Investigation of Impact Contact Force Testing and Damage Analysis on Potatoes

Abstract

To investigate the influencing factors and intrinsic relationships between potato impact force and impact damage during potato soil separation, a testing system for potato impact force was established. The impact force test system is composed of a base, a height adjustment device, a simple separation screen, a soil storage tank, an impact force sensor, and so on. By allowing potatoes to fall freely to simulate the collision process, impact force data are collected, and a high-speed camera is used to locate the impact position and analyze the degree of damage. Through the response surface analysis method, the influencing factors and laws of the impact force and impact damage during the collision process between potatoes and rods under soil and no-soil conditions were studied. The results of the response surface analysis indicate that when the screen inclination is within the range of 14.12° to 14.77°, falling height ranges from 453.83 mm to 500 mm, screen rod spacing falls within 36.50 mm to 40 mm, and the screen rod material is rubber. Potatoes can still be at a relatively low damage level when enduring a large impact force. This study has significant implications for reducing potato impact damage during harvesting, enhancing economic benefits in the potato industry, and advancing the technical level of potato harvesting equipment. In the future, based on the results of this study, further exploration can be made to optimize the design of potato harvesting equipment so as to better reduce the damage to potatoes during harvesting and subsequent processing processes and promote the sustainable development of the potato industry.

1. Introduction

Potatoes represent one of the most crucial global food crops. In recent years, there has been a consistent increase in the cultivation area for potatoes; from 1991 to 2021, the global sown area of potatoes increased from 20.700 million hectares to 23.915 million hectares [1]. Furthermore, potatoes are abundant in water, protein, starch, and various trace elements, rendering them an economical source of carbohydrates [2]. Their significance is evident. With the continuous expansion of potato cultivation areas, there is a growing demand for mechanized harvesting methods while addressing the increasingly prominent issue of potato damage during harvesting. Survey results indicate that approximately 70% of tuber damage stems from the potato harvesting process [3]. Harvesting stands as the pivotal stage in mechanized potato production; achieving complete separation of potatoes from soil and impurities while controlling damage rates presents a highly challenging problem [4,5]. Henceforth, it is clear that providing a theoretical foundation and reference data for developing low-damage potato harvesting machinery holds paramount importance.

In the process of mechanical potato harvesting, potatoes on the separation screen will collide repeatedly, which can easily cause breakage, damage, and scratches, thus causing significant economic losses for potato farmers. At the same time, the structural parameters and operating parameters of the machinery will also have a significant impact on potato damage. Therefore, most research on potato damage is focused on the stage of potato–soil separation. In the present day, research on potato tuber mechanical damage mainly concentrates on agricultural materials science and the factors that cause damage in harvesting machines [6]. Killick R J measured the mechanical forces exerted on seven potato varieties’ tubers to investigate the effects of potato density and variety on damage and found that injured potato tubers had a higher density than undamaged tubers, and there was no significant varietal difference in damage levels. Potato tuber density was not correlated with damage levels [7]. Baritelle and others studied the effect of potato density on the sensitivity of potato tubers to falling impact and concluded that the higher the density of potato tubers, the higher their impact sensitivity [8]. Ito and others studied the laws of impact damage on potatoes caused by falling height and falling material [9]. M. Bentini and others conducted research on impact damage during potato harvesting, analyzed the effects of harvesting techniques and soil moisture content on impact damage, and conducted harvesting tests under different soil and working conditions [10]. Through the research of these scholars, it can be found that conducting potato impact damage tests in a laboratory environment is one of the effective strategies for studying potato mechanical harvesting damage. At the same time, impact damage to potatoes is also a major research direction. In this context, “impact damage” refers to the harm or deterioration inflicted on potatoes when they are subjected to a forceful collision. However, during the process of separating potatoes from the soil, soil is always involved. There are relatively few studies on the impact of soil on potato damage in the existing literature. Soil plays a crucial role in the potato harvesting process. Firstly, soil adheres to potatoes, so there must be an efficient separation mechanism. In addition, soil conditions can also affect the mechanical stress on potatoes during the harvesting process. If the soil is too wet, it may increase the adhesion and load of potatoes, making them more prone to damage, while dry soil may lead to more abrasive contact and potential scratches on the potato surface.

Potato damage can be broadly divided into surface damage and internal damage [11], where internal damage refers to the damage to potatoes that occurs during harvesting due to more violent collisions or impacts. Surface damage mainly results from the friction and impact between potatoes and the objects they come into contact with during the process of separating potatoes from the soil, causing partial surface damage or peeling in some areas. In recent years, researchers have conducted comprehensive and systematic classifications of both internal and external forms of damage [12,13,14] and proposed breathing rate, damage area, damage volume, and damage ratio as damage evaluation indicators [15,16,17], but studies on the establishment of comprehensive damage indices are relatively scarce. With the continuous improvement of mechanization degree, although the efficiency of harvesting operations has been improved, it has also brought new challenges. Powerful machinery and high-speed operations can lead to more violent collisions and impacts on potatoes, increasing the risk of internal and surface damage. In addition, different soil conditions, such as wet or dry soil, can also affect the harvesting process. Therefore, in the context of the rapidly changing potato harvesting industry today, it is difficult to comprehensively evaluate the collision damage problem of potatoes.

In this paper, through a self-built potato collision impact force test system for the component of the rod-strip separation screen, the collision impact damage between potatoes and the separation screen and the soil was analyzed, revealing the influencing factors of the impact force and damage suffered by potatoes during the potato–soil separation process; a comprehensive damage index evaluation model was constructed to analyze the relationship between each factor and the comprehensive damage index; the damage laws of potatoes during the potato–soil separation process with and without soil participation were explored. This study is of great significance for reducing the economic losses caused by potato damage during the harvest process for farmers and improving the economic benefits of the potato industry and the technical level of potato harvesting equipment.

2. Materials and Methods

The experiment was conducted at the Laboratory of Agricultural Mechanization, Inner Mongolia Agricultural University, in the Inner Mongolia Autonomous Region. The laboratory is situated at geographic coordinates 110°46′ E and 40°51′ N, with an elevation of 1050 m. The geographical environment is conducive to potato cultivation, and there are numerous large-scale potato cultivation bases.

The experimental potato was excavated from the school crop planting base by manual harvesting and brought back to the laboratory. The potato variety was Kexin No.1. The tubers of Kexin No. 1 potatoes are usually oval, large, and neat. Their specific sizes may vary among individuals, and the weight is generally between 200 and 400 g. Measured results show that the water content of the potatoes used in the experiment is within the range of 75 to 85%. Potatoes without obvious pests, diseases, and mechanical damage were selected as samples. The selected potato samples were cleaned to remove the surface soil and impurities. The cleaning process should be as gentle as possible to avoid causing additional damage to the potatoes. After cleaning, the potatoes were placed in a well-ventilated place to air dry naturally to ensure that there was no residual moisture on the surface.

