Derivation method of empirical formula for trunk frequency of Camellia oleifera tree based on allometric law

Abstract

The present invention discloses a method for deriving an empirical formula for the trunk frequency of a tea oil tree based on the law of allometric growth, and belongs to the technical field of tree natural frequency calculation. The method defines an ideal branching model of a tea oil tree, measures allometric growth parameters, and then simulates and analyzes the natural frequency of the trunk of the tree, and finally derives an empirical formula for the natural frequency of the tea oil tree. Based on the principle of energy conservation, the present invention uses a parameter identification method to derive an empirical formula for calculating the first-order natural frequency of the trunk of a basic unit of a two-branch tea oil tree, and compares the simulated natural frequency to verify the accuracy of the empirical formula, thereby providing a theoretical basis for the design and optimization of a vibration picking device.

Description

Technical Field

[0001] The invention belongs to the technical field of tree natural frequency calculation, and in particular relates to a method for deriving an empirical formula for the trunk frequency of an oil-tea tree based on the law of allometric growth. Background Art

[0002] The natural frequency refers to a specific frequency determined only by the nature of the system itself when the structural system is stimulated by external factors and moves. It is also called the natural frequency. The natural frequency has nothing to do with external excitation and is an inherent property of the tree. Regardless of whether there is external excitation, the natural frequency of the tree exists. When there is external excitation, the tree will vibrate in response to the natural frequency. Vibrating picking devices mostly generate high-frequency or low-amplitude vibrations through vibration. The vibration transmits the mechanical vibrations generated by the fuselage to the tree, which swings to generate impact force and causes the fruit to fall. However, the current vibration picking does not control the vibration frequency. Strong vibration and inappropriate vibration frequency will reduce the picking rate and cause damage to the tree.

[0003] Therefore, it is urgent to invent a method for deriving an empirical formula for the trunk frequency of tea oil trees based on the law of allometric growth, so as to provide a theoretical basis for the design and optimization of vibration picking devices. Summary of the invention

[0004] The present invention discloses a method for deriving an empirical formula for the trunk frequency of a tea oil tree based on the law of allometric growth, which provides a theoretical basis for the design and optimization of a vibration picking device and a theoretical basis for optimal operating parameters in vibration harvesting, so that the vibration picking device can control the external vibration frequency within a certain range, reduce tree damage, and greatly improve the picking rate, thereby overcoming the shortcoming of low efficiency of manual picking, thereby effectively solving at least one technical problem involved in the background technology.

[0005] To achieve the above object, the technical solution of the present invention is:

[0006] A method for deriving an empirical formula for the trunk frequency of a tea oil tree based on the law of allometric growth comprises the following steps:

[0007] Step 1, defining an ideal branching model of the tea tree;

[0008] Step 2, measuring the allometric growth parameters of the oil-tea tea tree;

[0009] Step 3, simulation analysis of the natural frequency of the tea tree;

[0010] Step 4: Derive the empirical formula for the natural frequency of the tree.

[0011] As a preferred improvement of the present invention, the step 1 specifically comprises the following steps:

[0012] Step 11, define the ideal tea tree as an infinitely iterated unidirectional tree consisting of cylindrical branches of different diameters and lengths;

[0013] Step 12, the length and diameter of the cylindrical branch satisfy the allometric growth law, and the expressions of the area reduction coefficient λ and the allometric growth coefficient β in the allometric growth law are as follows:

[0014]

[0015]

[0016] Where D k is the branch diameter of the kth segment of the tree, L k is the branch length of the kth segment of the tree.

[0017] As a preferred improvement of the present invention, the step 1 further comprises the following steps:

[0018] Step 13, generating an ideal tree algorithm, specifically includes:

[0019] Given the trunk diameter D1, length L1 and angle of the tree;

[0020] The first branch appears and the branch diameter is calculated and branch length

[0021] The ideal branching model of Camellia oleifera tree was obtained by iterative arrangement in the same direction.

[0022] As a preferred improvement of the present invention, the step 2 specifically comprises the following steps:

[0023] Step 21, select a bifurcated branch, measure the length and diameter of the main branch and the two branches respectively, and use an angle measuring instrument to measure the angle between the two branches, and record the measurement results;

[0024] Step 22, performing polynomial fitting on the measurement results to obtain the area reduction coefficient λ, the allometric coefficient β and the range of the angle between the two branches;

[0025] Step 23, measuring the bending elastic modulus of the tree branch to obtain the bending elastic modulus of the tree branch.

