Analyzing Rice Grain Collision Behavior and Monitoring Mathematical Model Development for Grain Loss Sensors

Abstract

Grain loss in the harvesting process of combine harvesters not only causes economic losses to farmers but also affects the soil environment because of the lost grain covering the soil, influencing crop growth in the next season. Grain sieve loss-monitoring sensors represent an important accessory in combine harvesters, as they can not only provide current grain loss levels for the operator to adopt a rational action in time but also serve as an important performance signal for the control system. To reflect the rice grain sieve loss level of combine harvesters in real time, an indirect grain sieve loss-monitoring system is proposed in this paper. First, the grain collision rise time was obtained by the finite element method (FEM), and the parameters of the grain loss sensor signal processing circuit were determined accordingly to upgrade the monitoring accuracy. Then, grain loss distribution behind the cleaning shoe was analyzed in detail under different working parameters. Grain loss distribution functions at the end of the sieve and a monitoring mathematical model with relevant variables were established based on the laboratory experiment results. Finally, calibration experiments were carried out to verify the measurement accuracy of the sensor on a cleaning test bench, with an obtained relative monitoring error ≤6.41 % under different working conditions.

1. Introduction

Grain loss is an important indicator used to judge the performance of combine harvesters. The total grain loss ratio can be as high as 10% in the field operation of combine harvesters made Chinese companies due to the inadequate manufacturing technology and a lack of relevant basic research. Grain loss in the harvesting process of combine harvesters not only causes economic losses to farmers but also affects the soil environment, influencing crop growth in the next season. According to field investigations, the main reasons for grain loss in combine harvesters are as follows:

• Due to the concentrated working time of combine harvesters, the high working intensity, the complicated working environment, and the unilateral pursuit of working efficiency by the operator, the feeding rates generally exceeds the rated machine value, resulting in excessive grain loss.
• With the emergence of family farms in China, a large number of farmers have purchased their own combine harvesters. However, new operators are not proficient in operating such machinery and are not able to adjust settings according to changes in operating conditions, owing to a lack of operational experience and insufficient training, resulting in a considerable grain loss.
• Due to the low level of intelligence of combine harvesters made in China, the operators cannot obtain machine performance information in real time and can only judge the grain loss level by checking for grain in the field after shutting down the machine, which is a lagging indicator that cannot accurately identify the source of grain loss. The measures taken are often inappropriate, and the grain loss cannot be corrected in a timely manner.

Informatization and intelligence are effective means to improve combine harvester performance. In order to accurately measure grain loss in real time, scholars began to study grain loss autodetection technology as early as the 1960s [1,2,3,4,5,6,7,8,9,10,11,12]. Grain loss sensors have proven an indispensable accessory in combine harvesters. Equipment made by flagship combine harvester manufactures in Europe and the USA helps operators to understand the grain loss situation in real time, and settings can be adjusted with an intelligent control system that integrates multi-sensor information, significantly reducing grain loss [13,14,15]. However, grain loss sensors are still not available in China. In order to reduce the grain loss of rice combine harvesters, it is necessary to upgrade the monitoring ability of grain loss sensors when harvesting high-yield rice so as to strengthen the informatization and intelligence level of equipment made in China.

Most existing grain loss sensors are based on the piezoelectric effect [1,2,10,11]. Therefore, understanding the collision mechanical characteristics between grain and the sensor is the key to developing a high-performance grain loss sensor. The grain collision force and the force rise time, i.e., the time for the collision force to change from 0 to the maximum value, are two important factors in the design of the signal processing circuit used to distinguish rice grains from MOG (material other than grain). A considerable amount of research has been conducted on plate particle impact in recent years. Most such studies have been based on the discrete element method (DEM) [16,17,18], i.e., a discrete element model of particles and plates is developed, the material properties and contact boundary conditions are set and submitted for analyzing, and the required collision signal characteristics are analyzed according to the calculation results. However, the DEM simulation results, largely based on boundary conditions and models authenticity, accuracy fluctuates greatly. While the finite element method (FEM) is a method to simulate and calculate the stress and strain of the object under stress through finite grid elements [19], was used to study particle collision process in this study.

