A method and apparatus for high-speed high advance ratio rotor transient dynamics analysis

Abstract

The application provides a high-speed high advance ratio rotor transient dynamics analysis method, the method comprises the following steps: establishing a variable speed transient process dynamics equation, wherein the variable speed transient process dynamics equation comprises a system kinetic energy term; two coordinate systems are established, and the system kinetic energy term is derived based on the coordinate systems to obtain a system kinetic energy equation; a transient aeroelastic analysis model is established based on the system kinetic energy equation; variable speed transient dynamics analysis is carried out based on the transient aeroelastic analysis model to obtain transient aeroelastic response results; meanwhile, the application also provides a high-speed high advance ratio rotor transient dynamics analysis device; the application develops a high-speed high advance ratio rotor transient dynamics calculation method, studies the transient aeroelastic behavior characteristics in the variable speed process, and provides a theoretical basis and technical support for the development of high-speed high advance ratio rotors.

Description

Technical Field

[0001] This application belongs to the field of helicopter rotor dynamics technology, specifically relating to a method and apparatus for transient dynamic analysis of high-speed rotors with large advance ratios. Background Technology

[0002] The transient dynamics of high-speed, high-progression-ratio rotors mainly studies the transient aeroelastic response of high-speed helicopters during variable rotor speeds in forward flight, and analyzes the impact of variable rotor speed strategies on transient dynamics. During variable rotor speeds, on the one hand, changes in rotor speed cause variations in rotor excitation frequency, altering the modal characteristics of the blades and potentially leading to rotor loads, vibrations, and other problems. On the other hand, changes in rotor speed also affect the helicopter's trim, handling, and stability, even jeopardizing flight safety. Simultaneously, a decrease in rotor speed increases airflow asymmetry on the rotor disk, resulting in greater loads at the blade roots.

[0003] Currently, our understanding of the transient aeroelastic dynamics problems caused by changes in rotor speed, control, and flow field wake during variable speed transient processes is insufficient, and we lack effective analytical methods for their aerodynamic and dynamic behavior. Summary of the Invention

[0004] The purpose of this invention is to develop a transient dynamics calculation method for high-speed rotors with a large advance ratio, addressing the transient dynamics problem of variable speed processes during the forward flight of high-speed helicopters, and to study the transient aeroelastic behavior characteristics during variable speed processes, thereby providing theoretical basis and technical support for the development of high-speed rotors with a large advance ratio.

[0005] In a first aspect, this application provides a transient dynamics analysis method for high-speed, high-progression-ratio rotors, the method comprising:

[0006] Establish the dynamic equations for the transient process with variable speed, wherein the dynamic equations for the transient process with variable speed include the system kinetic energy term;

[0007] Establish two coordinate systems, and derive the system kinetic energy term based on the coordinate systems to obtain the system kinetic energy equation;

[0008] A transient aeroelastic analysis model is established based on the system kinetic energy equation.

[0009] Based on the transient aeroelastic analysis model, a transient dynamic analysis with varying rotational speed is performed to obtain the transient aeroelastic response results.

[0010] Preferably, establishing the dynamic equations for the transient process with varying rotational speed includes:

[0011] Based on Green's strain and moderately deformable beam theory, dynamic equations for transient processes with varying rotational speeds are established using Hamilton's principle.

[0012] Preferably, the coordinate system includes an undeformed blade coordinate system and a deformed blade coordinate system.

[0013] Preferably, the step of establishing two coordinate systems and deriving the system kinetic energy term based on the coordinate systems to obtain the system kinetic energy equation includes:

[0014] Obtain the radius vector of the isolated rotor from the undeformed blade coordinate system;

[0015] Differentiating the radius vector of the isolated rotor yields its velocity.

[0016] Based on the velocity of the isolated rotor, the system kinetic energy equation is obtained.

[0017] Preferably, the system kinetic energy equation is the equation in the coordinate system after the blade deformation.

[0018] Preferably, the step of establishing a transient aeroelastic analysis model based on the system kinetic energy equation includes:

[0019] A transient aeroelastic analysis model is established based on the rotor speed variation term and the system kinetic energy equation.

