Design and Test of Automatic Feeding Device for Substrate Filling

: An automatic feeding device for substrate filling was designed to address the challenges of difficult feeding and low efficiency in the citrus seedling pot filling and transferring machine. The device comprises a framework, tracks, overturning frame, drive system, etc. In order to ensure optimal performance, the frame’s turning angle was set at a minimum of 110 ◦ and the angle between the frame’s horizontal plane and slope was determined to be 120 ◦ . Following optimization, the number and intensity of sudden changes in velocity, angular velocity, and thrust were reduced, thereby prolonging the device’s service life. The prototype test demonstrated that the device has an average feeding time of 9.86 s, is capable of raising 0.14 m 3 of substrate in a single cycle, and has a handcart turning angle of 111 ◦ . Furthermore, no residual substrate remained in the handcart, and the handcart fixing mechanism operated correctly. The torque measurement results of the motor output shaft were found to be consistent with the simulation results in ADAMS, with a maximum force difference of only 298 N. The simulation was found to be accurate, with an error rate of only 3.67%. This model can be utilized as a dependable reference for the optimization of the design of the automatic feeding device.


Introduction
Container seedlings have the advantages of a short seedling cycle and a high survival rate, and container seeding is the main seedling cultivation method in citrus seedling cultivation bases in China [1,2].The developed citrus seedling bowl filling and transferring machine can effectively fill and transfer seedling bowls, with a single filling time of about 60 s and a filling number of 105 bowls [3].This is a significantly higher rate than the manual filling rate of 60-80 bowls per person per hour, and it greatly improves the efficiency of seedling raising.However, the installation height of the silo of the filling and transporting machine is relatively high, which makes it time-consuming and laborious to manually add matrix soil to the silo [3].To facilitate the work of the citrus seedling bowl filling and transferring machine and enable its automatic feeding process, it is necessary to design an automatic feeding device to replace the manual completion of the barn substrate soil adding operation, essentially realizing the mechanization and automation of the citrus seedling process, thereby further promoting the development of the Chinese citrus industry.
The research into foreign loading devices commenced at an early stage, with a greater investment of funds.Following a lengthy period of technical accumulation, automation, and mechanization, the degree of development is now higher, and the devices are now developing in the direction of intelligence.The German company Haller has developed a mechanical arm garbage can recovery device [4,5].The driver in the cab is able to grasp garbage cans at arbitrary angles and recover them in the bucket operation.The Dutch company JAVO has developed automatic pot-filling equipment [6][7][8][9], which is equipped with a special automatic substrate soil feeding device, with a filling efficiency of up to 4000 pots/h.Foreign feeding devices tend to be expensive and specialized for specific working conditions, and therefore cannot be used in the main seedling cultivation method in citrus seedling cultivation bases in China.Chinese feeding devices originated in the last century after a lengthy period of development.Currently, there are a variety of devices, including trash bucket lifting and turning devices, screw feeders, bucket elevators, belt conveyors, and others.However, the direct use of these models for citrus seedling bowl filling transfer machine bins for substrate soil addition operations often results in unclean discharge, machine jamming, and other issues [10][11][12].
In conclusion, this paper presents the design of an automatic loading device for a citrus seedling bowl substrate.The device was created using Solidworks (2018) to model the overall structure in three dimensions and the Adams (2020) to simulate the loading process.The loading process was optimized using a multi-objective optimization of the flip frame structure.Finally, the test prototype was processed for performance testing.The findings of this study can serve as a foundation for the development and optimization of subsequent automatic loading equipment for citrus seedling bowl filling substrates.

Structure and Working Principle of the Whole Machine 2.1. Whole Machine Structure
The automatic loading device, which is responsible for the loading of the substrate, is composed of a number of different components.These include a rack, track, overturning frame, transmission system, control system, and so forth.The overall structure of the machine is shown in Figure 1.
Appl.Sci.2024, 14, 4206 2 of 18 and mechanization, the degree of development is now higher, and the devices are now developing in the direction of intelligence.The German company Haller has developed a mechanical arm garbage can recovery device [4,5].The driver in the cab is able to grasp garbage cans at arbitrary angles and recover them in the bucket operation.The Dutch company JAVO has developed automatic pot-filling equipment [6][7][8][9], which is equipped with a special automatic substrate soil feeding device, with a filling efficiency of up to 4000 pots/h.Foreign feeding devices tend to be expensive and specialized for specific working conditions, and therefore cannot be used in the main seedling cultivation method in citrus seedling cultivation bases in China.Chinese feeding devices originated in the last century after a lengthy period of development.Currently, there are a variety of devices, including trash bucket lifting and turning devices, screw feeders, bucket elevators, belt conveyors, and others.However, the direct use of these models for citrus seedling bowl filling transfer machine bins for substrate soil addition operations often results in unclean discharge, machine jamming, and other issues [10][11][12].
In conclusion, this paper presents the design of an automatic loading device for a citrus seedling bowl substrate.The device was created using Solidworks (2018) to model the overall structure in three dimensions and the Adams (2020) to simulate the loading process.The loading process was optimized using a multi-objective optimization of the flip frame structure.Finally, the test prototype was processed for performance testing.The findings of this study can serve as a foundation for the development and optimization of subsequent automatic loading equipment for citrus seedling bowl filling substrates.

Whole Machine Structure
The automatic loading device, which is responsible for the loading of the substrate, is composed of a number of different components.These include a rack, track, overturning frame, transmission system, control system, and so forth.The overall structure of the machine is shown in Figure 1.

Operating Principle
Prior to loading, the operator must manually push the dump truck full of subsoil to the tilting frame.At this time, the clamp plate must clamp the dump truck ramp and switch the locking mechanism of the dump truck to the locked state.This action ensures that the axle of the dump truck is fixed, thus achieving complete fixation of the dump

