Coaxial dual-rotor transient pitch prediction method

Abstract

The invention provides a coaxial dual-rotor transient pitch prediction method. The method comprises the following steps: establishing a finite element model of a blade unit; deducing a kinetic equation of a rotor and fuselage coupling system according to the finite element model of the blade unit; using a free wake model to calculate the induced velocity of each position of the blade; according to the induced speed of each position of the blade, calculating the aerodynamic load of the blade; substituting the aerodynamic load of the blade into a kinetic equation of the rotor and fuselage coupling system, and calculating to obtain a transient response of the blade; and converting the blade transient response into a blade tip spacing.

Description

Technical Field

[0001] The present application belongs to the field of aviation technology, and in particular relates to a method for predicting the transient blade tip spacing of a coaxial twin rotor. Background Art

[0002] The blade tip spacing is an important factor affecting the flight safety of coaxial rotors. Once the blade tip spacing is too small, blade collision will lead to serious safety accidents. Since coaxial rotor helicopters are generally only equipped with propulsion propellers and the conventional helicopter tail rotor is eliminated, the heading damping of coaxial rotor helicopters is much smaller than that of conventional configurations. Transient excitation during forward flight often leads to more obvious fuselage movement. At the same time, the movement of the fuselage will also greatly affect the rotor inflow and the aerodynamic force of the fuselage. Therefore, the influence of the fuselage movement on the blade tip spacing must be considered in the process of calculating the variation law of the blade tip spacing of the coaxial rotor.

[0003] According to current research, the blade tip spacing of coaxial rotors is not prone to problems during steady-state forward flight, but transient control and transient excitation during forward flight are often the reasons for the blade tip spacing to be too small. Therefore, it is very necessary to establish a method for calculating the transient blade tip spacing that takes into account the motion of the fuselage.

[0004] Currently, in the prediction of the blade tip spacing of coaxial rotor aircraft, the isolated rotor is usually used as the calculation model, and the Pitt-Peters dynamic inflow model is used for calculation. However, it cannot reflect the influence of fuselage motion on the blade tip spacing, which is quite different from the actual flight of the coaxial rotor aircraft. Summary of the invention

[0005] Purpose of the invention: A method for predicting the transient blade tip spacing of a coaxial twin-rotor is proposed, which adopts a coaxial rotor blade tip spacing calculation model that takes fuselage motion into consideration, which is more in line with the actual situation.

[0006] The present application provides a method for predicting the transient blade tip spacing of a coaxial twin rotor, the method comprising:

[0007] Establish the finite element model of the blade unit;

[0008] Derivation of the dynamic equations of the rotor-fuselage coupling system based on the finite element model of the blade unit;

[0009] Using the free wake model, the induced velocity at each blade position is calculated;

[0010] The aerodynamic load of the blade is calculated according to the induced speed at each position of the blade;

[0011] Substituting the aerodynamic load of the blade into the dynamic equation of the rotor and fuselage coupling system to calculate the transient response of the blade;

[0012] The blade transient response is converted to blade tip pitch.

[0013] Preferably, the establishing of the finite element model of the blade unit comprises:

[0014] The blades are discretized by finite element, and the finite element model of the blade unit is established using the 15-degree-of-freedom medium deformation beam model.

[0015] Preferably, the deriving of the dynamic equation of the rotor-fuselage coupling system based on the finite element model of the blade unit includes:

[0016] According to the finite element model of the blade unit, the dynamic equation of the blade is established by considering the influence of the fuselage motion on the strain energy variation and kinetic energy variation of the blade;

[0017] The dynamic equation of the rotor and fuselage coupling system is derived based on the dynamic equation of the blade.

[0018] Preferably, the free wake model is expressed as:

[0019]

[0020] Among them, r b represents the position vector of the vortex element at the radial position r on the blade, μ is the free velocity vector, ψ is the azimuth angle, is the vortex age, The tail distortion.

[0021] Preferably, the use of the free wake model to calculate the induced velocity at each position of the blade includes:

[0022] According to the free wake model, the vortex element annulus is calculated;

[0023] The induced velocity at each position of the blade is calculated using the vortex element circulation and induced velocity calculation formula.

[0024] Preferably, the induced velocity calculation formula is as follows:

[0025]

[0026] in, is the induced velocity, Γ is the vortex element circulation, is the vortex element vector, l is the distance from the induced velocity point to the vortex element distance.

[0027] Preferably, the calculating the aerodynamic load of the blade according to the induced speed at each position of the blade includes:

[0028] According to the induced speed at each position of the blade, the aerodynamic load of the blade is calculated by the ONERA model.

