Hypersonic dynamic jet flow test device and test method based on forced vibration

Through the hypersonic dynamic jet test device and method based on forced vibration, the aerodynamic characteristics of the aircraft under hypersonic and dynamic maneuvering conditions are simulated, and the problem of difficulty in studying the impact of non-constant spoiler in the prior art is solved, and the modeling accuracy and control effect of the maneuverability of the aircraft are improved.

CN119827098AActive Publication Date: 2025-04-15CHINA AERODYNAMICS RES AND DEV CENT ULTRA-HIGH SPEED AERODYNAMICS RES INST
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Patent Information

Application Number
CN202510181227.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-19
Publication Date
2025-04-15
Estimated Expiration
2045-02-19

AI Technical Summary

Technical Problem

The prior art is difficult to effectively study the aerodynamic characteristics and jet interference phenomena of aircraft under hypersonic speed and dynamic maneuvering conditions, especially in complex control environments under the influence of non-constant spoiler.

Method used

Using a hypersonic dynamic jet test device and method based on forced vibration, the aerodynamic characteristics of the aircraft under maneuverable flight and jet control are simulated by forced vibration, including installing a forced vibration device and nozzle on the aircraft model, and measuring aerodynamic and torque using balances and displacement sensors.

Benefits of technology

The study on the impact of the interference characteristics of the non-static spoiler lateral jet in the aircraft maneuvering flight was realized, and the modeling accuracy of direct force/aperture composite control was improved, and the aerodynamic/motion nonlinear characteristics were effectively predicted, and the maneuverability of the aircraft was improved.

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Abstract

The invention belongs to the technical field of hypersonic wind tunnel tests, and discloses a hypersonic dynamic jet flow test device and test method based on forced vibration. The test device comprises a forced vibration device located on the central axis of the aircraft model. The device further comprises a plurality of spray pipes fixed on the aircraft model, outlets of the spray pipes are in smooth transition with the surface of the aircraft model, and the rear ends of the spray pipes are externally connected with an air source through jet flow pipelines located in an inner cavity of the aircraft model. The test method comprises the steps of determining forced vibration simulation parameters; installing a hypersonic speed jet flow test device; a test device for testing hypersonic jet flow; performing a hypersonic dynamic jet flow test based on forced vibration; according to the test device and the test method, the aerodynamic characteristics of the aircraft under the simultaneous action of maneuvering flight and jet flow control are simulated through a forced vibration method, and the test result has engineering practical value for improving the maneuvering characteristics of the aircraft.
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Description

Technical Field

[0001] The present invention belongs to the technical field of hypersonic wind tunnel tests, and in particular relates to a hypersonic dynamic jet test device and a test method based on forced vibration. Background Art

[0002] High-precision, fast-response guidance and control technology based on direct force / aerodynamic composite control is the core technology for modern advanced aircraft to improve maneuverability and achieve precision guidance. Aerodynamic control mainly changes the flight attitude by changing the deflection angle of the aerodynamic control surface to generate pitch, yaw and roll torque. The aerodynamic torque generated by the aerodynamic control surface is related to the dynamic pressure, which is proportional to the atmospheric density and the square of the flight speed. In the case of high-altitude, low-density or low-speed flight, the efficiency of the control surface is significantly reduced and cannot meet the control requirements; direct force control is mainly obtained by generating a transverse jet from a micro-pulse engine, a gas generator or a main engine. On the one hand, it directly provides control force and torque, and on the other hand, when used in the atmosphere, it uses the additional control force and torque generated by the interference between the transverse jet and the free flow.

[0003] Direct force / aerodynamic compound control involves high maneuvering flight of aircraft under conditions of large angle of attack, large sideslip and large rudder deflection angle, which not only includes the mutual interference between the lateral jet and the external flow field, but also includes the nonlinear coupling between aerodynamics and motion, and the mutual influence between motion and the lateral jet. The rapid maneuvering of the aircraft will inevitably cause drastic changes in the surrounding airflow, which in turn triggers the lateral jet interference phenomenon caused by the influence of unsteady turbulence under dynamic conditions.

