CN107451352B - Method for measuring weight of rice in silo based on finite element analysis - Google Patents
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Abstract
The invention provides a method for measuring the weight of rice in a silo based on finite element analysis, and relates to the field of grain measurement. The measuring method comprises the following steps: carrying out a triaxial axial compression test and an anisotropic isobaric compression test on the rice, and calculating to obtain parameters of the rice correction Cambridge model: stress ratio in critical state, isotropic expansion index, logarithmic hardening modulus and poisson ratio; dividing the rice heap in the silo in the uncompacted state intoNA layer; each layer of rice heap is divided from the center to the outside into a part with the central axis collinear with the central axis of the siloMA unit; the relation between the strain and the stress of each unit conforms to a modified Cambridge model; using ABAQUS to solve and correct the Cambridge model to obtain the height of each unit of the rice pile in the compacted state, and calculating the height of each unit in the compacted stateN×MIndividual unit volume strain, calculationN×MCalculating the weight of each layer of the rice heap according to the unit density, and calculating the total weight of the rice heap in the siloW。The measuring method is simple, short in time consumption, accurate in measuring result and high in precision.
Description
Technical Field
The invention relates to the field of grain measurement, in particular to a method for measuring the weight of rice in a silo based on finite element analysis.
Background
The silo is one of the main silo types for storing rice, is a grain storage container with the highest mechanization degree and is mainly used for storing bulk grains. The rice is a typical granular body, when stored in a silo, the static characteristic of the rice is elastic and plastic, and the rice is subjected to self weight, internal friction force and supporting force of the silo wall and the silo bottom. The stress is generated in the rice heap due to the action of the forces, so that elastic and plastic deformation is generated, the volume of the rice heap is reduced, and the density is increased; along with the increase of the depth of the grain layer, the compressive stress and the shear stress of the rice heap are increased, the volume strain is increased, and the density is increased; due to the influence of bin wall friction, the stress, strain and density of different rings on the same grain layer are different. Thus, the bulk density of the rice in the silo is not a constant but a function of spatial position. The inspection of the grain storage quantity is an important inspection content of grain inventory, and the current detection methods mainly comprise a weighing method and a volume density method. The weighing method is a checking method for weighing the grain by using a weighing apparatus which meets the legal measuring standard, and has the advantages that the measuring result can accurately reflect the actual quantity of the checked grain generally, but the weighing method has the defects of large workload, low efficiency and the like, and is difficult to be widely applied to large-scale inventory checking. The volume density method is an inspection method for obtaining the total weight of grains in a warehouse by measuring and calculating the volume of a grain pile and the surface density of the grains, multiplying the surface density of the grains by a correction coefficient to obtain the average density of the grain pile and multiplying the volume by the average density.
The average density of the grain heap varies depending on the geometry of the silo, the height of the grain heap, the compression characteristics, the internal friction characteristics, and the friction characteristics between the silo wall and the grain, and so far, the correction factor for calculating the average density has been empirically estimated. In the research of the new method for measuring the density distribution of the grain pile, researchers use microwaves to detect the density of the grain pile, the method is to measure the dielectric constant when the microwaves pass through the grain pile, and the density of the grain pile is obtained according to the relation between the dielectric constant and the density, but the method can not measure the density at the deep part of a silo, and the microwave reaching the deep part of the grain pile is easy to interfere, so that the density of the grain pile at the deep part of two meters can only be measured at present. And researchers also install force sensors on the wall and the bottom of the bin, and push out the total weight of the stored grain according to the stress distribution of the bin wall and the bottom, but the method has two problems that firstly, an accurate mathematical model needs to be established for the total weight of the stored grain piled according to the stress distribution of the bin wall and the bottom, otherwise, the error of measurement and calculation is large, and secondly, the cost is large, and the popularization is difficult.
Disclosure of Invention
The invention aims to provide a method for measuring the weight of rice in a silo based on finite element analysis, which is simple, short in time consumption, accurate in measurement result and high in precision.
The purpose of the invention is realized by adopting the following technical scheme.
The method for measuring the weight of the rice in the silo based on finite element analysis is characterized by comprising the following steps of:
(1) carrying out a triaxial axial compression test and an anisotropic isobaric compression test on the rice, and calculating to obtain parameters of the rice correction Cambridge model: stress ratio M in a critical state, isotropic expansion index kappa, logarithmic hardening modulus lambda and Poisson ratio upsilon;
(2) measuring the internal diameter d (in m) and the height H (in m) of the silo; measuring the height h (m) of the heap in the silo in the compacted state, and estimating the height h' (m) of the heap in the uncompacted state; dividing a rice heap in a silo under an uncompacted state into N layers; each layer of rice grain pile is divided into M units with the central axis collinear with the central axis of the silo by the center outwards, the M units consist of 1 cylinder and M-1 circular ring columns, and the cylinder is positioned in the center of each layer; wherein, the units of each layer of the rice heap are numbered in sequence from the center to the outside; obtaining N × M units in total; the relation between the strain and the stress of each unit conforms to a modified Cambridge model; solving and correcting a cambridge model by using large finite element software ABAQUS to obtain the height of each unit of the rice heap in a compacted state, and respectively calculating the volume strain of NxM units of the rice heap in the silo in the compacted state according to a formula (A)
according toEquation (B) calculates rho of the respective NxM cell densitiesnm：
(N-1, 2, …, N; M-1, 2, …, M) formula (B),
in the formula (B), n is the number of layers (natural number), m is the number of columns (natural number), ρnmIs the density of the n-th layer and m-column unit, kg/m3；ρ0Is the density of the surface layer of the rice heap in kg/m3；
Is the volume strain of the nth layer, m columns of cells;
(3) the weight of each heap was calculated according to formula (C),
in the formula (C), WnIs the weight, kg, of the nth layer of the rice bunch; (ii) a RhonmIs the density of the n-th layer and m-column unit, kg/m3；hnmThe height of the nth layer and the m rows of units of the rice heap in a compacted state; rmDenotes the outer diameter of the m-th column unit (when m is 1, R1Refers to the diameter of the cylinder); n is the number of layers (natural number), m is the number of columns (natural number), N is 1,2, …, N; m is 1,2, …, M;
calculating the total weight W of the rice heap in the silo by adopting a formula (D):
w in the formula (D)nIs the weight of the nth layer of the rice heap, N is 1,2, …, N.
