Method for calculating strength of propeller blade

Abstract

FIELD: aviation.SUBSTANCE: invention relates to methods for calculating the strength of a propeller blade (PB) made of polymer composite materials (PCM) and calculating the dynamic characteristics of the PB blade. The method includes preparing a geometric 3D model of the blade, constructing a mesh using volumetric and flat finite elements; specifying constant values characterizing the properties of materials; specifying properties for the finite elements of the blade; adjusting the masses of large-sized attachments of the blade model using the non-structural mass parameter; adjusting the total mass and position of the centre of gravity of the blade model; applying the distribution of aerodynamic loads of the blade in the form of pressure fields to flat finite elements; applying inertial loads to the blade; calculating the internal force factors of the blade using the numerical finite element method; processing the results of calculating the internal force factors of the blade and obtaining the values of the internal force factors in the design sections of the blade; constructing diagrams of the internal force factors; calculating the strength of the blade using the beam theory based on the obtained values of the internal force factors.EFFECT: accurate and universal method for calculating the strength of a PCM PB blade for static and dynamic strength.1 cl, 13 dwg

Description

[0001] Field of technology to which the invention relates

[0002] The invention relates to the field of aviation, namely to methods for calculating the strength of a propeller blade (PB) made of polymer composite materials (PCM) and calculating the dynamic characteristics of the PB blade.

[0003] A propeller is a bladed propulsion device driven by an engine and designed to generate thrust. The blade, in turn, is the main working part of the propeller, creating thrust during its rotation (Propeller Aerodynamics: A Manual / A.D. Obukhovsky. - 2nd ed. - Novosibirsk: NSTU Publishing House, 2016. - P. 4).

[0004] Calculating the strength of a rotor blade is a rather complex task. Blade loading and operating conditions differ significantly from those of a wing. The key feature is that the loads determining blade strength are variable. Therefore, the blade design must satisfy a wide variety of and often conflicting requirements (Strength Calculation of Main Rotor Blades and Hubs: A Textbook / S.P. Montvila et al. - Kharkov. Kharkov Higher Military Aviation Engineering Red Banner School, 1987 - p. 3).

[0005] Technology Level

[0006] In performing engineering calculations related to the analysis of the strength of structures, various calculation methods are used in practice. The most widely used method for analyzing stresses and strains in engineering structures is the finite element method (FEM). In FEM, the structure under study is mentally divided into separate parts - the finite elements, connected to each other and attached to the base, form a calculation scheme called a finite element scheme or finite element model (Application of the finite element method in solving problems of applied mechanics: a teaching aid / A.O. Shimanovsky, A.V. Putyato - Gomel. Belarusian State University of Transport, Department of Technical Physics and Theoretical Mechanics, 2008 - pp. 6-7).

[0007] In turn, when modeling engineering structures, the so-called beam theory of calculating thin-walled structures is used. Based on this theory, when calculating a thin-walled structure, an assumption is made that a beam finite element is taken as a finite element. It is a linear (one-dimensional) element capable of working both in tension-compression and in bending with torsion. Thus, the calculation of the finite element is carried out based on the beam theory of calculating thin-walled structures (Beam theory of calculating thin-walled structures: textbook / I.V. Zatsepina - Kuibyshev. Ministry of Higher and Secondary Specialized Education of the RSFSR Kuibyshev Order of the Red Banner of Labor Aviation Institute named after S.P. Korolev, 1987 - pp. 3-47).

[0008] In addition, nonlinear analysis gives rise to types of geometric nonlinearity, namely, the so-called large displacements and follower forces. Large displacements are the displacements and rotations of a structure under load without significant deformations, while follower forces are the changes in the direction of the load when the section moves and rotates with the applied load (Implicit Nonlinear Analysis Using MSC Nastran and Patran NAS400 Course Notes / NAS400, Appendix C, 2017 - S2-8, S2-11).

[0009] Document D1 ("Air Propellers," V.L. Alexandrov, Moscow, 1951, Part IV, Chapter XVI, Section 1) is known from the prior art and describes a simplified strength calculation for propeller blades. However, the calculation method presented in D1 does not include calculation of the blade torque, nor does it take into account the blade's unloading from centrifugal force.

