A method for predicting transient tip path clearance for coaxial rotors

Abstract

The application provides a coaxial dual-rotor transient tip clearance distance prediction method, the method comprising: establishing a finite element model of a blade unit; deriving a dynamics equation of a rotor and fuselage coupling system according to the finite element model of the blade unit; calculating induced velocities at various positions of the blade using a free wake model; calculating aerodynamic loads of the blade according to the induced velocities at the various positions of the blade; substituting the aerodynamic loads of the blade into the dynamics equation of the rotor and fuselage coupling system to calculate blade transient responses; and converting the blade transient responses into tip clearance distances.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aviation, and particularly relates to a coaxial dual-rotor transient tip clearance prediction method. BACKGROUND

[0002] The tip clearance problem is an important factor affecting the flight safety of coaxial rotors. Once the tip clearance is too small, blade collision will cause serious safety accidents. Since coaxial rotor helicopters generally only set a propulsion blade, the tail rotor of the conventional helicopter is cancelled, so the heading damping of the coaxial rotor helicopter is much smaller than that of the conventional configuration. In the forward flight process, transient excitation often leads to obvious body movement. At the same time, the body movement will greatly affect the rotor inflow and the body aerodynamic force, so the influence of the body movement on the tip clearance must be considered in the process of calculating the tip clearance variation law of the coaxial rotor.

[0003] According to the current research, the tip clearance of the coaxial rotor is not prone to problems in the steady-state forward flight process, but transient manipulation and transient excitation in the forward flight process often cause the tip clearance to be too small. Therefore, it is necessary to establish a transient tip clearance calculation method considering the body movement.

[0004] At present, in the tip clearance prediction work of coaxial rotor aircraft, an isolated rotor is usually used as a calculation model, and the Pitt-Peters dynamic inflow model is used for calculation, which cannot reflect the influence of the body movement on the tip clearance, and has great difference with the actual flight of the coaxial rotor aircraft. SUMMARY

[0005] The application provides a coaxial dual-rotor transient tip clearance prediction method, which adopts a coaxial rotor tip clearance calculation model considering the body movement, and is more in line with the actual situation.

[0006] The application provides a coaxial dual-rotor transient tip clearance prediction method, which adopts a coaxial rotor tip clearance calculation model considering the body movement, and is more in line with the actual situation.

[0007] A finite element model of the blade unit is established;

[0008] According to the finite element model of the blade unit, a dynamic equation of a rotor and body coupling system is derived;

[0009] The induced velocity of each position of the blade is calculated by using a free wake model;

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

[0011] The transient response of the blade is calculated by substituting the aerodynamic load of the blade into the dynamic equation of the rotor and body coupling system;

[0012] The blade transient response is converted into a blade tip spacing.

[0013] Preferably, the finite element model of the blade element is established, comprising:

[0014] The finite element model of the blade element is established by finite element discretization of the blade using a 15-degree-of-freedom moderate deformation beam model.

[0015] Preferably, the dynamics equation of the rotor-fuselage coupling system is derived according to the finite element model of the blade element, comprising:

[0016] The dynamics equation of the blade is established according to the finite element model of the blade element, considering the influence of fuselage motion on the strain energy variation and kinetic energy variation of the blade;

[0017] The dynamics equation of the rotor-fuselage coupling system is derived according to the dynamics equation of the blade.

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

[0019]

[0020] where 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, is the wake distortion.

[0021] Preferably, the induced velocity at each position of the blade is calculated using the free wake model, comprising:

[0022] The vortex element circulation is calculated according to the free wake model;

[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] where, 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 .

[0027] Preferably, the aerodynamic load of the blade is calculated according to the induced velocity at each position of the blade, comprising:

[0028] According to the induced velocity of 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 element, Cz1 represents the lift coefficient of the airfoil without considering dynamic stall, Cz2 represents the correction term of the lift coefficient for dynamic stall, and dL is the length of the blade element.

[0032] Preferably, the converting the blade transient response into the tip clearance includes:

[0033] The tip response varies with the rotor azimuth angle ψ, and the double rotors rotate in opposite directions.

[0034] The tip clearance is calculated by separately extracting the blade transient response of one rotation period of the upper and lower rotors, converting the same reference rotor azimuth angle, and then calculating the corresponding tip clearance calculation result.

[0035] The beneficial technical effects of the present application are:

[0036] The present application proposes a coaxial double-rotor transient tip clearance calculation method considering the coupling motion of the fuselage, uses a free wake model to consider the aerodynamic interference of the upper and lower rotors, and uses a Newmark integration method to solve the aero-elastic dynamic model of the rotor and the fuselage coupling, i.e. to convert the ordinary differential equation into an algebraic equation to solve the velocity and displacement at time t+Δt, and further improve the accuracy of the transient response calculation. BRIEF DESCRIPTION OF DRAWINGS

[0037] Fig. 1 is the blade transient response calculation flowchart provided by the embodiment of the present application;

[0038] Fig. 2 is the blade transient tip clearance calculation result (XH-59A) graph provided by the embodiment of the present application. DETAILED DESCRIPTION

[0039] Please refer to Figs. 1-2 In order to more accurately calculate the transient tip response of the coaxial rotor, the Newmark integration is introduced to calculate the aero-elastic response of the blade under the transient excitation condition.

