A method and device for analyzing transient dynamics characteristics of a flapping-pitch coupled rotor

Abstract

The application provides a method for analyzing the transient dynamic characteristics of a flapping-pitch coupled rotor, which comprises the following steps: constructing a rotor transient control equation; calculating the rotor dynamic equation at the moment based on the rotor transient control equation; iteratively solving the rotor dynamic equation at the moment to obtain an aeroelastic response convergence result; obtaining the hub load at the moment based on the aeroelastic response convergence result at the moment; updating the rotor control, rotating speed and flow field information at the next moment according to the hub load and the aeroelastic response convergence result at the moment, until the whole calculation process is completed, and the transient dynamic characteristics of the flapping-pitch coupled rotor in the whole process are obtained; meanwhile, the application also provides a device for analyzing the transient dynamic characteristics of the flapping-pitch coupled rotor; and the application can solve the calculation problem of the transient dynamic characteristics of the flapping-pitch coupled rotor.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of variable-pitch rotor aircraft dynamics, and particularly relates to a method and device for analyzing transient dynamics characteristics of a coupled rotor with flapping and pitch. BACKGROUND

[0002] For a variable-pitch rotor aircraft, the existing dynamic calculation method adopts a Hamilton method based on generalized degrees of freedom, which needs to assume that the rotor speed is in a steady state when establishing the equation, and does not consider the boundary conditions brought by the pitch mechanism.

[0003] At the same time, the existing dynamic calculation method can only take values for the blade azimuth angle at certain angle intervals, and cannot simulate the process of continuous change of the blade azimuth angle, and cannot transfer the pitch change caused by the blade flapping to the pitch.

[0004] Therefore, the current dynamic calculation method is not suitable for the transient process of the coupled rotor with flapping and pitch. SUMMARY

[0005] The application aims to provide a method and device for analyzing transient dynamics characteristics of a coupled rotor with flapping and pitch, which can accurately simulate the process of continuous change of the blade azimuth angle, can transfer the pitch change caused by the blade flapping to the pitch, and can solve the transient dynamic response of the coupled rotor with flapping and pitch.

[0006] In a first aspect, the application provides a method for analyzing transient dynamics characteristics of a coupled rotor with flapping and pitch, which comprises:

[0007] constructing a rotor transient control equation;

[0008] based on the rotor transient control equation, calculating a rotor dynamics equation at this moment;

[0009] iteratively solving the rotor dynamics equation at this moment to obtain an aeroelastic response convergence result;

[0010] based on the aeroelastic response convergence result at this moment, obtaining a blade root load at this moment;

[0011] updating rotor control, speed and flow field information at the next moment according to the blade root load and the aeroelastic response convergence result at this moment, until the entire calculation process is completed, and the transient dynamic characteristics of the coupled rotor with flapping and pitch in the entire process are obtained.

[0012] Preferably, the method for constructing a rotor transient control equation comprises:

[0013] based on the Hamilton principle, establishing a rotor transient control equation at this moment, which has the following expression:

[0014]

[0015] wherein, Π is the system potential energy; U is the system strain energy; T is the system kinetic energy; W is the system external force virtual work; t is the time integral domain, t1, t2 are the upper and lower limits of integration; δ is the variation symbol.

[0016] Preferably, the system kinetic energy T addition item in the transient process compared with the steady-state process comprises:

[0017]

[0018] wherein, e g is the distance from the profile center of gravity to the elastic axis; θ is the pitch angle; x is the profile spanwise coordinate.

[0019] Preferably, the rotor dynamic equation at the moment is calculated based on the rotor transient control equation, comprising:

[0020] For the rotor transient control equation, the rotor dynamic equation at the moment is calculated, and the expression is as follows:

[0021]

[0022] wherein, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F is the load column vector, x is the response of the generalized degree of freedom, which is acceleration, velocity, displacement, respectively;

[0023] M, C, K, F matrixes are calculated according to δU, δT, δW.

[0024] Preferably, the rotor dynamic equation at the moment is iteratively solved to obtain the aeroelastic response convergence result, comprising:

[0025] Given the initial response, the Newmark integration method is used to iteratively solve the rotor dynamic equation at the moment to obtain the aeroelastic response convergence result.