[0010] Thus, the strength calculation of the propeller blade disclosed in D1 does not provide an accurate calculation of the mass data of the blade and an accurate calculation of the distribution of the aerodynamic load along the length of the blade.

[0011] The closest analogue to the claimed invention, accepted as a prototype, is document D2 (Aircraft Designers' Guide, Volume III, Book 5, Issue 1, Calculation Methods for Studying the Strength of Propellers, TsAGI Publishing Department, 1979), which describes the method for calculating the strength of propeller blades in more detail, specifically taking into account the unloading of the blade from the action of centrifugal force. However, the calculation method presented in D2 does not provide for the ability to calculate the torque due to inertial and aerodynamic forces, and also does not take into account the distribution of the blade mass along its length.

[0012] Thus, the strength calculation of the propeller blade disclosed in D2 does not provide an accurate calculation of the strength of the propeller blade, in particular, an accurate calculation of the distribution of the aerodynamic load along the length of the blade.

[0013] Disclosure of the essence of the invention

[0014] The objective of the claimed solution is to eliminate the above-mentioned shortcomings identified in the analogues and prototype, in relation to the claimed invention.

[0015] The technical result provided by the claimed invention consists in the creation of an accurate and universal method for calculating the strength of a PCM propeller blade for static and dynamic strength, namely, the calculation of the acting stresses in the structural elements of the blade and the frequency characteristics of the assembled blade by implementing a certain procedure that takes into account the mass-inertial and rigidity characteristics of the blade materials.

[0016] The technical result is achieved in that the method for calculating the strength of a propeller blade consists of the following steps:

[0017] preparation of the geometric 3D model of the blade for constructing a mesh on the outer surface of the blade;

[0018] building a mesh using volumetric and flat finite elements on prepared geometry;

[0019] setting constant values ​​characterizing the properties of materials used in the blade design;

[0020] setting properties for the blade finite elements;

[0021] setting the mass of large-sized attachments of the blade model by means of the non-structural mass parameter;

[0022] Adjusting the total mass and center of gravity position of the blade model;

[0023] application of the distribution of aerodynamic loads of the blade in the form of pressure fields on flat finite elements of the outer surface of the blade;

[0024] application of inertial loads to the blade in the form of angular velocities of rotation of the blade relative to the axis of rotation of the propeller simultaneously taking into account the rotation of the aircraft around the center of gravity, as well as the linear acceleration at the center of gravity of the aircraft;

[0025] Calculation of internal force factors of the blade using the numerical finite element method;

[0026] processing the results of calculating the internal force factors of the blade and obtaining the values ​​of the internal force factors in the calculated sections of the blade;

[0027] construction of diagrams of internal force factors;

[0028] blade strength calculation using beam theory based on the obtained values ​​of internal force factors.

[0029] Brief description of drawings

[0030] The essence of the claimed invention is explained by drawings.

[0031] Figure 1 - Example of preparing blade geometry for grid construction and determination of design sections;

[0032] Figure 2 - Description of the design, discretization diagram and arrangement of flat finite elements on the outer surface of the blade spar skin;

[0033] Figure 3 - Full cross-section of the blade model, with a description of the blade elements and modeling of the filler with volumetric elements;

[0034] Figure 4 - Diagram of the construction of flat finite elements on faces and using nodes of volumetric finite elements;

[0035] Figure 5 - Modeling changes in the properties of the blade finite elements depending on the blade section;

[0036] Figure 6 - Groups of finite elements of large-sized attachments;

[0037] Figure 7 - Diagram of the location of the blade center of gravity;

[0038] Figure 8 - Example of superposition of the pressure field obtained in the aerodynamic calculation on the model for calculating the blade strength;

[0039] Figure 9 - Diagram of inertial loading of the blade by vectors of angular velocities and translational accelerations;

[0040] Figure 10 - Diagram of the location and organization of the calculated cross-section of the blade;

[0041] Figure 11 - Diagram of the acting internal force factors of the calculated blade section;

[0042] Figure 12 - Diagrams of internal force factors of the blade;

[0043] Figure 13 - Diagrams of normal blade stresses.

