Finite element analysis method for arm folding mechanism of heavy-load unmanned aerial vehicle
By using finite element analysis and topology optimization calculations, the problem of unclear stress distribution in the arm structure of heavy-duty UAVs was solved, achieving a reasonable distribution of materials, reducing weight and cost, and improving load-bearing capacity and endurance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-02-28
- Publication Date
- 2026-05-15
AI Technical Summary
Existing technologies struggle to accurately identify the stress distribution patterns and concentration points of heavy-duty drone arm structures, leading to excessive material usage and increased structural weight, which fails to meet the needs of power infrastructure transportation and emergency repairs.
Finite element analysis was used to establish a finite element model of the boom folding mechanism. Static and modal analyses were performed, and topology optimization calculations were combined to achieve concentrated material distribution in critical stress areas and reasonable weight reduction in non-critical areas, thereby reducing the boom's self-weight.
While ensuring structural strength and rigidity, the weight of the boom is reduced, the load-bearing capacity and endurance are improved, material consumption is reduced, and manufacturing costs are lowered.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of finite element analysis technology, and in particular to a finite element analysis method for the arm folding mechanism of a heavy-duty unmanned aerial vehicle. Background Technology
[0002] Power infrastructure projects are mostly located in remote mountainous areas, swamps, wetlands, and other areas with poor transportation access, placing high demands on equipment for emergency disaster relief. Materials such as towers and cables are large, heavy, and easily damaged; traditional transportation methods are inefficient, risky, or costly. Conventional transportation methods are prone to failure during natural disasters, leading to delays in repairs. Existing lightweight drones have insufficient payload capacity, and heavy-duty solutions have limitations in payload or cost, making it difficult to meet the transportation and emergency repair needs of power infrastructure projects.
[0003] Heavy-duty drones need to carry more payloads to achieve long-duration flights, placing higher demands on the design of their boom structures. Current boom designs rely on traditional calculations, which cannot accurately predict the actual stress state under complex loads, and struggle to precisely identify stress distribution patterns and concentration points. This uncertainty in stress distribution can easily lead to excessively large safety margins in boom structure design, resulting in overuse of materials and increased structural weight. Summary of the Invention
[0004] To address the problem of insufficient precision in identifying the stress distribution and concentration points of boom structures in existing technologies, leading to excessive material usage and increased structural weight in boom design, this invention provides a finite element analysis method for the boom folding mechanism of a heavy-duty UAV. This method enables concentrated material distribution in critical stress areas and reasonable weight reduction in non-critical areas, effectively solving the problems of material waste and increased structural weight caused by over-reliance on safety margins in traditional designs. While ensuring structural strength and stiffness, it reduces the boom's self-weight and improves the load-bearing capacity of the heavy-duty UAV. The specific technical solution is as follows: This invention provides a finite element analysis method for the arm folding mechanism of a heavy-duty unmanned aerial vehicle (UAV), including: A finite element model of the arm folding mechanism is established, and the finite element model is meshed based on preset material properties and boundary conditions; Static analysis was performed on the finite element model to obtain the maximum deformation and equivalent stress distribution of the arm folding mechanism under a preset load. Modal analysis was performed on the finite element model to obtain the first multiple mode shapes and natural frequencies of the arm folding mechanism; Based on the results of the static and modal analyses, a topology optimization mathematical model with material density as the variable is established, and topology optimization calculations are performed to obtain the optimal material distribution scheme of the arm folding mechanism. The solid model of the arm folding mechanism is reconstructed based on the optimal material distribution scheme. The reconstructed entity model is verified and analyzed. If it meets the preset usage conditions, the current entity model is determined to be the final target entity model.
[0005] Preferably, the preset material properties include: The connecting components in the arm folding mechanism are made of metal and have a first set of Young's modulus, Poisson's ratio, density and yield strength parameters. The main body of the arm in the arm folding mechanism is made of composite material and has a second set of Young's modulus, Poisson's ratio, density and yield strength parameters. The first set of parameters is different from the second set of parameters.
[0006] Preferably, the preset boundary conditions include applying loads and constraints in the finite element model. Specifically, a fixed constraint is applied at the connection between the arm and the center plate in the finite element model, and a load determined based on the maximum output capacity of the motor is applied at the drive end of the arm.
[0007] Preferably, a finite element analysis method for the arm folding mechanism of a heavy-duty UAV further includes: When performing mesh generation, the finite element model is meshed using multiple mesh sizes, and the size with the best element mesh quality is selected as the final mesh generation standard.
