Similitude Study of Soil-Machine System (I)

Similitude of Rectangular Blades in Dry Sand

Abstract

For the similitude study on the draft of bulldozing action of the vertical blade in pure dry sand, dimensional analysis was applied and dimensionless parameters which are called ∏ terms were derived as the operating and design conditions. The equation used to relate these terms was,
D/ρgb³=(v²/hg, h/b, α)
where, D=draft force
b=width of blade
h=height of blade
v=speed of blade with respect to sand
g=gravitational acceleration
α=angle of blade surface to the direction of draft
ρ=bulk density of sand
Similar rectangular blades having various sizes were tested under the conditions of the same value of the ∏ terms except v²/hg. Though the designed speed to each blade could not be given by our experimental installation, the four categories of speed were adopted successfully. In the preliminary tests, we found that D/ρgb³ is constant for any value of v²/hg within the limits of the speed. And the following results were obtained.
1. Dynamic similarity was found in six similar blades and it was proved that dimensional analysis is an available and feasible method to get the operating and design conditions.
2. Draft force D is not influenced by the speed of blade within the limits of values of v²/hg tested in this study.
3. Draft force D on a blade is proportional to the third power of characteristic length of a blade.
4. Value of D/ρgb³ is constant for a given value of h/b and α. And it is proportional to (h/b)².
5. Value of D/ρgb³ is influenced by α and it is marked in case of blades of large values of h/b.