Research on the Tensile and Impact Mechanical Properties of Millet Ear Petals

Abstract

In response to the low threshing efficiency of millet ear petals, this study investigated the tensile and impact mechanical properties of millet petals during the millet threshing process. Jingu 21, Zhangza 16, and Changza 466 were used as experimental subjects to study the effects of tensile angle and growth part on fracture strength, and to determine the influence of impulse and growth part on drop and breakage rates. The results indicated that both growth part and tensile angle have a highly significant impact on the tensile fracture strength of the millet petals. The tensile fracture strength decreases with the increase in the tensile angle, and increases with the growth part from top to bottom. The variety, growth part, and impulse significantly affect the impact drop and breakage rates of the millet petals, with the main factors affecting the drop rate being impulse, variety, and growth part, in that order. When the impulse is 2.296 N·s, the threshing effect for Jingu 21 is optimal, with a drop rate of 65.091% and a breakage rate of 13.487%. This research provides theoretical insights into the simulation of the millet ear threshing process and the optimization of the performance of millet threshing equipment.

1. Introduction

Millet, known for its drought resistance, tolerance to poor soil, rich nutritional content, and high protein levels in fodder, serves as a strategic reserve crop to address future water shortages, an ecological crop supporting sustainable agriculture, and a specialty crop helping to adjust dietary structures and balance nutrition [1,2,3]. However, it is difficult to detach the millet petals and grains in a combine harvester, due to the multi-level structure of millet ears, petals, and grains. The existing universal combine harvester still has the problems of high loss rate and high crushing rate when harvesting millet. Therefore, studying the mechanical changes of tensile and impact during the threshing process of millet ear petals is essential for the development and optimization of the threshing components of combined millet harvesters.

Domestic and foreign scholars’ research on the threshing process of crop harvest mainly focuses on large grain crops such as rice and corn [4,5,6,7]. For example, Liu et al. [8] designed a new type of comb buckwheat harvesting device. Through single factor test and orthogonal test, the effects of machine forward speed, comb speed and inclination angle of the threshing mechanism on threshing rate, crushing rate and loss rate were explored. The results show that, by optimizing these parameters, the threshing rate can be effectively improved, and the crushing rate and loss rate can be reduced. Que et al. [9] studied the influence of unbalanced excitation on the stability of the threshing cylinder. Through the dynamic signal test and analysis system, the axial trajectory of the threshing cylinder was tested, and the influence of unbalanced excitation caused by straw winding on the axial trajectory was analyzed. The results show that, by distributing the counterweight on the drum to simulate the radial distribution of the straw winding, it can be clearly seen that, with the increase in the counterweight weight, the trajectory deviation characteristics of the drum axis become more obvious.

In order to provide a theoretical basis for the development and optimization of operation equipment in grain harvesting, processing, storage and transportation, many scholars have achieved phased results in the influence of static load, such as compression and shear on the mechanical properties of grains [10,11,12,13,14,15]. For instance, Shi et al. [16] established a mechanical model of wheat straw with failure characteristics. The bonding parameters of the straw model were calibrated by tensile, compression, three-point bending, shear test and response surface methods. It was concluded that the straw model can accurately reflect the mechanical properties of wheat straw with failure characteristics. The study was conducted to investigate some physical properties of soybean at various moisture levels, As the moisture content of the soaked soybean increases, the value of sphericity, aspect ratio, bulk density, true density and porosity decreased [17]. Chandio et al. [18] explored the mechanical properties of corn grains under differing moisture levels and compression loading speeds, uncovering patterns in vertical and transverse fracture forces, hardness, and the relationship with moisture content and loading speed. Gupta et al. [19] loaded samples with different water contents in vertical and horizontal directions, and the seeds loaded in the horizontal direction produced hull cracks at a lower force level than the seeds loaded in the vertical direction. Babić et al. [20] studied the average values of length, width, thickness, geometric diameter, surface area, porosity, single grain weight, sphericity, bulk density, true density, thousand-grain weight and friction coefficient of maize seeds. The linear model showed that the secant elastic modulus of all hybrids decreased with the increase in seed moisture content. Li et al. [21] studied the effects of moisture content and loading rate on the shear resistance of five wheat varieties. The results showed that the shear resistance decreased with the increase in moisture content and loading rate. Furthermore, Zhang et al. [22] used the Maxwell model to perform relaxation tests on intact Chinese cabbage under lateral and longitudinal loads to determine its viscoelastic properties, and evaluated the differences in relaxation properties in different compression directions. It was concluded that the relaxation parameters of Chinese cabbage are very different in different positions, and the loading direction seems to affect the Maxwell model parameters and peak force response. As for wheat grains, Liu et al. [23] developed a viscoelastic–plastic contact model to investigate mechanical parameters, like the yield overlap and damping coefficients, through calibration experiments. Additionally, Xu and Li [24] established a contact mechanics-based model for the distribution of compression displacement and maximum pressure during collisions between threshing elements and rice grains, deriving critical velocity formulas for impact damage and establishing a nail-tooth impact model for rice grains. Within our research group [25,26], the effects of different varieties and different moisture contents on the viscoelastic mechanical indexes of millet grain groups were studied. Moreover, the research investigated the variation in the shear strength, specific shear energy, bending strength, elastic modulus, and bending stiffness at different internode positions of the stems of Changza 466, Zhangza 16, and Jingu 21 during their maturity period. Despite existing research by other scholars on the mechanical properties of different crop grains, it is evident that moisture content plays a crucial role in shaping the mechanical characteristics of grains [27,28,29,30], highlighting a research gap in the understanding of the impact and collision dynamics of millet.