[0008] Preferably, static analysis is performed on the finite element model to obtain the maximum deformation and equivalent stress distribution of the arm folding mechanism under a preset load, including: After applying a fixed constraint at the connection between the arm and the center plate, a load determined based on the maximum output capacity of the motor is applied to the drive end of the arm. The total deformation distribution of the boom folding mechanism under the load is obtained by finite element method calculation, and then the equivalent stress value of each part of the boom folding mechanism is calculated to determine the location of the maximum stress and the stress concentration area.
[0009] Preferably, modal analysis is performed on the finite element model to obtain the first multiple mode shapes and natural frequencies of the arm folding mechanism, including: The kinematic equations of the arm folding mechanism are established based on the assumption of an undamped linear system, and the system kinematic equations are transformed into homogeneous equations of mass matrix and acceleration terms, and stiffness matrix and displacement terms. By solving the eigenvalue problem composed of the system mass matrix and stiffness matrix, the natural frequencies and corresponding mode shapes of the arm folding mechanism are obtained. The first natural frequency is configured to be higher than the highest excitation frequency when the motor is working.
[0010] Preferably, based on the results of the static and modal analyses, a topology optimization mathematical model with material density as the variable is established, and topology optimization calculations are performed to obtain the optimal material distribution scheme for the arm folding mechanism, including: The key connections and installation parts in the arm folding mechanism are set as non-optimized areas, while the main load-bearing structural components are set as optimized areas. Using the variable density method, with the material density of each unit in the optimization region as the design variable and the minimization of the overall structural flexibility as the optimization objective, a topology optimization mathematical model is constructed, and mass constraints or volume constraints and penalty factors are set based on a preset weight reduction ratio. The topology optimization mathematical model is iteratively calculated to obtain a material distribution scheme with optimal stiffness under the given constraints.
[0011] Preferably, the non-optimized area includes the joint shaft bolt, clamping bolt, and positioning screw of the arm folding mechanism; the optimized area includes joint A, joint B, and locking buckle of the arm folding mechanism.
[0012] Preferably, the verification analysis of the reconstructed entity model includes: Perform static verification and prestressed modal analysis on the reconstructed solid model in sequence; Static verification was performed, and the maximum deformation and equivalent stress of the reconstructed solid model were obtained under the same load, material and constraint conditions as before. Based on the static analysis, prestressed modal analysis is performed to obtain the natural frequencies and mode shapes of the reconstructed solid model.
[0013] Preferably, the conditions for satisfying the preset usage include: The first condition for use is that the maximum equivalent stress is less than the previous maximum equivalent stress; The second condition for use is that the maximum deformation is less than or equal to the previous maximum deformation. The third condition for use is that the weight is reduced compared to the previous one.
[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a finite element analysis method for the arm folding mechanism of a heavy-duty UAV. By establishing a finite element model of the arm folding mechanism and conducting static analysis, the equivalent stress distribution law and stress concentration location under a preset load are obtained. Modal analysis is used to determine the first multiple mode shapes and natural frequencies of the arm folding mechanism. Combined with the static analysis results, a topology optimization mathematical model is constructed to achieve concentrated material distribution in critical stress areas and reasonable weight reduction in non-critical areas. This effectively solves the problems of material waste and increased structural weight caused by over-reliance on safety margins in traditional designs. Under the premise of ensuring structural strength and stiffness, the self-weight of the arm is reduced, improving the load-bearing capacity and endurance of the heavy-duty UAV, while reducing material consumption and manufacturing costs. Attached Figure Description
[0015] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.
[0016] Figure 1 A flowchart of a finite element analysis method for a folding arm mechanism of a heavy-duty UAV provided in an embodiment of the present invention.
[0017] Figure 2 A simplified schematic diagram of the finite element model of the arm folding module provided in an embodiment of the present invention.
[0018] Figure 3 The overall deformation cloud diagram of the arm folding mechanism provided in the embodiment of the present invention.
[0019] Figure 4 Equivalent stress cloud diagram of the arm folding mechanism provided in the embodiment of the present invention.
[0020] Figure 5 The diagram shows the reconstruction and optimization results of the arm folding module provided in this embodiment of the invention.
[0021] Figure 6 The figure shows the static analysis results of the reconstructed arm folding module structure provided in the embodiment of the present invention. Detailed Implementation
[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0023] It should be understood that, when used in this specification, the terms “comprising” and “including” indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.
[0024] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.
[0025] It should also be further understood that the term "and / or" as used in this specification refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes such combinations.
[0026] Please refer to the following examples. Figures 1 to 6 .