The soil used in the experiment is sandy loam. The proportions of sand particles, silt particles, and clay particles are 0.908, 0.0123, and 0.0794, respectively [18]. This soil has the characteristics of fine particles, loose texture, good ventilation, and moderate water retention. It is extremely beneficial for the growth of potato roots and the expansion of tubers. However, due to the relatively high sand content in sandy loam, it is easier to cause damage to the potato epidermis during the harvest.

2.1. Potato Impact Testing Platform

As shown in Figure 1, the test stand consists of two parts: the base and the height adjustment device. The base ensures the stability of the test system, and the adjustable pulley can regulate the falling height of the potato. The experiment simulates the collision process between the potato and the separation screen during the potato–soil separation process by letting the potato fall freely. To investigate the influence of soil on the impact damage of potatoes, a simple separation screen and a soil storage trough are set up above the test stand. The soil storage trough is used to store soil, making the soil surface flush with the upper surface of the separation screen’s screen rod. By adjusting the height of the fastening nut on the soil storage trough, the inclination angle of the separation screen’s screen surface can be precisely controlled. Adjusting the distance between the fastening nuts on the separation screen can achieve the regulation of the screen rod spacing. The impact force sensor is placed below the soil storage trough and used to collect the impact force of the potato on the screen rod.

2.2. Experimental Principle and Methods

The spacing of the screen rods directly affects the magnitude of collision force between potatoes and the separation screen. Figure 2 illustrates a simplified schematic diagram depicting the force exerted by potatoes on the screen rod.

Derived from the equilibrium condition:

$$G+F_Y=F_{N1}\mathit{cos}\alpha +F_{N2}\mathit{cos}\beta$$

(1)

$$F_Y=m{a}_Y$$

(2)

where G —gravity of the potato, N; F_N1—support force of the left end rod, N; F_N2— support force of the right end rod, N; F_Y—component of the inertial force in the Y direction, N; $a_{\mathrm{Y}}$—instantaneous acceleration of the potato in the Y direction, m/s².

It can be known from Figure 2 that the change of the center distance d of the screen rods will lead to the changes in the direction and magnitude of the forces FN1 and F_N2. When the distance between the screen rods decreases, the angles α and β will also become relatively smaller, thereby reducing the forces F_N1 and F_N2. Similarly, if the distance between the screen rods increases, it will cause the angles α and β to become relatively larger, and the forces F_N1 and F_N2 will also increase accordingly. During the test, the potatoes perform free-fall motion through the fixed pulley, and the change in the inclination angle of the screen surface will also affect the size of the collision contact force between the potatoes and the separation screen. Figure 3 shows the force analysis of the collision process between potatoes and the separation screen when the inclination angle of the screen surface is α.

With the separation screen’s screen surface as the reference system, when potato tubers come into contact with the screen surface, they will experience their own gravity, inertia force, friction force exerted by the separation screen, and support force. The collision process of potato tubers can be divided into the elastic compression stage and the plastic compression stage. When potato tubers collide with the rod, the support force exerted by the screen surface will continuously change with the compression of the potato tubers. In this case, the support force is a dynamic support force and also the contact force between the potato tubers and the screen surface. At this time, the equilibrium equation perpendicular to the screen surface is as follows:

$$F_t=\left(G+F_{Inertia}\right)\mathit{cos}\alpha$$

(3)

Assuming the separation screen and the potato as a whole, the equilibrium equation of the force measured by the impact force sensor below at this time is as follows:

$$F_m=G+G_1+F_{Inertia}$$

(4)

From Equations (3) and (4), we can obtain:

$$F_t=\left(F_m-G_1\right)\mathit{cos}\alpha$$

(5)

where F_t—the dynamic supporting force in the perpendicular direction of the sieve surface when potatoes contact the sieve rods, N; F_Inertia—the inertia force of potatoes, N; G—the gravity of potatoes, N; G₁—the gravity of the simple separation sieve, N; α—the inclination angle of the sieve surface, °; F_m—the force measured by the impact force sensor, N.

In the mechanized harvesting process of potato tubers, the damage mainly comes from impact injury caused by collisions [19]. Potato damage can be divided into two aspects: surface damage and internal damage. In this experiment, the surface damage and internal damage of potatoes were analyzed and measured separately, and the comprehensive damage index (DI) was defined for damage evaluation. The following are the measurement methods for the two types of damage:

(1) Method for measuring epidermal damage: First, cut the damaged potato cuber and place it on a calibrated ruler. Take a picture of the damaged area using a camera. Then, import the photograph into the ImageJ 1.x software and establish coordinate axes using the ruler. Finally, calculate the area of epidermal damage. The specific procedure is shown in Figure 4.

(2) The measurement method of internal damage is as follows: After the test is completed, place the damaged potatoes in a room temperature environment for 48 h until the damaged parts show browning. Then, make thin slices along the direction parallel to the damaged surface using a vernier caliper (with an accuracy of 0.05 mm) and control the thickness of the slices to be about 2mm. When approaching the maximum damaged area, in order to achieve an accurate measurement of the maximum damaged area, it is necessary to increase the accuracy of the slice thickness to about 1mm until the maximum damaged area is reached. Then, measure the lengths of the long and short axes of the maximum damaged area, cut along the direction perpendicular to the damaged surface to determine the damaged depth [20], and calculate the damage volume of the potatoes according to Equation (6). Internal damage is shown in Figure 5.

$$V={\displaystyle \frac{\pi abh}{6}}$$

(6)

where $a$ is the length of the long axis of the maximum damaged area, mm; b is the length of the short axis of the maximum damaged area, mm; h is the damaged depth, mm; V is the damage volume of the potato, mm³.

In order to comprehensively evaluate the different degrees of damage to potatoes, weighting factors were assigned to the surface damage and internal damage [21]. Before the weighting factors were assigned, the different indicators were normalized using Equation (7), and the method for calculating the damage comprehensive index is shown in Equation (8).

$$X_{m^{\prime }\left(k\right)}={\displaystyle \frac{X_{m\left(k\right)}-X_{min}}{X_{max}-X_{min}}}$$

(7)

where ${\mathrm{X}}_{{\mathrm{m}}^{\prime }\left(\mathrm{k}\right)}$ represents dimensionless processing; represents the original data of the kth element derived from the evaluation index; ${\mathrm{X}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ represents the minimum value of the same evaluation index; ${\mathrm{X}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ represents the maximum value of the same evaluation index.

$$DI=0.25·X_{C^{\prime }}+0.75·X_{I^{\prime }}$$

(8)

where $\mathrm{D}\mathrm{I}$ represents the comprehensive damage index; ${\mathrm{X}}_{C^{\prime }}$ represents the dimensionless data of epidermal damage; ${\mathrm{X}}_{I^{\prime }}$ represents the dimensionless data of internal damage.

