A method for coupled dynamics calculation of a complex three-dimensional profile layout rotor

Abstract

The application discloses a rotor coupling dynamics calculation method of complex three-dimensional shape layout. A coordinate conversion relationship caused by a front protrusion / after-sweeping / downward-reversing configuration is established; nonlinear elastic deformation of elastic blades waving, oscillating and twisting and nonlinear coupling relationship among them are described; nonlinear motion caused by the complex three-dimensional shape layout is described based on the coordinate conversion relationship and the nonlinear coupling relationship; and the relationship among strain energy, kinetic energy and virtual work of external force of the rotor is established based on the Hamilton principle according to the description of the nonlinear motion, and a finite element method of a 15-degree-of-freedom beam element is used to establish a rotor dynamics equation. The application can effectively reflect the structural coupling characteristics and coupling degree of the waving-torsion direction caused by the front / rear sweep of the blade tip, effectively reflect the structural coupling characteristics and coupling degree of the oscillation-torsion direction caused by the upward / downward reversal of the blade tip, and effectively reflect the rotor dynamics characteristic behaviors caused by the three-dimensional shape of the blade.

Description

Technical Field

[0001] This invention relates to the field of helicopter rotor design and theoretical modeling technology, and in particular to a rotor coupling dynamics calculation method with complex three-dimensional shape layout, which is applied to the aeroelastic coupling analysis and research of rotors with complex aerodynamic layouts such as forward thrust, backward sweep and downward dihedral. Background Technology

[0002] The unique vertical takeoff and landing, low-altitude, and low-speed flight characteristics of helicopters make them irreplaceable in both military and civilian applications. The rotor system is the core component of a helicopter, and its performance directly reflects and determines the level of the helicopter's capabilities. During the rotor design phase, multiple objectives, such as rotor performance, noise, and vibration, must be comprehensively considered and balanced, forcing rotor design to employ more advanced design methods. Currently, foreign helicopter companies are adopting unconventional large forward-swept geometry configurations (see...). Figure 1 However, this also brings a series of rotor dynamics-related problems. Compared with traditional straight blades, the most direct and significant feature is that the elastic axis of the blade spars is no longer a straight line, but a broken line or curve. Large forward and backward sweeps of the blades cause the aerodynamic center and chordal center of gravity of the blade profile to move away from the pitch axis, and the changes are very drastic. These geometric layout features and the resulting parameter changes will have a significant impact on the structural characteristics and aeroelastic dynamics of the blades, among which the impact on the torsional dynamics of the blades is particularly significant and important.

[0003] On the one hand, blades with a forward-swept, downward-reverse configuration cause a series of strong structural coupling problems, including complex coupling effects such as bending-torsional coupling, tension-torsional coupling, and tension-bending coupling. These effects have varying degrees of impact on the blade's structural dynamic characteristics, aeroelastic response, and aeroelastic stability, making its dynamic behavior more complex than that of conventional straight blades. On the other hand, the sweeping and forward-sweeping of the blade sections cause the blade's aerodynamic center and chordal center of gravity to move away from the pitch axis, resulting in very strong aerodynamic / inertial coupling. The superposition of multiple factors leads to a very strong flapping / torsional coupling effect in this geometric configuration, making the rotor's aeroelastic stability problem particularly prominent. Therefore, during the rotor design and development phase, it is essential and urgent to establish a rotor coupling dynamics method applicable to complex three-dimensional shapes and accurately predict the rotor coupling dynamics behavior of complex three-dimensional shapes. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the coupled dynamics of rotors with complex three-dimensional shapes. This invention can effectively reflect the structural coupling characteristics and degree of coupling in the flapping-torsion direction caused by the forward / backward sweep of the blade tip, the structural coupling characteristics and degree of coupling in the shimmy-torsion direction caused by the upward / downward reflection of the blade tip, and the rotor dynamics characteristics caused by the three-dimensional shape of the blade.

