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CN115258147B - Rotor and noise reduction method based on the silent flying principle of owl - Google Patents

Rotor and noise reduction method based on the silent flying principle of owl Download PDF

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Publication number
CN115258147B
CN115258147B CN202210935078.7A CN202210935078A CN115258147B CN 115258147 B CN115258147 B CN 115258147B CN 202210935078 A CN202210935078 A CN 202210935078A CN 115258147 B CN115258147 B CN 115258147B
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trailing edge
owl
blade
winglet
winglets
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CN115258147A (en
Inventor
陈希
李尧
招启军
丁岩
蒋相闻
赵国庆
王博
张夏阳
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B64AIRCRAFT; AVIATION; COSMONAUTICS
    • B64CAEROPLANES; HELICOPTERS
    • B64C27/00Rotorcraft; Rotors peculiar thereto
    • B64C27/32Rotors
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B64AIRCRAFT; AVIATION; COSMONAUTICS
    • B64CAEROPLANES; HELICOPTERS
    • B64C27/00Rotorcraft; Rotors peculiar thereto
    • B64C27/32Rotors
    • B64C27/46Blades
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B64AIRCRAFT; AVIATION; COSMONAUTICS
    • B64CAEROPLANES; HELICOPTERS
    • B64C27/00Rotorcraft; Rotors peculiar thereto
    • B64C27/32Rotors
    • B64C27/46Blades
    • B64C27/473Constructional features

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Toys (AREA)

Abstract

The invention discloses a rotor wing based on a owl flying silence principle and a noise reduction method, which relate to the technical field of aircrafts and comprise blades, wherein a plurality of trailing edge winglets are rotatably arranged at the tail parts of the blades and are sequentially arranged along the length direction of the blades, the rotating shafts of the trailing edge winglets are parallel to the length direction of the blades, rotating mechanisms are arranged between the trailing edge winglets and the blades, the rotating mechanisms are electrically connected with a controller, and the controller is used for controlling the rotating mechanisms to act and enabling the rotating mechanisms to drive the trailing edge winglets to rotate. The rotor wing based on the owl flying silence principle and the noise reduction method can reduce the sound pressure level of the aerodynamic noise of the rotor wing of the helicopter and improve the sound stealth characteristic of the helicopter.

Description

Rotor wing based on owl flight silencing principle and noise reduction method
Technical Field
The invention relates to the technical field of aircrafts, in particular to a rotor wing based on a owl flight silencing principle and a noise reduction method.
Background
Helicopter has the advantage that fixed wing aircraft such as vertical take-off and landing, hovering are incomparable, but because helicopter vibration is big, the characteristics that noise is big, its use is restricted in many cases. The improvement of the sound stealth performance of the military helicopter can greatly improve the survivability of the military helicopter, and in civil aspects, the helicopter is prohibited from flying in the air in some areas due to the large loudness of the aerodynamic noise of the helicopter and the long propagation direction. The requirements of modern helicopter designs on low noise emissions are increasingly stringent, both for military use and for civilian use, as are the requirements of the international civilian aviation organization on the noise levels of helicopters. The noise level of helicopters is almost as important as performance, safety, and reliability design criteria.
Disclosure of Invention
The invention aims to provide a rotor wing based on a owl flying silence principle and a noise reduction method, so as to solve the problems in the prior art, reduce the sound pressure level of aerodynamic noise of a helicopter rotor wing and improve the sound stealth characteristic of the helicopter.
In order to achieve the above object, the present invention provides the following solutions:
The invention provides a rotor wing based on a owl flying silence principle, which comprises a blade, wherein a plurality of trailing edge winglets are rotatably arranged at the tail of the blade, the trailing edge winglets are sequentially arranged along the length direction of the blade, the rotating shafts of the trailing edge winglets are parallel to the length direction of the blade, rotating mechanisms are arranged between the trailing edge winglets and the blade, the rotating mechanisms are electrically connected with a controller, and the controller is used for controlling the rotating mechanisms to act and enabling the rotating mechanisms to drive the trailing edge winglets to rotate.
Preferably, the trailing edge winglet corresponds to one of the rotating mechanisms on both sides in the length direction, and the rotating mechanism is mounted on the blade.