The multi-level connection structure of millet ear, millet petal and grain is very different from the threshing process of rice, wheat and other crops. Research on the impact of the threshing mechanism of millet has not been reported yet. This paper mainly studies the tensile mechanical properties and impact threshing effect of millet ear-millet petal of three kinds of millet, Jingu 21, Zhangza 16 and Changza 466, which are regionally representative. A response model of the tensile breaking strength of millet petal with factors of variety, growth part and tensile angle is constructed, and the influence of different varieties, growth part and impulse on the falling rate and crushing rate of millet grains is obtained, in order to provide theoretical reference for optimizing the design of millet harvesting equipment.

2. Materials and Methods

2.1. Materials and Equipment

Three widely cultivated varieties in Shanxi region, Jingu 21, Zhangza 16, and Changza 466 millets, were selected at the mature stage.

The main equipment used in the experiment includes a CMT-6104 universal material testing machine (Shenzhen XinSanSi Material Testing Co., Ltd., Shenzhen, China; test force range: 0~10 KN, accuracy 0.01 N), SZ680 continuous zoom body microscope (Suzhou Jin Song Measuring Instruments Co., Ltd., Suzhou, China; objective magnification range 0.68~4.70X, eyepiece 10X/23 mm); Pendulum Impact Load Tester (Shenzhen XinSanSi Material Testing Co., Ltd., Shenzhen, China; maximum impact energy: 50 J); American Fowler digital vernier caliper, range 0–150 mm, resolution 0.01 mm (Canton, MA, USA).

2.2. Experimental Methods

2.2.1. Tensile Test

In this experiment, different varieties, growth parts and stretching angles were used as experimental factors to study the influence of various factors on the tensile fracture strength of ear petal. According to the growth position, the millet ears were divided into three parts: upper (the top 1/3 part), middle (the middle 1/3 part) and lower (the bottom 1/3 part), which were evenly cut with scissors in turn, as shown in Figure 1. The samples of different growth parts were placed in a sealed plastic bag and refrigerated in a refrigerator at 2 °C to ensure the stability of moisture content. Before the test, the test sample should be taken out of the refrigerator in advance and allowed to stand at room temperature for about 0.5 h to restore it to room temperature of 20 °C.

The experiment was carried out using a tensile grip fixture, as illustrated in Figure 2. The main stem portion of the test sample is clamped in the lower fixture during the tensile mechanical test of the millet petals. The target millet petal is then clamped at various angles with the lower test sample in the upper fixture, and the test procedure is initiated. Subsequently, the force required to fracture the millet petal from different growth parts of the main stem and the diameter of the pedicel are measured and documented. Each test is conducted at a loading speed of 20 mm/min, and the test data are meticulously recorded, with each trial repeated 5 times.

