A heavy load multi-rotor propeller design optimization method

Abstract

The application provides a heavy-load multi-rotor propeller design optimization method, and relates to the technical field of multi-rotor propeller design.The application realizes fine design of the blade shape through parameterized modeling, can flexibly adjust key parameters for different radius positions, and effectively matches the complex working condition requirements.Combining segmented aerodynamic force analysis and blade element momentum theory, the overall thrust and torque of the propeller can be accurately obtained to provide data basis for structure and performance evaluation.Through finite element method, structural static force and vibration modal analysis are carried out to identify stress concentration areas and potential resonance risks, so that system evaluation of multi-target performance is realized.Combining the multi-target optimization model of aerodynamic efficiency and structural safety, the optimal geometric parameters of the blade are automatically iteratively searched, the structural stress and vibration risk are effectively reduced while meeting the heavy-load thrust requirement, and the stability and reliability of the aircraft are improved.

Description

Technical Field

[0001] This invention relates to the field of multi-rotor design technology, specifically to a method for optimizing the design of heavy-duty multi-rotor propellers. Background Technology

[0002] With the rapid development of heavy-duty multi-rotor UAVs and other flight platforms, increasingly stringent requirements have been placed on the aerodynamic efficiency, structural safety, and vibration performance of propellers. Most existing propeller designs rely on empirical formulas or simple polynomials for geometric parameter modeling, making it difficult to simultaneously optimize the complex aerodynamic flow field and actual structural characteristics. In practical applications, mismatches between aerodynamic shape and load distribution often lead to insufficient thrust, low efficiency, and localized stress concentration. Furthermore, traditional structural analyses often apply simplified or uniformly distributed loads, neglecting the impact of aerodynamic force distribution on different parts of the blade under real-world conditions, making it difficult to promptly identify and prevent potential resonance risks. Faced with multi-objective and multi-constraint engineering requirements, existing optimization methods mainly rely on manual empirical parameter tuning or single-objective optimization, making it difficult to achieve synergistic optimization of aerodynamic, structural, and vibration performance. This limits the design capabilities and engineering reliability of high-performance heavy-duty propellers, especially in complex mission scenarios such as logistics transportation and aerial operations, where the need for balanced optimization of thrust, strength, vibration, and other performance aspects is particularly prominent.

[0003] In the prior art, CN117390765A discloses an aerodynamic optimization design method for a multi-condition UAV propeller, particularly a method based on genetic algorithm and strip theory for optimizing the design of a low Reynolds number, small advance ratio UAV propeller. This method belongs to the field of aerodynamic performance technology for micro fixed-wing UAVs. It optimizes the thrust coefficient, hovering and cruise efficiency of the propeller of a low Reynolds number, small advance ratio UAV in hovering and cruise conditions. The chord length and twist angle of the corresponding propeller blades are obtained through the optimized thrust coefficient, hovering and cruise efficiency, and the UAV propeller configuration is designed based on the chord length and twist angle of the propeller blades.

[0004] While the existing technology can set efficiency targets and tension constraints for different operating conditions, and then select the optimal blade configuration through objective functions and penalty term mechanisms, it does not consider structural stress and vibration modes, and only focuses on aerodynamic efficiency. It lacks a comprehensive assessment of structural safety and vibration risk, has a single optimization objective, and has limited engineering applicability and safety.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a design optimization method for heavy-duty multi-rotor propellers to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for optimizing the design of a heavy-load multi-rotor propeller, comprising the following steps:

[0009] S1: The geometric parameters of the propeller blades are mathematically parameterized, the blades are divided into several discrete segments along the radial direction, and the aerodynamic force is calculated at the center point of each discrete segment to obtain the approximate distribution of the aerodynamic force of the entire propeller.

[0010] S2: The propeller is modeled using the finite element method. Aerodynamic loads are applied based on the approximate distribution of propeller aerodynamic forces, and the propeller is simulated and analyzed to extract the maximum stress value and vibration mode.

