Bionic tail fin elastic parameter design method

Abstract

The invention provides a bionic tail fin elastic parameter design method, which comprises the following steps of: constructing a tail fin propelling system dynamic model, and calculating the cruising speed and tail fin propelling efficiency of an aircraft under different tail joint stiffness and damping conditions according to the tail fin propelling system dynamic model. And selecting a combination of rigidity K and damping C parameters which meet cruise speed design requirements and have optimal propulsion efficiency, and outputting the combination as bionic tail fin elastic parameters. According to the method, through dynamic modeling of the tail fin propelling system, the positive effect of fluid-solid coupling in the bionic fish propelling system on efficiency improvement is considered, the elastic parameters of the connecting joint between the tail fin and the tail handle are optimally designed, the tail fin propelling efficiency is improved, and the problem of bionic tail fin propelling efficiency improvement is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater bionics, and particularly relates to a method for designing the elastic parameters of a bionic tail fin, which is applicable to guiding the design of the elastic parameters of the bionic tail fin joint and the dynamic simulation modeling of the tail fin. Background Technique

[0002] Due to the advantages of high efficiency, strong low-speed maneuverability, and low noise in the propulsion of the tail fins of fish in water, it has received wide attention in the field of hydrodynamic research. However, after years of research, there is still a large gap between bionic tail fin propulsion and the expected high-efficiency goal of biological propulsion, and improving the propulsion efficiency has become the key to the development of bionic tail fin propulsion technology. For the research on bionic tail fin propulsion, most domestic and foreign universities, enterprises, etc. currently carry out it from the perspective of flow field optimization, and have achieved good results in aspects such as the hydrodynamic principle of bionic propulsion and vortex propulsion technology. However, when the flow mechanism becomes gradually clear and the flow field optimization becomes increasingly perfect, the optimization effect is gradually decreasing; most of the drive control and structural design of bionic fish vehicles aim to achieve the deformation law of fish. After years of optimization design by a large number of researchers, various structural design methods of bionic fish vehicles have been obtained, and the further optimization effect is limited; in a small number of studies on the structure-flow coupling of fish-like propulsion, it is qualitatively recognized that the fluid-structure coupling in fish-like propulsion has a positive effect on improving efficiency, but an effective theoretical design method has not been established to provide an optimization means for improving the high-efficiency design of bionic tail fins. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for designing the elastic parameters of a bionic tail fin. By dynamically modeling the tail fin propulsion system and considering the positive effect of fluid-structure coupling in the bionic fish propulsion system on improving efficiency, the elastic parameters of the connection joint between the tail fin and the tail stock are optimized to improve the tail fin propulsion efficiency and solve the problem of improving the efficiency of bionic tail fin propulsion.

[0004] The technical solution adopted by the present invention to achieve the above purpose is as follows:

[0005] As one aspect of the present invention, a method for designing the elastic parameters of a bionic tail fin is provided, including the following steps:

[0006] Construct a dynamic model of the tail fin propulsion system, and the dynamic model of the tail fin propulsion system includes:

[0007] The torque of the tail joint:

[0008] The force of the tail joint: F 12 = ma - F l

[0009] The hydrodynamic force of the tail fin: F l = L + D + F λ

[0010] Hydrodynamic moment of the caudal fin: M l = r m2 ×(L + D) + M λ

[0011] Caudal fin motion control equation:

[0012] Vehicle motion control equation:

[0013] Where M 12 is the moment of force of the tail joint, K and C are the stiffness and damping of the tail joint respectively, β is the swing angle of the caudal fin relative to the caudal peduncle, F 12 is the force of the tail joint, m is the mass of the caudal fin, a is the translational acceleration of the centroid of the caudal fin; F l is the hydrodynamic force of the caudal fin, L is the lift of the caudal fin, D is the drag of the caudal fin, F λ is the added mass force of the caudal fin, M l is the hydrodynamic moment of the caudal fin, M λ is the moment caused by the added mass of the caudal fin, r m2 is the vector from the centroid of the caudal fin to the center of pressure, I is the moment of inertia of the caudal fin relative to the tail joint, M a is the moment of the inertial force of the caudal fin acting at the tail joint position, is the angular acceleration of the caudal fin, U is the vehicle's navigation speed, T is the thrust of the caudal fin, ρ is the water density, Cx is the vehicle's drag coefficient, S is the reference area of the vehicle's drag coefficient, m0 is the vehicle's mass;

[0014] According to the dynamic model of the caudal fin propulsion system, calculate the cruising speed of the vehicle and the propulsion efficiency of the caudal fin under different tail joint stiffness and damping conditions, select the combination of stiffness K and damping C parameters that meet the design requirements of the cruising speed and have the optimal propulsion efficiency, and output as the elastic parameters of the bionic caudal fin.