2.2.2. Impact Test

The impulse, variety and growth part of millet petals were taken as experimental factors, and the grain drop rate and breakage rate of each millet petal were taken as experimental indexes. The single millet petal in different regions of the same spike is fixed on the self-made baffle fixture in a specific direction (the material of the baffle is Q235 steel plate), and the pendulum is lifted at a certain angle. The angle between the pendulum and the vertical direction can be obtained on the side display screen. After the pendulum is released from the static state, the millet petal is impacted. After the impact is completed, the rebound limit angle is observed, as shown in Figure 3. Finally, the falling grains were collected with a self-made collection tank, and then the collected grains were placed under a microscope with pointed tweezers to observe the damage degree of the grains and record the number of broken grains and the number of falling grains (as shown in Figure 4). The number of grains that did not fall on the millet petal was counted, and the experimental data were recorded. Finally, the drop rate and breakage rate of the grains were measured. Each experiment was repeated 5 times.

During the impact test on the millet petal, the pendulum is first raised to an angle θ, as shown in Figure 3b. It swings freely and impacts the fixed millet petal. Subsequently, after the impact, the pendulum rebounds to an angle α, reaching the highest point, as shown in Figure 3c. The recorded angle values of θ and α are then utilized for conducting further tests and analyses on the millet petal grains.

According to the law of conservation, the energy of the system can be obtained:

$${\displaystyle \frac{1}{2}}{m}_{1}gh(1 - \cos \theta ) + m_{2}gh(h + {\displaystyle \frac{b}{2}})(1 - \cos \theta ) = {\displaystyle \frac{1}{2}}J{\omega }^2$$

(1)

$$J = {\displaystyle \frac{1}{3}}{m}_1{h}^2 + m_2{(h + {\displaystyle \frac{b}{2}})}^2 + {\displaystyle \frac{1}{12}}{m}_2(a^2 + b^2)$$

(2)

$$v_1 = {\displaystyle \frac{1}{2}}\omega h$$

(3)

$$v_2 = (h + {\displaystyle \frac{b}{2}})\omega$$

(4)

Through Equations (3) and (4), the speed of c and d points can be obtained when the pendulum is in contact with the millet petal, where m₁ is the mass of the link, kg; m₂ is the mass of the pendulum, kg; h is the length of the link, m; a is the length of the pendulum, m; b is the height of the pendulum, m; θ is the angle between the axis of the pendulum and the vertical direction, (°); J is the moment of inertia, kg·m²; g is the acceleration of gravity, m/s²; ω is the angular velocity of the pendulum in contact with the millet petal, rad/s; v₁ is the linear velocity at point c when it is in contact with the millet petal, m/s; and v₂ is the linear velocity at point d when the pendulum is in contact with the millet petal, m/s.

After measurement, m₁ = 0.514 kg, m₂ = 0.812 kg, h = 0.36 m, a =0.076 m, b = 0.112 m. Bring in Equations (1) and (2) to obtain:

$$\omega = \sqrt{52.48(1 - \cos \theta )}$$

(5)

The velocity of points c and d when the pendulum is in contact with the millet petal is calculated, which is brought into Equations (3) and (4). After the pendulum impacts the millet petal, the maximum angle α of the reverse swing is observed. Through Equations (1)–(4), the instantaneous velocity v_1′ and v_2′ of points c and d when the pendulum impacts the millet petal can be calculated again. Equation (6) can calculate the momentum before and after the collision.

$$\Delta p = {m_1{v}_1}^{\prime } - (-m_1{v}_1) + {m_2{v}_2}^{\prime } - (-m_2{v}_2)$$

(6)

According to the momentum theorem, the impulse in the impact process is calculated as shown in Equation (7).

$$I = {\displaystyle \int \frac{dp}{dt}}dt = \Delta p$$

(7)

where ∆p is the momentum change, kg·m/s; and I is the finger impulse, N·s.

2.3. Test Indicators

Based on the reference to General Specifications for the Determination of Agricultural Machinery Test Conditions (GB/T 5262-2008) [31], the test indicators are defined as follows.

2.3.1. Tensile Fracture Strength

At the end of the tensile test, the tensile fracture strength was calculated according to Equation (8) based on the measured data.

$$\sigma = {\displaystyle \frac{F}{S}}$$

(8)

$$S = {\displaystyle \frac{1}{4}}\pi d^2$$

(9)

where σ is the tensile fracture strength, MPa; F is the tensile fracture force, N; S is the cross-sectional area of ear bar, and mm²; d is the diameter of the ear bar, mm.

2.3.2. Grain Drop Rate

After each impact test, the number of falling and non-falling grains was measured, and the grain drop rate was calculated according to Equation (10).

$$Z_x = {\displaystyle \frac{S_x}{S_w + S_x}} \times 100\%$$

(10)

where Z_x is the grain drop rate, %; S_x is the Number of falling; and S_w is the Number of not falling.