[0026] Preferably, the rotor dynamic equation at the moment is iteratively solved to obtain the aeroelastic response convergence result, comprising:

[0027] Given the initial response, the Newmark integration method is used to iteratively calculate the aeroelastic response, and after each round of iterative calculation, the hinge whirl angle is transmitted to the pitch angle through the coupling mechanism to update the initial response for the next round of iterative calculation, until the response difference of two rounds of calculation is less than the tolerance, and the aeroelastic response convergence result at the moment is obtained.

[0028] Preferably, the hub load at the moment is obtained based on the aeroelastic response convergence result at the moment, comprising:

[0029] The aerodynamic load and structural load distribution of the blade at the moment are calculated based on the aeroelastic response convergence result at the moment, the hub load at the moment is obtained by integrating the aerodynamic load and the structural load to the hub, and the hub load at the moment is obtained by coordinate transformation.

[0030] Preferably, the rotor control, the rotating speed and the flow field information at the next moment are updated based on the hub load at the moment and the aeroelastic response convergence result, until the whole calculation process is completed, and the whole process of the dynamic characteristics of the oscillation-pitch coupling rotor is obtained.

[0031] The flow field information is recalculated based on the hub load at the moment and the aeroelastic response convergence result, the rotor control and the rotating speed are updated, the dynamic characteristics of the rotor at the next moment are analyzed, until the calculation time reaches the set value, the whole calculation process is completed, and the whole process of the dynamic characteristics of the oscillation-pitch coupling rotor is obtained.

[0032] In the second aspect, the application further provides a device for analyzing the dynamic characteristics of an oscillation-pitch coupling rotor, comprising:

[0033] The construction module is configured to construct a rotor transient control equation.

[0034] The calculation module is configured to calculate the rotor dynamic equation at the moment based on the rotor transient control equation.

[0035] The solving module is configured to iteratively solve the rotor dynamic equation at the moment to obtain an aeroelastic response convergence result.

[0036] The solving module is further configured to obtain the hub load at the moment based on the aeroelastic response convergence result at the moment.

[0037] The updating module is configured to update the rotor control, the rotating speed and the flow field information at the next moment based on the hub load at the moment and the aeroelastic response convergence result, until the whole calculation process is completed, and the whole process of the dynamic characteristics of the oscillation-pitch coupling rotor is obtained.

[0038] The application has the following beneficial technical effects:

[0039] The application can solve the problem of calculating the dynamic characteristics of an oscillation-pitch coupling rotor. The method of the application can calculate the dynamic characteristics at any moment when constructing the transient control equation of the oscillation-pitch coupling rotor, and the preset rotor control, rotating speed change and time history can be arbitrarily given, so that the dynamic characteristics of the oscillation-pitch coupling rotor can be completely reflected in one calculation. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The principle schematic diagram of the swing-pitch coupling configuration provided by the embodiment of the application;

[0041] Figure 2 The calculation flowchart of the swing-pitch coupling boundary condition of the aerodynamic response at this moment derived from the last moment;

[0042] Figure 3 The swing-pitch coupling rotor transient blade tension calculated by the method is compared with the test value.

[0043] Figure 4 The swing-pitch coupling rotor transient blade torque calculated by the method is compared with the test value.

[0044] 1, hub; 2, swing-pitch coupling mechanism. DETAILED DESCRIPTION

[0045] Please refer to Figures 1-4 The variable-pitch rotor aircraft related to the application changes the rotation speed of the rotor, so that the blade swing angle changes, and then the swing-pitch coupling effect is realized to change the pitch. The transient change of the pitch will interfere with the expected rotation speed of the current rotor, thereby affecting the final tension output value.

[0046] The method described in the application is supplemented and improved on the basis of the traditional Hamilton method. For the swing-pitch coupling configuration, there is no need to re-deduce and model, and the workload is greatly reduced. At the same time, since the method described in the application is not limited to the steady state in the calculation process, the swing-pitch coupling model is closer to the actual situation, and the method is more consistent with the actual situation of the swing-pitch coupling rotor at the transient moment than the traditional Hamilton method.

[0047] The application provides a swing-pitch coupling rotor transient dynamics calculation method. The method is developed for the transient dynamics problem of the swing-pitch coupling rotor rotation speed change process, studies the transient dynamics characteristics of the rotation speed change process, and provides theoretical basis and technical support for the development and application of the swing-pitch coupling rotor.