[0011] S3: Based on the vibration mode, the vibration risk index of the propeller is generated. Then, with the optimization objectives of minimizing the maximum stress, minimizing the vibration risk index, and maximizing the aerodynamic efficiency, and with the thrust meeting the heavy load requirements as a constraint, a multi-objective optimization model is established.

[0012] S4: Iterate the multi-objective optimization model to update the geometric parameters of the propeller blades. After the optimization objectives converge, output the final geometric parameters as the optimal design scheme.

[0013] Preferably, the geometric parameters include, but are not limited to, blade chord length and blade twist angle. The mathematical parameterization of the geometric parameters is expressed using a B-spline curve function, the function expression of which is:

[0014]

[0015]

[0016] In the formula , Let these represent the blade chord length distribution function and the blade twist angle distribution function, respectively. , They represent the first The B-spline basis function corresponding to the chord length control point and the chord length control point B-spline basis functions corresponding to each torsion angle control point , They represent the first The blade chord length at the first chord control point and the first chord length control point Blade twist angle at each twist angle control point, subscript , These represent the indices of the chord length control point and the torsion angle control point, respectively. , These represent the total number of chord length control points and torsion angle control points, respectively.

[0017] Preferably, the aerodynamic forces include lift, drag, thrust, and torque, and the logic for the approximate distribution of the aerodynamic forces generating the propeller is as follows:

[0018] Divide the blade radially from the blade root to the blade tip into equal intervals. Each discrete segment is calculated based on the BEM model, determining the relative airflow velocity and angle of attack for each segment.

[0019] Calculate the local lift and local drag corresponding to each discrete segment based on the relative airflow velocity and angle of attack of each discrete segment.

[0020] By summing the local lift and local drag of all discrete sections on each blade, the overall thrust and torque of the propeller are obtained, thus yielding an approximate distribution of the aerodynamic forces of the entire propeller.

[0021] Preferably, the calculation methods for the relative airflow velocity and angle of attack in the discrete segment are as follows:

[0022]

[0023]

[0024] In the formula , , Representing radii of The relative airflow velocity, angle of attack, and twist angle at the location, and the radius Indicates the first The distance from the center point of the discrete segment to the center plane of the propeller. Indicates a discrete segment index. This indicates the propeller speed under standard operating conditions. This indicates the axial airflow velocity under standard operating conditions;

[0025] Based on the angle of attack and the airfoil characteristics of the propeller blades, the corresponding lift and drag coefficients are obtained to calculate the local lift and local drag. The calculation methods are as follows:

[0026]

[0027]

[0028] In the formula , , Representing radii of Local lift, local drag, and chord length at the point. , These respectively represent the angle of attack as The lift coefficient and drag coefficient at that time This indicates air density.

[0029] Preferably, the local lift and local drag of all discrete sections on each blade are summed to calculate the overall thrust and torque of the propeller. The calculation methods are as follows:

[0030]

[0031]

[0032]

[0033] In the formula , These represent the overall thrust and torque of the propeller, respectively. This indicates the number of propeller blades. Indicates radius as The angle of airflow at that location.

[0034] Preferably, the vibration modes include the frequencies of each vibration mode and the corresponding vibration patterns. The logic for performing finite element analysis on the propeller is as follows:

[0035] Finite element modeling is performed on the propeller, and aerodynamic loads are applied to the propeller based on the approximate distribution of aerodynamic forces on the propeller.

[0036] Perform structural static analysis to solve the stress and strain fields in the finite element model of the propeller, extract the principal stress distribution at various points on the blade, and record the maximum principal stress.

[0037] By solving the structural dynamics eigenvalue problem, the vibration modes and vibration patterns of the propeller at each order are obtained.

[0038] Preferably, the vibration risk index is calculated as follows:

[0039]

[0040] In the formula Indicates the vibration risk index. Indicates the excitation frequency. Indicates the first First vibration mode frequency, Indicates the first Response intensity at the first vibration modal frequency, The index representing the order of vibration modal frequencies. It represents the total order of the vibration modal frequencies.