2.3.3. Grain Breakage Rate

At the end of each impact test, the number of broken grains and the number of unbroken grains were measured respectively, and the grain breakage rate was calculated according to Equation (11).

$$Z_p = {\displaystyle \frac{S_{xp} + S_{wp}}{S_x + S_w}} \times 100\%$$

(11)

where Z_p is the grain breakage rate, %; S_xp is the number of falling broken; and S_wp is the number of unfallen broken.

3. Results and Analysis

3.1. Effect of Millet Ear Petal Tensile Fracture Strength

The tensile mechanical tests of different growth parts of Jingu 21, Zhangza 16 and Changza 466 were carried out at different angles. The test results are shown in

Table 1. Results of millet ear petal tensile test.

Variety	Angle (°)	Tensile Fracture Strength (MPa)
		Upper Part	Middle Part	Lower Part
Jingu21	0	19.013 ± 0.426 b	21.315 ± 0.913 b	23.71 ± 0.721 ab
	90	6.409 ± 0.647 d	7.281 ± 0.832 d	8.299 ± 0.705 d
	180	2.534 ± 0.205 f	3.518 ± 0.303 f	4.11 ± 0.264 e
Zhangza16	0	23.814 ± 1.039 b	26.012 ± 1.008 a	28.357 ± 1.048 a
	90	8.148 ± 1.08 cd	10.188 ± 0.992 c	12.249 ± 0.903 c
	180	4.173 ± 0.673 e	5.179 ± 0.433 e	6.395 ± 0.956 de
Changza466	0	19.557 ± 0.822 b	23.487 ± 0.51 a	25.992 ± 0.931 a
	90	7.473 ± 0.559 d	8.339 ± 0.633 c	9.155 ± 0.744 c
	180	2.834 ± 0.366 f	3.805 ± 0.64 f	4.909 ± 0.757 e

Note: Different lowercase letters mean significant differences at p < 0.05 among different treatments at 0.05 level.

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It can be seen that, under the same tensile angle, the tensile fracture strength of the lower part of the three millet varieties is the largest, followed by the middle, and the tensile fracture strength of the upper part is the smallest. Specifically, when considering the same tensile angle and growth part, Zhangza 16 displays a higher tensile fracture strength in comparison to the other two varieties. This suggests that, under identical conditions, the millet petal of Zhangza 16 presents greater resistance to detachment than the millet petals of Changza 466 and Jingu 21, with Changza 466 following as the second most resistant, and Jingu 21 as having the easiest detachment of the millet petal.

The tensile test results for millet ear petal were analyzed for variance using SAS, and the findings are displayed in

Table 2. Variance analysis of tensile test results.

Source of Variation	DF	Tensile Fracture	Strength
		F-Value	p-Value
Variety	2	5.04	0.0261
Growth Part	2	59.19	<0.0001
Tensile Angle	2	524.22	<0.0001
R2 = 0.9195

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The results of variance analysis showed that the significant p-value of the variety was 0.0261, and the significant p-values of the two effects of growth part and tensile angle were less than 0.0001. The coefficient of determination of the fracture force model reached 0.9195. Consequently, variety significantly influences the tensile fracture force of the millet petal. Moreover, the effects of growth part and tensile angle on the tensile fracture force of the millet petal are both highly significant. By observing the F-values in the table, the primary test factors impacting tensile fracture strength are, in sequence, tensile angle, growth part, and variety.

3.1.1. Effect of Tensile Angle on Millet Ear Petal Tensile Fracture Strength

The relationship between the effect of growth part and tensile angle on the tensile fracture strength of millet ear petal is shown in Figure 5.

The tensile fracture strength of the millet ear petal is significantly affected by the tensile angle. As the tensile angle increases, the tensile fracture strength required for millet petal breakage decreases gradually. Specifically, for the same growth part, the highest tensile fracture strength is observed at a tensile angle of 0°, ranging from 19.013 MPa to 28.357 MPa. This is followed by the tensile angle of 90°, with a range of 6.409 MPa to 12.249 MPa, and the lowest strength is found at a tensile angle of 180°, ranging from 2.534 MPa to 6.395 MPa. The relationship between tensile angle and tensile fracture strength in the millet petal is evident. Upon observing and analyzing the breakage of the millet petal at various tensile angles, it becomes apparent that the breakage mode of the millet petal changes with different tensile angles (as shown in Figure 6).

