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

The Delft Sand, Clay & Rock Cutting Model.
Analyzing the equations for the influence of the weight (gravity) and the influence of the inertial forces shows a
significant difference. The gravitational forces are proportional to the density of the soil ρs, the gravitational
constant g, the thickness of the layer cut hi squared and the width of the blade w. The inertial forces are proportional
to the density of the soil ρs, the cutting velocity vc squared, the thickness of the layer cut hi and the width of the
blade w. This implies that the ratio between these two forces does not only depends on the geometry, but even
stronger on the layer thickness hi and the cutting velocity vc. The thicker the layer cut, the higher the influence of
gravity and the higher the cutting velocity, the higher the influence of inertia. One cannot say simply the higher
the cutting velocity the higher the influence of inertia.
2
s i
2
s c i
Gravitation : F g h w
(5-18)
Inertia : F v h w
(5-19)
The contribution of the inertial forces is determined by the following dimensionless parameter:
2
c
v
i
(5-20)
g h
i
In dredging a layer thickness of the magnitude of centimeters is common, while for a bulldozer a layer thickness
of a magnitude of a meter is not strange. At the same cutting velocity, the relative influence of inertial forces will
differ between dredging applications and the operation of bulldozers. If inertial forces dominate the cutting process,
the cutting forces can be expressed as:
2
h s c i HI
F v h w
sin( ) cos( )
With : HI
sin( )
sin( ) sin( )
(5-21)
2
s c i VI
F v h w
sin( ) cos( )
With : VI
cos( )
sin( ) sin( )
(5-22)
These equations are derived from equations (5-6), (5-7), (5-9) and (5-10). The shear angle β can be derived
analytically for the inertial forces, giving:
2
(5-23)
2 2
Figure 5-13 shows the percentage of the contribution of the inertial forces to the horizontal cutting force for a layer
thickness hi of 1.0 m at a cutting velocity of 0.5 m/sec, giving λi=0.025. Figure 5-14 shows the percentage of the
contribution of the inertial forces to the horizontal cutting force for a layer thickness hi of 0.1 m at a cutting
velocity of 15.7 m/sec, giving λi=250.
Table 5-1 shows the inertial effect for the dimensionless inertial effect parameter λi ranging from 0.025 to 250.
The percentage contribution of the inertial effect on the horizontal force is given as well as the shear angle, both
horizontal and vertical cutting force coefficients based on equations (5-21) and (5-22) and both horizontal and
vertical cutting force coefficients based on equations (5-13) and (5-14) for the case where the blade height hb
equals the layer thickness hi. The table shows that the inertial effect can be neglected at very small values of the
dimensionless inertial effect parameter λi, while at large values the gravitational effect can be neglected. The shear
angle β decreases with an increasing dimensionless inertial effect parameter λi. Since the inertial forces are not
influenced by the blade height hb, the cutting forces are not dependent on the blade height at high cutting velocities.
At low cutting velocities there will be an effect of the blade height.
Page 112 of 454 TOC Copyright © Dr.ir. S.A. Miedema