Optimum Design of Profiled Root–Trimming Device for Pull–Cut Harvester of Leading–Drawing–Cutting Type

Abstract

In this study, a leading–drawing–cutting–type profiled root–trimming device was designed to address the problems of high impurity and damage rates that occur with the operation of a pull–cut garlic harvester. The main components of the designed device include a pull–clamp mechanism, roll–pulling mechanism, root–trimming knife mechanism, lifter, gearbox, universal drive shaft, motor, and frame that, together, can complete the root–trimming operation for a pull–cut garlic harvester. An orthogonal regression test was carried out by taking the roller diameter, the roller inclination angle, the knife rotation speed, and the working speed as factors and by taking the impurity rate and the damage rate as indices. The results of the orthogonal regression test showed that the impurity rate was most strongly affected by the roller diameter, followed by the knife rotation speed, the working speed, and the roller inclination angle. Meanwhile, the damage rate was most strongly affected by the knife rotation speed, followed by the roller diameter, the working speed, and the roller inclination angle. The regression analysis showed that when the roller diameter was 100 mm, the roller inclination angle was 25°, the knife rotation speed was 200 r·min⁻¹, and the working speed was 1.22 km·h⁻¹, the comprehensive trimming quality reached its maximum value of 97.82%. The verification result of the parallel test gave a value of 97.52%, which was mainly affected by the irregular sizes of the bulbs, but it showed no significant difference from the regression analysis results. The tests verified that the profiled root–trimming device could be applied to develop the technology of garlic pull–cut harvesters.

1. Introduction

Garlic is a famous edible and medicinal plant of the Allium genus. The FAO’s statistics show that garlic is planted in more than 130 countries [1], with a total planting area of more than 1.6 million hectares and an annual yield of more than 30 million tons. China, with its garlic planting area, yield, and export trade volume ranking first in the world [2,3], is globally known as “the hometown of garlic”.

Harvesting is one of the key links in garlic production [4,5,6]. In developed countries, harvesting is carried out by machines [7], but it is mainly completed by means of manual labor in China [8]. As a result, the cost of harvesting is about CNY 18,000 per hectare, accounting for about 40% of the total cost of planting. Currently, the usage rate of garlic–harvesting machinery in China is less than 10% [9], and the production mode of garlic is in the key stage of changing from a traditional to a mechanized process [10,11]. A pull–cut garlic harvester can complete digging, pulling, clearing, and other operations with high operating efficiency and a low garlic damage rate [12,13]. Such harvesters are widely used in developed countries and have been widely promoted in China in recent years [14,15]. However, Chinese garlic harvesting requires a high degree of cleanliness, and the existing harvesters leave too much root soil on the garlic to meet the cleanliness requirements [16,17]. Therefore, in order to achieve the cleanliness requirements associated with garlic harvesting in China, it is necessary to carry out research on the root–trimming devices used with pull–cut harvesters.

Many studies on garlic harvesting technology have been carried out around the world [18,19,20]. However, few companies and units have carried out research on root–trimming technology for pull–cut harvesters [21,22,23]; only Yanmar Co., Ltd., in Japan, the Nanjing Institute of Agricultural Mechanization in China, and Shandong Agricultural University in China [24,25,26] have carried out such research. All of them used the method of gradually clamping the top of the garlic to locate the position of the garlic root for root trimming; in the resulting data [21], the damage rate was 2.78%, and the root-cutting rate was 93.17%. A high damage rate causes garlic to easily mildew and rot, making it difficult to store, transport, and sell.

This study aimed to address the high impurity and damage rates that occur with the operation of a pull–cut garlic harvester. To this end, a leading–drawing–cutting–type profiled root–trimming device was developed. The key structural parameters and operating parameters were determined via a combination of theoretical analyses and bench testing, and the comprehensive trimming quality (represented by the impurity rate and damage rate) in root–trimming operations was assessed in order to promote the development of pull–cut garlic harvester technology.

2. Main Structure and Working Principle

2.1. Main Structure

In this study, a root–trimming device was designed for garlic harvesting. Structural diagrams of the device are shown in Figure 1. The main components of the device include a pull–clamp mechanism, roll–pulling mechanism, root–trimming knife mechanism, lifter, gearbox, universal drive shaft, motor, and frame.

