A modeling method for flexible wheat ears at maturity based on discrete element method

Abstract

The present invention is applicable to the field of plant modeling and analysis technology and provides a method for modeling flexible wheat ears at maturity based on the discrete element method. The method comprises the following steps: analyzing the geometric morphology and characteristic dimensional parameters of several wheat ears at maturity of the variety to be modeled; determining the geometric parameters of the wheat ear model and the arrangement of the filling balls; calculating the coordinates of the filling balls; filling the filling balls to establish a geometric model of the wheat ear; measuring and calibrating the wheat ear contact mechanical parameters and wheat ear adhesion mechanical parameters; adding the mechanical parameters to the mechanical model; and inputting the geometric and mechanical models into discrete element software to obtain a flexible wheat ear model based on the discrete element method. This method proposes an efficient and accurate wheat ear modeling method, which reduces computational complexity and improves simulation efficiency while ensuring model accuracy, providing a more efficient simulation method for the development and optimization of wheat harvesting machinery.

Description

Technical Field

[0001] The present invention belongs to the technical field of plant modeling and analysis, and in particular relates to a modeling method of flexible wheat ears in the mature stage based on a discrete element method. Background Art

[0002] Wheat is one of the world's major grain crops, and mechanized planting and harvesting have been achieved in most parts of my country. During the wheat harvesting process, which includes harvesting, transporting, threshing, and cleaning, various plant organs, especially the wheat ears, are in a complex interaction with agricultural machinery components. Existing agricultural machinery component design methods primarily rely on physical testing, which often requires repeated trial production, testing, and optimization. This not only results in long R&D cycles and high costs, but is also subject to seasonal restrictions, making it difficult to meet the demand for efficient, precise, and intelligent wheat harvesting machinery.

[0003] The Discrete Element Method (DEM) provides an effective numerical simulation tool for studying the operating mechanisms of wheat harvesting machinery. DEM simulation allows for intuitive simulation of the crop's motion and force distribution within the mechanical system in a virtual environment. This allows for in-depth analysis of the interaction between wheat ears and mechanical components at a microscopic level, providing theoretical support for structural optimization and parameter adjustment of agricultural machinery components. However, the accuracy and computational efficiency of DEM simulations depend significantly on the rationality and simplification of the wheat ear model.

[0004] At present, the discrete element modeling of wheat ears mainly adopts the particle aggregation method, that is, multiple discrete particles are aggregated to form grain and ear structures to simulate their geometric characteristics and mechanical behavior. However, this method has problems such as large computational load, low simulation efficiency, high modeling complexity, and difficulty in balancing accuracy and computational efficiency. Due to the large number of particles, computing resources are consumed significantly, resulting in a long simulation time, which is difficult to meet the needs of large-scale engineering applications. Therefore, how to reduce computational complexity and improve simulation efficiency while ensuring model accuracy has become a key technical problem that needs to be solved in the field of wheat modeling. At the same time, the existing methods are more complicated in setting particle parameters, such as contact parameters and bonding parameters, which increases the difficulty of model construction and adjustment. In addition, when the number of particles is reduced to improve computational efficiency, the geometric accuracy and mechanical properties of the model are often difficult to maintain accurately, affecting the reliability of the simulation results, thereby limiting the application of this method in the optimization design of wheat harvesting machinery. Summary of the Invention

[0005] The purpose of the embodiment of the present invention is to provide a modeling method for flexible wheat ears in the mature stage based on the discrete element method, aiming to solve the problems raised in the above background technology.

[0006] The embodiment of the present invention is implemented as follows: a method for modeling flexible wheat ears at maturity based on discrete element method, comprising the following steps:

[0007] Step 1: Analyze the geometric morphology and characteristic size parameters of wheat ears at several maturity stages of the variety to be modeled;

[0008] Step 2: Based on the analysis results of the geometric shape and characteristic size parameters, determine the geometric parameters of the wheat ear model and the arrangement of the filling balls;

[0009] Step 3: Calculate the coordinates of the filling balls based on the geometric parameters of the wheat ear model and the arrangement of the filling balls;

[0010] Step 4: Fill the filling balls according to their coordinates to establish a geometric model of the wheat ears;

[0011] Step 5: Measure and calibrate the wheat ear contact mechanical parameters and wheat ear bonding mechanical parameters;

[0012] Step 6: Add mechanical parameters to the mechanical model. The mechanical model includes a contact model and a bonding model. The contact model is the Hertz-Mindlin contact model, and the bonding model is the parallel bonding model.

