A method for calculating the hydrodynamic force of an X-rudder underwater vehicle

Abstract

The application discloses a kind of X rudder underwater vehicle's hydrodynamic calculation method, it is related to underwater vehicle hydrodynamic performance design field.The method comprises: obtaining the attitude angle and angular velocity in the navigation process of underwater vehicle, the rudder of the underwater vehicle is X rudder;Based on the attitude angle and angular velocity, the local geometric drift angle of each vane of the X rudder is calculated;Based on the local geometric drift angle of each vane and the nominal rudder angle of each vane, the local flow attack angle of each vane is calculated, the nominal rudder angle refers to the steering angle of steering vane during steering vane steering process;Based on the nominal rudder angle and the local flow attack angle of each vane, regression is carried out, and the hydrodynamic expression of each vane in the X rudder is obtained.The refined X rudder hydrodynamic expression proposed in the application can truly reflect the flow characteristics of the local flow attack angle of different vane of X rudder, and a more accurate hydrodynamic expression is obtained.

Description

Technical Field

[0001] This application relates to the field of hydrodynamic performance design of underwater vehicles, and in particular to a hydrodynamic calculation method for an X-rudder underwater vehicle. Background Technology

[0002] Compared to the traditional cruciform rudder tail control surface layout of underwater vehicles, the X-rudder has outstanding advantages such as better rudder efficiency, high rudder redundancy, and strong roll control capability, making it a trend in the development of modern and future underwater vehicles. However, the complex hydrodynamic interference and difficult steering brought by the X-rudder have also become prominent challenges in the practical application of X-rudder engineering. In particular, during X-rudder steering, there is no coupling problem between attitude angle and rudder angle when the vehicle is sailing straight; however, when the underwater vehicle is sailing at an angle or turning / pitching, the lateral / vertical incoming flow and the turning angular velocity will induce coupling problems between the rudder and attitude angle, and between the rudder and angular velocity. This results in a large difference in the angle of attack of the incoming flow on different rudder blades, which will further lead to a significant difference in rudder efficiency between different X-rudder blades. In severe cases, the rudder efficiency of some X-rudder blades will increase rapidly, while the rudder efficiency of other blades will decrease sharply to zero. If the X-rudder experiences a diving rudder jamming incident, although the rudder angle δx of the rudder downward is the same as that of the rudder upward, it can theoretically balance the rudder force of the rudder upward. However, because the angle of attack of the incoming current of the underwater vehicle is coupled, the local angle of attack of the incoming current of the rudder upward increases, and the rudder effect increases sharply. Meanwhile, the local angle of attack of the incoming current of the rudder downward decreases, and the rudder effect decreases sharply, which will lead to an irreversible dangerous situation in actual operation.

[0003] Currently, the hydrodynamic expression of the X-rudder and its coupling with attitude angle and angular velocity still uses the expression form of the cross rudder. It calculates the hydrodynamics of the X-rudder based on the lateral / vertical velocity and the horizontal / vertical angular velocity at the buoyancy center of the underwater vehicle. This calculation method fails to truly reflect the difference in the local incoming flow angle of attack of different blades of the X-rudder, and the hydrodynamic expression is inaccurate. Summary of the Invention

[0004] In response to the aforementioned problems and technical requirements, the applicant has proposed a hydrodynamic calculation method for an X-rudder underwater vehicle. The technical solution of this application is as follows:

[0005] On the one hand, a hydrodynamic calculation method for an X-rudder underwater vehicle is provided, including the following steps:

[0006] The attitude angles and angular velocities of the underwater vehicle during its navigation process are obtained, and the stern rudder of the underwater vehicle is the X rudder;

[0007] Based on the attitude angle and the angular velocity, calculate the local geometric drift angle of each blade in the X-rudder;

[0008] Based on the local geometric drift angle of each rudder blade and the nominal rudder angle of each rudder blade, the local incoming flow angle of attack of each rudder blade is calculated. The nominal rudder angle refers to the control rudder angle during the rudder blade turning process.

