CN111241739B - Method for constructing vibration model of fruit tree with leaves - Google Patents
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Abstract
The invention discloses a method for constructing a vibration model of a fruit tree with leaves, which comprises the following steps: scanning the fruit tree branches through a laser scanning device to obtain point cloud information of the fruit tree branches; based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points; two skeleton points with adjacent topological relations are used as two nodes of a space cylindrical beam unit to form a space cylindrical beam unit, and a plurality of space cylindrical beam units are sequentially connected according to the topological relations to form a tree trunk vibration model; obtaining the distribution rule of fruits and leaves on the fruit trees in a statistical mode; E. and combining the vibration model of the fruit tree trunk, the distribution rule of the fruits and the leaves on the fruit tree to obtain the vibration model of the fruit tree with the leaves. According to the invention, the vibration model is constructed by combining the laser scanning technology with the finite element method, and the natural frequency of the fruit tree is calculated by adopting the vibration model, so that the method is more suitable for accurate vibration harvesting of the orchard.
Description
Technical Field
The invention relates to the field of harvesting of fruit trees in agriculture and forestry, in particular to a method for constructing a vibration model of a fruit tree with leaves.
Background
The harvesting operation of the forest fruits is the most time-consuming and labor-consuming link in the production of the forest fruits, and the most effective harvesting mode at present is mechanical vibration harvesting for dry fruit type forest fruits such as red dates, walnuts and gingko, wherein the harvesting effect of the vibration harvesting machine is related to various factors including the growth characteristics of fruit trees and the working parameters of mechanical vibration. In the past, students at home and abroad study the vibration of the fruit tree by establishing a simplified mechanical model of the vibration of the trunk and the branches, and in recent years, a plurality of students utilize a three-dimensional modeling and finite element method to analyze the mode and vibration response of the fruit tree. However, the traditional modeling mode is only suitable for modeling the fruit tree with complex multi-morphology after being greatly simplified, and the finite element modeling method can construct a model of the fruit tree with complex morphology, but the traditional modeling method ignores the influence of leaves and fruits on the fruit tree, and the theoretical model has practical application value and guiding significance in response to modeling the fruit-bearing and leaf-bearing fruit tree which is more consistent with the actual fruit tree with complex morphology.
Disclosure of Invention
The invention aims at solving the problems existing in the prior art and provides a method for constructing a vibration model of a fruit tree with leaves; according to the construction method, the laser scanning technology is combined with the finite element method, so that the mode characteristics of the fruit trees can be well calculated according to the study on the mode characteristics of the fruit trees in the field of forest fruit vibration harvesting, and the natural frequency of any fruit tree is calculated according to the vibration model, so that the construction method is more suitable for accurate vibration harvesting of the orchard.
The invention aims at solving the problems through the following technical scheme:
a method for constructing a vibration model of a fruit tree with leaves is characterized by comprising the following steps: the construction method comprises the following steps:
A. scanning the fruit tree branches through a laser scanning device to obtain point cloud information of the fruit tree branches;
B. based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points;
C. two skeleton points with adjacent topological relations are used as two nodes of a space cylindrical beam unit to form a space cylindrical beam unit, and a plurality of space cylindrical beam units are sequentially connected according to the topological relations to form a tree trunk vibration model;
D. obtaining the distribution rule of fruits and leaves on the fruit trees in a statistical mode;
E. and C, combining the vibration model of the fruit tree branches in the step C with the distribution rule of the fruits and the leaves on the fruit tree in the step D to obtain the vibration model of the fruit tree with the leaves.
The fruit tree branches in the step A are the fruit tree branches without fruit and leaves, and the best scheme is that the point cloud information adopted by the fruit tree branches without fruit and leaves is the most clear; in essence, the laser scanning device is used for scanning the fruit tree branch with leaves, and the point cloud information of the fruit tree branch can be obtained.
Because the fruit tree is in linear vibration under small deformation vibration, the vibration of the fruit tree can be regarded as space rigid body vibration, so the fruit tree vibration model with leaves in the step E is to apply a three-dimensional space cylinder beam structure damping general vibration differential equation in a mechanical vibration theory to the fruit tree, and form a fruit tree vibration differential equation:
in the formula (1) [ K ]]、[C]And [ M ]]Respectively a rigidity matrix, a damping matrix and a quality matrix of the fruit tree; quality matrix of fruit tree [ M]From a branch quality matrix [ M z ]Leaf quality matrix [ M ] y ]And fruit quality matrix [ M ] g ]Three parts are formed; rigidity matrix [ K ] of fruit tree]The system consists of branch stiffness matrixes;
{ u } is the acceleration vector, the velocity vector and the displacement vector of the skeleton point respectively; { p (t) } is the excitation force vector.
