A Modeling Method for a Six-Degree-of-Freedom ROV Hydrodynamic Model Considering Fluid Memory Effects

Abstract

The present invention discloses a six-degree-of-freedom ROV hydrodynamic model and a modeling method considering the fluid memory effect. The method includes five steps: Step 1 is to establish a steady-state hydrodynamic model of the ROV and calculate the inertial and viscous hydrodynamic coefficients of the ROV; Step 2 is to establish an unsteady viscous hydrodynamic model; Step 3 is to calculate the frequency-domain response of the hydrodynamic memory effect and perform a frequency-domain transformation on the unsteady viscous hydrodynamic model; Step 4 is to calculate the time-domain response of the hydrodynamic memory effect; Step 5 is to establish a six-degree-of-freedom ROV hydrodynamic model. This method establishes a six-degree-of-freedom ROV hydrodynamic model through impulse motion response experiments, and can not only calculate the hydrodynamic force that changes with time and is affected by the instantaneous motion of the ROV, but also calculate the influence of the motion history of the ROV on the current hydrodynamic force, and is applicable to the hydrodynamic force of the ROV during continuous motion in both positive and negative directions of six degrees of freedom.

Description

Technical Field

[0001] The present invention relates to a modeling method for a six-degree-of-freedom ROV hydrodynamic model considering fluid memory effect, belonging to the field of ships. Background Art

[0002] Among underwater robots, the work-class remotely operated vehicle (ROV) with a cable is mainly used for (offshore engineering installation operations) to support drilling operations and is applied to the whole process from the first drilling to the completion of the well. During drilling operations, the ROV will complete operations such as observing the seabed environment, installing well pipe seals, guides, guiding tools, and auxiliary drilling equipment into the well. In underwater structure installation and disassembly operations, ROVs are commonly used to set up or assemble subsea structures, including setting or pulling rigging, assisting in the towing and positioning of large underwater structures, moving heavy pieces, laying and burying cables and pipelines, and assisting in the installation of mattress mats. The ROV is one of the important tools in ocean resource development and exploration, and underwater structure installation and maintenance operations. With the development of deep-sea oil and gas, the demand for underwater structure installation, maintenance, and disassembly operations in deep-water areas is gradually increasing, and the role played by the work-class ROV in offshore operations is becoming increasingly important. Therefore, researching the dynamics of ROV operations and inventing a six-degree-of-freedom ROV hydrodynamic model and modeling method considering fluid memory effect have important engineering significance for improving offshore operation safety and enhancing operation efficiency, etc.

[0003] When a rigid body moves stably in water, it is usually assumed that the hydrodynamic forces and moments are uniquely determined by the perturbations of the steady motion at that moment. Based on this assumption, the "quasi-steady flow" hydrodynamic derivatives are defined, and the motion is described using constant-coefficient linear or nonlinear equations. This method is widely used in the research of the motion, stability, and control of floating bodies and underwater robots, etc., but there are defects in dealing with the ROV hydrodynamic forces because the shape of the ROV is more complex than that of ships and submarines, it has more degrees of freedom of motion, and it will not always be in a steady motion state during underwater operations. In the unsteady motion of the ROV, the hydrodynamic forces include the added mass forces related to acceleration, the resistance related to the wake, and the influence of viscosity. When the ROV is sailing in deep water, there are complex flows, positive and negative vortices, and a mixture of flows on the stern and the wake of the ROV. The intensity of these flows and their influence on the hydrodynamic forces increase with the increase of the Reynolds number. Therefore, the hydrodynamic forces of the ROV in deep water are related to the past history of the motion, and there is a "memory effect" in the hydrodynamic forces. Based on linear theory and functional analysis, a hydrodynamic model of a ship considering the memory effect can be established, but this method cannot describe the ROV hydrodynamic forces with the characteristics of nonlinearity, asymmetry, and coupling. Therefore, inventing a six-degree-of-freedom ROV hydrodynamic model and modeling method considering fluid memory effect has important academic value.

[0004] The existing ROV hydrodynamic models have the following deficiencies:

[0005] 1. Although a six-degree-of-freedom dynamic model of the ROV has been established, the memory effect of the fluid cannot be considered. Existing ROV hydrodynamic models can calculate the changes in hydrodynamic forces over time and motion, but they cannot calculate the lag effect of the motion history on the magnitude and phase of the hydrodynamic forces.

[0006] 2. In existing ROV hydrodynamic models, the asymmetry and non-linearity of the ROV hydrodynamic forces are only manifested as unequal hydrodynamic coefficients in different motion directions, and the effects of the motion history and fluid memory effect on the asymmetry and non-linearity of the ROV hydrodynamic forces cannot be expressed. Summary of the Invention

[0007] Object of the Invention: To overcome the deficiencies in the prior art, the present invention provides a method for modeling a six-degree-of-freedom ROV hydrodynamic model considering the fluid memory effect, which can consider the influence of the motion history, consider the changes in the amplitude and phase of the hydrodynamic forces caused by the fluid memory effect, and can also calculate the fluid memory effect affected by the motion history during the process of the ROV changing its course.

