*2.1. Test Materials*

Four wheat samples with varying moisture content (10%, 13%, 15%, and 18%) were prepared by screening complete and plump wheat grains to simulate harvest conditions [10]. The working components of the combine harvester during wheat harvesting are typically composed of rubber, structural steel, and other materials. In order to simulate the collision recovery coefficient in the realistic environment of wheat grain collision, the test materials selected were structural steel Q235 and rubber. The material properties of the chosen materials can be ascertained by consulting the material library parameters as displayed in Table 1 [11].


**Table 1.** Collision material properties.

#### *2.2. Experimental Setup*

To measure the collision recovery coefficient between wheat grain and collision material, a kinematic model of the grain impact process was established, and a test apparatus for grain elasticity recovery coefficient was constructed as illustrated in Figure 1. The test apparatus primarily consists of the overall support of the test bench, the grain collection plane, the collision plate or the loss sensor striking the force plate, the grain feeding mechanism, and the grain height lifting lead screw. The collision plate was mounted at a 45-degree angle in front of the grain collection plane of the test bench, and the wheat grain sample was positioned in the grain dispensing mechanism directly above.

#### *2.3. Test Principle*

Collision represents a prevalent mechanical phenomenon, characterized by a brief duration of the collision process [12], minimal displacement of the colliding objects, considerable velocity alterations, substantial impact force exerted by the colliding entities, and energy dissipation. Consider two objects possessing masses *m*<sup>1</sup> and *m*2, colliding at velocities *v*<sup>1</sup> and *v*2, respectively. In accordance with the conservation of momentum principle, the momentum conversion formula during the collision process involving these two objects can be deduced, as demonstrated in Equation (1) [13]:

$$\begin{cases} \begin{array}{c} m\_1 \upsilon\_1 + m\_2 \upsilon\_2 = m\_1 \upsilon\_1' + m\_2 \upsilon\_2'\\ k = \frac{\upsilon\_2' - \upsilon\_1'}{\upsilon\_1 - \upsilon\_2} \end{array} \tag{1} $$

**Figure 1.** Grain impact test bench. 1. test bed bracket; 2. grain collection plane; 3. collision plate; 4. grain delivery mechanism; 5. grain height lifting screw.

After derivation and calculation, velocities *v*<sup>1</sup> and *v*<sup>2</sup> after the collision can be ascertained, as indicated in Equation (2):

$$\begin{cases} \ v\_1' = \upsilon\_1 - (1+k) \frac{m\_2}{m\_1+m\_2} (\upsilon\_1 - \upsilon\_2) \\ \ v\_2' = \upsilon\_2 + (1+k) \frac{m\_1}{m\_1+m\_2} (\upsilon\_1 - \upsilon\_2) \end{cases} \tag{2}$$

when *k* is equal to 1,

$$\begin{cases} \ v\_1' = v\_1 - \frac{2m\_2}{m\_1 + m\_2}(v\_1 - v\_2) \\\ v\_2' = v\_2 + \frac{2m\_1}{m\_1 + m\_2}(v\_1 - v\_2) \end{cases} \tag{3}$$

when *k* is equal to 0,

$$\upsilon\_1 = \upsilon\_2 = \frac{m\_1 \upsilon\_1 + m\_2 \upsilon\_2}{m\_1 + m\_2} \tag{4}$$

where *m*<sup>1</sup> and *m*<sup>2</sup> denote the masses of the two colliding objects, with the unit in kg. *v*<sup>1</sup> and *v*<sup>2</sup> represent the pre-collision velocities of the two colliding objects, expressed in m/s; and *v*<sup>1</sup> and *v*<sup>2</sup> correspond to the post-collision velocities of the objects, with the unit in m/s. The reference formatting has been adjusted.

Upon analyzing Equations (3) and (4), it becomes apparent that the k value dictates the post-collision velocity alteration of the objects. When *k* = 1, a perfect elastic collision transpires, and the velocities of the two objects are transferred. Notably, when *m*<sup>1</sup> = *m*2, the velocities of the two objects are exchanged following the collision. When *k* = 0, an imperfectly elastic collision occurs. Post-collision, the velocities become identical and the two objects proceed in unison.

In addition to their velocity, the kinetic energy of the two objects undergoes alteration following the collision, with the most pronounced change being kinetic energy loss. Equation (5) illustrates the pre- and post-collision kinetic energy equation, with *T*<sup>1</sup> and *T*<sup>2</sup> representing the cumulative kinetic energy before and after the collision, respectively.

$$\begin{cases} \quad T\_1 = \frac{1}{2}m\_1v\_1^2 + \frac{1}{2}m\_2v\_2^2\\ \quad T\_2 = \frac{1}{2}m\_1v\_1^2 + \frac{1}{2}m\_2v\_2^2 \end{cases} \tag{5}$$

The total kinetic energy loss of the two objects post-collision can be derived, as displayed in Equation (6):

$$\begin{array}{l}\triangle T = T\_1 - T\_2\\=\frac{m\_1 m\_2}{2(m\_1 + m\_2)}(1 + k)^2 (v\_1 - v\_2)^2\end{array} \tag{6}$$

when *k* = 1, kinetic energy loss is expressed as Equation (7):

$$
\triangle T = T\_1 - T\_2 = 0 \tag{7}
$$

where *T*<sup>1</sup> signifies the aggregate kinetic energy of the two objects prior to the collision, with the unit in J; *T*<sup>2</sup> represents the total kinetic energy of the two bodies following the collision, with the unit in J; and Δ*T* denotes the difference in kinetic energy between the two objects pre- and post-collision, expressed in J.