[0027] This invention provides a finite element analysis method for the arm folding mechanism of a heavy-duty unmanned aerial vehicle (UAV), including: Step S1: Establish a finite element model of the arm folding mechanism. The finite element model is meshed based on preset material properties and boundary conditions. In establishing the finite element model, the material properties of the folding arm mechanism must first be determined. In this embodiment, the main body of the arm is made of high-strength carbon fiber material with a density of 1800 kg / m³ and a Young's modulus of 2.9 × 10⁻⁶. ^5 The strength is 4870 MPa, with a Poisson's ratio of 0.300 and a yield strength of 4870 MPa. The connecting components of the arm folding mechanism are made of 6061-T6 aluminum alloy, with a density of 2700 kg / m³ and a Young's modulus of 6.90 × 10⁻⁶. ^4 The material properties include a strength of 240 MPa, a Poisson's ratio of 0.330, and a yield strength of 240 MPa. These material properties directly affect the accuracy of the finite element analysis and need to be precisely measured based on the actual material being used or obtained by consulting relevant material handbooks.
[0028] Specifically, the geometric modeling of the boom folding mechanism needs to consider the actual structural features. The connection between the boom and the center plate is designed as a fixed support structure, which bears the entire load transmitted from the boom. A motor and propeller are mounted at the other end of the boom. For example, under normal operating conditions, the motor can provide a maximum lift of 342.85 Newtons. When establishing the geometric model, it is necessary to accurately reflect all components of the boom folding mechanism, including key components such as joint A, joint B, locking buckles, pivot bolts, clamping bolts, and positioning screws.
[0029] The boundary conditions have a significant impact on the finite element analysis results. A fixed support constraint is applied at the connection point between the boom and the center plate, restricting displacement and rotation in three directions. A load of 342.85 Newtons is applied vertically downwards at the motor mounting end of the boom to simulate the reaction force generated by the motor and propeller at maximum power output. The load is applied uniformly distributed on the motor mounting surface.
[0030] Therefore, in this implementation, the boundary conditions preset in the finite element model specifically refer to the application of loads and constraints in the finite element model. This is achieved by applying fixed constraints at the connection between the arm and the center plate in the finite element model, and applying a load determined based on the maximum output capacity of the motor to the drive end of the arm, with the maximum value of the load set to 342.85 N.
[0031] When performing mesh generation, the finite element model is meshed using multiple mesh sizes, and the size with the best element mesh quality is selected as the final mesh generation standard.
[0032] In this embodiment, the finite element model of the boom folding mechanism is established by comparing the mesh division quality of the boom folding mechanism using multiple mesh sizes, and selecting the mesh size with the best average mesh cell quality as the analysis benchmark. The mesh sizes include six specifications: 5 mm, 4 mm, 3 mm, 2 mm, 1 mm and 0.5 mm.
[0033] It should be noted that mesh generation is a crucial step in finite element analysis, directly impacting computational accuracy and efficiency. Six different mesh sizes (5 mm, 4 mm, 3 mm, 2 mm, 1 mm, and 0.5 mm) were used to mesh the boom folding mechanism. By comparing the computational results and mesh quality indicators under different mesh sizes, the optimal mesh parameters were determined. Mesh quality evaluation primarily considered factors such as the shape quality, aspect ratio, and torsion of the mesh elements.
[0034] The mesh quality reaches its optimal state when the mesh size is 1 mm. At this size, the total number of mesh elements is 1,181,327, the total number of mesh nodes is 1,878,102, and the average mesh quality is 0.81749. An average mesh quality close to 1.0 indicates that the mesh element shape is close to ideal, ensuring computational accuracy. While smaller mesh sizes can improve local computational accuracy, they significantly increase computation time and memory requirements, while larger mesh sizes may lead to insufficient computational accuracy, especially in stress concentration regions.
[0035] Step S2: Perform static analysis on the finite element model to obtain the maximum deformation and equivalent stress distribution of the arm folding mechanism under a preset load; In practice, static analysis includes: A fixed constraint is applied at the connection between the robotic arm and the center plate of the arm folding mechanism; a load determined based on the maximum output capacity of the motor is applied at the other end (drive end) of the robotic arm, the load value being set according to the actual working conditions of the heavy-duty UAV. The total deformation distribution of the arm folding mechanism under the load was obtained by finite element method calculation. Calculate the equivalent stress values of each part of the arm folding mechanism to determine the location of maximum stress and the stress concentration area.
[0036] By establishing a finite element model of the arm folding mechanism and conducting static analysis, the equivalent stress distribution law and stress concentration location under the preset load can be accurately obtained, avoiding design blindness caused by unclear stress distribution.
