A method for calculating the damping of a rotor blade of any profile shape

Abstract

The application provides a method for calculating the damping of a rotor blade with an arbitrary profile shape, which is based on a damping calculation model of a composite laminate plate, and the cross section of the complex profile shape blade is discretized, and the arbitrary profile shape is divided into a plurality of arc segment units, and each unit is regarded as a rectangular cross section laminate plate. Starting from the stress-strain relationship on the blade profile, the stress-strain relationship of each layer of the arc segment unit in the local coordinate system is obtained by using the coordinate conversion formula, and then the strain energy generated by each layer of the arc segment unit in the bending process is calculated according to the damping calculation model of the laminate plate, and the dissipation energy caused by the longitudinal stress, the transverse stress and the shear stress in the unit is calculated. Finally, the sum of the dissipation energy and the sum of the strain energy of each arc segment unit are obtained by layer-by-layer summation, and the damping performance of the composite rotor blade is obtained by energy summation of each unit. The application can accurately calculate the damping of the composite rotor blade with a complex profile shape.

Description

Technical Field

[0001] This invention belongs to the field of helicopter technology, and in particular relates to a method for calculating the damping of rotor blades with arbitrary cross-sectional shapes. Background Technology

[0002] Calculating rotor blade damping is a crucial step in analyzing the dynamic response and stability of a helicopter rotor system. During rotation, rotor blades are subjected to a combination of aerodynamic loads, centrifugal forces, and inertial forces. These factors lead to a series of vibration and fatigue problems. To ensure the safety and durability of the helicopter, a detailed study of the blade damping characteristics is necessary. Due to the asymmetric shape and variable cross-section of the rotor blade profile, it is difficult to accurately describe the mechanical properties of the entire profile using conventional engineering methods, thus hindering the determination of blade damping.

[0003] Currently, most composite rotor blade damping is obtained through experimental measurement methods, such as free vibration tests and forced vibration tests. This is because experimental measurement is more time-efficient and accurate compared to computational models. However, experimental measurement cannot fully reflect the influence of blade design parameters on its damping. Summary of the Invention

[0004] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a method for calculating the damping of rotor blades with arbitrary cross-sectional shapes.

[0005] Technical solution: This invention discloses a method for calculating the damping of rotor blades with arbitrary cross-sectional shapes, specifically including the following steps:

[0006] Step 1: Construct a YZ coordinate system with the direction from the leading edge of the blade to the trailing edge of the blade as the Y-axis and the direction perpendicular to the blade chord as the Z-axis. Discretize the blade along the outer contour into A arc segment elements. For any arc segment element s, establish an mn coordinate system with the tangent direction at any point on the blade profile as the m-axis and the direction perpendicular to the tangent as the n-axis.

[0007] Step 2: Calculate the angle α between the m-axis and the Y-axis of the arc segment element s. s ;

[0008] Step 3: Establish the fiber coordinate system xy and the principal coordinate system of the single-layer plate in the arc segment unit s. The first axis of the principal coordinate system is in the direction of blade length, and the second axis is in the direction of blade width.

[0009] Step 4: Based on the included angle α s Construct the stiffness matrix of the arc element s according to Calculate the tensile stiffness A of the arc element s. ij Coupling stiffness B ij and bending stiffness Dij i = 1, 2, 6; j = 1, 2, 6, 6 represents the shearing direction in the principal coordinate system.

[0010] Step 5: Obtain the bending stiffness K of the entire blade profile based on the tensile stiffness, coupling stiffness, and bending stiffness of the blade arc segment element, and calculate the s-th moment of the arc segment element s. k Strain of a single-layer plate in fiber coordinate system and stress

[0011] Step 6: Calculate the energy dissipation of each layer of the arc segment element s. With strain energy

[0012] Step 7: Stack the dissipated energy and strain energy of each arc segment unit layer by layer, and then sum the dissipated energy and strain energy of all arc segment units along the profile to obtain the damping value of the blade.

[0013] Furthermore, in step 2, the included angle α s The expression is:

[0014]

[0015] Where (y1,z1) and (y2,z2) are the coordinates of the two ends of the neutral layer of the arc segment element s in the YZ coordinate system, respectively.

[0016] Furthermore, step 4 specifically involves:

[0017] Step 4.1: Calculate the stiffness matrix of the arc element s

[0018]

[0019] in, The sth arc segment element s k Stiffness matrix of a single-layer plate in fiber coordinate system For the s-th arc segment element s k Stiffness matrix of a single-layer plate in the principal coordinate system For the s-th arc segment element s k The strain transformation matrix of a single-layer plate; and The expression is as follows:

[0020]

[0021] in, For the s-th arc segment element s k The angle between the x-axis of the fiber coordinate system and the 1-axis of the principal coordinate system of the single-layer lamella;

[0022] Step 4.2: Calculate the tensile stiffness A according to the following formula. ij Coupling stiffness B ij and bending stiffness D ij :

[0023]

[0024] Where h is the thickness of the arc segment element s, and n is the thickness of the s-th segment. k The distance from the single-layer slab to the neutral layer. Stiffness matrix The amount.

