Method for calculating damping of rotor blade with any section shape

Abstract

The invention provides a method for calculating damping of a rotor blade with any section shape, which comprises the following steps of: discretizing the cross section of a blade with a complex section shape based on a damping calculation model of a composite laminated plate, dividing the section with any shape into a plurality of arc section units, and regarding each unit as a laminated plate with a rectangular section. Starting from a stress-strain relationship on a blade section, a stress-strain relationship of each layer of an arc section unit under a local coordinate system is obtained by utilizing a coordinate conversion formula, and then strain energy generated by each layer of each arc section unit in a bending process is calculated according to a laminated plate damping calculation model; and dissipated energy in the unit caused by longitudinal, lateral and shear stresses. And finally, summing layer by layer to obtain the sum of dissipated energy and the sum of strain energy of each arc section unit, and summing the energy of the units one by one to obtain the damping performance of the composite rotor blade. According to the method, the damping of the composite rotor blade with the complex section shape can be accurately calculated.

Description

Technical Field

[0001] The invention belongs to the technical field of helicopters, and in particular relates to a method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape. Background Art

[0002] The damping calculation of blades is an important part of analyzing the dynamic response and stability of helicopter rotor systems. The rotor blades are subjected to the combined effects of aerodynamic loads, centrifugal forces, and inertial forces during rotation. These factors will lead to a series of vibration and fatigue problems. In order to ensure the safety and durability of helicopters, it is necessary to conduct a detailed study on the damping characteristics of blades. Due to the characteristics of asymmetric shapes and variable cross-sections in the blade profile, it is difficult to accurately describe the mechanical properties of the entire profile through conventional engineering methods to obtain blade damping.

[0003] At present, the damping of composite rotor blades is mostly obtained by experimental measurement methods, such as free vibration test, forced vibration test, etc. This is because compared with the calculation model, experimental measurement is more time-saving and more accurate, but experimental measurement is difficult to reflect the impact of the blade's design parameters on its damping. Summary of the invention

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

[0005] Technical solution: The present invention discloses a method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape, which specifically comprises the following steps:

[0006] Step 1: Take 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 to construct a YZ coordinate system. Discretize the blade into A arc segment units along the outer contour. For any arc segment unit s, take the tangent direction at any point of the blade section as the m axis, and the direction perpendicular to the tangent as the n axis to establish an mn coordinate system.

[0007] Step 2: Calculate the angle α between the m-axis and the Y-axis of the arc segment unit 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, wherein the 1-axis direction of the principal coordinate system is the blade length direction, and the 2-axis direction is the blade width direction;

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

[0010] Step 5: Obtain the bending stiffness K of the entire blade section based on the tensile stiffness, coupling stiffness and bending stiffness of the blade arc segment unit, and calculate the sth k Strain of a single-layer plate in the fiber coordinate system and stress

[0011] Step 6: Calculate the dissipated energy of each layer of arc segment unit s and strain energy

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

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

[0014]

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

[0016] Furthermore, the step 4 is specifically as follows:

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

[0018]

[0019] in, The sth arc unit s k The stiffness matrix of a single-layer plate in the fiber coordinate system is: is the sth arc unit s k The stiffness matrix of a single-layer plate in the principal coordinate system is: is the sth arc unit s k Strain transformation matrix of single-layer plate; and The expression is as follows:

[0020]

[0021] in, is the sth arc unit s k The angle between the x-axis of the fiber coordinate system of the single-layer board and the 1-axis of the principal coordinate system;

[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] Among them, h is the thickness of arc segment unit s, n is the sth k The distance from the single-layer board to the neutral layer, is the stiffness matrix The amount.

[0025] Furthermore, the bending stiffness K of the entire blade section is calculated in step 5 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 unit to the Z axis in the YZ coordinate system.

[0028] Furthermore, in step 5, the following formula is used to calculate the sth arc segment unit s k Strain of a single-layer plate in the fiber coordinate system

[0029]

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

[0031] ε sX =Y1κ

[0032] Where Y1 is the distance from any arc segment of the blade section to the Z axis, and κ is the curvature of the blade when it bends in the swing direction. 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 arc unit s is calculated according to the following formula k Stress of a single-layer plate

[0036]

[0037] Furthermore, in step 6, the sth arc unit s is calculated according to the following formula k Dissipated energy of a single-layer board

[0038]

[0039] The sth arc unit s is calculated according to the following formula k Strain energy of a single-layer plate

[0040]

[0041] Where v represents the volume, is the sth arc unit s k The stress of a single-layer plate in the x, y, and xy directions is is the sth arc unit s k The strain of the layer in the x, y, and xy directions, ψ L is the specific damping capacity of the single-layer plate in the fiber direction, ψ T is the specific damping capacity of the single-layer plate in the vertical fiber direction, ψ LT is the specific damping capacity of the single-layer plate in the shear direction.

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

[0043]

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

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

[0046] An electronic device / system for calculating the damping of a rotor blade with an arbitrary cross-sectional shape comprises a processor and a memory, wherein the memory stores execution instructions of the processor, and the processor is configured to execute the execution instructions to implement the method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape.