2.3. Experimental Design

2.3.1. Test Apparatus

The impact force sensor used in the experiment is manufactured by Suzhou Aobataier Automation Equipment Co., Ltd. (Suzhou, China). The sensor model was LSZ-F04C/1000N, as shown in Figure 6, and the specific parameters are shown in

Table 1. LSZ-FO4C Sensor Parameters.

Parameters	Numerical Quantity
Measuring Range (N)	0~1000 N
Thickness (mm)	24
Diameter (mm)	72
Sensing Range Diameter (mm)	58.5
Reaction Time (ms)	<1
Operating temperature (°C)	−10 °C~70 °C

. The test device is shown in Figure 7.

Before the test, the test stand should be adjusted to the position above the vibrating sieve separator, and it should be ensured that the potatoes fall exactly on the screen rods of the separator. The center of gravity of the potatoes should be adjusted to be level with the test drop height. At the same time, when conducting the test with soil participation, the soil should be added to the storage trough, and the soil height should be kept level with the upper surface of the screen rods to ensure that the potatoes come into contact with the soil. After the collision, the impact position of the potato is precisely located and marked using a high-speed camera, and the degree of damage to the potato is then analyzed.

2.3.2. Experimental Plan

The impact generated when potatoes come into contact with the mechanical components of the separation screen is one of the main reasons for potato damage. Based on the previous theoretical analysis, in order to explore the effect of soil and the interaction between various factors on the impact force and impact damage of potatoes, taking potato mass (A), screen surface inclination angle (B), falling height (C), screen rod spacing (D), and screen rod material (E) as factors, response surface tests were conducted under both soil and no-soil conditions [22]. The factor levels of the response surface test are shown in

Table 2. Response Surface Experimental Factor Levels.

Level	Potato Mass A (g)	Screen Surface Inclination Angle B (°)	Falling Height C (mm)	Screen Rod Spacing D (mm)	Screen Rod Material E
1	200	7.7	300	30	65 MN
2	300	14.7	500	40	Rubber
3	400	21.7	700	50	Plastic

. Each test condition was repeated seven times. This repetition is crucial for considering the possible variability in the results. Through multiple repetitions, we can more accurately assess the variability of the measured impact force and comprehensive damage index. To consider the variability of the results, we performed statistical analysis on the data obtained from repeating each test condition seven times, calculated the average values of the maximum contact force F (impact force) and the comprehensive damage index DI, and constructed confidence intervals to provide a range within which we can reasonably be confident that the true value lies.

Descriptive statistics were first employed to summarize the basic characteristics of the data. Subsequently, analysis of variance and regression analysis were utilized to test hypotheses and identify significant differences. Using Design-expert 13 software, statistical analysis and correlation analysis were carried out on the obtained data by response surface methodology.

The experiment was carried out in a relatively stable indoor environment. The temperature and humidity were controlled within a certain range to reduce the interference of environmental factors on the experimental results. At the same time, no obvious airflow interference in the experimental site was ensured.

In terms of variable manipulation:

Falling height: With the help of a height adjustment device, set different falling height values.

Screen surface inclination angle: Adjust the angle of the simple separation screen to change it within a specific range.

Screen rod spacing: Change the screen rod spacing of the simple separation screen and set different spacing values.

Screen rod material: Use 65 Mn steel rods with a diameter of 10 mm (marked as 65 Mn), 65 Mn steel rods with a diameter of 10 mm wrapped with 2 mm thick polyvinyl chloride plastic (marked as plastic), and 65 Mn steel rods with a diameter of 10 mm wrapped with 2 mm thick rubber (marked as rubber).

According to the factors and levels in Table 2, a response surface experiment was conducted using the Box–Behnken central composite design theory, as shown in

Table 3. Response Surface Experimental Plan and Results.

Test Number	Potato Mass (g)	Screen Surface Inclination Angle (°)	Falling Height (mm)	Screen Rod Spacing (mm)	Screen Rod Material	Under Soil-Free Conditions				Under Soil Conditions
						Impact Force (N)	Depth of Injury (cm)	Area of Epidermal Injury (cm2)	Combined Injury Index	Impact Force (N)	Depth of Injury (cm)	Area of Epidermal Injury (cm2)	Combined Injury Index
1	200	7.7	500	40	2	102.384	0.11	0.00	0.002	139.203	0.00	0.17	0.044
2	400	7.7	500	40	2	304.529	0.74	0.13	0.508	233.442	0.56	0.12	0.368
3	200	21.7	500	40	2	113.963	0.67	0.24	0.217	101.74	0.44	0.56	0.192
4	400	21.7	500	40	2	216.239	0.58	0.24	0.148	233.676	0.53	0.33	0.435
5	300	14.7	300	30	2	122.537	0.09	0.01	0.022	165.178	0.00	0.08	0.025
6	300	14.7	700	30	2	215.505	0.70	0.05	0.311	189.746	0.40	0.13	0.081
7	300	14.7	300	50	2	155.248	0.08	0.11	0.127	107.519	0.06	0.09	0.023
8	300	14.7	700	50	2	242.025	0.65	0.06	0.241	225.996	0.59	0.10	0.076
9	300	7.7	500	40	1	194.257	0.79	0.07	0.367	147.424	0.68	0.24	0.345
10	300	21.7	500	40	1	217.551	0.44	0.00	0.134	150.112	0.39	0.23	0.782
11	300	7.7	500	40	3	196.465	0.13	0.00	0.003	150.263	0.09	0.15	0.364
12	300	21.7	500	40	3	161.259	0.32	0.00	0.062	129.458	0.28	0.32	0.231
13	200	14.7	300	40	2	86.233	0.09	0.01	0.004	126.804	0.00	0.04	0.006
14	400	14.7	300	40	2	207.856	0.58	0.24	0.233	198.213	0.21	0.43	0.109
15	200	14.7	700	40	2	156.199	0.80	0.05	0.272	139.046	0.48	0.05	0.126
16	400	14.7	700	40	2	344.32	0.53	0.16	0.297	288.87	0.45	0.32	0.233
17	300	14.7	500	30	1	204.568	0.83	0.17	0.422	166.535	0.67	0.25	0.382
18	300	14.7	500	50	1	186.729	0.78	0.26	0.404	143.771	0.56	0.25	0.332
19	300	14.7	500	30	3	199.63	0.53	0.00	0.103	168.453	0.42	0.20	0.172
20	300	14.7	500	50	3	174.719	0.45	0.00	0.149	129.325	0.41	0.15	0.105
21	300	7.7	300	40	2	138.033	0.17	0.03	0.037	142.063	0.08	0.08	0.028
22	300	21.7	300	40	2	138.533	0.07	0.11	0.045	116.689	0.00	0.36	0.102
23	300	7.7	700	40	2	260.736	0.75	0.12	0.166	204.659	0.46	0.30	0.145
24	300	21.7	700	40	2	194.434	0.56	0.03	0.101	155.755	0.38	0.45	0.242
25	200	14.7	500	30	2	135.506	0.64	0.12	0.187	144.895	0.46	0.08	0.078
26	400	14.7	500	30	2	244.385	0.70	0.08	0.458	258.346	0.48	0.59	0.222
27	200	14.7	500	50	2	123.072	0.23	0.04	0.185	150.85	0.12	0.05	0.012
28	400	14.7	500	50	2	258.155	1.03	0.19	0.473	247.237	0.88	0.28	0.192
29	300	14.7	300	40	1	161.441	0.51	0.09	0.142	106.663	0.33	0.23	0.282
30	300	14.7	700	40	1	270.186	0.63	0.06	0.307	180.379	0.61	0.30	0.453
31	300	14.7	300	40	3	117.947	0.07	0.00	0.001	94.287	0.02	0.17	0.086
32	300	14.7	700	40	3	206.056	0.62	0.62	0.180	166.08	0.61	0.21	0.318
33	200	14.7	500	40	1	110.899	0.83	0.15	0.334	110.405	0.73	0.11	0.269
34	400	14.7	500	40	1	286.097	0.44	0.49	0.449	244.914	0.54	0.49	0.750
35	200	14.7	500	40	3	126.639	0.50	0.06	0.073	99.288	0.46	0.20	0.231
36	400	14.7	500	40	3	257.127	0.56	0.09	0.242	235.521	0.58	0.26	0.333
37	300	7.7	500	30	2	214.696	0.55	0.02	0.333	208.246	0.31	0.04	0.200
38	300	21.7	500	30	2	181.41	0.12	0.09	0.038	147.786	0.14	0.35	0.398
39	300	7.7	500	50	2	208.189	0.18	0.05	0.021	181.307	0.11	0.24	0.201
40	300	21.7	500	50	2	168.898	0.86	0.27	0.385	140.312	0.62	0.30	0.162
41	300	14.7	500	40	2	181.801	0.22	0.08	0.033	204.396	0.16	0.11	0.086
42	300	14.7	500	40	2	186.801	0.18	0.06	0.049	209.396	0.18	0.12	0.119
43	300	14.7	500	40	2	190.801	0.14	0.07	0.069	199.156	0.11	0.10	0.106
44	300	14.7	500	40	2	195.801	0.14	0.06	0.065	194.588	0.13	0.11	0.068
45	300	14.7	500	40	2	173.801	0.20	0.07	0.016	214.258	0.13	0.12	0.050
46	300	14.7	500	40	2	176.801	0.16	0.07	0.020	207.118	0.16	0.14	0.042

