Gyro load calculation method and system based on 2D finite elements

Abstract

The present application relates to the field of gyroscopic load calculation, and discloses a gyroscopic load calculation method and system based on 2D finite elements, which comprises the following steps: establishing a ring element model for the axisymmetric structure in an aero-engine rotor, and using integration and isoparametric transformation to calculate the gyroscopic load expression of all ring elements in the ring element model; establishing a plane stress element model for the non-axisymmetric structure in the aero-engine rotor, and calculating the gyroscopic load expression of all plane stress elements according to the element thickness of the plane stress elements in the plane stress element model; generating a system total load equation according to the gyroscopic load expression of the ring elements and the gyroscopic load expression of the plane stress elements, and solving the system total load equation to obtain the gyroscopic load of the aero-engine rotor; and the system comprises a data acquisition module, a modeling module and a calculation module. The present application can improve the accuracy of the calculation results, simplify the calculation process, improve the calculation efficiency, and save a large amount of manpower.

Description

Technical Field

[0001] This invention relates to the field of gyroscope load calculation technology, and in particular to a gyroscope load calculation method and system based on 2D finite element method. Background Technology

[0002] When an aircraft engine flies at high speed, it frequently undergoes turning maneuvers. Due to the high rotational speed of the engine rotor, and the significant rotational amplitude of certain blade disks within the rotor (fan blade disks, booster stage blade disks, compressor blade disks, high-pressure turbine blade disks, low-pressure turbine blade disks, etc.), substantial gyroscopic torque loads are generated. This can adversely affect the rotor shaft and bearings, even causing rubbing damage between the blades and stators, resulting in safety hazards. Therefore, it is essential to perform strength testing on the engine rotor and bearings. A common method is to perform strength calculations on the engine rotor and bearings based on the gyroscopic torque load, which is classified as a flight maneuver load.

[0003] When performing strength calculations on the entire engine rotor, methods such as... are generally used. Figure 2 The diagram illustrates a finite element analysis method for simulating an engine rotor using 2D elements. The finite element method is currently a major method for structural analysis. Its basic principle is to use many small, regularly shaped "elements" (e.g., quadrilaterals used in this invention) to simulate complex-shaped structures (such as...). Figure 2 (As shown). An approximation method is used within regularly shaped units to satisfy the physical equations. Then, all units are combined to approximately satisfy the physical equations across the entire part, and finally, a solution that satisfies the physical equations is obtained.

[0004] Compared to 3D element analysis, the finite element method (FEM) saves significant manpower and shortens the computation cycle. However, existing commercial software cannot automatically calculate gyroscopic loads. To address this issue, current methods involve using commercial CAD software to calculate the mass parameters (such as mass, center of gravity coordinates, and moment of inertia) of each blade disk, then calculating the gyroscopic load based on the aircraft's angular velocity Ω and rotor speed ω, and applying it to the corresponding parts of the rotor shaft for finite element strength calculations. However, this method only considers the gyroscopic effect of the blade disks, neglecting the gyroscopic effect of the shaft itself. Furthermore, the entire process is cumbersome, labor-intensive, and time-consuming. Moreover, the gyroscopic load acts not only on the shaft but also on the blades and disks, and this method ignores this effect, leading to errors and potentially dangerous conclusions drawn from the calculations. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a gyroscope load calculation method and system based on 2D finite element method, which can improve the accuracy of calculation results, simplify the calculation process, improve calculation efficiency, and save a lot of manpower.

[0006] To address the aforementioned technical problems, this invention provides a gyroscope load calculation method based on 2D finite element method, comprising:

[0007] S1: Establish a ring element model for the axisymmetric structure in the aero-engine rotor, and use integration and isoparametric transformation to calculate the gyro load expression for all ring elements in the ring element model;

[0008] S2: Establish a plane stress element model for the non-axisymmetric structure in the aero-engine rotor, and calculate the gyro load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model;

[0009] S3: Generate the total system load equation based on the gyro load expression of the ring element and the gyro load expression of the plane stress element, and solve the total system load equation to obtain the gyro load of the aero-engine rotor.

[0010] Preferably, the step of establishing a ring element model for the axisymmetric structure in the aero-engine rotor specifically involves:

[0011] Establish a cylindrical coordinate system (r, x, θ) with the direction of the rotation center line along the axisymmetric structure as the x-axis, the direction perpendicular to the x-axis as the r-axis, and the axis determined by the right-hand rule based on the x-axis and r-axis as the θ-axis.

