Analysis of driving moment characteristic of multi-section wing based on the centroid self- trim compensation morphing

doi:10.21203/rs.3.rs-3982826/v1

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Analysis of driving moment characteristic of multi-section wing based on the centroid self- trim compensation morphing

https://doi.org/10.21203/rs.3.rs-3982826/v1

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Based on the research of sweep and reverse angle deformation laws of the elbow and hand wing sections during the flight of large birds, a multi-section variable-sweep wing structure adapted to large-size UAVs is proposed in this paper. The feasibility of the centroid self-trim compensation morphing process by using collaborative deformation of inner and outer sections is ex-plored. Firstly, a calculation and evaluation method of the driving moment required for morphing based on the vortex lattice method is established. Then, five preselection models with different span ratios of the inner and outer sections of the multi-section variable sweep-wing UAV are constructed. Finally, from the aspects of static stability margin, changes in aerodynamic characteristics, and performance requirements of the drivers during the collaborative morphing process, the influence of multi-parameters on the comprehensive performance of the multi-section morphing wing is analyzed, and the reasonable design range of the span ratio of the inner and outer wing sections of the research object is given. The results show that the multi-section morphing wing proposed in this paper has a significant advantage in solving the problems of drastic changes in aerodynamic, dynamic, and operational characteristics caused by large-size wing morphing. The maximum output power requirement of the drivers in the symmetrical self-trim compensation morphing process can be reduced by increasing the ratio of the inner wing section to the preselected model, and the efficiency of the driver can be improved. The preselection model of the multi-section variable swept-wing UAV with optimal driving moment performance is determined by the comprehensive analysis results, and the corresponding span ratio of the inner and outer wing sections in the morphing sections is about 64.03% and 35.97%, respectively.

Physical sciences/Engineering/Aerospace engineering

Biological sciences/Biophysics

Physical sciences/Engineering

Multi-section morphing wing

Centroid self-trim compensation morphing

Vortex lattice method

Static stability analysis

Aerodynamic characteristic analysis

Driving moment

A morphing wing can improve the aerodynamic performance by changing the local or overall shape, thus improving the mission flexibility and the overall performance within the flight envelope of the aircraft^1–5. However, with the increase of deformation scale and task complexity, complex changes of aerodynamic and dynamic characteristics during the wing morphing process bring new challenges to the design of control systems and flight simulation. Using biological anatomy, researchers have found that birds constantly change wing shape and area by overlapping their wing feathers in response to different tasks and conditions⁶. Through the study of the changes in wing shape and the corresponding glide speed in flight, it’s found that birds change the plane shape of wings by moving shoulder and elbow joints forward and wrist joints backward. Birds spread their wings at low speeds and turn maneuvers and fold them at high speeds. In addition, birds also increase the curvature of the airfoil and the reverse angle of the airfoil during takeoff and landing by the rotation of wings along the longitudinal axis of the joint, to improve the lift coefficient, stall characteristics, and roll stability⁷. It can be found that when the hand wing section is swept back, the sweep angle of the elbow wing section changes in the opposite direction, and the reverse angle of the hand wing section and elbow wing section also shows an opposite trend⁸. Therefore, through reasonable airfoil selection, shape design, weight distribution, and centroid configuration of the multi-section wing, the wing centroid and aerodynamic center can be fixed or moved according to a certain law during the wing morphing process.

Based on the results of bionics research, a multi-section sweep-wing structure adapted to large-size aircraft has been proposed. Through the asymmetric collaborative morphing of the inner and outer wing sections, the self-trim compensation of the centroid in the morphing process is realized, and the drastic changes in aerodynamic, dynamics, and operating stability characteristics caused by the large-scale movement of the centroid and the aerodynamic center are effectively solved. At present, the research on multi-section morphing wings mainly focuses on lightweight thin-film wings of bird size. Due to the small wingspan, the problem of the centroid and aerodynamic center movement caused by configuration changes is not prominent. The influence on stability and maneuverability due to the movement of the centroid and aerodynamic center and the change of moment of inertia during the morphing process is not considered in the design. A great deal of relevant research has focuses on intelligent morphing structure design and aerodynamic characteristics analysis^9–11.