[0029] Preferably, the ONERA model is as follows:

[0030]

[0031] Wherein, dF is the unsteady aerodynamic force of the blade unit, Cz1 ​​represents the lift coefficient of the airfoil without considering dynamic stall, Cz2 represents the correction term for the lift coefficient due to dynamic stall, and dL is the length of the blade unit.

[0032] Preferably, converting the blade transient response into blade tip pitch comprises:

[0033] The blade tip responses all vary with the rotor azimuth angle ψ, while the twin rotors rotate in opposite directions;

[0034] To calculate the blade tip spacing, it is necessary to separately extract the transient response of the blades of the upper and lower rotors for one rotation cycle and convert them into the same reference rotor azimuth angle, and then calculate the corresponding blade tip spacing calculation result.

[0035] Beneficial technical effects of this application:

[0036] This invention proposes a method for calculating the transient blade tip spacing of coaxial twin rotors taking into account the coupled motion of the fuselage, uses a free wake model to consider the aerodynamic interference of the upper and lower rotors, and uses the Newmark integration method to solve the aeroelastic dynamics model of the rotor and fuselage coupling, that is, converting the ordinary differential equation into an algebraic equation to solve the velocity and displacement at time t+Δt, thereby further improving the accuracy of the transient response calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a blade transient response calculation flow chart provided in an embodiment of the present application;

[0038] Figure 2 This is a diagram of the calculation results of the transient tip spacing of blades (XH-59A) provided in an embodiment of the present application. DETAILED DESCRIPTION

[0039] See also Figure 1-Figure 2 In order to more accurately calculate the transient tip response of the coaxial rotor, the Newmark integral is introduced to calculate the aeroelastic response of the blade under transient excitation conditions.

[0040] The present application provides a method for predicting the transient blade tip spacing of a coaxial twin rotor, comprising the following steps:

[0041] Step 1, finite element discretization of the blades;

[0042] Among them, the blade is first discretized by finite element, and the 15-degree-of-freedom medium deformation beam model is used to establish the finite element model of the blade unit. The specific degrees of freedom used are as follows:

[0043]

[0044] Step 2, establish the dynamic equation of the rotor and fuselage coupling system;

[0045] Among them, the influence of the fuselage motion of the coaxial rotor on the kinetic energy variation and strain energy variation of the rotor system is further considered, and the dynamic equation of the rotor and fuselage coupling system is established, in which the fuselage motion can be expressed by a five-degree-of-freedom vector:

[0046] M F T =[x F y F z F α s φ s ] (2)

[0047] In the above formula, x F ,y F , z F is the body motion in reference to the inertial system, α s is the pitch motion of the fuselage, with the head down being positive, φ s It is the roll of the fuselage, with right roll being positive.

[0048] The strain energy variation δU of the blade considering the motion of the fuselage is obtained by integration b and kinetic energy variation δT b The expression is as follows:

[0049]

[0050] In the above formula: u, v, w, φ are the blade extension, shimmy, flapping, and torsion degrees of freedom, ψ h is the rotor rotation speed, x F ,y F , z F , α s ,φ s The freedom of movement of the fuselage.

[0051] Since the rotor system is affected by non-conservative forces such as aerodynamics and damping forces, based on the generalized Hamiltonian principle, the strain energy variation δU of the blades considering the motion of the fuselage is b and kinetic energy variation δT b The dynamic equations of the rotor and fuselage coupling system can be further established.

[0052]

[0053] δU——system strain energy; δT——system kinetic energy; δW——system external force virtual work.

[0054] Step 3: Use the free wake model to solve the aerodynamic loads on the blades;

[0055] First, the blade response under steady-state trim conditions is used as the calculation input, and the non-distorted fixed wake of uniform inflow is used as the initial wake. After the initial wake is given, the free wake model is used to reflect the wake distortion caused by non-uniform induced velocity, and the attached vortex, trailing vortex and blade tip vortex models are established to further reflect the aerodynamic interference of the upper and lower rotors. The free wake model used in this patent can be expressed as:

[0056]

[0057] Among them, r b represents the position vector of the vortex element at the radial position r on the blade, μ is the free velocity vector, ψ is the azimuth angle, is the vortex age, The tail distortion.

[0058] The wake is discretized using a straight vortex segment, and the Biot-Savart (BS) law is used to calculate the induced velocity at any point in space. The induced velocity at any point in space is obtained by integrating the wake. The induced velocity calculation formula is as follows:

[0059]

[0060] in, is the induced velocity, Γ is the vortex element circulation, is the vortex element vector, l is the distance from the induced velocity point to the vortex element distance.