[0005] The technical solution of this invention is as follows: A method for calculating the coupled dynamics of a rotor with a complex three-dimensional shape, which establishes the coordinate transformation relationship caused by forward / sweep / downward inversion configurations; describes the nonlinear elastic deformation of the elastic blades, including flapping, oscillation, and torsion, as well as the nonlinear coupling relationship between them; describes the nonlinear motion caused by the complex three-dimensional shape based on the coordinate transformation relationship and the nonlinear coupling relationship; and, based on the description of the nonlinear motion, establishes the relationship between rotor strain energy, kinetic energy, and virtual work of external forces according to Hamilton's principle, and establishes the rotor dynamic equations using the finite element method with 15-DOF beam elements.

[0006] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the coordinate transformation relationship is established as follows:

[0007] When a blade with a complex three-dimensional shape has configurations such as forward thrust, backward sweep, and vertical inversion, there is a bend angle Λ in the two segments before and after the inflection point. i Among them, the coordinate transformation matrix for blade forward / backward sweep for:

[0008]

[0009] coordinate transformation matrix for blade up / down rotation

[0010]

[0011] Coordinate transformation matrix corresponding to blade pre-twist angle

[0012]

[0013] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the nonlinear motion is described as follows:

[0014] First, establish a unified coordinate system and position vector expression to obtain the transformation relationship between the undeformed blade coordinate system and the inertial coordinate system:

[0015]

[0016] Where [i, j, k] represent the undeformed coordinate system matrix of the blade; [I, J, K] represent the inertial coordinate system matrix; T FI T represents the transformation matrix from the inertial coordinate system to the fuselage coordinate system. HF T represents the transformation matrix from the fuselage coordinate system to the rotor hub rotation coordinate system. RH T represents the transformation matrix from the rotating coordinate system of the propeller hub to the non-rotating coordinate system of the propeller blade. UR This represents the transformation matrix from the non-rotating coordinate system of the blade to the undeformed coordinate system of the blade;

[0017] The displacement vector of any point Q on a complex three-dimensional blade with forward / sweep / downward inversion configurations is established in the blade's undeformed coordinate system. The expression is as follows:

[0018]

[0019] Where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0020] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, deformation compatibility conditions also exist for adjacent blade segments at nodes:

[0021] U2=T s U1

[0022] D2 = T s D1

[0023] Where U represents the undeformed coordinates, D represents the deformed coordinates, subscripts 1 and 2 represent the numbers of two adjacent blade segments at the node, and T... s The transformation matrix between elements ensures both the coordination and continuity of deformation displacement between elements, as well as the continuity of bending slope; that is, the continuity of translational and rotational degrees of freedom.

[0024] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the strain energy is established as follows:

[0025] Using the theory of moderately deformable beams and based on Green's strain tensor relation, considering tension-bending coupling and bending-torsional coupling, a variational expression for strain energy is established:

[0026]

[0027] Where R represents the blade radius, A represents the cross-sectional area, σ represents stress, and ε represents strain. The moderate variable beam theory considers the stress and strain in the three directions of xx, xη, and xζ in the blade deformation coordinate system [x,η,ζ].

[0028] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the kinetic energy is established as follows:

[0029] Based on the established spatial displacement vector and velocity at any point, establish the variational expression for the blade kinetic energy:

[0030]

[0031] Where R represents the blade radius, A represents the cross-sectional area, ρ represents the blade cross-sectional linear density, and V represents the resultant velocity at any point on the blade. x V η V ζ These are the velocity components in three directions, and [x,η,ζ] represents the three directions of the blade deformation coordinate system.

[0032] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the virtual work of external forces is established as follows:

[0033] Virtual work is generated by the external force on the propeller blades, primarily from the aerodynamic force of the blades; among which... For the blades in stretching (u), oscillation (v), flapping (w), and torsion... Aerodynamic components in the direction;

[0034]

[0035] In the aforementioned method for calculating the coupled dynamics of rotors with complex three-dimensional shapes, the blade aerodynamic forces are calculated using a nonlinear quasi-steady aerodynamic model.