[0009] Based on the nominal rudder angle of each rudder blade and the local incoming flow angle of attack, a regression is performed to obtain the hydrodynamic expression for each rudder blade in the X rudder.

[0010] The further proposed solution is as follows:

[0011] The calculation of the local geometric drift angle of each blade in the X-rudder based on the attitude angle and the angular velocity includes:

[0012] Based on the distance from the centroid of each rudder blade to the center of gravity of the underwater vessel, and combined with the attitude angle and the angular velocity, the local geometric drift angle of each rudder blade in the X rudder is calculated.

[0013] The method for calculating the local geometric drift angle of each blade in the X-rudder is as follows:

[0014]

[0015] Where, β R Let β be the local geometric drift angle, and x be the attitude angle. R The distance from the centroid of the rudder blade to the center of gravity of the underwater vehicle is given by r, angular velocity is given by V, and speed is given by V.

[0016] The method for calculating the local angle of attack of each rudder blade is as follows:

[0017] α R =δ x ±β R

[0018] Where, α R δ is the angle of attack of the local incoming flow. x The nominal rudder angle is as stated.

[0019] When the angular velocity is in the same direction as the nominal rudder angle, the local angle of attack of each rudder blade in the X rudder is calculated as follows: α R =δ x -β R ;

[0020] When the angular velocity is opposite to the nominal rudder angle, the method for calculating the local angle of attack of each rudder blade in the X rudder is: α R =δ x +β R .

[0021] Taking into account the rectification effect of the underwater vehicle, the local geometric drift angle of the X-rudder is as follows:

[0022] β′ R =εβ R

[0023] Where ε is the rectification coefficient.

[0024] The regression based on the nominal rudder angle and the local incoming flow angle of attack of each rudder blade yields the hydrodynamic expression for each rudder blade in the X rudder, including:

[0025] Obtain the overall hydrodynamics of the underwater vehicle;

[0026] Based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local incoming flow angle of attack, a global regression is performed to obtain the hydrodynamic expression of the X rudder.

[0027] The overall hydrodynamics of the underwater vehicle includes the lateral force, yaw moment, vertical force, and pitch moment of the underwater vehicle.

[0028] The method for obtaining the hydrodynamic expression of the X rudder by performing a global regression based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local incoming current angle of attack is as follows:

[0029] A regression equation is established based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local angle of attack of the incoming flow.

[0030] The regression equation is as follows:

[0031]

[0032] Wherein, Y is the lateral force of the underwater vehicle, N is the yaw moment of the underwater vehicle, Z is the vertical force of the underwater vehicle, and M is the pitching moment of the underwater vehicle; The lateral force of the rudder blade. The yaw moment of the rudder blade. The vertical force on the rudder blade. The pitching moment of the rudder blade;

[0033] Based on the regression equation, an overall regression is performed to obtain the expressions for the lateral force, yaw moment, vertical force, and pitch moment of the rudder blade.

[0034] The beneficial technical effects of this application are:

[0035] This application proposes a refined method for calculating the hydrodynamic expression of the X-rudder. During the calculation, the geometric drift angle of each rudder blade is calculated based on the attitude angle and angular velocity of the underwater vehicle. Then, combined with the rudder angle of each blade, the local incoming flow angle of attack for each blade is calculated. Finally, based on the local incoming flow angle of attack and the rudder angle, the local hydrodynamic expression of the X-rudder is regressively obtained. Compared to the calculation methods in related technologies, the refined hydrodynamic expression of the X-rudder proposed in this application uses different local rudder blades in the X-rudder as a benchmark, truly reflecting the flow characteristics around different local incoming flow angles of attack of the X-rudder, thus obtaining a more accurate hydrodynamic expression. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of a cruciform rudder layout and an X-rudder layout provided in an exemplary embodiment of this application;

[0037] Figure 2 This is a schematic diagram of the local incoming flow on the X-rudder surface of an underwater vehicle in a straight-ahead state, provided by an exemplary embodiment of this application.

