Rotor cycle variable pitch pneumatic advance control angle calculation method considering forward flight speed and non-uniform inflow

Abstract

The invention discloses a rotor cycle variable pitch pneumatic advance control angle calculation method considering forward flight speed and non-uniform inflow, and belongs to the field of rotor pneumatic advance control angle design, the method comprises the following steps: 1, deducing a forward flight flapping kinetic equation analytical solution in a matrix form; step 2, order reduction of an analytical solution of the waving motion equation; step 3, carrying out gradient decoupling on the inflow based on the dynamic inflow; and 4, deducing to obtain a final control matrix of the periodic variable pitch of the rotor wing to the flapping chamfer of the propeller disc. Compared with a traditional advance control angle calculation method, the method has the advantages that the calculation precision of the pneumatic advance control angle under the flight working conditions of hovering and forward flight can be effectively improved, the correction effect on the rotor wing with the large rotor wing rigidity is good, and the method can be used for optimizing rotor wing control system design and flight control decoupling.

Description

Technical Field

[0001] This invention belongs to the field of rotor aerodynamic advance control angle design, specifically a method for calculating rotor cyclic pitch aerodynamic advance control angle considering forward flight speed and non-uniform inflow. Background Technology

[0002] The aerodynamic advance control angle of a rotor has a significant impact on the design of the rotor control system and flight control decoupling. The aerodynamic advance control angle (rotor flapping response hysteresis angle) is caused by the inherent characteristics of blade flapping. Macroscopically, it is reflected as a hysteresis angle between the rotor disk tilt angle (flapping response) and pitch control (external excitation). Figure 1 As shown.

[0003] For an ideal, purely center-articulated rotor, this hysteresis angle is 90°. However, the actual rotor design needs to consider the characteristics of helicopter flight dynamics. For example, to increase the rotor's control effectiveness and angular velocity damping, the flapping hinge offset and flapping hinge spring stiffness can usually be increased in the rotor mechanism; to reduce the flapping effect, the flapping adjustment coefficient can be increased, etc.

[0004] Therefore, the hysteresis angle will be affected by the spring stiffness k at the swing hinge. β The influence of flapping hinge offset e, flapping pitch adjustment coefficient K1, and blade flapping mass static moment M. β Blade waving inertia I β The lag is not a standard 90° due to the influence of parameters such as the blade loco number γ. The lag angle φ can be obtained by deriving the hovering flaring motion equation. lag The following relationship exists between these parameters:

[0005]

[0006] The above formula is currently the most commonly used calculation formula in engineering. However, the aerodynamic advance control angle calculated using this formula will have a certain deviation from the measured value. Generally speaking, the theoretical calculated value of the aerodynamic advance control angle is larger than the measured value. This is because the current calculation method solves the blade flapping motion equation in the helicopter's hovering state and does not consider the changes in the inflow gradient caused by cyclic pitch control, thus affecting the advance control angle. Furthermore, the effect of forward speed on the aerodynamic advance control angle during helicopter forward flight is different for longitudinal and lateral cyclic pitch. Currently, no specific calculation formula for the aerodynamic advance control angle as a function of forward speed has been clearly given domestically or internationally. Moreover, traditional formulas have significant limitations when calculating hingeless and bearingless rotors. Summary of the Invention

[0007] This invention provides a method for calculating the aerodynamic advance control angle of a rotor with cyclic pitch, taking into account the influence of non-uniform inflow and forward velocity on the rotor advance control angle. Compared with traditional advance control angle calculation methods, this invention can effectively improve the calculation accuracy of aerodynamic advance control angle under hovering and forward flight conditions, and has a particularly good correction effect on rotors with high rotor stiffness. It can be used to optimize rotor control system design and decouple flight control.