[0036] In the aforementioned method for calculating rotor coupled dynamics of complex three-dimensional shapes, the rotor dynamics equations are established as follows:

[0037] Based on a 15-DOF beam element model, the mass matrix M, damping matrix C, stiffness matrix K, and external force term F of the finite element are solved using the 5-point Gaussian integral method. The element matrix is ​​then transformed to the global coordinate system using the current element transformation matrix Λ. Finally, the global matrix is ​​obtained through the finite element assembly method, forming the dynamic equations of the rotor system.

[0038]

[0039] The transformation relationship for the translational degrees of freedom (tension u, oscillation v, flapping w) between elements is linear, and the transformation is as follows: T s This is the inter-node transformation matrix, where the subscripts 1 and 2 represent the cell numbers of two adjacent vertices;

[0040]

[0041] For rotational degrees of freedom (torsional) between elements The transformation relationship between the oscillation deformation deflection v′ and the flapping deformation deflection w′ is nonlinear, and its transformation is as follows, where the subscripts 1 and 2 represent the element numbers of two adjacent inflection points, and T AR It includes not only the elements of the inter-section transformation matrix, but also the blade deformation degrees of freedom;

[0042]

[0043] Beneficial effects

[0044] Compared with existing technologies, this invention proposes a rotor coupling dynamics calculation method for complex three-dimensional blade layouts. Compared with traditional straight blades, this invention establishes a coordinate transformation matrix between blade transition nodes in the kinematic description of any point on the blade, thus effectively reflecting the three-dimensional shape characteristics of the blade, such as forward thrust, backward sweep, and downward reflection. When describing the nonlinear elastic deformation of the elastic blade flapping, oscillation, and torsion, as well as the nonlinear coupling relationship between them, by establishing deformation compatibility conditions between blade transition nodes, it ensures both the coordination and continuity of deformation displacement between elements, and the continuity of bending slope; that is, the continuity of translational and rotational degrees of freedom. Finally, based on Hamilton's principle and the finite element method of 15-DOF beam elements, the rotor dynamics equations are established, ultimately forming a rotor coupling dynamics calculation method that considers blades with complex three-dimensional shapes, and has the ability to predict the dynamics of rotors with complex three-dimensional shapes.

[0045] This invention can effectively reflect the structural coupling characteristics and degree of coupling in the flapping-torsion direction caused by the tip sweep (see...). Figure 3 This effectively reflects the structural coupling characteristics and degree of coupling in the oscillation-torsion direction caused by the upward / downward reflection of the propeller tip (see...). Figure 4 It can effectively reflect the rotor dynamics characteristics caused by the three-dimensional shape of the blade. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the complex three-dimensional blade configuration layout involved in the present invention;

[0047] Figure 2 This is a schematic diagram of the dynamic model of the complex three-dimensional blade structure designed in this invention, where XYZ is the blade rotation coordinate system, O is the center of the blade hub; Λ is on the undeformed elastic axis. k The rotation angle of blade segment K relative to the previous blade segment; xyz is the coordinate system of point P on blade segment K before deformation, and ξηζ is the deformed coordinate system of point P on blade segment K after deformation.

[0048] Figure 3 The results are calculated for the torsional vibration modes at the fundamental frequency of flapping under different blade tip sweep angles, reflecting the degree of coupling between the flapping and torsional structures.

[0049] Figure 4 The results are the calculated torsional vibration modes at the fundamental frequency of the oscillation under different anti-reflection angles of the propeller tip, reflecting the degree of coupling between the oscillation and torsional structures. Detailed Implementation

[0050] Example 1. A method for calculating the coupled dynamics of a rotor with a complex three-dimensional shape includes:

[0051] (1) Kinematic description of a complex three-dimensional rotor blade. First, a unified coordinate system and position vector expression are established. In the rotor coordinate system, there is usually an inertial coordinate system (X... I ,Y I Z I ), fuselage coordinate system (X F ,Y F Z F The rotor hub does not select a coordinate system (X). H ,Y H Z H ), the undeformed coordinate system (i,j,k) and the deformed coordinate system (i ξ ,j η ,k ζ The transformation expression between the undeformed blade coordinate system and the inertial frame can be solved using the coordinate transformation matrix T (as follows), where the subscript U represents the undeformed coordinate system, R represents the non-rotating blade coordinate system, H represents the rotating hub coordinate system, F represents the fuselage coordinate system, and I represents the inertial coordinate system.