The fruit tree trunk vibration model in the step C obtains a mass matrix and a rigidity matrix of the 6-degree-of-freedom space cylindrical beam unit according to the finite element theory, namely a tree branch mass matrix [ M ] z ]And stiffness matrix of fruit tree [ K ]]：
In the formulas (2) and (3), r is the radius of the corresponding node space cylindrical beam, and the sectional area A=pi r of the corresponding space cylindrical beam unit 2 The method comprises the steps of carrying out a first treatment on the surface of the m is the unit mass of the corresponding space cylindrical beam unit; l is the unit length, i.e. the linear distance between two adjacent skeleton points; tensile stiffness H of a spatial cylindrical beam m =ea; the torsional rigidity of the space cylindrical beam is H t ＝Gmr 2 2; bending strength H of space cylindrical beam around y axis y ＝Em(3r 2 +L 2 ) Flexural Strength H of a spatial cylindrical Beam around the z-axis z ＝Em(3r 2 +L 2 ) 12; e is the elastic modulus of the fruit tree; g is the shear modulus of the fruit tree.
The distribution rule of the fruits and the leaves on the fruit tree in the step D comprises the branch diameter rule of the growing fruits and the leaves and the average number n of the fruits on the branches with unit length g And the average number of leaves n y Mass m of average individual fruit g Average individual leaf mass m y Obtaining [ M ] according to finite element theory y ]And fruit quality matrix [ M ] g ]；
Obtaining a quality matrix [ M ] of the fruit tree according to formulas (2), (4) and (5):
[M]＝[M z ]+[M y ]+[M g ] (6)
substituting the formula (6) into the formula (1) to obtain a new fruit tree vibration differential equation of the fruit tree vibration model with leaves:
when the natural frequency of the fruit tree is calculated, the damping term of the fruit tree is zero, no external excitation term is applied, and a simplified undamped free vibration differential equation of the fruit tree is obtained:
according to the mode shape definition in the linear vibration theory, when the fruit tree is in a certain mode shape { phi }, the ratio of the amplitudes of each point of the fruit tree is unique, and the displacement vibration response formula of each point when the fruit tree vibrates under the mode shape { phi }, is as follows:
{u}＝{φ}sin(ωt+θ) (9)
in the formula (9), ω represents a response frequency; t represents a time variable; θ represents the phase difference between the response and the excitation; taking equation (9) into equation (8) to cancel the co-factor yields:
([K]-ω 2 [M]){φ}＝{0} (10)
simplifying root constraint into fixed end constraint, combining formulas (10) and (3), eliminating the first 6 degrees of freedom of the bottom nodes of the fruit tree, and solving the characteristic determinant of the formula (10) to obtain the natural frequency of the fruit tree model constructed by the 6-degree-of-freedom three-dimensional space beam unit.
Compared with the prior art, the invention has the following advantages:
the construction method comprises the steps of scanning fruit tree branches through laser scanning equipment to obtain point cloud information of the fruit tree branches; based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points; constructing a fruit tree branch rod vibration model by adopting a finite element method; researching the distribution rule of fruits and leaves on the fruit tree in a statistical mode, constructing a vibration model with the fruits and the leaves, and calculating the natural frequency of the fruit tree by adopting the model; according to the construction method, the laser scanning technology is combined with the finite element method, so that the mode characteristics of the fruit trees can be well calculated according to the study on the mode characteristics of the fruit trees in the field of forest fruit vibration harvesting, and the natural frequency of any fruit tree is calculated according to the vibration model, so that the construction method is more suitable for accurate vibration harvesting of the orchard.