[0047] A computer-readable storage medium is used to store a program, and the program is executed to implement a method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape.

[0048] Beneficial effect: The damping of NACA0012 composite rotor blades was calculated by the method of the present invention, and the calculated result was 3.05×10 -3 , which is 3.45×10 -3In comparison, the calculation error is 11.6%, which meets the engineering estimation and preliminary blade design requirements, indicating that this method can accurately calculate the damping of composite rotor blades with complex cross-sectional shapes. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Schematic diagram of the arc segment unit in the coordinate system of the composite rotor blade section;

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

[0051] Figure 3 Schematic diagram of the fiber coordinate system and principal coordinate system of a single-layer plate in an arc segment unit. DETAILED DESCRIPTION

[0052] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0053] The present application provides a method for calculating the damping of a rotor blade of an arbitrary cross-sectional shape, which is described by taking the application of the method to a terminal as an example, and includes the following steps:

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

[0055] Establish the fiber coordinate system and principal coordinate system of the single-layer plate in the arc segment unit, such as Figure 3 As shown in the figure, according to the classical laminate theory, the stiffness matrix of the corresponding arc segment unit s is obtained. The stiffness matrix of the single-layer plate is expressed as:

[0056]

[0057] in is the sth arc unit s k The stiffness matrix of the single-layer plate in the principal coordinate system is: is the sth arc unit kThe stiffness matrix of the single-layer plate in the fiber coordinate system is the inherent material property of the single-layer plate. is the sth arc unit s k The stress transfer matrix of a single-layer plate, is the sth arc unit s k The strain transformation matrix of the single-layer plate, 1 is the length direction of the blade 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 of the stress conversion matrix and the strain conversion matrix are:

[0059]

[0060]

[0061] in is the sth arc unit s k The angle between the x-direction of a single-layer plate in the fiber coordinate system and the 1-axis direction of the principal coordinate system is positive if it is counterclockwise.

[0062] S2. According to the stiffness matrix of the single-layer plate of the arc unit s, the stiffness matrix components of the arc unit laminate are obtained. The stiffness matrix component expression is:

[0063]

[0064] Among them A ij is the tensile stiffness of the arc segment element s, B ij is the coupling stiffness of the arc segment unit s, D ij is the bending stiffness of the arc segment unit s, For the s k Single-layer plate stiffness matrix component (for example, when i = 1, j = 1 for ), h is the thickness of arc segment unit s, n is the sth arc segment unit s k The distance from the single-layer board to the neutral layer.

[0065] For pure bending deformation in the swing direction, the bending stiffness matrix of the entire blade section is obtained according to the stiffness matrix of the arc segment unit. The bending stiffness expression 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 unit to the Z axis, A11 ,B 11 ,D 11 Refers to A obtained when i=1,j=1 ij ,B ij ,D ij The components in the matrix, where A 11 is the tensile stiffness coefficient, B 11 is the tension-bending coupling stiffness coefficient, D 11 is the stiffness coefficient between bending moment and curvature.

[0068] According to the pure bending deformation in the swing direction, the relationship between the in-plane bending moment and the curvature of the blade is obtained. The expression for the relationship between the in-plane bending moment and the 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 section, and κ is the curvature of the blade when it bends in the swing direction.

[0071] According to the shimmy motion, which is the forward and backward vibration of the blade relative to the axis in the plane, a greater axial tension and compression is generated between the root and the tip of the blade, and the axial strain ε along the length direction of the blade is obtained. X In this embodiment, the in-plane warping on the blade cross section is ignored, and the strain along the contour direction, i.e., the m direction, and the out-of-plane normal direction, i.e., the n direction, is zero. The axial strain expression of the blade is:

[0072] ε sX =ε X =Y1κ

[0073] where ε sX is the strain of arc segment element s along axis 1, ε X is the strain of the blade section along the 1-axis direction in the cylindrical coordinate system, and Y1 is the distance from any arc segment unit of the blade section to the neutral axis Z axis.

[0074] S3. According to the strain at any arc unit of the blade section, the strain of each layer on the arc unit in the fiber coordinate system is obtained. k The strain expression of the layer is:

[0075]

[0076] According to the stress-strain relationship of the single-layer plate, the sth k The stress of the layer, the stress expression is:

[0077]

[0078] in is the sth arc unit s in the fiber coordinate systemk The vector formed by the stress of the layer in the x, y, and xy directions.

[0079] Arc unit s k The expression of the dissipated energy of the layer is:

[0080]

[0081] in is the sth arc unit on segment s k The dissipated energy of the layer, are the sth arc unit s k The stress of the layer in the x, y, and xy directions, are the sth arc unit s k The strain of the layer in the x, y, and xy directions, ψ L is the specific damping capacity of the single-layer plate in the fiber direction, ψ T is the specific damping capacity of the single-layer plate in the vertical fiber direction, ψ LT is the specific damping capacity of the single-layer plate in the shear direction, and v represents the volume.