[0052]

[0053] The displacement vector of any point Q on a complex three-dimensional blade with forward / sweep / downward inversion configurations, in the blade's undeformed coordinate system. The expression is as follows (see below) Figure 2 ), where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation.

[0054]

[0055] When a blade with a complex three-dimensional shape has configurations such as forward thrust, backward sweep, and vertical inversion, there is a bend angle Λ in the two segments before and after the inflection point. i The coordinate transformation matrix for the blade forward / backward sweep is as follows:

[0056]

[0057] The blade has an inverted coordinate transformation matrix for the upper / lower sides:

[0058]

[0059] The coordinate transformation matrix corresponding to the blade pre-twist angle:

[0060]

[0061] There are also deformation compatibility conditions for two adjacent blade segments at a node (as follows), where U represents the undeformed coordinates, D represents the deformed coordinates, and the subscripts represent the two adjacent blade segments at the node.

[0062] U2=T s U1

[0063] D2 = T s D1

[0064] T s The transformation matrix between elements must ensure both coordination and continuity of deformation displacement, as well as continuity of bending slope. That is, continuity of translational and rotational degrees of freedom.

[0065] (2) Establish the blade dynamic equation. Based on Hamilton's principle, derive the blade strain energy, kinetic energy, and virtual work terms to establish the blade dynamic equation. Adopt the moderately deformable beam theory and consider the tension-bending coupling and bending-torsional coupling based on Green's strain tensor relationship to establish the strain energy expression (as follows), where σ represents stress and ε represents strain. The moderately deformable beam theory considers stress and strain in three directions: x, xη, and xζ.

[0066]

[0067] The blade kinetic energy expression is established based on the spatial displacement vector expression of any point (as follows), where ρ is the blade profile linear density and V is the velocity of any point on the blade. The influence of the complex three-dimensional shape configuration is fully considered in the calculation of vector, velocity and acceleration.

[0068]

[0069] Virtual work is generated by the external force on the propeller blades, primarily from the aerodynamic force of the blades. For the blades in stretching (u), oscillation (v), flapping (w), and torsion... Aerodynamic components in the direction.

[0070]

[0071] The aerodynamic calculation model for the propeller blades adopts a nonlinear quasi-steady aerodynamic model.

[0072] Finally, the expansions of strain energy, kinetic energy, and virtual work are obtained by using the second-order approximation principle.

[0073] (3) Finite element discretization and assembly

[0074] Based on a 15-DOF beam element model, the mass matrix M, damping matrix C, stiffness matrix K, and external force term F of the finite element are solved using the 5-point Gaussian integral method. The element matrix is ​​then transformed to the global coordinate system using the current element transformation matrix Λ. Finally, the global matrix is ​​obtained through the finite element assembly method, forming the dynamic equations of the rotor system.

[0075]

[0076] The transformation relationship for the translational degrees of freedom (u,v,w) between elements is linear, and the transformation is as follows: T s This is the inter-segment transformation matrix.

[0077]

[0078] For rotational degrees of freedom (torsional) between elements The conversion relationship between the pendulum deformation deflection v′ and the waving deformation deflection w′ is nonlinear, and its conversion is as follows: T AR It includes not only the elements of the inter-segment transformation matrix, but also the blade deformation degrees of freedom.

[0079]