[0008] Technical Solution: To solve the above technical problems, a six-degree-of-freedom ROV hydrodynamic model and modeling method considering the fluid memory effect of the present invention, the hydrodynamic model comprises five steps, namely: establishing a steady-state hydrodynamic model of the ROV, establishing an unsteady hydrodynamic model of the ROV, calculating the frequency-domain and time-domain responses of the hydrodynamic memory effect, and establishing a six-degree-of-freedom ROV hydrodynamic model.

[0009] For the establishment of the steady-state hydrodynamic model of the ROV, a body-fixed coordinate system and a fixed coordinate system of the ROV are established, and the inertial and viscous hydrodynamic coefficients of the ROV are measured through a conventional submarine plane motion mechanism experiment, wherein the viscous hydrodynamic coefficients are divided into coefficients in the positive and negative two motion directions of each degree of freedom in the body-fixed coordinate system.

[0010] For the establishment of the unsteady hydrodynamic model of the ROV, according to the law that the hydrodynamic force is proportional to the square of the velocity, based on the relationship between the system impulse and the response, an unsteady hydrodynamic model related to the ROV motion trajectory, hydrodynamic coefficients and velocity is established.

[0011] For the frequency-domain response of the hydrodynamic memory effect, the unsteady hydrodynamic model is subjected to a frequency-domain transformation, and the frequency-domain response of the hydrodynamic memory effect is calculated based on the ROV viscous hydrodynamic force affected by the fluid memory effect obtained in the impulse motion response experiment.

[0012] The impulse motion response experiment measures the hydrodynamic force of the ROV by using the method of a single-degree-of-freedom oscillating ROV in a steady flow, and combines the inertial hydrodynamic coefficient calculated from the added mass and viscous hydrodynamic coefficient to measure the unsteady viscous hydrodynamic force of the ROV affected by the fluid memory effect.

[0013] The time-domain response of the hydrodynamic memory effect is subjected to a quasi-frequency domain transformation of the frequency-domain response of the hydrodynamic memory effect to obtain the time-domain response of the hydrodynamic memory effect of a single-degree-of-freedom.

[0014] The six-degree-of-freedom ROV hydrodynamic model is established. Based on the time-domain response of the hydrodynamic memory effect, a time-domain response model of the hydrodynamic memory effect considering the turning-back motion and hydrodynamic asymmetry is established, and a six-degree-of-freedom ROV hydrodynamic model considering the fluid memory effect is established.

[0015] A six-degree-of-freedom ROV hydrodynamic model and a modeling method considering the fluid memory effect of the present invention include the following steps:

[0016] Step 1: Establish the ROV steady hydrodynamic model

[0017] 1. Establish the ROV coordinate system

[0018] Define the fixed coordinate system O-x 0 y 0 z 0 and the body coordinate system G-xyz. Both of these coordinate systems are right-handed coordinate systems. The origin O is fixed at a point on the earth, and the Oz 0 axis is along the direction of gravity, the Ox 0 points north, and the Oy 0 points east. The origin G is fixed at the center of gravity of the ROV. The Gx and Gy axes point to the head and starboard of the ROV model respectively. Define the surge, sway, heave velocities (u, v, w) and the roll, pitch, and yaw angular velocities (p, q, r) in the body coordinate system; define the surge, sway, heave accelerations and the roll, pitch, and yaw angular velocities The density ρ of water, the length L of the ROV, and the gravitational acceleration g.

[0019] 2. Establish the steady hydrodynamic model

[0020]

[0021] where F ST represents the hydrodynamic force of the ROV, is the inertial hydrodynamic coefficient for surge motion, is the inertial hydrodynamic coefficient for sway motion, is the inertial hydrodynamic coefficient for heave motion, is the inertial hydrodynamic coefficient for roll motion, is the inertial hydrodynamic coefficient for pitch motion, is the inertial hydrodynamic coefficient for yaw motion. The longitudinal viscous hydrodynamic coefficient includes the positive-direction coefficient and the negative-direction coefficient The transverse viscous hydrodynamic coefficient including positive direction coefficients and negative direction coefficients vertical viscous hydrodynamic coefficients including positive direction coefficients and negative direction coefficients roll viscous hydrodynamic coefficients including positive direction coefficients and negative direction coefficients pitch viscous hydrodynamic coefficients including positive direction coefficients and negative direction coefficients yaw viscous hydrodynamic coefficients including positive direction coefficients and negative direction coefficients Measure the inertial and viscous hydrodynamic coefficients of the ROV through the existing conventional underwater vehicle planar motion mechanism experiment. The viscous hydrodynamic coefficients are divided into coefficients in the positive and negative motion directions of each degree of freedom in the body coordinate system.

