CN104317980A - Coaxial rigid rotor pneumatic elastic response method - Google Patents

Abstract

The invention provides a coaxial rigid rotor coupling pneumatic elastic response analysis method, and belongs to a helicopter kinetic analysis technology. The method is characterized in that according to the operation and control characteristics of a coaxial rigid rotor helicopter, a balance equation optimization solution method is built, and an optimization solution is found according to the given target and constraint conditions. According to the characteristic of complicated coaxial rigid rotor flow field environment, a rotor flow field is calculated by using a computational fluid dynamic method based on an Euler/N-S equation; and then, the coupling pneumatic elastic response is calculated by using a computational fluid dynamic/computational structural dynamic loose coupling analysis method. The coaxial rigid rotor coupling pneumatic elastic analysis method has the advantage that when the analysis method is used, balance operation and control parameters, blade response, rotor loads and the like of the coaxial rigid rotor helicopter can be calculated. The method has good analysis precision and engineering applicability; the relying of the development process on the test can be reduced; and the design period and the development cost can be greatly reduced.

Description

A kind of coaxial rigid rotor aeroelasticity response method

Technical field

The invention belongs to Helicopter Dynamics analytical technology, relate to a kind of aeroelasticity response analysis method for coaxial rigid rotor helicopter.

Background technology

Coaxial rigid rotor helicopter is a kind of new configuration high-speed helicopter, and its rotor system comprises the hingeless rotor of a pair coaxial, reversion, rigidity.It preserves the most important feature of conventional configuration helicopter---hovering and low speed efficiency.When large Speed Flight, advancing blade primarily of two secondary rotors produces lift, retreating blade is unloaded, thus avoid the speed and load-factor restriction that cause because of retreating blade stall, and utilize the side opposition that moves ahead of upper and lower reversion rotor to balance hub moment, realize transverse direction and rolling trim.Coaxial rigid rotor is gone straight up to function and is significantly improved forward flight speed and rotor efficiency, is one of popular research direction of new configuration high-speed helicopter.

Coaxial rigid rotor helicopter adopts two secondary rigid rotors, and rotor spacing is less, and two secondary rotors, rotor and fuselage and being coupled between rotor with auxiliary propulsion plant, interference phenomenon are even more serious.In addition, two secondary rotors all have respective installation position angle and can independently handle, the difference of its installation position angle and manipulation rule, all can have an impact to full machine coupling aeroelastic characteristic.Therefore, the dynamic phenomena of coaxial rigid rotor helicopter is more more complicated than pure helicopter, and vibration problem is more outstanding.About its dynamics problem, external existing scholar is studied these problems, but its work is mainly based on the test flight data of analysis and arrangement Xi Kesiji company XH-59A proof machine, or adopt the model simplified very much, analogue simulation is carried out to its flight quality and dynamics problem.Research shows, because the spacing of coaxial rigid rotor is less, there is stronger aerodynamic interference between two secondary rotors, and existing comparatively ripe theoretical Aerodynamic Model, is difficult to its aerodynamic characteristic of accurate analysis.At present about the simulation analysis of coaxial rigid rotor Aeroelastic Problems, there is not yet the achievement in research of renewal.

In addition, because every secondary rotor independently can carry out total distance and cyclic pitch control, also have auxiliary propulsion plant to provide longitudinal thrust, therefore its manipulated variable is more than conventional rotor simultaneously.When solving flight trim problem, its unknown quantity number more than equation number, namely can exist without array solution usually in theory.In existing research, generally choose the flat solution of an assembly according to test or experience, how to determine its optimum trim solution by theoretical method, have not yet to see correlative study.

The domestic research about coaxial rigid rotor helicopter is just at the early-stage, for the analytical approach of its problem such as flight trim, aeroelasticity response etc., does not also have substantial theoretical research and experimental verification at present.Therefore, studying the structure of coaxial rigid rotor and aerodynamic characteristic, grasp the coupling aeroelasticity response analysis method of coaxial rigid rotor helicopter, is very urgent and significant.

Summary of the invention

The technical problem to be solved in the present invention: propose a kind of coaxial rigid rotor coupling aeroelasticity response analysis method, for coaxial rigid rotor helicopter trim control parameter, blade response and rotor LOAD FOR.

Technical scheme of the present invention: according to the feature of coaxial rigid rotor manipulated variable more than equation number, for obtaining Theory Solution, establishing a kind of trim equation optimization method, finding optimum trim solution according to given target and constraint condition; According to the feature of coaxial rigid rotor flow field circumstance complication, adopt the CFD method based on Euler/N-S equation to solve rotor flow field, lifting line model is revised, then solve the response of coupling aeroelasticity by CFD/CSD loose coupling analytical approach.