Operating Principle
Prior to loading, the operator must manually push the dump truck full of subsoil to the tilting frame.At this time, the clamp plate must clamp the dump truck ramp and switch the locking mechanism of the dump truck to the locked state.This action ensures that the axle of the dump truck is fixed, thus achieving complete fixation of the dump truck and the tilting frame.During the loading operation, the loading button must be pressed, which will cause the motor to rotate in a positive direction and its output torque to act on the tipping frame through the transmission system.This will result in the tip-ping frame dragging the dumper along the track, as illustrated in Figure 2. Upon reaching the end of the circular section of the track, the front track wheel will be blocked to stop.At this point, the pull force of the drive system chain will continue to act on the tipping frame, enabling the tipping frame to designate the center of the front track wheel for the tipping movement.This allows the substrate soil to be dumped into the dump truck.At an angle of 110 • between the flip frame and the handcart, the substrate soil can be completely dumped.Simultaneously, the flip frame will contact the end position travel switch, which will cause the motor to cease operation, halting the movement and concluding the loading process.Upon returning, pressing the return button will reverse the motor, initiating a reversal of the overturning frame's movement along the path of the feeding process.Upon returning to the initial position, the dumper will contact the starting position travel switch, resulting in the motor being powered off and the movement being halted.Subsequently, the dumper locking mechanism must be disengaged in order to exit the dumper.
Appl.Sci.2024, 14, 4206 3 of 18 truck and the tilting frame.During the loading operation, the loading button must be pressed, which will cause the motor to rotate in a positive direction and its output torque to act on the tipping frame through the transmission system.This will result in the tipping frame dragging the dumper along the track, as illustrated in Figure 2. Upon reaching the end of the circular section of the track, the front track wheel will be blocked to stop.At this point, the pull force of the drive system chain will continue to act on the tipping frame, enabling the tipping frame to designate the center of the front track wheel for the tipping movement.This allows the substrate soil to be dumped into the dump truck.At an angle of 110° between the flip frame and the handcart, the substrate soil can be completely dumped.Simultaneously, the flip frame will contact the end position travel switch, which will cause the motor to cease operation, halting the movement and concluding the loading process.Upon returning, pressing the return button will reverse the motor, initiating a reversal of the overturning frame's movement along the path of the feeding process.Upon returning to the initial position, the dumper will contact the starting position travel switch, resulting in the motor being powered off and the movement being halted.Subsequently, the dumper locking mechanism must be disengaged in order to exit the dumper.

Design of Overturning Frame
The overturning frame constitutes the fundamental component of the whole automatic loading device.Its principal function is to carry the handcart in order to complete the loading operation.It mainly comprises a track wheel, pushrod, splint, and dump handcart fixing mechanism; its structure is shown in Figure 3.In order to facilitate cooperation with the handcart, the overall structure of the overturning frame is designed according to the shape of the handcart, with the angle between the horizontal surface of the overturning frame and the inclined surface being 120°.A splint is installed on the overturning frame to hold the tilting surface of the handcart.The splint and the handcart fixing mechanism together serve to fix the handcart.The splint is equipped with slotted holes on the side and is mounted on the overturning frame by bolts, thereby enabling the position of the splint relative to the tilting frame to be adjusted.This allows the overturning frame to be adapted to different sizes of handcarts.The overturning frame contains three sets of track wheels, with the names and roles of each track wheel presented in Table 1.The axle of the rear track wheel is connected to the chain via the side plate and is directly connected to the pushrod.Consequently, the traction force of the chain acts on the rear track wheel axle initially, subsequently transferring to the pushrod, which acts on the overturning frame to facilitate its movement along the track.The overturning frame constitutes the fundamental component of the whole automatic loading device.Its principal function is to carry the handcart in order to complete the loading operation.It mainly comprises a track wheel, pushrod, splint, and dump handcart fixing mechanism; its structure is shown in Figure 3.In order to facilitate cooperation with the handcart, the overall structure of the overturning frame is designed according to the shape of the handcart, with the angle between the horizontal surface of the overturning frame and the inclined surface being 120 • .A splint is installed on the overturning frame to hold the tilting surface of the handcart.The splint and the handcart fixing mechanism together serve to fix the handcart.The splint is equipped with slotted holes on the side and is mounted on the overturning frame by bolts, thereby enabling the position of the splint relative to the tilting frame to be adjusted.This allows the overturning frame to be adapted to different sizes of handcarts.The overturning frame contains three sets of track wheels, with the names and roles of each track wheel presented in Table 1.The axle of the rear track wheel is connected to the chain via the side plate and is directly connected to the pushrod.Consequently, the traction force of the chain acts on the rear track wheel axle initially, subsequently transferring to the pushrod, which acts on the overturning frame to facilitate its movement along the track.
In order for the overturning frame to reach the tilting preset overturning angle, it is necessary for the pushrod to have a specific length.In the context of the overturning motion, the overturning frame can be regarded as a crank slider mechanism.The crank center is the front track wheel center, the connecting rod is the pushrod, and the rear track wheel axle can be regarded as the slider.The coordinate system depicted in Figure 4 illustrates the rotation of the overturning frame from the solid line position to the dotted line position around the origin.Concurrently, the hinge moves from A 1 to A 2 , while the slider translates from B 1 to B 2 .

Track Wheel Function Guide wheel
Guiding, so the overturning frame can only move along the track Support wheel Supporting, so the overturning frame will not impact the chain Driver wheel Driving, so the overturning frame can move In order for the overturning frame to reach the tilting preset overturning angle, it is necessary for the pushrod to have a specific length.In the context of the overturning motion, the overturning frame can be regarded as a crank slider mechanism.The crank center is the front track wheel center, the connecting rod is the pushrod, and the rear track wheel axle can be regarded as the slider.The coordinate system depicted in Figure 4 illustrates the rotation of the overturning frame from the solid line position to the dotted line position around the origin.Concurrently, the hinge moves from A1 to A2, while the slider translates from B1 to B2.In the process of design, the position of point A1 (xA1, yA1) is initially established, and subsequently, the coordinates of the position of point A2 (xA2, yA2) can be determined in accordance with the following equation: where R is the rotation matrix: Table 1.The name and function of the track wheel.

Track Wheel Function
Guide wheel Guiding, so the overturning frame can only move along the track Support wheel Supporting, so the overturning frame will not impact the chain Driver wheel Driving, so the overturning frame can move

Track Wheel Function Guide wheel
Guiding, so the overturning frame can only move along the track Support wheel Supporting, so the overturning frame will not impact the chain Driver wheel Driving, so the overturning frame can move In order for the overturning frame to reach the tilting preset overturning angle, it is necessary for the pushrod to have a specific length.In the context of the overturning motion, the overturning frame can be regarded as a crank slider mechanism.The crank center is the front track wheel center, the connecting rod is the pushrod, and the rear track wheel axle can be regarded as the slider.The coordinate system depicted in Figure 4 illustrates the rotation of the overturning frame from the solid line position to the dotted line position around the origin.Concurrently, the hinge moves from A1 to A2, while the slider translates from B1 to B2.In the process of design, the position of point A1 (xA1, yA1) is initially established, and subsequently, the coordinates of the position of point A2 (xA2, yA2) can be determined in accordance with the following equation: where R is the rotation matrix:  In the process of design, the position of point A 1 (x A1 , y A1 ) is initially established, and subsequently, the coordinates of the position of point A 2 (x A2 , y A2 ) can be determined in accordance with the following equation: where R is the rotation matrix: where θ is the angle of rotation of the overturning frame around the origin, 50 • .The slider moves in parallel, and the design angle between the translation track and the x-axis angle is 60 • .The travel distance (b) of the slider is designed to be 235 mm; then, the relationship of position points B 1 (x B1 , y B1 ) and B 2 (x B2 , y B2 ) is The distance (e) between the straight line (B 1 B 2 ), where the track is located, and the line that crosses the origin and is parallel to it, is designed to be 155 mm; then, the track straight line equation is where y B1B2 is the linear vertical coordinate; x B1B2 is the linear horizontal coordinate.
According to the constant length of the pushrod, the following equation can be obtained: The joint Equations ( 1)-( 4) can be found as the pushrod length of 350 mm.