Drawings
FIG. 1 is a flow chart of a method for constructing a vibration model of a fruit tree with leaves;
FIG. 2 is a point cloud and skeleton point diagram of branches and stems of a fruit tree;
FIG. 3 is a vibration model of the branches of the fruit tree;
fig. 4 is a diagram of fundamental frequency vibration patterns of fruit trees obtained by solving natural frequencies of fruit trees by using the vibration model of the fruit tree with leaves constructed by the invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
As shown in fig. 1: a method for constructing a vibration model of a fruit tree with leaves comprises the following steps: A. scanning the fruit tree branches through a laser scanning device to obtain point cloud information of the fruit tree branches; B. based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points; C. two skeleton points with adjacent topological relations are used as two nodes of a space cylindrical beam unit to form a space cylindrical beam unit, and a plurality of space cylindrical beam units are sequentially connected according to the topological relations to form a tree trunk vibration model; D. obtaining the distribution rule of fruits and leaves on the fruit trees in a statistical mode; E. and C, combining the vibration model of the fruit tree branches in the step C with the distribution rule of the fruits and the leaves on the fruit tree in the step D to obtain the vibration model of the fruit tree with the leaves.
In the construction method, the fruit tree branches in the step A are the fruit tree branches without fruit and leaves, and the best scheme is that the point cloud information adopted by the fruit tree branches without fruit and leaves is the most clear; in essence, the laser scanning device is used for scanning the fruit tree branch with leaves, and the point cloud information of the fruit tree branch can be obtained.
Further, the fruit tree trunk vibration model in the step C obtains a 6-degree-of-freedom space cylinder according to the finite element theoryMass and stiffness matrices of beam units, i.e. branch mass matrices [ M ] z ]And stiffness matrix of fruit tree [ K ]]：
In the formulas (2) and (3), r is the radius of the corresponding node space cylindrical beam, and the sectional area A=pi r of the corresponding space cylindrical beam unit 2 The method comprises the steps of carrying out a first treatment on the surface of the m is the unit mass of the corresponding space cylindrical beam unit; l is the unit length, i.e. the linear distance between two adjacent skeleton points; tensile stiffness H of a spatial cylindrical beam m =ea; the torsional rigidity of the space cylindrical beam is H t ＝Gmr 2 2; bending strength H of space cylindrical beam around y axis y ＝Em(3r 2 +L 2 ) Flexural Strength H of a spatial cylindrical Beam around the z-axis z ＝Em(3r 2 +L 2 ) 12; e is the elastic modulus of the fruit tree; g is the shear modulus of the fruit tree.
The distribution rule of the fruits and the leaves on the fruit tree in the step D comprises the branch diameter rule of the growing fruits and the leaves and the average number n of the fruits on the branches with unit length g And the average number of leaves n y Mass m of average individual fruit g Average individual leaf mass m y Obtaining [ M ] according to finite element theory y ]And fruit quality matrix [ M ] g ]；
Obtaining a quality matrix [ M ] of the fruit tree according to formulas (2), (4) and (5):
[M]＝[M z ]+[M y ]+[M g ] (6)
in the formula (6) [ M ]]Is a quality matrix of the fruit tree; quality matrix of fruit tree [ M]From a branch quality matrix [ M z ]Leaf quality matrix [ M ] y ]And fruit quality matrix [ M ] g ]Three parts are formed; because the fruit tree is in linear vibration under small deformation vibration, the vibration of the fruit tree can be regarded as space rigid body vibration, so the fruit tree vibration model with leaves in the step E is to apply a three-dimensional space cylinder beam structure with damping general vibration differential equation in a mechanical vibration theory to the fruit tree, and a fruit tree vibration differential equation is formed:
in the formula (1) [ K ]]、[C]And [ M ]]Respectively a rigidity matrix, a damping matrix and a quality matrix of the fruit tree; rigidity matrix [ K ] of fruit tree]The system consists of branch stiffness matrixes;
{ u } is the acceleration vector, the velocity vector and the displacement vector of the skeleton point respectively; { p (t) } is an excitation force vector; substituting the formula (6) into the formula (1) to obtain a new fruit tree vibration differential equation of the fruit tree vibration model with leaves:
when the vibration model of the fruit tree with leaves, which is constructed by the invention, is used, because the actual damping of the fruit tree is very small, when the natural frequency of the fruit tree is calculated, the damping item of the fruit tree can be ignored and no external excitation item is applied, namely, the damping item and the excitation vector of the fruit tree are zero, and the simplified undamped free vibration differential equation of the fruit tree is obtained:
according to the mode shape definition in the linear vibration theory, when the fruit tree is in a certain mode shape { phi }, the ratio of the amplitudes of each point of the fruit tree is unique, and the displacement vibration response formula of each point when the fruit tree vibrates under the mode shape { phi }, is as follows:
{u}＝{φ}sin(ωt+θ) (9)
in the formula (9), ω represents a response frequency; t represents a time variable; θ represents the phase difference between the response and the excitation; taking equation (9) into equation (8) to cancel the co-factor yields:
([K]-ω 2 [M]){φ}＝{0} (10)
and simplifying root constraint into fixed end constraint, eliminating the first 6 degrees of freedom of the bottom node of the fruit tree, and solving the characteristic determinant of the solution (10) to obtain the natural frequency of the fruit tree model constructed by the 6-degree-of-freedom three-dimensional space beam unit.