[0025] Furthermore, in step 5, the bending stiffness K of the entire blade profile is calculated as follows:

[0026] K = ∮[A 11 z 2 +2B 11 zcosα s +D 11 cos 2 α s ]ds

[0027] Where z is the distance from the arc segment element to the Z-axis in the YZ coordinate system.

[0028] Furthermore, in step 5, the s-th arc segment unit s is calculated using the following formula. k Strain of a single-layer plate in fiber coordinate system

[0029]

[0030] in, For the s-th arc segment element s k The strain transformation matrix of a single-layer plate, ε sX For the strain of the arc segment element s along axis 1:

[0031] ε sX =Y1κ

[0032] Where Y1 is the distance from any arc segment of the blade profile to the Z-axis, and κ is the curvature of the blade when it bends in the direction of oscillation. κ is calculated using the following formula:

[0033] M=Kκ

[0034] Where M is the in-plane bending moment on the blade.

[0035] The sth digit of arc segment s is calculated using the following formula. k Stress of a single-layer plate

[0036]

[0037] Furthermore, in step 6, the s-th arc segment element s is calculated according to the following formula. k Energy dissipation of single-layer plates

[0038]

[0039] The sth digit of arc segment s is calculated using the following formula. k Strain energy of a single-layer plate

[0040]

[0041] Where v represents volume, For the s-th arc segment element s k The stress in the x, y, and xy directions of a single-layer plate. For the s-th arc segment element s k The strain of the layer in the x, y, and xy directions, ψ L ψ is the specific damping capacity along the fiber direction of a single-layer plate. T ψ is the specific damping capacity of a single-layer plate in the direction perpendicular to the fiber. LT This represents the specific damping capacity in the shear direction of a single-layer plate.

[0042] Furthermore, the expression for the damping value η of the blade in step 7 is as follows:

[0043]

[0044] Among them, S K denoted as the total number of single-layer plates in the arc segment element s.

[0045] Furthermore, in step 1, the finite element method is used to discretize the blade along its external contour into A arc segment elements.

[0046] An electronic device / system for calculating the damping of a rotor blade with an arbitrary profile shape includes a processor and a memory, the memory storing execution instructions of the processor, the processor being configured to execute the execution instructions to implement the method for calculating the damping of a rotor blade with an arbitrary profile shape.

[0047] A computer-readable storage medium for storing a program, which is executed to implement a method for calculating the damping of rotor blades with arbitrary cross-sectional shapes.

[0048] Beneficial effects: The damping of the NACA0012 composite material rotor blade was calculated using the method of this invention, and the calculated result is 3.05 × 10⁻⁶. -3 The actual measurement result is 3.45 × 10⁻⁶. -3In comparison, the calculation error is 11.6%, which meets the requirements of engineering estimation and preliminary blade design, indicating that this method can accurately calculate the damping of composite rotor blades with complex cross-sectional shapes. Attached Figure Description

[0049] Figure 1 Schematic diagram of an arc segment element in the cross-sectional coordinate system of a composite material rotor blade;

[0050] Figure 2 This is a schematic diagram of the coordinate system of the arc segment unit of the composite material rotor blade;

[0051] Figure 3 This is a schematic diagram of the fiber coordinate system and principal coordinate system of a single-layer plate within an arc segment unit. Detailed Implementation

[0052] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0053] This application provides a method for calculating the damping of rotor blades with arbitrary cross-sectional shapes. Taking the application of this method to a terminal as an example, the method includes the following steps:

[0054] S1, such as Figure 1 As shown, a blade profile coordinate system YZ is established (where the Y-axis points from the leading edge to the trailing edge of the blade, and the Z-axis is perpendicular to the blade chord and points upward). Using the finite element method, the blade is discretized along its outer contour into many arc segment elements, such as... Figure 2 A coordinate system mn is established for the arbitrary arc segment element (where the m-axis is the tangent direction at any point on the blade profile, with counterclockwise direction as positive, and the n-axis is perpendicular to the tangent at that point and points outward from the blade profile). The arbitrary arc segment element is regarded as a rectangular cross-section laminate. Based on the coordinates of the two ends of the neutral layer of the arc segment element in the YZ coordinate system, namely p1(y1,z1) and p2(y2,z2), the angle between the m-axis of the arc segment element and the Y-axis in the profile coordinate system is calculated.