[0020] Preferably, the rotor speed variation includes rotor angular acceleration.

[0021] Preferably, the step of performing variable-speed transient dynamic analysis based on the transient aeroelastic analysis model to obtain the transient aeroelastic response results includes:

[0022] Based on the transient aeroelastic analysis model, a variable speed transient dynamic analysis was performed to obtain the rotor hub load, blade aeroelastic response, and rotor root load.

[0023] Secondly, this application also provides a transient dynamics analysis device for a high-speed, high-progression-ratio rotor, the device comprising:

[0024] The first analysis module is used to establish the dynamic equations of the variable speed transient process, wherein the dynamic equations of the variable speed transient process include the system kinetic energy term;

[0025] The second analysis module is used to establish two coordinate systems and derive the system kinetic energy terms based on the coordinate systems to obtain the system kinetic energy equation;

[0026] The third analysis module is used to establish a transient aeroelastic analysis model based on the system's kinetic energy equation.

[0027] The processing module is used to perform variable speed transient dynamic analysis based on the transient aeroelastic analysis model to obtain transient aeroelastic response results.

[0028] The beneficial technical effects of this application are as follows:

[0029] This application provides a transient dynamics analysis method and apparatus for high-speed rotors with large advance ratios. It addresses the transient dynamics problem of high-speed helicopters during variable speed processes in forward flight, develops a transient dynamics calculation method for high-speed rotors with large advance ratios, and studies the transient aeroelastic behavior characteristics during variable speed processes, providing theoretical basis and technical support for the development of high-speed rotors with large advance ratios. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the coordinate system before and after blade deformation provided in an embodiment of this application;

[0031] Figure 2 A schematic diagram of the time-progression-based aeroelastic response solution process provided for embodiments of this application;

[0032] Figure 3 This is a schematic diagram of a variable speed strategy provided in an embodiment of this application;

[0033] Figure 4 This is a schematic diagram of the transient rotor thrust variation curve during the variable speed process provided in the embodiments of this application;

[0034] Figure 5 This is a schematic diagram of the transient rotor torque variation curve during the variable speed process provided in the embodiments of this application;

[0035] Figure 6 A schematic diagram of the transient blade flapping response change curve during the variable speed process provided in the embodiments of this application. Detailed Implementation

[0036] Please see Figures 1-6 This application provides a transient dynamics calculation method for high-speed rotors with large advance ratios. It addresses the transient dynamics problem of high-speed helicopters during variable speed processes in forward flight, develops a transient dynamics calculation method for high-speed rotors with large advance ratios, and studies the transient aeroelastic behavior characteristics during variable speed processes, providing theoretical basis and technical support for the development of high-speed rotors with large advance ratios.

[0037] In this application embodiment, the technical solution of the present invention is as follows:

[0038] (1) Dynamic equations for transient processes with varying rotational speeds: Based on Green's strain and moderately deformable beam theory, this paper establishes the rotor dynamic equations using Hamilton's principle. The expression is as follows:

[0039]

[0040] In the formula, ∏ represents the system potential energy; U represents the system strain energy; T represents the system kinetic energy; W represents the virtual work done by external forces on the system; t represents the integration domain, and t1 and t2 represent the upper and lower limits of integration; δ represents the variational symbol.

[0041] (2) For the transient process of a high-speed helicopter with variable speed, the special characteristics of the dynamic equations are mainly reflected in the system kinetic energy term. The blade kinetic energy of the transient process with variable speed is derived. Two coordinate systems are established, such as... Figure 1 , which are the undeformed coordinate system of the blade (xyz), and the basis vectors are . After the blade deformation, the coordinate system ξηζ has the following basis vectors:

[0042] Aperture vector of an isolated rotor for

[0043]

[0044] Therefore, the velocity at a point on an isolated rotor for

[0045]

[0046] In the formula, Ω0 is the initial angular velocity of the rotor; Ω(t) is the angular acceleration of the rotor at any time t; β p The pre-cone angle of the propeller hub.