The units of each layer of the rice heap are numbered in sequence from the center to the outside according to the column number, and the specific numbering method is as follows: the column at the center is column 1, then numbered sequentially outward as column 2, through column M. A schematic diagram of each layer of rice heap divided into 5 units is shown in fig. 1.
In the present invention, the compacted state of the rice heap refers to a stacked state of the rice heap after being loaded into the silo. The uncompacted state of the rice bunch refers to the piled state of the rice bunch when gravity is not applied.
In the present invention, the surface layer of the rice heap refers to a rice layer from the surface of the rice heap to a depth of 0.5 m. The gravity on the surface layer of the rice heap can be ignored.
In the present invention, the values of N are: n is more than or equal to h ' and less than or equal to 2h ', h ' is the height of the rice heap under the uncompacted state, and m; the value of M is: m is more than or equal to 0.5R and less than or equal to 2R, R is the radius of the rice heap, and M.
In the present invention, the values of h' are as follows: when 2m<When h is less than or equal to 5m, 1.04<h'/h is less than or equal to 1.06; when 5m<When h is less than or equal to 10m, 1.06<h'/h is less than or equal to 1.10; when the grain size is 10m<When h is less than or equal to 15 meters, 1.10<h'/h is less than or equal to 1.14; when the grain size is 15 meters<When h is less than or equal to 20m, 1.14<h'/h is less than or equal to 1.17; when the grain size is 20m<When h is less than or equal to 25m, 1.17<h'/h is less than or equal to 1.19; when the rice is 25m<When h is less than or equal to 30m, 1.19<h'/h is less than or equal to 1.20; where h is the height of the heap of rice in the silo in the compacted state. The value of h' is estimated by the following method: from the height h of the heap of rice in compacted condition, assuming a value of h', the height h of the heap of rice in compacted condition is obtained by obtaining the height (axial length) of N × M units of the heap of rice in compacted condition by the above method for measuring the weight of rice in a silo based on finite element analysis, and thus the height h of the heap of rice in compacted condition, if any
The value of h' assumed is equal; if it is
Then increase h', if
Then h' is decreased; the height of the grain pile in the compacted state is obtained by the method for measuring the weight of the rice in the silo based on finite element analysis
Re-comparison
And h, up to
Until now.
In the invention, the corrected Cambridge model parameters M, kappa, lambda and upsilon of the rice in the step (1) are obtained by calculation after triaxial axial compression and anisotropic isostatic compression tests are carried out by an SLB-6A strain control type triaxial apparatus (manufactured by Nanjing soil instruments Co., Ltd.).
Determining the stress ratio M of the critical state by adopting a triaxial axial compression test, and comprising the following steps of: loading a rice sample, respectively setting confining pressure to be 30, 50, 70, 90 and 110kPa, starting an SLB-6A type strain control type triaxial apparatus to apply axial force to axially compress the sample, recording stress value reading and sample volume reduction of a dynamometer once when the axial displacement of the rice sample increases by 0.4mm, recording a dynamometer reading peak value q and a corresponding average pressure stress p until the dynamometer reading has a peak value, drawing by taking p as an abscissa q as an ordinate, and obtaining the slope of a straight line through unary linear regression, wherein the slope is the critical state stress ratio M;
determining the logarithmic hardening modulus lambda and the isotropic expansion index kappa by using an anisotropic pressure test, comprising the steps of: loading the rice sample to a confining pressure of3The confining pressure sigma during loading was recorded from 0kPa to 200kPa in a sequence of 5kPa increments each time3And a corresponding sample volume reduction; then, the confining pressure is sequentially unloaded from 200kPa to 0kPa according to the reduction of 5kPa each time, and the confining pressure sigma in the unloading process is recorded3And corresponding sample volume increase; drawing a loading curve and an unloading curve; through unitary linear regression, taking the slope of a loading curve as lambda and the slope of an unloading curve as kappa; the abscissa of the loading curve and the unloading curve is lnp, the ordinate is e, and e is the rice heap void ratio, calculated as follows: e ═ V/[ V ═ V0(1-ε0)]-1; in the formula, V0Is the initial volume of the rice sample, m3(ii) a V is the pressed volume of the rice sample, m3；ε0Is the porosity of the surface layer of the rice heap; p is the average compressive stress, kPa.