Design of Handcart Fixing Mechanism
To ensure the stability of the movement of the overturning in the process of turning, the locking mechanism of the dumper is designed to realize the complete fixation of the dumper with the clamping plate, referring to the method in related articles [13][14][15][16][17].The handcart fixing mechanism mainly includes an axle splint, link, torsion spring, joystick, joystick plate, etc., as shown in Figure 5.The handcart fixing mechanism of the dump truck has two working states, locking and unlocking, as shown in Figure 6.When locking, the joystick is turned to drive the rotation of the shaft and the axle splint, and when the axle splint is turned vertical, the axle of the handcart can be fixed.There is a torsion spring installed in the rotating shaft of the joystick plate, which makes it have a self-locking function.When unlocking, the joystick plate is turned to make the joystick return to the horizontal state and unlock the axle splint to fix the axle of the handcart.
where  is the angle of rotation of the overturning frame around the origin, 50°.
The slider moves in parallel, and the design angle between the translation track and the x-axis angle is 60°.The travel distance (b) of the slider is designed to be 235 mm; then, the relationship of position points B1 (xB1, yB1) and B2 (xB2, yB2) is The distance (e) between the straight line (B1 B2), where the track is located, and the line that crosses the origin and is parallel to it, is designed to be 155 mm; then, the track straight line equation is where  is the linear vertical coordinate;  is the linear horizontal coordinate.According to the constant length of the pushrod, the following equation can be obtained: The joint Equation ( 1) to ( 4) can be found as the pushrod length of 350 mm.

Design of Handcart Fixing Mechanism
To ensure the stability of the movement of the overturning in the process of turning, the locking mechanism of the dumper is designed to realize the complete fixation of the dumper with the clamping plate, referring to the method in related articles [13][14][15][16][17].The handcart fixing mechanism mainly includes an axle splint, link, torsion spring, joystick, joystick plate, etc., as shown in Figure 5.The handcart fixing mechanism of the dump truck has two working states, locking and unlocking, as shown in Figure 6.When locking, the joystick is turned to drive the rotation of the shaft and the axle splint, and when the axle splint is turned vertical, the axle of the handcart can be fixed.There is a torsion spring installed in the rotating shaft of the joystick plate, which makes it have a self-locking function.When unlocking, the joystick plate is turned to make the joystick return to the horizontal state and unlock the axle splint to fix the axle of the handcart.The sketch of the handcart fixing mechanism is shown in Figure 7, and the mechanism is in a locked state at this time.
The length of the short rod of the rotating shaft is designated as L1, the length of the connecting rod is L2, and the length of the short rod of the joystick is L3.In accordance with the design specifications, when the handcart fixing mechanism is in the locked state, the angles α and β between the short rod of the rotating shaft and the short rod of the joystick and the horizontal plane are 45°.The horizontal distance (L) and vertical distance (h) The sketch of the handcart fixing mechanism is shown in Figure 7, and the mechanism is in a locked state at this time.
The length of the short rod of the rotating shaft is designated as L 1 , the length of the connecting rod is L 2 , and the length of the short rod of the joystick is L 3 .In accordance with the design specifications, when the handcart fixing mechanism is in the locked state, the angles α and β between the short rod of the rotating shaft and the short rod of the joystick and the horizontal plane are 45 • .The horizontal distance (L) and vertical distance (h) between the two fixed hinges are determined by the structure of the flip frame.The horizontal distance is 370 mm, while the vertical distance is 25 mm.To prevent the rods from interfering with the ground during the rotation process, the value of the short rod length (L 3 ) of the joystick cannot exceed 90 mm and is taken as 80 mm.The length of each rod can be determined by the geometric relationship illustrated in Figure 7: The length of L 1 is 44.6 mm and the length of L 2 is 395 mm, calculated by Equations ( 5) and ( 6).The sketch of the handcart fixing mechanism is shown in Figure 7, and the mechanism is in a locked state at this time.
The length of the short rod of the rotating shaft is designated as L1, the length of the connecting rod is L2, and the length of the short rod of the joystick is L3.In accordance with the design specifications, when the handcart fixing mechanism is in the locked state, the angles α and β between the short rod of the rotating shaft and the short rod of the joystick and the horizontal plane are 45°.The horizontal distance (L) and vertical distance (h) between the two fixed hinges are determined by the structure of the flip frame.The horizontal distance is 370 mm, while the vertical distance is 25 mm.To prevent the rods from interfering with the ground during the rotation process, the value of the short rod length (L3) of the joystick cannot exceed 90 mm and is taken as 80 mm.The length of each rod can be determined by the geometric relationship illustrated in Figure 7: The length of L1 is 44.6 mm and the length of L2 is 395 mm, calculated by Equations ( 5) and ( 6).

Import and Simplification of the Model
Referring to the related articles [13][14][15][16], the 3D model of the automatic loading device created in Solidworks ( 2018) is imported into Adams/View in the .x_tformat.Subsequently, the parts that are not related to the simulation motion are deleted.Finally, the Boolean operation is employed to merge the parts in order to streamline the motion components.The virtual prototype model of the automatic loading device is shown in Figure 8.

Import and Simplification of the Model
Referring to the related articles [13][14][15][16], the 3D model of the automatic loading device created in Solidworks ( 2018) is imported into Adams/View in the .x_tformat.Subsequently, the parts that are not related to the simulation motion are deleted.Finally, the Boolean operation is employed to merge the parts in order to streamline the motion components.The virtual prototype model of the automatic loading device is shown in Figure 8.The names of the main components are shown in Table 2.The names of the main components are shown in Table 2.

Simulation Parameter Setting
After the model is simplified, the initial conditions and the material of each part are set according to the actual parameters of the prototype, as are the moving and rotating subsets for the model according to the motion, as shown in Table 3.In the process of loading, the mass of substrate soil in the handcart will gradually decrease as the turning angle increases.To simulate the process of substrate dumping, a variable force is applied to the handcart, the direction is always kept vertically down, and the initial value is equal to the gravity of 0.14 m 3 of substrate soil, which is 1078 N. When the tipping angle of the handcart is less than or equal to 50 • , the magnitude of the variable force is 1078 N (indicating the state of full soil); when the tipping angle of the handcart is greater than 50 • , the size of the variable force decreases according to the cosine law (indicating that the substrate soil in the handcart begins to dump).

