝛽
𝑧 cos 𝛼 𝑥 sin 𝛼 sin 𝛽 𝑅  

                               𝑦 sin 𝛽 𝑧 cos 𝛼 𝑥 sin 𝛼 cos 𝛽 𝑘 
 

                 (15) 
Then the intersection point between the tooth tip circle 

and the rock plane is: 

𝑧 sin 𝛼 𝑥 cos 𝛼
𝑦 cos 𝛽
𝑧 cos 𝛼 𝑥 sin 𝛼 sin 𝛽 𝑅  

                          𝑦 sin 𝛽 𝑧 cos 𝛼 𝑥 sin 𝛼 cos 𝛽 𝑘 
𝑍 𝑘 𝐶 

 (16) 
Wherein, C is the eating depth of the cutting tooth, 

and the above equations can be used to solve𝑥 , 𝑦 , the 
contact angle of the cutting teeth of the runner can be 
obtained. 

3. Factors Influencing the Cutting Path 
of Runner 

Yang Yan [5] carried out unit experiment research on rock 
breaking of runner, and analyzed the movement law and rock 
breaking characteristics of runner under different rake angle, 
normal deflection angle, runner height, tooth shape and 

runner diameter. However, she did not find out the internal 
causes of various cutting trajectories. Therefore, based on 
Yang Yan, this paper analyzes the causes of various cutting 
trajectories in detail. 

In order to better describe the cutting track, the track length 
l, track width w and track spacing d are introduced, as shown 
in Figure 9. 

  
Figure 9. Cutting track parameters 

 
As shown in Figure 10, in the unit experiment of the runner, 

the top point of the cutting tooth of the runner is taken as the 
moving point, the runner is the dynamic coordinate system, 
and the rock is the static coordinate system. Then the motion 
of the moving point relative to the rock is absolute motion, 
and the trajectory is a complex spatial curve motion; The 
motion of the moving point relative to the runner is a relative 
motion, and its trajectory is a circle, while the motion of the 
runner relative to the rock is a drag motion, which is a linear 
translation of the rigid body. The relative velocity v of moving 
point𝑣   is decomposed into𝑣   and𝑣   where 𝑣  is 

the relative velocity 𝑣  The projection of on 
the 𝑥𝑜𝑦 plane 𝑣𝑟𝑥𝑦 is decomposed along the x and y axes to 

obtain 𝑣  and 𝑣 。Then the displacement corresponding to 

the track length in the cutting track is the speed 𝑣  related, 
track width and relative velocity  𝑣𝑟 The component of the 
projection of on the xoy plane along the x-axis 𝑣 , the depth 
of the trajectory perpendicular to the rock plane is related to 
𝑣 correlation. 

 
Figure 10. Speed breakdown of runner cutting teeth 

The length of the track is determined by the contact time 
between the cutting teeth and the rock and the implicated 
speed of the runner, while the width of the track is determined 
by the contact time between the cutting teeth and the rock, the 
track width and the relative speed v_ The component v of the 
projection of r on the xoy plane along the x-axis_ X is relevant. 
The distance between tracks is related to the length of tracks 
and the distance between adjacent teeth. 



 

22 

3.1. Influence of Normal Deflection Angle on 
Cutting Path: 

 

Figure 11. Schematic diagram of the influence of normal 
deflection angle on cutting path 

As shown in Figure 11, the red, green and blue boxes 
respectively represent the normal deflection angles of 15 °, 
10 ° and 5 °. The cutting path shape of tapered tooth is "V" 
when only normal deflection angle exists As the normal 
deflection angle increases, the length and width of the trace 
line will be shorter, and the spacing between the trace lines 
will be smaller. This is because when there is only the normal 
deflection angle, the two intersection points of the top circle 
of the runner and the rock plane are the positions where the 
cutting teeth start to contact the rock and leave the rock. The 
vertical planes of the two intersection points pass through the 
center of the top circle and are parallel to the axis of the runner. 
The intersection point of the vertical plane and the top circle 
is the farthest that the cutting teeth can reach Horizontal 
position. When you turn this point, the direction of the 
trajectory line will "turn back". With the increase of the 
normal deflection angle, the contact angle between the cutting 
teeth on the runner and the rock decreases gradually. Because 
the rotation speed of the runner is less affected by the normal 
deflection angle, the larger the normal deflection angle is, the 
shorter the action time between the cutting teeth on the runner 
and the rock, the shorter the length of the trajectory, and the 
smaller the width of the trajectory. The position where the two 
adjacent teeth start to contact the rock is independent of the 
normal deflection angle, so the distance between the positions 
where the two adjacent teeth just start to contact the rock in 
the track is equal. The greater the normal deflection angle is, 
the shorter the track line length is, so the distance between the 
two adjacent track lines is longer. 