A kind of coaxial rigid rotor aeroelasticity response analysis method, is characterized in that:

(1) foundation of rotor gas bullet analytical model.Adopt medium deformation beam theory, quasi-steady aerodynamic force and Drees linearly to enter flow model and set up coaxial rigid rotor aeroelastic dynamics analytical model, the kinetics equation of individual layer rotor is obtained by Hamiltonian's variational principle:

$\mathrm{\δ\Π}={\∫}_{t_1}^{t_2}(\mathrm{\δU}-\mathrm{\δT}-\mathrm{\δW})\mathrm{dt}=0$

Wherein, δ U is elasticity energy variation, and δ T is kinetic energy variation, and δ W is external force virtual work, and its one piece blade expression formula is respectively:

${\mathrm{\δU}}_b={\∫}_0^R{\∫\∫}_A({\mathrm{\σ}}_{\mathrm{xx}}{\mathrm{\δ\ϵ}}_{\mathrm{xx}}+{\mathrm{\σ}}_{\mathrm{x\η}}{\mathrm{\δ\ϵ}}_{\mathrm{x\η}}+{\mathrm{\σ}}_{\mathrm{x\ζ}}{\mathrm{\δ\ϵ}}_{\mathrm{x\ζ}})\mathrm{d\ηd\ζdx}$

${\mathrm{\δT}}_b={\∫}_0^R{\∫\∫}_A{\mathrm{\ρ}}_{s}V\·\mathrm{\δVd\ηd\ζdx}$

${\mathrm{\δW}}_b={\∫}_0^R(L_u^A\mathrm{\δu}+L_v^A\mathrm{\δv}+L_w^A\mathrm{\δw}+L_{\widehat{\mathrm{\φ}}}^A\mathrm{\δ}\widehat{\mathrm{\φ}})\mathrm{dx}$

Adopt the response of timing departure method solving system, the aeroelasticity response of upper and lower rotor independently solves.

(2) rotor flow field calculates.According to the Field Characteristics of coaxial rigid rotor, CFD method is adopted to solve rotor flow field.With unsteady flo w Euler/N-S equation for governing equation, realized elastic deformation and the rigid motion of blade by dynamic mesh and dynamic overlapping grid method.

(3) rotor trim calculates.According to the handling characteristic of coaxial rigid rotor helicopter, set up three power (longitudinal force, transverse force, vertical force) and three moments (pitching moment, rolling moment, yawing) totally six balance equations, its expression formula is as follows:

$\left\{\begin{array}{c}{F}_1=T_{\mathrm{pro}}-T\sin {\mathrm{\α}}_s-H\cos {\mathrm{\α}}_s-D_F=0\\ F_2=Y\cos {\mathrm{\φ}}_s+T\sin {\mathrm{\φ}}_s+T_{\mathrm{vr}}=0\\ F_3=T\cos {\mathrm{\α}}_s\cos {\mathrm{\φ}}_s-H\sin {\mathrm{\α}}_s-Y\sin {\mathrm{\φ}}_s\\ +T_{\mathrm{hr}}-W_F=0\\ F_4=M_x^H+T{y}_h-Y{z}_h-T_{\mathrm{vr}}{z}_{\mathrm{vr}}=0\\ F_5=M_y^H-T{x}_h+H{z}_h-T_{\mathrm{hr}}{x}_{\mathrm{hr}}=0\\ F_6=M_z^H+Y{x}_h+T_{\mathrm{vr}}{x}_{\mathrm{vr}}=0\end{array}\right.$

Given design variable, chooses required objective function and constraint condition, adopts the above-mentioned equation of Optimization Method.

(4) coaxial rigid rotor coupling aeroelasticity RESPONSE CALCULATION.Adopt CFD/CSD loose coupling analytical approach, iterative is carried out to (1) to (3) step, obtains the final steady-state response of rotor, flow field result and trim result.

Key point of the present invention is:

Establish a kind of aeroelasticity response analysis method of coaxial rigid rotor helicopter.The method has good analysis precision and engineering adaptability, can calculate rotor trim control parameter, blade response and rotor load etc.

Described rotor gas bullet analysis modeling, adopts medium deformation beam theory, quasi-steady aerodynamic force and Drees linearly to enter flow model and sets up coaxial rigid rotor aeroelastic dynamics analytical model, obtain system dynamics equation by Hamiltonian's variational principle.

Described rotor flow field calculates, and adopts CFD method, with unsteady flo w Euler/N-S equation for governing equation, is realized elastic deformation and the rigid motion of blade by dynamic mesh and dynamic overlapping grid method.

Described rotor trim calculates.Set up six rigid motion balance equations of coaxial rigid rotor helicopter, choose required objective function and constraint condition, adopt optimization method to try to achieve optimum trim result.