[0022] Step 2: Establish the unsteady viscous hydrodynamic model of the ROV

[0023] 1. Impulse motion response experiment

[0024] The impulse motion response experiment aims to measure the non-linear hydrodynamic forces with memory effects. To generate non-linear hydrodynamic forces, a relatively large velocity relative to the flow rate is required. The impulse motion response experiment described in the present invention uses a small-amplitude vibration table to meet the requirements for the appearance of non-linear hydrodynamic forces through a relatively high convective relative velocity. In the present invention, the ROV oscillates along the water flow direction. If measuring the forces in the opposite direction, the ROV needs to be rotated 180 degrees and reinstalled. In the impulse motion response experiment, the relative velocity with the flow is used as the velocity of the ROV. The motion equation of the ROV in the body coordinate system is: for forward motion, the longitudinal velocity u = Uc + aωcos(ωt), the transverse velocity v = Uc + aωcos(ωt), the vertical velocity w = Uc + aωcos(ωt), and the roll, pitch, and yaw velocities are the same as the roll, pure pitch, and pure yaw motions in the underwater vehicle planar motion mechanism experiment; for backward motion, the longitudinal velocity u = -Uc - aωcos(ωt), the transverse velocity v = -Uc - aωcos(ωt), the vertical velocity w = -Uc - aωcos(ωt), and the roll, pitch, and yaw velocities are the same as the roll, pure pitch, and pure yaw motions in the ship planar motion mechanism experiment, but the longitudinal motion of the ROV is -Uc. Wherein, Uc is the flow velocity in the body coordinate system, a is the motion amplitude, ω is the motion frequency, t is the time, the forward and backward motions indicate that each translational degree of freedom moves along the positive and negative directions of its body coordinate respectively, and in the rotational degrees of freedom, the forward and backward motions indicate that the ROV moves along the positive and negative directions of the body coordinate longitudinally respectively.

[0025] 2. ROV Viscous Hydrodynamic Model Affected by Fluid Memory Effect

[0026] ROV Viscous Hydrodynamic Model:

[0027]

[0028] Where F 2 is the ROV viscous hydrodynamic force affected by the fluid memory effect, including the longitudinal force X 2 , the lateral force Y 2 , the vertical force Z 2 , the rolling moment K 2 , the pitching moment M 2 , and the yawing moment N 2 , and F DY is the non - linear hydrodynamic force with memory effect measured by the impulse motion response experiment.

[0029] Considering the growth process of the ROV from rest to uniform motion at a speed U in a certain direction, the impulse motion starts from the origin of the fixed coordinate system. At this time, the non - dimensional displacement of the ROV where U is the speed of any one of the six degrees of freedom, and t is the time. In the time interval (τ 0 , τ 0 + dτ 0 ), the increment of the resultant motion velocity is where τ 0 is the starting non - dimensional displacement of any interval, dτ 0 represents the increment of the non - dimensional displacement in this interval, and dU represents the increment of the speed in this interval. When dτ 0 is small enough, the motion of the ROV can be considered a step motion. The increment of the unsteady viscous hydrodynamic force F 2i (where i = X, Y, Z, K, M, N, representing the longitudinal force X 2 , the lateral force Y 2 , the vertical force Z 2 , the rolling moment K 2 , the pitching moment M 2 , and the yawing moment N 2 ) is expressed as:

[0030]

[0031] where dF 2i is the increment of the unsteady viscous hydrodynamic force, and F′ UUi is the viscous hydrodynamic coefficient (where i = X, Y, Z, K, M, N, representing the longitudinal viscous hydrodynamic coefficient including the positive - direction coefficient and the negative - direction coefficient the lateral viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the vertical viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the roll viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the pitch viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the yaw viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient ), Φ i is the response function (where i = X, Y, Z, K, M, N, representing the longitudinal force response function Φ X , the lateral force response function Φ Y , the vertical force response function Φ Z , the roll moment response function Φ K , the pitch moment response function Φ M , the yaw moment response function Φ N ). According to the superposition principle and the Duhamet integral, the function F 2i (τ) of the unsteady viscous hydrodynamic force per unit time interval with respect to the dimensionless displacement for any time history can be obtained:

[0032]

[0033] If τ = 0 when the ROV motion starts, the unsteady viscous hydrodynamic model is simplified to:

[0034]

[0035] where U 0 is the initial velocity of the ROV. If the initial velocity of the ROV is 0 when τ < 0, the unsteady viscous hydrodynamic model is simplified to:

[0036] where i = X, Y, Z, K, M, N.

[0037] Step 3: Calculate the frequency domain response of the hydrodynamic memory effect

[0038] Define the dimensionless frequency Then all the aωcos(ωt) terms of the motion velocities in Step 2 become aωe jkτ . Taking the positive direction surge motion as an example, u = U C + aωe jkτ . When the small perturbation ε approaches 0, there is a limit:

[0039]

[0040] where \(j\) represents a complex number, \(\varPhi\) 1 is the longitudinal hydrodynamic response function, \(C\) X is the Theodorsen function of the longitudinal hydrodynamic force, \(A\) X is the amplitude of the Theodorsen function, is the argument of the Theodorsen function, \(F\) X is the real part of the Theodorsen function, \(G\) X is the imaginary part of the Theodorsen function. The Fourier transform of the above equation is:

[0041]

[0042] Substitute Equation (2) into Equation (1), considering and taking the real part:

[0043]

[0044] Use the above equation to fit the longitudinal viscous hydrodynamic force with memory effect measured in the impulse motion response experiment, and obtain the first-order coefficient \(A\) X1 , the second-order coefficient \(A\) X2 , the first-order phase the second-order phase