Analysis of Simulation Results
The simulation was run with a step size of 500 and a simulation time of 10 s.After the simulation was completed, the change curve of the flip angle, velocity, acceleration, angular velocity, and pushrod thrust in the process of feeding the overturning frame was obtained (Figures 9-13).
The change curve of the turning angle of the overturning frame and the handcart during the loading process is shown in Figure 9. From 0 s to 6.66 s, the overturning frame moves along the straight track at a constant speed, and the turning angle is always 0 • .From 6.66 s to 8.40 s, the front track wheel of the overturning frame enters the circular track; the overturning frame moves at a variable speed and the turning angle slowly increases from 0 • to 34 • .From 8.40 s to 8.60 s, the overturning frame turns around the front track wheel and the turning angle increases rapidly from 34 • to 50 • ; from 8.60 s to 9.94 s, the overturning frame continues to turn around the front track wheel while the substrate is removed from the bucket truck.In 8.40 s to 8.60 s, the overturning frame rotates around the front track wheel, and the overturning angle increased rapidly from 34 • to 50 • ; in 8.60 s to 9.94 s, the overturning frame continues to rotate around the front track wheel, while the subsoil is discharged from the bucket truck, and the overturning angle increases from 50 • to 110 • .
The horizontal acceleration change curve and horizontal velocity change curve of the overturning frame and handcart are shown in Figure 10.From 0 s to 6.66 s, the horizontal velocity of the overturning frame remains unchanged at 68.9 mm/s; from 6.66 s to 8.40 s, the horizontal acceleration of the overturning frame shows several small abrupt changes, among which the biggest change is from 734 mm/s 2 to 1405 mm/s 2 .Since the acceleration direction is generally positive, the horizontal velocity of the overturning frame increases from 68.9 mm/s to 225.9 mm/s; in the period from 8.40 s to 8.60 s, the horizontal acceleration of the overturning frame has several large abrupt changes.The largest abrupt change is from −7004 mm/s 2 to 7458 mm/s 2 ; an the abrupt change in the horizontal acceleration makes the horizontal velocity of the overturning frame to have many large abrupt changes.The largest of which was from 62.1 mm/s to 402.4 mm/s.In 8.60 s to 9.94 s, the horizontal acceleration of the overturning frame showed several small abrupt changes, the largest of which was from 3760 mm/s 2 to −1760 mm/s 2 , and the horizontal velocity increased from 411.9 mm/s to the maximum value of 626.6 mm/s.
The change curve of the turning angle of the overturning frame and the handcart during the loading process is shown in Figure 9. From 0 s to 6.66 s, the overturning frame moves along the straight track at a constant speed, and the turning angle is always 0°. From 6.66 s to 8.40 s, the front track wheel of the overturning frame enters the circular track; the overturning frame moves at a variable speed and the turning angle slowly increases from 0° to 34°.From 8.40 s to 8.60 s, the overturning frame turns around the front track wheel and the turning angle increases rapidly from 34° to 50°; from 8.60 s to 9.94 s, the overturning frame continues to turn around the front track wheel while the substrate is removed from the bucket truck.In 8.40 s to 8.60 s, the overturning frame rotates around the front track wheel, and the overturning angle increased rapidly from 34° to 50°; in 8.60 s to 9.94 s, the overturning frame continues to rotate around the front track wheel, while the subsoil is discharged from the bucket truck, and the overturning angle increases from 50° to 110°.The horizontal acceleration change curve and horizontal velocity change curve of the overturning frame and handcart are shown in Figure 10.From 0 s to 6.66 s, the horizontal velocity of the overturning frame remains unchanged at 68.9 mm/s; from 6.66 s to 8.40 s, the horizontal acceleration of the overturning frame shows several small abrupt changes, among which the biggest change is from 734 mm/s 2 to 1405 mm/s 2 .Since the acceleration direction is generally positive, the horizontal velocity of the overturning frame increases from 68.9 mm/s to 225.9 mm/s; in the period from 8.40 s to 8.60 s, the horizontal acceleration of the overturning frame has several large abrupt changes.The largest abrupt change is from −7004 mm/s 2 to 7458 mm/s 2 ; an the abrupt change in the horizontal acceleration makes the horizontal velocity of the overturning frame to have many large abrupt changes.The largest of which was from 62.1 mm/s to 402.4 mm/s.In 8.60 s to 9.94 s, the horizontal acceleration of the overturning frame showed several small abrupt changes, the largest of which was from 3760 mm/s 2 to −1760 mm/s 2 , and the horizontal velocity increased from 411.9 mm/s to the maximum value of 626.6 mm/s.The variation curves of the vertical acceleration and vertical velocity of the overturning frame and handcart are shown in Figure 11.In the period from 0 s to 6.66 s (the first stage), the vertical direction velocity of the overturning frame remained unchanged at 114.6 mm/s; in the period from 6.66 s to 8.40 s, the vertical direction acceleration of the overturning frame showed several large abrupt changes, the largest of which was from −9591 mm/s 2 to 1567 mm/s 2 .The abrupt change in the vertical acceleration results in a multitude of minor fluctuations in the vertical velocity of the overturning frame.Because the acceleration direction is positive, the vertical velocity of the flipper increases from 114.6 mm/s to 371.6 mm/s and then decreases to 341.7 mm/s.In the period from 8.40 s to 9.94 s, the vertical acceleration of the flipper shows several large abrupt changes, the largest of which is from −2821 mm/s 2 to 6433 mm/s 2 .The overall trend of acceleration changed from positive to negative, so the vertical velocity first increased from 341.7 mm/s to the maximum value of 541.6 mm/s, and then decreased to the minimum value of −13.9 mm/s, with a large range of vertical velocity change.The variation curves of the vertical acceleration and vertical velocity of the overturning frame and handcart are shown in Figure 11.In the period from 0 s to 6.66 s (the first stage), the vertical direction velocity of the overturning frame remained unchanged at 114.6 mm/s; in the period from 6.66 s to 8.40 s, the vertical direction acceleration of the overturning frame showed several large abrupt changes, the largest of which was from −9591 mm/s 2 to 1567 mm/s 2 .The abrupt change in the vertical acceleration results in a multitude of minor fluctuations in the vertical velocity of the overturning frame.Because the acceleration direction is positive, the vertical velocity of the flipper increases from 114.6 mm/s to 371.6 mm/s and then decreases to 341.7 mm/s.In the period from 8.40 s to 9.94 s, the vertical acceleration of the flipper shows several large abrupt changes, the largest of which is from −2821 mm/s 2 to 6433 mm/s 2 .The overall trend of acceleration changed from positive to negative, so the vertical velocity first increased from 341.7 mm/s to the maximum value of 541.6 mm/s, and then decreased to the minimum value of −13.9 mm/s, with a large range of vertical velocity change.
The change curves of the angular velocity of the overturning frame and handcart are shown in Figure 12.From 0 s to 6.66 s, the angular velocity of the overturning frame remained constant at 0 rad/s; from 6.66 s to 8.40 s (the second stage), the angular velocity of the overturning frame increased from 0 rad/s to 0.56 rad/s and then decreased to 0.52 rad/s; from 8.40 s to 8.60 s, the angular velocity of the overturning frame showed several large abrupt changes, the largest of which was from 0.52 rad/s to the maximum value of 1.04 rad/s.In the period from 8.60 s to 9.94 s (the third stage: subsoil sliding stage), the angular velocity of the overturning frame showed several small changes, with an overall change from 0.62 rad/s to 0.98 rad/s.which was from −9591 mm/s 2 to 1567 mm/s 2 .The abrupt change in the vertical acceleration results in a multitude of minor fluctuations in the vertical velocity of the overturning frame.Because the acceleration direction is positive, the vertical velocity of the flipper increases from 114.6 mm/s to 371.6 mm/s and then decreases to 341.7 mm/s.In the period from 8.40 s to 9.94 s, the vertical acceleration of the flipper shows several large abrupt changes, the largest of which is from −2821 mm/s 2 to 6433 mm/s 2 .The overall trend of acceleration changed from positive to negative, so the vertical velocity first increased from 341.7 mm/s to the maximum value of 541.6 mm/s, and then decreased to the minimum value of −13.9 mm/s, with a large range of vertical velocity change.The change curves of the angular velocity of the overturning frame and handcart are shown in Figure 12.From 0 s to 6.66 s, the angular velocity of the overturning frame remained constant at 0 rad/s; from 6.66 s to 8.40 s (the second stage), the angular velocity of the overturning frame increased from 0 rad/s to 0.56 rad/s and then decreased to 0.52 rad/s; from 8.40 s to 8.60 s, the angular velocity of the overturning frame showed several large abrupt changes, the largest of which was from 0.52 rad/s to the maximum value of 1.04 rad/s.In the period from 8.60 s to 9.94 s (the third stage: subsoil sliding stage), the angular velocity of the overturning frame showed several small changes, with an overall change from 0.62 rad/s to 0.98 rad/s.The change curve of the pushrod thrust during the motion is shown in Figure 13.In the period from 0 s to 6.66 s, the overturning frame moves at a constant speed and the pushrod thrust is constant at 1476 N; in the period from 6.66 s to 8.10 s, the front track wheel of the overturning frame begins to enter the circular arc section of the track, and the force arm of the pushrod thrust decreases rapidly relative to the force arm of the gravity on the overturning frame, the subsoil, and the dump truck, so that the pushrod thrust increases from 1476 N to 4426 N. In the period from 8.10 s to 8.40 s, the front track wheel of the overturning frame is about to move to the end of the circular arc section of the track, and the force arm of the gravity decreases compared with the force arm of the thrust.The arm of gravity decreases compared with the arm of thrust, so the thrust of the pushrod decreases from 4426 N to 4088 N. In the period from 8.40 s to 8.60 s, the overturning motion of the overturning frame is carried out, and the thrust of the pushrod changes abruptly from 4088 N to 7460 N because its support wheel is off the track; in this stage, the pushrod thrust reaches the maximum value of 7800 N, while there are several large abrupt changes, the largest of which is from 5044 N to 7800 N. From 8.60 s to 9.94 s, the required pushrod thrust starts to decrease because the mass of the subsoil in the handcart starts to decrease.The change curve of the pushrod thrust during the motion is shown in Figure 13.In the period from 0 s to 6.66 s, the overturning frame moves at a constant speed and the pushrod thrust is constant at 1476 N; in the period from 6.66 s to 8.10 s, the front track wheel of the overturning frame begins to enter the circular arc section of the track, and the force arm of the pushrod thrust decreases rapidly relative to the force arm of the gravity on the overturning frame, the subsoil, and the dump truck, so that the pushrod thrust increases from 1476 N to 4426 N. In the period from 8.10 s to 8.40 s, the front track wheel of the overturning frame is about to move to the end of the circular arc section of the track, and the force arm of the gravity decreases compared with the force arm of the thrust.The arm of gravity decreases compared with the arm of thrust, so the thrust of the pushrod decreases from 4426 N to 4088 N. In the period from 8.40 s to 8.60 s, the overturning motion of the overturning frame is carried out, and the thrust of the pushrod changes abruptly from 4088 N to 7460 N because its support wheel is off the track; in this stage, the pushrod thrust reaches the maximum value of 7800 N, while there are several large abrupt changes, the largest of which is from 5044 N to 7800 N. From 8.60 s to 9.94 s, the required pushrod thrust starts to decrease because the mass of the subsoil in the handcart starts to decrease.