[0037] Step S3: Perform modal analysis on the finite element model to obtain the first multiple mode shapes and natural frequencies of the arm folding mechanism; In specific implementation, the modal analysis includes: The system kinematic equations are established using linear analysis, while neglecting the influence of the damping matrix. The system kinematic equations of a free vibration system are simplified into homogeneous equations consisting of the mass matrix and acceleration terms, and the stiffness matrix and displacement terms. The system displacement is defined as the product of a constant column vector and a time function, wherein the time function is represented by a sine function; The natural frequencies and corresponding mode shapes of the arm folding mechanism are obtained by solving the eigenvalue problems of the mass matrix and stiffness matrix. The first natural frequency of the arm folding mechanism is compared with the highest excitation frequency when the motor is working to ensure that the natural frequency is much greater than the excitation frequency.
[0038] Step S4: Based on the results of the static and modal analyses, establish a topology optimization mathematical model with material density as the variable, and perform topology optimization calculations to obtain the optimal material distribution scheme for the arm folding mechanism; specifically including: To ensure the practicality of topology optimization, the folding arm mechanism needs to be rationally divided into optimized and non-optimized regions. Key load-bearing components in the folding arm mechanism, such as pivot bolt holes, clamping bolt holes, and positioning screw holes, are designated as exclusion regions. These regions maintain their original geometry and material distribution during optimization. The selection of exclusion regions primarily considers functional requirements and manufacturing constraints, ensuring that the reconstructed structure still achieves its intended function.
[0039] In specific implementation, the key connection and installation parts in the boom folding mechanism are set as non-optimized areas, and the main load-bearing structural components are set as optimized areas; by setting the key connection and installation parts such as the joint shaft bolts, clamping bolts and positioning screws in the boom folding mechanism as non-optimized areas; and setting the load-bearing structural components such as joint A, joint B and locking buckle in the boom folding mechanism as optimized areas.
[0040] Components such as joint A, joint B, and locking buckles are designated as optimization zones, and the material distribution in these zones can be adjusted during the optimization process. The selection of optimization zones requires comprehensive consideration of the structure's stress characteristics and weight reduction potential; typically, zones with lower stress levels and smaller contributions to overall stiffness are chosen. When setting optimization zones, manufacturing limitations must also be considered to ensure that the reconstructed structure can be manufactured using existing processing methods.
[0041] The SIMP (Variable Density Method) is used for optimization. The material density of each unit in the optimization region is used as the design variable, and the overall structural flexibility is minimized as the optimization objective. A topology optimization mathematical model is constructed, and a mass constraint or volume constraint and a penalty factor based on a preset weight reduction ratio are set. The mass constraint based on the preset weight reduction ratio is used as a mass response constraint, and the constraint limit is set to 85% of the mass before optimization.
[0042] The constraint is set as a retention constraint, meaning the reconstructed structural mass does not exceed 85% of the original structural mass. This constraint ensures the weight reduction effect of the optimization while avoiding structural performance degradation due to over-optimization. The optimization objective is set as minimum flexibility, which is to maximize the overall stiffness of the structure. Flexibility is the ratio of displacement to load; minimizing flexibility is equivalent to maximizing structural stiffness. This objective setting helps maintain the structure's load-bearing capacity.
[0043] The topology optimization mathematical model is iteratively calculated to obtain a material distribution scheme with optimal stiffness under the given constraints.
[0044] In specific implementation, the topology optimization calculation includes: Based on setting boundary conditions and constraints for topology optimization, setting non-optimized and optimized regions, and setting constraint responses; The maximum number of iterations is set to 500, the convergence accuracy is 0.1%, and the optimization objective is minimum compliance. The material density distribution optimization results of the arm folding mechanism are obtained through iterative calculation, and the material distribution scheme with optimal stiffness under the set constraint response conditions is obtained.
[0045] Step S5: Reconstruct the solid model of the arm folding mechanism based on the optimal material distribution scheme; Based on the topology optimization results, the size and shape of the arm folding mechanism were adjusted in the 3D modeling software to reconstruct the solid model.
[0046] Step S6: Verify and analyze the reconstructed entity model. If it meets the preset usage conditions, then determine that the current entity model is the final target entity model.
[0047] In practice, static verification and prestressed modal analysis are performed on the reconstructed solid model in sequence. Static verification analysis is performed on the reconstructed solid model, and finite element calculations are performed to verify the static properties under the same load, material and constraint conditions as before reconstruction. The reconstructed solid model was subjected to prestressed modal analysis to verify its dynamic characteristics, and the first six natural frequencies and mode shapes were obtained.