The method for measuring the elastic modulus E and Poisson ratio upsilon by adopting a triaxial axial compression test comprisesThe method comprises the following steps: loading a rice sample, setting confining pressure, axially compressing the sample until the sample is damaged, and measuring the maximum main stress difference (the difference between the axial compressive stress and the confining pressure during the damage); taking out the damaged rice sample, then re-loading a new rice sample, carrying out a pressurization experiment, applying axial pressure in 4 stages, wherein the 1 st stage pressure is 1/10 of the maximum main stress difference, and the pressure of each stage is increased by 1/10 of the maximum main stress difference compared with the pressure of the previous stage; recording the axial pressure applied and the axial displacement of the sample at 1 minute after each pressurization every 1-stage pressure application until the 4 th-stage pressure application; gradually releasing pressure until all applied axial pressure is released, and releasing pressure in 4 stages, wherein the pressure releasing sequence is opposite to the pressurizing sequence; after repeated pressurization and pressure relief for 4 times, axial pressurization is carried out until the pressure is destroyed; making loading curve and unloading curve in the last pressure relief experiment, and calculating elastic modulus E, E ═ delta P/(delta h)e/hc) (ii) a Wherein, Δ P is the increasing or decreasing value of the axial pressure, kPa; Δ heIs the axial elastic deformation of the rice, mm; h iscThe height of the rice sample after sample loading is mm; determining the bulk variable elastic modulus B of the rice sample by adopting a triaxial anisotropic isobaric test, and calculating according to a formula B which is delta sigma/(delta V/V), wherein the delta sigma is the confining pressure increment of the rice sample, namely kPa; Δ v is the volume compression of the rice sample, m3(ii) a V is the volume of the rice sample after sample loading, m3(ii) a The poisson ratio v is calculated according to the formula v ═ 3B-E)/6B.
In the invention, the step (2) of solving the modified Cambridge model by using the ABAQUS large-scale finite element software comprises the following steps: in a Part module of ABAQUS, an axisymmetric CAX4 unit is adopted to create a silo and a rice Part; in the Property module, defining the steel material Property of the silo and the Property of the rice grain heap, selecting a modified Cambridge model to represent the strain and stress relation of the rice grain heap, and then assigning each material Property to each part; assembling two parts of a silo and a rice stack into a whole in an Assembly module; establishing an analysis Step in a Step module; defining a constraint relation between two components in an Interaction module, and describing friction behavior between two surfaces through a friction coefficient; defining loads and boundary conditions in a Load module; in Mesh module according to partsCarrying out grid division on the structure (the rice heap and the silo), and dividing the rice heap in the silo into the N multiplied by M units; submitting the operation in the Job module for analysis; after the analysis is finished, checking three main strains of each unit of the rice pile in a compaction state in a Visualization module
And height h of each unitnmAccording to
Calculating the volume strain of the n-th layer and m-column unit
In the formula (I), the compound is shown in the specification,
is the three principal strains of the nth layer, m columns of cells; h isnmRefers to the height of the n-th layer and m columns of units in a compacted state.
The establishment of the silo and the rice component specifically means defining the inner diameter, the height, the thickness of the silo wall and the uncompacted height of a grain stack of the silo, wherein the silo component is a rectangular plane which is a half of the outer diameter section of the silo divided by a central axis; the rice grain heap member is a rectangular plane which is a half of a diameter section of the cylindrical rice heap divided by the central axis.
The steel material attribute for defining the silo refers to defining the elastic modulus and the Poisson ratio of the steel material, and the attribute for defining the rice grain heap refers to defining the modified Cambridge model parameters of the rice grain heap.
The constraint relation between the two components is defined as a friction contact relation in the Interaction module, and the friction behavior between the two surfaces is described by the friction coefficient mu between the rice and the silo wall.
Defining the Load as volume force in the Load module, the boundary conditions are: the paddy contacted with the bottom of the silo has no vertical displacement, and the paddy on the central axis of the cylindrical paddy pile has no horizontal displacement.
The Load in the Load module is described by using the volume force, and other acting forces are described by the interaction between the rice heap and the silo wall and silo bottom.
The Interaction between the grain pile and the bin wall is defined in the Interaction module and is simulated by setting contact, the contact is opposite to a selection point and opposite to a discrete method, the inner side of the bin wall is selected by a main control surface, and the outer side of a grain pile model is selected by a subordinate surface. The contact surface interaction mechanical model adopts a common friction model, and the friction behavior between two surfaces is described through a friction coefficient.
Before determining parameters of the rice modified Cambridge model, measuring the friction coefficient mu between the rice and the silo wall and the internal friction angle of the rice heap
Density rho of the surface layer of the rice grain bulk0And the water content MC of the rice heap; determination of the porosity epsilon of the surface layer of a Rice heap0And is composed of0Calculating to obtain the porosity ratio of the surface layer of the rice heap
Internal friction angle of rice heap
Measuring the friction coefficient mu between the paddy and the silo wall by using a direct shear apparatus; determination of the internal Angle of Friction of the Paddy heap
When in use, rice is placed between an upper sample box and a lower sample box, vertical compressive stress sigma is applied to the rice, and then horizontal pushing stress tau is applied to the rice, so that the rice is sheared on a horizontal plane between the upper sample box and the lower sample box until the rice is damaged; according to the formula
Calculating the internal friction angle
Wherein σ is a vertical compressive stress applied to the rice, kPa; τ is the horizontal pushing stress exerted on the rice, kPa; tg is positiveA cut function;
is the internal friction angle, °; when the friction coefficient mu between the rice and the silo wall is measured, the upper sample box is filled with the rice, the lower sample box is filled with a stainless steel plate or a concrete plate, vertical compressive stress sigma is applied to the rice, then horizontal pushing stress tau is applied to enable the rice to be sheared on a contact surface until the rice is damaged, the friction coefficient mu is calculated according to the mu, tau/sigma, and the sigma is the vertical compressive stress applied to the rice and kPa; τ is the horizontal pushing stress exerted on the rice, kPa.