[0047] (3) According to the definition, the kinetic energy T of the entire blade is b for

[0048]

[0049] In the formula, ρ s Let be the blade linear density, R be the blade radius, and x be the blade footprint. Taking a variational approach to the blade kinetic energy, we have...

[0050]

[0051] In the formula, u e ,v,v',w,w', For generalized coordinates, T v T v ', T w T w ', T represents the corresponding generalized force.

[0052] Due to the influence of changes in rotational speed, the corresponding angular acceleration term needs to be added to the corresponding generalized force. The added content includes the following parts:

[0053]

[0054] In the formula, e g θ is the distance from the centroid of the cross section to the elastic axis, with a positive value indicating the centroid is further forward; θ is the geometric twist angle of the blade.

[0055] (4) Since the input of each calculation step comes from the output of the previous calculation step during the variable speed transient process, and the azimuth angle of the calculation step changes continuously with the progress of the calculation time, for each calculation step, after satisfying the aeroelastic iteration convergence, the blade aerodynamic load, structural parameters and hub load under that calculation step are calculated separately.

[0056] The solution process in the self-written program is as follows:

[0057] a) At 100% speed, the aeroelastic response (displacement, velocity, and acceleration at the blade finite element nodes) and hub load coefficients (thrust coefficient, roll moment coefficient, and pitch moment coefficient) that satisfy the convergence criterion are obtained through steady-state iterative calculation.

[0058] b) The converged hub load coefficient is used as the input data for the first calculation step of the variable speed process. At the same time, the forward ratio of the current step is obtained by interpolation according to the time corresponding to the current step. The inflow is calculated by the dynamic inflow model to obtain the inflow distribution corresponding to the current calculation step.

[0059] c) The converged aeroelastic response and the inflow distribution in b) are used as inputs. The rotor angular velocity, angular acceleration, control collective pitch and periodic pitch of the current step are interpolated. The space is discretized using the finite element method to obtain the mass matrix, stiffness matrix, damping matrix and load column vector of the blade element. Then the blade element matrix is ​​assembled into the blade global matrix. The aeroelastic iterative calculation is then performed using the Newmark algorithm to obtain the converged aeroelastic response of the current step.

[0060] d) Based on the inflow distribution in b) and the aeroelastic response in c), the blade aerodynamic load and structural parameters are calculated. The hub load and hub load coefficient of the current step are calculated by the load superposition method.

[0061] e) Use the aeroelastic response in c) and the hub load coefficient in d) as inputs for the next calculation step, and repeat steps b) to e) for iterative calculation until the number of iterations reaches the set value. Finally, obtain the results of aeroelastic response, blade aerodynamic load, hub load and other parameters for the entire variable speed process.

[0062] The high-speed, high-progression-ratio transient dynamics calculation method of the present invention considers the effect of rotor speed change on transient dynamics equations during variable speed processes, and also takes into account the influence of rotor roll and roll on inflow distribution.

[0063] Taking the XH-59A rotor as the research object, this paper analyzes the blade and hub loads during the rotor speed change process at high speed (200 km / h). During the speed transition process, the rotor thrust is kept constant at 2000 kg. In steady state, rotor trim is performed according to wind tunnel trim, and the rotor disk tilt angle is set to 0 degrees. In transient state, rotor control is interpolated based on the steady-state trim value corresponding to the speed during the transition. The speed change range is from the rotor's rated speed of 345 rpm to 295 rpm. The first 15 seconds and the last 15 seconds are in a constant speed state, with a transition state in between. The speed transition time is 5 seconds. The speed change is as follows: Figure 3 The transient rotor thrust, blade flapping response, and blade root flapping moment changes during variable speed operation are as follows: Figure 4 As shown, as the rotor speed decreases, the centrifugal stiffness of the blades decreases, the blades "soften," and the root flapping moment increases, leading to a larger blade flapping response. Furthermore, the same computer used a self-written program and an externally sourced program to calculate the same variable speed process, requiring 1 hour (to complete the variable speed process calculation) and over 20 hours (still not completing the variable speed process calculation). Therefore, the transient dynamics calculation method invented here can significantly improve calculation efficiency (over 90%) while maintaining accuracy.

