Helicopter multi-modal coupling ground resonance calculation method

Abstract

The application belongs to the field of helicopter structure strength design, and relates to a helicopter multi-modal coupling ground resonance calculation method. The method comprises the following steps: selecting a typical weight state and a typical lift state of a certain type of helicopter, and calculating the compression stiffness and compression damping of the main landing gear, the tail landing gear and the buffer strut; simulating the compression stiffness and compression damping of the main landing gear and the tail landing gear in the full machine dynamics model, and establishing the full machine dynamics model on the landing gear; performing body complex modal calculation on the full machine dynamics model on the landing gear, and selecting six rigid body modes, modal mass, damping ratio and modal shape of the body on the main landing gear and the tail landing gear from the calculation results; and on the basis of the body motion, considering the hub center two directions and the blade oscillation motion, combining several modes to perform ground resonance stability calculation. The application can obtain more real ground resonance stability curve, and provides an accurate and reliable calculation method for ground resonance design.

Description

Technical Field

[0001] The invention belongs to the field of helicopter structural strength design and relates to a helicopter ground resonance calculation method based on multi-mode coupling. Background Art

[0002] The problem of helicopter ground resonance is essentially the dynamic instability of the rotor with elastic supports in the rotation plane. It is related to the vibration characteristics of the rotor system and the vibration characteristics of the hub center. The vibration characteristics of the hub center depend on the performance parameters of the helicopter body on the landing gear. If the parameters are selected appropriately, then after external interference, the vibrations of the two vibration systems will offset each other, weaken each other, and the amplitude will gradually decrease, ensuring that the possibility of ground resonance is effectively eliminated.

[0003] The limitations of the traditional "planar dynamic model" in calculating ground resonance are as follows:

[0004] 1. Only two body modes are supported to calculate ground resonance;

[0005] 2. Unable to consider multi-degree-of-freedom coupling and unreasonable modal simplification;

[0006] 3. Only the vibration mode in a single direction can be considered, which is inconsistent with the actual movement of the body. Summary of the Invention

[0007] Purpose of the Invention: This invention supports the coupling of multiple airframe modalities on the landing gear to calculate ground resonance, taking into account multi-degree-of-freedom coupling. Compared to existing methods, this method more accurately reflects the vibration characteristics of the hub center, simplifies program input and operation, and more accurately simulates actual conditions, forming a universal calculation and analysis method for helicopter ground resonance. This method has high engineering value in applications such as stability calculations.

[0008] Technical solution:

[0009] A method for calculating ground resonance of a helicopter based on multi-modal coupling is provided, comprising:

[0010] Based on the consideration of multi-degree-of-freedom coupling, it supports the coupling of multiple airframe modes on the landing gear to perform ground resonance calculation.

[0011] Furthermore, based on the consideration of multi-degree-of-freedom coupling, the ground resonance calculation is supported by coupling multiple airframe modes on the landing gear, including:

[0012] Select a certain type of aircraft under typical weight and lift conditions to calculate the compression stiffness and compression damping of the main wheel, tail wheel and buffer strut.

[0013] The compression stiffness and compression damping of the main and tail landing gears are simulated in the full aircraft dynamics model, and the full aircraft dynamics model is built on the landing gears;

[0014] For the full aircraft dynamics model on the landing gear, the complex modal calculation of the airframe is performed. From the calculation results, six rigid body modes, modal masses, damping ratios, and modal vibration shapes of the airframe on the main and tail landing gears are selected.

[0015] On the basis of the body motion, several modes are combined to calculate the ground resonance stability, considering the two directions of the hub center and the blade swing motion.

[0016] Furthermore, based on the motion of the airframe, the coupled motion equations corresponding to the two directions of the hub center and the blade oscillation motion are:

[0017] ;

[0018] in, , , , ,

[0019] , ,

[0020] represents the moment of inertia of a blade about its flap hinge; represents the angular damping of the blade shimmying motion; It represents the mass moment of a blade about its shimmy hinge; Indicates the blade vibration frequency; and Indicates the forward and backward degrees of freedom of motion of the first-order shimmy mode; and Indicates the displacement of the hub center in the heading and lateral directions; N indicates the number of blades; Indicates the mass of a blade; represents the rotor speed; q represents the modal coordinate, 、 、 are the n-order modal mass, modal damping and modal stiffness matrices respectively, for Mode shape matrix at the hub center.