When *k* = 0, kinetic energy loss is expressed as Equation (8):

$$
\triangle T = \frac{m\_1 m\_2}{2(m\_1 + m\_2)}(v\_1 - v\_2)^2 \tag{8}
$$

In accordance with the definition of the recovery coefficient *e* (both *e* and k are designated as elastic recovery coefficients), the proportion of the separation velocities of two objects in the normal direction at the contact point before and after collision represents the elastic recovery coefficient. Consequently, a schematic illustration of the determination of the elastic recovery coefficient is depicted in Figure 2. It is merely necessary to obtain the approaching velocity prior to the collision and the separating velocity following the collision to deduce the elastic recovery coefficient. To enhance the precision of velocity detection, this test employs the principle of kinematic equations, calculating the requisite velocity values through an indirect method.

After the grain experiences impact and rebound, a parabolic trajectory is formed, where *s* signifies the horizontal displacement following the grain rebound, and *h* represents the distance from the grain collection plane to the rebound point. From this, the *x*-axis directional velocity after the collision can be determined, as demonstrated in Equation (9):

$$
v\_x = s \sqrt{\frac{g}{2h}}\tag{9}$$

where *s* denotes the horizontal displacement of seeds post-rebound, with the unit being millimeters; *h* is the vertical distance between the rebound point and the grain collection plane (unit: mm). Additionally, *g* corresponds to neutral acceleration, measured in m/s2; *vx* refers to the velocity along the x-axis after the grain collision, with the unit expressed in m/s.

The grain descends from the feeding mechanism, undergoing free-fall motion, with H being the distance from the seed falling point to the impact point. From this information, the *y*-axis directional velocity prior to grain collision can be calculated, as shown in Equation (10):

$$v\_{\mathcal{Y}} = \sqrt{2gH} \tag{10}$$

where *H* is the height of grain fall and the unit is mm.

Finally, the formula for computing the recovery coefficient is derived by utilizing the definition of the recovery coefficient, as presented in Equation (11). In this equation, *θ* symbolizes the angle between the Y-axis velocity and the normal vector velocity before grain collision, while *β* represents the angle between the X-axis direction velocity and the normal vector velocity prior to grain collision.

$$e = \frac{v\_1}{v\_0} = \frac{v\_x \cos \beta}{v\_y \cos \theta} = \frac{s \cos \beta}{2 \cos \theta \sqrt{Hg}} \tag{11}$$

where *e* refers to the elastic recovery coefficient, *θ* is the angle between the velocity along the Y-axis and the normal vector preceding grain collision, and *β* is the angle between the velocity along the X-axis and the normal vector before the grain collision.

**Figure 2.** Schematic diagram of elastic recovery coefficient determination. 1. test bed bracket; 2. grain collection plane; 3. collision plate; 4. grain delivery mechanism; 5. grain height lifting screw.

#### *2.4. Experimental Methods*

The wheat recovery coefficient primarily correlates with moisture content, collision material, material thickness, and fall height of wheat. To emulate the actual harvest scenario, wheat samples with varying moisture contents of 10%, 13%, 15%, and 18% were employed in the experiment. The chosen materials comprise Q235 steel plate and rubber; the material thicknesses selected are 2 mm, 4 mm, and 8 mm; the seed drop heights are 120 mm, 180 mm, and 240 mm; and the factor levels constituting the wheat univariate test are presented in Table 2.


**Table 2.** The level of univariate test factors.

/: indicates that no data exists.

In accordance with the factor level in Table 2, four sets of single-factor influence tests were conducted. In the test on the effect of moisture content on the recovery coefficient, Q235 steel served as the collision material, the material thickness remained at 4 mm, and the drop height was set at 180 mm, resulting in four sets of data. In the test regarding the impact of collision material on the wheat recovery coefficient, the material thickness remained at 4 mm, and the drop height was set at 180 mm, yielding eight sets of data. In the test regarding the effect of material thickness on the wheat recovery coefficient, Q235 steel served as the collision material, and the drop height was set at 180 mm, procuring 12 sets of data under distinct moisture conditions. In the test regarding the impact of fall height on the wheat recovery coefficient, Q235 steel served as the collision material, and the material thickness remained at 4 mm, obtaining 12 sets of data under varying moisture conditions.

#### **3. Results and Analysis**