Claims

1. A method for calculating the coupled dynamics of a rotor with a complex three-dimensional shape, characterized in that, Establish coordinate transformation relationships caused by forward / sweep / downward reversal configurations; describe the nonlinear elastic deformation of the elastic blades during flapping, oscillation, and torsion, as well as their nonlinear coupling relationships; describe the nonlinear motion caused by complex three-dimensional shape layouts based on coordinate transformation relationships and nonlinear coupling relationships; based on the description of nonlinear motion, establish the relationship between rotor strain energy, kinetic energy, and virtual work of external forces based on Hamilton's principle, and establish the rotor dynamic equations using the finite element method with 15-DOF beam elements; The coordinate transformation relationship is established as follows: When a blade with a complex three-dimensional shape has a forward-protruding, backward-sweeping, or vertically reversed configuration, there is a bend angle Λ in the two segments before and after the inflection point. i Among them, the coordinate transformation matrix for blade forward / backward sweep for: ； coordinate transformation matrix for blade up / down rotation : ； Coordinate transformation matrix corresponding to blade pre-twist angle : ； Nonlinear motion is described as follows: First, establish a unified coordinate system and position vector expression to obtain the transformation relationship between the undeformed blade coordinate system and the inertial coordinate system: ； Where [i, j, k] represent the undeformed coordinate system matrix of the blade; [I, J, K] represent the inertial coordinate system matrix; T FI T represents the transformation matrix from the inertial coordinate system to the fuselage coordinate system. HF T represents the transformation matrix from the fuselage coordinate system to the rotor hub rotation coordinate system. RH T represents the transformation matrix from the rotating coordinate system of the propeller hub to the non-rotating coordinate system of the propeller blade. UR This represents the transformation matrix from the non-rotating coordinate system of the blade to the undeformed coordinate system of the blade; The displacement vector of any point Q on a complex three-dimensional blade with forward / sweep / downward inversion configurations is established in the blade's undeformed coordinate system. The expression is as follows: ； Where O is the hub center, k is the blade segment number, A is the node number, P is any point on the undeformed elastic axis of blade segment k, P1 is any point on the elastic axis of blade segment k after deformation, and Q is any point on the cross section of blade segment k P1 after deformation. For two adjacent blade segments at a node, there is also a deformation compatibility condition: U2=T s U1, D2=T s D1, Where U represents the undeformed coordinates, D represents the deformed coordinates, subscripts 1 and 2 represent the numbers of two adjacent blade segments at the node, and T... s This is the inter-segment transformation matrix; The strain energy is established as follows: Using the theory of moderately deformable beams and based on Green's strain tensor relation, considering tension-bending coupling and bending-torsional coupling, a variational expression for strain energy is established: ； Where R represents the blade radius, A represents the cross-sectional area, σ represents stress, and ε represents strain. The moderate variable beam theory considers the stress and strain in the three directions of xx, xη, and xζ in the blade deformation coordinate system [x,η,ζ]. The kinetic energy is established as follows: Based on the established spatial displacement vector and velocity at any point, establish the variational expression for the blade kinetic energy: ； Where R represents the blade radius, A represents the cross-sectional area, ρ represents the blade cross-sectional linear density, and V represents the resultant velocity at any point on the blade. x V η V ζ These are the velocity components in three directions, and [x,η,ζ] represent the three directions of the blade deformation coordinate system. The rotor dynamics equations are established as follows: Based on a 15-DOF beam element model, the mass matrix M, damping matrix C, stiffness matrix K, and external force term F of the finite element are solved using the 5-point Gaussian integral method. The element matrix is ​​then transformed to the global coordinate system using the current element transformation matrix Λ. Finally, the global matrix is ​​obtained through the finite element assembly method, forming the dynamic equations of the rotor system. ； The translational degree of freedom transformation relationship between elements is linear, and the transformation is as follows: T s This is the inter-node transformation matrix, where the subscripts 1 and 2 represent the cell numbers of two adjacent vertices; ； The transformation relationship of rotational degrees of freedom between elements is nonlinear, and its transformation is as follows, where the subscripts 1 and 2 represent the element numbers of two adjacent inflection points, and T AR It includes not only the elements of the inter-section transformation matrix, but also the blade deformation degrees of freedom; 。 2. The rotor coupling dynamics calculation method for complex three-dimensional shape layout according to claim 1, characterized in that the virtual work of external forces is established as follows: Virtual work is generated by the external force on the propeller blades, primarily from the aerodynamic force of the blades; among which... For the blades in stretching (u), oscillation (v), flapping (w), and torsion... Aerodynamic components in the direction; 。 3. The rotor coupling dynamics calculation method for complex three-dimensional shape layout according to claim 2, characterized in that, The aerodynamic forces of the propeller blades were calculated using a nonlinear quasi-steady aerodynamic model.

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