The main functions of each component of the root–trimming device are as follows: The pull–clamp mechanism realizes the clamping and conveyance of garlic plants. The roll–pulling mechanism realizes the deformation and downward transportation of the garlic root–soil composite. The root–trimming knife mechanism realizes the repeated cutting of the garlic root–soil composite. The lifter can adjust the inclination angle of the roller. The frame, motor, gearbox, and universal drive shaft mainly provide support, power, and power transmission.

2.2. Working Principle

The root–trimming process is divided into three stages, namely leading, drawing, and cutting, as shown in Figure 2. In the first stage, the pull–clamp mechanism clamps the garlic stem, and the garlic bulb with attached root–soil composite is introduced above the roll–pulling mechanism. As the roller rotates inward, the root–soil composite is extruded and transported downward, and part of the root–soil composite is removed by the root–trimming knife. In the second stage, most of the root–soil composite is extruded and transported downward until the garlic bulb comes into contact with the roller, and most of the root–soil composite is removed by the root–trimming knife. In the third stage, the garlic bulb slips onto the roller, and the root–trimming knife continues to cut the residual root–soil composite until the bulb has left the roller mechanism. Multiple root–trimming knives cut the root–soil composite, which greatly reduces the impurity rate. The device has good adaptability to the length of the garlic stem and the size and position of the garlic during the whole root–trimming process.

In the root–trimming process, the motion relationship satisfies the following:

$$v={\displaystyle \frac{\pi n_1{r}_1}{30}}$$

(1)

In this formula, $v$ is the conveyance speed of the garlic stem, m·s⁻¹; $n_1$ is the rotation speed of the belt pulley in the pull–clamp mechanism, r·min⁻¹; and $r_1$ is the effective radius of the belt pulley in the pull–clamp mechanism, m.

Through a mechanical analysis (Figure 3), the following formulas were obtained.

$$f\cos \theta +F+mg=N\sin \theta$$

(2)

$$f=\mu N$$

(3)

$$\cos \theta =\left(p+d_2\right)/\left(d+d_2\right)$$

(4)

$$N<\delta <D$$

(5)

$$d>p$$

(6)

In the above, $f$ is the friction between the garlic bulb and the rollers of the roll–pulling mechanism, N; $\theta$ is the angle between N and the horizontal plane, °; F is the pulling force of the roller on the garlic root, N; N is the support force of the roller on the garlic bulb, N; m is the combined weight of the garlic stem, garlic bulb, and root–soil composite, kg; g is the acceleration due to gravity, m·s⁻²; $\mu$ is the sliding friction coefficient between the bulb and roller; p is the gap between the rolls, m; d is the equivalent diameter of the bulb, m; $d_2$ is the roller diameter, m; $\delta$ is the contact area between the roller and the bulb, cm²; and D is the fruit hardness of the bulb, N·cm⁻²;

A formula for the rotation speed of the root–trimming knife was thus obtained.

$$n_3=30v_3/\pi r_3$$

(7)

Here, $n_3$ is the rotation speed of the root–trimming knife, r·min⁻¹; $v_3$ is the knife’s trimming speed, m·s⁻¹; and $r_3$ is the knife’s radius, m.

Through an analysis of the structure and position relationships (Figure 4), the following formula was obtained:

$$\sqrt{{\left({\displaystyle \frac{d_2+d}{2}}\right)}^2-{\left({\displaystyle \frac{d_2+l}{2}}\right)}^2}+L-{\displaystyle \frac{d_3+d}{2}}\ge 0$$

(8)

In the above, l is the distance between the rollers, m; L is the distance between the roller and the drive shaft of the knife, m; and $d_3$ is the diameter of the knife, m.

3. Bench Test

3.1. Test Method

The test materials were “purple garlic of Jinxiang” planted in silty loam soil from China’s Shandong province. All materials were collected on 12 May 2024. The garlic bulbs were symmetrical, with diameters ranging from 55 to 65 mm, and the average equivalent diameter was 60 mm. The soil moisture content was 18.1% to 23.1%, measured using a soil moisture meter (Product Model: TDR300, Spectrum Technologies, Inc., Washington, DC, USA). In total, more than 3000 qualified samples were selected, and 30 groups of tests were carried out with 100 samples in each group. Each garlic plant sample was wrapped in a fresh–keeping bag after harvest to maintain the soil moisture and improve the repeatability of the test. The initial impurity rate was more than 50%. All the impurity rates and damage rates in each test were recorded as valid data. Examples from the garlic root–trimming test are shown in Figure 5.