[0015] Furthermore, the calculation method of the caudal fin propulsion efficiency includes the following steps:

[0016] Calculate the force exerted by the caudal fin on the tail joint and the moment of force of the caudal fin on the tail joint according to the dynamic model of the caudal fin propulsion system;

[0017] Calculate the driving moment of the lumbar joint, and then calculate the driving power of the lumbar joint;

[0018] Calculate the power of the caudal fin thrust doing work;

[0019] Calculate the ratio of the power of the caudal fin thrust doing work to the driving power of the lumbar joint to obtain the caudal fin propulsion efficiency.

[0020] Furthermore, the force exerted by the caudal fin on the tail joint and the moment of force of the caudal fin on the tail joint are respectively:

[0021] F 21=-F 12

[0022] M 21 =-M 12

[0023] Wherein, F 12 is the force on the tail joint, and M 12 is the torque on the tail joint;

[0024] The driving torque of the lumbar joint is:

[0025] M 01 =M 21 +s1×F 21

[0026] Wherein, s1 is the position vector of the end of the tail handle;

[0027] The driving power of the lumbar joint is:

[0028]

[0029] Wherein, is the angular velocity of the tail handle swinging relative to the trunk;

[0030] The work power of the tail fin thrust is:

[0031] P T =TU

[0032] Wherein, U is the navigation speed of the vehicle, and T is the tail fin thrust.

[0033] Furthermore, the hydrodynamic calculation method of the tail fin is as follows:

[0034] Calculate the tail fin speed:

[0035]

[0036] Wherein, u is the tail fin speed, is the angle between the tail fin speed and the horizontal plane, ang() is the complex angle operator, and v is the combined velocity vector of the tail fin pressure center;

[0037] Calculate the tail fin lift and tail fin drag:

[0038]

[0039] Wherein, A is the reference area of the tail fin, ρ is the water density, C L , C D are the lift coefficient and drag coefficient of the tail fin respectively;

[0040] Calculate the added mass force of the tail fin:

[0041]

[0042] real(F′ λ ) = -λ 11 a′ x

[0043]

[0044] where F λ ' is the added mass force of the caudal fin in the body-fixed system, real(F′ λ ), imag(F′ λ ) are the axial component and the normal component of the added mass force of the caudal fin in the body-fixed system, respectively, is the angular acceleration of the caudal fin, represents the added mass corresponding to the force in the j1 direction divided by the acceleration in the j2 direction, where j1 and j2 take values of 1, 2, and 6, The subscript values of 1, 2, and 6 correspond to the X-axis, Y-axis, and the rotational direction about the Z-axis, respectively; a′ x , a′ y are the axial separation and the normal component of the translational acceleration of the centroid of the caudal fin in the body-fixed system of the caudal fin, respectively;

[0045] By summing the lift force of the caudal fin, the drag force of the caudal fin, and the added mass force of the caudal fin, the hydrodynamic force F l .

[0046] Furthermore, the moment M λ caused by the added mass of the caudal fin is:

[0047]

[0048] where, is the angular acceleration of the caudal fin, represents the added mass corresponding to the force in the j1 direction divided by the acceleration in the j2 direction, where j1 and j2 take values of 1, 2, and 6, The subscript values of 1, 2, and 6 correspond to the X-axis, Y-axis, and the rotational direction about the Z-axis, respectively; a′ x , a′ y are the axial separation and the normal component of the translational acceleration of the centroid of the caudal fin in the body-fixed system of the caudal fin, respectively.

[0049] Furthermore, the calculation method of the combined velocity of the center of pressure of the caudal fin is as follows:

[0050]

[0051] where θ2 represents the rotation angle of the caudal fin, θ1 is the swing angle of the caudal peduncle relative to the trunk, β = θ2 - θ1, β is the swing angle of the caudal fin relative to the caudal peduncle, R is the rotation radius of the caudal peduncle, r is the rotation radius of the caudal fin, and U is the navigation speed of the vehicle;

[0052] θ1 = A T sin(2πft)

[0053] where A T is the amplitude of the tail-stock swing, and f is the frequency.

[0054] Furthermore, the calculation method of the translational acceleration of the center of mass of the caudal fin is as follows:

[0055] a = a1 + a2

[0056]

[0057] where a1 and a2 are the accelerations of the tail joint and the acceleration of the center of mass of the caudal fin relative to the tail joint respectively, θ1 is the swing angle of the tail-stock relative to the trunk, is the angular velocity of the tail-stock relative to the trunk swing, is the angular acceleration of the tail-stock relative to the trunk swing, θ2 represents the rotation angle of the caudal fin, is the angular velocity of the caudal fin, is the angular acceleration of the caudal fin, R is the rotation radius of the tail-stock, l is the distance from the center of mass of the caudal fin to the tail joint, and U is the navigation speed of the vehicle.

[0058] Furthermore, the angular velocity of the caudal fin is calculated as:

[0059]

[0060] where M 12 is the torque of the tail joint, r 12 is the vector from the tail joint to the center of pressure of the caudal fin, L is the lift of the caudal fin, D is the drag of the caudal fin, r m1 is the vector from the center of mass of the caudal fin to the tail joint, a1 is the acceleration of the tail joint, a′ 1y is the normal component of a1 transformed to the body-fixed system, I z is the moment of inertia of the caudal fin relative to the center of mass of the caudal fin, l is the distance from the center of mass of the caudal fin to the tail joint, and m is the mass of the caudal fin.

