CN113821926A - Discrete element numerical simulation method for nut shell crushing - Google Patents
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Abstract
The invention discloses a discrete element numerical simulation method for nut shell crushing, which comprises the following steps: firstly, measuring the characteristic size of nut particles, and determining the size of broken nuts according to mass conservation; secondly, carrying out single and repeated crushing tests on the nuts by means of a conventional physical mechanical testing machine to obtain the nut fracture energy distribution, and determining the total fracture energy, the crushing probability and the accumulated crushing distribution of the nuts; thirdly, constructing a nut crushing probability model and acquiring effective impact energy; then, constructing and iteratively solving a nut cumulative damage model to obtain a cumulative damage factor, and establishing an attenuation model; finally, establishing a numerical simulation method of discrete elements for nut shell crushing according to the steps 2, 3 and 4 by using a particle replacement method in the discrete elements for reference; in addition, the discrete element simulation method provided was verified using a nut shatter test. The invention can be used for numerically analyzing the shell crushing mechanism and optimizing and designing the structural parameters of the shell crushing device.
Description
Technical Field
The invention relates to the technical field of numerical simulation in a food processing process, in particular to a discrete element numerical simulation method for nut shell crushing.
Background
Nuts are seeds of woody plants, having hard or flexible hulls, and the more common nuts are walnuts, almonds, pistachios, pecans, and the like. Currently, nut kernels are popular health foods for consumers due to their abundant nutrients. In addition, nut shells contain abundant lignin, and can be used for producing chemical products such as adsorbents and the like and preparing various materials such as filter materials and the like. In order to maximize the economic benefit of nut fine and deep processing and reduce the processing cost of later processes such as shell and kernel separation, shell and kernel crushing and the like as much as possible, the key point is to realize shell and kernel breaking and finishing in the primary processing shell breaking and kernel taking link. At present, the initial processing of nuts in the industry is mainly carried out in a manual shell breaking mode, and although the method shows a good shell breaking effect, the method has the defects of high cost, low efficiency and the like, and potential health risks exist because the food sanitation cannot be guaranteed. Therefore, various mechanical nut shell breaking devices with single function or multiple functions are developed at home and abroad, such as patents with publication numbers of CN106858634A, CN107224227A, CN110495617A and CN105326064A and documents (Development and performance tests of a shelling cracker, Design and Development of a shelling cracker), but the shell breaking devices still have the prominent problems of kernel damage, incomplete shell breaking and the like generally, and the reason is that the shell breaking devices still depend on a Design method of a black box such as engineering experience, intuition of feeling and the like, and the Development law of cracks and the Development mechanism of the shells are not fully known.
In recent years, with the continuous development of computers and numerical simulation technologies, particle crushing simulation technology based on a discrete unit method is widely applied to the field of food processing. However, the conventional crushing simulation technology usually employs a particle adhesion model, such as patents and documents (discriber element method of impact breaking of ingredient of the invention) CN107657128A, CN104346498A and CN109740263A, but the method has limited application due to high simulation cost and low calculation efficiency, and the material strength is not gradually attenuated by the internal crack generated by the impact collision between the material and the processing equipment, which causes a certain deviation between the crushing simulation and the actual nut processing.
The invention provides a novel discrete element numerical simulation method for nut shell crushing, which can truly simulate the nut shell crushing process on the basis of remarkably reducing the test workload and the cost and greatly shortening the development period of a shell crushing device, is convenient to analyze the cracking mechanism of the nut shell crushing process, and provides an efficient way and method for the design and test of the nut shell crushing device. In view of the well-known literature and patent documents, no report has been made on a discrete element numerical simulation method for nut shell cracking in view of the reduction in shell strength.
Disclosure of Invention
The invention aims to provide a discrete element numerical simulation method for nut shell crushing, which breaks through the difficulty that the strength of nut shells cannot be attenuated in discrete element simulation in the nut processing process, and ensures that the crushing simulation is closer to the actual shell crushing.