[0013] Step 7: Input the geometric model obtained in step 4 and the mechanical model obtained in step 6 into the discrete element software to obtain a flexible wheat ear model based on the discrete element method.

[0014] The embodiment of the present invention provides a method for modeling flexible wheat ears at maturity based on the discrete element method, which has the following beneficial effects:

[0015] (1) Reduce the amount of calculation and improve the simulation efficiency: This method optimizes the geometric modeling structure of the wheat ear, while reducing the number of particles while maintaining the geometric accuracy and mechanical properties of the model, effectively reducing the amount of simulation calculation and improving the calculation efficiency, making large-scale wheat harvesting machinery simulation analysis more feasible;

[0016] (2) Enhance the accuracy of the wheat ear model and improve the reliability of simulation: By optimizing the arrangement of discrete element particles, the simulation results are made more stable and reliable, and the mechanical properties of wheat ears during mechanical operation can be accurately reproduced, providing more accurate data support for studying the interaction between wheat and mechanical components. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of the characteristic dimensions of wheat grains;

[0018] Figure 2 Correlation analysis of characteristic dimensions of LC2 wheat grains, where a is the correlation between thickness and length, and b is the correlation between thickness and width;

[0019] Figure 3 This is a schematic diagram of the wheat ear structure;

[0020] Figure 4 is the geometric model of wheat grain;

[0021] Figure 5 Geometric modeling of wheat ears, where a is the wheat ear modeling process and b is the wheat ear geometric model;

[0022] Figure 6 is the wheat grain compression test, where a is the grain compression test and b is the Young's modulus of the grain;

[0023] Figure 7 Cob tensile and shear tests, where a is the cob tensile test and b is the cob shear test;

[0024] Figure 8 The tensile test and shear test of the cob-kernel connection are shown in Figure 1, where a is the tensile test of the cob-kernel connection and b is the shear test of the cob-kernel connection.

[0025] Figure 9 It is the wheat ear stretching and shearing simulation, where a is the wheat ear stretching simulation and b is the wheat ear shearing simulation;

[0026] Figure 10 The simulation and experimental comparison of the maximum tensile force and shear force of wheat ears, where a is the maximum tensile force and b is the maximum shear force. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0028] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0029] like Figure 1-Figure 5 As shown, a method for modeling flexible wheat ears at maturity based on discrete element method is provided in one embodiment of the present invention, comprising the following steps:

[0030] Step 1: Analyze the geometric morphology and characteristic size parameters of wheat ears at several maturity stages of the variety to be modeled;

[0031] Step 2: Based on the analysis results of the geometric shape and characteristic size parameters, determine the geometric parameters of the wheat ear model and the arrangement of the filling balls;

[0032] Step 3: Calculate the coordinates of the filling balls based on the geometric parameters of the wheat ear model and the arrangement of the filling balls;

[0033] Step 4: Fill the filling balls according to their coordinates to establish a geometric model of the wheat ears;

[0034] Step 5: Measure and calibrate the wheat ear contact mechanical parameters and wheat ear bonding mechanical parameters;

[0035] Step 6: Add mechanical parameters to the mechanical model. The mechanical model includes a contact model and a bonding model. The contact model is the Hertz-Mindlin contact model, and the bonding model is the parallel bonding model.

[0036] Step 7: Input the geometric model obtained in step 4 and the mechanical model obtained in step 6 into the discrete element software to obtain a flexible wheat ear model based on the discrete element method.

[0037] like Figure 1 As shown in a preferred embodiment of the present invention, in steps 1 and 2, three representative wheat varieties in Northeast China (Longchun No. 2, i.e. LC2; Longmai No. 35, i.e. LM35; Xinkehan No. 9, i.e. XKH9) were selected as research objects to model the wheat ears.

[0038] The shape of wheat grains is close to ellipsoidal, and their characteristic dimension can be defined as length ,width and thickness .