[0012] The smallest cyclic element in the sectional plane of the axisymmetric structure is taken as the cyclic element.

[0013] Preferably, the calculation of the gyro load expression for all ring elements in the ring element model using integration and isoparametric transformation is specifically as follows:

[0014] The gyroscopic torque M experienced by the ring unit g for:

[0015] M g =J z ωΩ,

[0016] Among them, J z Let ω be the rotational inertia of the ring element about the z-axis, ω be the rotor speed, and Ω be the deflection velocity vector of the spacecraft about the y-axis.

[0017] The moment of inertia J of any particle q on the ring unit about the z-axis zq for:

[0018] J zq =mr 2 sin 2 θ,

[0019] Where m is the mass of particle q, r is the distance of particle q from the origin of the cylindrical coordinate system, and θ is the circumferential angle of particle q;

[0020] Combining the moment of inertia J of the particle q about the z-axis zq and the gyroscopic torque M experienced by the ring unit g Obtain the gyroscopic torque M of the point mass q gq for:

[0021] M gq =ωΩmr 2 sin 2 θ;

[0022] The amplitude F of the gyroscopic force is obtained based on the fact that the gyroscopic force varies with sinθ along the circumference. gq for:

[0023] F gq =ωΩmr;

[0024] In the ring unit, take any infinitesimal area dA = drdx, and the infinitesimal volume of the infinitesimal area dV = rdθdrdx, where r is the average radius of the infinitesimal area;

[0025] Combining the micro-volume dV and the gyroscopic force amplitude F gq The gyroscopic force F of the microring is obtained by integrating along the circumference. gx for:

[0026] F gx =2πωΩρr 2 drdx,

[0027] Where ρ is the material density;

[0028] The gyroscopic force F on the microring gx Perform isoparametric transformation of the local coordinates to obtain the global coordinates in the same cylindrical coordinate system;

[0029] Integrating over the ring element corresponding to the overall coordinates yields the gyro load expression for each node in the ring element along the x-axis.

[0030] Preferably, the gyroscopic force F on the microring... gx Performing an isoparametric transformation of the local coordinates yields the global coordinates in the same cylindrical coordinate system, specifically:

[0031] Establish gyroscopic force F gx The gyroscopic force F is obtained by using the local coordinate system (η,ξ) of the corresponding micro-ring. gx The local coordinates of the corresponding microrings are then transformed using isoparametric methods to obtain the global coordinates (r(η,ξ), x(η,ξ)) of all nodes within the ring element in the same cylindrical coordinate system:

[0032]

[0033] Where r(η,ξ) is the r-axis coordinate of the global coordinates of the nodes on the ring element, and x(η,ξ) is the x-axis coordinate of the global coordinates of each node on the ring element; i Let x be the r-axis coordinate of the local coordinates of the nodes within the ring element. i Here, is the x-coordinate of the local coordinates of a node within the ring element; n is the number of nodes in the ring element, N1, N2, ..., N... n The shape function for local coordinates.

[0034] Preferably, the shape functions N1, N2, ..., N of the local coordinates are... n Specifically:

[0035] Construct a ring element with 8 nodes, where the shape function for each node is:

[0036] N1=(1-ξ)(1-η)(-ξ-η-1) / 4,

[0037] N2=(1-ξ 2 (1-η) / 2,

[0038] N3=(1+ξ)(1-η)(ξ-η-1) / 4,

[0039] N4=(1-η 2 (1+ξ) / 2,

[0040] N5=(1+ξ)(1+η)(ξ+η-1) / 4,

[0041] N6=(1-ξ 2 (1+η) / 2,

[0042] N7=(1-ξ)(1+η)(-ξ+η-1) / 4,

[0043] N8=(1-η 2 )(1-ξ) / 2.

[0044] Preferably, the gyroscopic load expression {F} of each node in the ring unit in the x-axis direction is... x}for:

[0045]

[0046] Where N = [N1N2…N] n ] T T denotes matrix transpose, and |J| is the Jacobian determinant value.