[0038] Figure 3 This is a schematic diagram of the coupling between the X-rudder attitude angle and the angle of attack of an underwater vehicle in oblique flight state, provided by an exemplary embodiment of this application;

[0039] Figure 4 This is a schematic diagram of the geometric drift angle and nominal rudder angle of an underwater vehicle provided in an exemplary embodiment of this application;

[0040] Figure 5 This is a flowchart of a hydrodynamic calculation method for an X-rudder underwater vehicle provided in an exemplary embodiment of this application. Detailed Implementation

[0041] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0042] like Figure 1 As shown, it illustrates schematic diagrams of both the cruciform and X-shaped rudder configurations. Compared to the cruciform rudder, the X-shaped rudder offers superior steering efficiency. During X-shaped rudder steering, as... Figure 2 As shown, during straight-line navigation, the angle of attack of the incoming flow at the rudder surface is theoretically equal to the rudder angle δ. x In this process, there is no coupling issue between attitude angle and rudder angle; however, during the oblique, turning, or pitching motion of an underwater vehicle, the lateral or vertical incoming flow, as well as the turning angular velocity, can cause coupling issues between the rudder and attitude angle, and between the rudder and angular velocity, resulting in significant differences in the angle of attack of the incoming flow to different rudder blade surfaces. For example... Figure 3 As shown, this illustrates the coupling problem between the attitude angle and rudder angle of the X-rudder during oblique navigation of an underwater vehicle at an attitude angle α, and the incoming flow angle α of the upper rudder blade. R1 The angle of attack α of the incoming flow from the lower rudder blade R2They are not the same at the same attitude angle α. In related technologies, when calculating the hydrodynamic expression of the X-rudder, the expression form of the cruciform rudder is still used, which uses the lateral velocity v, vertical velocity w, horizontal angular velocity |r|, and vertical angular velocity |q| at the hull's center of buoyancy to write the hydrodynamics as an expression against δ. x vδ x wδ x 、|r|δ x 、|q|δ x The derivative form of Y δx N δx Z δx M δx Y vδx N vδx Z wδx M wδx Y |r|δx N |r|δx Z |q|δx M |q|δx This approach does not consider the differences in the angle of attack of the local incoming flow caused by the coupling problem of different rudder blades. The hydrodynamic expression cannot truly reflect the coupling characteristics between the X-rudder and the attitude angle. It reflects the hydrodynamics of the entire rudder rather than the differences in local positions.

[0043] To address the aforementioned issues, this application provides a hydrodynamic calculation method for an X-rudder underwater vehicle. Based on the coupling mechanism between attitude angle and rudder angle, and considering the actual steering conditions of the X-rudder, it proposes a hydrodynamic expression for the X-rudder based on the actual local incoming flow angle, ensuring a true reflection of the coupling characteristics between the X-rudder and attitude angle. This application can provide solid technical support for subsequent hydrodynamic prediction and evaluation of X-rudder underwater vehicles. The method is illustrated using a computer device as an example. The method includes the following steps:

[0044] Step S1: Obtain the attitude angle and angular velocity of the underwater vehicle during its navigation process. The stern rudder of the underwater vehicle is the X rudder.

[0045] This application proposes a method for calculating hydrodynamics based on the local angle of attack of the X-rudder. During the navigation of an underwater vehicle (including oblique navigation, turning, pitching, etc.), the attitude angles and angular velocities of the underwater vehicle will change. These changes in attitude angles and angular velocities will cause changes in the geometric drift angle of the X-rudder, and different blades within the X-rudder will have different local geometric drift angles even with the same attitude angle and angular velocity. In this calculation method, during the underwater vehicle's motion, the attitude angles and angular velocities of the underwater vehicle are first obtained to calculate the local geometric drift angle of the X-rudder.

[0046] Step S2: Based on the attitude angle and angular velocity, calculate the local geometric drift angle of each blade in the X rudder.

