CN109299577A - A kind of woods fruit tree dynamic modeling method based on physics bar - Google Patents
A kind of woods fruit tree dynamic modeling method based on physics bar Download PDFInfo
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- 235000013399 edible fruits Nutrition 0.000 title claims abstract description 92
- 238000000034 method Methods 0.000 title claims abstract description 39
- 230000033001 locomotion Effects 0.000 claims abstract description 55
- 238000004088 simulation Methods 0.000 claims abstract description 25
- 238000005452 bending Methods 0.000 claims description 3
- 239000000463 material Substances 0.000 claims description 3
- 238000001228 spectrum Methods 0.000 abstract description 4
- 238000003306 harvesting Methods 0.000 description 8
- 238000010586 diagram Methods 0.000 description 5
- 235000011201 Ginkgo Nutrition 0.000 description 4
- 241000218628 Ginkgo Species 0.000 description 4
- 235000008100 Ginkgo biloba Nutrition 0.000 description 4
- 238000004519 manufacturing process Methods 0.000 description 4
- 230000004044 response Effects 0.000 description 4
- 238000013016 damping Methods 0.000 description 3
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- 238000009313 farming Methods 0.000 description 2
- 230000005484 gravity Effects 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 239000002420 orchard Substances 0.000 description 2
- 240000007049 Juglans regia Species 0.000 description 1
- 235000009496 Juglans regia Nutrition 0.000 description 1
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- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 235000021022 fresh fruits Nutrition 0.000 description 1
- 238000005381 potential energy Methods 0.000 description 1
- 230000001932 seasonal effect Effects 0.000 description 1
- 235000020234 walnut Nutrition 0.000 description 1
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Abstract
The invention discloses a kind of woods fruit tree dynamic modeling method based on physics bar, trunk and limb are using the simulation of the non-extensible physics bar of cross-section or variable cross-section, comprising steps of firstly, setting the length of trunk as l, quality is m, and the angle between limb is θ={ θ1,θ2,...,θk‑1, between trunk and ground by rigidity be kθ1Torsional spring connection, by rigidity be k between limbθ2Torsional spring connection；Then, set the rotation angle of trunk asThe rotation angle of limb is2≤i≤k building woods fruit tree equivalent movement model, with the specified woods fruit tree of motion model simulation；And the movement difference equations of motion model are established using multivariant Lagrange's equation and solution obtains the structural parameters of motion model；Finally, the initial motion position of setting trunk, limb, solves movement difference equations using the Runge-Kutta method of variable step, the resonance frequency for obtaining motion model corresponds to the resonance frequency of woods fruit tree growth as motion model；The present invention preferably can theoretically calculate the eigenfrequency spectrum characteristic for obtaining woods fruit tree.
Description
Technical field
The invention belongs to agriculture and forestry fruit tree production recovery arrangement the field of test technology, specially a kind of woods fruit tree based on physics bar
Dynamic modeling method.
Background technique
China is main production and fruit farming state of the world, and woods fruit type is abundant, is broadly divided into fresh fruit and dry fruit.Woods fruit recovery operations
Not only time-consuming but also laborious, while Seasonal Harvest is strong, collecting time Relatively centralized, labour are costly, expense accounts for about entire woods
Fruit production process cost
50%~70%.For the dry fruits woods fruit such as jujube, walnut, ginkgo, current most effective picking methods are mechanical
Vibration harvest, currently, external main production and fruit farming state generally all realizes the harvesting mechanization of woods fruit, domestic woods fruit recovery operations by
Step tends to mechanization.The kinetic characteristics of research woods fruit tree individual are conducive to reasonably designed and excellent mechanical to vibration harvesting
Change, and Dynamic Modeling is to study the effective means of kinetic characteristics.