[0048] In the embodiment of the application, a swing-pitch coupling rotor transient dynamics calculation method is provided. The method comprises:

[0049] 1) Constructing a rotor transient control equation, establishing the rotor transient control equation at this moment based on the Hamilton principle, and the expression is as follows:

[0050]

[0051] Where, Π is the potential energy of the system; U is the strain energy of the system; T is the kinetic energy of the system; W is the virtual work of external force; t is the time integral domain, t1 and t2 are the upper and lower limits of integration; δ is the variation symbol.

[0052] In the undeformed coordinate system xyz of the blade (the base vectors are ), the velocity of a point with coordinates [x1 y1 z1] on the isolated rotor is

[0053]

[0054] Where, is the vector radius; Ω(t) is the angular velocity of the rotor at any time t; β p is the pre-cone angle.

[0055] The kinetic energy of the whole blade is

[0056]

[0057] Where, ρ s is the density of the blade; is the area integral, ∫dx is the line integral; R is the radius of the blade.

[0058] After taking the variation of the kinetic energy, we have

[0059]

[0060] Where, u e , v, v', w, w', are generalized coordinates, T v , T v' , T w , T w' , T F are the corresponding generalized forces.

[0061] Since the rotor speed Ω is derived with respect to time t in the transient process is not 0, therefore, compared with the steady-state process, the additional term of the kinetic energy T of the system in the transient process includes:

[0062]

[0063] Where, e g is the distance from the center of gravity of the section to the elastic axis; θ is the pitch angle; x is the section spanwise coordinate.

[0064] 2) Based on the rotor transient control equation, the rotor dynamics equation at this time is calculated, and its expression is as follows:

[0065] ​

[0066] where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F is the load column vector, x is the response of generalized freedom, which is acceleration, velocity, displacement respectively. The contribution of δU, δT, δW in 1) to M, C, K, F matrix is calculated; the initial response is given, and the Newmark integration method is used for multiple rounds of aeroelastic iteration to solve the response convergence results at this time.

[0067] 3) According to the response at this time, the load and structural load distribution of the blade at this time are calculated, the blade root load at this time is obtained by integrating the aerodynamic load and the structural load to the blade root, and the blade hub load at this time is obtained through coordinate transformation.

[0068] 4) According to the blade hub load and response at this time, the rotor control, rotating speed and other parameters at the next time are updated until the whole calculation process is completed, and the results of the whole process of the flapping-pitch coupling rotor transient dynamics are obtained.

[0069] It should be noted that 1) when constructing the rotor transient control equation, the influence of the rotor speed change needs to be considered. For the transient process, since the rotor angular acceleration term is not 0, the system kinetic energy T of the dynamic equation is a time-varying term, which can be written as so that M, C, K, F matrix are all time-varying terms.

[0070] 2) The boundary condition processing of the flapping-pitch coupling rotor. When the flapping-pitch coupling rotor moves, the blade flapping displacement directly affects the rigid torsion angle at this time under the action of the coupling mechanism. Therefore, when the response convergence results at a certain time are solved by aeroelastic iteration, the flapping angle v' obtained in the last round is coupled to the rigid torsion angle at the hinge (v' is defined as positive for forward swing, positive for lifting head, and ALAG is defined as positive for the coupling of blade forward swing-lifting head), which is further superimposed into the pitch input θ of the next round of aeroelastic iteration.

[0071] 3) For the rotor transient process, the rotor control and response at the last time are taken as input to construct the rotor transient control equation and the rotor dynamic equation at the next time for solving, so as to obtain the rotor control and response at the next time. Therefore, the dynamic equation can continuously reflect the dynamic characteristics at any time, so as to perform transient dynamics simulation on the flapping-pitch coupling rotor.

[0072] In other embodiments of the present application, a flapping-pitch coupling rotor transient dynamics calculation method is provided to solve the problem that the flapping-pitch coupling rotor transient dynamics response is difficult to calculate.

[0073] Specifically includes the following steps:

[0074] Step 1: input rotor parameters, including blade configuration, physical characteristics, geometric dimensions, number of rotors, rotor solidity, number of blades, blade radius; input blade structure parameters, blade structure unit division, aerodynamic unit division, airfoil C81 table, and perform dimensionless processing on blade structure parameters; input calculation state table, including rotor speed, forward flight speed, control amount, attitude angle; determine total number of calculation steps and transient process calculation step size dt;

[0075] Step 2: assume the previous time t n , the corresponding response is Now solve the response at the current time t n+1 = t n + dt Through interpolation, the rotor speed, forward flight speed, control amount, and attitude angle at the current time t n+1 are obtained, and the inflow λ1 at the current time t n+1 is calculated, and the azimuth angle ψ corresponding to the time t n+1 is determined;

