Propeller system performance prediction and vibration suppression method based on shell unit

Abstract

The invention discloses a propeller system performance prediction and vibration suppression method based on a shell unit, and the method comprises the steps: firstly determining the structural parameters and geometric information of a propeller blade, and generating corresponding nodes and unit numbers through employing uniform grid division; on the basis, a finite element model is established, a stiffness matrix and a mass matrix of each unit are calculated, and then a kinetic equation of the system is constructed. Through modal analysis, the inherent frequency and vibration mode characteristics of the blade are obtained, and a key vibration mode is identified. And performing dynamic response analysis by using an external load condition, and outputting a response curve of each node and vibration characteristics of key nodes. And finally, adjusting design parameters through a parameter sensitivity analysis and optimization technology so as to effectively suppress vibration and improve performance. The method provides an effective tool for dynamic characteristic analysis and optimization design of the propeller.

Description

Technical Field

[0001] This invention belongs to the field of aviation propulsion technology, specifically relating to a method for predicting the performance and suppressing vibration of a propeller system based on a shell unit. Background Technology

[0002] In aero-engine systems, there are complex torque transmission relationships among the engine, transmission system, and propeller (or rotor). During operation, the system is prone to torsional vibration and thrust pulsation, leading to reduced transmission efficiency and increased structural fatigue damage. To mitigate these problems, existing research mainly focuses on dynamic control and structural damping optimization.

[0003] In existing research, Miao Lizhen et al. proposed a turboshaft engine control method based on torsional vibration suppression. By establishing a simplified five-degree-of-freedom torsional vibration system model including the rotor, hub, transmission system, engine, and fuselage, they achieved real-time simulation and control of the engine's transmission torque. Xu Huichun et al. proposed a novel high-damping propeller structure, introducing high-stiffness springs and hydraulic dampers into the conventional blade structure to improve system damping while maintaining blade stiffness, thereby effectively suppressing longitudinal pulsating thrust and peak blade vibration. While these methods improve system vibration characteristics to some extent, they primarily target specific structures or control strategies and cannot comprehensively reflect the dynamic characteristics of complex propeller systems.

[0004] On the other hand, in the dynamic analysis of propellers and composite material structures, existing technologies have proposed a dynamic prediction method for thin-shell composite materials based on isogeometric analysis (IGA). This method takes thin-shell composite materials as the research object, utilizes non-uniform rational splines (NURBS) to achieve the integration of geometric modeling and numerical analysis, calculates the stiffness matrix, mass matrix, and internal force matrix of the composite material, establishes the overall dynamic equation, and solves the dynamic response under external forces through an implicit time integration algorithm, thereby improving the accuracy and stability of the dynamic analysis.

[0005] However, existing technologies still have the following shortcomings: existing modeling methods are suitable for structures with relatively simple geometry, but modeling propellers or transmission systems with complex geometry is difficult, and geometric accuracy and analysis efficiency are limited; finite element analysis models usually use hexahedral elements, which have large computational load and low solution efficiency, making it difficult to meet the application requirements of complex aerospace power systems in real-time simulation or rapid optimization design. Summary of the Invention

[0006] This invention addresses the technical problems of existing finite element method (FEM) software for propeller dynamic analysis, which requires manual operation, involves complex modeling, and suffers from slow computation speed. The aim is to provide a shell element-based method for predicting propeller system performance and suppressing vibration. This method automatically establishes a shell element model of the propeller blade based on its parameters, derives the dynamic equations, and directly solves these equations numerically to obtain the dynamic characteristics. This method offers rapid computation and facilitates convenient optimization of propeller dynamic parameters.

[0007] To solve the technical problem, the technical solution of the present invention is as follows:

[0008] A method for performance prediction and vibration suppression of a propeller system based on shell elements, the method comprising:

[0009] S1: Obtain the geometric parameters and material properties of the propeller blades, perform mesh generation, and obtain node and element information;

[0010] S2: Based on node and element information, the multi-node shell element theory is adopted. The geometric parameters of the element are calculated using node coordinates and thickness information, and the shape function is constructed. The relationship between strain and displacement is derived to obtain the stiffness matrix and mass matrix of each element.

[0011] S3: Input the stiffness matrix and mass matrix of all elements, assemble them into a global stiffness matrix and mass matrix according to the node connection relationship, establish the damping matrix using the Rayleigh damping assumption, and finally construct the dynamic equation of the propeller system.