The growth form of the millet petal is closely related to this phenomenon due to the direction in which the millet petals grow. When the stretching angle is 0°, the millet petals extend towards the upper side, resulting in the material stretching in the same direction as the growth of the millet petals. This alignment leads to a larger tensile fracture strength. Conversely, at a stretching angle of 180°, the material stretches in the opposite direction to the growth of the millet petals, resulting in the tearing of the root of the branch shanks. As a result, the tensile fracture strength is smaller in this scenario.

3.1.2. Effect of Growth Part on Millet Ear Petal Tensile Fracture Strength

The growth part significantly affects the tensile fracture strength of the millet ear petal. Observations and analysis of the growth of millet plants show that the main stem of the millet tapers from the bottom up, and the pedicels connecting the millet ear petal follow the same trend. The tensile fracture strength of the millet ear petal decreases gradually from the lower to the upper growth part. The lower part corresponds to the highest tensile fracture strength, with a range of 4.11 MPa to 28.357 MPa; the middle part is next, with a range of 3.518 MPa to 26.012 MPa; and the upper part corresponds to the lowest tensile fracture strength, with a range of 2.534 MPa to 23.814 MPa.

3.2. Effect of Millet Petal Impact Drop Rate

The test results of the millet petal impact drop rate are shown in

Table 3. Drop results of millet petal impact test.

Variety	Angle θ (°)	Impulse (N·s)	Drop Rate (%)
			Upper Part	Middle Part	Lower Part
Jingu21	20°	1.074	39.744 ± 2.216 d	23.108 ± 1.721 f	18.406 ± 1.516 fg
	30°	1.387	56.954 ± 1.841 b	35.972 ± 1.943 e	27.611 ± 1.612 f
	40°	2.296	72.887 ± 1.162 a	65.091 ± 1.574 a	42.873 ± 1.241 c
	50°	2.827	78.007 ± 2.055 a	74.319 ± 2.575 a	48.638 ± 2.003 bc
Zhangza16	20°	1.074	27.136 ± 1.782 e	22.253 ± 1.968 fg	14.295 ± 1.859 gh
	30°	1.387	38.439 ± 1.727 d	34.568 ± 1.863 de	24.777 ± 1.917 f
	40°	2.296	56.521 ± 1.961 b	55.164 ± 1.399 b	42.782 ± 1.258 c
	50°	2.827	63.039 ± 1.627 ab	60.186 ± 1.57 b	50.386 ± 1.93 bc
Changza466	20°	1.074	9.55 ± 1.794 gh	7.738 ± 1.778 h	5.203 ± 1.902 h
	30°	1.387	22.58 ± 1.94 f	17.593 ± 1.674 g	16.648 ± 1.438 g
	40°	2.296	40.65 ± 2.502 d	35.352 ± 1.691 cd	32.333 ± 1.755 e
	50°	2.827	44.126 ± 2.501 c	41.226 ± 2.144 cd	40.442 ± 1.392 d

Note: Different lowercase letters mean significant differences at p < 0.05 among different treatments at 0.05 level.

.

The results demonstrate a consistent increase in the drop rate as the impulse intensifies. Among all three millet varieties, the upper part exhibits the highest drop rate, followed by the middle part, and finally the lower part. Notably, when comparing the drop rate under identical impulses and growth part, Jingu 21 exhibits the highest drop rate, followed by Zhangza 16, with Changza 466 displaying the lowest drop rate. Specifically, Jingu 21 stands significantly higher than the other two varieties, indicating that Jingu 21 millet grains have a higher tendency to detach and are more easily separated during the harvesting process.

Variance analysis of the drop rate test results was performed using SAS, and the results are shown in

Table 4. Analysis of variance for drop rate.

Source of Variation	DF	Drop Rate
		F-Value	p-Value
Variety	2	302.05	<0.0001
Growth Part	2	115.28	<0.0001
Impulse	3	797.83	<0.0001
Variety × Growth Part	4	25.04	<0.0001
Variety × Impulse	6	2.87	0.0215
Growth Part × Impulse	6	7.99	0.0148
R2 = 0.9648

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The analysis of variance was performed to examine the impact of various factors on the grain drop rate. Independent variables included variety, growth part, impulse, variety × growth part, variety × impulse, and growth part × impulse, while the dependent variable was drop rate. The results, presented in descending order of F-values, revealed that impulse, variety, growth part, variety × growth part, growth part × impulse, and variety × impulse had F-values of 797.83, 302.05, 115.28, 25.04, 7.99, and 2.87, respectively. The results showed that the main factors affecting the drop rate of millet grains were impulse and variety, followed by growth part, variety × growth part, and growth part × impulse, and variety × impulse had the least effect on the falling rate. Notably, both impulse and variety demonstrated notably higher F-values compared to the other factors investigated.