Beneficial effect of the present invention: the present invention's coaxial rigid rotor coupling aeroelastic analysis method, utilizes this analytical approach can calculate the trim control parameter of coaxial rigid rotor helicopter, blade response and rotor load etc.The method has good analysis precision and engineering adaptability, can reduce R&D process to test according to patience, significantly reduce design cycle and development cost.

Accompanying drawing explanation

Fig. 1 is that different rotor hub configuration is to the response of cyclic pitch control;

Fig. 2 is the schematic diagram that the coaxial rigid rotor that the present invention relates to handles Γ=30, angle ° in advance;

Fig. 3 is rotor aeroperformance definition in fore-and-aft plane;

Fig. 4 is the rotor blade resonance figure that the present invention calculates;

Fig. 5 is the rotor system stress and strain model and overlapping grid method schematic diagram that the present invention relates to;

Fig. 6 is the change of the rotor trim result that calculates of the present invention with iterations;

Fig. 7 is that the blade blade tip that the present invention calculates waves the change of response results with iterations;

Fig. 8 is the change of the one piece blade total life that calculates of the present invention with iterations;

Fig. 9 is the rotor blade lift distribution cloud atlas that the present invention calculates.

Figure 10 is the vertical distortion cloud charts of rotor blade that the present invention calculates.

Figure 11 is the rotary wing performance that calculates of the present invention with the variation relation of forward flight speed and lift side-play amount, and with the contrast of flight test result.

Embodiment

Below in conjunction with accompanying drawing, coaxial rigid rotor aeroelasticity response analysis method involved in the present invention is described in further details.

The first step: rotor aeroelastic analysis modeling, the aeroelastic dynamics equation by Hamiltonian's variational principle derivation rotor: wherein, δ U is elasticity energy variation, and δ T is kinetic energy variation, and δ W is external force virtual work.Paddle blade structure model adopts medium deformation beam theory to set up, and namely supposes that blade is an anisotropy beam, creates medium deformation and small strain.The elasticity energy variation of one piece blade is: ${\mathrm{\δU}}_b={\∫}_0^R{\∫\∫}_A({\mathrm{\σ}}_{\mathrm{xx}}{\mathrm{\δ\ϵ}}_{\mathrm{xx}}+{\mathrm{\σ}}_{\mathrm{x\η}}{\mathrm{\δ\ϵ}}_{\mathrm{x\η}}+{\mathrm{\σ}}_{\mathrm{x\ζ}}{\mathrm{\δ\ϵ}}_{\mathrm{x\ζ}})\mathrm{d\ηd\ζdx};$ The kinetic energy variation of one piece blade is: ${\mathrm{\δT}}_b={\∫}_0^R{\∫\∫}_A{\mathrm{\ρ}}_{s}V\·\mathrm{\δVd\ηd\ζdx}.$

The external force acted on blade is exactly aerodynamic force.In theoretical aerodynamic force, quasi-steady aerodynamic force model (comprise circular rector power and acyclic is measured one's own ability) and Deers is adopted linearly to enter flow model to calculate the aerodynamic loading in blade cross section.Finally obtain the external force virtual work on one piece blade: ${\mathrm{\δW}}_b={\∫}_0^R(L_u^A\mathrm{\δu}+L_v^A\mathrm{\δv}+L_w^A\mathrm{\δw}+L_{\widehat{\mathrm{\φ}}}^A\mathrm{\δ}\widehat{\mathrm{\φ}})\mathrm{dx}.$ Adopt the response of timing departure method solving system, in theoretical Aerodynamic Model, do not consider the aerodynamic interference between upper and lower layer rotor, therefore the aeroelasticity response of upper and lower rotor can independently solve.

Second step: rotor flow field calculates, according to the feature of coaxial rigid rotor flow field interference phenomenon complexity, adopts Fluid Mechanics Computation method to solve rotor flow field, for revising the theoretical aerodynamic force in the first step.In CFD method with unsteady flo w Euler/N-S equation for governing equation, realized elastic deformation and the rigid motion of blade by dynamic mesh and dynamic overlapping grid method.In calculating, convective flux adopts Roe form, adopts dual-time scale to carry out time stepping method, and each swing circle is divided into 720 physical time steps, carries out the iterative computation of 20 pseudo-time steps in each physical time step.In addition, in CFD calculates, only consider rotor system, do not consider the impact of fuselage.