The porosity ε of the surface layer of a rice grain bulk was measured using an LKY-1 type grain porosity meter (manufactured by Nanjing soil instruments Ltd.)0The surface layer of the rice heap has a void ratio of
In the present invention, the density ρ of the surface layer of the rice grain bulk0The following methods were used for the measurements: sampling in the surface layer of the rice heap, determining the mass m of the sample0And volume V0According to the formula (3) < rho >0＝m0/V0Calculating to obtain rho0。
In the present invention, the water content refers to the mass of water contained in the grain and the grainTotal massThe ratio of (A) to (B) is expressed in percentage. According to the national standard GB/T5497-85, the water content is measured by a constant weight method at 105 ℃, and the water content of the rice is calculated according to the following formula: w ═ m1-m2)/(m1-m0) X 100%, wherein: m is0G is the mass of the aluminum box; m is1G, the mass of the rice sample and the aluminum box before drying; m is2G, the mass of the dried rice sample and the aluminum box; w is the water content, w.b.
Has the advantages that: the method for measuring the weight of the rice in the silo is simple, short in time consumption and accurate in measurement result. The method of the invention is adopted to measure the rice storage weight in 2 bins, the measured value is almost consistent with the actual account number of the grain weight, and the errors are respectively 0.32 percent and 2.00 percent, which shows that the method of the invention has accurate measurement and high precision.
Detailed Description
Example 1 Using the method of the present invention, the storage weight of rice in silo No. 7 of experimental base for Xiaotang mountain in Beijing was measured
The method of the invention is adopted to measure the storage weight of the rice in the silo No. 7 of the experimental base of the small soup mountain in Beijing. The inner cavity of the silo is cylindrical.
(1) The inner diameter d and the height H of a silo No. 7 in the Xiaotang mountain experiment base are shown in a table 1. The height of the rice in the silo in a compacted state is 7.21m (measured value); the height h ' of the rice heap in the silo under the non-compacted state is 1.06< h '/h < 1.10 when 5m < h < 10m, and the value of h ' is 7.7 m.
TABLE 1 Silo and parameters of its materials
(2) Measuring the friction coefficient mu between rice and silo wall and the internal friction angle of rice heap
Density rho of the surface layer of the rice grain bulk0And the water content MC of the rice heap; determination of the porosity epsilon of the surface layer of a Rice heap0And is composed of0Calculating to obtain the porosity ratio of the surface layer of the rice heap
Internal friction angle of rice heap
Measuring the friction coefficient mu between the paddy and the silo wall by using a direct shear apparatus; determination of the internal Angle of Friction of the Paddy heap
When in use, rice is placed between an upper sample box and a lower sample box, vertical compressive stress sigma is applied to the rice, and then horizontal pushing stress tau is applied to the rice, so that the rice is sheared on a horizontal plane between the upper sample box and the lower sample box until the rice is damaged; according to the formula
Calculating the internal friction angle
Wherein σ is a vertical compressive stress applied to the rice, kPa; τ is the horizontal pushing stress exerted on the rice, kPa; tg is the tangent function;
is the internal friction angle, °; when the friction coefficient mu between the rice and the silo wall is measured, the upper sample box is filled with the rice, the lower sample box is filled with a stainless steel plate or a concrete plate, vertical compressive stress sigma is applied to the rice, then horizontal pushing stress tau is applied to enable the rice to be sheared on a contact surface until the rice is damaged, the friction coefficient mu is calculated according to the mu, tau/sigma, and the sigma is the vertical compressive stress applied to the rice and kPa; τ is the horizontal pushing stress exerted on the rice, kPa. And (3) measuring results: the friction coefficient mu between the paddy and the silo wall of the silo is 0.35, and the internal friction angle of the paddy pile
Is 30 deg..
The porosity ε of the surface layer of a rice grain bulk was measured using an LKY-1 type grain porosity meter (manufactured by Nanjing soil instruments Ltd.)0The surface layer of the rice heap has a void ratio of
Calculated moisture content is 11.90% w.b. porosity ratio e of the rice heap0It was 1.555.
Density rho of the surface layer of the rice grain bulk0The following methods were used for the measurements: sampling in the surface layer of the rice heap, determining the mass m of the sample0And volume V0According to the formula (3) < rho >0＝m0/V0Calculating to obtain rho0. Density rho of the surface layer of the rice grain bulk0Is 585.00kg/m3。
The water content refers to the quality of water contained in the grain and the grainTotal massRatio of (A) to (B) in percentAnd (4) showing. According to the national standard GB/T5497-85, the water content is measured by a constant weight method at 105 ℃, and the water content of the rice is calculated according to the following formula: w ═ m1-m2)/(m1-m0) X 100%, wherein: m is0G is the mass of the aluminum box; m is1G, the mass of the rice sample and the aluminum box before drying; m is2G, the mass of the dried rice sample and the aluminum box; w is the water content, w.b. And (3) measuring results: the water content MC of the rice heap is 11.90% w.b.