[0004] In the past, a large number of studies were conducted on static models. Now, dynamic aerodynamic characteristics have gradually received attention, especially the drastic changes in the airflow around the aircraft caused by rapid and high angle of attack maneuvers, which in turn trigger the lateral jet interference phenomenon under dynamic conditions due to the influence of unsteady turbulence. During the forced pitch oscillation of the interceptor missile model, obvious unsteady hysteresis may occur, and the jet interference amplification factor changes with the pitch angle period and deviates from the steady state value.

[0005] Currently, there is an urgent need to develop a hypersonic dynamic jet test device and test method based on forced vibration. Summary of the invention

[0006] One technical problem to be solved by the present invention is to provide a hypersonic dynamic jet test device based on forced vibration, and another technical problem to be solved by the present invention is to provide a hypersonic dynamic jet test method based on forced vibration.

[0007] The hypersonic dynamic jet test device and test method based on forced vibration of the present invention simulate the aerodynamic characteristics of an aircraft under the simultaneous effects of maneuvering flight and jet control by means of a forced vibration method.

[0008] The hypersonic dynamic jet test device based on forced vibration of the present invention comprises a forced vibration device located at the central axis of an aircraft model; and further comprises a plurality of nozzles fixed on the aircraft model, wherein the outlets of the nozzles smoothly transition with the surface of the aircraft model, and the rear ends of the nozzles are connected to an external gas source through a jet pipe located in the inner cavity of the aircraft model; The forced vibration device comprises a front cone section, a balance, a yaw frame and a tail strut which are sequentially connected from front to back; a cross elastic hinge and a yaw shaft are sequentially fixed in the yaw frame from front to back, a joint bearing is mounted on the yaw shaft, and the yaw shaft and the joint bearing are fixed in the cantilever groove; an internal transmission shaft and a rear chamber are arranged in the tail strut, the front end of the internal transmission shaft is connected to the yaw shaft, and the rear end of the internal transmission shaft is connected to the driving shaft of the driving motor fixed in the rear chamber; The inner cavity of the aircraft model is provided with a conical model bushing matching the front cone section of the forced vibration device, a plurality of counterweights are fixed on the inner wall of the aircraft model, and the model center of mass of the aircraft model coincides with the center of the cross elastic hinge.

[0009] Furthermore, the balance adopts a four-column beam measuring element for measuring the normal force, lateral force, pitch moment, yaw moment and roll moment of the aircraft model.

[0010] Furthermore, the design and production requirements of the aircraft model are that, under the premise of ensuring the strength and rigidity of the aircraft model, the mass and moment of inertia of the aircraft model are gradually reduced to reduce the inertia force and inertia moment of the aircraft model and improve the natural frequency and measurement accuracy of the hypersonic dynamic jet test device.

[0011] The hypersonic dynamic jet test method based on forced vibration of the present invention comprises the following steps: S10. Determine forced vibration simulation parameters; The simulation parameters are the aerodynamic pitch damping moment of the aircraft model; the aerodynamic pitch damping moment is calculated by the applied torque amplitude, the maximum pitch angular displacement, the phase angle between the applied torque and the vibration angular displacement, the angular velocity of the maximum pitch motion and the mechanical damping of the hypersonic jet test device; S20. Install the hypersonic jet test device; First, fix the tail strut on the middle bracket of the hypersonic wind tunnel; second, install the drive motor in the rear chamber of the tail strut; third, connect the drive shaft of the drive motor to the internal transmission shaft; finally, fix the aircraft model on the front cone section from front to back; S30. Test the hypersonic jet test device; The hypersonic jet test device is started, and the driving shaft of the driving motor sequentially drives the internal transmission shaft and the yaw shaft. The yaw shaft drives the joint bearing to present a cam motion, converting the rotational motion of the driving shaft of the driving motor into the pitch motion of the balance. Under the constraint of the yaw frame, the aircraft model is made to perform a pitch motion around the center of the cross elastic hinge. During the test, if it is found that the pitching motion of the aircraft model around the center of the cross elastic hinge has deviation, the hypersonic jet test device is removed, the model bushing and the counterweight are adjusted, and the test is repeated until the pitching motion of the aircraft model around the center of the cross elastic hinge is achieved; S40. Conduct hypersonic dynamic jet test based on forced vibration; First, the hypersonic jet test device was started to achieve the pitch motion of the aircraft model around the center of the cross elastic hinge; Secondly, open the gas source, and let the jet gas that meets the jet requirements enter the jet pipe through the jet air inlet, and then spray it out through the nozzle outlet; Finally, the hypersonic wind tunnel is started, and after the hypersonic flow field is stabilized, the displacement sensor measures the vibration angular displacement of the aircraft model, and the balance measures the aerodynamic force and moment of the aircraft model; S50. Calculate aerodynamic pitch damping moment; Calculate the aerodynamic pitch damping moment and evaluate the simulation results.