[0048] The reconstructed solid model was imported into finite element analysis software. Under the same load, material, and constraint conditions as before reconstruction, static analysis was performed to obtain the optimized maximum deformation and equivalent stress. Based on the static analysis, prestressed modal analysis was performed on the reconstructed solid model to obtain its first six natural frequencies and mode shapes. The obtained first six natural frequencies are 145.52Hz, 148.88Hz, 562.27Hz, 569.9Hz, 1345.6Hz, and 1415.9Hz.
[0049] After adjusting the size and shape of the boom folding module in the 3D modeling software and reconstructing the solid model, the reconstructed boom folding mechanism meets the following usage conditions: The first condition for use is that the maximum equivalent stress is less than the previous maximum equivalent stress; The second condition for use is that the maximum optimized deformation is less than or equal to the maximum deformation before optimization. The third condition for use is that the mass is reduced compared to before optimization; It should be noted that the reduction in mass, the reduction in equivalent stress, and the improvement in deformation before and after the calculations verify the effectiveness of the structural optimization in terms of lightweighting and performance enhancement. The verification analysis following the reconstruction of the solid model ensures that the optimized boom folding mechanism meets the preset usage conditions and its mechanical properties are guaranteed. The optimized boom structure exhibits stronger environmental adaptability and structural stability when facing complex working conditions such as power infrastructure transportation in remote areas and emergency repairs after natural disasters. This effectively avoids transportation interruptions or repair delays caused by boom structure failure, indirectly improving the emergency response capabilities of the power system.
[0050] This invention provides a finite element analysis method for the arm folding mechanism of a heavy-duty UAV. By establishing a finite element model of the arm folding mechanism and conducting static analysis, the equivalent stress distribution law and stress concentration location under a preset load are obtained. Modal analysis is used to determine the first multiple mode shapes and natural frequencies of the arm folding mechanism. Combined with the static analysis results, a topology optimization mathematical model is constructed to achieve concentrated material distribution in critical stress areas and reasonable weight reduction in non-critical areas. This effectively solves the problems of material waste and increased structural weight caused by over-reliance on safety margins in traditional designs. Under the premise of ensuring structural strength and stiffness, the self-weight of the arm is reduced, improving the load-bearing capacity and endurance of the heavy-duty UAV, while reducing material consumption and manufacturing costs.
[0051] This embodiment illustrates a specific case study of a finite element analysis method for a boom folding mechanism. In this case, the method establishes an accurate finite element model to conduct a comprehensive mechanical performance analysis of the boom folding mechanism, providing a scientific basis for structural optimization design. This method is particularly suitable for the design and verification of boom folding mechanisms in heavy-load aircraft such as heavy-load UAVs.
[0052] (1) Establishing a finite element model To verify whether the arm folding mechanism meets the topology optimization conditions, this project selects a maximum pulling force of 342.85N when the motor is at 100% output. Based on the actual working conditions of the agricultural drone, the arm and the arm folding mechanism are made of high-strength Carbon Fiber and 6061-T6 respectively. The relevant properties of the materials are shown in Table 1.
[0053] Table 1 - Material Properties Table To better analyze the static and modal characteristics of the boom folding mechanism, the boom and its folding module are taken as the research objects. (See below.) Figure 2 As shown ( Figure 2 (This is a simplified schematic diagram of the finite element model of the boom folding module). Fixed support constraints are applied at the connection between the boom and the center plate, and a load of 342.58 N is applied at the other end. The boom folding module is meshed with six mesh sizes: 5 mm, 4 mm, 3 mm, 2 mm, 1 mm, and 0.5 mm, and the mesh quality is compared. The best mesh quality is achieved with a mesh size of 1 mm, containing 1,181,327 mesh elements and 1,878,102 mesh nodes, with an average mesh quality of 0.81749.
[0054] (2) Static analysis Based on boundary conditions, load distribution, and mesh generation, a finite element analysis was performed on the folding module of the robotic arm. The maximum deformation and equivalent stress distribution were calculated. Figure 3 and Figure 4As shown, the maximum deformation of the arm folding module occurs near the motor end, with a maximum displacement of 0.41129 mm under a load of 342.85 N. Currently, the positioning error of heavy-duty UAVs is within 10 cm, so this 0.41129 mm deformation will not affect the flight attitude or operational performance of the multi-functional heavy-duty UAV. Under a load of 342.85 N, the maximum equivalent stress of the arm folding module is 107.28 MPa, located at the connection point between joints A and B. The yield strength of 6061-T6 is 240 MPa, so the strength far exceeds the requirements. The results indicate that the arm folding module still has room for weight reduction and can be further optimized to obtain a better model.
[0055] (3) Modal analysis This project uses linear analysis to perform modal analysis on the boom folding module, obtaining the vibration characteristics of the system at each stage, which provides a basis for subsequent structural optimization.