[0061] As another aspect of the present invention, there is provided a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the method described above.

[0062] As another aspect of the present invention, there is provided an electronic device including a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method described above.

[0063] Advantages of the present invention compared with the prior art:

[0064] The present invention provides a method for designing the elastic parameters of a bionic caudal fin. Through the dynamic modeling of the caudal fin propulsion system, considering the positive effect of fluid-structure interaction in fish-like propulsion on improving efficiency, the elastic parameters of the connecting joint between the caudal fin and the caudal peduncle are optimized to improve the propulsion efficiency of the caudal fin.

[0065] The method for designing the elastic parameters of the bionic caudal fin provided by the present invention can be used to guide the design of the bionic caudal fin and the kinematic simulation modeling, and support the design of the bionic caudal fin propulsion scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings included are used to provide a further understanding of the embodiments of the present invention, and constitute a part of the specification, for illustrating the embodiments of the present invention, and are used to explain the principles of the present invention together with the written description. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0067] Figure 1 It is a schematic structural diagram of a two-joint caudal fin propulsion system provided for a specific embodiment of the present invention;

[0068] Figure 2 It is a schematic diagram of the caudal fin movement speed provided for a specific embodiment of the present invention;

[0069] Figure 3 It is a schematic diagram of the non-inertial reference frame of the caudal joint provided for a specific embodiment of the present invention;

[0070] Figure 4 It is a schematic diagram of the caudal fin body-fixed system provided for a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0071] The present invention will be described in detail below with reference to the drawings and embodiments.

[0072] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0073] Aiming at the problem of improving the efficiency of bionic caudal fin propulsion, the present invention provides a method for designing the elastic parameters of a bionic caudal fin. Through the dynamic modeling of the caudal fin propulsion system, considering the positive effect of fluid-structure interaction in fish-like propulsion on improving efficiency, the elastic parameters of the connecting joint between the caudal fin and the caudal peduncle are optimized to improve the propulsion efficiency of the caudal fin. This method can be used to guide the design of the bionic caudal fin and for the design and dynamic simulation modeling of the bionic caudal fin.

[0074] For ease of understanding, the coordinate system used in the present invention is first described as follows:

[0075] Body axis system: Taking the overall center of mass of the vehicle as the origin, the X-axis is along the axis of the torso and points in the direction of motion (horizontal navigation), and the Y-axis is perpendicular to the X-axis and points upward.

[0076] Complex plane system: Taking the axis of the joint connecting the caudal peduncle and the torso (abbreviated as "waist joint") as the origin, the imaginary axis is in the Y direction, and the real axis is in the -X direction.

[0077] Non-inertial reference system of the caudal joint: Taking the axis of the joint connecting the caudal fin and the caudal peduncle (abbreviated as "caudal joint") as the origin, the x1-axis is parallel to the real axis, and the y1-axis is parallel to the imaginary axis.

[0078] Ground system: Taking the initial position of the center of mass of the vehicle as the origin, the horizontal navigation direction as the X0-axis, and the skyward direction as the Y0-axis.

[0079] Caudal fin body-fixed system: Taking the center of mass of the caudal fin as the origin, the x'-axis points to the caudal joint, and the y'-axis is perpendicular to the x'-axis and points upward.

[0080] As one aspect of the present invention, a method for designing the elastic parameters of a bionic caudal fin is provided, and the main principle is as follows:

[0081] Construct a dynamic model of the caudal fin propulsion system, and the dynamic model of the caudal fin propulsion system includes:

[0082] Torque of the caudal joint:

[0083] Force of the caudal joint: F 12 = ma - F l

[0084] Hydrodynamic force of the caudal fin: F l = L + D + F λ

[0085] Hydrodynamic torque of the caudal fin: M l = r m2 × (L + D) + M λ

[0086] Motion control equation of the caudal fin: A

[0087] Motion control equation of the vehicle body:

[0088] Among them, M 12 is the torque of the caudal joint, K and C are the stiffness and damping of the caudal joint respectively, β is the swing angle of the caudal fin relative to the caudal peduncle, F 12 is the force of the caudal joint, m is the mass of the caudal fin, and a is the translational acceleration of the center of mass of the caudal fin; F lFor the hydrodynamic force of the caudal fin, L is the lift force of the caudal fin, D is the drag force of the caudal fin, F λ is the added mass force of the caudal fin, M l is the hydrodynamic moment of the caudal fin, M λ is the moment caused by the added mass of the caudal fin, r m2 is the vector from the centroid of the caudal fin to the center of pressure, I is the moment of inertia of the caudal fin relative to the caudal joint, M a is the moment of the inertial force of the caudal fin acting at the position of the caudal joint, is the angular acceleration of the caudal fin, U is the navigation speed of the vehicle, T is the thrust of the caudal fin, ρ is the water density, Cx is the drag coefficient of the vehicle, S is the reference area of the drag coefficient of the vehicle, m0 is the mass of the vehicle;

[0089] According to the dynamic model of the caudal fin propulsion system, calculate the cruising speed of the vehicle and the propulsion efficiency of the caudal fin under different stiffness and damping conditions of the caudal joint, and select the combination of stiffness K and damping C parameters that meet the design requirements of the cruising speed and have the optimal propulsion efficiency, and output it as the elastic parameters of the bionic caudal fin.