[0012] Furthermore, the calculation process of the aerodynamic pitch damping moment of S10 is as follows: The aircraft model performs simple harmonic vibration with fixed frequency and amplitude in the pitch direction. The motion differential equation of simple harmonic vibration is: ; in, is the inertia moment of the aircraft model during pitch motion, , and are the angular displacement, angular velocity and angular acceleration of the pitch motion respectively, is the mechanical damping torque of the hypersonic jet test device, is the mechanical damping of the hypersonic jet test device, is the aerodynamic pitch damping moment of the hypersonic jet test device, is the aerodynamic pitch damping moment derivative of the hypersonic jet test device, is the elastic restoring moment of the hypersonic jet test device, is the aerodynamic pitch restoring moment of the hypersonic jet test device, is the elastic hinge constant of the hypersonic jet test device, is the aerodynamic pitch recovery damping moment of the hypersonic jet test device, is an imaginary unit, is the angular velocity of the maximum pitch motion, For time, is the external forced torque; Equation (1) is a linear, second-order non-homogeneous differential equation with constant coefficients. The solution of equation (1) consists of two parts, one is the general solution of the homogeneous form corresponding to equation (1), and the other is the special solution of the non-homogeneous equation, namely: ; In the formula, is the maximum pitch angle displacement, is the phase angle between the applied torque and the vibration angular displacement; Substituting equation (2) into equation (1), we obtain: ; in, is the amplitude of the applied torque; Since the imaginary parts at both ends of equation (3) are equal, the aerodynamic pitch damping moment derivative of the aircraft model is obtained as: ; From equation (4), it can be seen that by measuring the amplitude of the applied torque , Maximum pitch angle displacement , the phase angle between the applied torque and the vibration angular displacement , the angular velocity of the maximum pitch motion Mechanical damping of hypersonic jet test equipment , the aerodynamic pitch damping moment derivative can be calculated .

[0013] The hypersonic dynamic jet test device and test method based on forced vibration of the present invention, based on the research on the static steady lateral jet interference characteristics of the aircraft, carried out the research on the influence of the unsteady turbulent lateral jet interference characteristics of the aircraft maneuvering flight, and obtained the unsteady coupling characteristics of aerodynamic / motion / lateral jet in the direct force / aerodynamic composite control process. The test results have engineering practical value for improving the modeling accuracy of direct force / aerodynamic composite control, effectively predicting the nonlinear modeling characteristics of aerodynamic / motion, and reasonably designing the flight control law to achieve the effective allocation of the control surface and the lateral jet, thereby improving the maneuverability of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the installation of the hypersonic dynamic jet test device based on forced vibration of the present invention; Figure 2 It is a schematic structural diagram of a forced vibration device in a hypersonic dynamic jet test device based on forced vibration of the present invention; Figure 3 It is a schematic diagram of the aircraft model in the hypersonic dynamic jet test device based on forced vibration and the adjustment principle of the test device.

[0015] In the figure: 1. forced vibration device; 2. aircraft model; 3. nozzle; 4. jet pipe; 101. Balance; 102. Swing frame; 103. Cross elastic hinge; 104. Swing axis; 105. Internal transmission shaft; 106. Tail support rod; 107. Front cone section; 108. Rear chamber; 201. Model bushing; 202. Model center of mass; 203. Counterweight. DETAILED DESCRIPTION