[0056] The kinematic equations of motion for an n-stage linear system are: (Equation 1) in, for The mass matrix of the 1 / 2-order structure. for Damping matrix of the first-order structure. for The stiffness matrix of the first-order structure. , , For each system The displacement, velocity, and acceleration vectors of the first-order nodes. for The external load vector is of order and time-dependent; t is time. Since the vibration of the mechanical system is not significantly related to damping, and in a free vibration system, the external load is zero. Substituting the above conditions into equation (1), we obtain the equation for undamped free vibration: (Equation 2) As can be seen from the above equation, the nodal displacements of the system have a crucial impact on the natural frequency analysis. Therefore, the displacement equation of the system is assumed to be: (Equation 3) in, for A constant column vector of order, representing the mode shape, denoted as . The angular frequency of the vibration; The phase angle; For time.
[0057] Equation (3) and its second derivative Substitute into the free vibration equation (2) and eliminate the time term. ,get: (Equation 4) To make the mode shape vector in equation (4) For a solution to have a non-zero value, the determinant of its coefficient matrix must be zero. (Equation 5) Solve equation (5) about The nth-degree equation yields the n eigenvalues of the system. Each eigenvalue arithmetic square root This is the i-th natural angular frequency of the system. Each By substituting back into equation (4), the corresponding non-zero vector can be obtained. That is, the i-th mode shape. Natural frequency. With angular frequency The conversion relationship is as follows: (Equation 6) Starting from the forced vibration equation (1), through simplification, assumptions, and derivation, the modal analysis problem is ultimately transformed into solving the matrix eigenvalue problem, thereby quantifying the natural frequencies of the system. or ) and mode shape ( ).
[0058] The brushless motor and propeller excitation cause periodic vibrations in the multi-functional heavy-load UAV during actual operation. Due to the effects of gravity and lift on the folding arm module, stress is generated within the structure. Therefore, it is necessary to first analyze the static stress under load conditions, then perform prestressed modal analysis, comparing the natural frequencies with the actual operating frequencies to determine if resonance occurs. By performing prestressed modal analysis on the folding arm module, the first six mode shapes are calculated.
[0059] The natural frequency of the arm folding module increases with the modal order. The power system selected for the multi-functional heavy-duty UAV in this project has a maximum motor speed of 3740 r / min during plant protection operations; therefore, the highest excitation frequency of the UAV during operation is 62.33 Hz. Modal analysis shows that the first-order modal natural frequency of the arm folding mechanism is 145.52 Hz, which is significantly higher than the highest excitation frequency during operation, thus preventing resonance.
[0060] Table 2 - First Six Natural Frequencies of the Arm Folding Module Currently, topology optimization technology has been widely applied in the field of agricultural machinery. This technology can perform material removal processing on a set optimization region based on the stress conditions of the structure. The material model for topology optimization uses the SIMP method, assuming that the intermediate density of the element is related to the elastic modulus of the structural material. The optimization variable is set as the density of each element within the optimization region. A penalty factor is used to cause the intermediate density of each element to cluster towards the 0-1 extremes. This method transforms the structural optimization problem into the problem of optimal material distribution for each element. The specific process is as follows: Consider a design domain discretized by finite element method. It is divided into The problem involves finding the optimal material distribution within the design domain to maximize the overall stiffness of the structure given material constraints.
[0061] By defining each unit relative density The design variables are the set of variables that constitute the design variable vector. .
[0062] in, It is a very small positive number used to avoid numerical oddities, representing a state with no material; 1 represents a state with material.
[0063] The material interpolation model (SIMP) uses a solid isotropic material penalty (SIMP) model, which correlates the relative density of the element with its elastic modulus to penalize intermediate density values, driving the design variables to converge toward the extremes of 0 or 1.
[0064] in, It is a unit The elastic modulus; It is the elastic modulus of a solid material; It is a very small elastic modulus, used to represent the void region; It is a penalty factor (usually) ), used to penalize intermediate density values.
[0065] The optimization objective is to minimize the overall flexibility of the structure. That is, the total strain energy of a structure under a given load is equivalent to maximizing the overall stiffness.
[0066] in, This is the global node load vector. For the equilibrium equation The obtained global nodal displacement vector. For those that depend on design variables The global stiffness matrix.
[0067] The total material volume of the optimized structure must not exceed a preset fraction of the initial design domain volume. .
[0068] in, It is a unit volume, It is the initial total volume of the design domain.
[0069] Design variable boundary constraints: Among them, optimizing the regional area ( () indicates the region where material distribution is allowed to change; within this region, To optimize variables. Non-optimization domain ( Areas where the material or geometry remains unchanged must be preserved. It is fixed at 1 and does not participate in optimization.