Establishment of Multi-Objective Function
In order to reduce the load on the motor and improve the stability of the operation, the structure of the automatic loading device must be optimized, referring to the related articles [17][18][19].The angular velocity of the device and the thrust force of the pusher are taken as the optimization objectives, and the new optimization objective function is constructed by the linear weighted sum method: The change curve of the pushrod thrust during the motion is shown in Figure 13.In the period from 0 s to 6.66 s, the overturning frame moves at a constant speed and the pushrod thrust is constant at 1476 N; in the period from 6.66 s to 8.10 s, the front track wheel of the overturning frame begins to enter the circular arc section of the track, and the force arm of the pushrod thrust decreases rapidly relative to the force arm of the gravity on the overturning frame, the subsoil, and the dump truck, so that the pushrod thrust increases from 1476 N to 4426 N. In the period from 8.10 s to 8.40 s, the front track wheel of the overturning frame is about to move to the end of the circular arc section of the track, and the force arm of the gravity decreases compared with the force arm of the thrust.The arm of gravity decreases compared with the arm of thrust, so the thrust of the pushrod decreases from 4426 N to 4088 N. In the period from 8.40 s to 8.60 s, the overturning motion of the overturning frame is carried out, and the thrust of the pushrod changes abruptly from 4088 N to 7460 N because its support wheel is off the track; in this stage, the pushrod thrust reaches the maximum value of 7800 N, while there are several large abrupt changes, the largest of which is from 5044 N to 7800 N. From 8.60 s to 9.94 s, the required pushrod thrust starts to decrease because the mass of the subsoil in the handcart starts to decrease.