.

3. Results

3.1. Results and Analysis of Response Surface Experiment

The results of the response surface experiment are presented in Table 3. By using a quadratic linear regression to construct the relationship model between each experimental performance indicator and each experimental factor and conducting an analysis of variance, the results are listed in

Table 4. F₁ Regression Model Analysis of Variance.

Variance Source	Sum of Squares	Degree of Freedom	Mean Squares	F Value	p Value	Significance
Maximum impact force on potatoes without soil F1
Model	133,300	20	6663.73	30.49	<0.01	**
A	84,653.87	1	84,653.87	387.35	<0.01	**
B	3220.63	1	3220.63	14.74	<0.01	**
C	36,255.4	1	36,255.4	165.89	<0.01	**
D	0.0902	1	0.0902	0.0004	0.984	ns
E	2301.26	1	2301.26	10.53	<0.01	**
AB	2493.43	1	2493.43	11.41	<0.01	**
AC	1105.5	1	1105.5	5.06	0.033	*
AD	171.66	1	171.66	0.7855	0.383	ns
AE	499.75	1	499.75	2.29	0.143	ns
BC	1115.63	1	1115.63	5.1	0.032	*
BD	9.02	1	9.02	0.0412	0.840	ns
BE	855.56	1	855.56	3.91	0.059	ns
CD	9.58	1	9.58	0.0438	0.835	ns
CE	106.46	1	106.46	0.4871	0.491	ns
DE	12.5	1	12.5	0.0572	0.812	ns
A2	269.09	1	269.09	1.23	0.277	ns
B2	1.29	1	1.29	0.0059	0.939	ns
C2	6.45	1	6.45	0.0295	0.865	ns
D2	48.54	1	48.54	0.2221	0.641	ns
E2	252.92	1	252.92	1.16	0.292	ns
Residual error	5463.72	25	218.55
Summation	138,700	45
Correlation coefficient	R2 = 0.96, adjusted R2 = 0.92
CV(%)	7.81

Note: p < 0.05 (*, significant); p < 0.01 (**, highly significant).

,

Table 5. F₂ Regression Model Analysis of Variance.

Variance Source	Sum of Squares	Degree of Freedom	Mean Squares	F Value	p Value	Significance
Maximum impact force of potato under soil condition F2
Model	99,470.74	20	4973.54	39.01	<0.01	**
A	53,822.36	1	53,822.36	422.14	<0.01	**
B	3337.34	1	3337.34	26.18	<0.01	**
C	15,197.71	1	15,197.71	119.2	<0.01	**
D	943.57	1	943.57	7.4	0.011	*
E	375.66	1	375.66	2.95	0.098	ns
AB	355.27	1	355.27	2.79	0.107	ns
AC	1537.26	1	1537.26	12.06	<0.01	**
AD	72.8	1	72.8	0.571	0.456	ns
AE	0.743	1	0.743	0.0058	0.939	ns
BC	138.41	1	138.41	1.09	0.307	ns
BD	94.71	1	94.71	0.7429	0.396	ns
BE	137.99	1	137.99	1.08	0.308	ns
CD	2204.7	1	2204.7	17.29	<0.01	**
CE	0.9249	1	0.9249	0.0073	0.932	ns
DE	66.95	1	66.95	0.5251	0.475	ns
A2	189.54	1	189.54	1.49	0.234	ns
B2	5990.41	1	5990.41	46.98	<0.01	**
C2	5047.12	1	5047.12	39.59	<0.01	**
D2	887.68	1	887.68	6.96	0.014	*
E2	13,596.56	1	13,596.56	106.64	<0.01	**
Residual error	3187.44	25	127.5
Summation	102,700	45
Correlation coefficient	R2 = 0.96, adjusted R2 = 0.94
CV(%)	6.58

Note: p < 0.05 (*, significant); p < 0.01 (**, highly significant).

,

Table 6. Variance Analysis for DI₁ Regression Model.