3.2. Test Factors and Indices

In this paper, the impurity and damage rates were selected as the test indices. The following formulas were obtained:

$$P_1={\displaystyle \frac{H_1}{H_0}}\times 100\%$$

(9)

$$P_d={\displaystyle \frac{M_d}{M}}\times 100\%$$

(10)

In the above, $P_1$ is the garlic impurity rate, %; $H_1$ is the impurity content of garlic samples after root trimming, g; $H_0$ is the weight of garlic samples before root trimming, g; $P_d$ is the rate of damage to garlic bulbs, %; $M_d$ is the total weight of garlic bulbs with mechanical injuries after root trimming, g; and $M$ is the total weight of garlic samples in the same set of tests before root trimming, g.

A large number of pre–test results showed that the roller diameter, the roller inclination angle, the knife rotation speed, and the working speed were the factors with a strong influence on these indices. In this study, an orthogonal regression test was carried out to construct a regression response model of the objective function, and the relationships between the factors and indices were thus established.

$$G=b_0+{\displaystyle \sum _{I=1}^N{b}_I{X}_I+{\displaystyle \sum _{I=1}^{N-1}{\displaystyle \sum _{J=I+1}^N\left(b_{I,J}{X}_I{X}_J\right)+{\displaystyle \sum _{I=1}^N\left(b_{I,J}{X}_I^2\right)}}}}+\epsilon$$

(11)

In this formula, $b_0$ is a constant; $b_I$ is the linear coefficient of the factor $X_I$; $b_{I,J}$ is the coefficient of the cross term; $b_{I,J}$ is the coefficient of the quadratic term; and $\epsilon$ is the residual error between the estimated value and the actual value. Tests were designed and conducted by means of the Box–Behnken design carried out using Design Expert software. The pre–test results showed that the suitable range for the roller diameter was from 60 mm to 100 mm, that for the roller inclination angle was from 5° to 25°, that for the knife rotation speed was from 200 r·min⁻¹ to 600 r·min⁻¹, and that for the working speed was from 200 km·h⁻¹ to 600 km·h⁻¹. The test factors and levels are shown in

Table 1. Factors and levels in Box–Behnken design.

Level	$\mathbf{Roller}\mathbf{Diameter}{\mathit{X}}_1$/ (mm)	$\mathbf{Roller}\mathbf{Inclination}\mathbf{Angle}{\mathit{X}}_2$/ (°)	$\mathbf{Knife}\mathbf{Rotation}\mathbf{Speed}{\mathit{X}}_3$/ (r·min−1)	$\mathbf{Working}\mathbf{Speed}{\mathit{X}}_4$/ (km·h−1)
−1	60	5	200	0.5
0	80	15	400	1
1	100	25	600	1.5

.

3.3. Results and Analysis

The results of the orthogonal regression test are shown in

Table 2. Results of orthogonal regression test for Box–Behnken design.