3.2.1. Effect of Impulse on Millet Petal Impact Drop Rate

The variation in impact drop rate with impulse for different varieties of millet petal is shown in Figure 7.

The influence of impulse on the impact drop rate of millet petal is extremely significant (p < 0.001), and the impact drop rate of millet petals of the three varieties increases with the increase in impulse. For Jingu 21, the lowest drop rates at the three parts were 39.744% for the upper part, 23.108% for the middle part, and 18.406% for the lower part at an impulse of 1.074 N·s; the highest drop rates were 78.007% for the upper part, 74.319% for the middle part, and 48.638% for the lower part at an impulse of 2.827 N·s. For Zhangza 16, the lowest drop rates at the three parts were 27.136% for the upper part, 22.253% for the middle part, and 14.295% for the lower part at an impulse of 1.074 N·s; the highest drop rate for the upper part was 63.039% at an impulse of 2.827 N·s, with the middle and lower parts at 60.186% and 50.386% respectively. For Changza 466, the lowest drop rates for the three parts were 9.55% for the upper part, 7.738% for the middle part, and 5.203% for the lower part at an impulse of 1.074 N·s; the highest drop rate for the upper part was 44.126% at an impulse of 2.827 N·s, with the middle and lower parts at 41.226% and 40.442% respectively. When the impulse increases from 1.074 N·s to 2.296 N·s, the drop rate increases rapidly. When the impulse increases from 2.296 N·s to 2.827 N·s, the drop rate increases slowly. When the impulse increases to a certain extent, the drop rate is basically unchanged.

3.2.2. Effect of Variety on Millet Petal Impact Drop Rate

Variety is the main experimental factor affecting the impact drop rate of millet petals. Under the same impulse, Jingu 21 has the highest impact drop rate of millet petals, with a range of 18.406% to 78.007%; Zhangza 16 is next, with a range of 14.295% to 63.039%; Changza 466 has the lowest impact drop rate of millet petals, with a range of 5.203% to 44.126%. It can be seen that the connection force between the grains and the rachis of Jingu 21 is relatively small, followed by Zhangza 16, while Changza 466 has a relatively large connection force between the grains and the rachis.

3.3. Effect of Millet Petal Impact Breakage Rate

The test results for the impact breakage rate of the millet petal are shown in

Table 5. Break results of millet petal impact test.

Variety	Angle (°)	Impulse (N·s)	Breakage Rate (%)
			Upper Part	Middle Part	Lower Part
Jingu21	20°	1.074	2.409 ± 1.346 gh	1.876 ± 1.718 gh	1.855 ± 1.412 h
	30°	1.387	10.981 ± 1.517 e	8.256 ± 2.294 f	6.077 ± 1.603 g
	40°	2.296	16.352 ± 1.754 c	13.487 ± 1.751 d	12.451 ± 1.742 d
	50°	2.827	34.864 ± 2.387 a	30.377 ± 1.892 a	28.115 ± 1.719 b
Zhangza16	20°	1.074	4.871 ± 1.683 g	2.687 ± 1.609 g	0.835 ± 0.522 h
	30°	1.387	14.33 ± 1.533 d	12.403 ± 1.492 d	10.703 ± 1.652 e
	40°	2.296	20.884 ± 2.146 b	18.954 ± 1.963 c	14.784 ± 1.727 c
	50°	2.827	38.52 ± 1.829 a	35.012 ± 1.655 a	29.089 ± 1.52 ab
Changza466	20°	1.074	1.396 ± 0.816 h	0.963 ± 0.579 h	0.377 ± 0.127 q
	30°	1.387	7.787 ± 1.615 f	6.085 ± 1.344 f	5.21 ± 1.544 g
	40°	2.296	11.149 ± 1.778 e	10.212 ± 1.384 e	8.216 ± 1.312 f
	50°	2.827	24.165 ± 1.669 b	23.547 ± 1.761 b	20.704 ± 1.688 c

Note: Different lowercase letters mean significant differences at p < 0.05 among different treatments at 0.05 level.

