**2. Materials and Methods**

*2.1. Rotational Tillage Mechanism*

2.1.1. Structure of Rotary Blades

The tractor is connected to the rotary tiller by a towing device and transmits power through a universal coupling. The schematic diagram of the rotary tiller is shown in Figure 1a. The rotary tiller moves forward with a tractor. The rotary tiller shaft rotates through the gearbox, following the tractor power output shaft to drive the rotary tiller. The scraper impacts and levels the scattered soil to achieve a flat cultivated land. In order to study the interaction rule of rotary tillage blade-soil-straw more intuitively, this paper first studies the operation mechanism of rotary tillage single blade-soil-straw and then optimizes the form and structure parameters of rotary tillage single blade.

**Figure 1.** Standard rotary tiller structure.

The blade is the key working part of the rotary tiller. The shape and structural parameters of the blade badly affected the quality and power consumption of the rotary tiller. The blade in this paper is designed and researched based on a standard rotary tillage cutter according to the research objectives, as shown in Figure 1b. The remaining are implemented in accordance with GBT 5669-2017 Rotary Tillage Machine Blades and Holders. The main structural parameters are shown in Table 1.

**Table 1.** The main structural parameters.


2.1.2. Mechanisms of Rotary Blades

The values of forward velocity and linear velocity of the blade endpoint determine the normal progress of soil cutting operation. The blade endpoint presents a composite motion; therefore, arrangements of velocity parameters will have diverse trajectories.

Let *Vd*—the tangential velocity of the blade endpoint, m/s;

$$V\_d = R\omega \tag{1}$$

$$
\lambda = \frac{V\_d}{V\_m} \tag{2}
$$

The blade velocity ratio *λ* and the motion trajectory are shown in Figure 2.

(1) When *λ* < 1, that is, the forward velocity *Vm* is greater than the blade linear velocity *V*d, its motion trajectory is a short cycloid, the direction of the horizontal component of the linear velocity at any point on the cycloid is consistent with the forward direction, and it is hardly difficult to realize the operation of post throwing soil blocks.

(2) When *λ* = 1, that is, the two values are equal, its motion trajectory is a cycloid curve, The horizontal velocity at any point is zero, and the same as above cannot realize soil throwing.

(3) When *λ* > 1, that is, the forward velocity *Vm* is less than the blade's linear velocity *Vd*, its motion trajectory is a complementary cycloid. The horizontal partial velocity direction of any point below the maximum cross chord is opposite to the forward direction, exact converse above, the soil block can be reprojected effectively at present.

**Figure 2.** Blade end point motion track.

Set point *M* is set as the blade cutting point; it will meet the normal working conditions of the rotary cultivator from the beginning of soil penetration to the end of soil throwing and leaving the ground; there are:

$$\mathbf{x} = \mathbf{R}\cos\alpha t + V\_m t \tag{3}$$

$$y = R\sin\cot t = R - h \tag{4}$$

where *R* is the radius of gyration of a blade, with the unit of m, *Vm* is forward velocity, with the unit of m/s, *ω* is angular velocity, with the unit of rad/s, *t* is time, with the unit of s, *h* is tillage depth, with the unit of m.

To meet the condition of throwing soil backward, the horizontal partial velocity *Vx* of the absolute velocity at any point on the absolute motion track of the blade is less than 0, according to the above equation, let:

$$V\_x = \frac{d\_x}{d\_t} = v\_m - 2\omega\sin\omega t < 0\tag{5}$$

$$
\sin \cot = \frac{R}{R - h} \sin \omega t = \frac{R}{R - h} \tag{6}
$$

$$V\_m < (R - h)\omega \tag{7}$$

The movement locus of the blade endpoint is shown in Figure 2b. As can be seen from the above equation: *R* increases, H increases, but the increased torque leads to increased power consumption, which leads to a decrease in speed and, therefore, productivity. Therefore, generally, *R* = 215, 245, 260 mm, and in this study, a range of 150 to 240 mm was chosen in order to explore whether a small radius could be used for rototilling under ground level.