[0064] In other embodiments of this application, the provided method includes the following steps:

[0065] Step 1: Establish the dynamic equations for the transient process with varying speed.

[0066] Among them, based on Green's strain and moderately deformable beam theory, the rotor dynamics equations are established through Hamilton's principle, and their expressions are as follows:

[0067]

[0068] Step 2: Establish two coordinate systems, derive the system kinetic energy term based on the coordinate systems, and obtain the system kinetic energy equation.

[0069] The two coordinate systems are the undeformed blade coordinate system xyz, and the basis vectors are... After the blade deformation, the coordinate system ξηζ has the following basis vectors:

[0070] By definition, the strain energy U of the entire blade is... b It can be written as

[0071]

[0072] σ xx , σ xη , For stress term, ε xx , ε xη , This is the strain term.

[0073] Taking the variational expression for the strain energy per unit length of the blade, we have:

[0074]

[0075] E is the elastic modulus, and G is the shear modulus.

[0076] Below we write out ε respectively. xx ε xη , The expression:

[0077]

[0078] In the formula, u e v, w and The deformation of the reference axis is θ, which is the fitted part at any section of the blade, including the blade pre-twist angle and the control input.

[0079] For ε xx ε xη , Take the variation, that is, for u e v, w and Perform variational operations on its derivatives. Substituting this back into the strain energy formula, we have...

[0080]

[0081] Therefore, the strain energy of the entire blade is

[0082]

[0083] The kinetic energy term of the system is now derived, with the radius vector of the isolated rotor being...

[0084]

[0085] Therefore, the velocity at a point on an isolated rotor is

[0086]

[0087] The rotational speed of an isolated rotor can be written as

[0088]

[0089] Then there is

[0090]

[0091] In conclusion,

[0092]

[0093] right After taking the variation, we have

[0094]

[0095] In the formula,

[0096]

[0097] By definition, the kinetic energy of the entire blade is

[0098] In the formula,

[0099]

[0100] Taking the variational factor of the blade kinetic energy, we have

[0101]

[0102] In the formula,

[0103]

[0104] Similarly, the system kinetic energy in the dynamic equations can be written as...

[0105]

[0106] Due to the influence of changes in rotational speed, the corresponding angular acceleration term needs to be added to the corresponding generalized force. The added term includes the following:

[0107]

[0108] Step 3: Establish a transient aeroelastic analysis model based on the system kinetic energy equation.

[0109] This study focuses on the XH-59A rotor as the research object, analyzing the hub load during rotor speed variation at high speed (200 km / h). During the speed transition, the rotor thrust is kept constant at 2000 kg. In steady state, rotor trim is performed according to wind tunnel trim procedures, with the rotor disk tilt angle set to 0 degrees. In transient state, rotor control is interpolated based on the steady-state trim values ​​corresponding to the speed variation during the transition. The speed variation range is from the rotor's rated speed of 345 rpm to 295 rpm, with the first and last 15 seconds representing a constant speed state, and the middle being a transition state with a transition time of 5 seconds. The speed variation is as follows: Figure 3 .

[0110] Step 4: Perform transient dynamic analysis with varying rotational speed based on the transient aeroelastic analysis model to obtain the transient aeroelastic response results.

[0111] The average hub load showed little change over time after initial stabilization, with a slight increase in the transient process as the speed decreased, but the overall change was not significant. Harmonic loads changed more noticeably over time; at low speeds, the harmonic loads increased, but the changes were relatively small. Simultaneously, the hub torque decreased as the speed decreased, consistent with the transmission law. At low speeds, the torque harmonic load increased and the fluctuations were more pronounced, indicating a greater need to focus on the rotor torque load at low speeds. Regarding the tip flapping response, the decrease in speed led to a reduction in the centrifugal stiffness of the blades, causing them to "soften," resulting in a larger root flapping moment and consequently a larger tip flapping response.