The technical scheme adopted by the invention is as follows: a discrete element numerical simulation method for nut shell crushing is characterized by comprising the following steps: it comprises the following steps:
step 1, obtaining an initial size of a nut particle approximate to a geometric solid based on measurement of an actual nut particle characteristic size, constructing complete nut particles by adopting an overlapped ball method, and determining a broken shell size according to mass conservation;
step 2, carrying out a single crushing test on nuts by means of a conventional physical mechanical testing machine, obtaining the distribution of nut shell breaking energy, and determining the total breaking energy required by nut shell crushing;
3, carrying out a single crushing test on the nuts again by using the conventional physical mechanical testing machine in the step 2 to obtain the nut shell crushing probability under different impact energy;
step 4, constructing a nut shell breakage probability model according to the weakest link breakage theory and the similarity analysis method, and obtaining effective impact energy when the nut shells are broken;
step 5, utilizing the conventional physical mechanical testing machine in the step 2 to carry out a successive crushing test on nuts and obtain the accumulated crushing distribution of nut shells under different impact energies and different impact times;
step 6, constructing nut shell accumulation according to Hertz contact theory and damage fracture mechanics
A damage model;
step 7, solving the nut shell accumulated damage model by using an iterative algorithm based on the nut shell accumulated crushing distribution obtained in the step 5 and the nut shell accumulated damage model constructed in the step 6, obtaining nut shell accumulated damage factors, and establishing a nut shell fracture energy attenuation model;
step 8, establishing a discrete element numerical simulation method for nut shell crushing according to the step 2, the step 4 and the step 7 by using a particle replacement method in discrete elements;
and 9, verifying the proposed nut shell crushing discrete element simulation method by using a walnut vibration crushing test.
Preferably, in the step 4, according to the weakest chain breaking theory and the similarity analysis method, the nut shell breaking model is constructed as follows:
PB＝1-exp[-fNut·x·k·(Ecol-Ecol,min)]
in the formula, PBThe nut shell breakage probability; ecolThe impact energy to which the nut shells are subjected; x is the nut shell diameter; k is the impact frequency; f. ofNutIs a nut shell material constant, the magnitude of which is used to quantify the ability of the nut material to resist breakage due to external loads or stresses; ecol,minEffective impact energy of nut shell, and its value is used for judging nut shellIf the condition for determining whether the nut shell is broken effectively is greater than this value, the impact is considered to contribute to the nut shell breakage, and conversely, the impact is not effective for the nut shell breakage.
Preferably, in the step 6, according to hertzian contact theory and damage fracture mechanics, the model of accumulated damage of nut shells is constructed as follows:
En＝En-1(1-Dn)
in the formula, EnAnd En-1The fracture energy of the nuts after n and n-1 times of impact respectively; dnIs a nut shell strength damage variable; gamma is a nut shell damage accumulation factor; ekIs the impact energy that the nut shell is subjected to at the k-th impact.
Preferably, in the step 7, according to the intensity decay theory, the nut shell fracture energy decay model is established as follows:
in the formula, E and EnewThe initial fracture energy and the updated total fracture energy of the nut shell are respectively obtained; d is the damage variable after the impact on the nut.
Preferably, in the step 8, by using a particle replacement method in discrete elements, the simulation method of the nut shell breaking discrete elements is established as follows:
1) before simulation begins, presetting total fracture energy and effective impact energy required by nut shell crushing respectively;
2) after the simulation is started, monitoring the contact impact conditions of all nut particles in the shell breaking device, and counting the impact energy generated by each nut particle in each impact;
3) impact energy was compared to total fracture energy. Defining the nut particles to satisfy a brittle fracture condition if the impact energy is greater than the total fracture energy, thereby replacing intact nut particles with crushed shells;
4) the impact energy is compared to the effective impact energy. If the impact energy is greater than the effective impact energy and less than the total fracture energy, defining that the impact of the nut particles belongs to the effective impact, namely the impact contributes to nut shell fracture, and updating the total nut shell fracture energy by using the nut shell strength attenuation model established in the step 8; defining the impact of the nut particles as being an ineffective impact if the impact energy is less than the effective impact energy and disregarding;
5) and (5) repeating the steps 2) to 4) by adopting a loop iteration algorithm until the simulation of the crushing condition of the nut particles is completed.