Preferably, the rotating mechanism comprises a gear, two diamond amplifiers, two pull rods and two racks, one diamond amplifier is correspondingly connected with one end of one pull rod, the other end of the pull rod is connected with one end of one rack, the other end of the rack extends towards the direction close to the trailing edge winglet, the moving direction of the pull rod is perpendicular to the length direction of the blade, the gear is arranged at the root of the trailing edge winglet, the periphery of the gear is meshed with the two racks respectively, the two racks are parallel and oppositely arranged, the diamond amplifiers can drive the pull rod to move towards the direction close to the gear, the racks are driven to move towards the direction far away from the diamond amplifiers, so that the gear can drive the trailing edge winglet to rotate.
Preferably, the diamond amplifier comprises a plurality of piezoelectric stacks and two expansion plates, each piezoelectric stack is arranged between two expansion plates, the pull rod is connected with one side, far away from the piezoelectric stacks, of one expansion plate, and the piezoelectric stacks can stretch when the piezoelectric stacks are electrified and drive the expansion plates and the pull rod to move.
Preferably, the number of the trailing edge winglets is nine, and the deflection angle range of each trailing edge winglet is-10 degrees to +10 degrees.
The invention also provides a noise reduction method based on the owl flight muting principle, which adopts any one of the technical schemes to realize the rotor based on the owl flight muting principle, and comprises the following steps:
S1, selecting an observation point as a calculation point, and solving a force L r required to be applied for canceling the noise in a plane to be zero;
S2, transmitting the L r value calculated in the S1 to a controller, controlling each rotating mechanism to act through the controller, and enabling the rotating mechanism to control the deflection angle of the trailing edge winglet compared with the blade, so that the trailing edge winglet generates an L r value with resistance smaller than twice, and noise reduction is achieved.
Preferably, in S1, the formula for solving L r is
Where τ is delay time, c 0 is sound velocity, M r is mach number component of the connection between the sound source and the observation point, M is mach number at the sound source, p' T is thickness noise sound pressure value corresponding to the observation point, and r is distance from the sound source to the observation point.
Compared with the prior art, the invention has the following technical effects:
According to the rotor wing based on the owl flying mute principle and the noise reduction method, the tail of the blade is rotatably provided with the plurality of trailing edge winglets, the plurality of trailing edge winglets are sequentially arranged along the length direction of the blade, the saw-tooth structure of the owl wings is simulated, so that the airflow blown through the rotor blade is rectified by simulating the flying state of the owl, the rotating shaft of the trailing edge winglet is parallel to the length direction of the blade, the rotating plane of the trailing edge winglet is perpendicular to the blade, the angle of the trailing edge winglet relative to the blade can be adjusted, sound pressure load noise with the opposite sound pressure direction of thickness noise is generated, the thickness noise in the plane of the blade is reduced, rotating mechanisms are arranged between the trailing edge winglets and the blade, the rotating mechanisms are electrically connected with a controller, the controller is used for controlling the rotating mechanisms to rotate, active control is realized, the sound pressure level of the helicopter is reduced, the sound pressure level of the helicopter is improved, the sound pressure noise of the saw-tooth structure of the owl wings is simulated by deflecting up and down, the flying noise of the helicopter is reduced, meanwhile, the thickness noise can be reduced, and the air lift can be more completely cut off through the adjustment of the trailing edge winglet, and the wind noise can be more silenced.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic view of a rotor according to the first embodiment based on the principle of owl fly silence in a non-operating state;
fig. 2 is a schematic diagram of a rotor based on the principle of owl fly silence in the first embodiment in an operating state;
FIG. 3 is an enlarged schematic view at A of FIG. 2;
FIG. 4 is a schematic view of a rotating mechanism according to the first embodiment;
FIG. 5 is a schematic diagram of a diamond amplifier in accordance with one embodiment;
FIG. 6 is a schematic view of the mounting position of the gear in the first embodiment;
FIG. 7 is a schematic diagram of the position of a far field observation point in a forward fly/hover state in the second embodiment;
FIG. 8 is a schematic diagram of effective noise reduction area in suspended state in the second embodiment;
FIG. 9 is a schematic diagram of effective noise reduction area in the forward flight state in the second embodiment;