[0026] As a preferred improvement of the present invention, the step 3 includes creating a binary branch tea oil tree simulation model, performing finite element simulation analysis, and obtaining the simulated natural frequency of the tree.

[0027] As a preferred improvement of the present invention, the step 4 specifically comprises the following steps:

[0028] Step 41, obtaining the torsional elastic coefficient of the tree trunk;

[0029] Step 42, calculating the moment of inertia of the trunk and the sum of the moment of inertia of the branches;

[0030] Step 43, according to the trunk moment of inertia and the branch moment of inertia, the empirical formula of the natural frequency of the trunk is obtained, which is expressed as follows:

[0031]

[0032] Where E is the bending elastic modulus, I is the section inertia moment, m is the mass of the tree trunk, l1 is the trunk length, α is the unknown coefficient, d2 is the branch diameter, l2 is the branch length, It is half the angle between the two branches.

[0033] Beneficial effects of the invention: The invention provides a theoretical basis for the design and optimization of a vibration picking device, and provides a theoretical basis for the optimal operating parameters in vibration harvesting, so that the vibration picking device can control the external vibration frequency within a certain range, reduce tree damage, and greatly improve the picking rate, overcoming the shortcoming of low efficiency of manual picking. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0035] Figure 1 A schematic diagram of an ideal tea tree with sympodial branches provided by the present invention;

[0036] Figure 2 A schematic diagram of the actual measurement of the dichotomous tea tree provided by the present invention;

[0037] Figure 3 A schematic diagram of the measurement data of the basic unit of the dichotomy of the oil-tea tree provided by the present invention;

[0038] Figure 4 A schematic diagram of the calculation results of the area reduction coefficient λ provided by the present invention;

[0039] Figure 5 This is a test diagram of the elastic modulus of oil-tea tree branches provided by the present invention;

[0040] Figure 6 A schematic diagram of displacement-load results of a bending test of a tea tree branch provided by the present invention;

[0041] Figure 7 A schematic diagram of a binary bifurcation tea oil tree simulation model provided by the present invention;

[0042] Figure 8 A schematic diagram of the vibration mode of the first-order frequency of the dichotomous tea tree provided by the present invention;

[0043] Fig. 9 A schematic diagram of the first-order natural frequency simulation value provided by the present invention;

[0044] Fig.10 A comparison chart of the empirical formula calculation value of the natural frequency with the branching angle provided by the present invention and the ANSYS simulation value;

[0045] Fig.11 A comparison chart of the empirical formula calculation value of the natural frequency with the trunk length provided by the present invention and the ANSYS simulation value;

[0046] Fig.12 This is a comparison chart of the empirical formula calculation value of the natural frequency as the trunk diameter changes provided by the present invention and the ANSYS simulation value. DETAILED DESCRIPTION

[0047] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0049] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0050] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0051] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0052] The present invention provides a method for deriving an empirical formula of the natural frequency of a tree trunk based on the law of allometric growth, comprising the following steps:

[0053] Step 1, defining an ideal branching model of the tea tree;

[0054] The step 1 specifically comprises the following steps:

[0055] Step 11, define the ideal tea tree as an infinitely iterated unidirectional tree consisting of cylindrical branches of different diameters and lengths, such as Figure 1 As shown;

[0056] Step 12, the length and diameter of the cylindrical branch satisfy the allometric growth law, and the expressions of the area reduction coefficient λ and the allometric growth coefficient β in the allometric growth law are as follows:

[0057]

[0058]

[0059] Where D k is the branch diameter of the kth segment of the tree, L k is the branch length of the kth segment of the tree;

[0060] Step 13, generating an ideal tree algorithm, specifically includes:

[0061] Given the trunk diameter D1, length L1 and angle of the tree;

[0062] The first branch appears and the branch diameter is calculated and branch length

[0063] The ideal branching model of Camellia oleifera tree was obtained by iterative arrangement in the same direction.