Establishment of Multi-Objective Function
In order to reduce the load on the motor and improve the stability of the operation, the structure of the automatic loading device must be optimized, referring to the related articles [17][18][19].The angular velocity of the device and the thrust force of the pusher are taken as the optimization objectives, and the new optimization objective function is constructed by the linear weighted sum method: where f ′ 1 and f ′ 2 are the functions after dimensionless processing of the sub-objective function, λ 1 andλ 2 are weighting coefficients; For the weighting coefficients λ 1 and λ 2 of the sub-objective functions, the judgment matrix method [18] is used to calculate them.Based on Table 4, the judgment matrix A = a ij m×m is constructed.In this matrix, each element is called a scalar value, where a 11 = 1.The optimization is a multi-objective optimization function reconstruction of the two sub-objective functions of the angular velocity of the overturning frame as well as the pushrod thrust, so that m = 2.According to engineering experience, the pushrod thrust affects the service life of the motor, while the fluctuation of the angular velocity is within the safety range, so the pushrod thrust is considered much more important than the angular velocity, so the judgment matrix is Table 4. Scale values and their meanings.

Scale Values Meanings
In the comparison of 2 elements, they are equally important 3 In the comparison of 2 elements, the former is slightly more important than the latter 5 In the comparison of 2 elements, the former is significantly more important than the latter 7 In the comparison of 2 elements, the former is much more important than the latter The magnitude of the geometric mean of the scale values can be used to represent the importance of the sub-objective functions [20][21][22][23]: where w i is the magnitude of the geometric mean of the scalar values, m is the matrix order, and a ij is the elements of the i column and j row of the judgment matrix.The formula for calculating the weighting coefficient of the sub-target function can be obtained by Equation (9).
where i is the weighting factor, w i is the magnitude of the geometric mean of the scalar values, m is the matrix order, and a pj is the elements of the p column and j row of the judgment matrix.

