Dropping impact experiment of crisp pears and contact pressure analysis

ABSTRACT Efforts have been made to streamline the abstract as follows. If further changes are made we are concerned that the integrity of the content may be compromised. We hope you will understand. This study aimed to investigate the impact damage experienced by Pucheng crisp pears during various stages, including harvest, transportation, and processing. Drop impact tests were conducted on pears, considering drop height and collision contact material as factors influencing damage. The bruise area was used as an indicator for damage evaluation. Additionally, the pressure-sensitive film technique was employed to measure the contact stress distribution characteristics of Pucheng crisp pears after the drop impact. The relationship between contact stress distribution and damage area was examined, and the stress area range close to the damage area was determined. The results revealed that the damage area of pears increased linearly with the increasing drop height. Among the four contact materials, foam board exhibited the best cushioning properties, with a maximum safe drop height of 20 cm. The pressure distribution tended to follow a normal distribution, with a pressure range of 0.2-0.3 MPa covering the largest area, corresponding to the majority of the bruise area on the pears. Furthermore, the pressure area and average pressure were found to be related to the severity of bruising. When pears were dropped onto steel, rubber plate and corrugated board, for the former two the stress area exceeding 0.2 MPa closely approximated the damage area, with an average relative error of 7.2%. For the latter, the closest range was above 0.3 MPa, with an average relative error of 3.6%. However, when dropped onto foam board, the average relative error was 75%. This research provides valuable insights for designing packaging tools to minimize damage and serves as a theoretical basis for predicting and assessing pear bruise area using finite element analysis.


Introduction
Pucheng crisp pear, a geographical landmark product of China and a characteristic agricultural product of Shaanxi Province, is known for its lush and juicy texture, sweet and refreshing taste, and rich nutritional content, making it highly popular among consumers.However, due to its delicate flesh and high moisture content, Pucheng crisp pear is vulnerable to various types of damage during picking, sorting, and transportation, leading to rotting and wastage.Statistics show that annual production losses of pears, apples, peaches, and other fruits can reach up to 30%.Among these, falling impact is the primary cause of damage. [1,2]Therefore, studying the impact damage of pear fruit during the falling process is of great significance for preventing damage throughout the entire operational process.
In recent years, domestic researchers have conducted numerous investigations into mechanical damage to fruits, [3][4][5][6][7][8][9][10][11][12][13][14][15] often utilizing pressure-sensitive film technology.For instance, RABELO [16] measured the distribution of static load contact stress in citrus using a sensor plate array.Z Feng [5] studied the distribution characteristics of contact stress in apples under static pressure and found that enzymatic browning damage occurred at a stress of 0.29 MPa, with the main areas of apple damage experiencing stress ranging from 0.20 to 0.40 MPa.HZ Xu [17] analyzed the relationship between fall height, fruit mass, impact material, and damage factors through pressure-sensitive film tests, discovering that the degree of damage to loquat was positively correlated with each factor, and the maximum safe fall height for loquat was 0.4 m.However, no relevant research has been conducted on Pucheng crisp pear.
This study aimed to investigate the change in damage patterns of Pucheng crisp pears by considering drop height and contact material as influencing factors and using damage area as the measuring index.Drop impact tests were conducted on a self-built drop test platform to provide insights into damage reduction, protection, and packaging design during pear operations.Additionally, the prescale pressuresensitive film technique was employed to measure and analyze the distribution of contact stress on Pucheng crisp pears under drop impact.This research aimed to explore the relationship between contact stress distribution and fruit damage and identify the stress area range closest to the damage area.These findings can serve as an effective basis for the development of a finite element impact model for pear simulation tests, as well as for predicting, assessing, and analyzing damage areas.

Crisp pear sample preparation
The samples were carefully handpicked from Zijing Plateau Orchard, Pucheng County, Shaanxi Province, on October 10, 2021.Only ripe fruits with regular shape, uniform color, no damage, and no signs of pests or diseases were selected.Following the picking process, the pears were promptly refrigerated at a temperature ranging from −2°C to 0°C, with a relative humidity of 85% to 90%.The average weight of the pears was determined to be 205.25 ± 15.26 g, while the average hardness measured 6.08 ± 1.03 N. Prior to the test, the pears were allowed to sit at room temperature for 48 h at 20°C.