3rd step: rotor trim calculates.The same with conventional rotor system, coaxial rigid rotor is also handle by changing always distance and feathering.In addition, it can also handle angle in advance by adjustment, and differential total distance and differential feathering are handled and performance optimization rotor.The feathering expression formula of upper and lower rotor is respectively:

θ _U＝(θ ₀+Δθ ₀)-(A ₁+ΔA ₁)cos(ψ _U+Γ)

-(B ₁+ΔB ₁)sin(ψ _U+Γ)

θ _L＝(θ ₀-Δθ ₀)-(A ₁-ΔA ₁)cos(ψ _L+Γ)

+(B ₁-ΔB ₁)sin(ψ _L+Γ)

Wherein,

${\mathrm{\θ}}_0=\frac{{\mathrm{\θ}}_{0U}+{\mathrm{\θ}}_{0L}}{2},{\mathrm{\Δ\θ}}_0=\frac{{\mathrm{\θ}}_{0U}-{\mathrm{\θ}}_{0L}}{2}$

$A_1=\frac{A_{1U}+A_{1L}}{2},{\mathrm{\ΔA}}_1=\frac{A_{1U}-A_{1L}}{2}$

$B_1=\frac{B_{1U}-B_{1L}}{2},{\mathrm{\ΔB}}_1=\frac{B_{1U}+B_{1L}}{2}$

In above-mentioned two formulas, subscript U and L represents upper and lower rotor parameter respectively.θ ₀, A ₁and B ₁be respectively total distance, vertical and horizontal feathering; Δ θ ₀, Δ A ₁with Δ B ₁be respectively differential total distance, vertical and horizontal feathering; Γ handles angle in advance.

Because coaxial rigid rotor blade rigidity is large, therefore its cyclic pitch control phase place and pure helicopter different.For articulated rotor, periodical input must required maximum wave a little before 80 ~ 90 °; For infinitely firm rotor, required lead is 0 substantially; And for coaxial rigid rotor, feathering input should before required moment exports 30 ~ 40 °, as shown in Figure 1.This cycle is handled phasing degree and is defined as and handles angle Γ in advance, and is just time contrary with rotor wing rotation direction, is the manipulation position angle corresponding to Γ=30 ° as shown in Figure 2.

The same with pure helicopter, the trim of coaxial rigid rotor helicopter, also be calculate its three power (longitudinal force, transverse force, vertical force) and three moments (pitching moment, rolling moment, yawing) totally six balance equations, its expression formula is as follows:

$\left\{\begin{array}{c}{F}_1=T_{\mathrm{pro}}-T\sin {\mathrm{\α}}_s-H\cos {\mathrm{\α}}_s-D_F=0\\ F_2=Y\cos {\mathrm{\φ}}_s+T\sin {\mathrm{\φ}}_s+T_{\mathrm{vr}}=0\\ F_3=T\cos {\mathrm{\α}}_s\cos {\mathrm{\φ}}_s-H\sin {\mathrm{\α}}_s-Y\sin {\mathrm{\φ}}_s\\ +T_{\mathrm{hr}}-W_F=0\\ F_4=M_x^H+T{y}_h-Y{z}_h-T_{\mathrm{vr}}{z}_{\mathrm{vr}}=0\\ F_5=M_y^H-T{x}_h+H{z}_h-T_{\mathrm{hr}}{x}_{\mathrm{hr}}=0\\ F_6=M_z^H+Y{x}_h+T_{\mathrm{vr}}{x}_{\mathrm{vr}}=0\end{array}\right.$

Wherein, F ₁, F ₂and F ₃body at the equilibrium equation of X, Y and Z-direction, F ₄, F ₅and F ₆around the pitching of body center of gravity, rolling and yaw freedom balance equation.Under T, H and Y represent propeller hub coordinate system, the total pulling force of two secondary rotors, rearward-directed force and side force, its application point is positioned at lower rotor hub central point; with under propeller hub system, total rolling of two secondary rotors, pitching and yawing.D _fand W _frepresent resistance and the gravity of fuselage, T _prorepresent propeller thrust.X _h, y _hand z _hin fuselage coordinates system, the coordinate of lower rotor hub central point.T _hrand T _vrrepresent horizontal tail and vertical fin aerodynamic force, x _hr, y _hr, z _hrand x _vr, y _vr, z _vrthen be respectively in fuselage coordinates system, the coordinate figure of horizontal tail and vertical fin mid point.α _sand φ _sfuselage attitude (come back just is) and side rake angle (right is just).

In above-mentioned equation, the required trim variable separated comprises: rotor is total apart from q ₀, longitudinal feathering A ₁, horizontal feathering B ₁, differential total apart from Δ θ ₀, differential longitudinal feathering Δ A ₁, differential horizontal feathering Δ B ₁, auxiliary propulsion plant thrust T _pro, horizontal tail angle of attack α _hr, vertical fin angle of attack α _vr, and the angle of pitch a of fuselage _swith side rake angle φ _s, totally 9 manipulated variables and 2 attitude angle.Can find out, the trim variable of ABC helicopter is far more than pure helicopter, but trim equation only has 6 equally.If therefore do not carry out suitable constraint or restriction, then balance equation will exist without array solution.