[0012] S4: After obtaining the system dynamic equations, solve the generalized eigenvalue problem, use the Lanczos iterative method to obtain eigenvalues ​​and eigenvectors, and obtain modal information, namely the natural frequency and mode shape characteristics of the blade;

[0013] S5: Based on the dynamic equations, modal information and external loads, specific working conditions are applied to the system. The Nermark method or modal superposition method is used to solve the system response, calculate the vibration amplitude and time response of key nodes, and output the dynamic response curves of each node and the vibration characteristics of key nodes.

[0014] S6: Referring to the response results obtained in step S5, change the design parameters, repeat the response analysis, evaluate the impact of parameter changes on the vibration of key nodes, adjust the parameters according to the sensitivity results, and iteratively calculate to minimize the vibration amplitude or optimize the frequency distribution, and finally obtain the optimized parameters and the final dynamic model.

[0015] Furthermore, the method also includes:

[0016] The optimized parameters are substituted back into the final dynamic model for a complete solution. The vibration suppression effect of the optimized blade is verified based on the solution results, and the parameter-performance response relationship is established. Finally, the verified optimized model and rapid performance prediction results are output.

[0017] Furthermore, the geometric parameters include: chord length, paddle length, twist angle, and thickness distribution; the material properties include: density, elastic modulus, and Poisson's ratio.

[0018] Furthermore, step S1 specifically includes:

[0019] Input the geometric parameters and material properties of the propeller blades, and then calculate the number of chordal elements. and radial element number Perform uniform mesh generation, generate node coordinates and element connection relationships, define thickness and local coordinate system for each node, and output basic data file containing node number, coordinates, thickness and element topology information for building finite element model.

[0020] Furthermore, step S2 specifically includes: establishing a finite element model of the blade using the following shell element theory:

[0021] For an 8-node shell element, the coordinate equations of any point within the element are defined using the isoparametric element method.

[0022] (1)

[0023] The definition rule for this formula is as follows: Assume the shell elements have the same displacement in the thickness direction. First, define an 8-node isoparametric element in the plane, where the coordinate variables of the parent element are... Thus, the plane is obtained Coordinates; regarding the thickness direction, The thickness of the surface at each node, The coordinates are in the parent element. Since the thickness direction is simply defined, the mapping between the parent element and the child element is linear.

[0024] For an 8-node shell element, the displacement of any point within the element can be obtained through shape function interpolation:

[0025] (2)

[0026] The first term on the right-hand side of the equation represents the displacement values ​​of each node. By applying the isoparametric element method to this term, the displacement of any node within the element in the shell's mid-plane can be obtained. The right-hand side of the equation represents the influence of the shell element's thickness and the rotational degrees of freedom of the nodes within the element on the displacement of any point within the shell element. Indicates the angular displacement of the node. The matrix defines the direction of the influence of the rotational angular displacement of a node on the node displacement;

[0027] The strain-displacement relationship of the 8-node shell element can be obtained using formula (2);

[0028] (3)

[0029] The stress-strain relationship is as follows:

[0030] (4)

[0031] Based on the principle of virtual work, the stiffness matrix expression for an N-node shell element is derived as follows:

[0032] (5)

[0033] The mass matrix expression for an N-node shell element is:

[0034] (6)

[0035] The shape function matrix is ​​the matrix expression of the displacement-node coordinate relationship, as shown in formula (7):

[0036] For a node with 5 displacements, the shape function is:

[0037] (7).

[0038] It can be understood that step 1 generates geometry and mesh → step 2 uses mesh to calculate unit matrix → step 3 assembles into system equations; step 4 modal analysis provides modal basis for step 5 response solution; step 5 response results serve as evaluation basis for step 6 parameter optimization; step 6 optimized parameters return to step 7 to verify closed loop, forming a complete technology chain.

[0039] Compared with the prior art, the advantages of the present invention are as follows:

[0040] First, modeling with 8-node shell elements allows for a more accurate capture of the complex geometry and dynamic behavior of the propeller blades, ensuring the reliability of the dynamic response. Second, modal analysis, by accurately identifying natural frequencies and mode shapes, effectively avoids resonance phenomena, guaranteeing structural safety. Furthermore, the combination of parameter sensitivity analysis and optimization design provides optimization schemes to further improve system performance and stability. This method balances computational accuracy and efficiency, quickly obtaining a large optimization sample space, which helps designers achieve rapid performance prediction and dynamic characteristic improvement in practical engineering, thereby enhancing the overall effectiveness of propeller design. Attached Figure Description

[0041] Figure 1 Vibration response of node E in the z-direction under different thicknesses. Detailed Implementation

[0042] The specific implementation of the present invention is described below with reference to embodiments:

[0043] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0044] Furthermore, the terms such as "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity of description and are not intended to limit the scope of the invention. Any changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0045] Example 1:

[0046] In one exemplary embodiment, in order to address some shortcomings of existing propeller dynamics analysis methods, this invention provides a propeller dynamics analysis method based on shell elements. By establishing a propeller shell element dynamics model, rapid variable parameter analysis can be achieved when studying propeller dynamics characteristics, satisfying a sufficient sample space for optimization design, ensuring the high efficiency of propeller dynamics characteristic analysis and parameter optimization, and improving the propeller dynamics analysis system.