[0047] Because the rudder blades in the X-rudder have different layout positions, the corresponding local geometric drift angles of the rudder blades will also be different under the same attitude angle and angular velocity. During the calculation process, the attitude angle, angular velocity, and the layout positions of different rudder blades in the X-rudder can be combined to calculate the local geometric drift angles of different rudder blades. It should be noted that in this embodiment, the rudder blades are used as the dividing point to calculate the local geometric drift angle of each rudder blade, thereby calculating the hydrodynamics of each rudder blade. However, other methods of division are also possible, such as detailed division to different points on the same rudder blade. This embodiment does not limit this approach.

[0048] In one possible implementation, the local geometric drift angle of the entire rudder blade can be calculated based on the centroid position of the rudder blade. In this process, the local geometric drift angle of each rudder blade can be calculated based on the distance from the centroid position of each rudder blade to the underwater center of gravity, combined with attitude angles and angular velocities. The calculation method is as follows:

[0049]

[0050] Where, β R β is the local geometric drift angle, x is the attitude angle, and β is the attitude angle. R ω is the distance from the centroid of the rudder blade to the center of gravity of the underwater vehicle, r is the angular velocity, and V is the speed.

[0051] like Figure 4 As shown, during the underwater vehicle's motion at attitude angle β and angular velocity r, the distance x from the centroid R of the rudder blade to the underwater vehicle's center of gravity G is considered. R The local geometric drift angle β can be calculated. R .

[0052] By measuring the distance from the centroid of each rudder blade to the underwater vehicle's center of gravity, and considering the overall attitude angles and angular velocities of the underwater vehicle, the local geometric drift angles of different rudder blades can be obtained. Combined with... Figure 1 As shown, the local geometric drift angles of the four rudder blades can be calculated separately.

[0053] It should be noted that the above local geometric drift angles were calculated without considering the influence of underwater vehicles on water flow.

[0054] Furthermore, if we consider the rectification effect of the underwater vehicle and the propeller on the underwater vehicle, we also need to introduce a rectification coefficient.

[0055] Taking into account the rectification effect of the underwater vehicle, the local geometric drift angle of the X rudder is as follows:

[0056] β′ R =εβ R

[0057] Where ε is the rectification factor. The rectification factor varies for different underwater vehicles, ranging from 0.2 to 0.7. For example, when the underwater vehicle is a submarine, the rectification factor can be taken as 0.7.

[0058] Step S3: Based on the local geometric drift angle of each rudder blade and the nominal rudder angle of each rudder blade, calculate the local incoming flow angle of attack of each rudder blade. The nominal rudder angle refers to the control rudder angle during the rudder blade turning process.

[0059] After calculating the local geometric drift angle of each rudder blade, the nominal rudder angle of each blade is obtained to calculate the local angle of attack of the incoming flow. The nominal rudder angle is the rudder angle manipulated during steering (the rudder angle indicated in the steering command), not the actual angle the rudder blade rotates according to the steering command. That is, the nominal rudder angle is the planned rudder angle, not the actual rudder angle. For example, if during steering, the rudder blade needs to be controlled to rotate 10°, but the rudder blade actually rotates 9°, then the nominal rudder angle should be 10°.

[0060] Based on the nominal rudder angle of each rudder blade and the local geometric drift angle of each rudder blade, the local angle of attack of each rudder blade can be calculated. The calculation method is as follows:

[0061] α R =δ x ±β R

[0062] Where, α R For the local angle of attack of the incoming flow, δ x The nominal rudder angle.

[0063] Wherein, the local geometric drift angle β R The sign of the rudder angle is related to the similarity or difference between the nominal rudder angle and the direction of the angular velocity.

[0064] When the angular velocity and the nominal rudder angle are in the same direction, the local angle of attack of each rudder blade in the X-rudder is calculated as follows: α R =δ x -β R That is, at the angular velocity r and the nominal rudder angle δ x When both signs are the same, the negative sign is used. This is illustrative of the relationship between angular velocity r and nominal rudder angle δ during steady rotational motion. x If they are in the same direction, then the local angle of attack α of the incoming flow is... R =δ x -β R .