Method of drop test
Test equipment details are given in Table 1.This study employed a single-factor test to examine the impact of drop height and contact material on the drop damage of crisp pears.Prior to the experiment, the pears were carefully weighed, grouped, and assigned numbers.Figure 1 illustrates the pear drop impact test equipment used in this study.The equipment utilized the negative pressure generated by an air compressor and vacuum generator to firmly attach suction cups to the pears.By closing the switching valve, the negative pressure was released, causing the pear specimen to fall freely and collide with the contact material on the test bench.Immediately after impact, the crisp pear was promptly retrieved to prevent any secondary impacts and to mark the location of the damage on the impact surface.The impact positions were marked according to the method depicted in Figure 2. The drop heights were set at 20, 40, 60, and 80 cm, respectively, based on the various drop situations observed during the actual operating session of the crisp pear fruit. [18]Crisp pears of the same quality range were carefully selected for testing, and each set of drop tests was repeated 30 times.A consistent contact material was placed directly below the suction cup on the test bench, and the crisp pear was dropped from the suction cup outlet onto the contact material.Only one sample was damaged during the test, and the extent of the damage was measured at the end of the test.Similarly, steel plates, rubber, corrugated cardboard, and foam were chosen as contact materials for the drop test, as they are commonly used in the mechanized and automated operation and packaging process of crisp pears.Thirty replicate tests were conducted using each contact material.The properties of the four contact materials    2. Pears within the same mass range were adjusted to the same drop height for the test.The extent of damage was measured after conducting the four sets of drop tests.

Methods for measuring the fruit hardness
The fruit hardness was measured using a fruit hardness tester.The test involved selecting a test head with a diameter of 3.5 mm and three measuring points positioned at the equator of the pear.The hardness tester was then pressed evenly into the peeled pear sample, perpendicular to its surface.The hardness value of the pear was determined by reading the display when the hardness tester indenter reached the scale line at 10 mm.The test data was recorded, and the average value was taken as the test result, with the unit expressed in N.

Method for measuring the extent of fruit drop damage
The surface damage area of the pear can be easily identified with the naked eye, which aids in determining the extent of damage.Therefore, the damage area method is employed to quantify the degree of damage to the pear.After the pear is damaged, the skin in the affected area is carefully removed using a knife, and the long semi-axis (a) and short semi-axis (b) of the damaged area are measured using vernier calipers.The damaged area is depicted in Figure 3.The area of damage is calculated using the following equation. [19]¼ πab (1)   where S means the area of crisp pear damage (mm 2 ), a denotes the long semi-axis of the damage area (mm), and b indicates the short semi-axis of the damage area (mm).

Method for measuring the contact stress distribution in fruit drops
The Prescale® LLLW double-layer ultra-low pressure film (measuring range 0.20 to 0.60 MPa, test accuracy ≤ ±10%) from Fuji, Japan, was applied onto the surface of the contact material for a drop impact test.The test was conducted at an ambient temperature of 20°C to 25°C and a relative humidity of 35% to 85%.After the drop impact, the pressure-sensitive film was scanned using a J232D Perfection TV 370 Photo scanner (Epson, Japan).The contact stress distribution characteristics were adjusted using a color correction plate.Finally, the FPD-8010E pressure image digital measurement and analysis system was utilized to analyze the data numerically based on the instantaneous contact model.This analysis provided the peak and mean values of contact stresses as well as the area of contact stress distribution.

Statistical analysis
All trial data were collated and analyzed using Excel, SPSS 25.0, and expressed as mean ± standard deviation.The images were all plotted using Origin 2015 software.

Damage analysis of crisp pear after drop impact test
When the same mass level of crisp pears was dropped from heights of 20, 40, 60, and 80 cm, the resulting damage area from collisions with steel plate, rubber plate, corrugated cardboard, and foam board is shown in Figure 4.It is evident that as the fall height increased, the damage area of the crisp pear exhibited a linear increasing trend.Additionally, as the drop impact height increased, the damage area of the pear also increased.The order of damage area from high to low when colliding with the four contact materials is as follows: steel plate, rubber plate, corrugated board, and foam board.Furthermore, there was no significant difference in the damage area of the crisp pear when it impacted the steel plate and rubber plate.This suggests that the cushioning performance of these two materials was similar, resulting in similar energy loss for the crisp pear.
From Figure 4 and the data, it can also be observed that the crisp pear sustained obvious impact damage when dropped from heights of 20 to 80 cm onto the steel plate and rubber plate.However, when the crisp pear collided with the corrugated board, no damage was observed at a drop height of 20 cm.Damage began to appear when the falling height reached 40 cm.On the other hand, when the pear collided with the foam board, no damage occurs even at drop heights below 40 cm.Therefore, when the fall impact occurs below 20 cm, both corrugated cardboard and foam board provide effective cushioning for the pear.When the fall impact height reached 40 cm, the foam board exhibits the best cushioning protection effect.Based on these initial findings, it can be inferred that 20 cm was the maximum safe fall height when the foam cushion is used to protect the crisp pear.