In terms of structural design, Luca et al. have designed a bionic folding wing by studying the deformation mechanism and inspired by the feather structure and deformation rule of bird wings, which can realize feather-like folding and deformation in a plane and roll control by shrinking a unilateral wing¹¹. Bharti et al. have designed a morphing scheme of wingspan and sweep angle by using scissor-like mechanism¹². Marks et al. have designed a set of four-link mechanism to simulate the skeletal structure of bird wings. Parameters such as sweep angle, wing area, and wingspan are changed by a deformable pattern similar to that of feathering in birds. The variable camber airfoil is used instead of the traditional cracked control surface to realize rolling maneuver and landing flight control¹³. Mattioni et al. have proposed a variable sweep angle wing based on a multi-stable structure, and analyzed the structure and motion characteristics¹⁴. Neal et al. have use pneumatic drivers to achieve changes in wingspan, sweep angle and torsion angle, and realize the sweep angle change through an electro-mechanical pilot screw actuator¹⁵. Wang et al. have proposed a morphing wing structure with two joints by studying the external morphology, internal muscle, bone structure and flight posture characteristics of pigeons, which realized a good simulation of bird wings in structure and function^16,17. Muharmmad et al. have designed a bionic foldable wing with wings cut from an epoxy resin web. The wing surface is made of polypropylene film, and the wings are connected by hinges so that the entire wing can be bent in a single plane⁹. Stowers et al. have designed a foldable wing by studying the wing morphology of birds and bats, which can expand on a plane by centrifugal acceleration¹⁰.

In terms of aerodynamic characteristics analysis, Grant et al have designed a multi-joint morphing wing with imitation seagull-wing, in which the inner and outer sections of the left and right wings can independently change the sweep angle. The results of aerodynamic analysis show that the symmetrical change of sweep angle can significantly reduce the turning radius, and the asymmetric change of sweep angle can improve the crosswind resistance of the aircraft¹⁸. Hartloper and Wolf et al. have studied the aerodynamic performance of a gull wing configuration^19,20. Verstraete et al. have used the unsteady vortex lattice method to establish a numerical calculation model simulating the nonlinear and unsteady aerodynamic forces in the morphing process of the seagull wings²¹. Obradovic et al. have proposed a numerical calculation method for dynamic load of morphing wing based on the vortex lattice method, and calculated the aerodynamic load and energy demand in the morphing process of the seagull wings²². Moller et al. have studied the relationship between wing morphology and take-off ability and agility of the European mynas²³. Langley Research Center (LRC) have established four bionic wing models, namely seagull wing, ripple wing, super elliptical wing and shark wing. Under the condition of the same aspect ratio and wing area, the improvement degree of the aerodynamic performance has been analyzed through the wind tunnel tests^24,25. Under the conditions of different deformation rates, angle of attack and Mach number, Han et al. have analyzed the unsteady aerodynamic characteristics of the aircraft in the process of symmetrical change of the outer wing sweep angle by the numerical simulation²⁶. Luca et al. have studied the aerodynamic characteristics of bionic wings composed of artificial feathers in different configurations through theoretical analysis and wind tunnel tests, and discussed the possibility of rolling maneuver control using asymmetric folding of sweep angle of the outer wing section¹¹. The research team of the Air Force Engineering University have designed the bionic wings of the seagull with a convex, curved and complete configuration respectively by referring to the optimal cross-section airfoil of the seagull wing, and carried out numerical calculation and wind tunnel test²⁷. Based on biological anatomy, the research team of Jilin University have analyzed the wing airfoil of the house swallow, the seagull and the carrier pigeon, etc. Through numerical calculation and wind tunnel test, the performance advantages of bionic airfoil in lift, lift-drag ratio and stalling angle of attack have been verified^28–32. Zhan et al. have studied the influence of asymmetric changes in wing curvature and sweep angle on longitudinal and transverse aerodynamic forces, and explored the feasibility of rolling maneuver control using asymmetric wing morphing^33,34.

Moreover, relevant studies only focus on aircraft with specific wingspan of the inner and outer wing section. There is a lack of research on the application of multi-section morphing wings in high aspect ratio combat UAVs. There are also few researches on the high aspect ratio wing using the reverse collaborative deformation of inner and outer wing sections to achieve the centroid self-trim morphing. In addition, the multi-section variable-sweep wing needs to overcome the aerodynamic load to achieve real-time adaptive wing morphing, which requires the driver to have high output capacity and fast response characteristics. Because the energy used for wing morphing is limited, the drivers should also have low energy consumption characteristics to ensure that the mechanism has a sufficient number of deformations during flight³⁵. Therefore, how to reduce the performance requirements of multi-section variable-sweep wing aircraft and improve driver efficiency through appropriate design of the span ratio of the inner and outer wing sections is also very important for reducing weight and energy consumption.