[0045] Considering then the frequency-domain response of the longitudinal hydrodynamic memory effect is The frequency-domain responses of other degrees of freedom are the same as that of the longitudinal force memory effect. For other translational motions:

[0046]

[0047]

[0048] where the first-order coefficient \(A\) Y1 , the second-order coefficient \(A\) Y2 , the first-order phase the second-order phase These four parameters are obtained by fitting the lateral viscous hydrodynamic force with memory effect measured in the impulse motion response experiment. The first-order coefficient \(A\) Z1 , the second-order coefficient \(A\) Z2 , the first-order phase the second-order phase These four parameters are obtained by fitting the vertical viscous hydrodynamic force with memory effect measured in the impulse motion response experiment. The frequency-domain response of the lateral hydrodynamic memory effect is The frequency-domain response of the vertical hydrodynamic memory effect is

[0049] For the rolling, pitching and yawing motions, the increment of the combined velocity within the time interval (τ 0 , τ 0 +dτ 0 ) in the above method is Fitting equation:

[0050]

[0051]

[0052]

[0053] where p 0 is the amplitude of the rolling angular velocity, the first-order coefficient A K1 and the first-order phase are obtained by fitting the rolling viscous hydrodynamic force with memory effect measured by the impulse motion response experiment. q 0 is the amplitude of the rolling angular velocity, the first-order coefficient A M1 and the first-order phase are obtained by fitting the pitching viscous hydrodynamic force with memory effect measured by the impulse motion response experiment. r 0 is the amplitude of the rolling angular velocity, the first-order coefficient A N1 and the first-order phase are obtained by fitting the yawing viscous hydrodynamic force with memory effect measured by the impulse motion response experiment. The frequency-domain response of the rolling hydrodynamic memory effect is The frequency-domain response of the pitching hydrodynamic memory effect is The frequency-domain response of the yawing hydrodynamic memory effect is

[0054] Step 4: Calculate the time-domain response of the hydrodynamic memory effect

[0055] Based on the hydrodynamic results of the impulse motion response experiment, calculate the frequency-domain response of the hydrodynamic memory effect at each motion frequency, and fit the frequency-domain response of the hydrodynamic memory effect by the least squares method to calculate the time-domain response of the hydrodynamic memory effect. Taking the longitudinal force as an example, the inverse Fourier transform of Equation (3) is:

[0056]

[0057] The time-domain responses of other hydrodynamic memory effects are:

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] Step Five: Establish a six-degree-of-freedom ROV hydrodynamic model

[0064] Nonlinear hydrodynamic force with memory effect:

[0065]

[0066] where is the dimensionless displacement of longitudinal motion, dimensionless displacement of lateral motion, dimensionless displacement of vertical motion, dimensionless displacement of rolling motion, dimensionless displacement of pitching motion, dimensionless displacement of yawing motion, and d is the increment. The above formula needs to satisfy the following conditions:

[0067]

[0068]

[0069] where is the longitudinal force response function for forward motion, is the lateral force response function for forward motion, is the vertical force response function for forward motion, is the rolling moment response function for forward motion, is the pitching moment response function for forward motion, is the yawing moment response function for forward motion, is the longitudinal force response function for reverse motion, is the lateral force response function for reverse motion, is the vertical force response function for reverse motion, is the rolling moment response function for reverse motion, is the pitching moment response function for reverse motion, is the yawing moment response function for reverse motion. The positive and negative directions are defined in the body coordinate system.

[0070] Beneficial effects: The advantages compared with the prior art are:

[0071] 1. The hydrodynamic forces calculated by the six-degree-of-freedom ROV hydrodynamic model of the present invention not only vary with time and are affected by the instantaneous motion of the ROV, but also can calculate the influence of the ROV's motion history on the current hydrodynamic forces. Compared with the hydrodynamic models widely used in the ship field, the hydrodynamic model of the present invention calculates the amplitude and phase of the hydrodynamic forces under the periodic motion of the ROV more accurately, and the non-linear expression of the hydrodynamic forces is more realistic.

[0072] 2. The frequency-domain response of the hydrodynamic memory effect of the present invention is calculated using the experimental results of impulse motion response. The ROV is driven by a small-amplitude motion mechanism to perform a harmonic motion along the flow direction, and the non-linear hydrodynamic forces are obtained by increasing the relative velocity. Different from the hydrodynamic forces measured by the planar motion mechanism widely used in the ship field on both sides of the course, by changing the installation direction of the ROV, the impulse motion response experiment can obtain the hydrodynamic forces only along any flow direction, which is suitable for establishing an asymmetric hydrodynamic model related to the direction. Moreover, the hydrodynamic forces measured by this method can take into account the influence of the fluid memory effect on the amplitude and phase of the non-linear hydrodynamic forces.