Example 1
In this embodiment, gingko is taken as an example to provide a method for constructing a vibration model of a fruit tree with leaves, and fig. 1 is a diagram of application steps of this embodiment. The details of fig. 1 are developed below.
Acquiring point cloud information of a fruit tree in a no-fruit and no-leaf state by using laser scanning equipment, and extracting skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and topological relations among the skeleton points, wherein the result is shown in figure 2; two skeleton points with adjacent topological relations are used as two nodes of a space cylindrical beam unit to form the space cylindrical beam unit, the fruit tree branch vibration model is formed by sequentially connecting a plurality of constructed space cylindrical beam units according to the topological relations, the result is shown in figure 3, and a branch quality matrix [ M ] is obtained based on finite element theory z ]And stiffness matrix of fruit tree [ K ]]The method comprises the steps of carrying out a first treatment on the surface of the Harvesting a small ginkgo tree with fruits and leaves suitable for indoor test in university campus of Nanjing forestry, researching the distribution rule of leaves and fruits at 317 axillary buds on the indoor ginkgo tree, and knowing the average number n of fruits on unit length g =1.43, average mass m of individual fruits g =6g; the actual fruits grow on branches with the diameter of 3-10mm, so that only units with the diameter of less than or equal to 10mm are listed in the ginkgo tree branch model, and an additional fruit quality matrix [ M ] is calculated by using the formula (4) g ]Average number of leaves per unit length n y =1.32, average mass m of individual leaves y For units with diameters less than or equal to 12mm in the branch model, the leaf mass matrix [ M ] is calculated by applying (5) =0.4g y ]. The mass matrix of the ginkgo tree fruit and leaf vibration model can be calculated by applying the formula (6), and the vibration differential equation of the ginkgo tree fruit and leaf can be obtained by combining the formula (1) or the formula (7). Further, the natural frequencies of the ginkgo tree with leaves can be calculated by combining the formulas (8), (9) and (10), and the fundamental frequency vibration modes are shown in table one and figure 4. When the fruit tree is excited by adopting the resonance frequency, the fruit tree can be strongly vibrated by using smaller energy, so that vibration harvesting is realized. By adopting the method, a large number of natural frequencies of the fruit trees are obtained in a calculation mode, and the vibration frequency of the harvesting machine in actual vibration harvesting is selected according to the calculation result. The natural frequency of any fruit tree can be calculated by the method, so that the method is more suitable for accurate vibration harvesting of the orchard.
Table one natural frequency of the fruit-bearing leafy ginkgo tree
The construction method comprises the steps of scanning fruit tree branches through laser scanning equipment to obtain point cloud information of the fruit tree branches; based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points; constructing a fruit tree branch rod vibration model by adopting a finite element method; researching the distribution rule of fruits and leaves on the fruit tree in a statistical mode, constructing a vibration model with the fruits and the leaves, and calculating the natural frequency of the fruit tree by adopting the model; according to the construction method, the laser scanning technology is combined with the finite element method, so that the mode characteristics of the fruit trees can be well calculated according to the study on the mode characteristics of the fruit trees in the field of forest fruit vibration harvesting, and the natural frequency of any fruit tree is calculated according to the vibration model, so that the construction method is more suitable for accurate vibration harvesting of the orchard.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by the above embodiments, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention; the technology not related to the invention can be realized by the prior art.