Based on the above comparison, the process of rice collision with a sensitive plate was studied in depth according to the FEM in the present study. The corresponding results can be used to optimize the signal processing circuit of grain loss sensors. Furthermore, the grain loss distribution behind the cleaning shoe was analyzed in detail under different working parameters, and a mathematical monitoring model was established with consideration of relevant variables. Finally, calibration experiments were carried out to verify the sensor measurement accuracy on a cleaning test bench.

2. Materials and Methods

2.1. Establishment of the Collision Model

Three-dimensional models of rice grains and a steel plate were established using the Solidworks software (PTC/CV, Dassault, MA, USA). Because the cross section of the rice model was similar to an ellipse, a sketch with an elliptical shape was established. With the major axis of the ellipse defined as A and the minor axis defined as B, the particle size ratio was defined as R = A/B to describe the difference in grain geometry. However, rice of different varieties usually has a different particle size ratio, R. According to previous studies, the minor axis, B, is approximately 2.4 mm; and the particle size ratio, R, usually ranges from 1 to 3 mm. The created sketch was rotated to obtain the rice grain model, and a steel plate with a thickness of 1.2 mm was established by rectangular extrusion. According to the symmetry of the rice model, HyperMesh (Altair Engineering Inc., Troy, MI, USA) was used to divide the grain model into eight equal parts along the center point, using ‘3D-solid map’ to mesh each part. As the mesh type was set to hexahedron, the grid size of the grain center was set to 0.1 mm, and the mesh size increased gradually from the center to the outside. The model was divided into four equal parts along the center point. Each part was meshed with ‘2D-automesh’. The mesh shape was hexahedral, and the grid size of upper and lower surface of steel plate was set to 0.3 mm. As the steel plate was regarded as an elastic material, ‘3D-Drag’ was used to divide the sides of the steel plate into five layers, and the grid height increased from the top to the bottom. Similarly, the complete steel plate grid model was obtained by mirroring. The meshed collision model is shown in Figure 1, and the models of the grain grid and the steel plate are shown in

Table 1. Comparison of grid models between the grain and steel plate.

Component	Number of Elements	Number of Nodes
Grain	79,104	81,141
Steel plate	178,220	216,270

.

2.2. Setting of Simulation Parameters

The grain density and steel plate density were obtained through actual measurement and calculation, respectively, and their moduli of elasticity and Poisson’s ratios were obtained by data query. The material parameters of rice grains and 304 stainless steel used in the simulation calculation are shown in

Table 2. Material parameters of collision simulation.

Material Property	Rice Grains	304 Stainless Steel
Density (kg/m3)	1350	7850
Modulus of elasticity (MPa)	200	80,000
Poisson’s ratio	0.25	0.29

. After the creation of entity units, the material properties were assigned to each model, followed by definition of the boundary conditions for the grains and steel plate. The Solver module of HyperMesh (Altair Engineering Inc., Troy, MI, USA) was used to define the surface contact constraint relationship between components, with the contact stiffness set at 0.2. The collision speed between rice grains and the steel plate was set to 2.5 m/s, with a sampling time of 10 kHz.

The rice grains were rotated with the ‘Tool-rotate’ function so that the grains would collide with the steel plate at different angles (0~90°). According to the principle of the control variable method, the grains were translated with ‘Tool-translate’ to ensure that the distance between the grains and the steel plate was the same at different angles, which was set to 1.2 mm. In the simulation, there was only one variable-the collision angle. Finally, simulations of rice collision with 304 stainless steel were carried out at different angles.