Constraint
Based on the dynamic simulation model combined with the specific structure of the device and methods from related articles [24][25][26][27], the length and position of the hinge pin, the position of the support wheel holder, and the length of the pushrod were determined as optimization objects; variables were created and their variation ranges were determined based on the 3D model, as shown in Table 5.The variables are parametrically modeled in Adams/View according to the variation of each variable so that the model can be modified quickly and the optimization can be carried out smoothly.After the optimization is completed, the change graphs of thrust force, angular velocity, and optimized objective function of the pushrod during the movement of 16 sets of different sizes of the overturning frame are obtained.The optimized thrust force is shown in Figure 14.The optimized angular velocity is shown in Figure 15.The optimized objective function is shown in Figure 16.
Appl.Sci.2024, 14, 4206 12 of 18 Adams/View according to the variation of each variable so that the model can be modified quickly and the optimization can be carried out smoothly.After the optimization is completed, the change graphs of thrust force, angular velocity, and optimized objective function of the pushrod during the movement of 16 sets of different sizes of the overturning frame are obtained.The optimized thrust force is shown in Figure 14.The optimized angular velocity is shown in Figure 15.The optimized objective function is shown in Figure 16.Adams/View according to the variation of each variable so that the model can be modified quickly and the optimization can be carried out smoothly.After the optimization is completed, the change graphs of thrust force, angular velocity, and optimized objective function of the pushrod during the movement of 16 sets of different sizes of the overturning frame are obtained.The optimized thrust force is shown in Figure 14.The optimized angular velocity is shown in Figure 15.The optimized objective function is shown in Figure 16.As shown in Figure 17, the variation in the maximum value of the objective function for 16 groups of different overturning frame sizes is shown.Observing the data of each group, it is found that the maximum value of the objective function in group 9 is the As shown in Figure 17, the variation in the maximum value of the objective function for 16 groups of different overturning frame sizes is shown.Observing the data of each group, it is found that the maximum value of the objective function in group 9 is the smallest, so the overturning frame size in group 9 is considered as the relative optimal size.Appl.Sci.2024, 14, 4206 13 of 18 smallest, so the overturning frame size in group 9 is considered as the relative optimal size.Figure 18 shows a comparison of the horizontal direction speed optimization during the movement of the overturning frame with the relative optimal size and the original size.Before optimization, the number of large abrupt changes in horizontal velocity is higher; the maximum abrupt change is from 62.1 mm/s to 402.4 mm/s and the maximum velocity is 626.6 mm/s.After optimization, the number of large abrupt changes in horizontal velocity is lower; the maximum abrupt change is from 53.1 mm/s to 262.5 mm/s and the maximum velocity is 397.6 mm/s.As illustrated in Figure 19, the optimized vertical velocity during the motion of the overturning frame in comparison to the optimal size is contrasted with the original size.Prior to optimization, the vertical velocity exhibited a notable increase from 114.6 mm/s to a maximum value of 541.6 mm/s, followed by a pronounced decline to −13.9 mm/s, encompassing a considerable range of variation.Following optimization, the vertical velocity initially increased from 114.6 mm/s to a maximum value of 368.9 mm/s, before subsequently reducing to 151.1 mm/s.Figure 18 shows a comparison of the horizontal direction speed optimization during the movement of the overturning frame with the relative optimal size and the original size.Before optimization, the number of large abrupt changes in horizontal velocity is higher; the maximum abrupt change is from 62.1 mm/s to 402.4 mm/s and the maximum velocity is 626.6 mm/s.After optimization, the number of large abrupt changes in horizontal velocity is lower; the maximum abrupt change is from 53.1 mm/s to 262.5 mm/s and the maximum velocity is 397.6 mm/s.smallest, so the overturning frame size in group 9 is considered as the relative optimal size.Figure 18 shows a comparison of the horizontal direction speed optimization during the movement of the overturning frame with the relative optimal size and the original size.Before optimization, the number of large abrupt changes in horizontal velocity is higher; the maximum abrupt change is from 62.1 mm/s to 402.4 mm/s and the maximum velocity is 626.6 mm/s.After optimization, the number of large abrupt changes in horizontal velocity is lower; the maximum abrupt change is from 53.1 mm/s to 262.5 mm/s and the maximum velocity is 397.6 mm/s.As illustrated in Figure 19, the optimized vertical velocity during the motion of the overturning frame in comparison to the optimal size is contrasted with the original size.Prior to optimization, the vertical velocity exhibited a notable increase from 114.6 mm/s to a maximum value of 541.6 mm/s, followed by a pronounced decline to −13.9 mm/s, encompassing a considerable range of variation.Following optimization, the vertical velocity initially increased from 114.6 mm/s to a maximum value of 368.9 mm/s, before subsequently reducing to 151.1 mm/s.As illustrated in Figure 19, the optimized vertical velocity during the motion of the overturning frame in comparison to the optimal size is contrasted with the original size.Prior to optimization, the vertical velocity exhibited a notable increase from 114.6 mm/s to a maximum value of 541.6 mm/s, followed by a pronounced decline to −13.9 mm/s, encompassing a considerable range of variation.Following optimization, the vertical velocity initially increased from 114.6 mm/s to a maximum value of 368.9 mm/s, before subsequently reducing to 151.1 mm/s.As illustrated in Figure 19, the optimized vertical velocity during the motion of the overturning frame in comparison to the optimal size is contrasted with the original size.Prior to optimization, the vertical velocity exhibited a notable increase from 114.6 mm/s to a maximum value of 541.6 mm/s, followed by a pronounced decline to −13.9 mm/s, encompassing a considerable range of variation.Following optimization, the vertical velocity initially increased from 114.6 mm/s to a maximum value of 368.9 mm/s, before subsequently reducing to 151.1 mm/s.As illustrated in Figure 20, the angular velocity optimization during the motion of the flip frame in relation to the optimal size is compared with the original size.Prior to optimization, the angular velocity of the overturning frame exhibited a greater degree of variability, with a maximum mutation of 0.52 rad/s to 1.04 rad/s and a maximum angular velocity of 1.04 rad/s.Following optimization, the angular velocity of the overturning frame exhibited a reduction in the number of large mutations, with a maximum mutation of 0.47 rad/s to 0.64 rad/s and a maximum angular velocity of 0.64 rad/s.As illustrated in Figure 20, the angular velocity optimization during the motion of the flip frame in relation to the optimal size is compared with the original size.Prior to optimization, the angular velocity of the overturning frame exhibited a greater degree of variability, with a maximum mutation of 0.52 rad/s to 1.04 rad/s and a maximum angular velocity of 1.04 rad/s.Following optimization, the angular velocity of the overturning frame exhibited a reduction in the number of large mutations, with a maximum mutation of 0.47 rad/s to 0.64 rad/s and a maximum angular velocity of 0.64 rad/s.As shown in Figure 21, the thrust force of the pushrod is optimized during the overturning frame's motion in comparison to its original size.Prior to optimization, the pushrod thrust exhibited a greater number of significant fluctuations, with the largest change occurring from 5044 N to 7800 N, and the maximum thrust reaching 7800 N. Following optimization, the number of significant fluctuations in the pushrod thrust was reduced, with the largest change occurring from 3612 N to 4985 N and the maximum thrust reaching 4985 N. Following the implementation of a multi-objective optimization strategy, the fluctuations in the operating parameters of the loading process of the overturning frame were significantly reduced.This resulted in a notable reduction in vibration during the movement, thereby enhancing safety.The number of horizontal speed mutations is As shown in Figure 21, the thrust force of the pushrod is optimized during the overturning frame's motion in comparison to its original size.Prior to optimization, the pushrod thrust exhibited a greater number of significant fluctuations, with the largest change occurring from 5044 N to 7800 N, and the maximum thrust reaching 7800 N. Following optimization, the number of significant fluctuations in the pushrod thrust was reduced, with the largest change occurring from 3612 N to 4985 N and the maximum thrust reaching 4985 N. As illustrated in Figure 20, the angular velocity optimization during the motion of the flip frame in relation to the optimal size is compared with the original size.Prior to optimization, the angular velocity of the overturning frame exhibited a greater degree of variability, with a maximum mutation of 0.52 rad/s to 1.04 rad/s and a maximum angular velocity of 1.04 rad/s.Following optimization, the angular velocity of the overturning frame exhibited a reduction in the number of large mutations, with a maximum mutation of 0.47 rad/s to 0.64 rad/s and a maximum angular velocity of 0.64 rad/s.As shown in Figure 21, the thrust force of the pushrod is optimized during the overturning frame's motion in comparison to its original size.Prior to optimization, the pushrod thrust exhibited a greater number of significant fluctuations, with the largest change occurring from 5044 N to 7800 N, and the maximum thrust reaching 7800 N. Following optimization, the number of significant fluctuations in the pushrod thrust was reduced, with the largest change occurring from 3612 N to 4985 N and the maximum thrust reaching 4985 N. Following the implementation of a multi-objective optimization strategy, the fluctuations in the operating parameters of the loading process of the overturning frame were significantly reduced.This resulted in a notable reduction in vibration during the movement, thereby enhancing safety.The number of horizontal speed mutations is reduced; the maximum mutation is optimized from 62.1 mm/s to 402.4 mm/s to 53.1 mm/s Following the implementation of a multi-objective optimization strategy, the fluctuations in the operating parameters of the loading process of the overturning frame were significantly reduced.This resulted in a notable reduction in vibration during the movement, thereby enhancing safety.The number of horizontal speed mutations is reduced; the maximum mutation is optimized from 62.1 mm/s to 402.4 mm/s to 53.1 mm/s to 262.5 mm/s, and the maximum value is reduced from 626.6 mm/s to 397.6 mm/s.The vertical speed variation range is reduced, and the maximum value is reduced from 541.6 mm/s to 368.9 mm/s.The number of sudden changes in angular velocity is reduced, and the maximum sudden change from 0.52 rad/s to 1.04 rad/s is optimized to 0.47 rad/s to 0.64 rad/s.Furthermore, the maximum angular velocity is reduced from 1.04 rad/s to 0.64 rad/s.The number of sudden changes in thrust force is reduced, and the maximum sudden change from 5044 N to 7800 N is optimized to 3612 N to 4985 N. From 3612 N to 4985 N, the maximum thrust is reduced from 7800 N to 4985 N, which contributes to the extended service life of the motor.
The changes in each variable before and after optimization are presented in Table 6.Based on this, it can be seen that the optimization of the overturning frame is as follows: the length of the hinge pin plate is modified from 35 mm to 10 mm; the position of the hinge pin plate relative to the overturning frame is moved upward along the slope by 13.3 mm on the original basis; the position of the support wheel frame relative to the overturning frame is moved downward along the slope by 9.3 mm on the original basis; and the length of the pushrod is changed from the original 350 mm to 225 mm.

Prototype Testing
The prototype is manufactured in accordance with the design results of the whole structure and the principal components, as illustrated in Figure 22.In order to ascertain whether the performance of the prototype of the automatic loading device meets the design requirements, performance tests are conducted on it.The changes in each variable before and after optimization are presented in Table 6.Based on this, it can be seen that the optimization of the overturning frame is as follows: the length of the hinge pin plate is modified from 35 mm to 10 mm; the position of the hinge pin plate relative to the overturning frame is moved upward along the slope by 13.3 mm on the original basis; the position of the support wheel frame relative to the overturning frame is moved downward along the slope by 9.3 mm on the original basis; and the length of the pushrod is changed from the original 350 mm to 225 mm.