[0008] This invention is implemented as follows:

[0009] Step 1: Derive the analytical solution of the forward flight flaring dynamics equation in matrix form:

[0010] When modeling rotor flapping motion, a rigid blade flapping dynamics model is adopted. Referring to the Helisim modeling method, center-hinged, seesaw, hingeless, and bearingless rotors can all be equivalent to a center-hinged rotor with a flapping hinge spring. The flapping dynamics equations are derived based on the condition that the resultant torque of the flapping hinge spring torque, blade aerodynamic torque, blade centrifugal torque, and blade inertial torque about the center hinge is zero. Figure 2 The diagram shows the forces acting on a micro-segment of the blade.

[0011] Without considering follow-up flapping, and using the small-angle assumption, the flapping dynamics equation of a single blade can be written in the following form by retaining the first harmonic term of the external excitation force:

[0012]

[0013] Where β is the blade flapping angle, γ is the blade lock number, μ is the rotor advance ratio, ψ is the rotor azimuth angle, and S β Let be the blade stiffness number. [β0,β 1c ,β 1s ] are respectively expressed as the taper angle of the propeller disk, the longitudinal chamfer (defined as forward chamfer as positive), and the side chamfer (defined as left chamfer as positive), [θ0, θ t ,θ 1s ,θ 1c [λ0,λ] represent the collective pitch at the blade root, the linear twist angle of the blade, the longitudinal periodic pitch, and the lateral periodic pitch, respectively. 1s ,λ 1c [ ] represent the average induced velocity, the transverse inflow gradient, and the longitudinal inflow gradient, respectively.

[0014] Based on the harmonic balance method, equation (1) is solved in matrix form as shown in equation (2).

[0015]

[0016] Where K βThe equivalent flapping hinge stiffness is composed of the actual flapping hinge stiffness, centrifugal force stiffness, structural stiffness caused by flapping offset, and aerodynamic stiffness caused by flapping adjustment. λ β To swing at a first-order frequency, S β The blade stiffness number is defined as shown in equations (3)-(6):

[0017]

[0018] Step 2: Reducing the order of the analytical solution of the swing motion equation:

[0019] Where the taper angle β0, the back chamfer β 1c Side chamfer β 1s The three terms are decoupled and do not interfere with each other. Since we mainly focus on the relationship between the transverse and longitudinal periodic pitch and the tilting and backward tilting, respectively, and considering that the thrust coefficient of the rotor is around a certain value in different actual flight conditions, we ignore the influence of the collective pitch of the blades under different flight conditions on the tilting and tilting of the rotor disk. Therefore, we can reduce the order of equation (2) and write it in the form of equation (7). It can be found that if the rotor design parameters are fixed, the rotor disk chamfer [β] 1c ,β 1s The rotor's advance ratio μ and control input [θ] are used to determine the rotor's advance ratio. 1s ,θ 1c ], inflow gradient [λ 1s ,λ 1c ]Decide.

[0020]

[0021] If the device is hovering, equation (7) can be written in the form of (8):

[0022]

[0023] Ignoring the influence of manipulation on the inflow gradient, the advance manipulation angle can be calculated as shown in equation (9), which is completely consistent with the theoretical calculation formula commonly used in engineering:

[0024]

[0025] Step 3: Decoupling the inflow gradient based on dynamic inflow:

[0026] However, taking hovering as an example, cyclic pitch control can also cause changes in the inflow gradient, which in turn affects the decoupling of the advance control angle. Therefore, it is necessary to derive the coupling relationship between the induced velocity, the propeller disk chamfer, and cyclic pitch control, and then derive the accurate advance control angle.

[0027] Therefore, we consider using the Pitt-Peters dynamic inflow model (Equations (10)-(11)) to calculate the response of the inflow gradient to maneuvering and paddle disc flapping.