[0040] The present application provides a coaxial double-rotor transient tip clearance prediction method, including the following steps:

[0041] Step 1, the blade is discretized by finite elements;

[0042] Firstly, the finite element model of the blade element is established by using the 15-degree-of-freedom moderate deformation beam model, and the specific degrees of freedom are as follows:

[0043]

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

[0045] Further considering the influence of the fuselage motion of the coaxial rotor on the kinetic energy variation and strain energy variation of the rotor system, the dynamic equation of the rotor and fuselage coupling system is established, wherein the fuselage motion can be represented 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 are the fuselage motions in the reference inertial system, α s is the pitch motion of the fuselage, and the downward motion is positive, and φ s is the roll motion of the fuselage, and the right roll is positive.

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

[0049]

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

[0051] Since the rotor system is subjected to non-conservative forces such as aerodynamic force and damping force, based on the generalized Hamilton principle, the strain energy variation δU b and kinetic energy variation δT b of the blade considering the fuselage motion can be further used to establish the dynamic equation of the rotor and fuselage coupling system.

[0052]

[0053] δU - system strain energy; δT - system kinetic energy; δW - system virtual work of external forces.

[0054] Step 3, using free wake model to solve blade aerodynamic load;

[0055] First, the blade response under the steady state trimming condition 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 model is established to further reflect the aerodynamic interference of the upper and lower rotors. The free wake model used in the patent can be expressed as:

[0056]

[0057] wherein r b represents the position vector of the vortex element at the radial position r of the blade, μ is the free velocity vector, ψ is the azimuth angle, is the vortex age, is the wake distortion.

[0058] The linear vortex segment is used to disperse the wake, and the Bi ot-Savart (B-S) law is used to calculate the induced velocity at any point in space. The induced velocity at any point in space is obtained by extending the wake integral. The induced velocity calculation formula is as follows:

[0059]

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

[0061] Then, the ONERA model is used to calculate the unsteady aerodynamic force.

[0062]

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

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

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

[0066]

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

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

[0069]

[0070] For this second-order ordinary differential equation, the Newmark integration method is used for solving, that is, the ordinary differential equation is converted into an algebraic equation for solving Let the velocity and displacement at time t+Δt be the following expressions:

[0071]

[0072] According to the above formula, the following can be solved: and

[0073]

[0074] Step 5, convert the blade transient response to the blade tip distance;

[0075] The calculated blade transient response is varied with the rotor azimuth angle ψ, and the double rotors rotate in opposite directions, so if you want to calculate the blade tip distance, you need to extract the blade transient response of the upper and lower rotors for one rotation period separately, and convert it to the same reference rotor azimuth angle, and then calculate the corresponding blade tip distance calculation result.

Claims

1. A method for predicting instantaneous tip-to-tip distance for a coaxial twin rotor, the method comprising: The method comprises: establishing a finite element model of a blade unit; deriving a dynamic equation of a rotor-fuselage coupling system according to the finite element model of the blade unit; calculating induced velocities at various positions of the blade by using a free wake model; calculating aerodynamic loads of the blade according to the induced velocities at the various positions of the blade; calculating blade transient responses by substituting the aerodynamic loads of the blade into the dynamic equation of the rotor-fuselage coupling system; converting the blade transient responses into tip clearance distances; wherein the conversion of the blade transient responses into the tip clearance distances comprises: the blade tip responses vary with a rotor azimuth angle ψ, and the two rotors rotate in opposite directions; the calculation of the tip clearance distances requires that the blade transient responses of one rotation period of the upper and lower rotors are extracted separately, converted into the same reference rotor azimuth angle, and then the corresponding calculation results of the tip clearance distances are calculated.

2. The method of claim 1, wherein, The establishment of the finite element model of the blade unit comprises: performing finite element discretization on the blade, and establishing the finite element model of the blade unit by using a 15-degree-of-freedom moderate deformation beam model.

3. The method of claim 2, wherein, The derivation of the dynamic equation of the rotor-fuselage coupling system according to the finite element model of the blade unit comprises: establishing a dynamic equation of the blade by considering the influence of fuselage motion on the strain energy variation and kinetic energy variation of the blade according to the finite element model of the blade unit; deriving the dynamic equation of the rotor-fuselage coupling system according to the dynamic equation of the blade.

4. The method of claim 1, wherein, The free wake model is expressed as: where 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 azimuthal angle, is the vortex age, is the wake distortion.

5. The method of claim 4, wherein, The calculation of the induced velocities at various positions of the blade by using the free wake model comprises: calculating vortex element circulation according to the use of the free wake model; calculating the induced velocities at the various positions of the blade by using the vortex element circulation and an induced velocity calculation formula.

6. The method of claim 5, wherein, The induced velocity calculation formula is as follows: where, is the induced velocity, Γ is the vortex element circulation, is the vortex element vector, and l is the distance from the induced velocity point to the vortex element center.

7. The method of claim 6, wherein, The calculation of the aerodynamic loads of the blade according to the induced velocities at the various positions of the blade comprises: calculating the aerodynamic loads of the blade by the ONERA model according to the induced velocities at the various positions of the blade.

8. The method of claim 7, wherein, The ONERA model is as follows: wherein dF is the unsteady aerodynamic force of the blade unit, Cz1 represents an airfoil lift coefficient without considering dynamic stall, Cz2 represents a correction term of the dynamic stall for the lift coefficient, and dL is the length of the blade unit.

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