Prototype Testing
The prototype is manufactured in accordance with the design results of the whole structure and the principal components, as illustrated in Figure 22.In order to ascertain whether the performance of the prototype of the automatic loading device meets the design requirements, performance tests are conducted on it.The test employs the wireless torque test system of Beijing BIT Technology Co., Ltd.(Beijing, China) to measure the torque variation of the motor output shaft during the operation of the automatic loading device, as shown in Figure 23, converting the measured torque into the measured value of the force acting on the actuator based on the relationship between the torque and the force acting on it.
where  is the torque on the output shaft of the motor in N•m,  is the motor output force in N, and  is the radius of the motor output shaft in 0.0175 m.The test employs the wireless torque test system of Beijing BIT Technology Co., Ltd.(Beijing, China) to measure the torque variation of the motor output shaft during the operation of the automatic loading device, as shown in Figure 23, converting the measured torque into the measured value of the force acting on the actuator based on the relationship between the torque and the force acting on it.
where T is the torque on the output shaft of the motor in N•m, F is the motor output force in N, and R is the radius of the motor output shaft in 0.0175 m.
(a) (b) The test employs the wireless torque test system of Beijing BIT Technology Co., Ltd.(Beijing, China) to measure the torque variation of the motor output shaft during the operation of the automatic loading device, as shown in Figure 23, converting the measured torque into the measured value of the force acting on the actuator based on the relationship between the torque and the force acting on it. =  •  (11) where  is the torque on the output shaft of the motor in N•m,  is the motor output force in N, and  is the radius of the motor output shaft in 0.0175 m.During the test, a handcart loaded with subsoil is pushed onto the overturning frame.This is carried out while observing whether the clamping plates on both sides of the overturning frame can smoothly clamp the ramp of the overturning cart.Once this is confirmed, the locking mechanism of the overturning cart is operated to verify whether it can fix the axle of the overturning cart.The automatic loading device is initiated to commence the loading process.The movement of the overturning frame is observed throughout the loading phase, and the ability of the overturning frame to carry the handcart during the overturning movement is then assessed.Upon cessation of the turning motion, it is necessary to ascertain whether all the subsoil has been successfully conveyed into the receptacle and whether any residual subsoil remains within the handcart.Additionally, it is essential to determine the angle between the inclined surface and the horizontal surface of the handcart using a horizontal angle meter.
The test was repeated three times.During the loading process, the device functioned as intended, with the clamping plate and the fixing mechanism of the bucket truck enabling the safe attachment of the bucket truck to the overturning frame.No substrate soil remained in the bucket truck, with the substrate falling into the bin.The loading time was 9.86 s, and the bucket truck rotated at an angle of 111 • , which met the design specifications.The measured values of the force acting on the pushrod are presented in Figure 24.During the test, a handcart loaded with subsoil is pushed onto the overturning frame.This is carried out while observing whether the clamping plates on both sides of the overturning frame can smoothly clamp the ramp of the overturning cart.Once this is confirmed, the locking mechanism of the overturning cart is operated to verify whether it can fix the axle of the overturning cart.The automatic loading device is initiated to commence the loading process.The movement of the overturning frame is observed throughout the loading phase, and the ability of the overturning frame to carry the handcart during the overturning movement is then assessed.Upon cessation of the turning motion, it is necessary to ascertain whether all the subsoil has been successfully conveyed into the receptacle and whether any residual subsoil remains within the handcart.Additionally, it is essential to determine the angle between the inclined surface and the horizontal surface of the handcart using a horizontal angle meter.
The test was repeated three times.During the loading process, the device functioned as intended, with the clamping plate and the fixing mechanism of the bucket truck enabling the safe attachment of the bucket truck to the overturning frame.No substrate soil remained in the bucket truck, with the substrate falling into the bin.The loading time was 9.86 s, and the bucket truck rotated at an angle of 111°, which met the design specifications.The measured values of the force acting on the pushrod are presented in Figure 24.As illustrated in the figure, the measured value of the force on the pushrod and the simulation value exhibit a parallel trend.The simulation calculation of the maximum value, 7800 N, aligns with the experimentally measured force maximum value of 8098 N, resulting in a difference of 298 N.This discrepancy represents a mere 3.67% error.The comparison of the simulation and experimental results validates the accuracy of the simulation model.This model can serve as a reference for subsequent design and further optimization of the automatic loading device.As illustrated in the figure, the measured value of the force on the pushrod and the simulation value exhibit a parallel trend.The simulation calculation of the maximum value, 7800 N, aligns with the experimentally measured force maximum value of 8098 N, resulting in a difference of 298 N.This discrepancy represents a mere 3.67% error.The comparison of

Figure 2 .
Figure 2. Scheme of the overturning process.

Figure 2 .
Figure 2. Scheme of the overturning process.

Figure 9 .
Figure 9.The change curve diagram of the overturning angle.

Figure 10 .
Figure 10.The change curve diagram of horizontal velocity and acceleration.(a) The change curve of horizontal acceleration; (b) the change curve of horizontal velocity.

Figure 11 .
Figure 11.The change curve diagram of vertical velocity and acceleration.(a) The change curve of vertical acceleration; (b) the change curve of vertical velocity.

Figure 11 . 18 Figure 12 .
Figure 11.The change curve diagram of vertical velocity and acceleration.(a) The change curve of vertical acceleration; (b) the change curve of vertical velocity.Appl.Sci.2024, 14, 4206 10 of 18

Figure 12 .
Figure 12.The change curve diagram of angular velocity.

18 Figure 12 .
Figure 12.The change curve diagram of angular velocity.

Figure 13 .
Figure 13.The curve diagram of pushrod thrust change.

Figure 13 .
Figure 13.The curve diagram of pushrod thrust change.

Figure 17 .
Figure 17.The change in the maximum value of the objective function.

Figure 17 .
Figure 17.The change in the maximum value of the objective function.

Figure 17 .
Figure 17.The change in the maximum value of the objective function.

Figure 22 .
Figure 22.Images of unloading device.(a) Image of test preparation; (b) image of prototype feeding effect.

Figure 22 .
Figure 22.Images of unloading device.(a) Image of test preparation; (b) image of prototype feeding effect.

Figure 22 .
Figure 22.Images of unloading device.(a) Image of test preparation; (b) image of prototype feeding effect.

Table 1 .
The name and function of the track wheel.

Table 1 .
The name and function of the track wheel.

Table 2 .
Main part name.
Part Name Model Name Handcart Handcart Front track wheel 1 and 2 Wheel 1 and 2 Support wheel 1 and 2 Wheel 3 and 4 Rear track wheel 1 and 2 Wheel 5 and 6 Pushrod Pushrod 1 and 2

Table 2 .
Main part name.

Table 5 .
Variables and their range of variation.

Table 5 .
Variables and their range of variation.

Table 5 .
Variables and their range of variation.

Table 6 .
Optimization of each variable.

Table 6 .
Optimization of each variable.