(3) The corrected Cambridge model parameters M, κ, λ and υ of the paddy rice are obtained by calculation after a triaxial axial compression test and an anisotropic isostatic compression test are carried out by an SLB-6A strain control type triaxial apparatus (manufactured by Nanjing soil instruments, Ltd.).
Determining the stress ratio M of the critical state by adopting a triaxial axial compression test, and comprising the following steps of: loading a rice sample, respectively setting confining pressure to be 30, 50, 70, 90 and 110kPa, starting an SLB-6A type strain control type triaxial apparatus to apply axial force to shear the sample, recording the stress value reading and the sample volume reduction of a dynamometer once when the axial displacement of the rice sample increases by 0.4mm, recording the reading peak value q of the dynamometer and the corresponding average pressure stress p until the reading peak value of the dynamometer appears, drawing by taking p as an abscissa q as an ordinate, and obtaining the slope of a straight line through unary linear regression, wherein the slope is the critical state stress ratio M;
determining the logarithmic hardening modulus lambda and the isotropic expansion index kappa by using an anisotropic pressure test, comprising the steps of: loading the rice sample to a confining pressure of3The confining pressure sigma during loading was recorded from 0kPa to 200kPa in a sequence of 5kPa increments each time3And a corresponding sample volume reduction; then, the confining pressure is sequentially unloaded from 200kPa to 0kPa according to the reduction of 5kPa each time, and the confining pressure sigma in the unloading process is recorded3And corresponding sample volume increase; drawing a loading curve and an unloading curve; through unitary linear regression, taking the slope of a loading curve as lambda and the slope of an unloading curve as kappa; the abscissa of the loading curve and the unloading curve is lnp, the ordinate is e, and e is the rice heap void ratio, calculated as follows: e ═ V/[ V ═ V0(1-ε0)]-1; in the formula, V0Is the initial volume of the rice sample, m3(ii) a V is the pressed volume of the rice sample, m3；ε0Is the porosity of the surface layer of the rice heap; p is the average compressive stress, kPa.
The method for measuring the elastic modulus E and Poisson ratio upsilon by adopting a triaxial axial compression test comprises the following steps: loading a rice sample, setting confining pressure, axially compressing the sample until the sample is damaged, and measuring the maximum main stress difference (the difference between the axial compressive stress and the confining pressure during the damage); taking out the damaged rice sample, then re-loading a new rice sample, carrying out a pressurization experiment, applying axial pressure in 4 stages, wherein the 1 st stage pressure is 1/10 of the maximum main stress difference, and the pressure of each stage is increased by 1/10 of the maximum main stress difference compared with the pressure of the previous stage; recording the axial pressure applied and the axial displacement of the sample at 1 minute after each pressurization every 1-stage pressure application until the 4 th-stage pressure application; gradually releasing pressure until all applied axial pressure is released, and releasing pressure in 4 stages, wherein the pressure releasing sequence is opposite to the pressurizing sequence; after repeated pressurization and pressure relief for 4 times, axial pressurization is carried out until the pressure is destroyed; making loading curve and unloading curve in the last pressure relief experiment, and calculating elastic modulus E, E ═ delta P/(delta h)e/hc) (ii) a Wherein, Δ P is the increasing or decreasing value of the axial pressure, kPa; Δ heIs the axial elastic deformation of the rice, mm; h iscThe height of the rice sample after sample loading is mm; determining the bulk variable elastic modulus B of the rice sample by adopting a triaxial anisotropic isobaric test, and calculating according to a formula B which is delta sigma/(delta V/V), wherein the delta sigma is the confining pressure increment of the rice sample, namely kPa; Δ v is the volume compression of the rice sample, m3(ii) a V is the volume of the rice sample after sample loading, m3(ii) a The poisson ratio v is calculated according to the formula v ═ 3B-E)/6B.
The results are shown in Table 2.
TABLE 2 corrected Cambridge model parameters for rice
(4) Dividing the rice heap in the silo in an uncompacted state (h' 7.7m) into N layers (N ═ 11); each layer of rice heap is divided into M units with the central axes collinear with the central axis of the silo from the center to the outside(M ═ 5), the M units consisting of 1 cylinder and M-1 circular cylinders, with the cylinder at the center of each layer (see fig. 1); numbering the units of each layer of the rice heap from the center to the outside in sequence; obtaining N × M units in total; the relation between the strain and the stress of each unit conforms to a modified Cambridge model; solving the modified Cambridge model by using a large finite element software ABAQUS, and calculating the height h of each unit of the rice pile in a compacted statenm(height of M rows of units on the nth layer), respectively calculating the volume strain of NxM units of the rice heap in the silo in a compacted state according to the formula (A)
rho of the N × M cell densities is calculated from the formula (B) respectivelynm：
(N-1, 2, …, N; M-1, 2, …, M) formula (B),
in the formula (B), n is the number of layers (natural number), m is the number of columns (natural number), ρnmIs the density of the n-th layer and m-column unit, kg/m3；ρ0Is the density of the surface layer of the rice heap in kg/m3；
Is the volume strain of the nth layer, m columns of cells;
the units of each layer of the rice heap are numbered in sequence from the center to the outside according to the column number, and the specific numbering method is as follows: the column at the center is column 1, then numbered sequentially outward as column 2, through column M. Each layer of the rice heap was divided into 5 units, see fig. 1. The compacted state of the rice heap refers to a stacked state of the rice heap after being loaded into the silo. The uncompacted state of the rice bunch refers to the piled state of the rice bunch when gravity is not applied. The surface layer of the rice heap refers to the rice layer from the surface of the rice heap to the depth of 0.5 m. The gravity on the surface layer of the rice heap can be ignored.