2.3. Verifying the Simulation Results by High-Speed Photography Experiment

A grain collision test platform was built with a high-speed camera and information acquisition system to verify the simulation results. To compare the experimental data with the simulation results more accurately, rice grains with parameters, such as material properties and particle size ratio, most consistent with those of the simulated grain model were selected as test objects, as well as a 304 stainless-steel sensitive sensor plate similar to that used in the simulation model. The device was composed of a high-speed photography display screen, a grain loss sensor with a mounting bracket, an Olympus high-speed camera, an acquisition program on the host computer, a fill-in light, etc. During the experiment the grain fall in to collision with the sensor, the image was took at the collision moment, the image was imported and saved. The i-SPEED post-processing suite (Olympus Corporation, Tokyo, Japan) was utilized to analyze the grain collision track and measure the collision angle. The information acquisition system with a sampling frequency of 200 kHz was used to process the rice grain collision signal generated from a YT-5 piezoelectric ceramic element. The obtained experimental signal data were then processed and analyzed by MATLAB software (MathWorks Inc., Natick, MA, USA) and compared with the simulation results to verify the simulation accuracy. The test platform is shown in Figure 2.

Through high-speed photography and an information acquisition system, a large number of experiments were carried out on rice grains with a particle size ratio of 2. After analysis and processing, the experimental results were compared with the simulation data to verify the correctness of the finite element simulation method. Once the simulation results were verified, i.e., confirmation that the simulation can reflect a real situation, then the simulation settings were adjusted to obtain some results that are difficult to achieve under experimental conditions.

2.4. Effects of Particle Size Ratio on Collision Signal

Firstly, according to the value range of particle size ratio (R) was taken as 1.5, 2, 2.5, and 3, and the minor axis (B) was 2.4 mm, so the size of the major axis (A) of the ellipse was obtained. SolidWorks software (Dassault Systèmes SOLIDWORKS Corp., Waltham, MA, USA) was used to establish the elliptical sketches according to different values of particle size ratio (R). Four rice grain models were obtained by rotation and then assembled with a steel plate with thickness of 1 mm to obtain the collision models under different particle size ratios. Secondly, HyperMesh (Altair, Shanghai, China) was used to simulate the four collision models, the LS-DYNA module of ANSYS Software (ANSYS Inc., Canonsburg, PA, USA) was used to compute and calculate the simulation files, and LS-Prepost (LST, Pittsburgh, PA, USA) was used to view the post-processing results. Finally, the simulation results were analyzed by MATLAB (MathWorks Inc., Natick, MA, USA). The parameters of the grain loss sensor signal processing circuit were determined according to the obtained results.

2.5. Establishment of the Grain Sieve Loss Monitoring Mathematical Model

To elucidate the grain distribution after leaving the sieve, an experiment was carried out on a test bench (Figure 3), with fan speed, guide plate angle, and sieve opening as experimental factors. The experiment material for the cleaning experiment was threshed output mixture from the thresh-separation test bench [20].

The properties of the experiment rice were: plant height, 750~850 mm; ear height, 150~170; straw moisture content, 58–67%; grain moisture content, 20~25%; straw/grain ratio, 1.9~2.2; one thousand grain weight, 31.2 g. Response surface methodology (RSM) was used to explore the relationships between several explanatory variables and one or more response variables. A response surface experiment was designed in JMP15.0 software (SAS, Cary, NC, USA) with I-optimal algorithm after 1000 steps of iterative computation to determine appropriate factors to predict cleaning performance [21]. It is also critical to understand grain loss distribution behind the cleaning shoe under different working parameters, as well as the relationship between grain mass in the sensor installation position and the total grain sieve losses. In each experiment, 49 boxes (in a 7 × 7 matrix; box size: 130 mm × 130 mm × 130 mm) were added to collect all the outputs from the cleaning shoes. The grains were obtained by removing MOG from each box using a re-cleaner (Agriculex ASC-3 Seed Cleaner, Guelph, ON, Canada). The total amount of threshed output was 60 kg, and the feed rate of the cleaning system was 2.5 kg/s (grain + MOG). The receiver boxes location of the is shown in Figure 4.

