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

6.13.3. Water Resistance.
The Delft Sand, Clay & Rock Cutting Model.
The water resistance is investigated under circumstances comparable with the cutting tests as far as scale; blade
width and cutting velocity are concerned. Since the water resistance during all these tests could be neglected in
comparison with the cutting forces, performed under the same conditions (maximum 2%), the water resistance
terms are neglected in the further verification. The water resistance could however be more significant at higher
cutting velocities above 2 m/s. It should be noted that at higher cutting velocities also the cutting forces will be
higher, especially for the non-cavitating cutting process. Further, the inertial force, which is neglected in this
research, may also play a role at very high cutting velocities.
6.13.4. The Influence of the Width of the Blade.
The blade on which the cutting forces are measured is embedded between two side blades. These side blades have
to take care of the three-dimensional side effects, so that on the middle blade a two-dimensional cutting process
takes place. The question now is how wide the side blades need to be, at a certain cutting depth, to avoid a
significant presence of the side effects on the middle blade. Essential is, that at the deepest cutting depth the side
effects on the middle blade are negligible. For this research the following blade configurations are used:
1. A middle blade of 150 mm and two side blades of 185 mm each.
2. A middle blade of 200 mm and two side blades of 160 mm each.
3. A middle blade of 250 mm and two side blades of 135 mm each.
The total blade width in each configuration is therefore 520 mm. The results of this research are, scaled to a middle
blade of 200 mm wide, shown in Table 6-2, in which every value is the average of a number of tests. In this table
the forces on the 0.20 m and the 0.25 m wide blade are listed in proportion to the 0.15 m wide blade. The change
of the direction of the forces in relation to the 0.15 m wide blade is also mentioned. From this table the following
conclusions can be drawn:
1. There is no clear tendency to assume that the side effects influence the cutting forces in magnitude.
2. The widening of the middle blade and thus narrowing the side blades, gives slightly more downward aimed
forces on the middle blade at a blade angle of 30. At a blade angle of 45 this tendency can be seen at a bladeheight/layer-thickness
ratio of 1 and 2, while at a blade-height/ layer-thickness ratio of 3 the forces are just
slightly aimed upward. The 60 blade angle gives the same image as the 45 blade angle, however with smaller
differences in proportion to the 0.15 m wide blade.
Table 6-2: The influence of the width ratio between the center blade and the side blades.
w=0.20 m (2) w=0.25 m (3)
hb/hi ct2/ct1 t2-t1 ct3/ct1 t3-t1
30° 1 0.95 +1.0° 1.02 +1.0°
30° 2 1.10 +2.0° 0.93 +4.0°
30° 3 0.96 +5.0° 1.05 +7.0°
45° 1 1.08 +3.0° 1.01 +5.0°
45° 2 0.93 +3.0° 0.93 +5.0°
45° 3 0.93 -8.0° 1.07 -5.0°
60° 1 1.09 +0.0° 1.00 +1.0°
60° 2 0.90 +1.0° 0.92 +2.0°
60° 3 1.04 -5.0° 0.99 -4.0°
The total measured cutting force ct and the force direction t, at a blade width of 0.20 m (ct2, t2) (2) and a blade
width of 0.25 m (ct3, t3) (3) in proportion to the total cutting force and direction at a blade width of 0.15 m (ct1,
t1) (1), according the blade configurations mentioned here.
6.13.5. Side Effects.
On the outside of the side blades a three-dimensional cutting process acts, in a sense that the shear zone here is
three-dimensional, but on top of that the water flows three-dimensional to the shear zone. This makes the cutting
forces differ, in magnitude and direction, from the two-dimensional cutting process. Additionally it is imaginable
that also forces will act on the blade in the transversal direction (internal forces in the blade). The influence of the
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