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

The Delft Sand, Clay & Rock Cutting Model.
Figure 8-21: The model of Evans.
Figure 8-20 shows the brittle-tear horizontal force coefficient λHT as a function of the wedge top angle α and the
internal friction angle φ. The internal friction angle φ does not play a role directly, but it is assumed that the
external friction angle δ is 2/3 of the internal friction angle φ. Comparing Figure 8-20 with Figure 8-42 (the brittletear
horizontal force coefficient λHT of the Miedema model) shows that the coefficient λHT of Evans is bigger than
the λHT coefficient of Miedema. The Miedema model however is based on cutting with a blade, while Evans is
based on the penetration with a wedge or chisel, which should give a higher cutting force. The model as is derived
in chapter 8.3 assumes sharp blades however.
8.3.2. The Model of Evans under an Angle ε.
When it is assumed that the chisel enters the rock under an angle ε and the fracture starts in the same direction as
the centerline of the chisel as is shown in Figure 8-22, the following can be derived:
2
i
h 2 r sin sin and h =2 r sin
(8-53)
sin
h h
sin
i
Substituting equation (8-53) in equation (8-45) for the cutting force gives:
Fc T hi
w
1 sin
2sin
(8-54)
sin
sin
T
h w sin sin cos
(8-55)
T
h w sin
sin
cos
The horizontal component of the cutting force is now:
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