No.	$\mathbf{Roller}\mathbf{Diameter}{\mathit{X}}_1$/ (mm)	Roller Inclination Angle ${\mathit{X}}_2$/ (°)	$\mathbf{Knife}\mathbf{Rotation}\mathbf{Speed}{\mathit{X}}_3$/ (r·min−1)	$\mathbf{Working}\mathbf{Speed}{\mathit{X}}_4$/ (km·h−1)	$\mathbf{Impurity}\mathbf{Rate}{\mathit{P}}_1$/ (%)	$\mathbf{Damage}\mathbf{Rate}{\mathit{P}}_{\mathit{d}}$/ (%)
1	−1	−1	0	0	10.89	0.78
2	1	−1	0	0	3.57	3.98
3	−1	1	0	0	9.07	2.38
4	1	1	0	0	2.88	7.70
5	0	0	−1	−1	5.60	6.62
6	0	0	1	−1	1.68	14.83
7	0	0	−1	1	18.69	1.34
8	0	0	1	1	8.06	2.85
9	−1	0	0	−1	11.59	3.60
10	1	0	0	−1	2.73	9.94
11	−1	0	0	1	31.45	0.86
12	1	0	0	1	7.59	4.82
13	0	−1	−1	0	10.68	1.90
14	0	1	−1	0	5.25	3.29
15	0	−1	1	0	4.03	3.17
16	0	1	1	0	4.05	7.78
17	−1	0	−1	0	12.10	1.06
18	1	0	−1	0	4.91	3.79
19	−1	0	1	0	9.00	5.76
20	1	0	1	0	1.92	20.16
21	0	−1	0	−1	10.24	4.99
22	0	1	0	−1	5.50	7.56
23	0	−1	0	1	17.04	1.21
24	0	1	0	1	10.50	2.05
25	0	0	0	0	6.30	4.36
26	0	0	0	0	11.17	4.93
27	0	0	0	0	11.17	4.14
28	0	0	0	0	9.66	3.42
29	0	0	0	0	10.50	4.39

.

The results of a variance analysis of the regression model are shown in

Table 3. Variance analysis of the regression model.

Source	$\mathbf{Impurity}\mathbf{Rate}{\mathit{P}}_1$				$\mathbf{Damage}\mathbf{Rate}{\mathit{P}}_{\mathit{d}}$
	Sum of Squares	Sum of Mean Squares	F	P	Sum of Squares	Sum of Mean Squares	F	P
Model	889.57	63.54	6.59	0.0006	433.56	30.97	6.69	0.0005
$X_1$	304.88	304.88	31.60	<0.0001	107.78	107.78	23.29	0.0003
$X_2$	30.71	30.71	3.18	0.0961	18.05	18.05	3.90	0.0684
$X_3$	67.65	67.65	7.01	0.0191	111.25	111.25	24.04	0.0002
$X_4$	261.26	261.26	27.08	0.0001	98.60	98.60	21.31	0.0004
$X_1{X}_2$	0.32	0.32	0.03	0.8591	1.13	1.13	0.24	0.6292
$X_1{X}_3$	0.00	0.00	0.00	0.9873	34.01	34.01	7.35	0.0169
$X_1{X}_4$	56.23	56.23	5.83	0.0301	1.41	1.41	0.30	0.5895
$X_2{X}_3$	7.42	7.42	0.77	0.3953	2.60	2.60	0.56	0.4661
$X_2{X}_4$	0.81	0.81	0.08	0.7763	0.75	0.75	0.16	0.6940
$X_3{X}_4$	11.24	11.24	1.17	0.2986	11.23	11.23	2.43	0.1416
$X_1^2$	0.11	0.11	0.01	0.9183	5.01	5.01	1.08	0.3157
$X_2^2$	22.85	22.85	2.37	0.1461	12.28	12.28	2.65	0.1256
$X_3^2$	52.46	52.46	5.44	0.0352	22.05	22.05	4.76	0.0466
$X_4^2$	48.89	48.89	5.07	0.0410	0.84	0.84	0.18	0.6759
Residual	135.08	9.65			64.79	4.63
Lack of fit	118.57	11.86	2.87	0.1606	63.59	6.36	21.24	0.0049
Pure error	16.52	4.13			1.20	0.30
Total	1024.65				498.35

Note: p < 0.01 (extremely significant), 0.01 ≤ p ≤ 0.05 (significant).

.