In this analytical approach, adopt optimization method to solve balance equation, according to actual flight state, given design variable, chooses required objective function and provides corresponding constraint condition, and then obtains optimum trim result.Its actual conditions arranges as follows:

(1) design variable

The design variable that this place is got is exactly the trim variable needing in balance equation to solve, said 9 manipulated variables and 2 attitude angle namely, that is:

v _i＝{θ ₀,Δθ ₀,A ₁,ΔA ₁,B ₁,ΔB ₁

,T _pro,α _hr,α _vr,α _s,φ _s}

In addition, according to actual needs, also can using parameters such as the angle Γ of manipulation in advance of rotor, forward flight speed and flying heights as design variable.

(2) objective function

Trim as required, can choose different objects as optimization aim in analyzing.Usually following objective function is adopted in analysis:

A) trim variable quantity

When adopting the method to carry out the analysis of CFD/CSD couple trim, usually need according to having the given initial trim parameter v of experience _i0, in analysis, make trim variable quantity minimum, one group and the immediate trim value of initial value can be obtained.Trim variable quantity is defined as follows:

${\mathrm{\Δv}}_{i0}=\sqrt{{(v_{\mathrm{ik}}-v_{i0})}^2}$

Wherein v _ikit is final stable state trim solution.

B) rotor efficiency

An important indicator of rotor efficiency when rotor lift-drag ratio in fore-and-aft plane flies before being, in trim is analyzed, makes rotor lift-drag ratio maximum, can obtain the trim value that one group of pneumatic efficiency is the highest.

The definitions of efficiency of the secondary rotor of coaxial rigid rotor helicopter list is as follows:

$\frac{L}{D_e}=\frac{L}{D+\frac{\mathrm{Q\Ω}}{V}}$

Wherein L is rotor lift, and D is rotor resistance, and Q is rotor shaft moment of torsion, and Ω is gyroplane rotate speed, and V is forward flight speed.Power in fore-and-aft plane as shown in Figure 3.It should be noted that rotor resistance D, be dimerous by the horizontal component of the horizontal component of rotor thrust T and horizontal force H, following form can be written as:

D＝Tsin(α _s)+Hcos(α _s)

C) lift side-play amount

The distance at lift side-play amount (LOS) the i.e. centre of lift skew propeller hub center of individual layer rotor, LOS value has material impact to rotor efficiency, propeller hub oscillating load and blade aerodynamic load etc.In trim is analyzed, can according to circumstances, make LOS maximum, minimum or level off to certain numerical value as far as possible.

(3) constraint condition

Constraint function in analysis mainly comprises following two classes:

A) balance equation

In Optimization analyses process, must ensure the steady flight attitude of helicopter, therefore meeting body 6 balance equations is bases that trim is analyzed.

Table 1 design variable variation range

B) design variable constraint

In Optimization analyses process, meet constraint condition and objective function mainly through adjusted design variable.In a practical situation, design variable all has certain variation range, therefore needs to retrain it in optimizing process.In this patent example, the variation range of associated design variables is as shown in table 1.

4th step: the response of coupling aeroelasticity solves.Adopt the loose coupling alternative manner of band trim to solve, CFD and CSD calculates data and often rotates a circle exchange once according to rotor, and while each exchanges data, carries out a suboptimization trim and analyze, upgrade trim variable.Concrete analysis step is as follows:

1., first according to given state of flight and requirement, choose suitable design variable, objective function and constraint condition.

2. one group of initial trim variable is rule of thumb set, adopts theoretical Aerodynamic Model to solve the aeroelasticity response of rotor, by the trim solution T of method for optimization analysis computing system ⁽¹⁾, and obtain corresponding paddle blade structure response R ⁽¹⁾and theoretical aerodynamic loading

3. according to the trim solution T of rotor ⁽¹⁾with RESPONSE CALCULATION result R ⁽¹⁾, carry out rotor flow field analysis, obtain the 1st CFD aerodynamic loading and then calculate the aerodynamic loading correction of the 1st time ${\mathrm{\ΔA}}^{\left(1\right)}=A_{\mathrm{CFD}}^{\left(1\right)}-A_{\mathrm{LL}}^{\left(1\right)}.$

4. carry out kth time (k=2,3 ... N) aeroelasticity response solves, and obtains new trim solution T ^(k), RESPONSE CALCULATION result R ^(k)with theoretical aerodynamic loading aerodynamic loading in this time analyzing adopts theoretical Aerodynamic Model and a front aerodynamic loading correction amount A ^(k-1)sum.