Claims (3)
1. A method for constructing a vibration model of a fruit tree with leaves is characterized by comprising the following steps: the construction method comprises the following steps:
A. scanning the fruit tree branches through a laser scanning device to obtain point cloud information of the fruit tree branches;
B. based on the obtained fruit tree point cloud information, extracting topological relations among skeleton points of fruit tree branches, fruit tree radiuses at the skeleton points and the skeleton points;
C. two skeleton points with adjacent topological relations are used as two nodes of a space cylindrical beam unit to form a space cylindrical beam unit, and a plurality of space cylindrical beam units are sequentially connected according to the topological relations to form a tree trunk vibration model;
D. obtaining the distribution rule of fruits and leaves on the fruit trees in a statistical mode;
E. combining the vibration model of the fruit tree branches in the step C with the distribution rule of the fruits and leaves on the fruit tree in the step D to obtain a vibration model of the fruit tree with the leaves;
the fruit tree trunk vibration model in the step C obtains a mass matrix and a rigidity matrix of the 6-degree-of-freedom space cylindrical beam unit according to the finite element theory, namely a tree branch mass matrix [ M ] z ]And stiffness matrix of fruit tree [ K ]]：
In the formulas (2) and (3), r is the radius of the corresponding node space cylindrical beam, and the sectional area A=pi r of the corresponding space cylindrical beam unit 2 The method comprises the steps of carrying out a first treatment on the surface of the m is the unit mass of the corresponding space cylindrical beam unit; l is the unit length, i.e. the linear distance between two adjacent skeleton points; tensile stiffness H of a spatial cylindrical beam m =ea; the torsional rigidity of the space cylindrical beam is H t ＝Gmr 2 2; bending strength H of space cylindrical beam around y axis y ＝Em(3r 2 +L 2 ) Flexural Strength H of a spatial cylindrical Beam around the z-axis z ＝Em(3r 2 +L 2 ) 12; e is the elastic modulus of the fruit tree; g is the shear modulus of the fruit tree;
the distribution rule of the fruits and the leaves on the fruit tree in the step D comprises the branch diameter rule of the growing fruits and the leaves and the average number n of the fruits on the branches with unit length g And the average number of leaves n y Mass m of average individual fruit g Average individual leaf mass m y Obtaining a leaf quality matrix [ M ] according to a finite element theory y ]And fruit quality matrix [ M ] g ]；
Obtaining a quality matrix [ M ] of the fruit tree according to formulas (2), (4) and (5):
[M]＝[M z ]+[M y ]+[M g ] (6)
substituting the formula (6) into the formula (1) to obtain a new fruit tree vibration differential equation of the fruit tree vibration model with leaves:
the fruit tree vibration model with leaves in the step E is formed by applying a general vibration differential equation with damping of a three-dimensional space cylindrical beam structure in a mechanical vibration theory to a fruit tree to form a fruit tree vibration differential equation:
in the formula (1) [ K ]]、[C]And [ M ]]Respectively a rigidity matrix, a damping matrix and a quality matrix of the fruit tree; quality matrix of fruit tree [ M]From a branch quality matrix [ M z ]Leaf quality matrix [ M ] y ]And fruit quality matrix [ M ] g ]Three parts are formed; rigidity matrix [ K ] of fruit tree]The system consists of branch stiffness matrixes;
{ u } is the acceleration vector, the velocity vector and the displacement vector of the skeleton point respectively; { p (t) } is the excitation force vector.
2. The method for constructing the vibration model of the fruit tree with leaves according to claim 1, wherein the method comprises the following steps: and (C) the fruit tree branches in the step A are fruit tree branches without fruits and leaves.
3. A method for calculating natural frequencies of fruit trees by using the fruit tree with leaves vibration model constructed by the method for constructing the fruit tree with leaves vibration model according to claim 1, which is characterized in that: when the natural frequency of the fruit tree is calculated, the damping term of the fruit tree is zero, no external excitation term is applied, and a simplified undamped free vibration differential equation of the fruit tree is obtained:
according to the mode shape definition in the linear vibration theory, when the fruit tree is in a certain mode shape { phi }, the ratio of the amplitudes of each point of the fruit tree is unique, and the displacement vibration response formula of each point when the fruit tree vibrates under the mode shape { phi }, is as follows:
{u}＝{φ}sin(ωt+θ) (9)
in the formula (9), ω represents a response frequency; t represents a time variable; θ represents the phase difference between the response and the excitation; taking equation (9) into equation (8) to cancel the co-factor yields:
([K]-ω 2 [M]){φ}＝{0} (10)
simplifying root constraint into fixed end constraint, combining formulas (10) and (3), eliminating the first 6 degrees of freedom of the bottom nodes of the fruit tree, and solving the characteristic determinant of the formula (10) to obtain the natural frequency of the fruit tree model constructed by the 6-degree-of-freedom three-dimensional space beam unit.
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