[0090] As another aspect of the present invention, a method for designing the elastic parameters of a bionic caudal fin is provided, which includes a method for dynamically modeling the caudal fin propulsion system and a method for optimizing the design of the stiffness K and damping C parameters of the joint connecting the caudal fin and the caudal peduncle. The technical solution of the present invention will be described in detail below with a specific embodiment.

[0091] In this embodiment, the vehicle includes a torso and a caudal fin propulsion system. The caudal fin propulsion system is a two-joint caudal fin propulsion system, including a caudal fin and a caudal peduncle. The torso, caudal fin, and caudal peduncle are connected in sequence.

[0092] (1) A method for dynamically modeling the caudal fin propulsion system

[0093] For a caudal fin propulsion vehicle motion system, carry out dynamic modeling. The input parameters of the model include:

[0094] Length of the caudal peduncle: The distance from the axis of rotation of the caudal peduncle joint (i.e., the axis of rotation of the lumbar joint) to the axis of rotation of the caudal joint, L1;

[0095] Total length of the caudal fin: The axial distance from the caudal joint to the tip of the caudal fin, L2;

[0096] Amplitude of the caudal peduncle swing A T and frequency f;

[0097] Mass of the caudal fin: m;

[0098] Moment of inertia of the caudal fin relative to the centroid of the caudal fin: I z ;

[0099] Distance from the centroid of the caudal fin to the caudal joint: l;

[0100] Added mass matrix of planar motion for the centroid position of the caudal fin: [λ];

[0101] The mass of the vehicle m0, the drag coefficient of the vehicle Cx.

[0102] ① The motion speed of the caudal fin

[0103] As Figure 1 shown, in the two-joint caudal fin propulsion system, the caudal fin and the caudal peduncle can be simplified as two rigid bodies connected by a joint (hinge). The caudal peduncle swings around the lumbar joint at the end of the bionic fish trunk, and the swing angle is θ1; while the caudal fin swings around the caudal joint at the end of the caudal peduncle while moving with the caudal peduncle, and the swing angle of the caudal fin relative to the caudal peduncle is β. Among them, the swing law of the caudal peduncle is:

[0104] θ1 = A T sin(2πft)

[0105] where, A T is the swing amplitude of the caudal peduncle, and f is the frequency.

[0106] The decomposition relationship of the relative fluid motion speed of the caudal fin is as Figure 2 shown, and it can be simplified to a planar motion problem. For the convenience of calculating the angles between vectors, a complex plane is used here for representation. Taking the lumbar joint connecting the caudal peduncle and the trunk as the origin, the imaginary axis is in the Y direction, and the real axis is in the -X direction.

[0107] The rotation radii of the caudal peduncle and the caudal fin are respectively: R = L1, r = L2 / 2

[0108] The position vector of the end of the caudal peduncle is

[0109]

[0110] The swing speed of the end of the caudal peduncle is

[0111]

[0112] The position vector of the center of pressure of the caudal fin is

[0113]

[0114] where, θ2 = θ1 + β, θ2 represents the rotation angle of the caudal fin, θ1 is the swing angle of the caudal peduncle relative to the trunk, β is the swing angle of the caudal fin relative to the caudal peduncle, R is the rotation radius of the caudal peduncle, and r is the rotation radius of the caudal fin.

[0115] The speed of the center of pressure of the caudal fin relative to the end of the caudal peduncle is

[0116]

[0117] The resultant velocity vector of the center of pressure of the caudal fin is

[0118]

[0119] Among them, U is the navigation speed of the vehicle.

[0120] Let the relative fluid flow velocity of the caudal fin be Then

[0121]

[0122] Among them, u is the caudal fin velocity, is the angle between the caudal fin velocity and the horizontal plane, and ang() is the complex angle operator, indicating to solve the angle between the combined velocity of the center of pressure of the caudal fin and the horizontal plane.

[0123] The angle of attack of the caudal fin is

[0124]

[0125] ② Force analysis of the caudal fin

[0126] The external forces acting on the caudal fin include the caudal joint force and moment, and the hydrodynamic force and moment.

[0127] The moment of the caudal joint force is:

[0128]

[0129] Among them, K and C are the caudal joint stiffness and caudal joint damping respectively, and β is the relative swing angle of the caudal fin with respect to the caudal peduncle.

[0130] The caudal joint force is F 12 , with unknown magnitude and direction, and the acting point is the position of the caudal joint.