[0047] Preferably, the step of establishing a plane stress element model for the non-axisymmetric structure in the aero-engine rotor specifically involves:

[0048] A three-dimensional coordinate system (x, y, z) is established for the non-axisymmetric structure in the aero-engine rotor. The non-axisymmetric structure in the aero-engine rotor is divided into a 3D element mesh containing multiple hexahedrons. The midpoints of the four edges of the hexahedron perpendicular to the plane direction of the non-axisymmetric structure are taken as the corner midpoints. The four corner midpoints are connected to obtain the quadrilateral plane stress element.

[0049] Transform the 3D coordinate system (x, y, z) into a cylindrical coordinate system (r, x). In the cylindrical coordinate system, x remains unchanged, and r = sqrt(y). 2 +z 2 ).

[0050] Preferably, the gyro load expression for all plane stress elements is calculated based on the element thickness of the plane stress elements in the plane stress element model, specifically as follows:

[0051] The thickness H of the plane stress element is calculated as follows:

[0052] H = N′ × V 3D / A 2D ,

[0053] Where N' is the number of blades in the non-axisymmetric structure, and V 3D Let A be the volume of the hexahedron. 2D This represents the area of ​​the plane stress element corresponding to the hexahedron;

[0054] The expression for the gyroscopic load {F} at each node in the plane stress element along the x-axis is calculated using integration and isoparametric transformation. x '}for:

[0055]

[0056] Preferably, the total system load equation is generated based on the gyroscopic load expression of the ring element and the gyroscopic load expression of the plane stress element, specifically as follows:

[0057] Assemble the gyroscopic load expression {f} of each node in the ring unit in the x-axis direction. x} and the gyroscopic load expression {F} of each node in the plane stress element in the x-axis direction. x The system load vector {F} is obtained.

[0058] Establish the system total load equation [K]{x}={F}, where [K] is the system total stiffness matrix and {x} is the system total displacement vector.

[0059] This invention also provides a gyroscope load calculation system based on 2D finite element method, including a data acquisition module, a modeling module, and a calculation module.

[0060] The data acquisition module acquires the parameters of the aero-engine rotor and transmits them to the calculation module.

[0061] The modeling module establishes a ring element model for the axisymmetric structure in the aero-engine rotor and a plane stress element model for the non-axisymmetric structure in the aero-engine rotor.

[0062] The calculation module uses integration and isoparametric transformation to calculate the gyroscopic load expression for all ring elements in the ring element model, and calculates the gyroscopic load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model; it generates the total system load equation based on the gyroscopic load expressions of the ring elements and the plane stress elements, and solves the total system load equation to obtain the gyroscopic load of the aero-engine rotor.

[0063] The technical solution of the present invention has the following advantages compared with the prior art:

[0064] This invention establishes a ring element model for axisymmetric structures and a plane stress element model for non-axisymmetric structures, while simultaneously considering gyroscopic loads acting on the axis and on non-axis components such as blades and disks. Based on this, the overall gyroscopic load of the aero-engine rotor is solved. This not only improves the accuracy of the calculation results but also simplifies the calculation process, increases calculation efficiency, and saves a significant amount of manpower. Attached Figure Description

[0065] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0066] Figure 1 This is a flowchart of the present invention.

[0067] Figure 2 This is a 2D unit schematic diagram of the aero-engine rotor in this invention.

[0068] Figure 3 This is a schematic diagram of the shape of the 2D unit established in this invention.

[0069] Figure 4 This is a schematic diagram of the ring unit on the axisymmetric structure of the engine rotor in this invention.

[0070] Figure 5 This is a schematic diagram of the moment of inertia of any mass point on the ring unit about the z-axis in this invention.

[0071] Figure 6This is a schematic diagram of any micro-area within the ring unit in this invention.

[0072] Figure 7 This is a finite element mesh diagram of a certain roulette wheel in this invention.

[0073] Figure 8 This is a schematic diagram illustrating the process of obtaining global coordinates by performing isoparametric transformation of the local coordinates of the gyroscopic force of the microring in this invention.

[0074] Figure 9 This is a schematic diagram illustrating how the non-axisymmetric structure in an aero-engine rotor is divided into a 3D unit mesh containing multiple hexahedrons, as described in this invention.

[0075] Figure 10 This is a schematic diagram of the hexahedron structure in this invention.

[0076] Figure 11 This is a schematic diagram of extracting planar stress elements from a hexahedron in this invention.

[0077] Figure 12 yes Figure 9 A schematic diagram of all 8-node quadrilateral plane stress elements after plane stress element extraction.