5. according to the trim solution T of previous step ^(k)with RESPONSE CALCULATION result R ^(k), recalculate CFD aerodynamic loading and then upgrade aerodynamic loading correction

Repeat step 4 and 5 until the response of trim result, blade and (or) rotor aerodynamic force meet the condition of convergence, the final steady-state response of rotor, flow field result and trim solution can be obtained.

Specific embodiment: for the XH-59A coaxial double-rotor helicopter of Xi Kesiji company of the U.S., its correlation parameter is in table 2.Under helicopter mode (not being with auxiliary propulsion plant), get full machine gross weight 5400Kg, 300 meters of sea level altitudes, 0 ° of fuselage attitude, handle angle in advance for 40 °, gyroplane rotate speed 340rpm.Adopt the method to propose, comprise the CFD/CSD loose coupling aero-elastic response analytical approach that full machine trim calculates, simulation analysis is carried out to the rotor blade steady-state response under different forward flight speed and horizontal lift side-play amount (LOS) and aerodynamic loading.Concrete steps are as follows:

Table 2XH-59A helicopter parameter

Parameter	Value
		Gross weight	5400kg
Main rotor radius	5.49m
		100% gyroplane rotate speed	345rpm
Rotor spacing	0.75m
		Rotor number	2 is secondary
Paddle blade number	3/ is secondary
		Blade contraction coefficient	2∶1
The pre-torsional angle of blade	-10 ° (non-linear)
		Total rotor solidity	0.127
Pre-cone angle	3°
		Top rake	0°
Horizontal tail area	5.57m 2
		Vertical fin area	2.79m 2
Elevating rudder	25% horizontal tail area
		Yaw rudder	30% vertical fin area

The first step: set up rotor aeroelastic analysis model, adopt medium deformation beam theory to set up resilient paddles model, every sheet blade is divided into 11 unit.Rotor calculation on Natural Frequency value under rated speed and with the contrast of trial value in table 3.Blade resonance figure is shown in Fig. 4.In theoretical aerodynamics evaluation, quasi-steady aerodynamic force model (comprise circular rector power and acyclic is measured one's own ability) and Deers is adopted linearly to enter flow model to calculate the aerodynamic loading in blade cross section.

Table 3 blade natural frequency

Second step: carry out rotor flow field calculating.According to the feature of coaxial rigid rotor flow field interference phenomenon complexity, with unsteady flo w Euler/N-S equation for governing equation, realized elastic deformation and the rigid motion of blade by dynamic mesh and dynamic overlapping grid method.Consider that Euler equation has reflected the key property in flow field, for saving computing time, in sample calculation analysis, governing equation adopts unsteady flo w Euler equation herein.In calculating, convective flux adopts Roe form, adopts dual-time scale to carry out time stepping method, and each swing circle is divided into 720 physical time steps, carries out the iterative computation of 20 pseudo-time steps in each physical time step.

Fig. 5 (a) is the nested grid assembling schematic diagram of rotor system, and wherein background grid is made up of seven gridblocks, comprises 2520345 grid cells; One piece blade grid is as shown in Fig. 5 (b), and blade adopts C-H type structured grid, and be made up of eight sub-gridblocks, number of meshes is 307632; Whole overlay network case system comprises a set of background grid and six cover blade grids, totally 4366134 grid cells.Fig. 5 (c) is on Y=0 tangent plane, the distortion of blade grid and effect schematic diagram of digging a hole, can find out, distortion of the mesh is normal, and the effect of digging a hole of blade and background grid overlapping region is very good, prove that dynamic mesh that the method adopts and dynamic overlapping grid method are effective.

3rd step: trim calculates.For ease of contrasting with flight test result, adopt the setting identical with existing document.In analysis, fuselage resistance adopts experimental formula to calculate, and gets during resistance coefficient 0.01, CFD calculates and only considers upper and lower rotor model, do not comprise fuselage.In addition, suppose that horizontal tail and the vertical fin angle of attack are 0 °, namely do not consider its aerodynamic force.

In this example, suppose that helicopter horizontal tail and the vertical fin angle of attack are 0 °, do not consider its aerodynamic force in namely analyzing, meanwhile, make fuselage roll angle be 0 °, handle angle in advance and get 40 °.Therefore, the trim variable solved needed in this time analyzing is: rotor is total apart from q ₀, longitudinal feathering A ₁, horizontal feathering B ₁, differential total apart from Δ θ ₀, differential longitudinal cycle handles Δ A ₁, the differential horizontal cycle handles Δ B ₁with the angle of pitch a of fuselage _s, totally 7 design variables.With 62m/s forward flight speed, LOS=10% rotor radius is example, and first rule of thumb, choosing one group of initial value is:

θ ₀＝7.5°,Δθ ₀＝0°,A ₁＝-5°,ΔA ₁＝0°

B ₁＝1°,ΔB ₁＝0°,α _s＝-3°

Then according to CFD/CSD coupling analytical method, by iterative, full machine trim variate-value, blade stable periodic responses value and aerodynamic loading etc. are obtained.Trim chooses LOS=0.1R as optimization aim in calculating.