[0065] When the angular velocity is opposite to the nominal rudder angle, the method for calculating the local angle of attack of each rudder blade in the X rudder is: α R =δ x +β R That is, at the angular velocity r and the nominal rudder angle δx When signs differ, a positive sign is used. This is illustrative of the angular velocity *r* and the nominal rudder angle *δ* during the reverse steering process at the start of a Z-shaped maneuver. x Conversely, the local incoming flow angle of attack α R =δ x +β R .

[0066] Step S4: Based on the nominal rudder angle of each rudder blade and the local incoming flow angle of attack, regression is performed to obtain the hydrodynamic expression of each rudder blade in the X rudder.

[0067] During the movement of an underwater vehicle, each blade of the X-rudder has a different local angle of attack from the incoming flow due to its different local position. In other words, each blade has different local flow characteristics, and consequently, different hydrodynamic forces. Calculating the hydrodynamic forces of each blade based on its local angle of attack can accurately reflect the actual force situation of the X-rudder.

[0068] After calculating the nominal rudder angle and local incoming flow angle of attack for each rudder blade, regression can be performed by combining the overall hydrodynamics of the underwater vehicle to obtain the local hydrodynamics of rudder X, including the hydrodynamic expression for each rudder blade. This process includes the following steps:

[0069] Step S41: Obtain the overall hydrodynamics of the underwater vehicle.

[0070] Optionally, the overall hydrodynamics of the underwater vehicle includes the lateral force, yaw moment, vertical force, and pitch moment. The overall hydrodynamics of the underwater vehicle can be pre-calculated based on its navigation parameters. It should be noted that the overall hydrodynamics of the underwater vehicle is calculated under conditions of varying rudder angles, attitude angles, and angular velocities. Variable rudder angles and attitude angles refer to the changes in attitude angles when the rudder angle changes, and variable rudder angles and angular velocities refer to the changes in angular velocity when the rudder angle changes. Then, using the variation curves of the overall lateral force, yaw moment, vertical force, and pitch moment of the underwater vehicle under varying rudder angles, attitude angles, and angular velocities, and combining them with the nominal rudder angle of the rudder blades and the local angle of attack of the incoming flow, regression is performed to obtain the hydrodynamic expression of the local rudder blades.

[0071] Step S42: Perform an overall regression based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local incoming flow angle of attack to obtain the hydrodynamic expression for the X rudder.

[0072] The overall regression method based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local angle of attack of the incoming flow is as follows:

[0073] First, a regression equation is established based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local angle of attack of the incoming flow.

[0074] The regression equation is as follows:

[0075]

[0076] Y represents the lateral force of the underwater vehicle, N represents the yaw moment of the underwater vehicle, Z represents the vertical force of the underwater vehicle, and M represents the pitching moment of the underwater vehicle. The lateral force of the rudder blade. The yaw torque of the rudder blade. The vertical force on the rudder blade, The pitching moment of the rudder blade;

[0077] After establishing the regression equation, an overall regression is performed based on the regression equation to obtain the expressions for the lateral force, yaw moment, vertical force, and pitch moment of the rudder blade.

[0078] Performing a global regression on the above regression equations, given that the lateral force, yaw moment, vertical force, and pitch moment of the underwater vehicle are known, and the nominal rudder angle δ of the rudder blades is... x and the local incoming flow angle of attack α R Given the information, the local hydrodynamic expression can be obtained through regression.

[0079] The hydrodynamic expression proposed in this application uses the local aspect of the X rudder as a reference to obtain the hydrodynamic expression at different locations within the X rudder. During the coupling of the rudder with attitude angles and with angular velocities, the hydrodynamic regression expression is no longer based on the attitude angles and angular velocities at the hull's center of buoyancy. Instead, it is based on the rudder force generation mechanism (the magnitude of the rudder force is related to the drift angle and angle of attack), determining the local incoming flow angle of attack based on the geometric drift angle and nominal rudder angle of the rudder blades. Then, regression is performed based on the local incoming flow angle of attack to obtain the local hydrodynamics (including...). as well as The corresponding expression. The hydrodynamic expression derived from the coupled expression of attitude angle and rudder angle, and angular velocity and rudder angle in related technologies includes Y. δx N δx Z δx M δx Y vδx N vδx Z wδx M wδx Y |r|δx N |r|δx Z |q|δx M |q|δx Compared with the methods in related technologies, the hydrodynamic expression of the X-rudder proposed in this application is more refined, accurate to the local rudder blade of the X-rudder, and the expression is greatly simplified without adding any additional hydrodynamic acquisition work, thus improving calculation efficiency while ensuring accuracy.