According to the results in Table 3, the roller diameter ($X_1$), the knife rotation speed ($X_3$), and the working speed ($X_4$) had a significant effect on the regression equations for the impurity rate ($P_1$) and damage rate ($P_d$). Additionally, the lack of fit was not significant, which showed that there was a high correlation between the regression model and the real situation within the constraints of the design variables. With regard to the impurity rate ($P_1$), the results showed that $X_1$ and $X_4$ had extremely significant effects and $X_3$, $X_1{X}_4$, $X_3^2$, and $X_4^2$ had significant effects, but $X_2$, $X_1{X}_2$, $X_1{X}_3$, $X_2{X}_3$, $X_2{X}_4$, $X_3{X}_4$, $X_1^2$, and $X_2^2$ had no significant effects. The impurity rate ($P_1$) was most strongly affected by $X_1$, followed by $X_4$, $X_3$, $X_1{X}_4$, $X_3^2$, and $X_4^2$. With regard to the damage rate ($P_d$), the results also showed that $X_1$, $X_3$, and $X_4$ had extremely significant effects and $X_1{X}_3$ and $X_3^2$ had significant effects, but $X_2$, $X_1{X}_2$, $X_1{X}_4$, $X_2{X}_3$, $X_2{X}_4$, $X_3{X}_4$, $X_1^2$, $X_2^2$, and $X_4^2$ had no significant effects. The damage rate ($P_d$) was most strongly affected by $X_3$, followed by $X_1$, $X_4$, $X_1{X}_3$, and $X_3^2$. After verifications were performed to ensure that the regression models were significant and the loss–of–fit terms were not significant, the regression equations for the impurity rate ($P_1$) and damage rate ($P_d$) could be expressed as follows:

$$P_1=8.67-5.04X_1+4.67X_4-2.37X_3-3.75X_1{X}_4-2.52X_3^2+3.06X_4^2$$

(12)

$$P_d=4.18+3.04X_3+3X_1-2.87X_4+2.92X_1{X}_3+1.86X_3^2$$

(13)

The influence of interactions between the factors on the impurity rate ($P_1$) is shown in Figure 6.

The data shown in Figure 6 could be analyzed as follows: With an increase in the roller diameter, the impurity rate decreases; this is mainly because the roll–pulling mechanism increases the root–soil composite deformation and the downward transportation speed. With an increase in the roller inclination angle and the rotation speed of the root–trimming knife, the impurity rate first increases and then decreases, which indicates that an increase in these two parameters is not initially conducive to the cutting of the root–soil composite, but it gradually becomes beneficial when it reaches a certain extent. With an increase in the working speed, the impurity rate increases mainly because the faster working speed is not beneficial to the cutting of the root–soil composite. As the roller diameter decreases and the working speed increases, the interaction between them exacerbates unfavorable cutting of the root–soil composite.

The influence of interactions between the factors on the damage rate ($P_d$) is shown in Figure 7.

The data shown in Figure 7 could be analyzed as follows: With an increase in the roller diameter, the damage rate increases, mainly because the roll–pulling mechanism increases the root–soil composite deformation and the downward transportation speed. Under these conditions, garlic bulbs are easily damaged through extrusion. With an increase in the roller inclination angle, the damage rate first increases and then decreases, which indicates that an increase in this parameter is beneficial to the cutting of the root–soil composite at the beginning, but it gradually becomes less beneficial when it reaches a certain extent, and the garlic bulb is easily damaged by the root–trimming knife. With an increase in the rotation speed of the root–trimming knife, the damage rate first decreases and then increases, indicating that an increase in this parameter is not conducive to the cutting of the root–soil composite at the beginning. It gradually becomes beneficial to the cutting of the root–soil composite when it reaches a certain extent, but then the garlic bulb is easily damaged by the root–trimming knife. With an increase in working speed, the damage rate decreases mainly because of the reduction in the interaction time between the root–trimming knife and the root–soil composite. With an increase in the roller diameter and the rotation speed of the root–trimming knife, the interaction between them exacerbates the increases in root–soil composite deformation and the downward transportation speed, and the garlic bulb is easily damaged by the root–trimming knife.

These analyses show that in order to reduce the impurity and damage rates, the roller diameter, the roller inclination angle, the knife rotation speed, and the working speed should take moderate values.

3.4. Parameter Optimization and Verification

A mathematical model was established by taking the roller diameter, the roller inclination angle, the knife rotation speed, and the working speed as independent variables and taking the impurity and damage rates as the targets within the range of independent variables.

$$\left\{\begin{array}{l}\min P_1\\ \min P_d\\ 60 \mathrm{mm}\le X_1\le 100 \mathrm{mm}\\ 5°\le X_2\le 25°\\ 200 \mathrm{r}/\min \le X_3\le 600 \mathrm{r}/\min \\ 0.5 \mathrm{km}/\mathrm{h}\le X_4\le 1.5 \mathrm{km}/\mathrm{h}\end{array}\right.$$

(14)

The importance of the two optimization objectives was subjectively evaluated. Five experts scored the importance of the impurity and damage rates, and the subjective weights given to these two indicators were 0.3 and 0.7, respectively. The objective function based on the impurity and damage rates can be expressed as follows:

$$\left\{\begin{array}{l}\max Z=[a_1\left(1-\min P_1\right)+a_2\left(1-\min P_d\right)]\times 100\%\\ a_1+a_2=1\end{array}\right.$$

(15)

In this formula, $a_1$ and $a_2$ are the weight coefficients, and Z represents the comprehensive trimming quality, %; a higher value of Z indicates a better comprehensive trimming quality.