2.6. Grain Loss Sensor Monitoring Accuracy Experiment

Understanding the relationship between the number of grains counted by the sensor and the actual grain sieve losses in the sensor installation position is also of paramount importance. To verify the performance of the grain sieve loss sensor under different working parameters, experiments were carried out on the cleaning test bench by installing a grain sieve loss sensor at the end of the cleaning shoe and using the obtained relationship between grain sieve loss at the sensor position and total grain loss in order to obtain the sensor monitoring error. The experimental setup used to test the monitoring accuracy of the grain loss sensor is shown in Figure 5.

3. Results and Discussion

3.1. Analysis of Simulation Results

Figure 6 shows the simulation curves when rice grains with R = 2 collide with 304 a stainless-steel plate at different angles. As shown in Figure 6, the maximum resultant force is 4.25 N when the grain collides with the steel plate at an angle of 0°, and the rise time is about 66 µs. When the steel plate is impacted at 30°, the maximum force is 1.84 N, and the rise time is 72 µs. When the steel plate is impacted at 45°, the maximum resultant force is 1.82 N, and the action time is 90 µs. When the steel plate is impacted at 60°, the maximum resultant force is 1.90 N, and the action time is 128 µs. When the steel plate is impacted at 90°, the maximum resultant force is 1.58 N, and the action time is 122 µs. The results show that the magnitude of the resultant force is the highest when the collision angle is 0° because of the maximum impact area, whereas the magnitude is similar (1.5~2 N) when the collision angle is 30°, 45°, 60°, and 90° because of a similar impact area.

3.2. Experimental Verification

Many experiments on rice with a particle size ratio of 2 colliding with 304 stainless-steel were carried out on the test platform. The high-speed camera captured the angle when the grain collided with the steel plate, and the information acquisition system collected the collision signal. Several data points were obtained through experiments. After analysis and processing, the time for the resultant force to changes from 0 to the maximum value was recorded as tr. A comparison between simulation results and experimental data is shown in Figure 7.

Figure 7 shows that the difference in tr between the data obtained by experiment and simulation is very small. The discrepancy largest discrepancy occurs when the collision angle is 90. When the collision angle is 45°, the discrepancy is the least (1 μs). The tr increases in both groups of data with increased collision angle. The simulation results are basically consistent with the experimental data, as the accuracy of the finite element simulation was verified by the experiment.

3.3. Effect of Particle Size Ratio on Collision Mechanical Properties

Figure 8 shows the simulation curve of the rise time (tr) of the impact force obtained by the collision of rice grains with 304 stainless steel at different angles under different values of particle size ratio (R). Figure 8 shows that the rise time (tr) increases with increased particle size ratio (R). The minimum value of tr appears in the range of 0~30°, the rise time (tr) is generally distributed in the range of 24~70 µs, and the frequency of the collision signal is generally distributed in the range of 3.6~10 kHz.

3.4. Relationship between Working Parameters and Total Grain Sieve Loss

Grain loss ratio refers to the ratio of lost grains to the total number of original grains. The cleaning performance experiment results are shown in

Table 3. Surface response experimental results with respect to cleaning performance.

Test No.	Fan Speed /rpm	Sieve Opening /mm	Guide Plate II Angle/°	Grain Loss Ratio /%
1	1300	25	45	0.39
2	1300	20	29	0.15
3	1100	20	45	0.14
4	1500	20	45	1.02
5	1500	30	45	0.93
6	1300	25	13	0.62
7	1100	20	13	0.25
8	1500	20	13	2.01
9	1300	30	29	0.53
10	1100	30	45	0.24
11	1500	30	13	1.80
12	1500	25	29	1.28
13	1300	25	29	0.69
14	1100	25	29	0.45
15	1100	30	13	0.60
16	1300	25	29	0.56

. Results of data analysis performed with JMP 12.0 software((SAS, Cary, NC, USA)) are shown in

Table 4. Surface response experimental results for grain sieve loss.

. Table 4 shows that fan speed and guide plate II angle can accurately reflect grain sieve loss variations. Therefore, fan speed and guide plate II angle were selected as variables to establish a mathematical grain sieve loss monitoring model on the basis of analyzing grain distribution at the rear of the sieve. Effects of fan speed and guide plate II on sieve loss are shown in Figure 9.