Claims

1. A transient dynamics analysis method for high-speed, high-progression-ratio rotors, characterized in that, The method includes: Establish the dynamic equations for the transient process with variable speed, wherein the dynamic equations for the transient process with variable speed include the system kinetic energy term; Establish two coordinate systems, and derive the system kinetic energy term based on the coordinate systems to obtain the system kinetic energy equation; A transient aeroelastic analysis model is established based on the system kinetic energy equation. Based on the transient aeroelastic analysis model, a variable rotation speed transient dynamic analysis was performed to obtain the transient aeroelastic response results; The step of performing variable-speed transient dynamic analysis based on the transient aeroelastic analysis model to obtain transient aeroelastic response results includes: a) At 100% speed, the aeroelastic response and hub load coefficient satisfying the convergence criterion are obtained through steady-state iterative calculation using a steady-state program. b) The converged hub load coefficient is used as the input data for the first calculation step of the variable speed process. At the same time, the forward ratio of the current step is obtained by interpolation according to the time corresponding to the current step. The inflow is calculated by the dynamic inflow model to obtain the inflow distribution corresponding to the current calculation step. c) The converged aeroelastic response and the inflow distribution in b) are used as inputs. The rotor angular velocity, angular acceleration, control collective pitch and periodic pitch of the current step are interpolated. The space is discretized using the finite element method to obtain the mass matrix, stiffness matrix, damping matrix and load column vector of the blade element. Then the blade element matrix is ​​assembled into the blade global matrix. The aeroelastic iterative calculation is then performed using the Newmark algorithm to obtain the converged aeroelastic response of the current step. d) Based on the inflow distribution in b) and the aeroelastic response in c), the blade aerodynamic load and structural parameters are calculated. The hub load and hub load coefficient of the current step are calculated by the load superposition method. e) Use the aeroelastic response in c) and the hub load coefficient in d) as inputs for the next calculation step, and repeat steps b) to e) for iterative calculation until the number of iterations reaches the set value. Finally, obtain the aeroelastic response, blade aerodynamic load, and hub load for the entire variable speed process.

2. The method according to claim 1, characterized in that, The establishment of the dynamic equations for the transient process with varying speed includes: Based on Green's strain and moderately deformable beam theory, dynamic equations for transient processes with varying rotational speeds are established using Hamilton's principle.

3. The method according to claim 2, characterized in that, The coordinate system includes the undeformed blade coordinate system and the deformed blade coordinate system.

4. The method according to claim 3, characterized in that, The process involves establishing two coordinate systems, deriving the system's kinetic energy term based on these coordinate systems, and obtaining the system's kinetic energy equation, including: Obtain the radius vector of the isolated rotor from the undeformed blade coordinate system; Differentiating the radius vector of the isolated rotor yields its velocity. Based on the velocity of the isolated rotor, the system kinetic energy equation is obtained.

5. The method according to claim 4, characterized in that, The system kinetic energy equation is the equation in the coordinate system after the blade deformation.

6. The method according to claim 1, characterized in that, The establishment of a transient aeroelastic analysis model based on the system kinetic energy equation includes: A transient aeroelastic analysis model is established based on the rotor speed variation term and the system kinetic energy equation.

7. The method according to claim 6, characterized in that, The rotor speed variation includes rotor angular acceleration.

8. A transient dynamics analysis device for a high-speed, high-progression-ratio rotor, characterized in that, The apparatus is used to implement the method as described in any one of claims 1-7, the apparatus comprising: The first analysis module is used to establish the dynamic equations of the variable speed transient process, wherein the dynamic equations of the variable speed transient process include the system kinetic energy term; The second analysis module is used to establish two coordinate systems and derive the system kinetic energy terms based on the coordinate systems to obtain the system kinetic energy equation; The third analysis module is used to establish a transient aeroelastic analysis model based on the system's kinetic energy equation. The processing module is used to perform variable speed transient dynamic analysis based on the transient aeroelastic analysis model to obtain transient aeroelastic response results.

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