[0047] 1) After determining the structural parameters of the blade, the blade is modeled using shell elements. First, the mesh density of the blade shell elements is determined and set as nx and ny, where nx is the number of elements in the chord direction and ny is the number of elements in the radial direction.

[0048] There are ny elements in the radial direction, which means there are ny+1 blade element sections. A uniform mesh is used, and the blade element sections are calculated at equal intervals from the blade root to the blade tip. Within each blade element section, nx elements are divided along the chord length, resulting in nx+1 points at equal intervals along the chord length. The coordinates of each point lie on the mid-arc line connecting the midpoints of the upper and lower surfaces of the blade element section. Each point on the blade element section is numbered, and the thickness of each point within the blade element section is calculated to provide parameters for building the finite element model. To ensure accurate representation of the blade's dynamic characteristics, the mesh density can be slightly higher. For each node, the normal to the mid-arc line and the tangent plane of the mid-arc line need to be calculated. A local coordinate system is established using the normal and the tangent plane for subsequent shell element creation. After numbering the nodes and recording the 3D coordinates, local coordinate system, and thickness of each node, the nodes are connected to form several quadrilateral elements, which are then numbered. The eight node numbers corresponding to each element are also recorded.

[0049] 2) After completing the mesh generation, the finite element model of the blade is established using the following shell element theory.

[0050] For an 8-node shell element, the coordinate equations of any point within the element are defined using the isoparametric element method.

[0051] (8)

[0052] The formula is defined as follows: Assume the shell elements have the same displacement in the thickness direction; therefore, the coordinate problem is actually a planar problem. Thus, we first define an 8-node isoparametric element in the plane, where the coordinate variables of the parent element are... Thus, the plane is obtained Coordinates. Regarding the thickness direction, The thickness of the surface at each node, The coordinates are in the parent element. Since the thickness direction is simply defined, the mapping between the parent element and the child element is linear.

[0053] For an 8-node shell element, the displacement of any point within the element can be obtained through shape function interpolation:

[0054] (9)

[0055] The first term on the right-hand side of the equation represents the displacement values ​​of each node. Applying the isoparametric element method to these values ​​yields the displacement of any node within the shell element on the shell's mid-plane. The right-hand side of the equation represents the influence of the shell element's thickness and the rotational degrees of freedom of the nodes within the element on the displacement of any point within the shell element. Indicates the angular displacement of the node. The matrix defines the direction of the influence of the rotational angular displacement of a node on the node displacement.

[0056] The strain-displacement relationship of the 8-node shell element can be obtained using formula (9).

[0057] (10)

[0058] The stress-strain relationship is as follows:

[0059] (11)

[0060] Based on the principle of virtual work, the stiffness matrix expression for an N-node shell element is derived as follows:

[0061] (12)

[0062] The mass matrix expression for an N-node shell element is:

[0063] (13)

[0064] Among them, the shape function matrix is ​​the matrix expression of the displacement-node coordinate relationship, as shown in formula (14).

[0065] For a node with 5 displacements, the shape function is:

[0066] (14)

[0067] 3) Based on the structural parameters of the propeller blade, complete the 8-node shell element mesh generation of the blade, and obtain the mass matrix and stiffness matrix of the blade shell element model through shell element theory, and establish the following dynamic equations.

[0068] (15)

[0069] After inputting the stiffness matrix and mass matrix and calculating the Rayleigh damping matrix, dynamic analysis can be performed on the blade shell element model.

[0070] The Lanczos iterative method can be used to obtain eigenvalues ​​and eigenvectors. By visualizing the values ​​of each eigenvector, the mode shapes can be obtained.

[0071] 4) Obtain the forces acting on the blades under specific working conditions, map the forces onto the F vector in the dynamic equation, and solve formula (15) using the Nermark method.