[0131] According to D'Alembert's principle, list the force balance equation of the center of mass of the caudal fin:

[0132] [[ID=4 7]]F 12 +F l -ma = 0 (9)

[0133] It can be obtained that

[0134] F 12 = ma - F l (10)

[0135] The hydrodynamic force of the caudal fin:

[0136] F l = L + D + F λ (11)

[0137] Among them, L is the lift of the caudal fin, D is the drag of the caudal fin, F λ is the added mass force of the caudal fin, m is the mass of the caudal fin, a is the translational acceleration of the center of mass of the caudal fin, and F l is the hydrodynamic force of the caudal fin.

[0138] Hydrodynamic moment of the caudal fin:

[0139] M l = r m2 ×(L + D)+M λ (12)

[0140] Wherein, M l is the hydrodynamic moment of the caudal fin, M λ is the moment caused by the added mass of the caudal fin, r m2 is the vector from the centroid of the caudal fin to the center of pressure, s m is the position vector of the centroid of the caudal fin, s2 is the position vector of the center of pressure of the caudal fin, l is the distance from the centroid of the caudal fin to the tail joint, r is the rotation radius of the caudal fin, and R is the rotation radius of the caudal peduncle.

[0141] The acting direction of the lift L of the caudal fin is perpendicular to the relative oncoming flow velocity, and the acting direction of the drag D of the caudal fin is the same as the relative oncoming flow velocity. The calculation methods are as follows:

[0142]

[0143] C L = C1α + C2α 2

[0144] C D = C3 + C4α + C5α 2

[0145] Wherein, A is the reference area of the caudal fin, which is taken as the product of the chord length and the span of the caudal fin; ρ is the water density; C L 、C D are the lift coefficient and drag coefficient of the caudal fin respectively, α is the angle of attack of the caudal fin, and C1, C2, C3, C4, and C5 are constants, which are obtained by fitting the curves of the lift and drag coefficients of the caudal fin varying with the angle of attack α. The curves of the lift and drag coefficients of the caudal fin varying with the angle of attack α can be obtained through numerical simulation. The acting points of the lift and drag of the caudal fin are defined at the motion reference point of the caudal fin (i.e., the center of pressure of the caudal fin) r = L2 / 2.

[0146] The calculation of the added mass force of the caudal fin requires the vector conversion between the ground system s and the caudal fin body-fixed system s'. The conversion formula is:

[0147]

[0148] According to the geometric relationship and the angular acceleration of the caudal fin in the ground system the translational acceleration a of the centroid of the caudal fin can be obtained as:

[0149]

[0150] Among them, a1 and a2 are the acceleration of the tail joint and the acceleration of the center of mass of the tail fin relative to the tail joint respectively, and θ1 is the swing angle of the tail stock relative to the trunk. is the angular velocity of the tail stock relative to the trunk swing. is the angular acceleration of the tail stock relative to the trunk swing. θ2 represents the rotation angle of the tail fin. is the angular velocity of the tail fin. is the angular acceleration of the tail fin. R is the rotation radius of the tail stock, l is the distance from the center of mass of the tail fin to the tail joint, and U is the navigation speed of the vehicle.

[0151] The translational acceleration a of the center of mass of the tail fin is transformed into the body-fixed system:

[0152]

[0153] Among them, a′ is the translational acceleration of the center of mass of the tail fin in the body-fixed system, a′ x and a′ y are the axial component and the normal component of a′ respectively.

[0154] The added mass force F′ of the tail fin in the body-fixed system λ is:

[0155]

[0156] Among them, real(F′ λ ), imag(F′ λ ) are the axial component and the normal component of the added mass force of the tail fin in the body-fixed system respectively. M λ is the moment caused by the added mass of the tail fin. is the angular acceleration of the tail fin in the ground-fixed system. [λ] is the added mass matrix of the planar motion of the center of mass position of the tail fin. represents the added mass corresponding to the force in the j1 direction divided by the acceleration in the j2 direction; j1 takes values of 1, 2, 6, and 1, 2, 6 correspond to the X-axis, Y-axis, and the rotation direction around the Z-axis respectively; j2 takes values of 1, 2, 6, and 1, 2, 6 correspond to the X-axis, Y-axis, and the rotation direction around the Z-axis respectively; the Z-axis satisfies the right-hand rule with the X-axis and Y-axis.

[0157] Considering the symmetry of the geometric model of the tail fin, λ 12 and λ 16 in the added mass matrix [λ] of the planar motion are zero. The actual added mass force of the tail fin in the body-fixed system is:

[0158] real(F′ λ ) = -λ 11 a′ x (19)

[0159]

[0160] When the added mass force of the caudal fin in the body-fixed system is transformed to the ground-fixed system, the added mass force F of the caudal fin is obtained. λ :

[0161]

[0162] Among them, F′ λ is the added mass force of the caudal fin in the body-fixed system, real(F′ λ ), imag(F′ λ ) are the axial component and the normal component of the added mass force of the caudal fin in the body-fixed system respectively. is the angular acceleration of the caudal fin, a′ x , a′ y are the axial component and the normal component of the translational acceleration of the center of mass of the caudal fin in the body-fixed system of the caudal fin respectively.