[0041] Preferably, the multi-objective optimization model takes minimizing maximum stress, minimizing vibration risk index, and maximizing aerodynamic efficiency as its optimization objectives, and its expression is:

[0042]

[0043] And the constraints are satisfied: , This indicates the preset overload requirements. ~ These represent the three function expressions in the multi-objective optimization model. This indicates the maximum stress.

[0044] Preferably, the multi-objective optimization model adopts a genetic algorithm, which achieves the convergence of the objective function through population iteration. The optimization process includes initializing the population, simulation calculation, non-dominated sorting selection, crossover and mutation operation, and termination determination.

[0045] The optimized geometric parameters are verified through simulation. Once the optimization effect is confirmed to meet the design objectives, it is output as the optimal design scheme.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] This invention achieves precise design of the propeller blade shape through parametric modeling, enabling flexible adjustment of key parameters for different radius positions to effectively match complex operating conditions. Combining segmented aerodynamic analysis and blade element momentum theory, it accurately obtains the overall thrust and torque of the propeller, providing a data foundation for structural and performance evaluation. Through finite element method analysis of structural static and vibration modes, it identifies stress concentration areas and potential resonance risks, thereby achieving a systematic evaluation of multi-objective performance. Furthermore, by combining a multi-objective optimization model for aerodynamic efficiency and structural safety, it automatically iteratively searches for the optimal geometric parameters of the propeller blade, effectively reducing structural stress and vibration risks while meeting heavy-load thrust requirements, thus improving the stability and reliability of the aircraft. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0049] Figure 2 This is a graph showing the variation trend of local lift of the blade under different models of the present invention;

[0050] Figure 3 This is a graph showing the variation trend of local blade drag under different models of the present invention;

[0051] Figure 4 This is a graph showing the error variation trend under different models of the present invention. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0053] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0054] Example:

[0055] Please see Figures 1-4 The present invention provides a technical solution:

[0056] A method for optimizing the design of a heavy-load multi-rotor propeller, comprising the following steps:

[0057] S1: The geometric parameters of the propeller blades are mathematically parameterized. The blades are divided into several discrete segments along the radial direction, and aerodynamic forces are calculated at the center point of each discrete segment to obtain an approximate distribution of aerodynamic forces for the entire propeller. The aerodynamic forces include lift, drag, thrust, and torque.

[0058] Geometric parameters include, but are not limited to, blade chord length and blade twist angle. Considering the good continuity and differentiability of B-spline curves, which can automatically generate smooth, abrupt shapes and avoid stress concentration and aerodynamic performance deterioration caused by sudden geometric changes, the mathematical parameterization of geometric parameters is expressed using B-spline curve functions. The function expression is as follows:

[0059]

[0060]

[0061] In the formula , Let these represent the blade chord length distribution function and the blade twist angle distribution function, respectively. , They represent the first The B-spline basis function corresponding to the chord length control point and the chord length control point B-spline basis functions corresponding to each torsion angle control point , They represent the first The blade chord length at the first chord control point and the first chord length control point Blade twist angle at each twist angle control point, subscript , These represent the indices of the chord length control point and the torsion angle control point, respectively. , These represent the total number of chord length control points and torsion angle control points, respectively.