[0070] In summary, the mathematical model for topology optimization can be fully expressed as follows: To ensure the quality and scope of topology optimization, stress-bearing components such as the hinge bolts, clamping bolts, and positioning screws of the boom folding module joint are designated as exclusion areas. Based on machining constraints, joints A, B, and the locking buckle are set as optimization areas. Constraints are retained, constraint responses are quality responses, constraint limits are set to 85%, and the optimization objective is minimum compliance. The maximum number of iterations is 500, with a convergence accuracy of 0.1%. The optimization results for the boom folding module are obtained from this solution, as shown below. Figure 5 As shown.
[0071] By combining the topology optimization results with the actual operating conditions of the multi-functional heavy-duty UAV, the size and shape of the arm folding module were adjusted in the 3D modeling software, and the solid model was redesigned.
[0072] The optimized and reconstructed solid model was imported into the corresponding software. Under the same load, material, and constraint conditions as before, static analysis was performed to verify whether the optimized arm folding module met the actual working conditions required for agricultural operations using a multi-functional heavy-duty UAV. The total deformation and equivalent stress after optimization were calculated, as follows: Figure 6 The results shown (i.e., the static analysis results after the optimization of the boom folding module structure, see [reference]) Figure 6 ).
[0073] A comparative analysis of the total deformation and equivalent stress before and after optimization of the boom folding module was conducted. As shown in Table 4-3, the maximum equivalent stress of the optimized boom folding module is 89.913 MPa, a reduction of 16.19% compared to the maximum equivalent stress of 107.29 MPa before optimization. The optimized strength still meets the usage requirements. The maximum deformation of the optimized model decreased from 0.41129 mm to 0.40711 mm, a relative reduction of 1.01%. The optimized boom folding mechanism meets the actual operational requirements in terms of strength and deformation resistance.
[0074] Table 3 - Comparison of values before and after Based on the static analysis of the arm folding module, prestressed modal analysis was performed to analyze the changes in the modal characteristics of the optimized arm folding module. By analyzing the first six stages of natural frequencies and mode shapes after optimization, it was determined whether size adjustment and shape change were key factors affecting the dynamic stiffness of the multi-functional heavy-load UAV. The results of the optimized modal analysis are shown in Table 4-4. Compared with the first six modal frequencies before optimization, the first, second, third, fourth, and sixth natural frequencies all increased, but the fifth natural frequency decreased from 1345.6Hz before optimization to 1295.8Hz after optimization, a relative reduction of 3.7%. The demonstration animation shows that the fifth natural frequency of the arm folding mechanism is generated by circumferential Y-direction vibration, and the reduction of the fifth natural frequency is beneficial to the fixation of the arm. The first six vibration frequencies after optimization are all much higher than the operating frequency (62.33Hz) of the multi-functional heavy-load UAV under a maximum tensile force of 342.58N. The reconstructed arm folding structure achieves lightweighting while increasing the vibration frequency of the arm, which is beneficial to improving the dynamic characteristics of the arm folding structure.
[0075] Table 4 - Comparison of Modal Analysis Results of Arm Folding Mechanism In summary, this invention discloses a finite element analysis method for a folding arm mechanism, addressing key technical problems faced by heavy-load aircraft such as unmanned aerial vehicles (UAVs) in actual operation, including excessive arm structural weight, severe stress concentration, and poor dynamic characteristics. This method establishes a precise finite element model, uses a 1 mm mesh size for mesh generation, and performs static analysis under a 342.85 Newton load condition, finding a maximum equivalent stress of 107.28 MPa and a maximum deformation of 0.41129 mm.
[0076] Subsequent prestressed modal analysis revealed the first six natural frequencies to be between 145.52 Hz and 1415.9 Hz, ensuring no resonance risk with the operating frequency. Based on the analysis results, a topology optimization mathematical model was established, aiming to minimize structural mass, and the optimal material distribution was obtained through iterative calculations. The reconstructed arm folding mechanism achieved a certain proportion of weight reduction, while simultaneously reducing the maximum equivalent stress and increasing the first natural frequency to a higher value. This ensures improved overall performance of the arm folding mechanism, providing a scientific basis and technical support for lightweight design and structural optimization of heavy-duty UAVs.
[0077] Those skilled in the art will recognize that the units of the various examples described in connection with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the invention.
[0078] In the embodiments provided by the present invention, it should be understood that the division of units is only a logical functional division. In actual implementation, there may be other division methods, such as multiple units can be combined into one unit, one unit can be split into multiple units, or some features can be ignored.