In this research, based on the aerodynamic calculation method of the vortex lattice method, a rapid calculation method of the moment required by the wing morphing to overcome the aerodynamic force is established, and the multi-parameter influence analysis is carried out. The influence of the span ratio of inner and outer wing sections on the performance requirements of the driver is studied. According to the difference in the initial configuration of the UAV, the changes of the aerodynamic moment required in the symmetrical wing morphing process and the rolling maneuvers caused by the asymmetric wing morphing are compared and analyzed.

The vortex lattice method provides a medium-precision method for aerodynamic calculation at low speed and medium-high Reynolds number. It has the characteristics of simple, fast, and high computational efficiency, and is especially suitable for the early design of bionic multi-section variable-sweep wing UAVs with high aspect ratios³⁶. In the vortex lattice method, the lift surface is arranged on the middle arc of the wing, then the vortex cell is divided on the lift surface, and the horseshoe vortex and control point are arranged on each vortex cell. The strength of the element horseshoe vortex can be solved by the boundary condition that the normal velocity at the control point is zero. The specific implementation steps are as follows:

The wing is divided into j columns along the spanwise side and i rows along the chordal side, that is, the lift surface is divided into several quadrilateral grids. The corresponding horseshoe vortices with the intensity of Γ_ij are arranged on the grid of each element.
Each attached vortex overlaps with the 1/4 string of the corresponding grid element, and the two free vortices extend from the two ends of the 1/4 string along the X-axis in the direction of the airflow to infinity downstream.
The control points are arranged on the 3/4 string midpoint of the corresponding grid cell. Based on the Biot-Savart law, the induced velocities of all the horseshoe vortices at the control points are calculated.
According to the boundary conditions, a set of equations with the intensity of the horseshoe vortex in each element is obtained. Then the corresponding aerodynamic coefficient of each unit can be obtained by solving the intensity of each unit.

After calculating the vorticity of each element, the aerodynamic force on the element grid can be expressed as follows:

1)Lift on the cell grid

$$\Delta {{\varvec{L}}_{ij}}=\left| {\rho {\varvec{V}} \times {\varvec{\Gamma}_{ij}}{l_{ij}}} \right|=\rho V{\Gamma _{ij}}\Delta {y_{ij}}$$

Where, l_j is the length of the attached vortex, and ${y_{ij}}$ is the span length of the cell grid. Then the lift coefficient on the cell grid can be expressed as:

$$\Delta {C_{L,}}_{{ij}}=\frac{{2{\Gamma _{ij}}}}{{V\Delta {x_{ij}}}}$$

Where, ${x_{ij}}$ is the chord length of the cell grid.

2)Drag on the cell grid

The induced resistance can be obtained by Eq. (3):

$$\Delta {{\varvec{D}}_{ind,j}}=\rho {w_{ind,j}}{\Gamma _j}\Delta {x_j}$$

Where, ${w_{ind,j}}$ represents the induced velocity of unit j, which is induced by two semi-infinite vortex lines. Since the vortex lattice method cannot calculate the viscous drag of the wing, the DATCOM empirical formula is used to modify it³⁷.Viscous resistance includes the frictional resistance and the differential pressure resistance, which can be calculated for the wing as follows:

$${C_{{D_{0w}}}}={R_{WF}}{R_{LS}}{C_{fw}}\left[ {1+0.6/{{\left( {x/c} \right)}_m}\left( {t/c} \right)+100{{\left( {t/c} \right)}^4}} \right]{S_{wetW}}/S$$

Where, R_WF is the wing-body interference factor, which is related to the airframe Reynolds number and Mach number. R_LS is a lifting surface correction factor, which is related to wing sweep angle and Mach number. C_fw is the friction resistance of the flat surface, which is related to the surface roughness of the wing, the turning point of the layer flow turbulence, and the Reynolds number. (x/c)_m is the chord position of the maximum thickness of the airfoil; (t/c) is the maximum thickness of the airfoil; S_wetW is the wetted area of the wing. The object of study in this paper is the wing with a high aspect ratio, and the viscous drag coefficient is assumed to be the same on each element.