[0076] Step 3: based on the rotor state at the current time, construct the rotor transient control equation δ∏ = ∫(δU-δT-δW)dt = 0; according to the finite element unit division, discrete to obtain the control equation of each element i δ∏ i = ∫(δU i -δT i -δW i )dt = 0; for each finite element unit i, the contribution of δU i , δT i , δW i to the M i , C i , K i , F i matrix in the dynamic equation is calculated, and finally the mass matrix M i , damping matrix C i , stiffness matrix K i and load column vector F i of the finite element unit are obtained;

[0077] Step 4: according to the node coordinate correspondence relationship of the finite element total matrix and the element matrix, complete the assembly of the finite element total matrix, and according to different blade configurations, consider the influence of blade structure damping and stiffness on C, K, F, and then consider the influence of rotor aerodynamic force on F matrix, finally obtain the total matrix M, C , K, F in the rotor dynamic equation at the current time;

[0078] Step 5: based on the previous time tn initial response The rotor dynamics equation is calculated by Newmark integral method for multi-round aeroelastic iteration, and the response at t n+1 is solved The difference between the two is Δq; let t n+1 The velocity and displacement at t

[0079]

[0080] In the formula, α and β are empirical coefficients; therefore, the acceleration at t n+1 is

[0081]

[0082] After substitution, we get

[0083]

[0084] Next, we calculate Δq. If the iteration is the first iteration, we can solve Δq by the following formula, and substitute it into the above formula to solve and get the response at t n+1

[0085]

[0086] A·Δq=B

[0087] If the iteration is not the first iteration, we solve Δq by the following formula, and get the response at t n+1

[0088]

[0089] A·Δq=B

[0090]

[0091] Step 6: solve the response at t n+1 After that, we calculate whether it is less than the preset tolerance ε1 (N strutc is the dimension of the response), if it is greater than the tolerance, we assign the calculated to It should be noted that the swing angle v' obtained in the last round is coupled to the rigid torsion angle at the hinge and then superimposed into the pitch θ of the next round of aeroelastic iteration operation, and step 4 is repeated until ​​​Up to this point, it is assumed that the obtained t n+1 The response at time t is convergent, at which point you can input t. n+1 The aeroelastic response and collective pitch at time, such as Figure 2 As shown in the figure (responses at times x1, dx1, and ddx1), The responses of x2, dx2, and ddx2 at corresponding time points ).

[0092] Step 7: Based on the response convergence results from Step 6 Calculate t n+1 Structural load F at time struct With aerodynamic load F aero The results of the blade spanwise distribution are obtained. The aerodynamic load is solved using a quasi-steady aerodynamic model. By calculating the velocity and angle of attack of each profile, and combining the airfoil C81 table, the corresponding lift, drag and moment coefficients are obtained, and finally the lift, drag and moment distribution of each profile is obtained.

[0093] Step 8: t n+1 Structural load F at time struct With aerodynamic load F aero Integrating to the paddle root, we obtain t n+1 The root load F in the undeformed blade coordinate system at time moment root Then, by using the transformation matrix between the non-rotating coordinate system of the propeller and the undeformed coordinate system of the propeller blade, t can be obtained. n+1 The grain load F at time hub :

[0094]

[0095] In the formula, F x ,F y ,F z M is a force in three directions. x M y M z For torque in three directions;

[0096] Step 9: Based on t n+1 The output result of the paddle load at time t is calculated after time step dt. n+1 The rotor inflow λ1 at time +dt is obtained, and the next time t is obtained by interpolation. n+1 The rotor speed, forward speed, control inputs, and attitude angles of +dt are used to recalculate the rotor transient dynamics.

[0097] Step 10: Repeat steps 2 through 9 until the calculation time t reaches the preset value, and output the transient dynamic characteristics of the oscillating variable-pitch coupled rotor throughout the entire process, including the response. Paddle Root Load Froot , the blade root load Fz hub time histories, where the calculated results of the blade root load Fz and the moment Mz are compared with the test results as shown in FIGS. Figure 3 , Figure 4 .

[0098] In summary, the present application proposes a method for calculating the transient dynamics of a flapping-pitch coupled rotor. The present application uses a time-stepping method to calculate the dynamic characteristics of the rotor at any time, and considers the coupling relationship between the blade root flapping angle and the blade pitch during the calculation of the response at each time. Therefore, the present application can continuously reflect the dynamic characteristics of the flapping-pitch coupled rotor at any time, and achieve the purpose of accurately calculating the transient dynamics of the flapping-pitch coupled rotor.