Variance Source	Sum of Squares	Degree of Freedom	Mean Squares	F Value	p Value	Significance
Comprehensive damage index DI1 of potato without soil
Model	0.9935	20	0.0497	25.91	<0.01	**
A	0.1475	1	0.1475	76.93	<0.01	**
B	0.0059	1	0.0059	3.06	0.092	ns
C	0.0999	1	0.0999	52.11	<0.01	**
D	0.0008	1	0.0008	0.4029	0.5314	ns
E	0.1912	1	0.1912	99.73	<0.01	**
AB	0.0824	1	0.0824	43.01	<0.01	**
AC	0.0103	1	0.0103	5.39	0.028	*
AD	0.0001	1	0.0001	0.0394	0.844	ns
AE	0.0007	1	0.0007	0.3708	0.548	ns
BC	0.0014	1	0.0014	0.7096	0.407	ns
BD	0.1085	1	0.1085	56.61	<0.01	**
BE	0.0213	1	0.0213	11.12	<0.01	**
CD	0.0076	1	0.0076	3.96	0.057	ns
CE	0.0001	1	0.0001	0.0202	0.8882	ns
DE	0.001	1	0.001	0.5255	0.4752	ns
A2	0.193	1	0.193	100.66	<0.01	**
B2	0.0044	1	0.0044	2.31	0.1414	ns
C2	0.0022	1	0.0022	1.14	0.2966	ns
D2	0.1477	1	0.1477	77.03	<0.01	**
E2	0.0699	1	0.0699	36.47	<0.01	**
Residual error	0.0479	25	0.0019
Summation	1.04	45
Correlation coefficient	R2 = 0.95, adjusted R2 = 0.91
CV(%)	23.88

Note: p < 0.05 (*, significant); p < 0.01 (**, highly significant).

and

Table 7. Variance Analysis for DI₂ Regression Model.

Variance Source	Sum of Squares	Degree of Freedom	Mean Squares	F Value	p Value	Significance
Comprehensive damage index DI2 of potato without soil
Model	1.26	20	0.0632	18.6	<0.01	**
A	0.1771	1	0.1771	52.13	<0.01	**
B	0.0448	1	0.0448	13.17	<0.01	**
C	0.0643	1	0.0643	18.92	<0.01	**
D	0.0129	1	0.0129	3.81	0.062	ns
E	0.1925	1	0.1925	56.67	<0.01	**
AB	0.0016	1	0.0016	0.4747	0.4972	ns
AC	1.82 × 10−6	1	1.82 × 10−6	0.0005	0.981	ns
AD	0.0003	1	0.0003	0.0954	0.759	ns
AE	0.036	1	0.036	10.6	<0.01	**
BC	0.0001	1	0.0001	0.041	0.8412	ns
BD	0.014	1	0.014	4.13	0.052	ns
BE	0.0814	1	0.0814	23.95	<0.01	**
CD	1.22 × 10−6	1	1.22 × 10−6	0.0004	0.985	ns
CE	0.0009	1	0.0009	0.2777	0.602	ns
DE	0.0001	1	0.0001	0.021	0.88	ns
A2	0.0433	1	0.0433	12.74	<0.01	**
B2	0.1337	1	0.1337	39.36	<0.01	**
C2	0.0106	1	0.0106	3.12	0.0893	ns
D2	0.0006	1	0.0006	0.1642	0.6887	ns
E2	0.4356	1	0.4356	128.23	<0.01	**
Residual error	0.0849	25	0.0034
Summation	1.35	45
Correlation coefficient	R2 = 0.93, adjusted R2 = 0.88
CV(%)	27.92

Note: p < 0.01 (**, highly significant).

. Based on the elements of misfit, signal-to-noise ratio, and correlation coefficient R² in the analysis of variance, it is possible to determine whether the relationship model constructed is suitable for predicting relevant experimental performance indicators, as well as the degree of fit between the predicted data and the experimental data [23,24,25].

From the variance analyses in Table 4, Table 5, Table 6 and Table 7, it can be concluded that the relationships between the maximum impact force F₁ and the comprehensive damage index DI₁ of potatoes grown in soil-free conditions, as well as the relationships between the maximum impact force F₂ and the comprehensive damage index DI₂ of potatoes grown in soil conditions, are all highly significant (p < 0.01). The residual terms of the constructed relationships are not significant (p > 0.05), and the signal-to-noise ratios are all greater than 17, which indicates that the constructed relationships are reasonable and of good quality and can be used for predicting the performance indicators of related experiments. The coefficient of determination R² and the adjusted R² are all greater than 0.88, which means that the predicted data of the constructed relationships have a high degree of fit with the experimental data.

Through the test results in Table 4, Table 5, Table 6 and Table 7, the test data were subjected to regression analysis and processing. The response surface regression models of the maximum impact force F₁, F₂ and the comprehensive damage index DI₁, DI₂ received by potatoes on the five independent variables of potato mass A, screen surface inclination angle B, falling height C, screen rod spacing D, and screen rod material E were established. The regression equations are shown in (9)–(12).

$$\begin{array}{c}{\mathrm{F}}_1=184.30+72.74\ast \mathrm{A}-14.19\ast \mathrm{B}+47.60\ast \mathrm{C}-0.0751\ast \mathrm{D}-11.99\ast \mathrm{E}-24.97\ast \mathrm{A}\mathrm{B}+16.62\ast \mathrm{A}\mathrm{C}+6.55\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{A}\mathrm{D}-11.18\ast \mathrm{A}\mathrm{E}-16.70\ast \mathrm{B}\mathrm{C}-1.50\ast \mathrm{B}\mathrm{D}-14.63\ast \mathrm{B}\mathrm{E}-1.55\ast \mathrm{C}\mathrm{D}-5.16\ast \mathrm{C}\mathrm{E}-1.77\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{D}\mathrm{E}+5.55\ast {\mathrm{A}}^2+0.3838\ast {\mathrm{B}}^2+0.8599\ast {\mathrm{C}}^2+2.36\ast {\mathrm{D}}^2+5.38\ast {\mathrm{E}}^2\end{array}$$

(9)

$$\begin{array}{c}{\mathrm{F}}_2=204.82+58.00\ast \mathrm{A}-14.44\ast \mathrm{B}+30.82\ast \mathrm{C}-7.68\ast \mathrm{D}-4.85\ast \mathrm{E}-9.42\ast \mathrm{A}\mathrm{B}+19.60\ast \mathrm{A}\mathrm{C}-4.27\ast \mathrm{A}\mathrm{D}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +0.4310\ast \mathrm{A}\mathrm{E}-5.88\ast \mathrm{B}\mathrm{C}-4.87\ast \mathrm{B}\mathrm{D}-5.87\ast \mathrm{B}\mathrm{E}+23.48\ast \mathrm{C}\mathrm{D}-0.4809\ast \mathrm{C}\mathrm{E}-4.09\ast \mathrm{D}\mathrm{E}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +4.06\ast {\mathrm{A}}^2-26.20\ast {\mathrm{B}}^2-24.05\ast {\mathrm{C}}^2-10.09\ast {\mathrm{D}}^2-39.47\ast {\mathrm{E}}^2\end{array}$$