[0044] Implementation of the invention

[0045] This section provides information disclosing how the invention can be implemented to fulfill the stated purpose of the invention and confirm the feasibility of achieving the technical result when implementing the invention. A detailed description of the claimed propeller blade design method is provided, including a detailed description of the sequence of steps characterizing the claimed propeller blade design method.

[0046] The claimed method for calculating the propeller blade includes the following steps:

[0047] (1) Preparing the 3D geometric model of the blade for constructing a mesh on the outer surface of the blade.

[0048] Preparing a blade's 3D geometric model for mesh generation involves dividing the blade into elements using cross-sectional calculations. A representation of the blade's 3D geometric model, prepared for division into elements using cross-sectional calculations, is shown in Fig. 1. The number and location of cross-sectional calculations are determined based on the laying of the composite layers; the cross-sectional planes are selected at the locations of layer discontinuities. This step is necessary to obtain coplanar nodes of the cross-section (Fig. 10) for the correct generation of internal force diagrams. The blade sections enclosed between two adjacent cross-sectional planes must be formed by the outer surfaces of the blade skin and spars and must have no more than 6 faces to obtain a high-quality finite element mesh (as close as possible in shape to a cube and a square).For this purpose, it is also permissible to separate volumes by longitudinal planes - in places where the geometry of the outer surface changes, in the planes of the side member walls, etc.

[0049] (2) Mesh generation using volumetric and planar finite elements on prepared geometry.

[0050] Finite element mesh construction begins with the creation of volumetric elements of the blade fillers, with the corresponding properties of the isotropic materials used as fillers. The free faces of the volumetric elements lie on the outer surfaces of the blade and the main load-bearing elements. Flat blade skin elements are constructed on the faces of the volumetric elements using nodes of the volumetric elements. The method for constructing the finite element mesh is shown in Figs. 2, 3, and 4.

[0051] (3) Setting constant values ​​that characterize the properties of the materials used in the blade design.

[0052] For all materials used in the blade design and considered in the model, in addition to the mandatory parameters of elastic modulus and Poisson's ratio, the material density must also be specified. The blade's composite properties are first specified as a set of mechanical properties of two-dimensional orthotropic materials (elastic modulus along and across the main fiber direction, Poisson's ratio, and material density), and then as layered composite materials assembled from monolayers of two-dimensional orthotropic materials. The number of layers varies along the blade's length, so it is necessary to specify a set of composite layups for each section of the blade's structural element—the skin, spar, tip, and stringers.Since the PCM blade is created by sequentially winding layers of spar material around a foam core, and then over the spar and foam edges, the layups in the finite element model are assigned for each section of the blade both along the length and along the chord, taking into account the total thicknesses and orientation of the layers (see Fig. 2).

[0053] (4) Setting properties for blade finite elements.

[0054] Properties are assigned to finite element groups using specified stacking patterns for a specific blade section. Since flat elements are constructed on the outer surfaces, an offset equal to half the skin thickness is applied when defining properties. Examples of defining properties as thickness distributions along the length are shown in Fig. 5.

[0055] (5) Setting the weights of large attachments of the blade model by the non-structural weight parameter.

[0056] The attachment weight is adjusted using the non-structural weight parameter. Large attachments for this blade model include heating and protective pads, as well as butt fairings. The non-structural weight parameter is calculated using the formula:

[0057]

[0058] where m is the mass of the suspended element that must be added for the finite element group,

[0059] F - the total area of ​​the group of finite elements corresponding to the geometry of the attachment.

[0060] An example of finite element groups of large-sized attachments for which the non-structural mass parameter is applied is shown in Fig. 6.

[0061] (6) Adjust the total mass and center of gravity position of the blade model.

[0062] Adjusting the total mass of the blade and the position of the center of gravity along the length (Z ЦТ , Fig. 7) and relative to the axis of the blade butt (X ЦТ, Fig. 7 Error! Reference source not found.) is produced by changing the densities of isotropic materials of the foam filler of the blade.

[0063] (7) Application of the distribution of aerodynamic loads of the blade in the form of pressure fields on flat finite elements of the outer surface of the blade.

[0064] The pressure field is applied to the flat finite elements of the blade's outer surface by interpolating the pressure field obtained from the aerodynamic calculation. A comparison of the pressure fields obtained from the aerodynamic calculation and the interpolated pressure field is shown in Fig. 8.