Claims

1. A method of analyzing transient dynamics characteristics of a flapping-geared rotor, characterized by, The method comprises: constructing a rotor transient control equation; based on the rotor transient control equation, calculating a rotor dynamics equation at the current time; iteratively solving the rotor dynamics equation at the current time to obtain an aeroelastic response convergence result; based on the aeroelastic response convergence result at the current time, obtaining a hub load at the current time; according to the hub load at the current time and the aeroelastic response convergence result, updating rotor control, rotational speed and flow field information at the next time until the entire calculation process is completed, obtaining rotor transient dynamics characteristic results of the entire process of flapping-pitch coupling; wherein the constructing a rotor transient control equation comprises: based on Hamilton's principle, establishing a rotor transient control equation at the current time, the expression is as follows: wherein, Π is the potential energy of the system; U is the strain energy of the system; T is the kinetic energy of the system; W is the virtual work of the system; t is the time integral domain, t1 and t2 are the upper and lower limits of integration; δ is the variation symbol.

2. The method of claim 1, wherein, Compared with the steady-state process, the system kinetic energy T in the transient process adds an item including: where e g is the distance from the elastic axis to the center of gravity of the section; θ is the pitch angle; and x is the spanwise coordinate of the section.

3. The method of claim 2, wherein, based on the rotor transient control equation, calculating a rotor dynamics equation at the current time, comprising: for the rotor transient control equation, calculating a rotor dynamics equation at the current time, the expression is as follows: wherein is the mass matrix, is the damping matrix, is the stiffness matrix, is the load column vector, is the response of the generalized degrees of freedom, acceleration, velocity, displacement, respectively. According to , , , calculate , , , array.

4. The method of claim 3, wherein, the iterative solution of the rotor dynamics equation at the current time to obtain an aeroelastic response convergence result, comprising: given the initial response, the rotor dynamics equation at the current time is solved iteratively by using the Newmark integration method to obtain the aeroelastic response convergence result.

5. The method of claim 4, wherein, the iterative solution of the rotor dynamics equation at the current time to obtain an aeroelastic response convergence result, comprising: given the initial response, the rotor dynamics equation at the current time is solved iteratively by using the Newmark integration method to obtain the aeroelastic response convergence result.

6. The method of claim 5, wherein, based on the aeroelastic response convergence result at the current time, obtaining a hub load at the current time, comprising: according to the aeroelastic response convergence result at the current time, the aerodynamic load and the structural load distribution of the blade at the current time are calculated, the aerodynamic load and the structural load are integrated to the hub to obtain the hub load at the current time, and the hub load at the current time is obtained through coordinate transformation.

7. The method of claim 6, wherein, according to the hub load at the current time and the aeroelastic response convergence result, updating rotor control, rotational speed and flow field information at the next time until the entire calculation process is completed, obtaining rotor transient dynamics characteristic results of the entire process of flapping-pitch coupling, comprising: according to the hub load at the current time and the aeroelastic response convergence result, updating rotor control, rotational speed and flow field information at the next time until the entire calculation process is completed, obtaining rotor transient dynamics characteristic results of the entire process of flapping-pitch coupling, comprising:

8. An apparatus for analyzing transient dynamics characteristics of an oscillating pitch coupled rotor, characterized by, The device comprises: a construction module for constructing a rotor transient control equation; a calculation module, configured to calculate a rotor dynamics equation at a current time based on the rotor transient control equation; a solution module, configured to iteratively solve the rotor dynamics equation at the current time to obtain an aeroelastic response convergence result; the solution module is further configured to obtain a hub load at the current time based on the aeroelastic response convergence result at the current time; an update module, configured to update rotor control, rotational speed and flow field information at a next time according to the hub load at the current time and the aeroelastic response convergence result, until the entire calculation process is completed to obtain an entire process flapping-pitch coupling rotor transient dynamics characteristic result; the construction module is further configured to establish the rotor transient control equation at the current time based on Hamilton's principle, and the rotor transient control equation is expressed as follows: in the formula, Π is a system potential energy; U is a system strain energy; T is a system kinetic energy; W is a system external force virtual work; t is a time integral domain, t1 and t2 are upper and lower limits of integration; and δ is a variation symbol.

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