Summary of the invention
It is a kind of based on physics bar object of the present invention is to provide for the eigenfrequency spectrum characteristic research of woods fruit tree of coming in every shape
Woods fruit tree dynamic modeling method, this method are realized by constructing the physics bar of prismatic physics bar or variable cross-section to fruit tree life
Long simulation, the method for establishing complicated tree-like woods fruit tree simplified model, preferably can theoretically calculate and obtain woods fruit
The eigenfrequency spectrum characteristic of tree provides certain theoretical basis for the vibration harvesting theory of woods fruit, and specific technical solution is as follows:
A kind of woods fruit tree dynamic modeling method based on physics bar, the trunk of woods fruit tree and limb are all made of non-extensible
Physics bar simulation, the method includes the steps:
S1, length is set as l, the physics bar that quality is m simulates trunk, and sets the angle between the physics bar of simulation limb
Degree is θ={ θ1,θ2,...,θk-1, passing through rigidity between trunk and ground is kθ1Torsional spring connection, between the limb
It is k by rigidityθm, 2≤m≤k torsional spring connection, wherein k indicates the number of the physics bar of simulation limb；
S2, set the rotation angle of trunk asThe rotation angle of limb isConstruct the equivalent fortune of woods fruit tree
Movable model, with the specified woods fruit tree of motion model simulation；
S3, the movement difference equations that the motion model is established using multivariant Lagrange's equation, solve the fortune
Dynamic equation group obtains the structural parameters of the motion model；
S4, the initial motion position for setting trunk, limb solve movement difference equations using the Runge-Kutta method of variable step,
The resonance frequency of the motion model is obtained, using the resonance frequency as the humorous of the corresponding woods fruit tree growth of the motion model
Vibration frequency.
Further, the physics bar is cross-section physics bar.
Further, the physics bar is variable cross-section physics bar.
Further, connection is rotated between the trunk and ground, and connection is rotated between the trunk and limb.
Further, the method also includes steps: the relative position of the trunk and ground rotation is adjusted, described in adjusting
Relative position between limb and trunk is to simulate the growth of corresponding woods fruit tree.
Further, the physics bar for simulating limb is isotropism and the rigid material system that will not occur bending and deformation
It is standby to be formed.
When further, using the trunk and branch of the physics bar simulation woods fruit tree of variable cross-section, meter is further comprised the steps of:
It can be regarded as the centroid position of the variable cross-section for limb, and calculate the rotary inertia of the limb based on the centroid position.
Woods fruit tree dynamic modeling method based on physics bar of the invention, by using cross-section or variable cross-section can not
Limb and the trunk of physics bar simulation woods fruit tree are extended, to construct the equivalent movement model of woods fruit tree, and passes through rotation connection
The physics bar that mode simulates trunk is connect with ground, the same, the connection simulated between limb by way of rotation connection is closed
System, by adjusting as the physics bar of trunk and the relative positional relationship on ground, and as the phase between the physics bar of limb
The growth of woods fruit tree is simulated to positional relationship, and the resonance frequency of woods fruit tree during the growth process is obtained with this；With the prior art
It compares, the true growthform of woods fruit tree can more accurately be depicted by the motion model of building by the present invention, with physics bar
Part carries out necessary simplification to trunk and limb feature, can preferably study the inherent characteristic of woods fruit tree, harvests for woods fruit tree
When excited frequency and amplitude setting provide certain theories integration, be conducive to orchard worker and take corresponding arrange according to analog result
It applies, to ensure that woods fruit tree can have good harvest.
Detailed description of the invention
Fig. 1 is the flow chart signal of the woods fruit tree dynamic modeling method based on physics bar described in the embodiment of the present invention；
Fig. 2 is that the present invention uses sample tree construction schematic diagram.
Fig. 3 is equivalent structure schematic diagram of the sample tree based on cross-section physics bar in the embodiment of the present invention；
Fig. 4 is motion model schematic diagram of the sample tree based on cross-section physics bar in the embodiment of the present invention；
Fig. 5 is variable cross-section limb schematic diagram in the embodiment of the present invention；
Fig. 6 is variable cross-section limb centroid position schematic diagram in the embodiment of the present invention；
Fig. 7 is the equivalent structure signal in the embodiment of the present invention after sample tree simulation growth based on variable cross-section physics bar；
Fig. 8 is the motion model signal in the embodiment of the present invention after sample tree simulation growth based on variable cross-section physics bar.
Specific embodiment
In order to enable those skilled in the art to better understand the solution of the present invention, below in conjunction in the embodiment of the present invention
Attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.