[0080] In summary, this application proposes a refined method for calculating the hydrodynamic expression of the X-rudder. During the calculation, the geometric drift angle of each rudder blade is calculated based on the attitude angle and angular velocity of the underwater vehicle. Then, combined with the rudder angle of each blade, the local incoming flow angle of attack for each blade is calculated. Finally, based on the local incoming flow angle of attack and the rudder angle, the local hydrodynamic expression of the X-rudder is regressively obtained. Compared to the calculation methods in related technologies, the refined hydrodynamic expression of the X-rudder proposed in this application uses different local rudder blades in the X-rudder as a benchmark, truly reflecting the flow characteristics around different local incoming flow angles of attack of the X-rudder, thus obtaining a more accurate hydrodynamic expression.

[0081] like Figure 5 The diagram illustrates a flowchart of the X-rudder hydrodynamic calculation process provided in an exemplary embodiment of this application. It includes the following steps:

[0082] Step 501: Obtain the attitude angle β and angular velocity r of the underwater vehicle during its curved motion.

[0083] Step 502, calculate the local geometric drift angle β of the X rudder blade. R .

[0084] In the solution process, the local geometric drift angle β is first calculated based on the attitude angle β and the angular velocity r. R Optionally, the local geometric drift angle β of each rudder blade can be calculated as a reference. R With local geometric drift angle β R When using the rudder blade centroid position as the reference, the calculation can be performed based on the reference position.

[0085] Step 503, obtain the nominal rudder angle δ of the X rudder blade. x .

[0086] The steering angle specified in the steering command for the rudder blade can be obtained, thus yielding the nominal rudder angle δ of the rudder blade. x .

[0087] Step 504, calculate the local incoming flow angle of attack α of the X rudder blade. R .

[0088] According to the nominal rudder angle δ x The difference between the direction of angular velocity r and the direction of angular velocity r is used to determine the local geometric drift angle β. R and nominal rudder angle δ x The method of calculating the local incoming flow angle of attack is used to obtain the local incoming flow angle of attack α. R .

[0089] Step 505: Calculate the hydrodynamic expression based on the local incoming flow angle of attack.

[0090] Based on the local angle of attack of each rudder blade, combined with the hydrodynamic expression of the underwater vehicle under varying rudder angles and attitude angles as well as varying rudder angles and angular velocities, the hydrodynamic expression of the local rudder blade can be calculated.

[0091] The calculation methods in steps 501 to 505 can be referred to in the above embodiments, and will not be repeated in this embodiment.

[0092] In the above embodiments, the hydrodynamic expression of each rudder blade is calculated based on the entire rudder blade. In another possible implementation, the rudder blade can be further refined, and calculations can be performed based on several positions within the rudder blade. Taking a certain position point within the rudder blade as an example, the distance from that position point to the underwater vehicle's center of gravity can be determined. Then, based on the distance and the attitude angle and angular velocity of the underwater vehicle, the local geometric drift angle corresponding to that position point can be calculated. Then, based on the local geometric drift angle and the nominal rudder angle of the rudder blade, the local angle of attack of the incoming flow at that position can be calculated. Finally, by combining the hydrodynamic expressions of the underwater vehicle under varying rudder angles and attitude angles, as well as varying rudder angles and angular velocities, a comprehensive regression is performed to obtain the hydrodynamic expression of that position.