[0079] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.
[0080] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.
[0081] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the specification of the present invention.
Claims
1. A finite element analysis method for the arm folding mechanism of a heavy-duty unmanned aerial vehicle (UAV), characterized in that, include: A finite element model of the arm folding mechanism is established, and the finite element model is meshed based on preset material properties and boundary conditions; Static analysis was performed on the finite element model to obtain the maximum deformation and equivalent stress distribution of the arm folding mechanism under a preset load. Modal analysis was performed on the finite element model to obtain the first multiple mode shapes and natural frequencies of the arm folding mechanism; Based on the results of the static and modal analyses, a topology optimization mathematical model with material density as the variable is established, and topology optimization calculations are performed to obtain the optimal material distribution scheme of the arm folding mechanism. The solid model of the arm folding mechanism is reconstructed based on the optimal material distribution scheme. The reconstructed entity model is verified and analyzed. If it meets the preset usage conditions, the current entity model is determined to be the final target entity model.
2. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 1, characterized in that, The preset material properties include: The connecting components in the arm folding mechanism are made of metal and have a first set of Young's modulus, Poisson's ratio, density and yield strength parameters. The main body of the arm in the arm folding mechanism is made of composite material and has a second set of Young's modulus, Poisson's ratio, density and yield strength parameters. The first set of parameters is different from the second set of parameters.
3. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 2, characterized in that, The preset boundary conditions include applying loads and constraints in the finite element model. Specifically, a fixed constraint is applied at the connection between the arm and the center plate in the finite element model, and a load determined based on the maximum output capacity of the motor is applied at the drive end of the arm.
4. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 3, characterized in that, Also includes: When performing mesh generation, the finite element model is meshed using multiple mesh sizes, and the size with the best element mesh quality is selected as the final mesh generation standard.
5. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 3, characterized in that, Static analysis is performed on the finite element model to obtain the maximum deformation and equivalent stress distribution of the arm folding mechanism under a preset load, including: After applying a fixed constraint at the connection between the arm and the center plate, a load determined based on the maximum output capacity of the motor is applied to the drive end of the arm. The total deformation distribution of the boom folding mechanism under the load is obtained by finite element method calculation, and then the equivalent stress value of each part of the boom folding mechanism is calculated to determine the location of the maximum stress and the stress concentration area.
6. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 5, characterized in that, Modal analysis was performed on the finite element model to obtain the first multiple mode shapes and natural frequencies of the arm folding mechanism, including: The kinematic equations of the arm folding mechanism are established based on the assumption of an undamped linear system, and the system kinematic equations are transformed into homogeneous equations of mass matrix and acceleration terms, and stiffness matrix and displacement terms. By solving the eigenvalue problem composed of the system mass matrix and stiffness matrix, the natural frequencies and corresponding mode shapes of the arm folding mechanism are obtained. The first natural frequency is configured to be higher than the highest excitation frequency when the motor is working.
7. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 1, characterized in that, Based on the results of the static and modal analyses, a topology optimization mathematical model with material density as the variable is established, and topology optimization calculations are performed to obtain the optimal material distribution scheme for the arm folding mechanism, including: The key connections and installation parts in the arm folding mechanism are set as non-optimized areas, while the main load-bearing structural components are set as optimized areas. Using the variable density method, with the material density of each unit in the optimization region as the design variable and the minimization of the overall structural flexibility as the optimization objective, a topology optimization mathematical model is constructed, and mass constraints or volume constraints and penalty factors are set based on a preset weight reduction ratio. The topology optimization mathematical model is iteratively calculated to obtain a material distribution scheme with optimal stiffness under the given constraints.
8. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 7, characterized in that, The non-optimized area includes the joint shaft bolts, clamping bolts, and positioning screws of the arm folding mechanism; the optimized area includes joint A, joint B, and locking buckle of the arm folding mechanism.
9. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 1, characterized in that, The verification analysis of the reconstructed entity model includes: Perform static verification and prestressed modal analysis on the reconstructed solid model in sequence; Static verification was performed, and the maximum deformation and equivalent stress of the reconstructed solid model were obtained under the same load, material and constraint conditions as before. Based on the static analysis, prestressed modal analysis is performed to obtain the natural frequencies and mode shapes of the reconstructed solid model.
10. The finite element analysis method for the arm folding mechanism of a heavy-load UAV as described in claim 9, characterized in that, The conditions for satisfying the preset usage include: The first condition for use is that the maximum equivalent stress is less than the previous maximum equivalent stress; The second condition for use is that the maximum deformation is less than or equal to the previous maximum deformation. The third condition for use is that the weight is reduced compared to the previous one.