After the lift coefficient and drag coefficient of each element are obtained, the moment required to overcome the aerodynamic force in the morphing process can be expressed as the sum of all elements. The vortex cell is assumed to be a plane, and the aerodynamic force in each time step is assumed to be constant, which can be expressed as follows:

$${T_{Wing}}=\sum\limits_{{{N_{TE}}}}^{{}} {\int_{0}^{1} {(\Delta {{\varvec{L}}_{ij}}+\Delta {{\varvec{D}}_{ij}})} } \cdot {{\varvec{b}}_{ij}}d\tau \approx \sum\limits_{{{N_{Wing}}}} {\sum\limits_{{t=0}}^{{t=T}} {\Delta {{\varvec{F}}_{ij}} \cdot {{\varvec{b}}_{ij}}} }$$

Where, τ is the dimensionless time constant; ΔF_ij represents the tangential projection of the aerodynamic force on each vortex cell; b_ij represents the movement of the control point on the aerodynamic plane in unit time. Figure 1 is the schematic diagram of the aerodynamic force on the vortex cell. Figure 2 is the schematic diagram of the aerodynamic force on the vortex cell in the process of sweep angle change, where the upper corner mark * represents the projection of the aerodynamic force on the plane of the grid cell.

Although morphing wing technology can bring many improvements in flight performance, combat UAVs have a high aspect ratio and large wing mass, and the centroid and aerodynamic center have a larger range of movement during the change of wing configuration, which is difficult to compensate by aerodynamic compensation and fuel or slider movement^38–40. It has a great impact on the stability and control system design of combat UAVs, which limits the application of morphing wings in high aspect ratio UAVs to a certain extent. Aircraft is a successful application of bionics. Based on bionics research, the concept of a multi-section morphing wing provides an effective way to solve the problem of centroid movement during the deformation of high aspect ratio wings.

Based on the results of bionics research, this paper presents a multi-section variable-sweep wing design scheme of reverse collaborative sweep angle change between the inner and outer wing sections. The design scheme not only improves the aerodynamic performance of the UAVs but also realizes the centroid self-trim compensation of the wing morphing process, as shown in Fig. 3. The high aspect ratio multi-section morphing wing is located in the middle of the fuselage and can be divided into three parts: weapon wing section, inner wing section, and outer wing section. The lower part of the weapon section is equipped with a weapon pylon. Because of the large mass of the weapon section, the change in its sweep angle has a great influence on the stability of the UAV, the sweep angle of the weapon section remains fixed during the wing morphing process. The centroid self-trim compensation of UAV in the process of wing configuration change is realized through the cooperative morphing of the inner and outer wing sections. The fuselage has a pair of V-shaped trapezoid tail fins with a drooping tail. The lower part of the fuselage has a retractable front three-point landing gear, and the external weapon mounts and main landing gear are distributed on both sides of the fuselage's centroid.

The design parameters of the multi-section variable-sweep wing are shown in Table 1.

Table 1

Design parameters of multi-section variable-sweep wing
Design parameters	Value
wing area	32.15m²
maximum wingspan	20m
wingspan of the deformable section	8.09m
root-tip ratio of the deformable section	1
root chord	1.79m
tip chord	1.59m
wingspan of the weapon section	1.91m
sweep angle of the weapon section	6.1°

For the multi-section morphing wing, if the wing span ratio of the inner section is too large, the aerodynamic performance benefit brought by the change of sweep angle will be reduced. However, if the wing span ratio of the inner section is too small, the aerodynamic center will move in a large range during the collaborative sweep angle change of the inner and outer wing sections and the stability and maneuverability of the UAVs will be significantly changed. It can be seen that it is the primary problem to determine the reasonable ratio of the span length between the inner and outer wing sections in the design of a multi-section variable-sweep wing. This plays a decisive role in reducing the influence of aerodynamic center shift and moment of inertia change in the process of wing morphing, to balance the contradiction of the morphing UAVs between aerodynamic performance improvement, stability, and maneuverability. According to the overall layout characteristics and flight conditions of the UAV, the number of the transverse stringers and longitudinal fin of the multi-section variable-sweep wing is determined to be 4 and 20, as shown in Fig. 4. According to the structure distribution law of the variable wing, and considering the load capacity and space required for wing morphing, the preselection models are established by selecting the different wingspan ratios of the inner and outer wing sections, which are named M1, M2, M3, M4, and M5 respectively. The wingspan and mass of the inner and outer wing sections of each preselected model are shown in Table 2.