Fig. 10 is a schematic diagram of noise reduction effect at the observation point at the position 100R in front of the propeller disc in the second embodiment;
FIG. 11 is a schematic diagram of a helicopter in motion at an observation point in the second embodiment;
FIG. 12 is a graph of area noise reduction effect under different control laws in the second embodiment;
in the figure, 100-a rotor wing based on the owl flying silence principle, 1-blades, 2-trailing edge winglets, 3-diamond amplifiers, 4-pull rods, 5-racks, 6-gears, 7-expansion plates and 8-piezoelectric stacks.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a rotor wing based on a owl flight silencing principle and a noise reduction method, so as to solve the technical problems of high noise and difficult noise reduction of the existing helicopter.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1
As shown in fig. 1-6, this embodiment provides a rotor 100 based on owl flight silence principle, including paddle 1, a plurality of trailing edge winglets 2 are installed in the afterbody rotation of paddle 1, and a plurality of trailing edge winglets 2 are arranged in proper order along the length direction of paddle 1, and then the zigzag structure of simulation owl wing, in order to realize imitating the state of flight of owl and commutate the air current that blows through rotor paddle 1, the pivot of trailing edge winglet 2 is parallel with the length direction of paddle 1, make the plane of rotation of trailing edge winglet 2 perpendicular with paddle 1, and then can produce the acoustic pressure load noise that can be opposite with thickness noise acoustic pressure direction sign through the angle of adjustment trailing edge winglet 2, reduce the thickness noise in the paddle plane, all be equipped with rotary mechanism between each trailing edge winglet 2 and the paddle 1, and each rotary mechanism all is connected with a controller electricity, the controller is used for controlling the action of rotary mechanism, and make rotary mechanism drive trailing edge winglet 2 rotate, realize initiative control, through the up-down deflection simulation of trailing edge winglet 2, can the aircraft blade 1 through the lift of a plurality of trailing edge winglet, can be more surmounting the helicopter, the noise level is reduced, the noise can be overcome through the aircraft, the aircraft is more surmounting the lift, the aircraft is more surmounting to the aircraft, the noise performance of the helicopter is improved, the aircraft is more surmounting the lift, the aircraft is more than the aircraft has, the lift the aircraft has been improved, and the lift the aircraft is more can, and the lift the aircraft can and the noise can be surly the noise can and the noise and has better.
Specifically, the two sides of the trailing edge winglet 2 in the length direction correspond to one rotation mechanism respectively, and the rotation mechanisms are mounted on the blade 1, and by arranging the rotation mechanisms on the two sides of the trailing edge winglet 2, the upper and lower surfaces of the trailing edge winglet 2 are avoided, and the influence on the resistance adjustment of the trailing edge winglet 2 can be avoided.
The rotating mechanism comprises a gear 6, two diamond amplifiers 3, two pull rods 4 and two racks 5, one diamond amplifier 3 is correspondingly connected with one end of one pull rod 4, the other end of the pull rod 4 is connected with one end of one rack 5, the other end of the rack 5 extends towards the direction close to the trailing edge winglet 2, the moving direction of the pull rod 4 is perpendicular to the length direction of the blade 1, and then the angle of the trailing edge winglet 2 compared with the blade 1 is convenient to adjust, so that resistance adjustment is achieved, the gear 6 is mounted at the root of the trailing edge winglet 2, the periphery of the gear 6 is meshed with the two racks 5 respectively, the two racks 5 are parallel and oppositely arranged, forward rotation and reverse rotation of the gear 6 can be achieved through the respective movement of the two racks 5, the upward deflection and downward deflection of the trailing edge winglet 2 are finally achieved, the diamond amplifier 3 can drive the pull rod 4 to move towards the direction close to the gear 6, the pull rod 4 drives the rack 5 to move towards the direction far away from the amplifier 3, in the process, the gear 6 can be meshed with the rack 5, the gear 6 can be driven to rotate along with the movement of the rack 5, the gear 6 is fixed to the gear, the thickness of the trailing edge winglet 2 is not to be overlapped with the trailing edge winglet 2, the acoustic pressure is adjusted, the acoustic pressure is reduced through the rotation of the trailing edge winglet 2, and the acoustic pressure is finally adjusted, and the acoustic pressure is adjusted. Meanwhile, when the diamond amplifier 3 drives one rack 5 to move, the power of the diamond amplifier is far greater than the resistance of the other rack 5 to the gear 6, so that the influence of the other rack 5 on the gear 6 is negligible.