[0021] Furthermore, the blade vibration motion equation is:

[0022] ;

[0023] ;

[0024] Furthermore, the body motion equation is expressed as:

[0025] ;

[0026] M, K, and C represent the mass matrix, stiffness matrix, and damping matrix at the center of the hub, respectively.

[0027] Further, .

[0028] Further, .

[0029] Further, .

[0030] Beneficial effects:

[0031] This invention provides a multi-modal coupling calculation method for ground resonance that takes into account multi-degree-of-freedom coupling. Compared to previous methods, it can more realistically simulate the vibration characteristics of the hub center and obtain a more realistic ground resonance stability curve, providing an accurate and reliable calculation method for ground resonance design. This method can obtain a realistic ground resonance stability curve, ensuring the safety requirements of ground resonance stability, and provides an accurate and reliable calculation method for ground resonance stability design, enabling more precise ground resonance design. It has high universality and engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of a helicopter ground resonance calculation method based on multi-modal coupling provided by the present invention;

[0033] Figure 2 It is a schematic diagram of a ground resonance stability frequency curve according to the present invention;

[0034] Figure 3 The present invention relates to a schematic diagram of a ground resonance stability damping curve. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the implementation of this application clearer, the technical solutions in the implementation of this application will be described in more detail below in conjunction with the drawings in the implementation of this application. In the drawings, the same or similar numbers throughout represent the same or similar elements or elements with the same or similar functions. The described implementation is a part of the implementation of this application, not all of the implementations. The implementation described below with reference to the drawings is exemplary and is intended to be used to explain this application, and should not be understood as a limitation on this application. Based on the implementation in this application, all other implementations obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The implementation of this application is described in detail below in conjunction with the drawings.

[0036] In the description of the present invention, it should be understood that the terms "center", "axial", "vertical", "up", "down", "upper end", "bottom end", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the scope of protection of the present invention.

[0037] Ground resonance involves the degrees of freedom of the rotor system including the first-order swing mode and , due to its periodic motion, the actual center of gravity of the rotor deviates from the hub center; for the body system, the main consideration is the displacement of the hub center in the heading and lateral directions. and When the number of blades is greater than 3, the blade shimmy motion equation is:

[0038] (1)

[0039] (2)

[0040] in,

[0041] represents the moment of inertia of a blade about its flap hinge, kg·m 2 ;

[0042] Indicates the angular damping of the blade shimmy motion, Nms / rad;

[0043] represents the mass moment of a blade about its shimmy hinge, kg·m;

[0044] Indicates blade vibration frequency, rad / s;

[0045] and Indicates the forward and backward degrees of freedom of motion of the first-order shimmy mode;

[0046] and Indicates the displacement of the hub center in the heading and lateral directions;

[0047] When only considering the blade shimmy degree of freedom, the inertial force generated by the blade motion at the hub center is:

[0048] (3)

[0049] (4)

[0050] Wherein, N represents the number of blades;

[0051] Indicates the mass of a blade, kg;

[0052] It represents the heading force generated at the hub center by the blade oscillation motion, N;

[0053] It represents the lateral force generated by the blade oscillation at the center of the hub, N;

[0054] The inertial force generated by the blade oscillation at the hub center acts on the fuselage. The equation of motion is:

[0055] (5)

[0056] M, K, and C represent the mass matrix, stiffness matrix, and damping matrix at the center of the airframe hub, respectively;

[0057] After substituting the inertial force generated by the blade motion at the center of the hub:

[0058] (6)

[0059] The two degrees of freedom of the body and Expressed in modal coordinates:

[0060] (7)

[0061] are the modal coordinates, The matrix composed of modal vectors of each order becomes the modal matrix .

[0062] The corresponding modal frequencies are:

[0063] The corresponding body motion equation is expressed as:

[0064] (8)

[0065] (9)

[0066] Multiply equation (8) on the left ,get:

[0067] (10)

[0068]

[0069]

[0070]

[0071] correspond 、 、 are the n-order modal mass, modal damping and modal stiffness matrices respectively, for The vibration mode matrix at the center of the hub, is the n-order modal frequency vector, is the n-order modal damping ratio vector, satisfying the following:

[0072]

[0073]

[0074] Considering the coupled motion equations of the two directions of the hub center and the blade shimmy motion, the equations are as follows:

[0075] (11)

[0076] in:

[0077] , , Rotor speed

[0078]

[0079]

[0080]

[0081] According to the above formula, the dynamic characteristics of the rotor system are calculated, and the plane dynamic model is used to calculate and analyze the ground resonance.