.

For the same variety of millet, the breakage rate continuously increases with the rise in impulse. The impact of different growth parts on the breakage rate follows a similar pattern to the drop rate: the upper part has the highest breakage rate, the middle part is next, and the lower part has the lowest. Under the same impact conditions, Zhangza 16 has the highest breakage rate, followed by Jingu 21, and Changza 466 has the lowest. The grains of Changza 466 are more resistant to breaking during the mechanized harvesting and threshing process; Jingu 21 and Zhangza 16 millet are more suitable for mechanical crushing processing. Under the same impulse, all three varieties show the upper part with the highest breakage rate, the middle part next, and the lower part with the lowest.

Variance analysis of the breakage rate test results was performed using SAS, and the results are shown in

Table 6. Analysis of variance for breakage rate.

Source of Variation	DF	Breakage Rate
		F-Value	p-Value
Variety	2	294.18	<0.0001
Growth Part	2	132.20	<0.0001
Impulse	3	741.16	<0.0001
Variety × Growth Part	4	9.01	0.0084
Variety × Impulse	6	28.77	<0.0001
Growth Part × Impulse	6	4.82	0.0153
R2 = 0. 9542

.

The analysis of variance was conducted with variety, growth part, impulse, variety × growth part, variety × impulse, growth part × impulse as independent variables and breakage rate as dependent variable, and in descending order of F-value, impulse, variety, growth part, variety × impulse, variety × growth part, growth part × impulse, the F-values were 741.16, 294.18, 132.20, 28.77, 9.01 and 4.82, respectively, indicating that the most important factors affecting grain breakage rate are impulse and variety, followed by growth part, variety × impulse, growth part × impulse, and growth part × impulse, with growth part × impulse having the least effect on the breakage rate; the F-value of impulse was much greater than that of other factors in all six factors. Therefore, when carrying out mechanical harvesting of cereals, choosing the appropriate impulse can significantly improve the quality of harvest.

3.3.1. Effect of Impulse on Millet Petal Impact Breakage Rate

The variation in impact breakage rate with impulse for different varieties of millet petal is shown in Figure 8.

The breakage rate of three millet varieties increases with the increase in impulse, demonstrating a significant impact on the millet petals’ breakage rate (p < 0.001). Observations of Jingu 21 revealed that the lowest breakage rates at three parts occurred at an impulse of 1.074 N·s, with percentages of 2.409% for the upper part, 1.876% for the middle part, and 1.855% for the lower part. Conversely, the highest breakage rates were achieved at an impulse of 2.827 N·s, with the upper part reaching 34.864%, the middle part 30.377%, and the lower part 28.115%. Similarly, for Zhangza 16, the lowest breakage rates at three parts were seen at an impulse of 1.074 N·s, registering 4.871% for the upper part, 2.687% for the middle part, and 0.835% for the lower part. In contrast, the highest breakage rates were recorded at an impulse of 2.827 N·s, with the upper and middle parts reaching 38.52% and 35.012%, respectively, while the lower part stood at 29.089%. Finally, for Changza 466, the lowest breakage rates were observed at an impulse of 1.074 N·s, with percentages of 1.396% for the upper part, 0.963% for the middle part, and 0.377% for the lower part. At an impulse of 2.827 N·s, the upper part registered the highest breakage rate at 24.165%, followed by the middle part at 23.547% and the lower part at 20.704%. Notably, the breakage rate exhibited a gradual increase when the impulse ranged from 1.074 N·s to 2.296 N·s, but accelerated notably as the impulse ranged from 2.296 N·s to 2.827 N·s.

3.3.2. Effect of Variety on Millet Petal Impact Breakage Rate

Under the same impulse, Changza 466 exhibits the lowest millet petal impact breakage rate, followed by Jingu 21, while Zhangza 16 has the highest impact breakage rate. Significantly, Changza 466 demonstrates a notably lower breakage rate compared to the other two varieties, suggesting that it possesses superior compressive performance and higher quality. Consequently, Changza 466 grains display enhanced resistance to breakage during the threshing process, whereas Zhangza 16 grains are more conducive to post-harvest processing.