The method for solving the modified cambridge model by using the ABAQUS comprises the following steps: in a Part module of ABAQUS, an axisymmetric CAX4 unit is adopted to create a silo and a rice Part; in the Property module, defining the steel material Property of the silo and the Property of the rice grain heap, selecting a modified Cambridge model to represent the strain and stress relation of the rice grain heap, and then assigning each material Property to each part; assembling two parts of a silo and a rice stack into a whole in an Assembly module; establishing an analysis Step in a Step module; defining a constraint relation between two components in an Interaction module, and describing friction behavior between two surfaces through a friction coefficient; defining loads and boundary conditions in a Load module; carrying out grid division on a structure (a rice grain heap and a silo) in a Mesh module according to components, and dividing the rice grain heap in the silo into the N multiplied by M units; submitting the operation in the Job module for analysis; after the analysis is finished, checking three main strains of each unit of the rice pile in a compaction state in a Visualization module
And height h of each unitnmAccording to
Calculating the volume strain of the n-th layer and m-column unit
In the formula (I), the compound is shown in the specification,
is the three principal strains of the nth layer, m columns of cells; h isnmRefers to the height of the n-th layer and m columns of units in a compacted state.
The establishment of the silo and the rice component specifically means defining the inner diameter, the height, the thickness of the silo wall and the uncompacted height of a grain stack of the silo, wherein the silo component is a rectangular plane which is a half of the outer diameter section of the silo divided by a central axis; the rice grain heap member is a rectangular plane which is a half of a diameter section of the cylindrical rice heap divided by the central axis. The steel material attribute for defining the silo refers to defining the elastic modulus and the Poisson ratio of the steel material, and the attribute for defining the rice grain heap refers to defining the modified Cambridge model parameters of the rice grain heap. The constraint relation between the two components is defined as a friction contact relation in the Interaction module, and the friction behavior between the two surfaces is described by the friction coefficient mu between the rice and the silo wall. Defining the Load as volume force in the Load module, the boundary conditions are: the paddy contacted with the bottom of the silo has no vertical displacement, and the paddy on the central axis of the cylindrical paddy pile has no horizontal displacement. The Load in the Load module is described by using the volume force, and other acting forces are described by the interaction between the rice heap and the silo wall and silo bottom. The Interaction between the grain pile and the bin wall is defined in the Interaction module and is simulated by setting contact, the contact is opposite to a selection point and opposite to a discrete method, the inner side of the bin wall is selected by a main control surface, and the outer side of a grain pile model is selected by a subordinate surface. The contact surface interaction mechanical model adopts a common friction model, and the friction behavior between two surfaces is described through a friction coefficient.
The weight of each heap was calculated according to formula (C),
in the formula (C), WnIs the n-thWeight of layered rice heap, kg; (ii) a RhonmIs the density of the n-th layer and m-column unit, kg/m3；hnmThe height of the nth layer and the m rows of units of the rice heap in a compacted state; rmDenotes the outer diameter of the m-th column unit (when m is 1, R1Refers to the diameter of the cylinder); n is the number of layers (natural number), m is the number of columns (natural number), N is 1,2, …, N; m is 1,2, …, M.
The weight of each layer of the rice bunch is shown in table 3.
TABLE 3 weight of rice in silo piled on each layer
(5) Calculating the total weight W of the rice heap in the silo by adopting a formula (D):
w in the formula (D)nIs the weight of the nth layer of the rice heap, N is 1,2, …, N.
The total weight of the rice heap in the silo was 121786.25 kg.
(6) And comparing the calculation result with the calculated value of the volume density method and the actual accounting number, wherein the correction coefficient of the volume density method is 1.015, and the comparison result is shown in table 4.
TABLE 4 error comparison of calculated values with actual account numbers
The result shows that the total weight of the rice storage obtained by the method is smaller than the common error of the volume density method, is closer to the actual account number, and embodies the advantages of the calculation method.
Example 2 determination of the storage weight of rice in silo 2 by the method of the present invention
(1) The internal diameter d and the bin height H of the silo No. 2 of the Wenzhou directly-owned warehouse for grain storage in the center are shown in a table 5. The inner cavity of the silo is cylindrical. Rice in silo under compacted stateThe height of the heap was 24.61m (measured); height h' of the rice heap in the silo in the uncompacted state, according to when 20m<When h is less than or equal to 25m, 1.17<h '/h is less than or equal to 1.19, and h' is 29.0 m. Following the procedure in example 1, the following were obtained: the friction coefficient mu between the rice and the silo wall of the silo is 0.3, and the internal friction angle of the rice heap
At 28 deg. the surface density of the rice heap ρ0Is 629.68kg/m3And the moisture content of the rice heap is 13.50% w.b.
Table 52 Cartridge and parameters of its Material
(2) The porosity ε of the surface layer of the rice grain heap was measured in accordance with the method described in example 10And calculating the porosity e of the rice heap according to experimental data0The water content was calculated to be 13.50% w.b. the void ratio of the rice heap was 1.527.