[0163] ③ Solution of the angular acceleration of the caudal fin

[0164] Taking the tail joint as the origin, a non-inertial reference frame is established, the x1 axis is parallel to the real axis, and the y1 is parallel to the imaginary axis, as Figure 3 shown. Then the transport acceleration of the caudal fin in the non-inertial reference frame is:

[0165]

[0166] Therefore, the inertial force acting on the center of mass of the caudal fin is:

[0167] F a =-ma1 (24)

[0168] The motion control equation of the caudal fin:

[0169]

[0170] Among them, I=I z +ml 2 , I is the moment of inertia of the caudal fin relative to the tail joint, I z is the moment of inertia of the caudal fin relative to the center of mass of the caudal fin, M a is the moment of the inertial force of the caudal fin acting at the position of the tail joint, M 12 is the moment of the force of the tail joint, M l is the hydrodynamic moment of the caudal fin.

[0171] The moment of the inertial force of the caudal fin acting at the position of the tail joint is

[0172] M a =r 1m ×F a (26)

[0173] Among them, is the vector from the tail joint to the center of mass of the caudal fin, l is the distance from the center of mass of the caudal fin to the tail joint, F ais the inertial force acting on the center of mass of the tail fin.

[0174] The hydrodynamic moment of the tail fin is:

[0175]

[0176] Among them, a′ 1x ,a′ 1y is the axial component and normal component of the tail joint translation acceleration in the tail fin system, is the corresponding item of the additional mass matrix of the tail fin relative to the tail joint in water. For the rigid body tail fin model, it can be obtained by converting the additional mass matrix of the tail fin center of mass:

[0177]

[0178] Substitute into the tail fin motion control equation (25), and replace Move the term to the left of the equal sign:

[0179]

[0180] Due to r m1 =-r 1m , r 1m is the vector from the tail joint to the center of mass of the tail fin, r m1 is the vector from the center of mass of the tail fin to the tail joint, that is:

[0181]

[0182] Among them, M 12 is the tail joint torque, r 12 is the vector from the tail joint to the tail fin pressure center, L is the tail fin lift, D is the tail fin drag, r m1 is the vector from the center of mass of the tail fin to the tail joint, a1 is the acceleration of the tail joint, a′ 1y is the imaginary part of a1 converted to the follower system (normal component of tail joint acceleration in the tail fin follower system), I z is the moment of inertia of the caudal fin relative to the center of mass of the caudal fin, l is the distance from the center of mass of the caudal fin to the tail joint, and m is the mass of the caudal fin.

[0183] The control equations of the vehicle motion are:

[0184]

[0185] Where U is the vehicle speed, T is the tail fin thrust (the real part of the sum of the tail fin lift and drag), ρ is the water density, Cx is the drag coefficient, and S is the reference area of the vehicle drag coefficient.

[0186] The unknown quantities such as force, moment and acceleration in Formula (25) and Formula (31) can all be expressed by θ2 and U and their first-order derivatives. By carrying out calculations through two control equations, the numerical solutions of θ2 and U can be obtained.

[0187] (2) A method for optimizing the design of the stiffness K and damping C parameters of the tail joint

[0188] The optimization criteria for the elastic parameters (stiffness K and damping C) of the tail joint are mainly the tail fin propulsion efficiency. The tail fin propulsion efficiency is generally defined as the ratio of the work power of the tail fin thrust to the output power of the pure drive of the tail fin by the lumbar joint. The specific calculation is as follows:

[0189] According to the dynamic model of the tail fin propulsion system, the force exerted on the tail joint by the tail fin is calculated:

[0190] F 21 =-F 12 (32)

[0191] And the moment of the force exerted on the tail joint by the tail fin:

[0192] M 21 =-M 12 (33)

[0193] Thus, the driving moment of the lumbar joint (the connection between the tail stock and the trunk) can be calculated:

[0194] M 01 =M 21 +s1×F 21 (34)

[0195] Among them, s1 is the position vector of the end of the tail stock;

[0196] The driving power of the lumbar joint:

[0197]

[0198] The work power of the tail fin thrust:

[0199] P T =TU (36)

[0200] The tail fin propulsion efficiency:

[0201]

[0202] Based on the established dynamic model of the bionic tail fin propulsion system and the calculation method of the tail fin propulsion efficiency, numerical calculations are carried out to obtain the cruising speed and propulsion efficiency of the bionic tail fin propulsion vehicle under different elastic stiffness K and damping C conditions of the tail fin joint. The distribution cloud diagrams of the cruising speed and propulsion efficiency in the stiffness K and damping C parameter space are drawn. According to the distribution cloud diagrams, the combination of stiffness K and damping C parameters that meets the design requirements of the cruising speed and has the optimal propulsion efficiency is selected.

[0203] It should be noted that the cruising speed of the caudal fin vehicle in the present invention refers to the cruising speed of the vehicle in a stable state.