4th step: the response of coupling aeroelasticity solves.Adopt the loose coupling alternative manner of band trim to solve, CFD and CSD calculates data and often rotates a circle exchange once according to rotor, and while each exchanges data, carries out a suboptimization trim and analyze, upgrade trim variable.By the calculating that iterates until the response of trim result, blade and (or) rotor aerodynamic force meet the condition of convergence, the final steady-state response of rotor, flow field result and trim solution can be obtained.

Fig. 6 is the change curve of each trim variate-value with coupling iterative computation number of times, when the changing value of all trim variablees is all less than 0.05 °, thinks and calculates convergence.As can be seen from the figure, after 5 iteration, convergence is calculated.Total distance and feathering are just basicly stable after third time iteration, and differential total distance and differential cyclic pitch control convergence comparatively slow, just tend towards stability after the 4th iteration.Because be permanent before fly state, so differential control amount is all smaller.

Fig. 7 is in each iterative computation, and the stable state blade tip that rotor blade rotates a circle waves deformation values.The position angle that it is pointed out that upper and lower rotor is herein all according to the definition of respective rotor wing rotation direction, and namely going up rotor is top view counterclockwise, lower rotor be top view clockwise.And to wave value be undefined at the rotating coordinate system of respective rotor, initial point is positioned at respective propeller hub center.In figure, primary deformation values is the result adopting theoretical aerodynamic force, can find out, for coaxial rigid rotor, the analytical error of conventional wisdom Aerodynamic Model is larger.After adding the correction of CFD aerodynamic force, in the 4th iteration, blade response restrains substantially.

Fig. 8 is that in each iterative computation, one piece blade total life is with azimuthal Changing Pattern.Lift is obtained by elasticity rotor flow field calculation procedure, and position angle is according to the definition of respective rotor wing rotation direction equally.As can be seen from the figure, carried out 4 CFD altogether and analyzed, primary aerodynamic force difference is comparatively large, is just tending towards convergence afterwards gradually, and this is mainly because trim variable and blade distortion have been tending towards convergence all.Synthesizing map 6-8 can find out, adopts the method to carry out the analysis of CFD/CSD couple trim to ABC helicopter, has good analysis precision and convergence.

Fig. 9 is rotor blade unit length lift with position angle and the exhibition Changing Pattern to position.As can be seen from the figure, the vibration of upper rotor lift is even more serious.In the side that moves ahead, its lift maximal value is greater than lower rotor; In rear row side, its lift minimum value is less than again lower rotor.Especially, after each upper and lower rotor blade intersects (0 °, 60 °, 120 °, 180 °, 240 ° and 300 ° of position angles place), the interference suffered by upper rotor lift will obviously be greater than lower rotor.

Figure 10 is the vertical elastic deformation of rotor blade with position angle and the exhibition Changing Pattern to position.Can find out, what upper rotor was downward wave, and deformation values is large, and lower rotor blade upwards to wave deformation values larger, the minimum blade tip spacing of upper and lower rotor, appears near 270 ° of position angles.

Within the scope of 50-125m/s forward flight speed, make LOS equal 0.1R, 0.2R and 0.3R respectively, carry out full machine trim and aero-elastic response analysis, in fore-and-aft plane, Figure 11 is shown in the analysis result of rotor lift-drag ratio and the contrast of flight test value.Can find out, under different lift transversal displacement, the calculated value of rotor efficiency and the contrast with test flight data thereof under XH-59A helicopter.In figure symbol is flight test measured value, and in flight test, LOS approximates 0.1R.As can be seen from the figure, the result of calculation of the method and experiment value coincide good, illustrate that these computing method are accurately.It should be noted that in friction speed section, rotor efficiency is also different with the Changing Pattern of LOS.At low speed segment (speed <70m/s), as LOS=0.2R, rotor efficiency is minimum, reduces or increase LOS all to make rotor efficiency increase; At medium speed's section (70m/s< speed <110m/s), rotor efficiency increases with the increase of LOS; At high regime (speed >110m/s), as LOS=0.2R, rotor is most effective, and the continuation with LOS increases rotor efficiency and can slightly decline.Therefore, in practical flight process, can, according to forward flight speed, select suitable lift side-play amount to improve rotor efficiency.

Claims (5)

1. a coaxial rigid rotor aeroelasticity response analysis method, is characterized in that:

The first, set up rotor aeroelastic analysis model;

The second, carry out rotor flow field calculating;

3rd, carry out rotor trim calculating;

4th, carry out coaxial rigid rotor coupling aeroelasticity RESPONSE CALCULATION.