Table 2

Parameters of the inner and outer wing sections of the preselected models
Model	Inner section		Outer section
Model	Wingspan/m	Mass/kg	Wingspan/m	Mass/kg
M1	3.72	132.21	4.37	89.99
M2	4.29	154.66	3.80	67.55
M3	4.73	158.43	3.39	63.77
M4	5.18	168.88	2.91	53.33
M4	5.63	178.65	2.46	43.55

In this paper, the scissors mechanism is used to realize the collaborative morphing of the wing sections. The scissors mechanism adaptively changes the sweep angle of each wing section according to the specific mission requirements. The wing section of each spanwise position carries on linear flow direction translation, and the closer the wing tip is, the greater the translation is. The wing tip always follows the flow direction, and the windward airfoil remains unchanged during the morphing process, which has little influence on the structure of the turbulent flow field⁴¹. Figure 5 shows the schematic diagram of the centroid self-trim compensation morphing mode for a multi-section variable sweep-wing UAV. The figure shows the morphing process of the sweep angle of the inner section Λ_in gradually increasing from 0° and the sweep angle of the outer section Λ_out gradually decreasing to 0°.

The collaborative morphing law of the sweep angle of the inner and outer wing sections of the preselected model is determined according to the centroid self-trim morphing mode. Figure.6 shows the variation of the longitudinal static stability margin ∂C_m/∂C_L with the sweep angle of the outer wing section Λ_out corresponding to the configuration. It can be seen that when the span length of the inner wing section of the preselected model is relatively small (the curve corresponding to M1 ~ M3), the change of Λ_out causes a relatively large change in Λin. In the process of collaborative morphing of the wing, the aerodynamic center moves forward gradually, making ∂C_m/∂C_L decrease with the increase of Λ_out. With the increase of the span ratio of the inner wing section in the preselected model, the change in Λ_in caused by the same Λ_out change gradually decreases. The forward movement of the aerodynamic center of the wing gradually reduced, so the reduction rate of ∂C_m/∂C_L gradually reduced. With the further increase of the wingspan ratio in the preselected model, as shown in the corresponding curves of M4 and M5 in the figure, the retraction of the aerodynamic center caused by the increase of Λ_out is greater than the advance of the aerodynamic center caused by the decrease of Λ_in. ∂C_m/∂C_L gradually decreases with the increase of Λ_out. The change rate of ∂C_m/∂C_L gradually increases with the increase of Λ_out.

For UAVs with both air-to-air and air-to-ground missions, the design range of longitudinal static stability margin can be appropriately relaxed, generally ranging from ˗3% to ˗10%, due to the large number of hanging points and large external mass ⁴². For multi-section variable-sweep wing UAVs, it is hoped that the influence of configuration change on the static stability margin can be reduced as much as possible. Therefore, from the perspective of longitudinal static stability margin changes during the collaborative morphing of the inner and outer wing sections of the preselected model, the static stability of M2-M5 is significantly better than that of M1, and the variation range of the static stability margin of M4 is the smallest. Therefore, the subsequent aerodynamic analysis and calculation are mainly carried out for M2 ~ M5.

Calculation accuracy verification of vortex lattice method

Before using the vortex lattice method to calculate the moment required to overcome the aerodynamic force in the morphing process, it is necessary to verify the accuracy of the calculation results of the vortex lattice method. GOE623 is selected as the multi-section variable-sweep wing UAV designed in this paper^37,43. Figure 7 shows the comparison between the results calculated by the vortex lattice method and those calculated by Fluent of M2 under different configurations when the incoming Mach number Ma = 0.3. It can be seen that before the stall angle of attack, the VLM results are in good agreement with those calculated by Fluent. In the overall design stage, the aerodynamic calculation results of the vortex lattice method can be used to analyze the aerodynamic changes in the process of wing deformation and the calculation of the moment required to overcome the aerodynamic force. The situation is similar for other models.

Analysis of aerodynamic characteristics of UAV in the centroid self-trim morphing process

For aircraft with a slow deformation rate, the error of aerodynamics parameters caused by the unsteady process is very small⁴⁴. Therefore, to facilitate analysis, the unsteady deformation process can be decomposed into a combination of steady states at the initial stage of design. The bionic multi-stage variable swept-wing UAV can be simplified into a fixed-wing UAV in several states to analyze its aerodynamic characteristics. In this paper, the wing is divided into three parts: weapon section, inner section, and outer section. Each wing section is divided into several parallel columns along the spanwise, and then into several rows according to the chord, so that the wing is divided into several small trapezoidal grid units. When calculating the rolling moment, the spanned column grid needs to be encrypted. When calculating the pitch moment, it is necessary to encrypt the chord line mesh. In this paper, a semi-circular mesh division is adopted to further encrypt the mesh of the front and rear edges, wing roots, and wing tips of the wings⁴⁵.