[0078] Figure 13 This is a schematic diagram of the connection between the ring element and the plane stress element in this invention. Detailed Implementation

[0079] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0080] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "second" or "first" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the term "comprising" is intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not limited to the listed steps or units but optionally including steps or units not listed, or optionally including other steps or units inherent to these processes, methods, products, or apparatuses.

[0081] Reference Figure 1 As shown in the flowchart, this invention discloses a method for calculating gyroscope load based on 2D finite element method, including:

[0082] S1: Establish a ring element model for the axisymmetric structure in the aero-engine rotor (including the axisymmetric structure of the aero-engine rotor shaft), and use integration and isoparametric transformation to calculate the gyro load expression for all ring elements in the ring element model.

[0083] S1-1: Establish a ring element model for the axisymmetric structure in the aero-engine rotor, specifically:

[0084] Because the engine rotor's structure, including the engine disk and shaft, exhibits axisymmetry after simplification, ring elements are used for calculation. A ring element is a 2D element, such as... Figure 3 The diagram shown is a schematic representation of the shape of the 2D unit established in this invention, including 8 nodes (1-8) and 4 edges (14, 12, 23, 34). Figure 2 All the small quadrilaterals on each structure are of this type of 2D unit structure. For example... Figure 4 The diagram shows a ring element on an axisymmetric structure of an engine rotor. A cylindrical coordinate system (r, x, θ) and a rectangular coordinate system (x, y, z) are established using the direction along the rotation center line of the axisymmetric structure as the x-axis. The direction perpendicular to the x-axis is taken as the r-axis, and the axis determined by the right-hand rule based on the x-axis and r-axis is taken as the θ-axis. Figure 4 In this system, r, x, θ represent a cylindrical coordinate system; the direction perpendicular to the x-axis is taken as the y-axis, and the axis determined by the right-hand rule is taken as the z-axis. Figure 4 In the figure, x, (y), and (z) represent the rectangular coordinate system (x, y, z). In the figure, y and z are enclosed in parentheses to distinguish them from the cylindrical coordinate system.

[0085] The smallest cyclic element in the sectional plane of the axisymmetric structure is taken as the ring element. Geometrically, the ring element is a 2D element. The nodes of the element generally adopt a cylindrical coordinate system with r and z coordinates. However, displacement, load, stress variables, etc. are affected by gyroscopic loads and do not only have r and z components. Therefore, the circumferential components (displacement, load, stress, etc.) of the ring element vary according to trigonometric functions (cosθ or sinθ), so it can also be said to be a quasi-3D element. Geometrically, a ring element actually represents a ring, and each node actually represents a circle.

[0086] S1-2: The specific expression for calculating the gyroscopic load of all ring elements in the ring element model using integration and isoparametric transformation is as follows:

[0087] S1-2-1: Calculate the gyroscopic torque acting on the ring unit. for:

[0088]

[0089] Among them, J z Let be the moment of inertia of the ring element about the z-axis. The rotor speed vector. The direction is the same as the x-axis; For the aircraft around the vertical axis ( Figure 4 The deflection velocity vector (as shown on the y-axis). The direction is the same as the y-axis;

[0090] Since the x and y axes are perpendicular, the gyroscopic torque M on the ring unit can be obtained by neglecting rotor deformation. g for:

[0091] M g =J z ωΩ,

[0092] Among them, J z Let ω be the moment of inertia of the ring element about the z-axis, and ω be the rotor speed, i.e., the vector. The value of Ω is the deflection velocity vector of the aircraft about the y-axis, i.e., the vector... The value;

[0093] S1-2-2: As Figure 5 The diagram shows the moment of inertia of a particle on a ring element about the z-axis. The moment of inertia J of any particle q on the ring element about the z-axis is... zq for:

[0094] J zq =my 2 =mr 2 sin 2 θ,

[0095] Where m is the mass of particle q, y is the distance of particle q along the y-axis, r is the distance of particle q from the origin of the cylindrical coordinate system, i.e., the radius, and θ is the circumferential angle of particle q.

[0096] S1-2-3: J zq =mr 2 sin 2 Substituting θ into formula M g =J z ωΩ, that is, the moment of inertia J of the particle q about the z-axis. zq and the gyroscopic torque M experienced by the ring unit g The gyroscopic torque M of the particle q is calculated. gq for:

[0097] M gq =ωΩmr 2 sin 2 θ;

[0098] From the relationship between force and torque: force = torque / lever arm, we can obtain the gyroscopic force, and the direction of the gyroscopic force is the -x direction.