[0039] For the experiment, 100 wheat grains from three varieties (LC2, LM35, and XKH9) were randomly selected as samples. The characteristic dimensions of the wheat grain samples were measured using a digital vernier caliper with an accuracy of 0.01 mm. The measurement results are shown in Table 1.

[0040] Table 1 Average values ​​of characteristic dimensions of wheat grains

[0041]

[0042] Correlation analysis between the three characteristic dimensions of LC2 wheat grains revealed a significant correlation between grain thickness, length, and width (e.g. Figure 2 Therefore, when constructing the wheat grain model, in order to achieve the accuracy of wheat modeling, the thickness of the grain is selected. As the main parameter variable of the grain, the length of the grain and thickness It is calculated based on the functional relationship between the fitted characteristic dimensions of the grains.

[0043] The three characteristic dimensions of wheat grains of LM35 and XKH9 also had the same significant correlation. The functional relationships between the characteristic parameters of the grains of the three varieties are summarized in Table 2.

[0044] Table 2 Correlation function of wheat grain characteristic parameters

[0045]

[0046] The spikelets are composed of segments connected by nodes. Each node grows a spikelet, which is staggered on both sides of the spikelet. After counting 50 wheat samples, most spikelets have 2 or 3 grains, with an average of 2.82. The grains in the spikelet grow at a certain angle to the spikelet, which is defined as the angle between the spikelet and the axis. , the angle between each side grain and the middle grain, that is, the outer offset angle is The measured geometric parameters of wheat ears are shown in Table 3.

[0047] Table 3 Average values ​​of wheat ear geometric parameters

[0048]

[0049] In order to make the wheat ear model proposed in this study universal, the correlation between the shapes and sizes of wheat ears was analyzed, including the length and width of wheat ears. Cob diameter 、Wheat ear length Number of spikelets The results of polynomial fitting are shown in Table 4. The results show that and 、 and There is a significant correlation between the spike diameter and the number of spikelets. Therefore, the spike length can be used to calculate the rachis diameter and the number of spikelets, which provides support for the generalization of the wheat plant model.

[0050] Table 4 Correlation analysis between wheat cob and wheat ear parameters

[0051]

[0052] As a preferred embodiment of the present invention, in steps 3 and 4, the wheat grains can be approximated by a double ellipsoid or a single ellipsoid model. The more sub-spheres that fill the grains, the closer the model shape is to the real grains and the higher the simulation accuracy, but it also increases the computational cost. Although the double ellipsoid model has higher simulation accuracy, its computational cost and simulation time are higher. Therefore, in order to balance simulation accuracy and computational efficiency, this method uses a single ellipsoid model based on 9 spheres as the discrete element model of the wheat grains, and its characteristic dimensions (length ,width and thickness ) has been measured. In this model, the major axis of the ellipsoid is the length of the wheat kernel , the minor axis is the equivalent width of the wheat grain (like Figure 4 shown).

[0053] The calculation process of the filling sphere particle position of the discrete element ellipsoid 9-sphere model can be divided into the following steps:

[0054] First, we need to determine the basic parameters of the ellipsoid, which are expressed mathematically as follows:

[0055] ;

[0056] ;

[0057] ;

[0058] in , is the radius of the ellipsoid along the x-axis (major axis), , are the radii of the ellipsoid along the y-axis and z-axis (minor axis). These parameters can accurately describe the geometric shape and size of the ellipsoid.

[0059] The ellipsoid is decomposed into nine discrete unit spheres. These nine discrete unit spheres consist of one central sphere and eight peripheral sub-spheres. The central sphere is located at the geometric center of the ellipsoid, and the peripheral sub-spheres are evenly distributed along the ellipsoid's major axis. The positions and sizes of the peripheral sub-spheres are determined by the lengths of the major and minor axes of the ellipsoid, so that the combination of discrete unit spheres closely approximates the geometric shape of the ellipsoid.

[0060] Then, the position of each discrete unit filling sphere is calculated. The coordinates of the center sphere are set to the geometric center of the ellipsoid, that is, ( ). The coordinates of the peripheral sub-spheres are offset equidistantly in the long axis direction relative to the central sphere, which can be expressed as:

[0061] ;

[0062] in, , is the degree of offset, the positive and negative signs indicate the offset on both sides of the major axis, the offset Divide the long axis into 10 equal parts, and distribute the outer sub-balls at the 1st to 4th dividing points.