(10)

$$\begin{array}{c}{\mathrm{D}\mathrm{I}}_1=0.0419+0.0960\ast \mathrm{A}-0.0191\ast \mathrm{B}+0.0790\ast \mathrm{C}+0.0069\ast \mathrm{D}-0.1093\ast \mathrm{E}-0.1436\ast \mathrm{A}\mathrm{B}-0.0508\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{A}\mathrm{C}+0.0043\ast \mathrm{A}\mathrm{D}+0.0133\ast \mathrm{A}\mathrm{E}-0.0184\ast \mathrm{B}\mathrm{C}+0.1647\ast \mathrm{B}\mathrm{D}-0.0730\ast \mathrm{B}\mathrm{E}-0.0435\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{C}\mathrm{D}+0.0031\ast \mathrm{C}\mathrm{E}+0.0159\ast \mathrm{D}\mathrm{E}+0.1487\ast {\mathrm{A}}^2+0.0225\ast {\mathrm{B}}^2+0.0158\ast {\mathrm{C}}^2+0.1301\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast {\mathrm{D}}^2+0.0895\ast {\mathrm{E}}^2\end{array}$$

(11)

$$\begin{array}{c}{\mathrm{D}\mathrm{I}}_2=0.0784+0.1052\ast \mathrm{A}+0.0529\ast \mathrm{B}+0.0634\ast \mathrm{C}-0.0284\ast \mathrm{D}-0.1097\ast \mathrm{E}-0.0201\ast \mathrm{A}\mathrm{B}+0.0007\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{A}\mathrm{C}+0.0090\ast \mathrm{A}\mathrm{D}-0.0949\ast \mathrm{A}\mathrm{E}+0.0059\ast \mathrm{B}\mathrm{C}-0.0593\ast \mathrm{B}\mathrm{D}-0.1426\ast \mathrm{B}\mathrm{E}-0.0006\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast \mathrm{C}\mathrm{D}+0.0154\ast \mathrm{C}\mathrm{E}-0.0042\ast \mathrm{D}\mathrm{E}+0.0704\ast {\mathrm{A}}^2+0.1238\ast {\mathrm{B}}^2-0.0349\ast {\mathrm{C}}^2+0.0080\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \ast {\mathrm{D}}^2+0.2234\ast {\mathrm{E}}^2\end{array}$$

(12)

Equations (9)–(12) were imported into Origin 2023 for processing, and corresponding response surfaces were plotted. The interaction effects among potato quality, inclination angle of the sieve surface, falling height, distance between sieve rods, and material of sieve rods on the maximum impact force and comprehensive damage index of potatoes were analyzed through the response surfaces, as shown in Figure 8, Figure 9, Figure 10 and Figure 11.

Figure 8a is the response surface diagram of the influence of potato mass and the inclination angle of the sieve surface on the maximum impact force F₁ received by potatoes under soil-less conditions. When the potato mass is large, the impact force received by the potato will decrease as the inclination angle of the sieve surface increases, which is consistent with the theoretical analysis above. However, when the potato mass is low, the impact force received by the potato gradually shows an increasing trend as the inclination angle of the sieve surface increases. The reason for this is that when the potato mass is low, the influence of the inclination angle of the sieve surface on the impact force received by the potato is difficult to highlight. Moreover, as the inclination angle of the sieve surface increases, the potato is subject to dynamic friction on the sieve surface, resulting in the case of a low potato mass, and the impact force it receives shows an increasing trend as the inclination angle of the sieve surface increases [26].

Figure 8b is the response surface diagram of the influence of potato mass and falling height on the maximum impact force F₁ received by potatoes under soil-less conditions. This response surface diagram is in a steep slope shape, indicating that the interaction between the two has an extremely significant influence on the impact force received by potatoes. With the increase in potato mass, the impact force received by potatoes will increase as the falling height increases, and the increase amplitude becomes more and more obvious. This indicates that the interaction between the two has a mutually reinforcing effect on the impact force received by potatoes. The maximum value F₁ is 327 N when the potato mass is 400 g, and the falling height is 700 mm.

Figure 8c is the response surface diagram of the influence of the inclination angle of the inclined sieve and the falling height on the maximum impact force received by potatoes under soil-less conditions. With the decrease in the inclination angle of the sieve surface, the impact force received by potatoes will increase as the falling height increases. It can be found from the response surface diagram that the curved surface of the falling height is steeper than that of the inclination angle of the sieve surface, which indicates that under the interaction, the influence of the falling height on the maximum impact force F₁ received by potatoes is greater than that of the inclination angle of the sieve surface. Moreover, when the falling height is low, the trend that the maximum impact force received by potatoes decreases with the increase in the inclination angle of the sieve surface is not obvious.

In conclusion, according to Figure 8, under the effect of the interaction test factors, with the increase in potato mass and falling height, the maximum impact force F1 received by potatoes shows an increasing trend. The interaction between the two promotes each other. When both increase simultaneously, the increase rate of the impact force received by potatoes is faster, indicating that the interaction between the two has a significant influence on the impact force received by potatoes. In addition, when the potato mass and the falling height are low, the influence of the inclination angle of the sieve surface on the impact force received by potatoes is not significant. However, when the potato mass and the falling height increase, the influence of the inclination angle of the sieve surface on the impact force received by potatoes becomes more and more significant. Therefore, when the potato mass and the falling height are large, this can be considered to increase the inclination angle of the sieve surface to reduce the impact force received by potatoes. The above conclusions indicate that the interaction of the test factors has a significant influence on the maximum impact force F₁ received by potatoes, which is consistent with the variance analysis results in Table 4.

Figure 9a is the response surface diagram of the influence of potato mass and falling height on the maximum impact force F₂ received by potatoes under soil conditions. With the increase in potato mass, the impact force it receives increases as the falling height increases. This situation is consistent with the theoretical analysis above, and this response surface is relatively similar to Figure 8b. The interaction between the two plays a mutually reinforcing role in the impact force received by potatoes. However, what is different is that this response surface diagram is relatively flatter, indicating that after adding soil, the soil plays a buffering role, resulting in a relatively slow increase in the impact force received by potatoes, reaching a maximum of 294 N when the potato mass is 400 g, and the falling height is 700 mm.

