The Delft Sand, Clay & Rock Cutting Model, 2019a

The General Cutting Process.
The velocity components of a grain in x, y and z direction can be determined by considering the absolute velocity
of grains in the shear surface, this leads to:
vr2 v d2 v d vr1
v
d1
(3-54)
v v cos cos v sin
(3-55)
x1 r1 d1
v v cos sin v cos
(3-56)
y1 r1 d1
z1
r1
v v sin
(3-57)
Figure 3-17: Velocity conditions.
Figure 3-18: Force directions.
The velocity components of a grain can also be determined by a summation of the drag velocity of the blade and
the relative velocity between the grains and the blade, this gives:
v v v cos cos v sin
(3-58)
x2 d r2 d2
v v cos sin v cos
(3-59)
y2 r2 d2
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