[0063] The radii of each discrete filling sphere are then determined. First, the radius of the central sphere is determined based on the geometric characteristics of the ellipsoid. The radii of the outer sub-spheres are then adjusted to make them tangential to the standard ellipsoid. Finally, the central sphere and outer sub-spheres are combined to form an ellipsoidal approximation. This method efficiently simulates the mechanical behavior of wheat kernels while preserving their geometric characteristics, reducing contact detection and computational complexity.

[0064] According to the actual shape of the cob (such as Figure 3 (as shown), using the "S"-shaped cob discrete element modeling method. The cob diameter measured in the experiment is the diameter of the middle part of the cob segment. The diameter of the particles in each cob segment increases linearly from bottom to top, so that the particle diameter in the middle part is equal to the cob diameter measured in the middle part of the small cob segment. , the number of particles per axis segment The spike and the wheat grain are indirectly connected by a small connecting ball, the radius of which is Since the structure of the husk in the wheat ear is relatively weak and has little effect on the mechanical properties and behavior of the plant as a whole, and the computational cost of modeling the thin husk structure in the discrete element method (DEM) is high, the physical structure of the husk is omitted in the wheat ear model to simplify the model and improve computational efficiency.

[0065] The modeling process of wheat ears is as follows Figure 5 As shown in a. Each cob segment consists of 5 particles. The first particle at the bottom of the segment is the local coordinate origin. The particle radius in the segment increases linearly. The particle radius is:

[0066] ;

[0067] in, For the The radius of the particle in the axis segment, is the axis segment particle radius coefficient, The diameter of the cob is then rotated along the X axis with the bottom of the cob as the rotation center. The cob segments and spikelets are rotated and arranged on the same side.

[0068] Solving the coordinates of the spikelet particles is more complicated. First, the local coordinate system is established with the center of the particle at the top of the corresponding spikelet segment as the coordinate origin. Then, the coordinates of the grain particles on each spikelet are determined by coordinate translation and rotation transformation. Before the transformation, the initial local coordinates of the spikelet particles are The growth angle of the spikelet is , the spikelets are staggered on both sides of the spikelet axis, that is, the angle between the spikelet and the Z axis is The outer deviation angle of the kernel in the spikelet is , that is, the angle between the grains on both sides of the spikelet and the middle grain is .

[0069] First, coordinate rotation transformation is performed on the connecting particles and the grain particles around the Y axis in the positive and negative directions to obtain the relative coordinate positions of the three grains in the spikelet. The transformation matrix of the coordinates of the grains on both sides of a spikelet can be expressed as:

[0070] ;

[0071] in and It is The initial three-dimensional coordinates of the spikelet particles, , is the rotation transformation matrix around the Y axis, which can be expressed as:

[0072] ;

[0073] Then, the Z-axis coordinates of the kernels are adjusted so that the spikelets are connected to the cob segments. Then, the kernels in the spikelets are rotated in the positive and negative directions around the X-axis to obtain the relative coordinate positions of the spikelets and the cob segments. The coordinate rotation transformation matrix of a spikelet can be expressed as:

[0074] ;

[0075] in, is the coordinate rotation transformation matrix around the X axis, which can be expressed as:

[0076] ;

[0077] Finally, the local coordinates of the spikelet particles, including the grain particles and the connecting ball particles, are converted into global coordinates through translation transformation. The conversion process is:

[0078] ;

[0079] in, It is The global coordinate transformation matrix of each spikelet.

[0080] Finally, the geometric model of wheat ears is assembled as follows Figure 5 As shown in Figure b, the grains and the small connecting balls, as well as the small connecting balls and the ear axis, are connected by bonding bonds of the bonding model, allowing the wheat ears to have flexible deformation and fracture conditions.

[0081] As a preferred embodiment of the present invention, in step 5, for the measurement of contact mechanics parameters:

[0082] The static friction coefficient between grains, cobs, and walls was measured using an incline test and a high-speed camera. Wheat grains and cobs were attached to a flat plate. The plate and the material to be tested were placed on the incline tester, allowing the grains or cobs to contact the material to be tested. The angle of the incline was controlled to change from small to large, and the change in angle was tracked using a high-speed camera. When the plate with the grains or cobs attached just slid, the value of the incline angle at that time was read out by the high-speed camera. The static friction coefficient between the two materials was calculated based on the angle value of the incline. The test was repeated five times between each two materials, and the static friction coefficients between the wheat grains, cobs, and acrylic plates, as well as between the grains and cobs, were finally obtained. The static friction coefficient measurement results are shown in Table 5.