Figure 9b presents the response surface diagram of the influence of the falling height and the distance between sieve rods on the maximum impact force F₂ received by potatoes under soil conditions. This diagram is convex, indicating that the interaction between the two has an extremely significant influence on the impact force received by potatoes. When the falling height is large, the impact force received by potatoes will increase as the distance between the sieve rods increases, which is consistent with the theoretical analysis above; that is, the larger the distance, the greater the supporting force of the sieve rods. However, when the falling height is small, the impact force received by potatoes gradually shows a decreasing trend as the distance between the sieve rods increases. The reason is that when the falling height is low, the impact force received by potatoes is small, and as the distance between the sieve rods increases, the contact area of potatoes on the sieve surface increases, and the soil that acts as a buffer also increases accordingly, thereby making the impact force received by potatoes decrease as the distance between the sieve rods increases when the falling height is low.

Comprehensively, considering Figure 8 and Figure 9, it can be known that under the effect of the interaction test factors, with the increase in potato mass and the increase in the falling height, the maximum impact force F received by potatoes shows an increasing trend, and the interaction between the two promotes each other. However, under soil conditions, due to the buffering effect of the soil, the increase in the impact force received by potatoes is relatively slow, and the maximum impact force of 294 N received by potatoes under soil conditions is smaller than 327 N under soil-less conditions, which indicates that the addition of soil has a great influence on the impact force received by potatoes. At the same time, under soil-less conditions, the interaction between the inclination angle of the sieve surface and the potato mass and the falling height is very significant, but it is not significant under soil conditions. This is because, after the addition of soil, potatoes come into contact with the soil. Since the soil is composed of loose soil particles, which are full of gaps and have low strength, the influence of changing the inclination angle of the sieve surface on the impact force becomes smaller. In addition, after the addition of soil, the interaction between the falling height and the distance between sieve rods is extremely significant. This is because changing the distance between sieve rods is equivalent to changing the mechanical properties of the sieve surface, just like reinforced concrete. The sieve rods are similar to the reinforcing bars in reinforced concrete, and the distance between the “reinforcing rods” leads to different impact forces received by potatoes. Therefore, in the actual harvesting process, the structural parameters of the harvester can be optimized from the perspective of changing the inclination angle of the sieve surface and adjusting the distance between sieve rods.

Figure 10a presents the response surface diagram of the influence of potato mass and the inclination angle of the sieve surface on the comprehensive damage index DI₁ of potatoes under soil-less conditions. When the potato mass is large, the comprehensive damage index of potatoes will decrease as the inclination angle of the sieve surface rises. When the potato mass is low, the comprehensive damage index of potatoes gradually shows an increasing trend as the inclination angle of the sieve surface increases. Through the analysis of the interaction between potato mass and the inclination angle of the sieve surface on the impact force of potatoes under soil-less conditions in the previous text, it can be known that due to the dynamic friction force, the impact force received by potatoes will increase as the inclination angle of the sieve surface increases when the potato mass is low, and this can also be verified from the change in the comprehensive damage index here. Similarly, when the potato mass is low, with the increase in the sieve surface, the proportion of the frictional damage to potatoes caused by dynamic friction becomes larger and larger, thus showing an increasing trend as the inclination angle of the sieve surface increases when the potato mass is low. Figure 10b is the response surface diagram of the influence of potato mass and falling height on the comprehensive damage index DI₁ of potatoes under soil-less conditions. This response surface diagram is concave, indicating that the interaction between the two has a strong influence on the comprehensive damage index of potatoes, and potatoes reach the lowest point of the comprehensive damage index between 200 g and 300 g, proving that potatoes are less likely to be damaged when the potato mass is between 200 g and 300 g. Figure 10c is the response surface diagram of the influence of the inclination angle of the sieve surface and the distance between sieve rods on the comprehensive damage index DI₁ of potatoes under soil-less conditions. This response surface is concave. When the inclination angle of the sieve surface is small, the comprehensive damage index of potatoes will decrease as the distance between sieve rods increases; when the inclination angle of the sieve surface is large, the comprehensive damage index of potatoes will increase as the distance between sieve rods increases. The optimal distance between sieve rods is within the range of 30 mm to 40 mm, and the optimal inclination angle of the sieve surface is within the range of 14.11° to 21.7°. Figure 10d is the response surface diagram of the influence of the inclination angle of the sieve surface and the material of sieve rods on the comprehensive damage index of potatoes under soil-less conditions. When the material of sieve rods remains unchanged, the comprehensive damage index of potatoes continues to decrease as the inclination angle of the sieve surface decreases; when the inclination angle of the sieve surface remains unchanged, the comprehensive damage index of rubber and plastic sieve rods does not differ much and is much smaller than that when the material of sieve rods is 65 MN.

Figure 11a presents the response surface diagram of the influence of potato mass and the material of sieve rods on the comprehensive damage index DI₂ of potatoes under soil conditions. This response surface is concave, indicating that the interaction between the two has a significant influence on the comprehensive damage index of potatoes. After the addition of soil, due to the different materials of the sieve rods, the mechanical properties of the entire sieve surface are different. When the material of the sieve rods is rubber, the lowest point of the comprehensive damage index of potatoes is reached. Figure 11b is the response surface diagram of the influence of the inclination angle of the sieve surface and the material of sieve rods on the comprehensive damage index DI₂ of potatoes under soil conditions. When the material of the sieve rods is fixed, the comprehensive damage index shows a trend of first decreasing and then increasing with the increase in the inclination angle of the sieve surface. The optimal range of the inclination angle of the sieve surface is from 10.49° to 16.51°, and the optimal material of the sieve rods is rubber.

In conclusion, based on Figure 10 and Figure 11, the following conclusion can be drawn: under the influence of interaction test factors, when the mass of potatoes is greater than or equal to 300 g, or when the falling height is greater than or equal to 600 mm, the internal damage caused by the impact of potatoes dominates in the comprehensive damage index of potatoes. When the mass of potatoes is less than 300 g, with the change in the inclination angle of the sieve surface, the epidermal damage caused by the dynamic friction between potatoes and the sieve surface due to the impact of potatoes accounts for the main proportion of the comprehensive damage index of potatoes. Through a comprehensive comparison of response surface diagrams under soil-less and soil conditions, it is found that when the weight of potatoes is strictly controlled within the interval of 200 g to 300 g, the inclination angle of the sieve surface is precisely limited between 14.11° and 16.51°, the falling height is within the range of 300 mm to 500 mm, and the spacing between sieve rods is strictly maintained within the interval of 30 mm to 40 mm, and when the material of sieve rods is rubber, it has been verified by multiple experiments that the comprehensive damage index of potatoes can be stabilized at a relatively low level.

3.2. Comparison between Soil-Less Impact Damage and Soil Impact Damage

When soil is present, it plays a buffering role in the impact process. Soil particles can absorb and disperse the impact force, thereby reducing the direct force on potatoes and thus lowering the damage depth of potatoes. However, fine gravel and stones in the soil can cause abrasion and scratches on the epidermis of potatoes. In addition, after adding soil, the contact area between potatoes and the surrounding medium will increase, and at the same time, the increase in contact area also leads to an increased possibility of epidermal damage.