[0064] Step 2, measuring allometric growth parameters, specifically includes the following steps:

[0065] Step 21, select the oil tea tree of the variety Huaxin as the test object to conduct field measurement test, such as Figure 2 Select appropriate two-branched tea tree branches, measure the length and diameter of the main branch, as well as the length and diameter of the two branches, and then use an angle measuring instrument to measure the angle between the two branches. A total of 5 typical samples were measured and the measurement results were recorded. The specific measurement results are shown in Figure 3 As shown;

[0066] Step 22, according to the expression of the allometric coefficient β in step 12, the allometric coefficient Solving β using the linear regression equation yields:

[0067]

[0068] Where P is a constant. Figure 3 The measured data in were fitted with polynomials using MATLAB, and β = 1.333, P = -0.04046 were obtained.

[0069] Will Figure 3 Substituting the measured data in into the expression of area reduction coefficient λ, the mean calculation method is used to calculate the area reduction coefficient λ of 5 typical samples = 0.4926. The calculation results of the two branches are as follows: Figure 4 shown.

[0070] Step 23, use an electronic scale to measure the mass of the branches, and then use the water immersion method to measure the volume of the branches. The average density of the Huaxin oil tea tree is calculated to be 1.038 g / cm 3 The bending elastic modulus of the tea tree branches was measured using a universal testing machine. A downward force was applied to the middle of the branch and the deformation displacement was recorded. The expression of the bending elastic modulus is as follows:

[0071]

[0072] Where E is the bending elastic modulus, l is the span, d is the branch diameter, F is the external load, and f is the deflection. Figure 5 As shown, a three-point bending test was performed with a test span of 50 mm and a pressure head movement speed of 10 mm / min. The load and deformation displacement curves of the bending test were recorded, as shown in Figure 6 shown.

[0073] Calculate the diameter of branches of different Substituting it into the elastic modulus calculation formula, the bending elastic modulus of the tea tree branches was obtained, and the average value of 8 sets of data, 1367.09 MPa, was taken as the average bending elastic modulus of the Huaxin tea tree branches.

[0074] Step 3, simulation analysis of the natural frequency of the tree;

[0075] The ANSYS software was used to create a simulation model of a dichotomous tea tree. Figure 7 The finite element simulation analysis of the dichotomous tea tree model was performed to obtain the modal vibration diagram of the first-order frequency of the tea tree body, as shown in Figure 8 Specifically, the angles of the two-branched tea tree branches shown in the figure are all 60°.

[0076] A simulation model of a tea tree with the same other parameters but different angles between the two bifurcated branches was established to obtain the simulated natural frequencies of the trunk of the tea tree at different angles, such as Fig. 9 shown.

[0077] Step 4, derive the empirical formula of the tree's natural frequency;

[0078] The step 4 specifically comprises the following steps:

[0079] Step 41, obtaining the torsional elastic coefficient of the tree trunk;

[0080] Step 42, calculating the moment of inertia of the trunk and the sum of the moment of inertia of the branches;

[0081] The trunk moment of inertia is

[0082] The expression of the sum of the branch moments of inertia is:

[0083]

[0084] Step 43, according to the trunk moment of inertia and the branch moment of inertia, the empirical formula of the natural frequency of the trunk is obtained, which is expressed as follows:

[0085]

[0086] In the formula, α is the unknown coefficient. To determine the value of the unknown coefficient, taking the trunk length l1 = 194.00 mm and the diameter d1 = 19.98 mm as an example, the branch length l2 = 148.60 mm and the diameter d2 = 14.13 mm are calculated, and the value of α can be obtained by combining the simulation data. The final average of α is 1.45, and the empirical formula expression is determined as:

[0087]

[0088] Where E is the bending elastic modulus.

[0089] During the experiment, first keep the trunk diameter and length unchanged, change the angle between branches, and compare the simulation value with the value calculated by the empirical formula. Taking the trunk length l1=400.00mm as an example, according to the relationship between the trunk length and the diameter, the trunk diameter d1=37.01mm can be obtained. Substituting the data into the expression of step 12, we can get l2=228.26mm, d2=20.23mm. Substituting the above data into the empirical formula of step 4, we can get the value calculated by the empirical formula. ANSYS Mechanical APDL 2020 software was used to create a two-branched tea oil tree simulation model, and a two-branched tea oil tree simulation model with multiple angle changes but unchanged length and diameter was established. The calculated value of the first-order frequency of the tree trunk was compared with the simulation value, as shown in the figure. Fig.10 As shown, the maximum error between the simulated value and the calculated value of the natural frequency corresponding to the angle change is 0.26%.