(3) And (3) performing triaxial axial compression and anisotropic isostatic compression tests on the rice heap, and calculating to obtain corrected Cambridge model parameters M, kappa, lambda and upsilon of the rice heap according to experimental data, wherein the specific method is the same as that in example 1. The results are shown in Table 6;
TABLE 6 corrected Cambridge model parameters for rice
(4) Dividing the rice grain heap under the non-compaction state into N layers (N is 30), dividing each layer into M units (M is 5), correcting a cambridge model according to the relation between strain and stress of each unit, solving the corrected cambridge model by applying large finite element software ABAQUS, and calculating the height h of each unit under the compaction statenm(height of m units in the nth row) and the spatial density distribution of the rice heap in the silo (i.e. density of 150 units of the rice heap in the silo), the weight of each layer of the rice heap was calculated in the same manner as in example 1, and the results are shown in Table 7.
TABLE 7 weight of rice in silo piled on each layer
(5) The total weight of the rice heap in the silo was obtained by summing the weight of each layer of the rice heap and the total weight was 7813825.08 kg.
(6) And comparing the calculation result with the calculated value of the volume density method and the actual accounting number, wherein the correction coefficient of the volume density method is 1.05, and the comparison result is shown in Table 8.
TABLE 8 error comparison of calculated values with actual account number
The results show that the total weight of the rice storage obtained by the calculation method has smaller error than that of the common volume density method, is closer to the actual account number, and shows the advantages of the measurement method.
Claims (10)
1. A method for measuring the weight of rice in a silo based on finite element analysis is characterized by comprising the following steps:
(1) carrying out a triaxial axial compression test and an anisotropic isobaric compression test on the rice, and calculating to obtain parameters of the rice correction Cambridge model: stress ratio M in a critical state, isotropic expansion index kappa, logarithmic hardening modulus lambda and Poisson ratio upsilon;
(2) measuring the inner diameter d and the height H of the silo; measuring the height h of the rice heap in the silo in a compacted state, and estimating the height h' of the rice heap in an uncompacted state; dividing a rice heap in a silo under an uncompacted state into N layers; each layer of rice grain pile is divided into M units with the central axis collinear with the central axis of the silo by the center outwards, the M units consist of 1 cylinder and M-1 circular ring columns, and the cylinder is positioned in the center of each layer; wherein, the units of each layer of the rice heap are numbered in sequence according to the direction from the center to the outside; obtaining N × M units in total; the relation between the strain and the stress of each unit conforms to a modified Cambridge model; using large finite element software ABAQUS to solve and repairObtaining the height of each unit of the rice heap under the compacted state through a positive Cambridge model, and respectively calculating the volume strain of NxM units of the rice heap in the silo under the compacted state according to a formula (A)
Wherein n in (A) is the number of layers and m is the number of columns,
is the volume strain of the n-th layer and m columns of units,
and
is the three principal strains of the nth layer, m columns of cells;
calculating densities ρ of N × M cells, respectively, according to the formula (B)nm：
In the formula (B), n is the number of layers, m is the number of columns, ρnmIs the density of the nth layer, m columns of cells; rho0Is the density of the surface layer of the rice heap,
is the volume strain of the nth layer, m columns of cells;
(3) the weight of each heap was calculated according to formula (C),
in the formula (C), WnIs the weight of the nth layer of the bunch of rice; rhonmIs the density of the nth layer, m columns of cells; h isnmIs the unit of the nth layer and the m rows of the rice pile in a compacted stateThe height of (d); rmRepresents the outer diameter of the m-th column unit; n is the number of layers, m is the number of columns, N is 1,2, …, N; m is 1,2, …, M;
calculating the total weight W of the rice heap in the silo by adopting a formula (D):
w in the formula (D)nIs the weight of the nth layer of the rice heap, N is 1,2, …, N.
2. The finite element analysis-based method for measuring the weight of rice in a silo as claimed in claim 1, wherein the surface layer of the rice heap is defined as the surface of the rice heap to a depth of 0.5 m.
3. A method as claimed in claim 1 or 2, wherein the finite element analysis based method for measuring the weight of rice in a silo is characterized in that N is selected from the group consisting of: n is more than or equal to h ' and less than or equal to 2h ', and h ' is the height of the rice heap under the uncompacted state; the value of M is: m is more than or equal to 0.5R and less than or equal to 2R, and R is the radius of the rice heap.
4. The finite element analysis-based method for measuring rice weight in silos according to claim 3, wherein the method comprises the following steps: the values of h' are as follows: when 2m < h < 5m, 1.04< h'/h < 1.06; when the m is more than 5m and less than or equal to 10m, the h'/h is more than 1.06 and less than or equal to 1.10; when 10m < h < 15m, 1.10< h'/h < 1.14; when the m is more than 15m and less than or equal to 20m, the h'/h is more than 1.14 and less than or equal to 1.17; when 20m < h < 25m, 1.17< h'/h < 1.19; when the m is more than 25m and less than or equal to 30m, the h'/h is more than 1.19 and less than or equal to 1.20; where h is the height of the heap of rice in the silo in the compacted state.
5. The method for measuring rice weight in a silo based on finite element analysis as claimed in claim 4, wherein the corrected Cambridge model parameters M, κ, λ and ν of the rice in the step (1) are calculated after triaxial axial compression and anisotropic isostatic compression tests by a strain controlled triaxial apparatus model SLB-6A.