The diamond amplifier 3 comprises a plurality of piezoelectric stacks 8 and two expansion plates 7, each piezoelectric stack 8 is arranged between the two expansion plates 7, the pull rod 4 is connected with one side, far away from the piezoelectric stacks 8, of one expansion plate 7, when alternating voltage is applied to the piezoelectric stacks 8, the piezoelectric stacks 8 stretch, the expansion plates 7 and the pull rod 4 are driven to generate tiny displacement, and deflection angle adjustment of the trailing edge winglet 2 is achieved through meshing of the racks 5 and the gears 6. When the trailing edge winglet 2 is required to deflect downwards, only the upper diamond amplifier 3 needs to be started by applying voltage, so that the trailing edge winglet 2 rotates downwards, the lower diamond amplifiers 3 need to be started, and the diamond amplifiers 3 on two sides of the trailing edge winglet 2 are connected in series and are connected in series, so that the two upper diamond amplifiers 3 act simultaneously, and the two lower diamond amplifiers 3 act simultaneously, so that the trailing edge winglet 2 is ensured to deflect stably. Meanwhile, the applied voltage can influence the distance that the diamond-shaped amplifier 3 drives the pull rod 4 to extend, so that the deflection amplitude of the trailing edge winglet 2 can be changed by controlling the alternating voltage, and when the applied voltage is stopped, the diamond-shaped amplifier 3 can restore the original shape.
Nine trailing edge winglets 2 are provided, the deflection angle range of each trailing edge winglet 2 is-10 degrees to +10 degrees, and in the actual production process, the number of the trailing edge winglets 2 can be adaptively changed according to actual requirements by a person skilled in the art.
Example two
As shown in fig. 7-12, the present embodiment provides a noise reduction method based on the principle of owl fly silence, using the rotor wing 100 based on the principle of owl fly silence in the first embodiment,
When the helicopter is in a normal flight state and noise control is not needed, each trailing edge winglet 2 is in a retracted state, namely the deflection angle of the trailing edge winglet 2 compared with the blade 1 is 0 degrees, the shape of the trailing edge winglet is basically consistent with that of a conventional rotor wing, and the influence on the aerodynamic performance of the helicopter can be reduced to the minimum;
When in-plane noise control is required to be carried out on the helicopter (for example, the civil helicopter flies to the upper part of a residential area or the military helicopter executes a battlefield task), alternating voltage is applied to the piezoelectric stack 8, so that the diamond-shaped amplifier 3 above or below the gear 6 controls the pull rod 4 to extend, drives the rack 5 to move and drives the gear 6 to rotate, and the trailing edge winglet 2 is controlled to rotate by a proper angle to achieve a working state;
If the trailing edge winglets 2 are in a working state, the deflection angle of each trailing edge winglet 2 needs to be controlled, and as the resistance direction required to be provided for counteracting needs to be connected with the observation point along the sound source, the generated load noise is consistent with the thickness noise to be counteracted, so that in the rotation process of the trailing edge winglets 2, the deflection angle of each trailing edge winglet 2 needs to be regulated by controlling the voltage, and the resistance directions generated by all the trailing edge winglets 2 can be ensured to be along the connection direction of the sound source and the observation point;
in the specific noise reduction adjustment process, an observation point is selected as a calculation point, and the force Lr required to be applied for canceling the noise in the plane to be zero is solved, wherein the solving formula is as follows:
Where τ is delay time, c 0 is sound velocity, mr is Mach number component of connection between sound source and observation point, M is Mach number at sound source, p' T is thickness noise sound pressure value corresponding to observation point, r is distance from sound source to observation point, and other values in the formula except Lr to be solved can be obtained in thickness noise calculation process by using CLORNS-sound pressure calculation code.