3.2. Effect of Rake Angle on Cutting Path 
As shown in Figure 11, when there is both normal 

deflection angle and rake angle, the shape of the track 
becomes oblique because the rake angle is added, so that the 
tooth top circular plane of the runner rotates an angle around 
the mid vertical plane of the two intersection points, which is 
equal to the magnitude of the rake angle. The vertical height 
of the tooth top circle in the front half of the vertical plane to 
the rock is lower, while the vertical height of the back half of 
the vertical plane to the rock is higher. At this time, the two 
intersection points of the top circle of the runner tooth and the 
rock plane are no longer symmetrical with respect to the 
vertical plane, and the position of the cutting tooth leaving the 

rock changes from the back half of the vertical plane to the 
front half of the vertical plane, Therefore, the trace line has no 
"turning back" shape. At the same time, the increase of the 
length and width of the trace line is due to, on the one hand, 
the rake angle makes the contact angle of the cutting teeth 
larger, and on the other hand, the addition of the rake angle 
makes the speed of the runner slower. Therefore, the 
superposition of the two makes the length and width of the 
trace line increase. The increase of the length of the trace line 
makes the distance between the two trace lines smaller. 

 
Figure 12. Diagram of influence of rake angle on cutting 

path 

3.3. Effect of Runner Diameter on Cutting 
Path 

 
Figure 13. Schematic diagram of influence of runner 

diameter on cutting path 
 

The contact angle of the cutting teeth of the runner 
decreases with the increase of the runner diameter, and the 
average speed of the runner also decreases with the increase 
of the runner diameter. However, after calculation, when there 
is only normal deflection angle, the contact time between 
cutting teeth and rock decreases with the increase of runner 
diameter. Therefore, as shown in the figure, the track line 
length of the 18mm runner is longer than that of the 30mm 
runner. But in the transverse direction, due to the component 
v of the relative velocity in the Y-axis direction_ The width 
change of cutting path is not obvious under the joint influence 
of 𝑣 and contact time. 

3.4 Effect of Cutting Depth on Cutting Path 

 
Figure 14. Schematic Diagram of the Influence of Cutting 

Depth on Cutting Path 
 



 

23 

With the increase of the depth of penetration, the contact 
angle of the cutting teeth also increases, so the contact time 
also increases, so the length and width of the trajectory line 
increase, and at the same time the spacing between the tracks 
becomes smaller. 

3.5 Influence of Cutting Tooth Profile on 
Cutting Path 

 

 
Figure 15. Comparison Diagram of Wedge Tooth, Taper 

Tooth and Steel Tooth Tracks 
 

Wedge tooth, tapered tooth and steel tooth with two section 
shapes, when the normal deflection angle ∆ is the same γ＝ 
When the angle is 15 °, the cutting path of the wedge tooth on 
the runner is "straight", the cutting path of the cone tooth is 
"V", and the cutting path of the steel tooth is "oblique". The 
length l of the cutting path of the wedge tooth is the longest, 
the width w is the widest, and the spacing d of the cutting path 
of the steel tooth is the smallest. 

4. Numerical Simulation Analysis of 
Rock Breaking Under Pre Damage 
of Vertical Runner 

4.1. Establishment of Geometric Model 
Based on ABAQUS software, this paper analyzes the 

microscopic interaction between the runner rock system. 
[6]The runner diameter is 30mm (taking the distance from the 
tip of the runner to the runner shaft as the radius). The hard 
alloy tapered teeth are used on the runner. The diameter of the 
teeth is 9mm, the diameter of the PDC teeth is 15.7mm, the 
tooth thickness is 7.5mm, the rake angle is 5 °, and the side 
angle is 0 °. Because of the irregular shape of the teeth and 
runner body, their grids are C3D10M;[7] Rock size is 80mm 
× 80mm × 40mm, the 8-node linear hexahedral reduced 
integral element (C3D8R) with hourglass control is used for 
discretization, and the local grid of rock is refined, as shown 
in Figure 3. Fixed constraints are imposed on the bottom of 
the rock, and symmetrical constraints are imposed on the 
symmetrical plane respectively. The fastest cutting speed of 
the runner is 0.3m/s, which increases linearly according to a 
certain amplitude. The simulation time is 0.3s. The rock 
property is yellow sandstone, the density is 2.08g/cm3, the 
compressive strength is 21.49Mpa, the elastic modulus is 
2.46Gpa, Poisson's ratio is 0.085, the internal friction angle of 
the rock is 22.87 °, and the fracture strain is 0.0134. 

 

 
Figure 16. Simulation model of runner pre crushing 

4.2. Analysis of Simulation Results 
4.2.1. Influence of Relative Height 

In this group of simulation experiments, the normal 
deflection angle of the runner is 20 °, and the cutting depth of 
the cutting teeth of the runner is fixed at 1mm. The rake angle 
of the PDC gear is 5 °, and the side angle is 0 °. As shown in 
Figure 17, Changing the cutting depth of the PDC gear, five 
groups of simulation experimental data are obtained, and their 
relative heights are respectively 0, 0.5, 1, 1.5, and 2 mm. The 
simulation results are shown in the figure below. The axial 
force and tangential force of PDC cutting teeth increase with 
the increase of relative height. The relative height increases 
from 0 mm to 2 mm, the tangential force increases from 24.57 
N to 142.18 N, an increase of 4.78 times, and the axial force 
increases from 6.68 to 23.88, an increase of 2.47 times. It can 
be seen that the force of PDC teeth is more sensitive to the 
change of relative height. The lower the relative height is, the 
more obvious the role of vertical wheel in auxiliary cutting is. 