Figure 8 shows the variation of the wing lift coefficient C_L and drag coefficient C_D with the sweep angle Λ_out corresponding to the configuration under different Mach numbers of M2 in the centroid self-trim compensation morphing mode. The angle of attack is AOA = 0°. The variation of wing lift drag coefficient at other angles of attack is similar to this condition. The following conclusions can be drawn from the calculation results:

C_L and C_D increase slightly at first and then decrease with the increase of Λ_out corresponding to the configuration. When the sweep angle of the outer wing section corresponds to the configuration change in the range of 0°~10°, the aerodynamic changes of the inner wing section and the outer wing section are similar, and the total aerodynamic changes of the wing are small.
For a given wing configuration, C_D decreases first and then increases with the increase of flight speed. In the whole morphing process, the resistance coefficient C_Dmin corresponding to configuration 1 is the smallest (i.e. Λ_in = 0°, Λ_out = 30°).

The fuselage drag coefficient is estimated according to the following formula⁴⁶.

$${C_{{D_{0F}}}}={R_{WF}}{C_{fF}}\left[ {1+60/{{\left( {{l_f}/{d_f}} \right)}^3}+\left( {{l_f}/{d_f}} \right)/400} \right]{S_{wetF}}/{S_F}$$

Where,${C_{fF}}$is the surface friction coefficient of the fuselage plate;${l_f}$is the fuselage length; ${d_f}$is the maximum diameter of the fuselage. For a non-circular fuselage, it should be expressed as the equivalent diameter${d_f}={(4\pi {A_F})^{0.5}}$, where${A_F}$is the maximum cross-sectional area of the fuselage.${S_F}$is the fuselage reference area;${S_{wetF}}$is the body wet area.

Figure 9 shows the lifting drag ratio L/D of the wing-body assembly corresponding to the preselected model with L/D corresponding to the configuration at different angles of attack when Ma = 0.3. The angles of attack listed in the figure are 0°, 6°, and 10° respectively, and the variation of lift drag ratio of the wing-body assembly under other Mach numbers is similar to this condition. The following conclusions can be drawn from the calculation results:

With the increase of AOA, the L/D of the preselected wing-body assembly increases first and then decreases. When AOA is small, the L/D of M2 is significantly smaller than that of other models. With the increase of the angle of attack, M2 has the largest L/D when the sweep angle of the outer wing section corresponding to the configuration is small.
With the increase of the Λ_out corresponding to the configuration, the difference of the L/D among different preselected models decreases first and then increases. When Λ_out varies in the range of 0°~10°, the difference of the L/D between M4 and M5 under different AOA is small.
With the increase of Λ_out corresponding to the configuration, the L/D firstly increases and then decreases when the ratio of wingspan length of the inner wing section is relatively small in the preselected model. When the wingspan length of the inner wing section is relatively large, the L/D decreases with the increase of the Λ_out corresponding to the configuration.

Analysis of the driving moment for the morphing process of the multi-section variable-sweep wing

Multi-section variable sweep-wing can maintain optimal flight performance under different working conditions through wing morphing, which is of great significance for improving the mission execution efficiency of combat UAVs⁴². Maximum lift coefficient(C_Lmax) and maximum lift-drag ratio(L/D_max) are two important parameters to measure the maneuverability and cruise performance of aircraft. Increasing the maximum lift coefficient can expand the left boundary of the flight envelope, reduce the minimum level flight speed, ensure the controllable and safe flight of the aircraft within the range of critical or supercritical angle of attack, and effectively improve its combat performance⁴⁷. In this section, the reasonable design range suitable for the span ratio of the inner and outer sections of the multi-section wing is explored from the aspects of the driving torque required to overcome the aerodynamic force in the process of collaborative morphing and asymmetric morphing.

Aerodynamic moment required by centroid self-trim compensation morphing

Because the aerodynamic force changes during the wing morphing process are complicated and the aerodynamic load on the wing is large, this paper mainly studies the change of the moment required to overcome the aerodynamic force during the morphing process. For maneuvering, UAVs are required to have a large lift coefficient. Therefore, this chapter analyzes the following situations: The UAV is in the C_Dmin configuration with the minimum drag coefficient, at which time it needs to be symmetrically deforming to the C_Lmax configuration with the maximum lift coefficient. At this time, the transverse control surface of the aircraft does not deflect, and the inner and outer wing sections need to overcome the aerodynamic force during the morphing process.