Analysis of contact stress of crisp pear drop impact
The contact stress distribution characteristics, average stress value, and contact stress area distribution of crisp pears of the same mass level dropped from heights of 20, 40, 60, and 80 cm onto steel plate, rubber plate, corrugated board, and foam board after impact are illustrated in Figures 5, 6 , and Figure 7, respectively.Figure 5 reveals that when the crisp pear collided with the steel plate and rubber plate, the contact stress distribution profile exhibited an elliptical shape with regular edges.However, when impacted by the corrugated board, the contact stress distribution characteristics began to display irregular contour edges.In the case of foam board impact, the contact stress distribution characteristics exhibited varying degrees of radial contour edges.This observation may be attributed to the different buffer deformation capacities of the various contact materials.
In addition, as depicted in Figure 6, the contact stress average value ranged from 0.28 to 0.31 MPa when the crisp pear collided with steel plate and rubber plate at various drop levels.However, there was no significant increase in the average stress value.Moreover, there was no significant difference in the average contact stress value between these two contact materials.On the other hand, when the crisp pear collided with the corrugated board and foam board, the average contact stress value ranged from 0.22 to 0.28 MPa.There was a significant increasing trend in the average stress value with the increase in height.Additionally, at lower drop levels, the average contact stress value was significantly lower compared to that of the steel plate and rubber plate.Thus, it is presumed that there is a correlation between the degree of damage to crisp pears and the average value of contact stress.
As shown in Figure 7, it can be observed that as the drop height increased, the contact stress area resulting from the impact with different contact materials also gradually increased, following a normal distribution pattern.The largest area of contact stress, ranging from 0.2 to 0.3 MPa, corresponds to the main stress area of the crisp pear.The peak contact stress experienced by the pear was approximately 0.50-0.64MPa, occupying an area of no more than 53 mm 2 .Therefore, the peak stress was not the primary cause of pear damage.The sporadic distribution of contact stress peaks was mainly concentrated near the contact center, possibly due to the stress value being lower than the failure stress of the pear pulp.Conversely, some contact stress peaks appear near the edge, indicating that the stress value exceeds the failure stress of the pear pulp.
Furthermore, the distribution characteristics of the contact stress area differ significantly depending on the contact material.When the crisp pear collided with a steel plate or rubber plate, the contact stress distribution area below 0.2 MPa (indicated in green) was small, mainly concentrated in the edge area, with occasional occurrences in the inner area.This may be attributed to the roughness and unevenness of the pear surface, resulting in insufficient contact.On the other hand, when impacted by the corrugated board and foam board, the contact stress distribution area below 0.2 MPa was noticeably larger.Additionally, as the mass of the pear and the drop height increased continuously, the contact stress distribution area below 0.2 MPa gradually expanded toward the edges.Notably, when colliding with the corrugated board, there were 3-4 bands of higher contact stress distribution area separated by lower stress areas, exhibiting a similar distribution pattern as the corrugated board.

Analysis of the relationship between crisp pear drop impact damage and contact stress distribution
According to the analysis above, there was a correlation between the average value of contact stress and the area of contact stress distribution of crisp pear and its damage degree.The impact force was determined by multiplying the average value of the contact stress and the area of the stress distribution.Table 3 presents the linear fitting relationship between the impact force and the damage area of the crisp pear.The fitting results indicate a strong linear correlation between the impact force and the damage area when the pear collided with the steel plate and rubber plate, with coefficients of determination R 2 of 0.98 and 0.98, respectively.Similarly, there was a linear correlation between the impact force and the fruit damage area on corrugated cardboard and foam board, with coefficients of determination R 2 of 0.96 and 0.93, respectively.
The contact stress distribution area resulting from the collision of a crisp pear on corrugated board and foam board differs significantly from the contact stress distribution area formed by the impact on rigid materials.When a linear regression analysis was conducted on the data relating the impact damage area of crisp pears on the four contact materials to the corresponding impact force, the coefficient of determination was found to be extremely low.Hence, it is not possible to establish a universally applicable linear regression model.However, when the data relating the impact damage area and impact force of crisp pears on two contact materials, namely steel plate and rubber plate, were subjected to linear fitting, the coefficient of determination R 2 for the damage area prediction was found to be 0.97, as depicted in Figure 8. Consequently, the model was able to more accurately assess and predict the extent of impact damage on crisp pears caused by rigid materials.