[0073] 3. Compared with the unsteady lift model commonly used in the aviation field, the six-degree-of-freedom ROV hydrodynamic model of the present invention can calculate the hydrodynamic forces of the ROV in both positive and negative directions of continuous motion for each degree of freedom. The six-degree-of-freedom ROV hydrodynamic model of the present invention takes into account the influence of the process of the ROV changing direction on the hydrodynamic forces and can express the influence of the motion history on the asymmetry of the ROV hydrodynamic forces. Description of the Drawings

[0074] Figure 1 It is a schematic diagram of the ROV coordinate system.

[0075] Figure 2 It is a schematic diagram of the impulse response motion. (a) Forward surge velocity, (b) Reverse surge velocity, (c) Forward sway velocity, (d) Reverse sway velocity, (e) Forward heave velocity, (f) Reverse heave velocity, (g) Forward roll velocity, (h) Reverse roll velocity, (i) Forward pitch velocity, (j) Reverse pitch velocity, (k) Forward yaw velocity, (l) Reverse yaw velocity.

[0076] Figure 3 It is the viscous hydrodynamic forces measured by the impulse motion experiment. The viscous hydrodynamic forces measured in the forward surge (a), the viscous hydrodynamic forces measured in the forward sway (b), the viscous hydrodynamic forces measured in the forward heave (c), and the legend (d).

[0077] Figure 4 It is the frequency-domain response of the hydrodynamic memory effect. Forward surge (a), Reverse surge (b), Forward / Reverse surge (c), Reverse surge (d), Forward surge (e), Reverse surge (f).

[0078] Figure 5It is the time-domain response of the hydrodynamic memory effect, the surge response function (a), the sway response function (b), and the heave response function (c).

[0079] Figure 6 It is the result calculated by the six-degree-of-freedom ROV hydrodynamic model considering the fluid memory effect; the forward surge (a1) is 0.942 rad / s, (a2) is 1.571 rad / s, (a3) is 2.199 rad / s, (a4) is 2.827 rad / s; the forward sway (b1) is 0.942 rad / s, (b2) is 1.571 rad / s, (b3) is 2.199 rad / s, (b4) is 2.827 rad / s; the forward heave (c1) is 0.942 rad / s, (c2) is 1.571 rad / s, (c3) is 2.199 rad / s, (c4) is 2.827 rad / s; (d) legend.

[0080] Figure 7 It is the flow chart of the present invention. Detailed implementation manners

[0081] The present invention will be further described below with reference to the accompanying drawings.

[0082] In order to verify the effectiveness and effect of the method of the present invention, the present invention will be further described below by taking an operation-class ROV as an example. This example includes the following steps, as Figure 7 shown:

[0083] Step 1: Establish a steady-state hydrodynamic model of the ROV

[0084] 1. Establish the ROV coordinate system

[0085] As Figure 1 shown, define the fixed coordinate system O-x 0 y 0 z 0 and the body-fixed coordinate system G-xyz. Both of these coordinate systems are right-handed coordinate systems. The origin O is fixed at a point on the earth, and the Oz 0 axis is along the direction of gravity. The origin G is fixed at the center of gravity of the ROV. The Gx and Gy axes point to the bottom and starboard of the ROV model respectively. Define the surge, sway, heave velocities (u, v, w) and roll, pitch, and yaw angular velocities (p, q, r) in the body-fixed coordinate system; define the surge, sway, heave accelerations and roll, pitch, and yaw angular velocities The density ρ of water, the length L of the ROV, and the gravitational acceleration g.

[0086] 2. Establish a steady-state hydrodynamic model

[0087]

[0088] Among them, F ST represents the hydrodynamic force of the ROV, is the added mass coefficient of surge motion, is the added mass coefficient of sway motion, is the added mass coefficient of heave motion, is the added mass coefficient of roll motion, is the added mass coefficient of pitch motion, is the added mass coefficient of yaw motion. The longitudinal viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient The lateral viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient The vertical viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient The roll viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient The pitch viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient The yaw viscous hydrodynamic coefficient includes the positive direction coefficient and the negative direction coefficient Measure the inertial and viscous hydrodynamic coefficients of the ROV through the planar motion mechanism experiment of a conventional submersible.

[0089] Step 2: Establish the unsteady viscous hydrodynamic model of the ROV

[0090] 1. Impulse motion response experiment

[0091] The impulse motion response experiment aims to measure the non - linear hydrodynamic force with memory effect. To generate non - linear hydrodynamic force, a relatively large speed relative to the water flow is required.

[0092] 1.1 Experimental equipment

[0093] The 3D - printed model of the ROV with a scale ratio of 1:4 is 0.732 m long, 0.41 m wide, and 0.45 m high. The model test follows the Froude similarity law. The model test is carried out in a non - linear wave flume, which is 40 m long, 4 m wide, and 1.8 m deep. A set of rectifiers is set along the channel, and the distance from the front and rear ends to the ROV model exceeds 15L. After rectification, the water flows into a 2 - m - wide water channel (working area) composed of a deflector plate and the side wall of the wave flume.

[0094] The oncoming flow velocity is measured by a Doppler velocimeter, which is set at a position 3 m away from the ROV model and at the same position as the ROV model in the horizontal and vertical directions. The trailer is fixed in the middle of the working area and is used to install measurement devices such as a six-degree-of-freedom vibration table, accelerometers, dynamometers, struts, and ROV models. The range of the two horizontal accelerometers is g = 9.81 m / s 2 , and the resolution is 3×10 -5 g. The dynamometer is a six-component balance with a measurement range of 600 N and 50 Nm.