[0062] B-spline parameterization differs from traditional linear or low-order polynomial descriptions. It can accurately and smoothly describe complex blade geometry (such as the nonlinear variation of chord length and twist angle with radius) using a finite number of control points. Furthermore, each control point has a clear physical meaning, allowing direct parameter adjustment at key radius locations to meet specific engineering and aerodynamic performance requirements. Specifically, the physical meaning of a control point is "the design parameter value at certain typical blade radius locations." The shape of the curve is determined by these points and basis functions. By adjusting these control point parameters, the entire blade geometry can be flexibly defined, achieving complex curve distributions, rather than being limited to fixed forms like linear or polynomials. In subsequent multi-objective optimization (such as genetic algorithms and particle swarm optimization), each set of control point parameters represents a candidate design scheme. The optimization algorithm iteratively adjusts the values ​​of these control points, evaluates the aerodynamic and structural performance under each set of parameters, and ultimately selects the set of control point parameters that optimizes the objective function (such as minimum stress and minimum vibration). In actual settings, since the physical meaning, variation law and design requirements of each parameter are different, the number of control points, distribution location and value range of each geometric parameter curve should be set independently according to the complexity of its own variation and design requirements.

[0063] The logic for generating an approximate distribution of aerodynamic forces for the propeller is as follows:

[0064] Divide the blade radially from the blade root to the blade tip into equal intervals. The system uses discrete segments to perform differentiated calculations on the aerodynamic characteristics of different blade sections (such as root, middle, and tip), fully reflecting the local aerodynamic changes on complex curved surfaces, and calculates the relative airflow velocity and angle of attack of each discrete segment based on the BEM model.

[0065] Calculate the local lift and local drag corresponding to each discrete segment based on the relative airflow velocity and angle of attack of each discrete segment.

[0066] By summing the local lift and local drag of all discrete sections on each blade, the overall thrust and torque of the propeller are obtained, thus yielding an approximate distribution of the aerodynamic forces of the entire propeller.

[0067] The BEM model is used because it integrates momentum theory and blade element theory, and can comprehensively consider core aerodynamic parameters such as velocity triangle, blade angle of attack variation, and induced velocity in fluid dynamics. Moreover, compared with full 3D CFD simulation, the BEM model has a significantly reduced computational load, making it easy to use efficiently in scenarios that require a large number of iterations, such as multi-objective optimization.

[0068] In this embodiment, the simulation results of the BEM model and the full 3D CFD model are compared. The CFD model uses the SST k-ω turbulence model with 5 million grids. The simulation conditions are as follows: a set of typical propeller geometry parameters are fixed, and the propeller speed is fixed at 1000 rpm and the axial airflow velocity is fixed at 10 m / s according to the standard operating conditions determined by the design requirements. The aerodynamic load distribution at different radius positions is calculated. Ten points are evenly divided along the blade radius direction, and the corresponding data are calculated for 10 typical radius positions (i.e., 0.1R~1R, where R is the blade radius). To simplify the calculation, only local lift and local drag are calculated for the aerodynamic load distribution. The specific data are shown in the table below:

[0069] Table 1: Comparison of local lift and local drag calculation results between BEM and CFD

[0070]

[0071] From the data in the table above and Figures 2-4 As can be seen, except for a very few points where the error exceeds 5%, the error of other points in BEM is within 5%, which is within an acceptable range. The overall calculation time is greatly shortened, making it more suitable for use in scenarios involving multi-objective optimization and requiring a large number of iterations.

[0072] By adopting the segmented discretization + BEM aerodynamic modeling method, it is possible to quickly adapt to any parameterized shape, ensuring that the new aerodynamic distribution can be obtained in a timely and accurate manner after each adjustment of geometric parameters. This not only accurately reflects the local aerodynamic characteristics of each section of the blade, but also efficiently and accurately derives the overall thrust and torque data, so that the thrust, efficiency targets and structural load constraints in the optimization model have a reliable data basis.

[0073] The methods for calculating the relative airflow velocity and angle of attack in the discrete segment are as follows:

[0074]

[0075]

[0076] In the formula , , Representing radii of The relative airflow velocity, angle of attack, and twist angle at the location, and the radius Indicates the first The distance from the center point of the discrete segment to the propeller center plane (i.e., the plane containing the propeller center point and perpendicular to the blade). Indicates a discrete segment index. This indicates the rotational speed of the propeller. This indicates the axial airflow velocity.