Compared with the prior art, the invention has the beneficial effects that:
compared with the traditional nut shell crushing discrete element numerical simulation method, the method has the advantages that the strength of the nut shell is gradually attenuated due to interaction (namely effective collision or impact) between the nut shell and the crushing device in the crushing process, so that the provided crushing simulation method based on the discrete element method can meet the requirements of the research on the crushing mechanism of the nut shell in the food processing process and the structure optimization design of the crushing device.
Drawings
FIG. 1 is a flow diagram of a method according to an embodiment of the invention;
FIG. 2 is a schematic view of spherical particles (broken shells) replacing whole walnut particles;
FIG. 3 is a schematic view of a 60s virtual crushing test of walnut shells in the EDEM of the present invention;
FIG. 4 is a graph comparing the breaking rate and time curve of walnut shells with the breaking rate and time curve under a simulation numerical test.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following detailed description of the present invention is provided with reference to the accompanying drawings in combination with a specific example of the discrete element numerical simulation of walnut shell cracking.
FIG. 1 is a flow chart of a discrete element numerical simulation method for walnut shell crushing according to the invention. An exemplary walnut variety is selected from a walnut sample with an initial moisture content of 6.67% at a temperature of 185', and exemplary discrete element simulation software is selected from commercial EDEM. According to the flow chart shown in fig. 1, the establishment of the discrete element simulation method for walnut shell cracking as an example comprises the following steps:
(1) the method comprises the steps of respectively measuring the characteristic sizes of 200 walnuts in the length direction, the width direction and the thickness direction of the walnuts in a sample, and establishing a complete walnut shell discrete element simulation model by using an overlapped ball method. As the walnuts are made of anisotropic materials, the shell fracture of the walnuts under the action of external loading has randomness, but the sizes of the cracked walnut shells approximately conform to the log-normal distribution, so that the walnut shell fragments are simplified into spheres with the log-normal distribution, as shown in figure 2. The diameter of the sphere is obtained according to the conservation of mass, the walnut shell fragments are characterized by 40 spherical particles, and the particle size distribution of the spherical particles accords with the log normal distribution with expectation and variance of 3.15 and 6.4 respectively.
(2) Carrying out a single impact crushing test on walnuts by using a drop hammer impact tester, and measuring the crushing probability of a walnut sample with the water content of 6.67% under different impact energies;
(3) according to the weakest strength chain fracture theory and the similarity analysis method, a walnut shell breakage probability model is constructed:
PB＝1-exp[-fNut·x·k·(Ecol-Ecol,min)]
in the formula, PBThe walnut shell breaking probability is shown; ecolThe impact energy borne by the walnut shells is obtained; x is the diameter of the walnut, and the mean value is 34.4 mm; k is the number of impacts, the value of which is 1; f. ofNatThe material constant of the walnut is used for quantifying the capacity of the walnut for resisting the fracture caused by external load or stress; ecol,minThe walnut critical impact fracture energy is used for judging whether effective impact occurs on the walnut or not, namely when the value is larger than the critical impact fracture energy, the impact is considered to be beneficial to walnut fracture, and otherwise, the impact is ineffective to walnut fracture.
(4) Based on the walnut shell crushing model obtained in the step 3 and the test data obtained in the step 2,fitting the walnut crushing model by means of a least square method to obtain effective impact energy E for walnut crackingcol,minThe value is 9.883J/Kg; walnut material constant fNatThe value is 1.586 Kg/J.m.