[0099] S1-2-4: Since the gyroscopic force varies with sinθ along the circumference, therefore F gq sinθ=sinθM gq / r=ωΩmr 2 sin 2 θ / (rsinθ)=ωΩmrsinθ, where F gq This represents the amplitude of the gyroscopic force, thus yielding the gyroscopic force amplitude F. gq for:

[0100] F gq =ωΩmr;

[0101] S1-2-5: As Figure 6 As shown, in the ring unit, take any infinitesimal area dA = drdx, where d() represents the integral along this direction, and the infinitesimal volume of the infinitesimal area dV = rdθdrdx, where r is the average radius of the infinitesimal area;

[0102] The mass m of a particle is equal to its infinitesimal volume dV × the material density ρ, i.e., m = ρdV = ρrdθdrdx; substituting dV = rdθdrdx into F gq =ωΩmr, that is, combining the micro-volume dV and the gyroscopic force amplitude F gq The gyroscopic force F of the microring is obtained by integrating along the circumference. gx for:

[0103]

[0104] Where ρ is the material density;

[0105] S1-2-6: As Figure 7 As shown, the 2D ring elements in each part of the roulette wheel are not necessarily as shown. Figure 6 The rectangle shown necessitates an isoparametric transformation of the original 2D ring element. For example... Figure 8 As shown, the gyroscopic force F on the microring gx Performing an isoparametric transformation of the local coordinates yields the global coordinates in the same cylindrical coordinate system, specifically:

[0106] Establish gyroscopic force F gx The corresponding micro-ring's local coordinate system is (η,ξ). The local coordinate system is represented by (η,ξ). The isoparametric transformation converts the local coordinate representation under (η,ξ) to the global coordinate representation under (r,x). Obtaining the gyroscopic force F. gx The local coordinates of the corresponding microrings are then transformed using isoparametric methods to obtain the global coordinates (r(η,ξ), x(η,ξ)) of all nodes within the ring element in the same cylindrical coordinate system:

[0107]

[0108] Where r(η,ξ) is the r-axis coordinate of the global coordinates of the nodes on the ring element, and x(η,ξ) is the x-axis coordinate of the global coordinates of each node on the ring element; i Let x be the r-axis coordinate of the node within the ring element, i.e., all micro-rings, in the local coordinate system (η,ξ). i Let be the x-axis coordinate of the node within the ring element, i.e., all micro-rings, in the local coordinate system (η, ξ); n is the number of nodes on the ring element, N1, N2, ..., N... n The shape function for local coordinates.

[0109] The shape functions N1, N2, ..., N of the local coordinates (η, ξ) n Specifically:

[0110] Construct a ring element with 8 nodes, where the shape function for each node is:

[0111] N1=(1-ξ)(1-η)(-ξ-η-1) / 4,

[0112] N2=(1-ξ 2 (1-η) / 2,

[0113] N3=(1+ξ)(1-η)(ξ-η-1) / 4,

[0114] N4=(1-η 2 (1+ξ) / 2,

[0115] N5=(1+ξ)(1+η)(ξ+η-1) / 4,

[0116] N6=(1-ξ 2 (1+η) / 2,

[0117] N7=(1-ξ)(1+η)(-ξ+η-1) / 4,

[0118] N8=(1-η 2 )(1-ξ) / 2.

[0119] S1-2-7: For the global coordinates, i.e., for the equation The integral of the ring element corresponding to the result after isoparametric transformation yields the expression for the gyro load of each node in the ring element in the x-axis direction.

[0120] The expression for the gyroscopic load at each node in the ring element along the x-axis direction {F x}for:

[0121]

[0122] Where N = [N1N2…N]n ] T T represents the matrix transpose, and |J| is the Jacobian determinant value. In this embodiment, for an 8-node ring element, {F x} is a vector, {F x It includes 8 elements, which are the gyroscope loads of 8 nodes in the x-axis direction.

[0123] S2: Establish a plane stress element model for the non-axisymmetric structure in the aero-engine rotor (including non-axisymmetric structures such as the rotor disc and blades of the aero-engine rotor), and calculate the gyro load expression of all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model.