[0028]

[0029] For C among them T C L C M These are the thrust coefficient, aerodynamic roll moment coefficient, and aerodynamic pitch moment coefficient, respectively. Based on the forward flight blade element theory, the following formulas apply. The aerodynamic moment coefficient is given by the following formula:

[0030]

[0031] Further derivation yields the relationship between the inflow gradient and the periodic pitch control and propeller chamfer as shown in equation (14):

[0032]

[0033] Where X1 and X2 are functions of parameters related to the wake inclination angle X, the advance ratio μ, and the average induced velocity λ0:

[0034]

[0035] When hovering, X = 0. Equation (8) can be further derived into equation (17):

[0036]

[0037]

[0038] Therefore, it can be seen that the advance control angle after considering the influence of the inflow gradient is different from the traditional calculation formula because it has more... The correction will result in a smaller aerodynamic advance control angle, which is consistent with the experimental results. It can also be found that this correction coefficient is a function of the average induced velocity. That is, the larger the tension coefficient, the smaller this correction is, and the closer it is to the traditional calculation result of the advance control angle.

[0039] Step 4: Derive the final control matrix for rotor periodic pitch and rotor disk flapping chamfer.

[0040] For forward flight, the calculation of this advance control angle is more complicated, but it is consistent with the hovering derivation method. The final control matrix of cyclic pitch control and propeller disk flapping chamfer is obtained as follows (19)-(21).

[0041]

[0042] The calculation formulas for X1 and X2 can be found in (15)-(16), and the derived formulas for the final lateral and longitudinal aerodynamic advance control angles are as follows:

[0043] φlag_lat =atan(H 11 / H 12 (46)

[0044] φ lag_lon =atan(H 22 / H 21 (47)

[0045]

[0046] The advantages of this invention compared to the prior art are as follows:

[0047] The method of this invention for calculating the advance control angle incorporates the effects of forward velocity and inflow gradient, reflecting the aerodynamic advance control angle characteristics with different forward velocities. Compared to the original calculation formula, it effectively improves calculation accuracy. Furthermore, it can reflect the variation characteristics of the lateral and longitudinal aerodynamic advance control angle with forward velocity at different first-order flapping frequencies, characteristics that traditional aerodynamic advance control angle formulas cannot reflect. Calculations can be performed with reference to the rotor design parameters of B0105, revealing that the aerodynamic advance control angle calculation for hovering and forward flight conditions is closer to the rotor nonlinear model than traditional methods, effectively improving the calculation accuracy of the aerodynamic advance control angle under different operating conditions. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the rotor aerodynamic advance control angle in the background art of this invention;

[0049] Figure 2 This is a schematic diagram of the forces acting on the micro-segment of the blade of the present invention;

[0050] Figure 3 This describes the variation characteristics of the longitudinal aerodynamic lateral / longitudinal aerodynamic advance control angle of the BO105 rotor with the advance ratio in this embodiment of the invention.

[0051] Figure 4 This describes the variation characteristics of the lateral aerodynamic advance control angle with the advance ratio in this embodiment of the invention.

[0052] Figure 5 This describes the variation of the longitudinal aerodynamic advance control angle with the advance ratio in an embodiment of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the following examples provide a more detailed description of the invention. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0054] The final advance control angle formula derived in this paper can be summarized as follows:

[0055] φ lag_lat =atan(H 11 / H 12 ) (twenty two)

[0056] φ lag_lon =atan(H 22 / H 21 ) (twenty three)

[0057]

[0058] The definitions of A, B, X1, and X2 can be found in the following formula:

[0059]

[0060]

[0061] The parameters used are: blade Lock number γ, blade dimensionless first-order flapping frequency λ. β Rotor advance ratio μ, blade stiffness number S β , parameter η β The average induced velocity λ0, the wake inclination angle parameter X, the lift line slope of the blade airfoil a0, and the rotor solidity s are the specific calculation formulas for reference (25)-(32).

[0062]

[0063] Where I β Let ρ be the blade flapping inertia, ρ be the atmospheric density under current operating conditions, c be the chord length of the blade's characteristic section, and K be the blade's chord length. β The equivalent flapping hinge stiffness is given by Ω, where Ω is the rotor speed, e is the blade flapping hinge offset, K1 is the flapping pitch coupling coefficient, ε = e / R, R is the blade radius, and a s χ is the angle of attack between the airflow and the rotor disk plane, v is the axial velocity of the incoming flow to the rotor disk, χ is the rotor wake angle, and N is the rotor wake angle. b η is the number of blades. β This is the stiffness coupling coefficient.