According to the Optimization module in Design Expert, the optimal parameter combination was a roller diameter of 100 mm, a roller inclination angle of 25°, a knife rotation speed of 200 r·min⁻¹, and a working speed of 1.22 km·h⁻¹. The highest comprehensive trimming quality was 97.82%, obtained when the impurity rate was 1.01% and the damage rate was 2.67%. The experimental verification was carried out under the condition of this parameter combination; the result was 97.52%, which was not significantly different from the theoretical result and indicated that the model result was reliable.

4. Conclusions and Discussion

4.1. Conclusions

(1) Research on improved root–trimming devices for pull–cut harvesters is required to achieve the cleanliness requirements of garlic harvesting in China. The existing methods, in which the top of the garlic bulb is gradually clamped to locate the position of the garlic roots for trimming, have poor adaptability and a high damage rate. The resulting damage causes the garlic to easily mildew and rot, making the garlic difficult to store, transport, and sell.

(2) In this study, a root–trimming device was designed. The main components included a pull–clamp mechanism, roll–pulling mechanism, root–trimming knife mechanism, lifter, gearbox, universal drive shaft, motor, and frame. The device was able to complete the root–trimming process for a pull–cut garlic harvester. Further research will focus on field experiments to promote the application of the device in conjunction with garlic combine harvesters.

(3) An orthogonal regression test was carried out by taking the impurity and garlic damage rates as the indices and taking the roller diameter, the roller inclination angle, the knife rotation speed, and the working speed as factors. The impurity rate was most strongly affected by the roller diameter, followed by the knife rotation speed, the working speed, and the roller inclination angle. The damage rate was most strongly affected by the knife rotation speed, followed by the roller diameter, the working speed, and the roller inclination angle. The regression analysis showed that when the roller diameter was 100 mm, the roller inclination angle was 25°, the knife rotation speed was 200 r·min⁻¹, and the working speed was 1.22 km·h⁻¹, the comprehensive trimming quality reached its maximum of 97.82%. The verification results of a parallel test gave a value of 97.52%, which was not significantly different from the predicted value. The parallel test indicated that the regression model was accurate and reliable and presented a good fit with the actual situation.

4.2. Discussion

(1) Symmetrical garlic bulbs with diameters ranging from 55 mm to 65 mm were studied herein. Our garlic root–trimming device was able to adapt to different garlic varieties and diameters, without any effect on the interactions between the mechanical components.

(2) Further research must be conducted to examine the relationship between the comprehensive trimming quality and the soil type, water content, and composition of the root–soil composite, and more comprehensive tests will be carried out to validate the robustness of the solution across varying conditions. Additionally, the interactions between different mechanical components should be further explored.

(3) Combined applications of the root–trimming device and pull–cut garlic harvesters also need to consider the limitations of transmission, speed, size, and other aspects, which remain to be studied.

(4) In reference [23], the best performance of their root–trimming device was associated with a damage rate of 0.63% and a root-cutting rate of 97.07%; in comparison, the profiled root–trimming device resulted in a damage rate of 2.67% and an impurity rate of 1.01%. The data indicate that the profiled root–trimming device realized a lower impurity rate but a higher rate of damage.

(5) In reference [21], under the optimal parameters for a floating root–cutting device, the damage rate was 2.78% and the root-cutting rate was 93.17%. The data indicate that the profiled root–trimming device realized lower impurity and damage rates.

(6) With the development of precision agriculture [27] and the advancement of intelligent agricultural machinery technology, root–trimming devices for garlic combine harvesters also need to be combined with modern farming systems to improve the intelligence of the harvesters’ operation.