[0077] Axial airflow velocity refers to the velocity component of the airflow along the propeller axis, that is, the velocity of the airflow perpendicular to the plane of propeller rotation and along the axial direction. For multi-rotor UAVs, the axial airflow velocity is usually the sum of the aircraft's forward velocity (or vertical takeoff and landing velocity) and the propeller's induced velocity. The overall forward velocity or vertical takeoff and landing velocity of the aircraft is a known quantity, while the induced velocity is the additional velocity generated by the propeller rotation within the flow field. Specifically, the axial airflow velocity can be obtained by directly measuring the velocity distribution of the flow field in front of and behind the propeller disk through wind tunnel experiments, aircraft flight tests, etc., or by numerically simulating the flow field around the propeller to obtain the axial velocity distribution. In some cases, if the propeller's operating state is known (such as fixed hovering, known takeoff and landing velocities), the aircraft velocity can be directly taken as the axial airflow velocity.

[0078] Based on the angle of attack and the airfoil characteristics of the propeller blades, the corresponding lift and drag coefficients are obtained to calculate the local lift and local drag. The calculation methods are as follows:

[0079]

[0080]

[0081] In the formula , , Representing radii of Local lift, local drag, and chord length at the point. , These respectively represent the angle of attack as The lift coefficient and drag coefficient at that time The value represents air density. The lift coefficient is a dimensionless coefficient characterizing the lift generated per unit dynamic pressure and per unit airfoil reference area when airflow passes through an airfoil. It reflects the airfoil's ability to "generate lift" at different angles of attack, and its variation with the angle of attack is non-linear (usually monotonically increasing and decreasing after the stall point). The drag coefficient represents the energy dissipation of the airfoil under different angles of attack and flow regimes. It typically increases with increasing angle of attack and rises even faster after stall. It is commonly used to evaluate aerodynamic efficiency and energy consumption, and designers aim to minimize drag while achieving the required lift. In engineering design, standard airfoil databases such as NACA and Eppler are commonly used. These databases contain lift and drag coefficient curves for different angles of attack, allowing the corresponding lift and drag coefficients to be obtained by looking up tables or interpolation based on the airfoil and angle of attack used.

[0082] The local lift and local drag of each blade on all discrete sections are summed to calculate the overall thrust and torque of the propeller. The calculation methods are as follows:

[0083]

[0084]

[0085]

[0086] In the formula , These represent the overall thrust and torque of the propeller, respectively. This indicates the number of propeller blades. Indicates radius as The angle of airflow at that location.

[0087] As can be seen from the two sets of summation formulas, the basic logic is based on the "blade element theory," which states that the aerodynamic performance (thrust, torque) of a propeller is the resultant force of the aerodynamic forces acting on "countless tiny segments (blade elements)" at different radii on each blade. By treating each blade element as a small airfoil segment and summing the aerodynamic contributions, the overall performance can be obtained. However, due to the rotation and forward movement of the propeller, the airflow direction is not completely perpendicular to the plane of rotation at each blade element position, so trigonometric decomposition is used for calculation.

[0088] For thrust, the airflow injection angle reflects the angle between the combined airflow and the direction perpendicular to the plane of rotation, allowing lift and drag to be correctly decomposed into axial (thrust) and tangential (torque) components. This part is used to represent the axial component of local lift, which makes a positive contribution to thrust. This part represents the axial component of the local resistance, which has a reverse effect on the thrust (reducing the thrust).

[0089] For torque, the aerodynamic torque on the rotating shaft must take into account the distance from the point of force application to the axis of rotation. Used to indicate the lever arm; This part represents the tangential component of lift, which makes a positive contribution to torque. This part represents the tangential component of the resistance, which does work directly on the rotating shaft. These components, multiplied by the radius, produce torque on the shaft.

[0090] S2: The propeller is modeled using the finite element method. Aerodynamic loads are applied based on the approximate distribution of propeller aerodynamic forces, and the propeller is simulated and analyzed to extract the maximum stress value and vibration mode.