 



 

24 

 
Figure 17. Schematic Diagram of Forces on Cutting Teeth at Different Relative Heights 

 

4.2.2. Influence of Normal Deflection Angle 
In this group of simulation experiments, the cutting depth 

of the runner cutting teeth and PDC cutting teeth is 1mm, and 
the normal deflection angles of the runner are 5 °, 10 °, 15 ° 
and 20 ° respectively. The rake angle of PDC cutting teeth is 
5 °, and the side angle is 0 °. The simulation results are shown 

in the following figure. The normal deflection angle of the 
runner has little effect on the force on the PDC cutting teeth. 
The maximum axial force of the PDC cutting teeth occurs 
when the normal deflection angle of the runner is 20 °, and 
the maximum tangential force occurs when the normal 
deflection angle of the runner is 10 °. However, the overall 
force on the PDC cutting teeth does not change significantly. 

 

 

Figure 18. Force of PDC teeth under different normal deflection angles 

 
4.2.3. Effect of Front Tilt 

In this group of simulation experiments, the cutting depth 
of the runner cutting teeth and PDC cutting teeth is 1mm, the 
normal deflection angle of the runner is 20 °, the variation 
range of the rake angle is from 5 ° to 20 °, the rake angle of 
the PDC cutting teeth is 5 °, and the side angle is 0 °. The 
simulation results are shown in the figure below. The normal 

deflection angle of the runner has little influence on the force 
on the PDC cutting teeth. The force on the PDC cutting teeth 
decreases first and then increases with the increase of the rake 
angle. When the rake angle is 10 °, the axial force and 
tangential force are the minimum, 36.72N and 8.54N 
respectively. 

 

24.57

47.21

75.65

105.53

142.18

6.68 10.55 13.23 18.21 23.88

0

20

40

60

80

100

120

140

160

0 0.5 1 1.5 2

F
or

ce
，

N

Relative height,mm
Tangential Axial

45.68

36.72

48.76

58.43

10.21 8.54 9.45 9.23

0

10

20

30

40

50

60

70

5 10 15 20

F
or

ce
, N

Normal declination angle,°

Tangential Axial



 

25 

 
Figure 19. Force changes of PDC teeth under different rake angles 

 

5. Conclusion 
The rotating condition of vertical PDC bit is that the contact 

angle of the cutting teeth on the vertical wheel must be greater 
than the center angle of the two adjacent teeth. The contact 
angle of the cutting teeth of the vertical wheel is related to the 
normal deflection angle, the rake angle, the diameter of the 
vertical wheel and the eating depth of the cutting teeth. 

The cutting track of the vertical wheel is essentially 
determined by the speed ratio of the vertical wheel body. The 
length of the track is determined by the contact time between 
the cutting teeth and the rock and the implicated speed of the 
runner. The width of the track is related to the contact time 
between the cutting teeth and the rock and the width of the 
track and the component of the projection of the relative speed 
on the xoy plane along the x-axis. The distance between tracks 
is related to the length of tracks and the distance between 
adjacent teeth. 

Under the pre damage effect of the vertical wheel, the force 
on the PDC tooth increases with the increase of the relative 
height between the PDC tooth and the vertical wheel cutting 
tooth. The normal deflection angle of the vertical wheel has 
little effect, and decreases first and then increases with the 
increase of the rake angle. When the rake angle is 10 °, the 
axial force and tangential force are minimum. 

References 
[1] Sun Weiwei Current situation and development trend of deep 

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[2] Wang Yaojia, Wang Zaixing, Shen Liyang, etc Current 
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deep well drilling technology [J] Petrochemical technology 
2016, 23(02): 52. 

[3] Bai Jing, Zhang Bin, Zhang Chaoping Current situation and 
development suggestions of ultra deep and ultra slim hole 
directional drilling technology [J] Drilling and production 
technology 2018, 41(6): 5-8. 

[4] Zhang Jingcheng, Ma Lijun, Liu Yong, et al Research and 
application of ultra deep and ultra slim hole directional drilling 
technology in Tarim Oilfield [J] Special oil and gas reservoirs 
2020, 27(02): 164-168. 

[5] Yang Yan Study on working mechanism and design method of 
vertical wheel PDC bit [D] Southwest Petroleum University, 
2020. 

[6] Feng Yuguo Application of ABAQUS in Geotechnical 
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[7] Wu Kaisong, Liao Feilong Discussion on rock breaking law of 
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2014, 42 (5): 29-33. 

 

45.68

36.72

48.76

58.43

10.21 8.54 9.45 9.23

0

10

20

30

40

50

60

70

5 10 15 20

F
or

ce
, N

Front inclination,°

Tangential Axial