(2) Force analysis under torque M n
Torque M n produces the maximum shear stress at the edge of each section, and at
center is 0. Obviously, there is the maximum shear stress at the edge of I À I
0
section:
s M n max ¼
M n
W n
¼
FR sin a
W n
¼
2F
p R sin a
ð
Þ
2
ð11:57Þ
W n is the section modulus in torsion, W n ¼
pd
3
16 , d is the diameter of cross section,
where d ¼ R sin a.
The shear stress produced by M n in J À J
0 section is as follows:
s JM n ¼
M n
W n
¼
FR sin a
W n
¼
2F sin a
pR 2
ð11:58Þ
11.5.2.4 Force Model Under Combined Action of Axial
and Tangential Loads
The process of the spherical teeth scraping at the bottom of the well can be seen as
the process of sliding friction of the spherical teeth against the rock and ploughing
the grooves on the rock surface. The shear failure of the teeth to the rock ridge in
the crushing pit is actually the result of the pushing action. Therefore, the relationship between the axial load P and the tangential load F can be reflected by the
relevant theory of tribology.
Fig. 11.32 Views of points
F; H; U; V
11.5 Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout
249