According to the calculation model of the moment required to overcome the aerodynamic force in the wing morphing process, it can be seen that the wing needs to overcome the lift component when the sweep angle increases, and the wing needs to overcome the resistance component when the sweep angle decreases. The following calculation results are all for the unilateral wing deformation. Figure 10 shows the change of the moment required by the aircraft to overcome the aerodynamic force in a period during the collaborative process with time at Ma = 0.3. Figure 10(a) shows the moment required for the wing to overcome lift and drag per unit time during the morphing process. Figure 10(b) shows the changes in aerodynamic moment required by different preselected models in the wing morphing process. The deformation law of the curve under other conditions and the Mach number are similar, and the analysis method and conclusion can be deduced by analogy. The following conclusions can be drawn from the calculation results:

With the change of UAVs from C_Dmin configuration to C_Lmax configuration, the aerodynamic load on the wing gradually increases, and the moment required for wing morphing per unit time gradually increases. However, because the trim angle of attack gradually decreases with the change of configuration, the increase rate of aerodynamic moment gradually decreases;
In the collaborative morphing process of the inner and outer wing sections, the moment required by the inner wing section to overcome the lift is greater than that required by the outer wing section to overcome the drag;
With the increase of the span ratio of the inner wing section in the preselected model, the deformation of the inner wing section decreases gradually, and the driving moment required to overcome the aerodynamic force in the morphing process decreases gradually. At the same time, the increased rate of the aerodynamic moment required for morphing gradually reduced, the performance demand for the driver gradually reduced, and the efficiency of the driver gradually improved.

Aerodynamic moment required by the asymmetric morphing of the outer wing section

The steady roll motion is often used to measure the roll control efficiency of the lateral control surface⁴⁸. In the case of the aileron, when it deflects at a certain angle, the aircraft accelerates from zero speed to roll. If the influence of deflection on sideslip and yaw motion is not considered, the aircraft will continue to accelerate the roll until the damping torque induced by the roll Angle velocity p is balanced with the aileron steering torque, and the aircraft will roll steadily at the rated angular rate. Therefore, the steady roll can be considered as a steady motion considering only the roll degrees of freedom, with the sideslip angle β and the yaw angle r being zero. Although this is a hypothetical mode of motion, it is close to the response of lateral control surface deflection in a short period. Therefore, the influence of parameters on the moment required to overcome the aerodynamic force in the rolling maneuver with the asymmetric morphing of sweep angle is analyzed in this paper. The reasonable design range of the span ratio between the inner and outer wing sections is proposed given the requirements of the morphing controller during maneuvering flight.

According to literature research, the rolling control efficiency with asymmetric sweep angle change is lower than that of the trailing edge deflection when the lift coefficient is small⁴⁸. The change of sweep angle is a large-scale deformation, which will have a great impact on the stability and maneuverability of the aircraft, and correspondingly increase the design difficulty of the control system, so it is not suitable for the conventional control surface. In this chapter, the convergent changes in the stable roll motion of the preselected model under redundant control are studied. Based on the Supervisory-Main controller architecture constructed in literature^48,49, the control laws of redundant controllers are designed. The main controller is the conventional control surface of the trailing edge of the outer wing section, and the asymmetric deflection of the sweep angle is used as a new roll attitude controller. This control architecture can add an auxiliary controller to the system without changing the design of the main controller, and at the same time exert the control efficiency of the main controller to the maximum extent to ensure the stability of the system⁵⁰.

When the aircraft is in the maximum lift C_Lmax configuration, the aircraft performs roll maneuvering under the collaborative effect of the deflection of the trailing edge of the left-wing section and the asymmetrical sweep angle change of the right-wing section. At this time, the deflection of the trailing edge of the left-wing section and the sweep angle change of the right outer-wing section need to work against the aerodynamic force. According to the defined model of the moment required to overcome the aerodynamic force in the morphing process, it can be seen that the wing needs to overcome the lift when the sweep angle increases. In the process of decreasing of sweep angle, the wing has to work against the drag. The following calculation results are all for unilateral wing morphing.