[0124] S2-2: Establish a plane stress element model for the non-axisymmetric structure in the aero-engine rotor, specifically:

[0125] When the blade has a non-axisymmetric structure, ring elements cannot be used; therefore, this invention employs plane stress elements. The number of nodes in the plane stress elements of the blade should be the same as that in the ring elements of the disk; therefore, in this embodiment, the plane stress elements are also set to 8 nodes.

[0126] Establish a three-dimensional coordinate system (x, y, z) for the non-axisymmetric structure in the aero-engine rotor, and divide the non-axisymmetric structure in the aero-engine rotor into the following components: Figure 9 The 3D unit mesh shown contains multiple hexahedrons, such as Figure 10 The diagram shows 20 points, including the 8 vertices and the midpoints of the 12 edges of the hexahedron, designated as nodes. (See diagram for example.) Figure 11 As shown, the midpoints of the four edges of the hexahedron perpendicular to the plane of the non-axisymmetric structure are taken as corner midpoints. Connecting the four corner midpoints yields a quadrilateral plane stress element. The midpoints of the line segments formed by the four corner midpoints and the midpoints of the four edges (i.e., the midpoints of the symmetrical edges of the hexahedron parallel to the plane of the non-axisymmetric structure) form eight points, resulting in an 8-node quadrilateral surface element identical to the ring element. Figure 11 As shown, by averaging along the thickness direction (i.e., averaging along a plane perpendicular to the non-axisymmetric structure), the... Figure 10 The 20-node hexahedral element is converted into Figure 11 The 8-node quadrilateral surface element shown by the dashed line in the middle. Figure 9 The 3D unit mesh shown is converted into, for example: Figure 12 The 2D planar structure shown.

[0127] Transform the 3D coordinate system (x, y, z) into a cylindrical coordinate system (r, x). In the cylindrical coordinate system, x remains unchanged, and r = sqrt(y). 2 +z 2 ).

[0128] S2-2: Calculate the gyro load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model, specifically:

[0129] The thickness H of the plane stress element is calculated as follows:

[0130] H = N′ × V 3D / A 2D ,

[0131] Where N' is the number of blades in the non-axisymmetric structure, and V 3x Let A be the volume of the hexahedron. 2D This represents the area of ​​the plane stress element corresponding to the hexahedron;

[0132] The expression for the gyroscopic load {F} at each node in the plane stress element along the x-axis is calculated using integration and isoparametric transformation. X '}for:

[0133]

[0134] Gyroscope load {F x The specific calculation process of '} is the same as that of {F}. x The same applies, so I will not repeat it here.

[0135] S3: Generate the total system load equation based on the gyro load expression of the ring element and the gyro load expression of the plane stress element, and solve the total system load equation to obtain the gyro load of the aero-engine rotor.

[0136] Gyroscopic loads are applied to all nodes; therefore, all gyroscopic effects in both symmetrical and asymmetrical structures must be considered. For example... Figure 13 As shown, the ring elements and plane stress elements are connected. The connection points of the ring elements and plane stress elements are one-to-one (the corresponding points and lines must coincide) and cannot be offset from each other. That is, when dividing the ring elements and the hexahedron, the total number of ring elements Na and the total number of plane stress elements Np are divided in reverse according to the connection points.

[0137] Assemble the gyroscopic load expression {F} of each node in the ring unit in the x-axis direction. x} and the gyroscopic load expression {F} of each node in the plane stress element in the x-axis direction. x The system load vector {F} is obtained.

[0138] Establish the system total load equation [K]{x}={F}, where [K] is the system total stiffness matrix and {x} is the system total displacement vector.

[0139] Assemble {F x} and {F xThe process of obtaining the system load vector {F} and solving the total system load equation is detailed in the literature "Basic Principles and Numerical Methods of Finite Element Method", which is existing technology and will not be elaborated further. Solving the total system load equation yields the stress, deformation, and bearing reaction forces of the parts considering the gyroscopic load. Based on the solved structure, the gyroscopic load of the aero-engine rotor can be derived.