[0016] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0017] Example: Figure 1~Figure 3 As shown, the hypersonic dynamic jet test device based on forced vibration of this embodiment includes a forced vibration device 1 located at the central axis of the aircraft model 2; and also includes a plurality of nozzles 3 fixed on the aircraft model 2, the outlet of the nozzle 3 smoothly transitions with the surface of the aircraft model 2, and the rear end of the nozzle 3 is connected to an external air source through a jet pipe 4 located in the inner cavity of the aircraft model 2; The forced vibration device 1 comprises a front cone section 107, a balance 101, a yaw frame 102 and a tail support rod 106 which are sequentially connected from front to back; a cross elastic hinge 103 and a yaw shaft 104 are sequentially fixed in the yaw frame 102 from front to back, a joint bearing is mounted on the yaw shaft 104, and the yaw shaft 104 and the joint bearing are fixed in the cantilever groove; an internal transmission shaft 105 and a rear chamber 108 are arranged in the tail support rod 106, the front end of the internal transmission shaft 105 is connected to the yaw shaft 104, and the rear end of the internal transmission shaft 105 is connected to the driving shaft of the driving motor fixed in the rear chamber 108; The inner cavity of the aircraft model 2 is provided with a conical model bushing 201 matching the front cone section 107 of the forced vibration device 1 , a plurality of counterweight blocks 203 are fixed to the inner wall of the aircraft model 2 , and the model center of mass 202 of the aircraft model 2 coincides with the center of the cross elastic hinge 103 .

[0018] Furthermore, the balance 101 adopts a four-column beam measuring element for measuring the normal force, lateral force, pitch moment, yaw moment and roll moment of the aircraft model 2 .

[0019] Furthermore, the design and production requirements of the aircraft model 2 are that, under the premise of ensuring the strength and rigidity of the aircraft model 2, the mass and moment of inertia of the aircraft model 2 are gradually reduced, so as to reduce the inertia force and moment of inertia of the aircraft model 2 and improve the natural frequency and measurement accuracy of the hypersonic dynamic jet test device.

[0020] The hypersonic dynamic jet test method based on forced vibration of this embodiment includes the following steps: S10. Determine forced vibration simulation parameters; The simulation parameters are the aerodynamic pitch damping moment of the aircraft model 2; the aerodynamic pitch damping moment is calculated by the applied torque amplitude, the maximum pitch angular displacement, the phase angle between the applied torque and the vibration angular displacement, the angular velocity of the maximum pitch motion and the mechanical damping of the hypersonic jet test device; S20. Install the hypersonic jet test device; First, the tail strut 106 is fixed to the middle bracket of the hypersonic wind tunnel; second, the drive motor is installed in the rear chamber 108 of the tail strut 106; third, the drive shaft of the drive motor is connected to the internal transmission shaft 105; finally, the aircraft model 2 is fixed to the front cone section 107 from front to back; S30. Test the hypersonic jet test device; The hypersonic jet test device is started, and the driving shaft of the driving motor sequentially drives the internal transmission shaft 105 and the yaw shaft 104. The yaw shaft 104 drives the joint bearing to present a cam motion, and converts the rotational motion of the driving shaft of the driving motor into a pitch motion of the balance 101. Under the constraint of the yaw frame 102, the aircraft model 2 is made to perform a pitch motion around the center of the cross elastic hinge 103; During the test, if it is found that the pitching motion of the aircraft model 2 around the center of the cross elastic hinge 103 has deviation, the hypersonic jet test device is removed, the model bushing 201 and the counterweight block 203 are adjusted, and the test is repeated until the pitching motion of the aircraft model 2 around the center of the cross elastic hinge 103 is achieved; S40. Conduct hypersonic dynamic jet test based on forced vibration; First, the hypersonic jet test device is started to achieve a pitching motion of the aircraft model 2 around the center of the cross elastic hinge 103; Secondly, open the gas source, and let the jet gas that meets the jet requirements enter the jet pipe 4 through the jet air inlet, and then spray out through the outlet of the nozzle 3; Finally, the hypersonic wind tunnel is started, and after the hypersonic flow field is stabilized, the displacement sensor measures the vibration angular displacement of the aircraft model 2, and the balance 101 measures the aerodynamic force and moment of the aircraft model 2; S50. Calculate aerodynamic pitch damping moment; Calculate the aerodynamic pitch damping moment and evaluate the simulation results.