(5) Carrying out a walnut repeated impact crushing test by means of a drop hammer impact tester, measuring the accumulated crushing distribution of walnut samples with the water content of 6.67% under different impact energies and impact times, and fitting test data by utilizing Weibull distribution to obtain the total breaking energy E of the walnutsfracture,tolThe value is 30.61J/Kg;
(6) according to the Hertz contact theory and damage fracture mechanics, the constructed walnut shell accumulated damage model is as follows:
En＝En-1(1-Dn)
in the formula, EnAnd En-1Respectively representing the fracture energy of the walnut shells before and after the nth impact; dnIs the walnut strength damage variable; gamma is the accumulated damage factor of walnut shells; ekImpact energy applied to the walnut shells;
(7) based on the walnut shell accumulated crushing distribution obtained in the step 5 and the walnut shell accumulated damage model constructed in the step 6, the walnut shell accumulated damage model is iteratively solved by using a Gauss-Newton algorithm, the damage accumulated factor when the walnut shell is crushed is obtained, the value of the damage accumulated factor is 5.8647, and according to the strength attenuation theory, the walnut shell breakage energy attenuation model is constructed as follows:
in the formula, Efracture,tolAnd Efracture,tol,newRespectively representing the initial fracture energy and the updated total fracture energy of the walnut shell; d is a damage variable of the walnut after the impact;
(8) by taking a particle replacement method in the discrete elements as a reference, and according to the step 1, the step 4 and the step 7, the established discrete element simulation method for walnut shell crushing comprises the following steps:
1) before simulation begins, the total breaking energy E required by walnut shell breaking is preset respectivelyfracture,tolAnd effective impact energy Ecol,min；
2) After the simulation is started, monitoring the contact impact conditions of all walnut particles in the shell breaking device, and counting the impact energy E generated by each walnut particle in each impactk；
3) Impact energy was compared to total fracture energy. If E iscol>Efracture,tolDefining the walnut particles to meet the brittle fracture condition, and replacing two spherical particles (broken shells) with the complete walnut particles by means of EDEM API;
4) the impact energy is compared to the effective impact energy. If the impact energy is larger than the effective impact energy and smaller than the total fracture energy, defining that the impact of the nut particles belongs to the effective impact, namely the impact is helpful for nut shell fracture, and updating the total fracture energy E of the current nut particles by utilizing the walnut shell fracture energy attenuation model established in the step 7fracture,tolTo obtain updated total fracture energy Efracture,tol,new(ii) a Defining the impact of the nut particles as being an ineffective impact if the impact energy is less than the effective impact energy and disregarding;
5) and (5) repeating the steps 2 to 5 by adopting a loop iteration algorithm until the simulation of the walnut shell crushing working condition is completed.
(9) By means of a vibration tester, 3000 walnuts are tested and simulated in a walnut vibration crushing test on an EDEM platform under the initial conditions of amplitude of 50mm and frequency of 50Hz, the provided nut shell crushing discrete element numerical simulation method is verified from a qualitative angle, and detailed figure 3 is shown. It should be noted that some walnuts in the figure are not shown in order to clearly visualize the walnut crushing simulation result. In addition, the crushing rate test and simulation results of walnut shells are compared from the quantitative angle, and the details are shown in fig. 4. Therefore, the method can better simulate the nut shell cracking process and has certain guiding significance for the clear nut shell cracking mechanism.
The above embodiments are only for illustrating the present invention, and the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution of the present invention within the technical scope of the present invention, and the technical solution of the present invention should be covered by the scope of the present invention.