[0083] Table 5 Static friction coefficient

[0084]

[0085] The coefficient of restitution (COR) represents a material's ability to recover after a collision and is typically expressed as the ratio of the velocities before and after the collision. The CORs of restitution between kernels, cobs, and walls were measured using an inclined drop test method and a high-speed camera. The results are shown in Table 6.

[0086] Table 6 Collision recovery coefficient

[0087]

[0088] The rolling friction coefficient between grains, cobs, and walls was calibrated using simulations and experimental comparisons of the stacking angle. First, the range of the inter-grain rolling friction coefficient was determined based on preliminary tests. A grain stacking simulation test was conducted using the inter-grain rolling friction coefficient as the experimental factor to obtain the corresponding simulated stacking angle values. These simulated values ​​were then fitted to obtain a linear relationship between the inter-grain rolling friction coefficient and the stacking angle. The actual experimental values ​​of the grain stacking angle were substituted into the relationship to obtain the calibrated value of the inter-grain rolling friction coefficient. The same method was used to conduct a cob stacking simulation test to obtain the calibrated value of the inter-cob rolling friction coefficient. The calculated rolling friction coefficient results are shown in Table 7.

[0089] Table 7 Rolling friction coefficient

[0090]

[0091] For the measurement of bonding mechanical parameters:

[0092] like Figure 6As shown in a, the mechanical parameters of wheat grains were measured using a texture analyzer. The wheat grains were compressed with the side with the ventral groove facing down. The pressing speed of the indenter was 10 mm / min. The texture analyzer output the force and displacement data during compression. The Young's modulus of the grains was calculated based on the parallel plate compression mode in the ASAE S368.4 DEC2000 (R2017) standard. Five repeated tests were performed for each variety. Young's modulus of the grains Obtained by the following formula:

[0093] ;

[0094] in, is the compression force, is the deformation during compression, is Poisson's ratio, and is the principal curvature radius of the grain compression contact point, is the curvature radius coefficient.

[0095] The Young's modulus of the grains was calculated based on the ASABE standard. Average value Figure 6 As shown in b, the Young's modulus of the grains of each variety ranges from 160 MPa to 189 MPa.

[0096] The mechanical parameters of wheat cobs were measured using a texture analyzer, such as Figure 7 As shown in a, the cob sample was clamped in the fixture of the texture analyzer and subjected to a tensile test at a stretching speed of 10 mm / min. The force and deformation curve of the cob during stretching was measured using the texture analyzer, and the effective length and diameter of the stretched cob were recorded. The experiment was repeated five times for each internode of each variety. The relationship between the force and displacement of the cob stretch was recorded using the texture analyzer. The linear elastic phase of the curve was linearly fitted, and the slope of the linear fitting equation was obtained as the actual stiffness of the cob, i.e., the tensile stiffness of the cob. Substituting this into the cross-sectional area of ​​the cob , through the formula The tensile stiffness per unit area of ​​the cob is calculated. By formula Calculated, where In the tensile test, when the tensile force is greater than the maximum tensile force, The cob will break when . Then, the normal ultimate stress can be calculated:

[0097] ;

[0098] like Figure 7As shown in b, the cob sample was fixed on the shear fixture of the texture analyzer for shear test. The cutting head of the texture analyzer cut the cob vertically at a speed of 10 mm / min, and the shear force and displacement curve was monitored in real time, and the maximum shear force was recorded. , the experiment was repeated 5 times for each cob internode of each variety. The critical shear stress of the cob can be calculated as:

[0099] ;

[0100] In addition, the shear modulus of the cob Young's modulus of the cob and Poisson's ratio Calculated, that is:

[0101] ;

[0102] Shear stiffness per unit area of ​​the cob Tensile stiffness per unit area and Poisson's ratio Calculated, that is:

[0103] ;

[0104] Finally, the measurement results of the mechanical parameters of wheat cobs are summarized in Table 8 below.