Comparative analysis of crisp pear drop impact damage area and contact stress distribution area
Based on the analysis above, it is evident that the peak contact stress area of the crisp pear was small and could not be used to predict the damage area of the pear.Therefore, the total area, contact stress area (>0.2 MPa), and contact stress area (>0.3 MPa) measured by the prescale pressure-sensitive film were calculated and compared with the pear damage area.The results are shown in Figure 9. From the figure, it can be observed that the total area of contact stress distribution on the pears was larger than the measured damage area.At the same impact level, the total area of contact stress distribution between the fruit and rigid materials (steel plate, rubber plate) measured by the prescale pressure-sensitive film was closer to the measured damage area of the crisp pears.However, when the impact involved corrugated board and foam board, the difference between the measured total area of contact stress distribution and the measured value of the damage area started to increase significantly.This was because when the pear collided with cushioning materials (corrugated cardboard, foam board), they deformed to increase the contact area with the pear, thereby absorbing the energy generated by the impact and reducing the degree of damage.On the other hand, when the pear collides with rigid materials, the limited deformation capacity results in more severe damage to the crisp pear.Furthermore, when the crisp pear collided with steel and rubber plates, the contact stress area (>0.2 MPa) was closest to the damage area, with an average relative error of 7.2%.The relative error remained relatively stable with changes in drop height, indicating that the stress range area could be used to predict the damage area of pears under different impact levels.When the fruit collided with corrugated board, the contact stress area (>0.3 MPa) was the closest to the damage area, with an average relative error of 3.6%.However, when colliding with foam board, the average relative error between the contact stress area (>0.3 MPa) and the damage area were 75%.This discrepancy may be attributed to the cushioning property of foam, which makes it difficult to accurately identify microscopic damage on the crisp pear, resulting in a large error in the actual measurement of the damage area.This further demonstrates the damage reduction effect of foam board on crisp pears.In conclusion, under different drop heights, the stress distribution area (>0.2 MPa) measured by the pressure-sensitive film when the pear collides with steel and rubber plates can effectively predict the degree of damage to the pear.When colliding with corrugated board, the stress distribution area (>0.3 MPa) can provide a preliminary prediction of the damage degree of the crisp pear.However, when colliding with foam board, the contact stress distribution area measured by the film was no longer able to accurately predict the actual damage area of the pear.

Conclusion
When the pear collided with different materials at various heights (steel plate, rubber plate, corrugated board, and foam board), the damage area showed a linear increasing trend with the increase in height.The order of damage area from high to low when colliding with the four contact materials was as follows: steel plate, rubber plate, corrugated board, and foam board.The contact stress area of the crisp pear after the drop impact followed a normal distribution.The peak stress ranged from 0.50 to 0.64 MPa, and the area did not exceed 53 mm 2 , indicating that it was not the main cause of the pear damage.The largest area occupied by the contact stress range of 0.2-0.3MPa contributed the most to the pear damage.When the fruit impacted materials (steel plate, rubber plate) with weaker buffering performance, the contact stress distribution profile was nearly elliptical, and the area occupied by the contact stress range of ≤0.2 MPa and >0.3 MPa was smaller.The average value of contact stress was 0.28-0.31MPa, showing no significant trend.In comparison, when the crisp pear impacted corrugated board and foam board, the average value of contact stress was 0.22-0.28MPa, with a significant increasing trend.The contact stress distribution profile showed a radial shape, and the good buffering performance of these materials significantly increased the stress area within the range of ≤0.2 MPa.The impact damage of crisp pear exhibited a high linear correlation with the collision impact force, which is the product of the contact stress distribution area and the average stress value.The linear regression model based on the contact stress distribution area and average stress value accurately predicted and evaluated the impact damage of crisp pears when colliding with rigid materials.The total area of contact stress distribution of crisp pears was always larger than the measured damage area.Under different drop heights, when pears impacted steel plates and rubber plates, the contact stress area in the range of >0.2 MPa was the closest to the damage area, with an average relative error of 7.2%.When the pear collided with corrugated board, the contact stress area in the range of >0.3 MPa was the closest, with an average relative error of 3.6%.However, the average relative error between the contact stress area and the damage area in the >0.3 MPa range reached as high as 75% when colliding with foam board.

Figure 1 .
Figure 1.Text apparatus of drop impact for pear fruit.

Figure 2 .
Figure 2. The mark of impact surface of pear fruit.

Figure 4 .
Figure 4. Relationship between impact bruise area and drop heights of crisp pear against four counter faces.

Figure 5 .
Figure 5. Images of pressure distribution diagram for crisp pear impacts against four counter faces at four drop heights.

Figure 6 .
Figure 6.Relationship between average contact pressure and drop heights for crisp pear impacts against four counter faces.

Figure 7 .
Figure 7. Contact pressure distribution of crisp pear against four counter faces.

Figure 8 .
Figure 8. Relationship between impact force and bruise area for crisp pear impacts against steel plate and rubber plate.

Figure 9 .
Figure 9. Comparisons of pressured area and bruise area for crisp pear impacts against four counter faces.

Table 1 .
Name and model of the test equipment.

Table 2 .
Material properties of the impact contact part.mentionedabove have been measured and are presented in Table

Table 3 .
Relationship between bruise (A) and impact force (P×A p ) fitted by linear regression for crisp pears against different counter-face materials.