[0055] Establish the fiber coordinate system and principal coordinate system of the single-layer plate within the arc segment unit, such as... Figure 3 As shown, the stiffness matrix of the corresponding arc segment element s is obtained according to classical laminated plate theory. The expression for the stiffness matrix of a single-layer plate is:

[0056]

[0057] in For the s-th arc segment element s k Stiffness matrix of a single-layer plate in the principal coordinate system For the s-th arc segment unit kThe stiffness matrix of a single-layer plate in the fiber coordinate system is an inherent material property of the single-layer plate. For the s-th arc segment element s k Stress transformation matrix of a single-layer plate For the s-th arc segment element s k The strain transformation matrix of a single-layer plate: 1 is the blade length direction in the principal coordinate system, 2 is the width direction in the principal coordinate system, and 6 is the shear direction in the principal coordinate system.

[0058] The expanded expressions for the stress transformation matrix and the strain transformation matrix are as follows:

[0059]

[0060]

[0061] in For the s-th arc segment element s k The angle between the x-direction of a single-layer plate in the fiber coordinate system and the axis 1 of the principal coordinate system is positive when it is counterclockwise.

[0062] S2. Based on the stiffness matrix of the single-layer plate of the arc segment element s, obtain the stiffness matrix components of the laminated plate of the arc segment element. The expression for the stiffness matrix components is as follows:

[0063]

[0064] Where A ij B is the tensile stiffness of the arc segment element s. ij Let D be the coupling stiffness of the arc segment element s. ij Let be the bending stiffness of the arc segment element s. For the sth k Stiffness matrix components of a single-layer plate (e.g., when i=1, j=1) for ), where h is the thickness of arc segment s, and n is the s-th element of arc segment s. k The distance from the single-layer slab to the neutral layer.

[0065] For pure bending deformation in the oscillation direction, the bending stiffness matrix of the entire blade profile is obtained based on the stiffness matrix of the arc segment element. The expression for the bending stiffness of the blade is:

[0066] K = ∮[A 11 z 2 +2B 11 zcosα s +D 11 cos 2 α s ]ds

[0067] Where z is the distance from the arc segment element to the Z-axis, A11 B 11 D 11 A is obtained when i=1, j=1. ij B ij D ij The components in the matrix, where A 11 B is the tensile stiffness coefficient. 11 D is the tension-bending coupling stiffness coefficient. 11 This is the stiffness coefficient between bending moment and curvature.

[0068] Based on the pure bending deformation in the oscillation direction, the relationship between the in-plane bending moment and curvature of the blade is obtained. The expression for the relationship between the in-plane bending moment and curvature of the blade is:

[0069] M=Kκ

[0070] Where M is the in-plane bending moment on the blade, K is the bending stiffness of the blade profile, and κ is the curvature of the blade when it bends in the direction of oscillation.

[0071] Based on the principle that tessellation is the back-and-forth vibration of the blade relative to its axis in a plane, it is determined that greater axial tension and compression occur between the blade root and tip, resulting in an axial strain ε along the blade's length. X The strain will be relatively large. In this embodiment, in-plane warping on the blade cross-section is ignored; therefore, the strain along the contour direction (m direction) and the out-of-plane normal direction (n direction) is zero. The expression for the axial strain of the blade is:

[0072] ε sX =ε X =Y1κ

[0073] Where ε sX Let ε be the strain of the arc element s along axis 1. X Y is the strain of the blade profile along the lower axis 1 in cylindrical coordinates, and Y1 is the distance from any arc segment element of the blade profile to the neutral axis Z.

[0074] S3. Based on the strain at any arc segment unit of the blade profile, obtain the strain of each layer on the arc segment unit in the fiber coordinate system, and the strain of the s-th layer in the fiber coordinate system. k The strain expression for the layer is:

[0075]

[0076] Based on the stress-strain relationship of a single-layer plate, the s-th stress in the fiber coordinate system is obtained. k The stress of the layer is expressed as follows:

[0077]

[0078] in Let s be the arc segment element s in the fiber coordinate system.k The vector formed by the stresses of the layer in the x, y, and xy directions.

[0079] Arc segment unit s k The expression for the dissipation energy of the layer is:

[0080]

[0081] in For the s-th arc segment unit s k The energy dissipation of the layer, The sth arc segment unit s k The stress of the layer in the x, y, and xy directions. The sth arc segment unit s k The strain of the layer in the x, y, and xy directions, ψ L ψ is the specific damping capacity along the fiber direction of a single-layer plate. T ψ is the specific damping capacity of a single-layer plate in the direction perpendicular to the fiber. LT ν represents the specific damping capacity in the shear direction of a single-layer plate, and v represents the volume.

[0082] The expression for the strain energy of an arc segment element is:

[0083]

[0084] in For the s-th arc segment element s k Strain energy of the layer.

