There should be no clearance between the teeth, so as to avoid the presence of
unresected rocks in the work, which will affect the driving speed and even cause
unnecessary damage.
11.5.3.4 Example of Rock-Breaking Dynamic Process Analysis of Bit
The impact of spherical teeth on rock is a transient action. The dynamic analysis of
the impact system of spherical teeth is needed to determine the displacement, stress,
and strain of rocks varying with time under impact load, so as to determine the
spacing of spherical teeth. LS-DYNA, nonlinear dynamic analysis software, can
simulate real complex problems and is suitable for solving the impact, penetration,
and pierce through problems of two-dimensional and three-dimensional nonlinear
structures. According to Newton’s law and Hamilton’s variational principle, the
second-order differential equation of structural dynamic response after finite element discretization can be obtained.
M €
U þ C €
U þ KU ¼ F
ð11:75Þ
where,
M
Mass matrix of impact system;
K
Stiffness matrix of system;
€
U; _
U; U System node displacement, system velocity vector and system acceleration vector;
F
Transient impact load of system;
C
Damping coefficient matrix of system determined by experiments.
The damping coefficient matrix is usually calculated by proportional damping
method, i.e.,
C ¼ a 0 M þ a 1 K
ð11:76Þ
where coefficients a 0 ; a 1 are determined by experiments. The difference in direct
integration method is used to solve the nonlinear transient dynamic response.
Figure 11.38 is a model diagram of rock breaking by combined impact of two
spherical teeth.
(1) Material Model
Assuming that the material of drill spherical teeth is YG8 hard metal, rigid body
model is adopted: density is 14500 kg=m
3 , elastic modulus is 5:88 Â 10
11 Pa,
Poisson’s ratio is 0:22. The rock is modeled by a plastic kinematic model with a
density of 2700 kg=m
3 , an elastic modulus of 4:55 Â 10
10 Pa, a Poisson ratio of 0:26,
a yield strength of 50 MPa and a failure strain of 0:06. The constitutive relation is
simple and the parameters are few. The parameters of material model can be
11.5 Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout
257
unresected rocks in the work, which will affect the driving speed and even cause
unnecessary damage.
11.5.3.4 Example of Rock-Breaking Dynamic Process Analysis of Bit
The impact of spherical teeth on rock is a transient action. The dynamic analysis of
the impact system of spherical teeth is needed to determine the displacement, stress,
and strain of rocks varying with time under impact load, so as to determine the
spacing of spherical teeth. LS-DYNA, nonlinear dynamic analysis software, can
simulate real complex problems and is suitable for solving the impact, penetration,
and pierce through problems of two-dimensional and three-dimensional nonlinear
structures. According to Newton’s law and Hamilton’s variational principle, the
second-order differential equation of structural dynamic response after finite element discretization can be obtained.
M €
U þ C €
U þ KU ¼ F
ð11:75Þ
where,
M
Mass matrix of impact system;
K
Stiffness matrix of system;
€
U; _
U; U System node displacement, system velocity vector and system acceleration vector;
F
Transient impact load of system;
C
Damping coefficient matrix of system determined by experiments.
The damping coefficient matrix is usually calculated by proportional damping
method, i.e.,
C ¼ a 0 M þ a 1 K
ð11:76Þ
where coefficients a 0 ; a 1 are determined by experiments. The difference in direct
integration method is used to solve the nonlinear transient dynamic response.
Figure 11.38 is a model diagram of rock breaking by combined impact of two
spherical teeth.
(1) Material Model
Assuming that the material of drill spherical teeth is YG8 hard metal, rigid body
model is adopted: density is 14500 kg=m
3 , elastic modulus is 5:88 Â 10
11 Pa,
Poisson’s ratio is 0:22. The rock is modeled by a plastic kinematic model with a
density of 2700 kg=m
3 , an elastic modulus of 4:55 Â 10
10 Pa, a Poisson ratio of 0:26,
a yield strength of 50 MPa and a failure strain of 0:06. The constitutive relation is
simple and the parameters are few. The parameters of material model can be
11.5 Design of Large Diameter DTH Hammer Bit and Spherical Tooth Layout
257