[0095] 1.2 Experimental method

[0096] In the pulse motion response experiment described in the present invention, a small-amplitude vibration table is used to meet the requirement of non-linear hydrodynamic forces by a relatively high convective relative velocity. The ROV in the present invention oscillates along the water flow direction. If the forces in the opposite direction are measured, the ROV needs to be rotated 180 degrees and reinstalled. In the pulse motion response experiment, the relative velocity with the flow is used as the velocity of the ROV. As Figure 2 shown, the motion equations of the ROV in the body-fixed coordinate system are: for forward motion, the longitudinal velocity u = Uc + aωcos(ωt), the lateral velocity v = Uc + aωcos(ωt), the vertical velocity w = Uc + aωcos(ωt), and the roll, pitch, and yaw velocities are the same as those in the roll, pure pitch, and pure yaw motions in the submarine plane motion mechanism experiment; for backward motion, the longitudinal velocity u = -Uc - aωcos(ωt), the lateral velocity v = -Uc - aωcos(ωt), the vertical velocity w = -Uc - aωcos(ωt), and the roll, pitch, and yaw velocities are the same as those in the roll, pure pitch, and pure yaw motions in the ship plane motion mechanism experiment, but the longitudinal motion of the ROV is -Uc. Among them, Uc is the flow velocity in the body-fixed coordinate system, a is the motion amplitude, ω is the motion frequency, t is the time, forward and backward motions mean that each translational degree of freedom moves along the positive and negative directions of its body-fixed coordinate respectively, and in the rotational degrees of freedom, forward and backward motions mean that the ROV moves along the positive and negative directions of the body-fixed coordinate longitudinally respectively.

[0097] The defined ROV motion velocity is realized by a six-degree-of-freedom vibration table, and the direction change of the ROV is realized by changing the relative position between the strut and the dynamometer. At the beginning of the experiment, the water pump flow velocity is observed through the results of the Doppler velocimeter, and the water pump power is adjusted to make the velocity reach 0.4 m / s. Input the motion amplitude, frequency, and phase of the ROV, center the six-degree-of-freedom vibration table and keep it stationary. After the flow velocity is stable, start the motion. Observe the measurement results of the accelerometer, and collect the dynamometer result F after the acceleration amplitude is stable DY, including longitudinal force, lateral force, vertical force, rolling moment, pitching moment, and yawing moment. After the amplitudes of all the force measurement results are stable and more than 5 cycles have passed, stop the six-degree-of-freedom shaking table and center it, and save the force measurement results. After the flow velocity is stable at 0.4 m / s again and the acceleration result is stable at 0, input a new motion frequency and repeat the experiment. After all the frequencies in one direction are measured, stop the six-degree-of-freedom shaking table and the water pump. After the water is still, adjust the direction of the ROV. Repeat the above process to measure the hydrodynamic forces in other directions.

[0098] 1.3 Experimental Conditions

[0099] Flow velocity: 0.4 m / s

[0100] Amplitude: 0.03 m

[0101] Frequency: 0.1 - 0.5 Hz, with an interval of 0.05 Hz.

[0102] ROV direction: Ox 0 The axis is the same as ±Gx, Ox 0 The axis is the same as ±Gy, Ox 0 The axis is the same as ±Gz.

[0103] 2. ROV Viscous Hydrodynamic Force Model Affected by Fluid Memory Effect

[0104]

[0105] Where F 2 is the ROV viscous hydrodynamic force affected by the fluid memory effect, including longitudinal force X 2 , lateral force Y 2 , vertical force Z 2 , rolling moment K 2 , pitching moment M 2 , and yawing moment N 2 , F DY is the non-linear hydrodynamic force with memory effect measured by the impulse motion response experiment, as Figure 4 shown.

[0106] Considering the growth process of the ROV from rest to uniform motion at a speed U in a certain direction, the impulse motion starts from the origin of the fixed coordinate system. At this time, the non-dimensional displacement of the ROV where t is time. In the time interval (τ 0 , τ 0 +dτ 0 ), the increment of the resultant motion velocity is where τ 0 is the starting non-dimensional displacement of any interval, dτ 0 represents the increment of the non-dimensional displacement in this interval, and dU represents the increment of the velocity in this interval. When dτ0 When it is small enough, the motion of the ROV can be considered a step motion, and the increment of the unsteady viscous hydrodynamic force F 2i (where i = X, Y, Z, K, M, N, representing the longitudinal force X 2 , the lateral force Y 2 , the vertical force Z 2 , the rolling moment K 2 , the pitching moment M 2 , and the yawing moment N 2 ) is expressed as:

[0107]