[0064] Taking the design parameters of a certain Bo105 rotor as an example:

[0065] Ω 44.4 rad / s <![CDATA[I β ]]> <![CDATA[231.7kg / m 2 ]]> γ 5.087 <![CDATA[λ β ]]> 1.1171 <![CDATA[S β ]]> 0.3911 <![CDATA[a0]]> 6.113 / rad s 0.07 <![CDATA[K β ]]> 113330 Nm / rad <![CDATA[N b ]]> 4 ρ <![CDATA[1.225kg / m 3 ]]>

[0066] For forward flight conditions, the above design parameters are substituted into equation (24) for solution. The rotor thrust coefficient is selected as its hovering thrust coefficient of 0.005. Based on slipstream theory, the average induced velocity at different speeds can be obtained. Finally, the H control matrix at different forward ratios can be obtained as follows:

[0067]

[0068]

[0069] Meanwhile, according to formulas (22)-(23), the lateral and longitudinal advance control angles under different advance ratios can be obtained as follows:

[0070] Progress ratio Lateral advance control angle longitudinal advance control angle μ = 0 59.0269° 59.0269° μ = 0.05 55.8023° 60.1652° μ = 0.1 55.7706° 64.9315° μ = 0.15 59.0931° 67.1219° μ = 0.2 62.0536° 67.9113° μ = 0.25 64.4627° 68.3413° μ = 0.3 66.4823° 68.6990°

[0071] The characteristics of the rotor's longitudinal aerodynamic lateral and longitudinal aerodynamic advance control angles as a function of the advance ratio are as follows: Figure 3 As shown.

[0072] It can be found that compared with the traditional method of calculating the advance control angle, the analytical formula proposed in this invention, which considers the influence of induced velocity gradient and forward velocity, is closer to the nonlinear model. Especially for rotors with small thrust coefficient and high stiffness, it can effectively reflect the asymmetric characteristics of lateral and longitudinal periodic variation during forward flight, thus improving the calculation accuracy of aerodynamic advance control angle.

[0073] The method of this invention for calculating the advance control angle incorporates the effects of forward velocity and inflow gradient, reflecting the aerodynamic advance control angle characteristics with different forward velocities. Compared to the original calculation formula, it effectively improves calculation accuracy. Furthermore, it can reflect the variation characteristics of the lateral and longitudinal aerodynamic advance control angle with forward velocity at different first-order flapping frequencies. Specific characteristics are as follows. Figures 4-5 These are characteristics that traditional aerodynamic advance control angle formulas cannot reflect. Calculations can be performed using the rotor design parameters of B0105, revealing that the aerodynamic advance control angle calculation for hovering and forward flight conditions is closer to the rotor's nonlinear model than traditional methods, effectively improving the calculation accuracy of the aerodynamic advance control angle for different operating conditions.

[0074] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward flight speed and non-uniform inflow, characterized in that, The method is as follows: Step 1: Derive the analytical solution of the forward flight flare dynamics equation in matrix form; Step 2: Reduce the order of the analytical solution of the swing motion equation; Step 3: Decouple the inflow gradient based on dynamic inflow; Step 4: Derive the final control matrix for the rotor periodic pitch change and the rotor disk flapping chamfer.