Refering to fig. 1, in embodiments of the present invention, a kind of woods fruit tree dynamic modeling method based on physics bar is provided,
Trunk and limb of the method using non-extensible physics bar simulation woods fruit tree, specifically include step:
Firstly, setting length as l, the physics bar that quality is m simulates trunk, and sets the k limbs simulated by physics bar
Between angle be θ={ θ1,θ2,...,θk-1, passing through rigidity between trunk and ground is kθ1Torsional spring connection, limb
Between by rigidity be kθm, 2≤m≤k torsional spring connection, wherein k indicates the number of the physics bar of simulation limb；Meanwhile
It is k that trunk, which is passed through rigidity,θ1Torsional spring connection on the ground, between limb by rigidity be kθm, 2≤m≤k rotation
Spring connection；Then, set analog tree dry reason bar rotation angle asSimulation limb physics bar rotation angle beThe equivalent movement model of woods fruit tree is constructed, with the specified woods fruit tree of motion model simulation；Specifically, the present invention passes through
The relative position for adjusting trunk and ground rotation adjusts the relative position between limb and trunk to simulate the life of corresponding woods fruit tree
It is long；Then, the movement difference equations of motion model are established using multivariant Lagrange's equation, are solved movement difference equations and are obtained
The structural parameters of motion model；Finally, the initial motion position of setting trunk, limb, is asked using the Runge-Kutta method of variable step
Movement difference equations are solved, the resonance frequency of motion model are obtained, using resonance frequency as the corresponding woods fruit tree growth of motion model
Resonance frequency.
In the specific embodiment of the invention, between trunk and ground rotate connection, between trunk and limb rotation connection and
The physics bar that limb is simulated in the present invention is isotropism and the rigid material that will not occur bending and deformation prepares to be formed.
In addition, in the present invention physics bar can by cross-section or variable cross-section, in conjunction with it is above-mentioned about of the invention based on object
The process steps description of the woods fruit tree dynamic modeling method of bar is managed, while refering to Fig. 2 and Fig. 3, variable cross-section and cross-section physics
The woods fruit tree of bar simulation is the ginkgo with multistage Y type sympodial branching as test sample used tree, it can be seen that, two
Level-one limb is B1Branch and B2Branch, from right side level-one limb B2On derive two second level limb C1Branch and C2Branch；In conjunction with Fig. 2 sample
Set the equivalent structure based on cross-section physics bar, physics bar be cross-section and it is close uniformly, the length of trunk is l1, quality m1, together
It with rigidity is k between groundθ1Torsional spring be attached；The length of first level-one limb B1 is l2, quality m2, with tree
Dry angle is θ2, it is k with rigidityθ2Torsional spring be attached；The length of second level-one limb B2 is l3, quality m3,
Angle with trunk is θ3, it is k with rigidityθ3Torsional spring be attached, bifurcation of two level-one limbs on trunk is
P；First second level limb C1Length be l4, quality m4, it is l apart from main bifurcation point P length6, with second level-one limb
B2Angle be θ4, it is k with rigidityθ4Torsional spring be attached；Second second level limb C2Length be l5, quality m5,
It is l apart from main bifurcation point P length7, the angle with second level-one limb B2 is θ5, it is k with rigidityθ5Torsional spring carry out
Connection；The analog case of equal cross section physics bar respectively and variable cross-section physics bar is described in detail below:
It for prismatic physics bar analog case, referring specifically to Fig. 4, can therefrom obtain, the rotation angle of trunk movement
ForEach limb move when rotation angle beIt can obtain in the case where ignoring gravity and damping, be based on
The total kinetic energy of motion model obtained in method in aforementioned present invention are as follows:Motion model
Total potential energy are as follows:Then, the present invention first passes through the multivariant Lagrange's equation of building:I=1,2,3,4,5, and the woods under cross-section physical analogy is obtained according to the Lagrange's equation
The movement difference equations of Apple Tree System are as follows:
In formula,
Due in movement difference equationsWithBetween there are Non-linear couplings, therefore it is Nonlinear System of Equations, with the non-thread of the movement difference equations
Property embody the elastic connection relationship between trunk and ground, between trunk and limb and between limb and limb, come with this
Simulation embodies the growthform of true woods fruit tree.