[0093] In solving the coupling between rudder and attitude angle, and between rudder and angular velocity, this expression no longer uses the attitude angle and angular velocity at the hull's center of buoyancy as the basis for hydrodynamic regression. Instead, it is based on the mechanism characteristics of rudder force generation, obtaining the local incoming flow angle of the X rudder through the geometric drift angle and nominal rudder angle of each X rudder piece, and then regressing to obtain the hydrodynamic expression of the X rudder relative to the local incoming flow angle. Compared to traditional steering hydrodynamic expressions, the refined X rudder hydrodynamic expression proposed in this application truly reflects the flow characteristics of the X rudder at different local incoming flow angles, with higher accuracy, without increasing any additional hydrodynamic acquisition workload, and is significantly simplified compared to traditional expressions.

[0094] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A hydrodynamic calculation method for an X-rudder underwater vehicle, characterized in that, The method includes: The attitude angles and angular velocities of the underwater vehicle during its navigation process are obtained, and the stern rudder of the underwater vehicle is the X rudder; Based on the distance from the centroid of each rudder blade to the center of gravity of the underwater vessel, and combined with the attitude angle and the angular velocity, the local geometric drift angle of each rudder blade in the X rudder is calculated. Based on the local geometric drift angle of each rudder blade and the nominal rudder angle of each rudder blade, the local incoming flow angle of attack of each rudder blade is calculated. The nominal rudder angle refers to the control rudder angle during the rudder blade turning process. Based on the nominal rudder angle of each rudder blade and the local incoming flow angle of attack, a regression is performed to obtain the hydrodynamic expression for each rudder blade in the X rudder.

2. The method according to claim 1, characterized in that, The method for calculating the local geometric drift angle of each blade in the X-rudder is as follows: in, For the local geometric drift angle, The attitude angle is... The distance from the centroid of the rudder blade to the center of gravity of the underwater vessel. The angular velocity is... For speed.

3. The method according to claim 1, characterized in that, The method for calculating the local angle of attack of each rudder blade is as follows: in, The local angle of attack of the incoming flow. The nominal rudder angle, The local geometric drift angle is denoted as .

4. The method according to claim 3, characterized in that, When the angular velocity is in the same direction as the nominal rudder angle, the method for calculating the local angle of attack of each rudder blade in the X rudder is as follows: ; When the angular velocity is opposite to the nominal rudder angle, the method for calculating the local angle of attack of each rudder blade in the X rudder is as follows: .

5. The method according to claim 2, characterized in that, Taking into account the rectification effect of the underwater vehicle, the local geometric drift angle of the X-rudder is as follows: in, This is the rectification factor.

6. The method according to any one of claims 1 to 5, characterized in that, The regression based on the nominal rudder angle and the local incoming flow angle of attack of each rudder blade yields the hydrodynamic expression for each rudder blade in the X rudder, including: Obtain the overall hydrodynamics of the underwater vehicle; Based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local incoming flow angle of attack, a global regression is performed to obtain the hydrodynamic expression of the X rudder.

7. The method according to claim 6, characterized in that, The overall hydrodynamic force of the underwater vehicle includes the lateral force, yaw moment, vertical force, and pitch moment of the underwater vehicle.

8. The method according to claim 7, characterized in that, The method for obtaining the hydrodynamic expression of the X rudder by performing a global regression based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local incoming current angle of attack is as follows: A regression equation is established based on the overall hydrodynamics of the underwater vehicle, the nominal rudder angle, and the local angle of attack of the incoming flow. The regression equation is as follows: in, The lateral force of the underwater vehicle. Z is the yaw moment of the underwater vehicle, Z is the vertical force of the underwater vehicle, and M is the pitching moment of the underwater vehicle. The lateral force of the rudder blade. The yaw moment of the rudder blade. The vertical force on the rudder blade, The pitching moment of the rudder blade. The local angle of attack of the incoming flow. The nominal rudder angle; Based on the regression equation, an overall regression is performed to obtain the expressions for the lateral force, yaw moment, vertical force, and pitch moment of the rudder blade.

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