6. The finite element analysis-based method for measuring rice weight in silos according to claim 5, wherein the method comprises the following steps: determining the stress ratio M of the critical state by adopting a triaxial axial compression test, and comprising the following steps of: loading a rice sample, respectively setting confining pressure to be 30, 50, 70, 90 and 110kPa, starting an SLB-6A type strain control type triaxial apparatus to apply axial force to axially compress the sample, recording the stress value reading and the sample volume reduction of a dynamometer once when the axial displacement of the rice sample increases by 0.4mm, recording the reading peak value q of the dynamometer and the corresponding average pressure stress p until the reading of the dynamometer has a peak value, drawing by taking p as an abscissa and q as an ordinate, and obtaining the slope of a straight line through unary linear regression, wherein the slope is the stress ratio M in a critical state;
determining the logarithmic hardening modulus lambda and the isotropic expansion index kappa by using an anisotropic pressure test, comprising the steps of: loading the rice sample to a confining pressure of3The confining pressure sigma during loading was recorded from 0kPa to 200kPa in a sequence of 5kPa increments each time3And a corresponding sample volume reduction; then, the confining pressure is sequentially unloaded from 200kPa to 0kPa according to the reduction of 5kPa each time, and the confining pressure sigma in the unloading process is recorded3And corresponding sample volume increase; drawing a loading curve and an unloading curve; through unitary linear regression, taking the slope of a loading curve as lambda and the slope of an unloading curve as kappa;
the method for measuring the elastic modulus E and Poisson ratio upsilon by adopting a triaxial axial compression test comprises the following steps: loading a rice sample, setting confining pressure, axially compressing the sample until the sample is damaged, and measuring the maximum main stress difference; taking out the damaged rice sample, then re-loading the rice sample, carrying out a pressurization experiment, applying axial pressure in 4 stages, wherein the 1 st stage pressure is 1/10 of the maximum main stress difference, and then increasing 1/10 of the maximum main stress difference for each stage of pressure; recording the applied axial pressure of each stage and the corresponding axial displacement of the sample; gradually releasing the pressure until the applied axial pressure is completely removed; after repeated pressurization and pressure relief for 4 times, axial pressurization is carried out until the pressure is destroyed; making loading curve and unloading curve in the last pressure relief experiment, and calculating elastic modulus E, E ═ delta P/(delta h)e/hc) (ii) a Wherein Δ P is the axial pressureIn kPa; Δ heThe axial elastic deformation of the paddy is expressed in mm; h iscThe height of the rice sample after sample loading is in mm; determining the bulk variable elastic modulus B of the rice sample by adopting a triaxial anisotropic isobaric test, and calculating according to a formula B which is delta sigma/(delta V/V), wherein the delta sigma is the confining pressure increment of the rice sample and the unit is kPa; Δ v is the volume compression of the rice sample in m3(ii) a V is the volume of the rice sample after sample loading, and the unit is m3(ii) a The poisson ratio v is calculated according to the formula v ═ 3B-E)/6B.
7. The finite element analysis-based rice weight measuring method in silos of claim 6, wherein the step (2) of solving the modified Cambridge model by using a large-scale finite element software ABAQUS comprises the following steps: in a Part module of ABAQUS, an axisymmetric CAX4 unit is adopted to create a silo and a rice Part; in the Property module, defining the steel material Property of the silo and the Property of the rice grain heap, selecting a modified Cambridge model to represent the strain and stress relation of the rice grain heap, and then assigning each material Property to each part; assembling two parts of a silo and a rice stack into a whole in an Assembly module; establishing an analysis Step in a Step module; defining a constraint relation between two components in an Interaction module, and describing friction behavior between two surfaces through a friction coefficient; defining Load and boundary conditions in a Load module, wherein the Load is described by volume force; carrying out grid division on the structure in a Mesh module according to components, and dividing the rice heap in the silo into the NxM units; submitting the operation in the Job module for analysis; after the analysis is finished, checking three main strains of each unit of the rice pile in a compaction state in a Visualization module
And height h of each unitnmAccording to
Calculating the volume strain of the n-th layer and m-column unit
In the formula (I), the compound is shown in the specification,
is the three principal strains of the nth layer, m columns of cells; h isnmThe height of the n-th layer, m columns of cells in the compacted state is shown.
8. A method as claimed in claim 7, wherein the parameters of the Cambridge model are determined before the rice weight is measured, and the coefficient of friction μ between the rice and the silo wall and the internal friction angle of the rice heap are determined
Density rho of the surface layer of the rice grain bulk0And the water content MC of the rice heap; determination of the porosity epsilon of the surface layer of a Rice heap0And is composed of0Calculating to obtain the porosity ratio of the surface layer of the rice heap
9. A method as claimed in claim 8, wherein the method comprises measuring the weight of the rice in the silo based on finite element analysis, wherein the internal friction angle of the rice heap
The friction coefficient mu between the paddy and the silo wall is measured by a direct shear apparatus.
10. The method as claimed in claim 8, wherein the porosity e of the surface layer of the rice heap is measured using a porosity measuring instrument for LKY-1 grain0The surface layer of the rice heap has a void ratio of
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| CN2368018Y (en) * | 1999-03-18 | 2000-03-08 | 曹全礼 | Rotary grain measuring apparatus |
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| CN2368018Y (en) * | 1999-03-18 | 2000-03-08 | 曹全礼 | Rotary grain measuring apparatus |
| CN101606580A (en) * | 2008-05-07 | 2009-12-23 | 费尔南多·鲁宾·塞费里诺·巴拉 | Acquisition is used for the method for the full paddy feed of ruminant |
| CN102619531A (en) * | 2012-03-06 | 2012-08-01 | 北京交通大学 | Multi-step sequence construction deformation control method for shallow-buried tunnel with big cross section |
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