Figure 11 shows the change law of moment required by the sweep angle change per unit time when Ma = 0.3 of the pre-selected model is used as the supervisory controller with the asymmetry of the sweep angle of the outer wing segment. At this time, the asymmetric sweep angle change of the outer wing section is introduced into the control system as a supervisory controller. At this time, the parameter of the main controller A= -0.3, and the parameter of the supervisory controller B= -0.5. The target rolling angle velocity p^d=0.1rad/s. The variation under other working conditions is similar to this working condition. It can be seen that with the increase in the proportion of the wingspan of the inner wing section in the preselected model:

The driving moment required by the sweep angle change in roll motion gradually decreases. For models M2 and M3, the moment required to overcome lift in the increase process of the wing sweep angle is greater than that to overcome drag in the decrease process. For models M4 and M5, the moment required to overcome lift in the increase process of the wing sweep angle is smaller than that to overcome drag in the decrease process.
In the morphing process, the difference between the aerodynamic moment required to overcome the lift and the drag decreases first and then increases. Among them, M4 requires the least change in the value of moment during the whole stable rolling motion, which can make the drivers work near the rated power and improve the drive efficiency. At this time, the span ratio of the inner and outer wing sections in the morphing sections is about 64.03% and 35.97%, respectively.

In this paper, a multi-section variable-sweep wing UAV is proposed, which attempts to achieve the centroid self-trim compensation during the wing morphing process through the reverse collaborative change of the sweep angle of the inner and outer wing sections. This scheme can improve the aerodynamic performance and reduce the adverse effects caused by the shift of the centroid and aerodynamic center and the change of moment of inertia, improve the stability and maneuverability of the aircraft, and reduce the difficulty of control system design in the morphing process. Aiming at the key problems to be solved in the application of multi-section variable-sweep wings in the high aspect ratio combat UAV, this paper firstly constructs several preselection models with different span ratios of the inner and outer wing sections. Then, the influence analysis and performance evaluation of the multi-section variable sweep-wing UAV under different working conditions are carried out, and the influence of Mach number, angle of attack, and span ratio of the inner and outer wing sections are discussed in detail. Finally, from the aspects of static stability margin, aerodynamic change, and performance requirements of the deformation driver during the morphing process, the reasonable design range of the span ratio of the inner and outer wing sections of the research object is given. Based on the calculation and analysis results, the following conclusions can be drawn:

Through the calculation and analysis of the aerodynamic moment required during the wing morphing process, the following conclusions can be reached:

The research object of this paper is a wing with a high aspect ratio and a positive camber airfoil with a high lift-drag ratio and high lift coefficient is used. Therefore, in the same case, the difference between the maximum lift coefficient configuration and the maximum lift drag ratio configuration gradually decreases with the increase of the wingspan proportion of the inner wing section in the preselected model.
The maximum driving moment for wing morphing required per unit time when the UAV is in the C_Lmax configuration, and the minimum driving moment for wing morphing required per unit time when the UAV is in the C_Dmin configuration;
The maximum output power requirement of the driver in the collaborative morphing process of the inner and outer wing sections can be reduced by increasing the wing span ratio of the inner wing section to the preselected model, and the efficiency of the driver can be improved.
In view of the situation of stable rolling maneuver with asymmetric morphing of the outer wing section, the preselection model of M4 requires the least change in the value of moment during the whole stable rolling motion, which can make the drivers work near the rated power and improve the drive efficiency. At this time, the span ratio of the inner and outer wing sections in the morphing sections is about 64.03% and 35.97%, respectively.

Author contributions statement

All the authors conceived the idea and developed the method. H.M. contributed to the formulation of methodology and original draft. Z.Z. contributed to the data curation and supervision. Z.D. contributed to the editing. All authors have read and agreed to the published version of the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Correspondence and requests for materials should be addressed to H.M.

Author Contribution

H.M. contributed to the formulation of methodology and original draft. Z.Z. contributed to the data curation and supervision. Z.D. contributed to the editing. All the authors conceived the idea and developed the method. All authors have read and agreed to the published version of the manuscript.

Acknowledgements

We would like to thank all the anonymous referees whose comments greatly strengthened this paper.

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Analysis of driving moment characteristic of multi-section wing based on the centroid self- trim compensation morphing

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Abstract

Figures

Introduction

Method of aerodynamic moment required for wing morphing based on VLM

Cooperative morphing scheme of the multi-section wing based on centroid self-trim

Analysis of examples

Calculation accuracy verification of vortex lattice method

Analysis of aerodynamic characteristics of UAV in the centroid self-trim morphing process

Analysis of the driving moment for the morphing process of the multi-section variable-sweep wing

Aerodynamic moment required by centroid self-trim compensation morphing

Aerodynamic moment required by the asymmetric morphing of the outer wing section

Conclusions

Declarations

Author contributions statement

Competing interests

Additional information

Author Contribution

Acknowledgements

References

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