[0204] According to the bionic caudal fin elastic parameter design method provided by the present invention, the following process is carried out in practical applications:

[0205] Step 1: Obtain input parameters. According to the actual situation of the designed caudal fin propulsion vehicle, obtain the input parameters of the dynamic model of the two-joint caudal fin propulsion vehicle, including:

[0206] Caudal peduncle length: the distance from the caudal peduncle rotation axis to the caudal joint, L1;

[0207] Total caudal fin length: the axial distance from the caudal joint to the caudal fin tip, L2;

[0208] Amplitude A of caudal peduncle swing T and frequency f;

[0209] Caudal fin mass: m;

[0210] Moment of inertia of the caudal fin relative to the center of mass of the caudal fin: I z ;

[0211] Distance from the center of mass of the caudal fin to the caudal joint: l;

[0212] Plane motion added mass matrix of the caudal fin relative to the reference point of the center of mass position in water: [λ];

[0213] Mass m0 of the vehicle and drag coefficient Cx of the vehicle;

[0214] Step 2: Establish a dynamic model of the two-joint caudal fin propulsion system, calculate the cruising speed and propulsion efficiency under different conditions of caudal fin joint elastic stiffness K and damping C, and draw the distribution cloud diagram of the cruising speed in the (K, C) parameter space and the distribution cloud diagram of the propulsion efficiency in the (K, C) parameter space.

[0215] Step 3: According to the designed cruising speed index requirements and combined with the cruising speed distribution diagram, obtain the value range of the K, C combination that meets the index requirements; and then, according to the propulsion efficiency distribution diagram, select the K, C parameter combination with the optimal efficiency within the value range.

[0216] According to the parameters of the caudal fin propulsion vehicle, the present invention establishes a dynamic model of the bionic caudal fin propulsion system, realizes the design of the optimal efficiency combination of the caudal fin joint elastic stiffness K and damping C parameters, with a simple method, easy to operate, and improves the design efficiency.

[0217] Features described and / or illustrated above for one embodiment can be used in the same or similar manner in one or more other embodiments, and / or combined with or replace features in other embodiments.

[0218] It should be emphasized that the term "comprising / including" as used herein refers to the presence of features, wholes, steps or components, but does not exclude the presence or addition of one or more other features, wholes, steps, components or combinations thereof.

[0219] Many features and advantages of these embodiments are apparent from this detailed description, and thus the appended claims are intended to cover all such features and advantages of these embodiments that fall within their true spirit and scope. Further, since many modifications and changes are readily envisioned by those skilled in the art, the embodiments of the present invention are not to be limited to the exact structures and operations illustrated and described, but may cover all suitable modifications and equivalents that fall within their scope.

[0220] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, various changes and modifications can be made to the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0221] The parts not detailed in the present invention are well-known techniques to those skilled in the art.

Claims

1. A method for designing the elastic parameters of a bionic caudal fin, characterized in that, It includes the following steps: Construct a dynamic model of the caudal fin propulsion system, and the dynamic model of the caudal fin propulsion system includes: Tail joint acting moment: Tail joint force: F 12 = ma - F l Tail fin hydrodynamic force: F l = L + D + F λ Tail fin hydrodynamic moment: M l = r m2 × (L + D) + M λ Tail fin motion control equation: Navigation body motion control equation: Among them, M 12 is the torque of the tail joint, K and C are the stiffness and damping of the tail joint respectively, β is the swing angle of the caudal fin relative to the caudal peduncle, F 12 is the force acting on the tail joint, m is the mass of the caudal fin, a is the translational acceleration of the center of mass of the caudal fin; F l is the hydrodynamic force of the caudal fin, L is the lift of the caudal fin, D is the drag of the caudal fin, F λ is the added mass force of the caudal fin, M l is the hydrodynamic torque of the caudal fin, M λ is the torque caused by the added mass of the caudal fin, r m2 is the vector from the center of mass of the caudal fin to the center of pressure, I is the moment of inertia of the caudal fin relative to the tail joint, M a is the torque of the inertial force of the caudal fin acting at the position of the tail joint, is the angular acceleration of the caudal fin, U is the navigation speed of the vehicle, T is the thrust of the caudal fin, ρ is the water density, Cx is the drag coefficient of the vehicle, S is the reference area of the drag coefficient of the vehicle, m0 is the mass of the vehicle; According to the dynamic model of the caudal fin propulsion system, calculate the cruising speed and caudal fin propulsion efficiency of the vehicle under different caudal joint stiffness and damping conditions, select the stiffness K and damping C parameter combination that meets the design requirements of the cruising speed and has the optimal propulsion efficiency, and output it as the elastic parameters of the bionic caudal fin.

2. The method according to claim 1, characterized in that, The calculation method of the caudal fin propulsion efficiency includes the following steps: Obtain the force exerted by the caudal fin on the caudal joint and the torque of the caudal fin on the caudal joint according to the dynamic model of the caudal fin propulsion system; Calculate the driving torque of the lumbar joint, and then calculate the driving power of the lumbar joint; Calculate the work done by the caudal fin thrust; Calculate the ratio of the work done by the caudal fin thrust to the driving power of the lumbar joint to obtain the caudal fin propulsion efficiency.

