*2.1. V-Shaped Toothed Roller Stalk Pulling Structure and Working Principle*

The V-shaped toothed roller stalk-pulling component, which mainly consists of a V-shaped toothed roller, stalk-clearing roller, reel wheel, and land wheel, as shown in Figure 1, is a key component of stalk-pulling machines. The key parameters are listed in Table 1. The V-shaped toothed plates are evenly distributed in three rows along the

the toothed plates.

**Figure 1.** Structural schematic of V-shaped toothed roller. 1. V-shaped toothed roller, 2. Stalk-clearing roller, 3. Land wheel, 4. Reel wheel, 5. V-shaped toothed plate.

circumferential direction of the V-shaped toothed roller and will hereafter be referred to as


During the pulling process, the reel wheel rotates to feed the upper part of the cotton stalk into the harvester and the V-shaped toothed roller moves forward and rotates to embed the cotton stalks with lengths within the harvest width into the V-shaped toothed plate through the appropriate space between the V-shaped toothed rollers. The reel wheel works with the V-shaped toothed roller to apply push–pull forces that ultimately extract the cotton stalks embedded in the toothed plates from the soil.

#### *2.2. Key Component Design*

#### 2.2.1. Determination of V-Shaped Toothed Roller Rotational Speed

The rotational speed of a V-shaped toothed roller should satisfy the following two conditions [10]: (1) the pulled-out, undetached cotton stalk must not hinder the operation of the adjacent toothed plate and (2) when the first toothed plate fails to pull out a cotton stalk, the second or third row of toothed plates must be able to embed and hold the cotton stalk (Figure 2). Considering that the driving speed of a tractor in a field ranges from 0.7 to 1.4 m/s and the plant spacing between cotton stalks typically ranges between approximately 18 and 25 cm, according to Equation (1), the rotational speed of the V-shaped toothed roller should exceed 156 r/min. The results of experimental tests indicate that the rotational speed of a V-shaped toothed roller should not be too high (i.e., it should be less than 500 r/min). This is because an excessively high rotational speed was found to be associated with excessive force being applied to the cotton stalk by the toothed plate, leading to a significantly higher stalk pull-out miss rate and fracture rate.

$$m\_0 = \frac{1000 \times 60 \times v\_0}{l\_0} \times \frac{2}{3} = \frac{4000v\_0}{l\_0} \tag{1}$$

*n*0—rotational speed of tooth roller;

*v*0—driving speed of tractor;

*l*0—line spacing of cotton stalk.

**Figure 2.** Schematic diagram showing the pull-out process of cotton stalk.

2.2.2. Determination of V-Shaped Toothed Plate Parameters

The maximum diameter of a cotton stalk is 22.75 mm; however, according to the results of multiple field measurements, the diameter of most cotton stalks in Wudi County, Shandong Province ranges from 10 to 18 mm. Thus, we mainly took cotton stalks with a diameter larger than 10 mm into consideration in the proposed V-shaped toothed roller stalk-pulling machine design. Note that the tooth width of the toothed plate was designed to be 30 mm. Additionally, the toothed roller was also designed to satisfy three requirements: (1) to improve the cotton stalk embedding and holding effectiveness, (2) to ensure that each cotton stalk remains embedded and held once it is extracted and swung backward, and (3) to ensure that the stalk-clearing roller can easily clear away each extracted cotton stalk from the toothed roller. The stress analysis results for cotton stalk extraction via the proposed V-shaped toothed roller are shown in Figure 3.

**Figure 3.** Stress analysis sketch of cotton stalk pulling.

According to the analysis of Figure 3, Formulas (2)–(4) can be obtained:

$$F\_h = 2F\_{h1} \cos(\frac{\pi}{2} - \frac{\theta}{2}) = 2F\_{h1} \sin\frac{\theta}{2} \tag{2}$$

$$F\_T = 2F\_3 \cos\frac{\theta}{2} = 2F\_{h1} \tan\alpha\_0 \cos\frac{\theta}{2} \tag{3}$$

$$F\_{\mathbf{h}} = F\_{\mathbf{T}} \tag{4}$$

*θ*—cogging angle (◦);

*F*h—combined force of pressure on cotton stalk produced by both sides of tooth cogging (N);


The simultaneous Formulas (2)–(4) show that the above formula holds when *θ* = 2*α*0. The frictional angle between the cotton stalk and the tooth plate can be converted by the friction coefficient, which could refer to the friction coefficient of 0.2~0.35 between wood and steel [24]. The converted *α*<sup>0</sup> value was 11.3◦~19.3◦, thus the value of *θ* was 22.6◦~38.6◦.

The depth of cogging can be calculated from Formula (5):

$$l\_{\mathbf{s}} = \frac{l\_{\mathbf{k}}}{\frac{2\tan\theta}{2}} = \frac{15}{\frac{\tan\theta}{2}}\tag{5}$$

When the cogging has a smaller angle and a long and sharp tooth tip, the strength of the tooth plate is reduced. Therefore, the cogging angle was suggested to be greater than or equal to 25◦ after comprehensive consideration (*θ* = 25◦, *l*<sup>s</sup> = 67 mm). To sum up, the range of the cogging angle is set at 25◦ ≤ *θ* ≤ 40◦.