The damage results obtained from the response surface test are further processed. The damages obtained at the levels of 200 g, 300 g, and 400 g are classified. Under soil and no-soil conditions, respectively, the average values of potato damage depth and epidermal damage area at the levels of 200 g, 300 g, and 400 g are calculated. The comparison results are shown in Figure 12. The results show that at these three levels of 200 g, 300 g, and 400 g, the average value of potato damage depth under soil conditions is lower than the corresponding value under no-soil conditions, which once again confirms the buffering effect of soil. However, the average value of the epidermal damage area under soil conditions is greater than the value under no-soil conditions. This also proves that the increase in contact area will lead to an increase in the degree of epidermal damage because potatoes have more opportunities to come into contact with potentially harmful elements in the soil.

4. Discussion

4.1. Parameter Optimization

Combined with the analysis of the response surface results in the actual production and harvesting process, considering the uneven quality of potatoes, this paper aims to explore methods to ensure that potatoes are at a low damage level when they are subjected to a large impact force under soil and soil-less conditions. Through the above analysis, the optimal falling height range of potatoes is between 300 mm and 500 mm. Within this range, the maximum impact forces obtained by potatoes under soil-less and soil conditions are 304.529 N and 258.346 N, respectively, which are defined as the large impact forces received by potatoes through Equation (13).

$$F_{max}\times 80\%\le F_{larger}\le F_{max}$$

(13)

The optimization module in Design-Expert 8.06 software was used to solve the five regression analyses. Through the analysis of the interaction between different factors, it was confirmed that the impact force received by potatoes was the key factor determining the damage suffered by potatoes. However, different factors could also enhance the tolerance ability of potatoes to the damage suffered. Therefore, based on the analysis results of the relevant models, the optimized conditions selected under both soil and soil-less conditions are shown in Figure 13.

Through optimization and solution, under soil conditions, it is concluded that the potato mass is 373.81–392.17 g, the inclination angle of the sieve surface is 14.12–16.51°, the falling height is 453.83–500 mm, the distance between sieve rods is 36.50–40 mm, and the material of sieve rods is rubber. Under soil-less conditions, the potato mass is 300.30–361.34 g, the inclination angle of the sieve surface is 14.11–14.77°, the falling height is 322.60–500 mm, the distance between sieve rods is 30–40 mm, and the material of sieve rods is rubber. Since the potato mass cannot be fixed in actual harvesting, combined with the excellent levels under soil and soil-less conditions, the optimal levels are determined to be as follows: inclination angle of the sieve surface of 14.12–14.77°, the falling height of 453.83–500 mm, the distance between sieve rods of 36.50–40 mm, and the rubber as the material of sieve rods. This can ensure that potatoes are at a low damage level when they are subjected to a large impact force during actual harvesting.

So far, in the field of damage research during potato harvesting, there may not be many directly conflicting studies. However, considering similar studies on impact damage and optimization of harvesting conditions, differences may arise due to several factors. For example, different potato varieties used in different studies may lead to different results. Some varieties may be more resistant to impact damage due to their unique physical characteristics or genetic makeup. Another possible source of variation may be the experimental setup. The design of separation screens, the accuracy of impact force measurement devices, or the environmental conditions during the experiment may all lead to differences in results. In addition, the data analysis methods and standards for defining low damage levels in different studies may also be different, such as surface damage and internal damage. Some studies may prioritize minimizing one type of damage, resulting in differences in optimized conditions.

4.2. Experimental Verification

In order to verify whether the regression model equation obtained above can be used to estimate the degree of potato collision damage and to verify the accuracy of the optimal parameters obtained above, five random experiments were carried out for verification (each group of experiments was repeated seven times, and the level factors were randomly selected within the optimal parameter range obtained above). The DI₁ under soilless conditions and the regression model prediction result DI₃ in the actual measurement results were compared with DI₂ under soil conditions and the regression model prediction result DI₄, respectively, and their error values were calculated. The prediction results of the regression model were calculated through Equations (11) and (12), and the verification test results are shown in

Table 8. Verification Test Results.

Test Number	A (g)	B (°)	C (mm)	D (mm)	E	DI1	DI2	DI3	DI4	Error E1 under Soil-Less Conditions(%)	Error E2 under Soil Conditions(%)
1	386.8	14.2	460.2	39.2	2	0.258	0.192	0.241	0.208	7	7.6
2	301.4	14.5	457.8	39.8	2	0.029	0.066	0.028	0.064	3.5	3.1
3	308.1	14.6	460.4	37.6	2	0.038	0.083	0.041	0.078	7.3	6.4
4	305.1	14.4	472.4	36.5	2	0.055	0.076	0.051	0.080	7.8	5
5	349.6	14.7	468.8	36.8	2	0.119	0.141	0.126	0.143	5.5	1.4

.

It can be seen from Table 8 that the error values under both soil-less and soil conditions are less than 10%, which indicates that the quadratic regression model of this response surface test can reflect the test conditions relatively well and can be used to predict relevant data. Moreover, through the results of the verification test, it is proved that within the level, the comprehensive damage index of potatoes is relatively low, and it also verifies again that the selection range of the optimal parameters is correct. At the same time, this study has certain limitations. First, the experiment is carried out in a controlled laboratory environment and may not be able to fully replicate the complex and variable field conditions during the actual potato harvesting process. Factors such as field weather conditions, soil changes, and machine wear may all lead to different results. Second, although the regression model shows good predictive ability within a certain range, this study is based on the sandy loam conditions in the local area. Different potato varieties and differences in soil quality will all have an impact on the damage to potatoes. Future research can consider expanding the scope of different factors and conducting field tests to further improve the accuracy and applicability of the model.

5. Conclusions

(1)

Through the response surface test analysis, under soil-less conditions, the interactions of potato mass and inclined sieve angle, potato mass and falling height, and inclined sieve angle and falling height have significant effects on the impact force received by potatoes. The interactions of potato mass and inclined sieve angle, potato mass and falling height, sieve surface inclination angle and sieve rod spacing, and inclined sieve angle and sieve rod material have significant effects on the comprehensive damage index of potatoes. Under soil conditions, the interactions of potato mass and falling height and potato mass and sieve rod spacing have significant effects on the impact force received by potatoes. The interactions of potato mass and sieve rod material and sieve rod spacing and sieve rod material have significant effects on the comprehensive damage index of potatoes.

(2)

It is clarified that under the same factor conditions, after adding soil, compared with the soil-less condition, the internal damage of potatoes will be reduced, but at the same time, the epidermal damage suffered by potatoes will increase.

(3)

Using the Design-Expert software, the optimal level that can most effectively reduce potato damage when subjected to a large impact force during the actual potato harvesting process was obtained. This level combination has been verified to meet the requirements of a lower comprehensive damage index and can be used for later field experiments.