[0085] S4. The dissipated energy and strain energy of each layer of the arc segment element are superimposed, and then the energy of all arc segment elements is superimposed element by element to obtain the damping of the blade in one vibration cycle. The expression for the blade damping is:

[0086]

[0087] Among them, S K Let s be the total number of single-layer plates in the arc segment element s, and A be the total number of arc segment elements.

[0088] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape, characterized in that, Specifically, the steps include the following: Step 1: Construct a YZ coordinate system with the direction from the leading edge of the blade to the trailing edge of the blade as the Y-axis and the direction perpendicular to the blade chord as the Z-axis. Discretize the blade along the outer contour into A arc segment elements. For any arc segment element s, establish an mn coordinate system with the tangent direction at any point on the blade profile as the m-axis and the direction perpendicular to the tangent as the n-axis. Step 2: Calculate the angle between the m-axis and the Y-axis of the arc segment element s. ; Step 3: Establish the fiber coordinate system xy and the principal coordinate system of the single-layer plate in the arc segment unit s. The first axis of the principal coordinate system is in the direction of blade length, and the second axis is in the direction of blade width. Step 4: Construct the stiffness matrix of the arc element s ,according to Calculate arc segment unit tensile stiffness Coupling stiffness and bending stiffness i = 1, 2, 6; j = 1, 2, 6, where 6 represents the shearing direction in the principal coordinate system; Step 5: Obtain the bending stiffness of the entire blade profile based on the tensile stiffness, coupling stiffness, and bending stiffness of the blade arc segment unit. And calculate the first arc segment element s Strain of a single-layer plate in fiber coordinate system and stress ; Step 6: Calculate the energy dissipation of each layer of the arc segment element s. With strain energy ; Step 7: Stack the dissipated energy and strain energy of each arc segment unit layer by layer, and then sum the dissipated energy and strain energy of all arc segment units along the profile to obtain the damping value of the blade.

2. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, The included angle in step 2 The expression is: ； in, and These are the coordinates of the two ends of the neutral layer of the arc segment element s in the YZ coordinate system.

3. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, Step 4 specifically involves: Step 4.1: Calculate the stiffness matrix of the arc element s : ； in, The arc segment unit s Stiffness matrix of a single-layer plate in fiber coordinate system Arc segment unit The Stiffness matrix of a single-layer plate in the principal coordinate system Arc segment unit The The strain transformation matrix of a single-layer plate; and The expression is as follows: ； ； in, Arc segment unit The Fiber coordinate system of single-layer laminate The angle between the axis and the 1-axis of the principal coordinate system; Step 4.2: Calculate the tensile stiffness according to the following formula. Coupling stiffness and bending stiffness : ； Where h is the thickness of the arc segment element s, and n is the thickness of the first arc segment element. The distance from the single-layer slab to the neutral layer. Stiffness matrix The amount.

4. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, Step 5 calculates the bending stiffness of the entire blade profile. Specifically: ； Where z is the distance from the arc segment element to the Z-axis in the YZ coordinate system.

5. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, In step 5, the arc segment unit s is calculated using the following formula. Strain of a single-layer plate in fiber coordinate system : ； in, Arc segment unit The The strain transformation matrix of a single-layer plate. For the strain of the arc segment element s along axis 1: ； Where Y1 is the distance from any arc segment of the blade profile to the Z-axis. The curvature of the blade when it bends in the direction of oscillation is calculated using the following formula. : ； in, The in-plane bending moment on the blade, For the blade section bending stiffness; The arc segment unit s is calculated according to the following formula. Stress of a single-layer plate : 。 6. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, In step 6, the arc segment element s is calculated according to the following formula. Energy dissipation of single-layer plates : ； The arc segment unit s is calculated according to the following formula. Strain energy of a single-layer plate : ； Where v represents volume, Arc segment unit The Single-layer board in Stress in three directions, Arc segment unit The Layer in Strain in three directions This refers to the specific damping capacity along the fiber direction of the single-layer plate. This represents the specific damping capacity of the single-layer plate in the direction perpendicular to the fiber. This represents the specific damping capacity in the shear direction of a single-layer plate.

7. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, Damping value of the blade in step 7 The expression is as follows: ； in, denoted as the total number of single-layer plates in the arc segment element s.

8. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that, In step 1, the finite element method is used to discretize the blade along its external contour into A arc segment elements.

9. An electronic system for calculating the damping of rotor blades with arbitrary cross-sectional shapes, characterized in that, The device includes a processor and a memory, the memory storing execution instructions of the processor, the processor being configured to execute the execution instructions to perform the method for calculating rotor blade damping of any one of claims 1-8.

10. A computer-readable storage medium for storing a program, characterized in that, The procedure is executed to implement any of the methods in claims 1-8 for calculating the damping of rotor blades with arbitrary cross-sectional shapes.

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