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

[0083]

[0084] in is the sth arc unit s k The strain energy of the layer.

[0085] S4. Superimpose the dissipated energy and strain energy of each layer of the arc segment unit, and then superimpose the energy on all arc segment units one by one to obtain the damping of the blade within one vibration cycle. The expression of the blade damping is:

[0086]

[0087] Among them, S K is the total number of single-layer plates in the arc segment unit s, and A is the total number of arc segment units.

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

Claims

1. A method for calculating the damping of a rotor blade of arbitrary cross-sectional shape, characterized in that: The specific steps include: Step 1: Take 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 to construct a YZ coordinate system. Discretize the blade into A arc segment units along the outer contour. For any arc segment unit s, take the tangent direction at any point of the blade section as the m axis, and the direction perpendicular to the tangent as the n axis to establish an mn coordinate system. Step 2: Calculate the angle α between the m-axis and the Y-axis of the arc segment unit s 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, wherein the 1-axis direction of the principal coordinate system is the blade length direction, and the 2-axis direction is the blade width direction; Step 4: According to the angle α s Construct the stiffness matrix of the arc segment element s according to Calculate the tensile stiffness A of the arc segment element s ij , coupling stiffness B ij and bending stiffness D ij ; i = 1, 2, 6; j = 1, 2, 6, 6 represents the shear direction in the principal coordinate system. Step 5: Obtain the bending stiffness K of the entire blade section based on the tensile stiffness, coupling stiffness and bending stiffness of the blade arc segment unit, and calculate the sth k Strain of a single-layer plate in the fiber coordinate system and stress Step 6: Calculate the dissipated energy of each layer of arc segment unit s and strain energy Step 7: Superimpose the dissipated energy and strain energy of each layer of the arc segment unit layer by layer, and then sum the dissipated energy and strain energy of all arc segment units along the cross-sectional contour to obtain the damping value of the blade.

2. A method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that: The angle α in step 2 s The expression is: Among them, (y1, z1) and (y2, z2) are the coordinates of the two ends of the neutral layer of the arc segment unit s in the YZ coordinate system.

3. A method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that: The step 4 is specifically as follows: Step 4.1: Calculate the stiffness matrix of the arc segment element s in, The sth arc unit s k The stiffness matrix of a single-layer plate in the fiber coordinate system is: is the sth arc unit s k The stiffness matrix of a single-layer plate in the principal coordinate system is: is the sth arc unit s k Strain transformation matrix of single-layer plate; and The expression is as follows: in, is the sth arc unit s k The angle between the x-axis of the fiber coordinate system of the single-layer board and the 1-axis of the principal coordinate system; Step 4.2: Calculate the tensile stiffness A according to the following formula: ij , coupling stiffness B ij and bending stiffness D ij : Among them, h is the thickness of arc segment unit s, n is the sth k The distance from the single-layer board to the neutral layer, is the 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: The bending stiffness K of the entire blade section is calculated in step 5 as follows: K=∮[A 11 z 2 +2B 11 zcosα s +D 11 cos 2 α s ]ds Where z is the distance from the arc segment unit 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 following formula is used to calculate the sth arc segment unit s. k Strain of a single-layer plate in the fiber coordinate system in, is the sth arc unit s k The strain transformation matrix of a single-layer plate, ε sX is the strain of arc segment element s along the 1-axis direction: e sX =Y1κ Where Y1 is the distance from any arc segment of the blade section to the Z axis, and κ is the curvature of the blade when it bends in the swing direction. κ is calculated using the following formula: M=Kκ Where M is the in-plane bending moment on the blade. The sth arc unit s is calculated according to the following formula k Stress of a single-layer plate 6. A 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 sth arc unit s is calculated according to the following formula k Dissipated energy of a single-layer board The sth arc unit s is calculated according to the following formula k Strain energy of a single-layer plate Where v represents the volume, is the sth arc unit s k The stress of a single-layer plate in the x, y, and xy directions is is the sth arc unit s k The strain of the layer in the x, y, and xy directions, ψ L is the specific damping capacity of the single-layer plate in the fiber direction, ψ T is the specific damping capacity of the single-layer plate in the vertical fiber direction, ψ LT is the specific damping capacity of the single-layer plate in the shear direction.

7. The method for calculating the damping of a rotor blade with an arbitrary cross-sectional shape according to claim 1, characterized in that: The expression of the damping value η of the blade in step 7 is as follows: Among them, S K is the total number of single-layer plates in the arc segment unit 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 the outer contour into A arc segment units.

9. An electronic device / system for calculating the damping of a rotor blade of arbitrary cross-sectional shape, characterized in that: It comprises a processor and a memory, wherein the memory stores execution instructions of the processor, and the processor is configured to execute the execution instructions to implement the method for calculating the damping of a rotor blade of arbitrary cross-sectional shape as claimed in any one of claims 1 to 8.

10. A computer-readable storage medium for storing a program, characterized in that: Execute the program to implement any one of claims 1-8, a method for calculating the damping of a rotor blade of arbitrary cross-sectional shape.

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