3. The method according to claim 2, wherein The force exerted by the caudal fin on the caudal joint and the torque of the caudal fin on the caudal joint are respectively: F 21 = -F 12 M 21 = -M 12 Among them, F 12 is the force acting on the tail joint, and M 12 is the torque of the force acting on the tail joint; The driving torque of the lumbar joint is: M 01 = M 21 + s1 × F 21 Where s1 is the position vector of the end of the caudal peduncle; The driving power of the lumbar joint is: Among them, is the angular velocity of the tail handle relative to the trunk swing; The work done by the caudal fin thrust is: P T = TU Where U is the cruising speed of the vehicle and T is the caudal fin thrust.

4. The method according to claim 1, wherein The calculation method of the caudal fin hydrodynamic force is as follows: Calculate the caudal fin speed: where u is the caudal fin velocity, is the angle between the caudal fin velocity and the horizontal plane, ang() is the complex angle operator, and v is the resultant velocity vector of the center of pressure of the caudal fin; Calculate the caudal fin lift and caudal fin drag: where A is the reference area of the caudal fin, ρ is the water density, C L and C D are the lift coefficient and drag coefficient of the caudal fin, respectively; Calculate the added mass force of the caudal fin: real(F λ ′) = -λ 11 a x ′ Among them, F’ λ is the added mass force of the caudal fin in the body-fixed system, real(F λ ′) and imag(F λ ′) are the axial component and the normal component of the added mass force of the caudal fin in the body-fixed system respectively, is the angular acceleration of the caudal fin, represents the added mass corresponding to the force in the j1 direction divided by the acceleration in the j2 direction. The values of j1 and j2 are 1, 2, and 6. The subscript values of 1, 2, and 6 correspond to the X-axis, Y-axis, and the rotation direction about the Z-axis respectively; a′ x and a′ y are the axial separation and the normal component of the translational acceleration of the center of mass of the caudal fin in the body-fixed system of the caudal fin respectively. The hydrodynamic force F of the caudal fin is obtained by summing the caudal fin lift force, the caudal fin drag force, and the caudal fin added mass force. l .

5. The method according to claim 4, wherein The moment M caused by the added mass of the caudal fin λ is as follows: Among them, is the angular acceleration of the caudal fin, represents the added mass corresponding to the force in the j1 direction divided by the acceleration in the j2 direction, where j1 and j2 take values of 1, 2, and 6. The subscript takes values of 1, 2, and 6 corresponding to the X-axis, Y-axis, and the rotation direction about the Z-axis respectively; a′ x and a′ y are the axial separation and normal components of the translational acceleration of the caudal fin centroid in the caudal fin follow-up system respectively.

6. The method according to claim 4, wherein The calculation method of the combined velocity of the caudal fin center of pressure is as follows: Where θ2 represents the caudal fin rotation angle, θ1 is the swing angle of the caudal peduncle relative to the trunk, β = θ2 - θ1, β is the swing angle of the caudal fin relative to the caudal peduncle, R is the rotation radius of the caudal peduncle, r is the rotation radius of the caudal fin, and U is the cruising speed of the vehicle; θ1 = A T sin(2πft) Among them, A T is the swing amplitude of the tail handle, and f is the frequency.

7. The method according to claim 1, characterized in that, The calculation method of the translational acceleration of the caudal fin center of mass is as follows: a = a1 + a2 where a1 and a2 are the acceleration of the tail joint and the acceleration of the center of mass of the caudal fin relative to the tail joint respectively, and θ1 is the swing angle of the caudal peduncle relative to the trunk, is the angular velocity of the caudal peduncle relative to the trunk, is the angular acceleration of the caudal peduncle relative to the trunk, θ2 represents the rotation angle of the caudal fin, is the angular velocity of the caudal fin, is the angular acceleration of the caudal fin, R is the rotation radius of the caudal peduncle, l is the distance from the center of mass of the caudal fin to the tail joint, and U is the navigation speed of the vehicle.

8. The method according to claim 7, wherein The angular velocity of the caudal fin The calculation method is as follows: Among them, M 12 is the torque of the caudal joint, r 12 is the vector from the caudal joint to the center of pressure of the caudal fin, L is the lift of the caudal fin, D is the drag of the caudal fin, r m1 is the vector from the center of mass of the caudal fin to the caudal joint, a1 is the acceleration of the caudal joint, a1′ y is the normal component of a1 transformed to the body-fixed system, I z is the moment of inertia of the caudal fin relative to the center of mass of the caudal fin, l is the distance from the center of mass of the caudal fin to the caudal joint, and m is the mass of the caudal fin.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, wherein when the computer program is executed by a processor, the method described in any one of claims 1 to 8 is implemented.

10. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that The processor executes the computer program to implement the method described in any one of claims 1 to 8.

Images