[0108] where dF 2i is the increment of the unsteady viscous hydrodynamic force, F′ UUi is the viscous hydrodynamic coefficient (where i = X, Y, Z, K, M, N, representing the longitudinal viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the lateral viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the vertical viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the rolling viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the pitching viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient the yawing viscous hydrodynamic coefficient including the positive direction coefficient and the negative direction coefficient ), Φ i is the response function (where i = X, Y, Z, K, M, N, representing the longitudinal force response function Φ X , the lateral force response function Φ Y , the vertical force response function Φ Z , the rolling moment response function Φ K , the pitching moment response function Φ M , and the yawing moment response function Φ N ). According to the superposition principle and the Duhamet integral, the function F 2i (τ) of the unsteady viscous hydrodynamic force per unit time interval with respect to the dimensionless displacement for any time history can be obtained:

[0109]

[0110] If τ = 0 at the start of the ROV movement, the above equation simplifies to:

[0111]

[0112] where U 0 is the initial velocity of the ROV. If the initial velocity of the ROV is 0 when τ < 0, the above equation simplifies to:

[0113]

[0114] Step 3: Calculate the frequency-domain response of the hydrodynamic memory effect

[0115] Define the dimensionless frequency Then the aωcos(ωt) terms of all the movement velocities in Step 2 become aωe ikτ , taking the longitudinal surge movement in the positive direction as an example, u = U C + aωe ikτ . When the small perturbation ε approaches 0, there is a limit:

[0116]

[0117] where i represents the complex number, Φ 1 is the longitudinal hydrodynamic response function, C X is the Theodorsen function of the longitudinal hydrodynamic force, A X is the amplitude of the Theodorsen function, is the argument of the Theodorsen function, F X is the real part of the Theodorsen function, G X is the imaginary part of the Theodorsen function. The Fourier transform of the above equation is:

[0118]

[0119] F X = 1, k → 0

[0120] F X = 0, k → +∞ (6)

[0122] Substitute Equation (2) into Equation (1), considering and take the real part:

[0123]

[0124] where A X1 is the first-order coefficient obtained by fitting the experimental results of X 2 using the above equation, A X2 is the second-order coefficient, is the first-order phase, is the second-order phase. The four parameters are obtained by fitting the longitudinal viscous hydrodynamic force with memory effect measured by the impulse motion response experiment. In the present invention, the experimental data is first low-pass filtered, and the 0-phase moment of the impulse motion is determined according to the acceleration sensor data. Calculate τ in each group of experiments according to the flow velocity, calculate k according to the motion frequency of each group, and establish a fitting equation. Use more than 5 cycles of relatively stable force measurement data, and use the least squares method to ensure the minimum error between the fitting result and the experimental result, and calculate all coefficients and phases.

[0125] Considering then the frequency-domain response of the longitudinal hydrodynamic memory effect is The other degrees of freedom are the same as the frequency-domain response of the longitudinal force memory effect. It should only be noted that for the roll, pitch and yaw motions, the motion composite velocity increment within the time interval (τ 0 , τ 0 + dτ 0 ) in the above method is The frequency-domain response of the hydrodynamic memory effect is as Figure 4 shown.

[0126] Step Four: Calculate the time-domain response of the hydrodynamic memory effect

[0127] Based on the hydrodynamic results of the impulse motion response experiment, calculate the frequency-domain response of the hydrodynamic memory effect at each motion frequency, and fit the frequency-domain response of the hydrodynamic memory effect by the least squares method for calculating the time-domain response of the hydrodynamic memory effect. Taking the longitudinal force as an example, the inverse Fourier transform of Equation (3) is as follows:

[0128]

[0129] The time-domain responses of other hydrodynamic memory effects are:

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] Step Five: Establish a six-degree-of-freedom ROV hydrodynamic model

[0136] The ROV nonlinear hydrodynamic force affected by the fluid memory effect

[0137]

[0138] wherein is the dimensionless displacement of longitudinal motion, is the dimensionless displacement of lateral motion, is the dimensionless displacement of vertical motion, is the dimensionless displacement of rolling motion, is the dimensionless displacement of pitching motion, is the dimensionless displacement of yawing motion, and d is the increment. The above formula needs to satisfy the following conditions:

[0139]

[0140]

[0141] wherein is the longitudinal force response function of forward motion, is the lateral force response function of forward motion, is the vertical force response function of forward motion, is the rolling moment response function of forward motion, is the pitching moment response function of forward motion, is the yawing moment response function of forward motion, is the longitudinal force response function of reverse motion, is the lateral force response function of reverse motion, is the vertical force response function of reverse motion, is the rolling moment response function of reverse motion, is the pitching moment response function of reverse motion, is the yawing moment response function of reverse motion. The positive and negative directions are defined in the body coordinate system.

[0142] The time-domain response of the hydrodynamic memory effect is as Figure 5 shown. The hydrodynamic results are as Figure 6 shown. In the case of low frequencies, the hydrodynamic estimations of the model of the present invention and the existing model are both good. When the frequency is 0.942 rad / s, the relative error of the calculation results is within 5%. As the frequency increases, there are significant differences between the results of the existing model and the measurement results. The hydrodynamic amplitude of the existing model is smaller than the measurement results. The phase of the existing model is earlier than the measurement. In most cases at higher frequencies, the relative error of the hydrodynamic of the model of the present invention is still less than 5%. The hydrodynamic peak of the model of the present invention and the measurement basically appear simultaneously within one cycle. Therefore, the model of the present invention can better estimate the force amplitude and phase delay caused by the memory effect than the existing model.