[0105] Table 8 Measurement results of cob mechanical parameters

[0106]

[0107] Figure 8 For the tensile test and shear test of the connection between the cob and the kernel (where Figure 8 a is the tensile test of the cob-kernel connection, Figure 8 (b) Shear test at the cob-kernel junction. The mechanical parameter measurements at the cob-kernel junction are similar to those for the cob itself. The cob sample with the kernel attached was clamped in the fixture of a texture analyzer for tensile and shear tests. The tensile and shear speeds were set to 10 mm / min, and the force-deformation curves during tensile and shearing were recorded using a texture analyzer. Five replicates were performed for each variety. Young's modulus at the cob-kernel junction. , tensile stiffness per unit area , normal limit stress , shear limit stress The calculation method is the same as that of the cob.

[0108] Shear modulus at the junction of the cob and kernel and shear stiffness per unit area The calculation method is similar to that of the cob. Finally, the measurement results of the mechanical parameters of the connection between the wheat cob and the grain are summarized in Table 9.

[0109] Table 9 Mechanical parameters of the connection between the cob and the kernel

[0110]

[0111] As a preferred embodiment of the present invention, the mechanical parameters of wheat ears are verified by comparing the maximum tensile force and the maximum shear force of wheat ears through tensile shear tests and simulations. Figure 9 As shown, the maximum tensile force and maximum shear force at the connection between the simulated kernel and the cob. Figure 9 Figure a shows a wheat ear stretching simulation. Using calculated contact and bonding parameters, a wheat ear with a single kernel and four rachis segments was placed in the center of a simulation fixture. The fixture was then moved horizontally toward the ear to clamp it. The upper fixture was then moved vertically upward at a speed of 1 mm / s until the ear was broken. The maximum tensile force was then read in the software post-processing. Figure 9 Figure b shows a wheat ear shearing simulation. The wheat ear model used in the tensile simulation is also used. The wheat ear is generated in the center of a simulation fixture, which is then moved horizontally toward the ear to clamp it. The tool is sheared vertically downward at a speed of 1 mm / s until the ear is severed. The maximum shear force is read in the software post-processing.

[0112] Comparison of the maximum tensile forces calculated from tensile and shear simulations and maximum shear force The maximum tensile force calculated from the experiment and maximum shear force ,like Figure 10 As shown (where Figure 10 a is the maximum tensile force, Figure 10 b is the maximum shear force). The maximum tensile force and maximum shear force values ​​obtained from the wheat ear tensile and shear simulation are both within the 5% error band of the maximum tensile force and maximum shear force values ​​obtained from the experiment. The relative error between the simulation results and the experimental results is small, which proves that the parameters of the established wheat ear model are accurate.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A modeling method for flexible wheat ears at maturity based on discrete element method, characterized in that: The following steps are involved: Step 1: Analyze the geometric morphology and characteristic size parameters of wheat ears at several maturity stages of the variety to be modeled; Step 2: Based on the analysis results of the geometric shape and characteristic size parameters, determine the geometric parameters of the wheat ear model and the arrangement of the filling balls; Step 3: Calculate the coordinates of the filling balls based on the geometric parameters of the wheat ear model and the arrangement of the filling balls; Step 4: Fill the filling balls according to their coordinates to establish a geometric model of the wheat ears; Step 5: Measure and calibrate the wheat ear contact mechanical parameters and wheat ear bonding mechanical parameters; Step 6: Add mechanical parameters to the mechanical model. The mechanical model includes a contact model and a bonding model. The contact model is the Hertz-Mindlin contact model, and the bonding model is the parallel bonding model. Step 7: Input the geometric model obtained in step 4 and the mechanical model obtained in step 6 into the discrete element software to obtain a flexible wheat ear model based on the discrete element method; In steps 3 and 4, a single ellipsoid model based on nine spheres is used as a discrete element model of wheat grains; The ellipsoid is decomposed into 9 discrete unit spheres, which include 1 central sphere and 8 peripheral sub-spheres. The central sphere is located at the geometric center of the ellipsoid, and the peripheral sub-spheres are evenly distributed along the long axis of the ellipsoid. The positions and sizes of the peripheral sub-spheres are determined according to the lengths of the long and short axes of the ellipsoid, so that the discrete unit spheres are combined to approximate the geometric shape of the ellipsoid. Then, the position of the filling sphere of each discrete unit is calculated; the coordinates of the central sphere are set to the geometric center of the ellipsoid, that is, , the coordinates of the peripheral sub-spheres are offset equidistantly in the long axis direction relative to the central sphere, expressed as: ； in, , is the degree of offset, the positive and negative signs indicate the offset on both sides of the major axis, the offset Divide the long axis into 10 equal parts, and distribute the outer balls at the 1st to 4th equal points; Then, the radius of each discrete filling sphere particle is determined. First, the radius of the central sphere is determined based on the geometric characteristics of the ellipsoid. Then, the radius of the peripheral sub-spheres is adjusted to make them tangent to the standard ellipsoid. Finally, the central sphere and the peripheral sub-spheres are combined to form an ellipsoidal approximation model. According to the actual shape of the cob, the "S"-shaped cob discrete element modeling method was used; the cob diameter measured in the experiment was the diameter of the middle part of the cob segment. The diameter of the particles in each cob segment increased linearly from bottom to top, so that the particle diameter in the middle part was equal to the cob diameter measured in the middle part of the small cob segment. ; At the same time, the physical structure of the husk is omitted in the wheat ear model to simplify the model and improve the calculation efficiency.