The controller controls the deflection angle of the trailing edge winglets 2 through the Lr value calculated by the controller, and the deflection angle of the trailing edge winglets 2 is changed by changing the voltage of the corresponding piezoelectric stacks 8 of each trailing edge winglet 2, so that the larger the upward deflection (maximum 10 degrees) of the trailing edge winglet 2 is, the larger the generated resistance is, and meanwhile, the larger resistance can be generated by utilizing different deflection angles of a plurality of the trailing edge winglets 2, so that the generated resistance is controlled.
When the force generated by deflection of all trailing edge winglets 2 is Lr, the thickness noise at the observation point can be cancelled to zero, and the noise reduction effect can be generated as long as the force generated by controlling the mechanism is less than twice Lr.
For a helicopter in a hovering working state, the method can reduce noise of an annular belt with a fixed distance surrounding the helicopter, and for a helicopter in a forward flying working state, the method can reduce noise of an area with a certain relative distance from the helicopter.
The method is mainly used for controlling thickness noise, and when other pneumatic noise is controlled:
the motion formula of the plurality of the trailing edge winglets 2 is obtained by observing the motion state of the trailing edge feathers of the owl, and each trailing edge winglet 2 is enabled to move in a formula-specific manner according to the obtained motion formula, namely, the diamond-shaped amplifier 3 at the upper end or the lower end is extended by applying alternating voltage, the pull rod 4 and the gear 6 are driven to act, so that the trailing edge winglet 2 rotates by a proper angle, the direction of the air flow blowing through the helicopter blade 1 is finally changed, the flying state of the owl is simulated, and the air flow blowing through the rotor blade 1 is rectified.
By using the rotor wing 100 based on the owl flight muting principle in the first embodiment and the noise reduction method based on the owl flight muting principle in the second embodiment, the aerodynamic noise of the rotor wing can be controlled in a targeted manner by installing nine trailing edge winglets 2 at the trailing edge of the blade 1. When the helicopter is in a hovering state, the plane noise in a certain distance range from the sound source can be controlled, so that the sound pressure level is reduced by more than 3dB, and the sound propagation range is reduced.
Noise reduction at a single control point is shown in fig. 10 and noise reduction in the paddle plane is shown in fig. 12.
The principles and embodiments of the present invention have been described in detail in this application, the above examples are provided to facilitate understanding of the method of the present invention and its core ideas, and modifications may be made by those skilled in the art in light of the present teachings, both in the detailed description and the application scope. In summary, the present description should not be construed as limiting the invention.

Claims (5)

1.一种基于猫头鹰飞行静音原理的旋翼,其特征在于:包括桨叶,所述桨叶的尾部转动安装有多个后缘小翼,且多个所述后缘小翼沿所述桨叶的长度方向依次排列,所述后缘小翼的转轴与所述桨叶的长度方向平行,各所述后缘小翼与所述桨叶之间均设有转动机构,且各所述转动机构均与一控制器电连接,所述控制器用于控制所述转动机构动作,并使所述转动机构带动所述后缘小翼转动;1. A rotor based on the silent flying principle of an owl, characterized in that: it comprises a blade, a plurality of trailing edge winglets are rotatably mounted at the tail of the blade, and the plurality of trailing edge winglets are arranged in sequence along the length direction of the blade, a rotating shaft of the trailing edge winglet is parallel to the length direction of the blade, a rotating mechanism is arranged between each trailing edge winglet and the blade, and each rotating mechanism is electrically connected to a controller, the controller is used to control the movement of the rotating mechanism, and the rotating mechanism drives the trailing edge winglet to rotate; 所述后缘小翼在长度方向上的两侧各对应一个所述转动机构,且所述转动机构安装于所述桨叶上;The two sides of the trailing edge winglet in the length direction each correspond to a rotating mechanism, and the rotating mechanism is installed on the blade; 所述转动机构包括齿轮、两个菱形放大器、两个拉杆和两个齿条,一个所述菱形放大器对应连接一个所述拉杆的一端,所述拉杆的另一端与一所述齿条的一端连接,所述齿条的另一端向靠近所述后缘小翼的方向延伸,所述拉杆的移动方向与所述桨叶的长度方向垂直,所述齿轮安装于所述后缘小翼的根部,所述齿轮的外周分别与两个所述齿条啮合,两个所述齿条平行且相对设置,所述菱形放大器能够带动所述拉杆向靠近所述齿轮的方向移动,并使所述齿条向远离所述菱形放大器的方向移动,以带动所述齿轮旋转,所述齿轮能够带动所述后缘小翼转动。