Some theoretical research on the Cut-in blade of power tiller

(1) An analytical representation of blade curve as cut-in angle constant

Abstract

1. An analytical difference between Pierce-in tine (so called Common tine) and Cut-in blade (nataba blade) was expressed by the equation (1).
2. The blade curve was analyzed through the equation (6) considering the cut-in angle γ is const. (Fig. 1). Some calculated examples were shown in Fig. 5.
For special cases, when the speed of rotary shaft u becomes zero, the equation (6) expresses the logarithmic spiral.
3. In case of u≠0 the tangential angle a can be expressed by the equation (7). (cf. Fig. 2)
4. The cut-in angle δ in operation will be the function of rotary angle θ, and it can be determined from the equation (10). (cf. Fig. 3)
5. As the Side blade has characteristics of Pierce-in tine, the transition part from Cut-in blade to Side blade will be obtained from the equation (9), in which γ=0. This shows the circle in which the center is located at (0, u/ω).
The patent dealing with the transition part (Kubota Co. etc.) can be considered as the special case of equation (9), where u=0. This is a circle of which the center is at (0, 0).
6. The section of Side blade consists of cylindrical surface, cut by any plane pararell to x-y plane, can also be expressed by equation (9).
The cut-in angle of the section under operation can be represented by the eqution (10).
For example, δ is around from -0°. 11 to -4°. -04, the negative sign means that the section has pierce-in effect.