[0091] Vibration modes include the frequencies of each vibration mode and their corresponding vibration patterns. The vibration mode frequency refers to the natural frequency at which a structure vibrates naturally in a free vibration state; it is also called the "natural frequency" or "natural frequency." The vibration pattern refers to the relative motion mode and deformation distribution of each point on the structure when it moves at the corresponding modal frequency. Specifically, a certain vibration mode frequency represents the vibration rate (usually in Hz) of the structure (in this example, a propeller) under the corresponding deformation mode, and its corresponding vibration pattern describes the principal vibration direction, amplitude, and phase of each part of the structure at that frequency. When external excitation (such as aerodynamic forces or mechanical vibrations) is close to a certain modal frequency, resonance may occur, leading to a sharp increase in amplitude and creating safety risks. Therefore, it can be used to assess potential risks.

[0092] The logic for performing finite element analysis on a propeller is as follows:

[0093] Finite element modeling is performed on the propeller, and aerodynamic loads are applied to the propeller based on the approximate distribution of aerodynamic forces on the propeller.

[0094] Perform structural static analysis to solve the stress and strain fields in the finite element model of the propeller, extract the principal stress distribution at various points on the blade, and record the maximum principal stress.

[0095] By solving the structural dynamics eigenvalue problem, the vibration modes and vibration patterns of the propeller at each order are obtained.

[0096] According to the principles of structural dynamics, the free vibration equation of any structure can be expressed as:

[0097]

[0098] in Represents the mass matrix, Represents the stiffness matrix. Represents the nodal displacement vector. The second derivative of the displacement is represented by the nodal acceleration vector.

[0099] Assume the solution is simple harmonic motion, that is:

[0100]

[0101] here This represents the eigenvector, which in this embodiment corresponds to the vibration mode. Represents the imaginary unit. This represents the angular frequency, which in this embodiment is the vibration modal frequency divided by... , Indicates the vibration time;

[0102] Substituting the values ​​will yield the structural dynamics eigenvalue problem:

[0103]

[0104] Finite element analysis is used to solve the eigenvalue equations. Typically, the first few frequencies (such as 1 to 6) are output. Each order corresponds to a modal frequency and a mode shape, which can then be displayed in tabular or contour plot form.

[0105] By employing an approximate aerodynamic force distribution (i.e., a refined aerodynamic force distribution obtained from a BEM or parametric piecewise model), the aerodynamic loads under actual operating conditions are accurately applied to the finite element model. Compared with traditional methods of "uniformly distributed load" or "equivalent concentrated load," this approach can reflect the true aerodynamic force changes experienced by various parts of the blade, improving the accuracy of structural analysis. Moreover, within the same finite element framework, both the static performance (maximum principal stress, strain distribution) and dynamic performance (modal frequencies and mode shapes) of the structure can be obtained, enabling simultaneous evaluation of multiple indicators.

[0106] S3: Based on the vibration mode, the vibration risk index of the propeller is generated. Then, with the optimization objectives of minimizing the maximum stress, minimizing the vibration risk index, and maximizing the aerodynamic efficiency, and with the thrust meeting the heavy load requirements as a constraint, a multi-objective optimization model is established.

[0107] The vibration risk index is calculated as follows:

[0108]

[0109] In the formula Indicates the vibration risk index. Indicates the excitation frequency. Indicates the first First vibration mode frequency, Indicates the first Response intensity at the first vibration modal frequency, The index representing the order of vibration modal frequencies. It represents the total order of the vibration modal frequencies.

[0110] As can be seen from the calculation method of the vibration risk index, its essence is to reflect the reciprocal of the distance between the excitation frequency of the structure and the frequencies of each modal, and to weight the response intensity of each mode, in order to measure the risk of resonance of the structure under actual working conditions. This is because mechanical structures are subjected to periodic excitations during operation (such as propeller rotation, periodic changes in aerodynamic forces, etc.). If the excitation frequency is close to the vibration modal frequency of a certain stage of the structure, resonance will occur, leading to a significant increase in amplitude, resulting in structural damage or even failure.