[0021] Furthermore, the calculation process of the aerodynamic pitch damping moment of S10 is as follows: Aircraft model 2 performs simple harmonic vibration with fixed frequency and amplitude in the pitch direction. The motion differential equation of simple harmonic vibration is: ; in, is the inertia moment of aircraft model 2 during pitch motion, , and are the angular displacement, angular velocity and angular acceleration of the pitch motion respectively, is the mechanical damping torque of the hypersonic jet test device, is the mechanical damping of the hypersonic jet test device, is the aerodynamic pitch damping moment of the hypersonic jet test device, is the aerodynamic pitch damping moment derivative of the hypersonic jet test device, is the elastic restoring moment of the hypersonic jet test device, is the aerodynamic pitch restoring moment of the hypersonic jet test device, is the elastic hinge constant of the hypersonic jet test device, is the aerodynamic pitch recovery damping moment of the hypersonic jet test device, is an imaginary unit, is the angular velocity of the maximum pitch motion, For time, is the external forced torque; Equation (1) is a linear, second-order non-homogeneous differential equation with constant coefficients. The solution of equation (1) consists of two parts, one is the general solution of the homogeneous form corresponding to equation (1), and the other is the special solution of the non-homogeneous equation, namely: ; In the formula, is the maximum pitch angle displacement, is the phase angle between the applied torque and the vibration angular displacement; Substituting equation (2) into equation (1), we obtain: ; in, is the amplitude of the applied torque; Since the imaginary parts at both ends of equation (3) are equal, the aerodynamic pitch damping moment derivative of aircraft model 2 is obtained as: ; From equation (4), it can be seen that by measuring the amplitude of the applied torque , Maximum pitch angle displacement , the phase angle between the applied torque and the vibration angular displacement , the angular velocity of the maximum pitch motion Mechanical damping of hypersonic jet test equipment , the aerodynamic pitch damping moment derivative can be calculated .

[0022] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and the embodiments, and can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional improvements and modifications can be easily realized without departing from the principles of the present invention. Therefore, without departing from the general concept defined by the claims and equivalent scope, the present invention is not limited to the specific details and the illustrations shown and described here.

Claims

1. A hypersonic dynamic jet test device based on forced vibration, characterized in that: The hypersonic dynamic jet test device comprises a forced vibration device (1) located on the central axis of an aircraft model (2); and also comprises a plurality of nozzles (3) fixed on the aircraft model (2), wherein the outlet of the nozzle (3) smoothly transitions with the surface of the aircraft model (2), and the rear end of the nozzle (3) is connected to an external air source through a jet pipe (4) located in the inner cavity of the aircraft model (2); The forced vibration device (1) comprises a front cone section (107), a balance (101), a yaw frame (102) and a tail support rod (106) which are sequentially connected from front to back; a cross elastic hinge (103) and a yaw shaft (104) are sequentially fixed in the yaw frame (102) from front to back, a joint bearing is mounted on the yaw shaft (104), and the yaw shaft (104) and the joint bearing are fixed in a cantilever groove; an internal transmission shaft (105) and a rear chamber (108) are arranged in the tail support rod (106), the front end of the internal transmission shaft (105) is connected to the yaw shaft (104), and the rear end of the internal transmission shaft (105) is connected to the driving shaft of a driving motor fixed in the rear chamber (108); The inner cavity of the aircraft model (2) is provided with a conical model bushing (201) matching the front cone section (107) of the forced vibration device (1), a plurality of counterweights (203) are fixed to the inner wall of the aircraft model (2), and the model center of mass (202) of the aircraft model (2) coincides with the center of the cross elastic hinge (103).

2. The hypersonic dynamic jet test device based on forced vibration according to claim 1, characterized in that: The balance (101) adopts a four-column beam measuring element and is used to measure the normal force, lateral force, pitch moment, yaw moment and roll moment of the aircraft model (2).

3. The hypersonic dynamic jet test device based on forced vibration according to claim 1, characterized in that: The design and production requirements of the aircraft model (2) are that, under the premise of ensuring the strength and rigidity of the aircraft model (2), the mass and moment of inertia of the aircraft model (2) are gradually reduced, so as to reduce the inertial force and moment of inertia of the aircraft model (2) and improve the natural frequency and measurement accuracy of the hypersonic dynamic jet test device.