2. The method for modeling flexible wheat ears at maturity based on discrete element method according to claim 1, characterized in that In steps 1 and 2, the characteristic size of the wheat grain is defined as the length ,width and thickness ; Wheat grains to be modeled were randomly selected as samples, and the characteristic dimensions of the wheat grain samples were measured using a digital vernier caliper with an accuracy of 0.01 mm. Therefore, when constructing the wheat grain model, in order to achieve the accuracy of wheat modeling, the thickness of the grain was selected. As a parameter variable of the grain, the length of the grain and width It is calculated based on the functional relationship between the fitted characteristic dimensions of the grains; The geometric parameters of wheat ears include length , number of spikelets , spikelet spacing , wheat ear quality , cob diameter , growth angle and outer offset angle ; Through the wheat ears Calculate cob diameter and spikelet number , thus providing support for the generalization of wheat plant models.

3. The method for modeling flexible wheat ears at maturity based on discrete element method according to claim 2, characterized in that: In the single ellipsoid model based on the nine spheres, the major axis of the ellipsoid is the length of the wheat grain. , the minor axis is the equivalent width of the wheat grain ; The calculation process of the filling sphere particle position of the discrete element ellipsoid 9-sphere model is divided into the following steps: First, we need to determine the basic parameters of the ellipsoid, which are expressed mathematically as follows: ； ； ； in , is the radius of the ellipsoid along the x-axis, , and are the radii of the ellipsoid along the y-axis and z-axis respectively. These parameters describe the geometric shape and size of the ellipsoid; Number of particles per axis segment The cob is indirectly connected to the wheat grain through a small connecting ball. The radius of the small connecting ball is ; When modeling wheat ears, each ear segment consists of 5 particles. The first particle at the bottom of the segment is taken as the local coordinate origin. The particle radius in the segment increases linearly. The particle radius is: ； in, For the The radius of the particle in the axis segment, is the radius coefficient of the particle in the cob segment; then the four particles on the upper part of each cob segment rotate along the X axis with the bottom end of the cob segment as the rotation center The cob segments and spikelets are rotated and arranged on the same side; When solving the coordinates of the spikelet particles, first, the local coordinate system is established with the center of the particle at the top of the corresponding spikelet segment as the coordinate origin; then, the coordinates of the grain particles on each spikelet are determined by coordinate translation and rotation transformation; before the transformation, the initial local coordinates of the spikelet particles are , the growth angle of the spikelet is , the spikelets are staggered on both sides of the spikelet axis, that is, the angle between the spikelet and the Z axis is , the outer deviation angle of the kernel in the spikelet is , that is, the angle between the grains on both sides of the spikelet and the middle grain is ; First, the connection particles and the grain particles are rotated in the positive and negative directions around the Y axis to obtain the relative coordinate positions of the three grains in the spikelet; The transformation matrix of the coordinates of the grains on both sides of a spikelet is expressed as: ； in and It is The initial three-dimensional coordinates of the spikelet particles, , is the rotation transformation matrix around the Y axis, expressed as: ； Then, the Z-axis coordinate of the grain is adjusted to connect the spikelet with the cob segment, and the grain in the spikelet is rotated in the positive and negative directions around the X-axis to obtain the relative coordinate position of the spikelet and the cob; The coordinate rotation transformation matrix of a spikelet is expressed as: ； in, is the coordinate rotation transformation matrix around the X axis, expressed as: ； Finally, the local coordinates of the spikelet particles, including the grain particles and the connecting ball particles, are converted into global coordinates through translation transformation. The conversion process is: ； in, It is The global coordinate transformation matrix of each spikelet; Finally, a geometric model of wheat ears was assembled, in which the grains and small connecting balls, and the small connecting balls and ear axes were connected by bonding bonds of the bonding model, respectively, so that the wheat ears have flexible deformation and fracture conditions.