[0111] The vibration risk index, by weighting and accumulating the response intensity of each vibration mode with the interval between the modal frequency and the actual excitation frequency, can characterize the resonance risk of the propeller structure under actual working conditions. It can also be directly embedded into a multi-objective optimization process to achieve synergistic optimization of aerodynamic efficiency, structural strength and vibration safety.

[0112] The multi-objective optimization model aims to minimize maximum stress, minimize vibration risk index, and maximize aerodynamic efficiency. Its expression is as follows:

[0113]

[0114] And the constraints are satisfied: , This indicates the preset overload requirements. ~ These represent the three function expressions in the multi-objective optimization model. This indicates the maximum stress.

[0115] S4: Iterate the multi-objective optimization model to update the geometric parameters of the propeller blades. After the optimization objectives converge, output the final geometric parameters as the optimal design scheme.

[0116] The multi-objective optimization model uses a genetic algorithm to achieve convergence of the objective function through population iteration. The optimization process includes population initialization, simulation calculation, non-dominated sorting selection, crossover and mutation operations, and termination determination.

[0117] The optimized geometric parameters are verified through simulation. Once the optimization effect is confirmed to meet the design objectives, it is output as the optimal design scheme.

[0118] Specifically, the termination criteria (i.e., optimization convergence conditions) can be determined using different methods depending on the engineering needs. For example: maximum number of iterations: the maximum number of iterations (or algebras) that the algorithm can perform. When this number is reached, the algorithm is forcibly terminated regardless of whether the objective function has converged or not; threshold method: if the change of the objective function (such as maximum stress, vibration risk index, aerodynamic efficiency, etc.) for several consecutive generations is lower than a certain set threshold (such as 1%, 0.1%, etc.), then it is considered to have converged; Pareto front stability: if the distribution change of the Pareto solution set (i.e., non-dominated solution set) for several consecutive generations (such as hypervolume index, congestion distance, etc.) is less than a set value, then the optimization is considered to have converged.

[0119] Propeller geometry is typically high-dimensional, nonlinear, and complex. Intelligent algorithms can efficiently explore the design space over a wide range to find the globally optimal or near-optimal solution. Through automatic iteration of the optimization process, non-dominated sorting selection (such as NSGA-II), and crossover and mutation operations, the quality of the population can be continuously improved, enhancing the multi-objective comprehensive performance of the design scheme until the objective function converges. Furthermore, in later stages, it can support more complex constraints (such as manufacturing processes and structural safety) and flexibly integrate other performance indicators, thereby improving design efficiency, accuracy, and overall product performance.

[0120] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0121] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0122] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0123] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the design of a heavy-duty multi-rotor propeller, characterized in that, The specific steps include: S1: The geometric parameters of the propeller blades are mathematically parameterized, the blades are divided into several discrete segments along the radial direction, and the aerodynamic force is calculated at the center point of each discrete segment to obtain the approximate distribution of the aerodynamic force of the entire propeller. S2: The propeller is modeled using the finite element method. Aerodynamic loads are applied based on the approximate distribution of propeller aerodynamic forces, and the propeller is simulated and analyzed to extract the maximum stress value and vibration mode. S3: Based on the vibration mode, the vibration risk index of the propeller is generated. Then, with the optimization objectives of minimizing the maximum stress, minimizing the vibration risk index, and maximizing the aerodynamic efficiency, and with the thrust meeting the heavy load requirements as a constraint, a multi-objective optimization model is established. S4: Iterate the multi-objective optimization model to update the geometric parameters of the propeller blades. After the optimization objectives converge, output the final geometric parameters as the optimal design scheme. The vibration risk index is calculated as follows: In the formula Indicates the vibration risk index. Indicates the excitation frequency. Indicates the first First vibration mode frequency, Indicates the first Response intensity at the first vibration modal frequency, The index representing the order of vibration modal frequencies. It represents the total order of the vibration modal frequencies.

2. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 1, characterized in that: The geometric parameters include the blade chord length and blade twist angle. The mathematical parameterization of these geometric parameters uses a B-spline curve function, the expression of which is: In the formula , Let these represent the blade chord length distribution function and the blade twist angle distribution function, respectively. , They represent the first The B-spline basis function corresponding to the chord length control point and the chord length control point B-spline basis functions corresponding to each torsion angle control point , They represent the first The blade chord length at the first chord control point and the first chord length control point Blade twist angle at each twist angle control point, subscript , These represent the indices of the chord length control point and the torsion angle control point, respectively. , These represent the total number of chord length control points and torsion angle control points, respectively.

3. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 2, characterized in that: The aerodynamic forces include lift, drag, thrust, and torque. The logic for the approximate distribution of the aerodynamic forces generating the propeller is as follows: Divide the blade radially from the blade root to the blade tip into equal intervals. Each discrete segment is calculated based on the BEM model, determining the relative airflow velocity and angle of attack for each segment. Calculate the local lift and local drag corresponding to each discrete segment based on the relative airflow velocity and angle of attack of each discrete segment. By summing the local lift and local drag of all discrete sections on each blade, the overall thrust and torque of the propeller are obtained, thus yielding an approximate distribution of the aerodynamic forces of the entire propeller.

4. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 3, characterized in that: The calculation methods for the relative airflow velocity and angle of attack in the discrete segment are as follows: In the formula , , Representing radii of The relative airflow velocity, angle of attack, and twist angle at the location, and the radius Indicates the first The distance from the center point of the discrete segment to the center plane of the propeller. Indicates a discrete segment index. This indicates the propeller speed under standard operating conditions. This indicates the axial airflow velocity under standard operating conditions; Based on the angle of attack and the airfoil characteristics of the propeller blades, the corresponding lift and drag coefficients are obtained to calculate the local lift and local drag. The calculation methods are as follows: In the formula , , Representing radii of Local lift, local drag, and chord length at the point. , These respectively represent the angle of attack as The lift coefficient and drag coefficient at that time This indicates air density.

5. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 4, characterized in that: The local lift and local drag of each blade on all discrete sections are summed to calculate the overall thrust and torque of the propeller. The calculation methods are as follows: In the formula , These represent the overall thrust and torque of the propeller, respectively. This indicates the number of propeller blades. Indicates radius as The angle of airflow at that location.

6. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 5, characterized in that: The vibration modes include the frequencies of each vibration mode and the corresponding vibration patterns. The logic for performing finite element analysis on the propeller is as follows: Finite element modeling is performed on the propeller, and aerodynamic loads are applied to the propeller based on the approximate distribution of aerodynamic forces on the propeller. Perform structural static analysis to solve the stress and strain fields in the finite element model of the propeller, extract the principal stress distribution at various points on the blade, and record the maximum principal stress. By solving the structural dynamics eigenvalue problem, the vibration modes and vibration patterns of the propeller at each order are obtained.

7. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 6, characterized in that: The multi-objective optimization model aims to minimize maximum stress, minimize vibration risk index, and maximize aerodynamic efficiency. Its expression is as follows: And the constraints are satisfied: , This indicates the preset overload requirements. ~ These represent the three function expressions in the multi-objective optimization model. This indicates the maximum stress.

8. The method for designing and optimizing a heavy-duty multi-rotor propeller according to claim 7, characterized in that: The multi-objective optimization model uses a genetic algorithm to achieve convergence of the objective function through population iteration. The optimization process includes population initialization, simulation calculation, non-dominated sorting selection, crossover and mutation operation, and termination determination. The optimized geometric parameters are verified through simulation. Once the optimization effect is confirmed to meet the design objectives, it is output as the optimal design scheme.

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