4. Discussion

Studying the threshing separation mechanism of the millet ear-grain and petal-grain is crucial for the design and parameter optimization of the threshing structure of millet harvesters. During the processes of harvesting, threshing, and processing, the grains and ears of millet are subjected to complex loads, such as tension, compression, and impact. Similar to the research of Fang et al. [32] on kiwifruit, this study utilized the measured tensile fracture force and stem diameter between the millet ears and millet petals to calculate the tensile fracture strength between the ears and millet petals and derived the variation pattern of the tensile fracture strength with the stem diameter. The results, similar to some patterns found in the tensile mechanical testing of different nodes of the millet stem, leaf sheath, leaf blade, and leaf ring by Li et al. [33], and the study of the connecting force performance between the millet petal and stem by Zhang et al. [34], provide valuable insights. Furthermore, this study analyzed the effects of variety, growth part, and tensile angle on the tensile fracture strength, and concluded that the main experimental factors influencing the tensile fracture strength are, in descending order, tensile angle, growth part, and variety.

Under the same variety, there are differences in the impact drop rate and breakage rate of millet petals from different parts [35]. A stratified analysis of the impulse in the impact zone was conducted, and a comparative analysis of the drop and breakage rates of different parts was performed [36]. The trend in increasing breakage rate with the increase in impulse is consistent with the influence pattern of impact load on millet grain damage by Yin et al. [37]. By comparing the impact breakage rates of ear petals from different parts, it was determined that the upper part has the highest grain breakage rate, followed by the middle part, and the lower part has the lowest. This result is consistent with the impact test results of different parts of the corn ear by Li et al. [38]. In addition, an analysis of the relationship between impulse and the drop rate of millet petals impact was conducted, and it was found that the grain drop rate continuously increases with the increase in impulse and eventually tends to stabilize.

This article explores the drop rate and breakage rate of grains during the threshing process by examining variety, growth part, and impulse. It reveals that the magnitude of impulse during impact significantly influences the drop and breakage rates of grains during threshing. The study suggests that adjusting factors such as drum rotation speed and the structure of the threshing drum can modify the impact force on the ears, leading to improved drop rates while minimizing the breakage rate. In addition, it was found that the tensile angle and growth part had a significant effect on the tensile fracture strength of the ear and the petal, indicating that the tensile fracture strength of different parts and different directions should be taken into account in the simulation modeling of the ear, so as to improve the authenticity of the threshing effect in the simulation process.

Therefore, future research should further explore how to improve the design of threshing machinery, especially the optimization of threshing structure and dynamic parameters. At the same time, considering the differences in the physical properties of grains under different types and growth conditions, it is also necessary to study the effects of these differences on the threshing process, which will be helpful in developing special threshing technology and equipment.

5. Conclusions

The study examined the tensile and impact mechanical properties of millet ear petals from different millet varieties, and discovered the patterns of influence for tensile angle and growth part on tensile fracture strength, as well as the effects of impulse and growth part on the falling and breakage rates.

(1)

The variety, tensile angle, and growth part all have a highly significant effect on tensile fracture strength. The tensile fracture strength of the millet petals’ pedicel decreases as the tensile angle increases, with the highest fracture strength corresponding to a tensile angle of 0°, ranging from 19.013 MPa to 28.357 MPa. At a tensile angle of 90°, the fracture strength is lower, with a range of 6.409 MPa to 12.249 MPa; the lowest fracture strength corresponds to a tensile angle of 180°, with a range of 2.534 MPa to 6.395 MPa. The lower part of the millet petals’ pedicel has the highest tensile fracture strength, followed by the middle part, and the upper part has the lowest. When designing the threshing structure, it can be considered that the millet petals are subjected to forces in different directions in the drum, thereby improving the threshing efficiency.

(2)

The impulse and variety significantly affect the drop rate of millet petals due to impact, with the drop rate increasing as the impulse increases. When the impulse increases from 1.074 N·s to 2.296 N·s, the drop rate increases more rapidly; when the impulse increases from 2.296 N·s to 2.827 N·s, the drop rate increases more slowly. Jingu 21 has the highest drop rate, followed by Zhangza 16, while Changza 466 has the lowest drop rate.

(3)

Impulse and variety are the main factors affecting the impact breakage rate of millet petals. The breakage rate increases with the increase in impulse, growing more slowly when the impulse increases from 1.074 N·s to 2.296 N·s, and more rapidly when the impulse increases from 2.296 N·s to 2.827 N·s. Zhangza 16 has the highest breakage rate, followed by Jingu 21, while Changza 466 has the lowest breakage rate.