For the physics bar analog case of variable cross-section, Fig. 5 and Fig. 6 are please referred to, for using the physics bar of variable cross-section to simulate
The growth of woods fruit tree, the present invention first passes through the centroid position for calculating the variable cross-section as limb, and is calculated and made based on centroid position
For the rotary inertia of the variable cross-section of limb, need first to define unit height diameter attenuation rate in the calculating process of centroid position to be α, and
By formulaExpression；Then pass through formula d (x)=d0The diameter d (x) of any position x on branch is calculated in+α x；
Pass through formulaThe area A (x) that any position x on branch is calculated can；Equally, pass through
FormulaIt can be calculated the elementary mass of the infinitesimal length dx of any position x on branch
dm；Specifically, can be obtained by the calculation formula for the quality m that length is whole section of branch of l in this way:
Centroid position for the variable cross-section as limb is that can pass through formulaIt is calculated, formula
In,For the distance of center of mass point C to o point and the ratio of limb length；This makes it possible to obtain pass through variable cross-section physics bar
The limb of the woods fruit tree of simulation passes through formula around the rotary inertia of mass center are as follows:
；In addition, by variable cross-section physics bar simulate limb around fixed point o rotary inertia calculation formula are as follows:ρ is the mass density of woods fruit tree in formula；It is excellent
Choosing, it is suitable for the woods fruit tree of homogeneous media in the present invention using the method for the physics bar simulation trunk of variable cross-section and limb；This
Sample, so that it may it obtains in the equivalent model that sample tree is simulated based on variable cross-section physics bar, in the case where ignoring gravity and damping,
The movement difference equations of multistage Y type sympodial branching Apple Tree System are as follows:
In formula,
Due in reality in the growth course of ginkgo, the diameter of limb and
Relationship is partial to linear relationship between length, therefore the present invention considers woods by the motion model that variable cross-section physics bar constructs
The allometry relative growth state of fruit tree, in this way, simulated compared to above-mentioned cross-section, can more actual response go out woods fruit tree and growing
Virtual condition in journey achievees the effect that simulate woods fruit tree growth by physical model.
Specifically, the physical model according to the woods fruit tree obtained above constructed based on cross-section and variable cross-section physics bar,
And the structural parameters for the ginkgo fruit tree given such as table 1 are combined, it is set for simulating the initial motion position of physics bar of woods branches of fruit trees
It is set toAnd the present invention is that the feelings of free vibration are carried out in the case where ignoring damping condition
Condition solves above-mentioned movement difference equations with the Runge-Kutta method of variable step in Matlab, dynamic of the trunk in 4s can be obtained
Time-domain response curve；Then, frequency response curve is obtained through Fast Fourier Transform (FFT)；Finally, can be with by frequency response curve
Obtain resonance frequency and experimental test of the woods fruit tree under the equivalent movement Model Condition constructed by physics bar the results are shown in Table 2.
1 fruit tree simplified model parameter of table
2 multistage Y type sympodial branching fruit tree physics rod model of table calculates and resonance frequency/Hz of test
In conjunction with Tables 1 and 2 it is found that calculating item based on cross-section or variable cross-section physics rod model by means of the present invention
Under part, the trunk of woods fruit tree can only all inspire fundamental frequency；And due to being limited by model freedom degree, fruit tree can only inspire and
The resonance frequency of motion model degree of freedom in system same number；Integrate the woods fruit tree based on physics bar it is found that through the invention
Dynamic modeling method can effectively obtain the eigenfrequency spectrum characteristic during woods fruit tree growth, have to the increment study of woods fruit tree
Especially important meaning.
Woods fruit tree dynamic modeling method based on physics bar of the invention, by using cross-section or variable cross-section can not
Limb and the trunk of physics bar simulation woods fruit tree are extended, to construct the equivalent movement model of woods fruit tree, and passes through rotation connection
The physics bar that mode simulates trunk is connect with ground, the same, the connection simulated between limb by way of rotation connection is closed
System, by adjusting as the physics bar of trunk and the relative positional relationship on ground, and as the phase between the physics bar of limb
The growth of woods fruit tree is simulated to positional relationship, and the resonance frequency of woods fruit tree during the growth process is obtained with this；With the prior art
It compares, the true growthform of woods fruit tree can more accurately be depicted by the motion model of building by the present invention, with physics bar
Part carries out necessary simplification to trunk and limb feature, can preferably study the inherent characteristic of woods fruit tree, adopts for the vibration of woods fruit
The setting of time receiving excited frequency and amplitude provides certain theories integration, be conducive to orchard worker take according to analog result it is corresponding
Measure, to ensure that woods fruit tree can have good harvest.