Figure 9 shows that the fan speed has a considerable effect on grain sieve loss; the grain sieve loss ratio increases with a rate of 0.75 g/rpm as the fan speed increases, and the decrease rate of the grain sieve loss is about 2.2 g/° with increased guide plate II angle. The relationship between grain sieve loss and that between fan speed and guide plate II angle can be expressed as Equation (1):

y = 1322 + 11.85x − 2.653y + 0.001582x² − 0.01083xy + 0.001366y², R² = 0.9981

(1)

where x is the guide plate II angle, and y is the fan speed.

To verify the accuracy of the established monitoring model, a calibration test was carried out in the cleaning bench. The relative errors between the theoretical value calculated by Equation (1) and the actual measured value were obtained, as shown in

Table 5. Relative error between theoretical and practical values for Equation (1).

No.	Fan Speed /rpm	Guide Plate II Angle/°	Actual Value /g	Calculated Value/g	Relative Error /%
1	1300	29	244.6	236.7	3.25
2	1500	45	461.2	442.8	3.99
3	1500	13	738.3	718.3	2.71
4	1100	13	110.8	112.0	1.12

.

Table 5 shows that the relative error between the theoretical grain sieve loss value calculated by the fitted mathematical model (Equation (1)) and the actual measurement value fluctuates slightly, and the maximum relative error under different combinations of working parameters is generally ≤3.9%, which proves that the fitted mathematical model achieves high accuracy.

3.5. Grain Loss Distribution in the Monitoring Area

As the generated transient collision signal when grains collide with the sensitive plate is an energy signal that takes time to attenuate, the grain loss sensor always has a limited resolution. Therefore, it is necessary to analyze the grain loss distribution along the sieve width direction.

The proportion of grain loss in each box under different working parameters along the sieve width direction shown in Figure 10. There are more grains in receiver boxes 3, 4, and 5 in the transverse direction of the sieve, but the grain mass ratio differences in the remaining boxes is not significant, which provides a favorable working environment for grain loss monitoring sensors. Data analysis results show that the sensor has to detect more than 70 grains/s to guarantee monitoring accuracy. Figure 10 shows that the total grain sieve loss within the monitoring area is not stable and fluctuates according to changes in working parameters. To quantify the variation trend of grain sieve loss according to working parameters in the monitoring area, the grain sieve loss was fitted to different fan speeds and guide plate II angles, as shown in Figure 11. Fan speed has a significant impact on the grain sieve loss in the monitoring area, and with an increase in the fan speed, the corresponding grain sieve loss increases significantly.

The relationship between grain sieve loss and working parameters in the monitoring area was fitted as follows:

f(x,y) = 153.8 + 2.101x − 0.3393y − 0.005208x² − 0.001645xy + 0.0001864y (R² = 0.9235)

(2)

where x is the guide plate II angle, and y is the fan speed.

The relative errors between the theoretical value calculated by Equation (2) and the actual measured value were obtained, as shown in

Table 6. Relative error between theoretical and practical values in the sensor monitoring area.

No.	Fan Speed /rpm	Guide Plate II Angle/°	Measurement Value/g	Calculated Value/g	Relative Error /%
1	1300	29	46.98	44.6	5.07
2	1500	45	78.21	74.4	4.87
3	1500	13	121.76	117.2	3.75
4	1100	13	17.28	18.0	4.00

. The relative error between the theoretical grain sieve loss value calculated by the fitted mathematical model (Equation (2)) and the actual measurement value fluctuates slightly, and the maximum relative error under different combinations of working parameters is generally ≤5.07%.

3.6. Grain Sieve Loss Monitoring Mathematical Model

The above analysis shows that the total grain sieve loss and grain sieve loss within the monitoring area are not constant values. The variation of the coefficient between the grain sieve loss in the monitoring area and the total grain loss under different working parameters is shown in Figure 12.