The rotating mechanism includes a gear, two diamond-shaped amplifiers, two pull rods and two racks. One of the diamond-shaped amplifiers is connected to one end of the pull rod, and the other end of the pull rod is connected to one end of the rack. The other end of the rack extends toward the direction close to the trailing edge winglet. The moving direction of the pull rod is perpendicular to the length direction of the blade. The gear is installed at the root of the trailing edge winglet. The outer periphery of the gear is respectively meshed with the two racks. The two racks are parallel and oppositely arranged. The diamond-shaped amplifier can drive the pull rod to move toward the direction close to the gear and move the rack away from the diamond-shaped amplifier to drive the gear to rotate. The gear can drive the trailing edge winglet to rotate. 2.根据权利要求1所述的基于猫头鹰飞行静音原理的旋翼,其特征在于:所述菱形放大器包括若干个压电堆和两个伸缩板,各所述压电堆均安装于两个所述伸缩板之间,且所述拉杆与其中一个所述伸缩板上远离所述压电堆的一侧连接,所述压电堆通电压时能够伸长,并带动所述伸缩板和所述拉杆移动。2. The rotor based on the owl's silent flight principle according to claim 1 is characterized in that: the diamond amplifier includes a plurality of piezoelectric stacks and two telescopic plates, each of the piezoelectric stacks is installed between the two telescopic plates, and the pull rod is connected to a side of one of the telescopic plates away from the piezoelectric stack, and the piezoelectric stack can extend when voltage is applied, and drive the telescopic plate and the pull rod to move. 3.根据权利要求1所述的基于猫头鹰飞行静音原理的旋翼,其特征在于:所述后缘小翼为九个,且各所述后缘小翼的偏转角度范围均为-10°~+10°。3. The rotor based on the owl flying silent principle according to claim 1 is characterized in that: there are nine trailing edge winglets, and the deflection angle range of each trailing edge winglet is -10° to +10°. 4.一种基于猫头鹰飞行静音原理的降噪方法,其特征在于:使用权利要求1-3中任一项所述的基于猫头鹰飞行静音原理的旋翼,包括以下步骤:4. A noise reduction method based on the silent flying principle of an owl, characterized in that: using the rotor based on the silent flying principle of an owl as described in any one of claims 1 to 3, comprising the following steps: S1:选定一观测点为计算点,求解将平面内噪声抵消为零所需要施加的力LrS1: Select an observation point as the calculation point and solve the force L r required to cancel the noise in the plane to zero; S2:将S1中计算得到的Lr值传输至控制器,通过所述控制器控制各所述转动机构动作,并使所述转动机构控制所述后缘小翼相较于所述桨叶的偏转角度,以使所述后缘小翼产生阻力小于两倍的Lr值,实现降噪。S2: The L r value calculated in S1 is transmitted to the controller, and the controller controls the actions of each of the rotating mechanisms, and the rotating mechanisms control the deflection angle of the trailing edge winglet compared to the blade, so that the drag generated by the trailing edge winglet is less than twice the L r value, thereby achieving noise reduction. 5.根据权利要求4所述的基于猫头鹰飞行静音原理的降噪方法,其特征在于:S1中,求解Lr的公式为5. The noise reduction method based on the owl flight silent principle according to claim 4 is characterized in that: in S1, the formula for solving L r is 其中,τ为延迟时间,c0为声速,Mr为声源与观测点连线的马赫数分量,M为声源处马赫数,p T为观测点处对应的厚度噪声声压值,r为声源到观测点的距离。Where τ is the delay time, c 0 is the speed of sound, Mr is the Mach number component of the line connecting the sound source and the observation point, M is the Mach number at the sound source, p T is the corresponding thickness noise sound pressure value at the observation point, and r is the distance from the sound source to the observation point.
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