Claims (6)
1. A discrete element numerical simulation method for nut shell cracking is characterized by comprising the following steps:
step 1, obtaining an initial size of a nut particle approximate to a geometric solid based on measurement of an actual nut particle characteristic size, constructing complete nut particles by adopting an overlapped ball method, and determining a nut shell breaking size according to mass conservation;
step 2, carrying out a single crushing test on nuts by means of a conventional physical mechanical testing machine, obtaining the distribution of nut shell breaking energy, and determining the total breaking energy required by nut shell crushing;
3, carrying out a single crushing test on the nuts again by using the conventional physical mechanical testing machine in the step 2 to obtain the nut shell crushing probability under different impact energy;
step 4, constructing a nut shell breakage probability model according to the weakest link breakage theory and the similarity analysis method, and obtaining effective impact energy when the nut shells are broken;
step 5, utilizing the conventional physical mechanical testing machine in the step 2 to carry out a successive crushing test on nuts and obtain the accumulated crushing distribution of nut shells under different impact energies and impact times;
step 6, constructing a nut shell accumulated damage model according to a Hertz contact theory and damage fracture mechanics;
step 7, solving the nut shell accumulated damage model by using an iterative algorithm based on the nut shell accumulated crushing distribution obtained in the step 5 and the nut shell accumulated damage model constructed in the step 6, obtaining nut shell accumulated damage factors, and establishing a nut shell fracture energy attenuation model;
step 8, establishing a discrete element simulation method for nut shell crushing according to the step 2, the step 4 and the step 7 by using a particle replacement model in a discrete element method for reference:
1) before simulation begins, presetting total fracture energy and effective impact energy required by nut crushing respectively;
2) after the simulation is started, monitoring the contact impact conditions of all nut particles in the shell breaking device, and counting the impact energy generated by each nut particle in each impact;
3) impact energy was compared to total fracture energy. Defining the nut particles to satisfy a brittle fracture condition if the impact energy is greater than the total fracture energy, thereby replacing intact nut particles with crushed shells;
4) the impact energy is compared to the effective impact energy. If the impact energy is greater than the effective impact energy and less than the total fracture energy, defining that the impact of the nut particles belongs to the effective impact, namely the impact contributes to nut shell fracture, and updating the total nut shell fracture energy by using the nut shell strength attenuation model established in the step 8; defining the impact of the nut particles as being an ineffective impact if the impact energy is less than the effective impact energy and disregarding;
5) and (4) repeating the steps 2 to 4 by adopting a loop iteration algorithm until the simulation of the nut shell crushing working condition is completed.
And 9, verifying the proposed nut shell crushing discrete element simulation method by using a walnut vibration crushing test.
2. The method of claim 1, wherein the discrete element numerical simulation comprises: the nut shell breakage probability model is constructed as follows:
PB＝1-exp[-fNut·x·k·(Ecol-Ecol,min)]
in the formula, PBThe nut shell breakage probability; ecolThe impact energy to which the nut shells are subjected; x is the nut shell diameter; k is the impact frequency; f. ofNatIs a nut material constant, the value of which is used to quantify the resistance of the nut material to external loads or stressesAbility to break; ecol,minThe effective impact energy of the nut shells is used for judging the judging condition whether the nuts are effectively cracked or not, namely when the effective impact energy is larger than the effective impact energy, the impact is considered to be favorable for cracking the nuts; conversely, this impact is not effective for nut breakage.
3. The method of claim 1, wherein the discrete element numerical simulation comprises: the constructed cumulative damage model of nuts is as follows:
En＝En-1(1-Dn)
in the formula, EnAnd En-1The fracture energy of the nuts after n and n-1 times of impact respectively; dnIs a nut shell strength damage variable; gamma is a nut shell damage accumulation factor; ekIs the impact energy that the nut shell is subjected to at the k-th impact.
4. The method of claim 1, wherein the discrete element numerical simulation comprises: in steps 1, 2 and 5, the conventional physical mechanical testing machine may be any one of a universal testing machine, a texture testing machine, a drop hammer impact testing machine and the like.
5. The method of claim 1, wherein the discrete element numerical simulation comprises: in step 7, the iterative algorithm may be any one of a Gauss-Newton method, a steepest descent method, a conjugate iterative method, a variable-scale iterative method, a least square method, a linear programming, a nonlinear programming, a simplex method, a penalty function method, a slope projection method, a genetic algorithm, and simulated annealing.
6. The method of claim 1, wherein the discrete element numerical simulation comprises: in step 7, the nut shell energy decay model is as follows:
in the formula, E and EnewThe initial fracture energy and the updated total fracture energy of the nut shell are respectively obtained; d is the damage variable after the impact on the nut.
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| 徐琨;周伟;马刚;常晓林;杨利福;: "基于离散元法的颗粒破碎模拟研究进展", 岩土工程学报, no. 05 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114613458A (en) * | 2022-04-19 | 2022-06-10 | 中南大学 | Particle crushing simulation method and system based on conventional state type near field dynamics |
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