2. axle rigid rotor aeroelasticity response analysis method according to claim 1, it is characterized in that: the foundation of rotor aeroelastic analysis model in described first step, adopt medium deformation beam theory, quasi-steady aerodynamic force and Drees linearly to enter flow model and set up rotor aeroelastic dynamics analytical model, the kinetics equation of individual layer rotor is obtained by Hamiltonian's variational principle:

$\mathrm{\&delta;\&Pi;}={\&Integral;}_{t_1}^{t_2}(\mathrm{\&delta;U}-\mathrm{\&delta;T}-\mathrm{\&delta;W})\mathrm{dt}=0$

Wherein, δ U is elasticity energy variation, and δ T is kinetic energy variation, and δ W is external force virtual work, and its one piece blade expression formula is respectively:

${\mathrm{\&delta;U}}_b={\&Integral;}_0^R{\&Integral;\&Integral;}_A({\mathrm{\&sigma;}}_{\mathrm{xx}}{\mathrm{\&delta;\&epsiv;}}_{\mathrm{xx}}+{\mathrm{\&sigma;}}_{\mathrm{x\&eta;}}{\mathrm{\&delta;\&epsiv;}}_{\mathrm{x\&eta;}}+{\mathrm{\&sigma;}}_{\mathrm{x\&zeta;}}{\mathrm{\&delta;\&epsiv;}}_{\mathrm{x\&zeta;}})\mathrm{d\&eta;d\&zeta;dx}$

${\mathrm{\&delta;T}}_b={\&Integral;}_0^R{\&Integral;\&Integral;}_A{\mathrm{\&rho;}}_{s}V\&CenterDot;\mathrm{\&delta;Vd\&eta;d\&zeta;dx}$

${\mathrm{\&delta;W}}_b={\&Integral;}_0^R(L_u^A\mathrm{\&delta;u}+L_v^A\mathrm{\&delta;v}+L_w^A\mathrm{\&delta;w}+L_{\widehat{\mathrm{\&phi;}}}^A\mathrm{\&delta;}\widehat{\mathrm{\&phi;}})\mathrm{dx}$

Adopt the response of timing departure method solving system, the aeroelasticity response of upper and lower rotor independently solves.

3. axle rigid rotor aeroelasticity response analysis method according to claim 1, it is characterized in that: in described second step, rotor flow field calculates, according to the Field Characteristics of coaxial rigid rotor, Fluid Mechanics Computation (CFD) method is adopted to solve rotor flow field; With unsteady flo w Euler/N-S equation for governing equation, realized elastic deformation and the rigid motion of blade by dynamic mesh and dynamic overlapping grid method.

4. axle rigid rotor aeroelasticity response analysis method according to claim 1, it is characterized in that: in described third step, rotor trim calculates, according to the handling characteristic of coaxial rigid rotor helicopter, set up three power (longitudinal force, transverse force, vertical force) and three moments (pitching moment, rolling moment, yawing) totally six balance equations, its expression formula is as follows:

$\left\{\begin{array}{c}{F}_1=T_{\mathrm{pro}}-T\sin {\mathrm{\&alpha;}}_s-H\cos {\mathrm{\&alpha;}}_s-D_F=0\\ F_2=Y\cos {\mathrm{\&phi;}}_s+T\sin {\mathrm{\&phi;}}_s+T_{\mathrm{vr}}=0\\ F_3=T\cos {\mathrm{\&alpha;}}_s\cos {\mathrm{\&phi;}}_s-H\sin {\mathrm{\&alpha;}}_s-Y\sin {\mathrm{\&phi;}}_s\\ +T_{\mathrm{hr}}-W_F=0\\ F_4=M_x^H+T{y}_h-Y{z}_h-T_{\mathrm{vr}}{z}_{\mathrm{vr}}=0\\ F_5=M_y^H-T{x}_h+H{z}_h-T_{\mathrm{hr}}{x}_{\mathrm{hr}}=0\\ F_6=M_z^H+Y{x}_h+T_{\mathrm{vr}}{x}_{\mathrm{vr}}=0\end{array}\right.$

Given design variable, chooses required objective function and constraint condition, adopts the above-mentioned equation of Optimization Method.

5. axle rigid rotor aeroelasticity response analysis method according to claim 1, it is characterized in that: coaxial rigid rotor coupling aeroelasticity RESPONSE CALCULATION in described 4th step, adopt Fluid Mechanics Computation/computational structural dynamics (CFD/CSD) loose coupling analytical approach, iterative is carried out to the first to third step, obtains the final steady-state response of rotor, flow field result and trim solution.