2. The method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward velocity and non-uniform inflow as described in claim 1, characterized in that, The first step is as follows: When modeling the flapping motion of a rotor, a rigid blade flapping dynamics model is adopted. Referring to the modeling method of Helisim, the centrally hinged, seesaw, hingeless, and bearingless rotors can all be equivalent to a centrally hinged rotor with a flapping hinge spring. The flapping dynamics equations are derived based on the condition that the resultant torque of the flapping hinge spring torque, blade aerodynamic torque, blade centrifugal torque, and blade inertial torque about the central hinge is 0. Without considering follow-up flapping, and using the small-angle assumption, retaining the first harmonic term of the external excitation force, the flapping dynamics equation of a single blade can be obtained as follows: Where β is the blade flapping angle, γ is the blade lock number, μ is the rotor advance ratio, ψ is the rotor azimuth angle, and S β [β0,β] represents the blade stiffness number; 1c ,β 1s ] are respectively expressed as the taper angle of the propeller disk, the longitudinal chamfer (defined as forward chamfer as positive), and the side chamfer (defined as left chamfer as positive), [θ0, θ t ,θ 1s ,θ 1c [λ0,λ] represent the collective pitch at the blade root, the linear twist angle of the blade, the longitudinal periodic pitch, and the lateral periodic pitch, respectively; 1s ,λ 1c [ ] represent the average induced velocity, the transverse inflow gradient, and the longitudinal inflow gradient, respectively.

3. The method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward velocity and non-uniform inflow as described in claim 2, characterized in that, Based on the harmonic balance method, equation (1) is solved in matrix form as shown in equation (2): Where K β The equivalent flapping hinge stiffness is composed of the actual flapping hinge stiffness, centrifugal stiffness, structural stiffness caused by flapping offset, and aerodynamic stiffness caused by flapping adjustment; λ β To swing at a first-order frequency, S β The blade stiffness number is defined as shown in equations (3)-(6):

4. The method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward velocity and non-uniform inflow as described in claim 1, characterized in that, The second step is specifically as follows: Taper angle β0, back chamfer β 1c Side chamfer β 1s The three terms are decoupled and do not interfere with each other. Equation (2) is reduced in order and written in the form of Equation (7). It can be found that if the rotor design parameters are fixed, the rotor disk chamfer [β] 1c ,β 1s The rotor's advance ratio μ and control input [θ] 1s ,θ 1c ], inflow gradient [λ 1s ,λ 1c ]Decide; If the device is hovering, equation (7) can be written in the form of (8): Neglecting the effect of manipulation on the inflow gradient, the manipulation angle φ can be considered to be ahead of schedule. lag The calculation is shown in equation (9), which is completely consistent with the theoretical calculation formula commonly used in previous engineering projects:

5. The method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward velocity and non-uniform inflow as described in claim 1, characterized in that, Step three specifically refers to: Hovering: Periodic pitch control can also cause changes in the inflow gradient, which in turn affects the decoupling of the advance control angle. Therefore, it is necessary to derive the coupling relationship between the induced velocity and the propeller chamfer and the periodic pitch control, and then derive the accurate advance control angle. Therefore, we consider the Pitt-Peters dynamic inflow model (10)-(11), which can be used to calculate the response of the inflow gradient to maneuvering and paddle disc flapping. For C among them T C L C M These are the thrust coefficient, aerodynamic roll moment coefficient, and aerodynamic pitch moment coefficient, respectively. Based on the forward flight blade element theory, the following formulas apply. The aerodynamic moment coefficient is given by the following formula: Further derivation yields the following relationship between the inflow gradient and the periodic pitch control and propeller chamfer: (14) As shown: Where X1 and X2 are functions of parameters related to the wake inclination angle X, the advance ratio μ, and the average induced velocity λ0: When hovering, X = 0. Equation (8) can be further derived into equation (17):

6. The method for calculating the advance control angle of a rotor cyclic pitch aerodynamics considering forward velocity and non-uniform inflow as described in claim 1, characterized in that, The fourth step is specifically as follows: The final control matrix for periodic pitch control and propeller flapping chamfering is obtained as follows: (19)-(21) The calculation formulas for X1 and X2 can be found in (15)-(16), and the derived formulas for the final lateral and longitudinal aerodynamic advance control angles are as follows: φ lag_lat =atan(H 11 / H 12 ) (22) φ lag_lon =atan(H 22 / H 21 ) (23)

Images