[0082] The specific steps are as follows:

[0083] [1] The compression stiffness and compression damping of the main wheel, tail wheel and buffer strut were calculated under the typical weight and lift conditions of a certain type of aircraft.

[0084] [2] The compression stiffness and compression damping of the main landing gear and tail landing gear are simulated in the full aircraft dynamics model, and the full aircraft dynamics model is established on the landing gear;

[0085] [3] Carry out complex modal calculation of the aircraft body based on the full aircraft dynamics model on the landing gear;

[0086] [4] Select six rigid body modes, modal mass, damping ratio and modal vibration shape of the aircraft during takeoff and landing;

[0087] [5] Freely select several modes and combine them to calculate ground resonance stability;

[0088] [6] obtained the ground resonance frequency curve and damping curve.

[0089] Application examples:

[0090] In order to prove the applicability and effectiveness of the present invention, the present invention was applied to calculate the ground resonance stability of a certain type of aircraft through scientific research test flights.

[0091] The specific implementation is as follows:

[0092] S1: During a certain aircraft research test flight, the typical state of the aircraft is taken for calculation to obtain the compression stiffness and compression damping of the main wheel, tail wheel, and buffer strut.

[0093] S2: Simulate the compression stiffness and compression damping of the main landing gear and tail landing gear in the full aircraft dynamics model, and build a full aircraft dynamics model based on the landing gear;

[0094] S3: Perform complex modal calculations on the full aircraft dynamics model on the landing gear;

[0095] S4: Based on the calculation results, the six rigid body modal frequencies, modal masses, damping ratios, and modal vibration shapes of the aircraft during takeoff and landing are obtained;

[0096] S5: In this example, four airframe modes, namely, the second-order lateral mode, the second-order axial mode, the first-order lateral mode, and the first-order axial mode, are selected and combined for multi-modal coupling calculation.

[0097] S6: Obtain ground resonance frequency curve and damping curve;

[0098] Other embodiments of the present disclosure will readily occur to those skilled in the art after considering the specification and practicing the disclosure herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being indicated by the following claims.

[0099] It should be understood that the present disclosure is not limited to the exact structures that have been described above and shown in the drawings, and that various modifications and changes can be made without departing from the scope thereof. The scope of the present disclosure is limited only by the appended claims.

Claims

1. A helicopter ground resonance calculation method based on multi-modal coupling, characterized in that: include: Select the typical weight state and typical lift state of the helicopter to calculate the compression stiffness and compression damping of the main wheel, tail wheel and buffer strut; The compression stiffness and compression damping of the main and tail landing gears are simulated in the full aircraft dynamics model, and the full aircraft dynamics model is built on the landing gears; For the full aircraft dynamics model on the landing gear, the complex modal calculation of the airframe is performed. From the calculation results, six rigid body modes, modal masses, damping ratios, and modal vibration shapes of the airframe on the main and tail landing gears are selected. Based on the motion of the airframe, several modes are combined to calculate the ground resonance stability, considering the two directions of the hub center and the blade oscillation motion. Based on the motion of the airframe, the coupled motion equations corresponding to the two directions of the hub center and the blade oscillation motion are: ； in, , , , , ， ， represents the moment of inertia of a blade about its flap hinge; represents the angular damping of the blade shimmying motion; It represents the mass moment of a blade about its shimmy hinge; Indicates the blade vibration frequency; and Indicates the forward and backward degrees of freedom of motion of the first-order shimmy mode; and Indicates the displacement of the hub center in the heading and lateral directions; N indicates the number of blades; Indicates the mass of a blade; represents the rotor speed; q represents the modal coordinate, 、 、 are the n-order modal mass, modal damping and modal stiffness matrices respectively, for Mode shape matrix at the hub center.

2. The method according to claim 1, characterized in that The equation of motion for blade oscillation is: ； 。 3. The method according to claim 2, characterized in that The body motion equation is expressed as: ； M, K, and C represent the mass matrix, stiffness matrix, and damping matrix at the center of the hub, respectively.

4. The method according to claim 3, characterized in that 。 5. The method according to claim 3, characterized in that 。 6. The method according to claim 3, characterized in that 。

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