[0061] Then the unsteady aerodynamic force is calculated using the ONERA model.

[0062]

[0063] Where dF is the unsteady aerodynamic force of the blade unit, Cz1 ​​represents the lift coefficient of the airfoil without considering dynamic stall, Cz2 represents the correction term for the lift coefficient due to dynamic stall, and dL is the length of the blade unit.

[0064] Step 4: coupling the aerodynamic model and the structural dynamics model;

[0065] Among them, after coupling the aerodynamic model and the structural dynamics model, the nonlinear system dynamics equation of the blade is obtained:

[0066]

[0067] G(q) is the dynamic control function, [M], [C], [K] are the mass matrix, damping matrix, stiffness matrix, and {F} is the aerodynamic load vector.

[0068] {F} is Taylor expanded and retained to the first order, and the dynamic increment equation is established based on the dynamic constraint equation.

[0069]

[0070] For this second-order ordinary differential equation system, the Newmark integration method is used to solve it, that is, the ordinary differential equation is converted into an algebraic equation for solution. The velocity and displacement at time t+Δt are expressed as follows:

[0071]

[0072] According to the above formula, we can solve and

[0073]

[0074] Step 5, converting the transient response of the blade into the blade tip pitch;

[0075] The calculated blade transient responses all change with the rotor azimuth angle ψ, and the twin rotors rotate in opposite directions. Therefore, if you want to calculate the blade tip spacing, you need to separately extract the blade transient responses of the upper and lower rotors for one rotation cycle and convert them to the same reference rotor azimuth angle, and then calculate the corresponding blade tip spacing calculation results.

Claims

1. A method for predicting the transient blade tip spacing of a coaxial twin rotor, characterized in that: The method comprises: Establish the finite element model of the blade unit; Derivation of the dynamic equations of the rotor-fuselage coupling system based on the finite element model of the blade unit; Using the free wake model, the induced velocity at each blade position is calculated; The aerodynamic load of the blade is calculated according to the induced speed at each position of the blade; Substituting the aerodynamic load of the blade into the dynamic equation of the rotor and fuselage coupling system to calculate the transient response of the blade; The blade transient response is converted to blade tip pitch.

2. The method according to claim 1, characterized in that The finite element model of the blade unit is established, comprising: The blades are discretized by finite element, and the finite element model of the blade unit is established using the 15-degree-of-freedom medium deformation beam model.

3. The method according to claim 2, characterized in that The deriving of the dynamic equation of the rotor-fuselage coupling system based on the finite element model of the blade unit includes: According to the finite element model of the blade unit, the dynamic equation of the blade is established by considering the influence of the fuselage motion on the strain energy variation and kinetic energy variation of the blade; The dynamic equation of the rotor and fuselage coupling system is derived based on the dynamic equation of the blade.

4. The method according to claim 1, characterized in that: The free wake model is expressed as: Among them, r b represents the position vector of the vortex element at the radial position r on the blade, μ is the free velocity vector, ψ is the azimuth angle, is the vortex age, The tail distortion.

5. The method according to claim 4, characterized in that The free wake model is used to calculate the induced speed at each position of the blade, including: According to the free wake model, the vortex element annulus is calculated; The induced velocity at each position of the blade is calculated using the vortex element circulation and induced velocity calculation formula.

6. The method according to claim 5, characterized in that The induced velocity calculation formula is as follows: in, is the induced velocity, Γ is the vortex element circulation, is the vortex element vector, l is the distance from the induced velocity point to the vortex element distance.

7. The method according to claim 6, characterized in that The step of calculating the aerodynamic load of the blade according to the induced speed at each position of the blade comprises: According to the induced speed at each position of the blade, the aerodynamic load of the blade is calculated by the ONERA model.

8. The method according to claim 7, characterized in that The ONERA model is as follows: Wherein, dF is the unsteady aerodynamic force of the blade unit, Cz1 ​​represents the lift coefficient of the airfoil without considering dynamic stall, Cz2 represents the correction term for the lift coefficient due to dynamic stall, and dL is the length of the blade unit.

9. The method according to claim 1, characterized in that: The converting the blade transient response into a blade tip pitch comprises: The blade tip responses all vary with the rotor azimuth angle ψ, while the twin rotors rotate in opposite directions; To calculate the blade tip spacing, it is necessary to separately extract the transient response of the blades of the upper and lower rotors for one rotation cycle and convert them into the same reference rotor azimuth angle, and then calculate the corresponding blade tip spacing calculation result.

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