[0140] This invention also discloses a gyroscopic load calculation system based on 2D finite element method, including a data acquisition module, a modeling module, and a calculation module. The data acquisition module acquires the rotational parameters of the aero-engine rotor, including rotational speed ω and yaw rate Ω, and transmits them to the calculation module. The modeling module establishes a ring element model for the axisymmetric structure in the aero-engine rotor and a plane stress element model for the non-axisymmetric structure; this includes establishing ring element mesh data for the shaft and disk, plane stress element mesh data for the blades, material density, and the total number of ring elements Na and the total number of plane stress elements Np. The calculation module uses integration and isoparametric transformation to calculate the gyroscopic load expression for all ring elements in the ring element model, and calculates the gyroscopic load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model; it generates the total system load equation based on the gyroscopic load expressions of the ring elements and the plane stress elements, and solves the total system load equation to obtain the gyroscopic load of the aero-engine rotor. Automated calculation through this system can further improve computational efficiency and save manpower.

[0141] This invention establishes a ring element model for axisymmetric structures and a plane stress element model for non-axisymmetric structures, while simultaneously considering gyroscopic loads acting on the axis and on non-axis components such as blades and disks. Based on this, the overall gyroscopic load of the aero-engine rotor is solved. This not only improves the accuracy of the calculation results but also simplifies the calculation process, increases calculation efficiency, and saves a significant amount of manpower.

[0142] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0143] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0144] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0145] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0146] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for calculating gyroscope load based on 2D finite element method, characterized in that, include: S1: Establish a ring element model for the axisymmetric structure in the aero-engine rotor, and use integration and isoparametric transformation to calculate the gyro load expression for all ring elements in the ring element model; S2: Establish a plane stress element model for the non-axisymmetric structure in the aero-engine rotor, and calculate the gyro load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model; The establishment of a plane stress element model for the non-axisymmetric structure in the aero-engine rotor is specifically as follows: A three-dimensional coordinate system (x, y, z) is established for the non-axisymmetric structure in the aero-engine rotor. The non-axisymmetric structure in the aero-engine rotor is divided into a 3D element mesh containing multiple hexahedrons. The midpoints of the four edges of the hexahedron perpendicular to the plane direction of the non-axisymmetric structure are taken as the corner midpoints. The four corner midpoints are connected to obtain a quadrilateral plane stress element. Transform the 3D coordinate system (x, y, z) into a cylindrical coordinate system (r, x). The x-axis remains unchanged in the cylindrical coordinate system, while the x-axis remains unchanged in the cylindrical coordinate system. ; The gyro load expression for all plane stress elements is calculated based on the element thickness of the plane stress elements in the plane stress element model, specifically as follows: The thickness H of the plane stress element is calculated as follows: ， Where N' is the number of blades in the non-axisymmetric structure. The volume of the hexahedron. This represents the area of ​​the plane stress element corresponding to the hexahedron; The expression for the gyroscopic load at each node in the plane stress element along the x-axis is calculated using integration and isoparametric transformation. for: ； S3: Generate the total system load equation based on the gyro load expression of the ring element and the gyro load expression of the plane stress element, and solve the total system load equation to obtain the gyro load of the aero-engine rotor.

2. The gyroscope load calculation method based on 2D finite element method according to claim 1, characterized in that: The establishment of a ring element model for the axisymmetric structure in the aero-engine rotor is specifically as follows: Establish a cylindrical coordinate system (r, x, θ) with the direction of the rotation center line along the axisymmetric structure as the x-axis, the direction perpendicular to the x-axis as the r-axis, and the axis determined by the right-hand rule based on the x-axis and r-axis as the θ-axis. The smallest cyclic element in the sectional plane of the axisymmetric structure is taken as the cyclic element.

3. The gyroscope load calculation method based on 2D finite element method according to claim 2, characterized in that: The calculation of the gyro load expression for all ring elements in the ring element model using integration and isoparametric transformation is specifically as follows: The ring unit is subjected to gyroscopic torque. for: ， in, Let be the moment of inertia of the ring element about the z-axis. The rotor speed is Let y be the deflection velocity vector of the aircraft about the y-axis; The moment of inertia of any particle q on the ring element about the z-axis for: ， Where m is the mass of particle q, r is the distance of particle q from the origin of the cylindrical coordinate system, and θ is the circumferential angle of particle q; Combining the moment of inertia of the particle q about the z-axis and the gyroscopic torque experienced by the ring unit Obtain the gyroscopic torque of point mass q for: ； According to the gyroscopic force along the circumference The change yields the amplitude of the gyro force. for: ； Take any small area in the ring unit micro-area and micro-volume , where r is the average radius of the micro-area; Combined with the micro-volume and the amplitude of the gyro force The gyroscopic force of the microring is obtained by integrating along the circumference. for: ， in The density of the material; gyroscopic force on the microring Perform isoparametric transformation of the local coordinates to obtain the global coordinates in the same cylindrical coordinate system; Integrating over the ring element corresponding to the overall coordinates yields the gyro load expression for each node in the ring element along the x-axis.