[0090] During the experiment, the trunk length l1=400.00mm is taken as an example, and the angle between the two branches is determined to be 60°. The trunk length is changed by increasing by 20mm each time, and then the trunk diameter is obtained based on the relationship between the trunk length and the diameter. Substitute the obtained trunk length and diameter into the expression of step 12 to obtain the length and diameter of the two branches. Substitute the above data into the empirical formula to obtain the calculated value of the empirical formula, and use ANSYS MechanicalAPDL 2020 software to create a two-branched tea oil tree simulation model, and establish multiple two-branched tea oil tree simulation models in which the angle does not change but the length changes and the diameter changes. The calculated value of the first-order frequency of the tree trunk is compared with the simulation value. Fig.11 As shown, the empirical formula calculated value of the first-order frequency of the tree trunk with the trunk length is almost consistent with the simulation value curve, and the maximum error is 0.09%.

[0091] In the experiment, the trunk diameter d1=30.00mm is taken as an example, and the angle between the two branches is determined to be 60°. The trunk diameter is changed by increasing by 2mm each time, and then the trunk length is obtained based on the relationship between the trunk length and the diameter. Substitute the obtained trunk length and diameter into the expression of step 12 to obtain the length and diameter of the two branches. Substitute the above data into the empirical formula to obtain the empirical formula calculation value, and use ANSYS MechanicalAPDL 2020 software to create a two-branched tea oil tree simulation model, and establish multiple two-branched tea oil tree simulation models in which the angle does not change but the diameter changes and the length changes. The calculated value of the first-order frequency of the tree trunk is compared with the simulation value. Fig.12 As shown, the empirical formula calculated value of the first-order frequency of the tree trunk as the trunk diameter changes is almost consistent with the simulation value curve, and the maximum error is 0.1%.

[0092] Beneficial effects of the invention: The invention provides a theoretical basis for the design and optimization of a vibration picking device, and provides a theoretical basis for the optimal operating parameters in vibration harvesting, so that the vibration picking device can control the external vibration frequency within a certain range, reduce tree damage, and greatly improve the picking rate, overcoming the shortcoming of low efficiency of manual picking.

[0093] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for deriving an empirical formula for the trunk frequency of oil tea trees based on the law of allometric growth, characterized in that: The following steps are involved: Step 1, defining an ideal branching model of a tea tree; specifically comprising the following steps: Step 11, define the ideal tea tree as an infinitely iterated unidirectional tree consisting of cylindrical branches of different diameters and lengths; Step 12, the length and diameter of the cylindrical branch satisfy the allometric growth law, and the expressions of the area reduction coefficient λ and the allometric growth coefficient β in the allometric growth law are as follows: Where D k is the branch diameter of the kth segment of the tree, L k is the branch length of the kth segment of the tree; Step 13, generating an ideal tree algorithm, specifically includes: Given the trunk diameter D1, length L1 and angle of the tree; The first branch appears and the branch diameter is calculated and branch length The ideal branching model of tea tree body was obtained by iterative arrangement in the same direction; Step 2, measuring the allometric growth parameters of the oil tea tree, specifically comprising the following steps: Step 21, select a bifurcated branch, measure the length and diameter of the main branch and the two branches respectively, and use an angle measuring instrument to measure the angle between the two branches, and record the measurement results; Step 22, performing polynomial fitting on the measurement results to obtain the area reduction coefficient λ, the allometric coefficient β and the range of the angle between the two branches; Step 23, measuring the bending elastic modulus of the branch to obtain the bending elastic modulus of the branch; Step 3, simulation analysis of the natural frequency of the tea tree; Step 4, deriving an empirical formula for the natural frequency of a tree; specifically comprising the following steps: Step 41, obtaining the torsional elastic coefficient of the tree trunk; Step 42, calculating the moment of inertia of the trunk and the sum of the moment of inertia of the branches; Step 43, according to the trunk moment of inertia and the branch moment of inertia, the empirical formula of the natural frequency of the trunk is obtained, which is expressed as follows: Where E is the bending elastic modulus, I is the section inertia moment, m is the mass of the tree trunk, l1 is the trunk length, α is the unknown coefficient, d2 is the branch diameter, l2 is the branch length, It is half of the angle between the two branches.

2. The method for deriving an empirical formula for the trunk frequency of tea oil trees based on the law of allometric growth according to claim 1, characterized in that: The step 3 includes creating a binary branch tea oil tree simulation model, performing finite element simulation analysis, and obtaining the tree body simulation natural frequency.

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