Figure 12 shows that when the fan speed is constant, with an increase in the guide plate II angle, the ratio first increases and then decreases because the guide plate II angle has a greater impact on the airflow direction in the cleaning shoe. The grain sieve loss monitoring mathematical model can be expressed as follows:

$$R(x,y)=\frac{153.8+2.101x-0.3393y-0.005208x^2-0.001645xy+0.0001864y^2}{1322+11.85x-2.653y+0.001582x^2-0.01083xy+0.001366y^2}$$

(3)

where x is the guide plate II angle, and y is the fan speed.

The relative errors between the theoretical value calculated by Equation (3) and the actual measured value were obtained, as shown in

Table 7. Relative error between theoretical and practical values for Equation (3).

No.	Fan Speed /rpm	Guide Plate II Angle/°	Measurement Value/g	Calculated Value/g	Relative Error /%
1	1300	29	0.192	0.188	2.00
2	1500	45	0.170	0.168	1.20
3	1500	13	0.165	0.163	1.00
4	1100	13	0.156	0.160	2.56

.

Table 7 shows that the maximum relative error under different combinations of working parameters is generally ≤2.56%. Figure 13 shows that the ratio between sieve loss in the monitoring area and total grain loss is generally distributed in the range of 14–18%. As long as the proportion is known, the grain loss can be calculated by converting the monitored grain loss to grain mass according the one thousand grain mass.

3.7. Grain Loss Sensor Monitoring Accuracy

Table 8. Grain loss monitoring accuracy under different working parameters.

Test No.	Fan Speed /rpm	Sieve Opening/mm	Guide Plate II Angel/°	Manually Measured Loss /g	Monitored Loss /g	Averaged Relative Error /%
1	1300	25	45	164.0	22.1	3.68
2	1300	20	29	41.0	5.6	2.32
3	1100	20	45	64.5	8.8	2.58
4	1500	20	45	593.4	78.8	5.16
5	1500	30	45	363.6	48.3	5.09
6	1300	25	13	314.6	42.3	4.03
7	1100	20	13	46.4	6.3	2.54
8	1500	20	13	936.0	122.6	6.41
9	1300	30	29	183.9	24.8	3.72
10	1100	30	45	134.0	18.2	3.05
11	1500	30	13	846.0	112.3	5.22
12	1500	25	29	529.4	71.3	3.77
13	1300	25	29	321.5	43.1	4.3
14	1100	25	29	139.0	18.8	3.25
15	1100	30	13	198.5	26.7	3.84
16	1300	25	29	321.5	43.0	4.57

shows that the relative monitoring error of the sensor under different working conditions is ≤6.41%. The monitored grain loss ratio is proportional to total grain loss, as with an increase in the total grain loss, the monitored error also increases because the sensor has a limited resolution. On the other hand, the lost grains would contact the sensor surface twice, and a measurement error will also occur when straw internodes collide with the sensor. In addition, when the rice density experiences a dramatic shift during harvesting, the number of discharged grains from the cleaning shoe exceeds the capacity of the sensor. The above test results show that the proposed grain loss monitoring system can monitor sieve loss in real time. The monitoring error of the optimized grain loss system declines significantly compared with the monitored results reported by Wang et al. [22], in which the averaged monitoring relative error was 12.98% and the maximum relative error was 17.64%.

4. Conclusions

To fulfill the task of monitoring rice grain sieve loss in real time, a mathematical monitoring model and a high-accuracy sensor were designed. The frequency of the collision signal is generally distributed in the range of 3.6~10 kHz, and the grain distribution in the transverse direction of the sieve is more uniform, which provides a favorable working environment for grain loss monitoring sensors. The maximum relative errors between the theoretical value calculated by the developed grain loss monitoring mathematical model and the actual measured value under different combinations of working parameters is generally ≤2.56%, which proves that the fitted mathematical model achieves high accuracy. The relative monitoring error of the sensor under different working conditions is ≤6.41%. In the future, the proposed grain loss sensor should be installed in combine harvesters and used to establish a mathematical grain loss monitoring model to monitor grain loss in real time, providing a grain loss level signal to the control system to adjust the relevant working parameters in order to decrease grain loss.