4. The method for modeling flexible wheat ears at maturity based on discrete element method according to claim 2, characterized in that: In step 5, for the measurement of contact mechanics parameters: The static friction coefficient between the kernel, cob, and wall was measured using an inclined plane test and a high-speed camera. The impact restitution coefficient between the kernel, cob, and wall was measured using an inclined plane drop test and a high-speed camera. The rolling friction coefficient between the kernel, cob, and wall was calibrated by comparing the stacking angle simulation with the test. For the measurement of bonding mechanical parameters: The mechanical parameters of wheat grains were measured using a texture analyzer. The wheat grains were compressed with the side with the ventral groove facing down. The pressing speed of the indenter was 10 mm / min. The texture analyzer output the force and displacement data during compression. The Young's modulus of the grains was calculated according to the parallel plate compression mode in the ASAE S368.4DEC2000 (R2017) standard. Five repeated tests were performed for each variety. Obtained by the following formula: ； in, is the compression force, is the deformation during compression, is Poisson's ratio, and is the principal curvature radius of the grain compression contact point, is the curvature radius coefficient; The Young's modulus of the grains was calculated based on the ASABE standard. On average, the Young's modulus of the grains of each variety ranged from 160 MPa to 189 MPa; The mechanical parameters of wheat cobs were measured using a texture analyzer. The cob samples were clamped in the fixture of the texture analyzer and tensile tests were performed at a stretching speed of 10 mm / min. The force and deformation curve of the cob during stretching was measured using the texture analyzer, and the effective length and diameter of the stretched cob were recorded. The experiment was repeated five times for each internode of each variety. The relationship curve between the force and displacement of the cob stretch was recorded using the texture analyzer, and a linear fit was performed on the linear elastic stage of the curve. The slope of the linear fit equation was obtained as the actual stiffness of the cob, that is, the tensile stiffness of the cob. ; Substitute it into the cross-sectional area of ​​the cob , through the formula Calculate the tensile stiffness per unit area of ​​the cob; Young's modulus of the cob By formula Calculated, where is the effective length; in the tensile test, when the tensile force is greater than the maximum tensile force The cob breaks when ; then, the normal ultimate stress is calculated as: ； The cob sample was fixed on the shear fixture of the texture analyzer for shear test. The cutting head of the texture analyzer cut the cob vertically at a speed of 10 mm / min, and the shear force and displacement curve was monitored in real time, and the maximum shear force was recorded. , the experiment was repeated 5 times for each cob internode of each variety; the critical shear stress of the cob was calculated as: ； In addition, the shear modulus of the cob Young's modulus of the cob and Poisson's ratio Calculated, that is: ； Shear stiffness per unit area of ​​the cob Tensile stiffness per unit area and Poisson's ratio Calculated, that is: ； The mechanical parameters of the connection between the cob and the grain were measured using the same method as the mechanical parameters of the cob; the cob sample with the grain was clamped on the fixture of the texture analyzer, and tensile and shear tests were performed. The tensile and shear speeds were set to 10 mm / min, and the change curves of force and deformation during tensile and shearing were recorded using the texture analyzer. The test was repeated 5 times for different varieties; the Young's modulus of the connection between the cob and the grain was , tensile stiffness per unit area , normal limit stress , shear limit stress The calculation method is the same as that for cobs; Shear modulus at the junction of the cob and kernel and shear stiffness per unit area The calculation method is similar to that of the cob.

Images