4. A hypersonic dynamic jet test method based on forced vibration, which is used in a hypersonic dynamic jet test device based on forced vibration as described in any one of claims 1 to 3, characterized in that: The test device installation method comprises the following steps: S10. Determine forced vibration simulation parameters; The simulation parameters are the aerodynamic pitch damping moment of the aircraft model (2); the aerodynamic pitch damping moment is calculated by the applied torque amplitude, the maximum pitch angular displacement, the phase angle between the applied torque and the vibration angular displacement, the angular velocity of the maximum pitch motion and the mechanical damping of the hypersonic jet test device; S20. Install the hypersonic jet test device; First, the tail strut (106) is fixed on the middle bracket of the hypersonic wind tunnel; second, the drive motor is installed in the rear chamber (108) of the tail strut (106); third, the drive shaft of the drive motor is connected to the internal transmission shaft (105); finally, the aircraft model (2) is fixed on the front cone section (107) from front to back; S30. Test the hypersonic jet test device; The hypersonic jet test device is started, and the driving shaft of the driving motor sequentially drives the internal transmission shaft (105) and the yaw shaft (104), and the yaw shaft (104) drives the joint bearing to present a cam motion, converting the rotational motion of the driving shaft of the driving motor into a pitch motion of the balance (101), and under the constraint of the yaw frame (102), the aircraft model (2) is made to perform a pitch motion around the center of the cross elastic hinge (103); During the test, if it is found that the pitching motion of the aircraft model (2) around the center of the cross elastic hinge (103) has deviation, the hypersonic jet test device is removed, the model bushing (201) and the counterweight (203) are adjusted, and the test is repeated until the pitching motion of the aircraft model (2) around the center of the cross elastic hinge (103) is achieved; S40. Conduct hypersonic dynamic jet test based on forced vibration; First, the hypersonic jet test device is started to achieve a pitching motion of the aircraft model (2) around the center of the cross elastic hinge (103); Secondly, the gas source is turned on, and the jet gas that meets the jet requirements is introduced into the jet pipe (4) through the jet air inlet, and then ejected through the outlet of the nozzle (3); Finally, the hypersonic wind tunnel is started, and after the hypersonic flow field is stabilized, the displacement sensor measures the vibration angular displacement of the aircraft model (2), and the balance (101) measures the aerodynamic force and moment of the aircraft model (2); S50. Calculate aerodynamic pitch damping moment; Calculate the aerodynamic pitch damping moment and evaluate the simulation results.

5. The hypersonic dynamic jet test method based on forced vibration according to claim 4 is characterized in that: The calculation process of the aerodynamic pitch damping moment of the S10 is as follows: The aircraft model (2) performs simple harmonic vibration with fixed frequency and amplitude in the pitch direction. The motion differential equation of simple harmonic vibration is: ; in, is the inertia moment of the aircraft model (2) during pitch motion, , and are the angular displacement, angular velocity and angular acceleration of the pitch motion respectively, is the mechanical damping torque of the hypersonic jet test device, is the mechanical damping of the hypersonic jet test device, is the aerodynamic pitch damping moment of the hypersonic jet test device, is the aerodynamic pitch damping moment derivative of the hypersonic jet test device, is the elastic restoring moment of the hypersonic jet test device, is the aerodynamic pitch restoring moment of the hypersonic jet test device, is the elastic hinge constant of the hypersonic jet test device, is the aerodynamic pitch recovery damping moment of the hypersonic jet test device, is an imaginary unit, is the angular velocity of the maximum pitch motion, For time, is the external forced torque; Equation (1) is a linear, second-order non-homogeneous differential equation with constant coefficients. The solution of equation (1) consists of two parts, one is the general solution of the homogeneous form corresponding to equation (1), and the other is the special solution of the non-homogeneous equation, namely: ; In the formula, is the maximum pitch angle displacement, is the phase angle between the applied torque and the vibration angular displacement; Substituting equation (2) into equation (1), we obtain: ; in, is the amplitude of the applied torque; Since the imaginary parts at both ends of equation (3) are equal, the aerodynamic pitch damping moment derivative of the aircraft model (2) is obtained as: ; From equation (4), it can be seen that by measuring the amplitude of the applied torque , Maximum pitch angle displacement , the phase angle between the applied torque and the vibration angular displacement , the angular velocity of the maximum pitch motion Mechanical damping of hypersonic jet test equipment , the aerodynamic pitch damping moment derivative can be calculated .

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