[0065] (8) Application of inertial loads to the blade in the form of angular velocities of rotation of the blade relative to the axis of rotation of the propeller simultaneously taking into account the rotation of the aircraft around the center of gravity, as well as the linear acceleration at the center of gravity of the aircraft.

[0066] Inertial loads in the form of angular velocities are specified relative to a coordinate system located at the aircraft's center of gravity. The longitudinal OY axis of the aircraft's CG coordinate system coincides with the propeller's axis of rotation. Angular velocities are specified relative to the axes of the aircraft's CG coordinate system, as components of the resulting vector. Fig. 9 shows an example of specifying an angular velocity vector, where:

[0067] = 31.7 rad / s - angular velocity of rotation of the propeller;

[0068] = 0.398 rad / s - angular velocity of rotation of the aircraft relative to the transverse axis OX;

[0069] = 0.398 rad / s - angular velocity of rotation of the aircraft relative to the vertical axis OZ;

[0070] This approach allows us to correctly take into account the distribution of the gyroscopic moment along the length of the blade for various combinations of angular velocities of rotation of the aircraft relative to the center of gravity at different azimuthal positions of the blade.

[0071] The normal overload at the aircraft's center of gravity is given by the forward acceleration A z (Fig. 9).

[0072] (9) Calculation of internal force factors of the blade by the numerical finite element method.

[0073] Fig. 11 shows the internal force factors.

[0074] The calculation of the internal force factors of the blade using the finite element method is performed using a nonlinear solution with the Large Displacements and Follower Forces options enabled.

[0075] (10) Processing the results of calculating the internal force factors of the blade and obtaining the values ​​of the internal force factors in the calculated sections of the blade.

[0076] Processing is performed to obtain the distribution of internal force factors—forces and moments—in the blade's design cross-sections. In each design cross-section, element nodes lying in the plane of the design cross-section are formed. The internal force factors are obtained as the sum of the forces from the inertial and aerodynamic loads of the cut-off portion of the blade. The cut-off portion of the blade is the portion of the blade from the tip to the plane of the design cross-section. The diagram of the blade's design cross-section is shown in Fig. 10. The internal force factors in the design cross-section are taken into account in the coordinate system of the design cross-section. The origin of the coordinate system of the design cross-section is located at the geometric center of gravity (CG) of the blade's design cross-section. The OZ axis is directed along the butt axis from the butt to the tip, the OX axis is parallel to the blade chord and is directed from the center of gravity of the section to the leading edge, the OY axis complements the coordinate system to the right and is directed along the action of the resulting aerodynamic load.The diagram of the arrangement of the coordinate system of the design section and internal force factors is shown in Fig. 11.

[0077] (11) Construction of diagrams of internal force factors.

[0078] Based on a set of internal force factors obtained through calculation, force and moment distribution diagrams along the blade length are constructed. Examples of force and moment diagrams are shown in Fig. 12, where:

[0079] Рх - shear force in the plane of the blade chords;

[0080] Ру - shear force in the plane of thrust;

[0081] Pz - centrifugal axial force of the blade;

[0082] Мх - bending moment in the plane of the blade thrust;

[0083] My - bending moment in the plane of the blade chords;

[0084] Mz - blade torque.

[0085] (12) Calculation of blade strength using beam theory based on the obtained values ​​of internal force factors.

[0086] The main internal force factors in the section are the acting axial centrifugal force Pz and the bending moment in the thrust plane Mx. The stresses acting in the design section are calculated using beam theory using the following formula:

[0087]

[0088] where: P z - the acting axial centrifugal force, F - the cross-sectional area of ​​the blade, M х - bending moment in the plane of thrust, J x - the moment of inertia relative to the OX axis of the coordinate system of the calculated blade section, y is the maximum distance from the OX axis to the blade surface (Fig. 11). An example of a diagram of the acting stresses for the upper and lower surfaces of the blade is shown in Fig. 13. The safety factor is calculated using the formula:

[0089]

[0090] where: σ is the effective stress in the calculated section of the blade, [σ] is the permissible stress of the blade material adopted for the calculation.

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