The foregoing is merely a prefered embodiment of the invention, is not intended to limit the scope of the patents of the invention, although referring to aforementioned reality
Applying example, invention is explained in detail, still can be to aforementioned each tool for coming for those skilled in the art
Technical solution documented by body embodiment is modified, or carries out equivalence replacement to part of technical characteristic.All benefits
The equivalent structure made of description of the invention and accompanying drawing content is directly or indirectly used in other related technical areas,
Similarly within the invention patent protection scope.
Claims (7)
1. a kind of woods fruit tree dynamic modeling method based on physics bar, which is characterized in that the trunk of woods fruit tree and limb are adopted
It is simulated with non-extensible physics bar, the method includes the steps:
S1, set length as l, the physics bar that quality is m simulates trunk, and set the angle between the physics bar of simulation limb as
θ={ θ1,θ2,...,θk-1, passing through rigidity between trunk and ground is kθ1Torsional spring connection, pass through between the limb
Rigidity is kθm, 2≤m≤k torsional spring connection, wherein k indicates the number of the physics bar of simulation limb；
S2, set the rotation angle of trunk asThe rotation angle of limb isConstruct the equivalent movement mould of woods fruit tree
Type, with the specified woods fruit tree of motion model simulation；
S3, the movement difference equations that the motion model is established using multivariant Lagrange's equation solve the movement side
Journey group obtains the structural parameters of the motion model；
S4, the initial motion position for setting trunk, limb solve movement difference equations using the Runge-Kutta method of variable step, obtain
The resonance frequency of the motion model, using the resonance frequency as the resonance of the corresponding woods fruit tree growth of motion model frequency
Rate.
2. the woods fruit tree dynamic modeling method according to claim 1 based on physics bar, which is characterized in that the physics
Bar is cross-section physics bar.
3. the woods fruit tree dynamic modeling method according to claim 1 based on physics bar, which is characterized in that the physics
Bar is variable cross-section physics bar.
4. the woods fruit tree dynamic modeling method according to claim 1 based on physics bar, which is characterized in that the trunk
Connection is rotated between ground, and connection is rotated between the trunk and limb.
5. the woods fruit tree dynamic modeling method according to claim 4 based on physics bar, which is characterized in that the method
The relative position for adjusting the trunk and ground rotation is further comprised the steps of:, the relative position between the limb and trunk is adjusted
To simulate the growth of corresponding woods fruit tree.
6. the woods fruit tree dynamic modeling method according to claim 5 based on physics bar, which is characterized in that simulation limb
The physics bar be isotropism and the rigid material that will not occur bending and deformation prepares to be formed.
7. the woods fruit tree dynamic modeling method according to claim 3 based on physics bar, which is characterized in that cut using becoming
When the trunk and branch of the physics bar simulation woods fruit tree in face, the mass center for calculating the variable cross-section as limb is further comprised the steps of:
Position, and calculate based on the centroid position rotary inertia of the limb.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110487584A (en) * | 2019-09-27 | 2019-11-22 | 华南农业大学 | A kind of emulation mandarin tree for spraying target detection and spray characteristics test |
| CN111241739A (en) * | 2020-01-17 | 2020-06-05 | 南京林业大学 | Construction method of fruit tree vibration model with fruits and leaves |
-
2018
- 2018-11-16 CN CN201811366882.8A patent/CN109299577A/en not_active Withdrawn
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110487584A (en) * | 2019-09-27 | 2019-11-22 | 华南农业大学 | A kind of emulation mandarin tree for spraying target detection and spray characteristics test |
| CN111241739A (en) * | 2020-01-17 | 2020-06-05 | 南京林业大学 | Construction method of fruit tree vibration model with fruits and leaves |
| CN111241739B (en) * | 2020-01-17 | 2023-06-23 | 南京林业大学 | Method for constructing vibration model of fruit tree with leaves |
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