4. The gyroscope load calculation method based on 2D finite element method according to claim 3, characterized in that: gyroscopic force on the microring Performing an isoparametric transformation of the local coordinates yields the global coordinates in the same cylindrical coordinate system, specifically: Establish gyro force The corresponding local coordinate system of the micro-ring ( ), to obtain gyro force The local coordinates of the corresponding micro-rings are used to perform isoparametric transformations on the local coordinates of all micro-rings to obtain the global coordinates of all nodes within the ring element in the same cylindrical coordinate system. )for: ， ； in, Let r be the global coordinate of the node on the ring element. The x-axis coordinate of the global coordinates of each node on the ring element; Let r be the r-axis coordinate of the local coordinates of the nodes within the ring element. The x-axis coordinate is the local coordinate of a node within the ring element. This represents the number of nodes on the ring element. , … The shape function for local coordinates.

5. The gyroscope load calculation method based on 2D finite element method according to claim 4, characterized in that: The shape function of the local coordinates , … Specifically: Construct a ring element with 8 nodes, where the shape function for each node is: ， ， ， ， ， ， ， 。 6. The gyroscope load calculation method based on 2D finite element method according to any one of claims 4-5, characterized in that: The gyroscopic load expression for each node in the ring element in the x-axis direction. for: ， in, T denotes matrix transpose. It is the value of the Jacobian determinant.

7. The gyroscope load calculation method based on 2D finite element method according to claim 1, characterized in that: The total system load equation is generated based on the gyroscopic load expression of the ring element and the gyroscopic load expression of the plane stress element, specifically as follows: Assemble the gyroscopic load expression of each node in the ring unit in the x-axis direction. and the gyroscopic load expression for each node in the plane stress element in the x-axis direction. The system load vector {F} is obtained. Establish the total load equation of the system , where [K] is the total stiffness matrix of the system, and {x} is the total displacement vector of the system.

8. A gyroscope load calculation system based on 2D finite element method, characterized in that: It includes a data acquisition module, a modeling module, and a calculation module. The data acquisition module acquires the parameters of the aero-engine rotor and transmits them to the calculation module. The modeling module establishes a ring element model for the axisymmetric structure in the aero-engine rotor and a plane stress element model for the non-axisymmetric structure in the aero-engine rotor. The calculation module uses integration and isoparametric transformation to calculate the gyro load expression for all ring elements in the ring element model, and calculates the gyro load expression for all plane stress elements based on the element thickness of the plane stress elements in the plane stress element model. The total system load equation is generated based on the gyro load expression of the ring element and the gyro load expression of the plane stress element. The gyro load of the aero-engine rotor is obtained by solving the total system load equation. The establishment of a plane stress element model for the non-axisymmetric structure in the aero-engine rotor is specifically as follows: A three-dimensional coordinate system (x, y, z) is established for the non-axisymmetric structure in the aero-engine rotor. The non-axisymmetric structure in the aero-engine rotor is divided into a 3D element mesh containing multiple hexahedrons. The midpoints of the four edges of the hexahedron perpendicular to the plane direction of the non-axisymmetric structure are taken as the corner midpoints. The four corner midpoints are connected to obtain a quadrilateral plane stress element. Transform the 3D coordinate system (x, y, z) into a cylindrical coordinate system (r, x). The x-axis remains unchanged in the cylindrical coordinate system, while the x-axis remains unchanged in the cylindrical coordinate system. ; The gyro load expression for all plane stress elements is calculated based on the element thickness of the plane stress elements in the plane stress element model, specifically as follows: The thickness H of the plane stress element is calculated as follows: ， Where N' is the number of blades in the non-axisymmetric structure. The volume of the hexahedron. This represents the area of ​​the plane stress element corresponding to the hexahedron; The expression for the gyroscopic load at each node in the plane stress element along the x-axis is calculated using integration and isoparametric transformation. for: 。

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