[0072] 5) After obtaining the system dynamic equations, numerical calculation methods can be used to observe the influence and sensitivity of various parameters on the tip dynamic response by changing the blade parameters, and the amplitude of key nodes can be used as the performance evaluation standard. The directness of the analysis process, the high efficiency of computation, and the convenience of optimization design are greatly improved, realizing the function of rapid performance prediction.

[0073] 6) Based on the rapid performance prediction results, using the vibration amplitude of key nodes as the evaluation object, vibration suppression function is achieved by changing key system parameters, such as... Figure 1 As shown.

[0074] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0075] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A shell-cell based propeller system performance prediction and vibration mitigation method, characterized by, The method comprises: S1: Obtain the geometric parameters and material properties of the propeller blade, perform mesh division, and obtain node and element information; S2: Based on the node and element information, use the multi-node shell element theory, calculate the element geometric parameters using node coordinates and thickness information, construct the shape function, derive the strain and displacement relationship, and obtain the stiffness matrix and mass matrix of each element; S3: Input the stiffness matrix and mass matrix of all elements, assemble them into global stiffness matrix and mass matrix according to the node connection relationship, establish the damping matrix using Rayleigh damping assumption, and finally construct the dynamics equation of the propeller system; S4: After obtaining the system dynamics equation, solve the generalized eigenvalue problem, obtain the characteristic value and eigenvector using Lanczos iteration method, and obtain the modal information, i.e. the natural frequency and mode shape characteristics of the blade; S5: According to the dynamics equation, modal information and external load, load the specific working condition into the system, solve the system response using Nermark method or modal superposition method, calculate the vibration amplitude and time response of the key nodes, and output the dynamic response curve and vibration characteristics of the key nodes; S6: Refer to the response results obtained in step S5, change the design parameters, repeat the response analysis, evaluate the influence of parameter change on the vibration of the key nodes, adjust the parameters according to the sensitivity results, and iteratively calculate to minimize the vibration amplitude or optimize the frequency distribution, and finally obtain the optimized parameters and final dynamics model.

2. The shell-cell based propeller system performance prediction and vibration mitigation method of claim 1, wherein, The method further comprises: Re-substitute the optimized parameters into the final dynamics model, perform complete solution, verify the vibration suppression effect of the optimized blade according to the solution results, establish the parameter-performance response relationship, and finally output the optimized model that passes the verification and the fast performance prediction results.

3. The shell-cell based propeller system performance prediction and vibration mitigation method of claim 1, wherein, The geometric parameters include chord length, blade length, twist angle and thickness distribution; the material properties include density, elastic modulus and Poisson's ratio.

4. The shell-cell based propeller system performance prediction and vibration mitigation method of claim 1, wherein, The step S1 specifically comprises: Input the geometry parameters and material properties of the propeller blade, and divide the blade into chord-wise and radial elements and radial elements Perform uniform meshing, generate node coordinates and element connection relationships, and define thickness and local coordinate system for each node. Output the basic data file containing node number, coordinates, thickness, and element topology information for establishing the finite element model.

5. The shell-cell based propeller system performance prediction and vibration mitigation method of claim 1, wherein, The step S2 specifically comprises: The finite element model of the blade is established by the following shell element theory: (1) where the definition rule of the formula is that the shell element is set to have the same displacement in the thickness direction, and 8-node isoparametric element in the plane is defined first, where the coordinate variable of the parent element is , and the thickness of the surface at each node is ; and in the thickness direction, , the thickness of the surface at each node is , the coordinate in the parent element, and since the definition in the thickness direction is simple, the mapping of the parent element and the child element is a linear relationship; For an 8-node shell element, the coordinate equation of any point in the element is defined using isoparametric element method; (2) In the formula, the first term on the right side is the displacement value of each node, and the isoparametric element method is used to obtain the displacement of any node in the shell surface; the right side of the formula represents the thickness of the shell element and the influence of the rotational freedom of the nodes in the element on the displacement of any point of the shell element, represents the rotational angular displacement of the node, The matrix defines the influence direction of the rotational angular displacement of the node on the displacement of the node; For an 8-node shell element, the displacement of any point in the element is obtained by shape function interpolation: (3) The strain-displacement relationship of the 8-node shell element can be obtained by formula (2); (4) The stress-strain relationship is: (5) The stiffness matrix expression of the N-node shell element is derived according to the virtual work principle: (6) The mass matrix expression of the N-node shell element is: Wherein, the shape function matrix is the matrix expression of the displacement-node coordinate relationship, as shown in formula (7): For 5 displacements of a node, the shape function is: (7)。

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