[0143] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A modeling method for a six-degree-of-freedom ROV hydrodynamic model considering fluid memory effect, characterized in that: The following steps are involved: Step 1: Establish ROV steady-state hydrodynamic model (1) Establishing the ROV coordinate system Define the fixed coordinate system O-x0y0z0 and the body coordinate system G-xyz. Both coordinate systems are right-handed coordinate systems. The origin O is fixed at any point on the earth. The Oz0 axis is along the gravity direction. Ox0 points to the north and Oy0 points to the east. The origin G is fixed at the center of gravity of the ROV. The Gx and Gy axes point to the bow and starboard of the ROV model respectively. Define the surge, sway, heave velocities (u, v, w) and roll, pitch and yaw angular velocities (p, q, r) in the body coordinate system; define the surge, sway, heave accelerations and roll, pitch and yaw angular rates The density of water ρ, the length of ROV L, the acceleration due to gravity g; (2) Establishment of a steady-state hydrodynamic model Among them, F ST represents the steady hydrodynamic force of the ROV, is the inertial hydrodynamic coefficient of turbulent motion, is the inertial hydrodynamic coefficient of the swaying motion, is the inertial hydrodynamic coefficient of heaving motion, is the inertial hydrodynamic coefficient of rolling motion, is the inertial hydrodynamic coefficient of pitch motion, is the inertial hydrodynamic coefficient of bow rolling motion; longitudinal viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Transverse viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Vertical viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Roll viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Pitch viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Bow roll viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient The inertial and viscous hydrodynamic coefficients of the ROV were measured by conventional submersible planar motion mechanism experiments, where the viscous hydrodynamic coefficients are divided into coefficients for the positive and negative directions of motion for each degree of freedom in the body coordinate system; Step 2: Establishing the ROV unsteady viscous hydrodynamic model Where F2 is the ROV viscous hydrodynamic force affected by the fluid memory effect, including longitudinal force X2, lateral force Y2, vertical force Z2, roll moment K2, pitch moment M2, and bow moment N2; Unsteady viscous hydrodynamic force F 2i The increment is expressed as: Where τ is the dimensionless displacement, τ0 is the starting dimensionless displacement of any interval, U is any velocity function of the ROV velocity, dU represents the velocity increment, and dF 2i is the unsteady viscous hydrodynamic increment, F U ' Ui is the viscous hydrodynamic coefficient, where i = X, Y, Z, K, M, N, representing the longitudinal viscous hydrodynamic coefficients respectively Include positive direction coefficient and negative direction coefficient Transverse viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Vertical viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Roll viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Pitch viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Bow roll viscous hydrodynamic coefficient Include positive direction coefficient and negative direction coefficient Φ i are response functions, respectively representing the longitudinal force response function Φ X , lateral force response function Φ Y , vertical force response function Φ Z , roll moment response function Φ K , pitch moment response function Φ M , bow pitch moment response function Φ N According to the superposition principle and Duhamet integral, the function F of the unsteady viscous hydrodynamic force per unit time interval of any time history with respect to the dimensionless displacement can be obtained: 2i (τ): If τ=0 when the ROV starts moving, the above equation can be simplified to: Where U0 is the initial velocity of the ROV, which is the combined velocity of the flow velocity and the ROV motion velocity. If the initial velocity of the ROV is 0 when τ<0, the above formula is simplified to: Step 3: Calculate the frequency domain response of the hydrodynamic memory effect The motion equation of ROV in the body coordinate system is: for positive motion, the longitudinal velocity u = Uc + aωcos(ωt), the lateral velocity v = Uc + aωcos(ωt), and the vertical velocity w = Uc + aωcos(ωt). The roll, pitch, and bow velocities are the same as the roll, pure pitch, and pure bow motion in the submersible plane motion mechanism experiment; for negative motion, the longitudinal velocity u = -Uc - aωcos(ωt), the lateral velocity v = -Uc - aωcos(ωt), and the vertical velocity w = -Uc - aωcos(ωt). The dimensionless frequency is defined as Uc is the velocity constant, a is the motion amplitude, ω is the motion frequency, then taking the positive direction longitudinal motion as an example, u=U C +aωe jkτ , there is a limit when the small perturbation ε approaches 0: Where j represents a complex number, Φ X is the longitudinal hydrodynamic response function, C X is the Theodorsen function of the longitudinal hydrodynamic force, A X is the amplitude of the Theodorsen function, is the argument of the Theodorsen function, F X is the real part of the Theodorsen function, G X is the imaginary part of the Theodorsen function, and the Fourier transform of the above formula is: Substituting equation (3) into equation (2), we consider And taking the real part, the longitudinal force X2 is expressed as: The first-order coefficient A X1 , second-order coefficient A X2 , first-order phase Second-order phase The four parameters are fitted using the longitudinal viscous hydrodynamic force with memory effect measured by the pulse motion response experiment; consider Then the frequency domain response of the longitudinal hydrodynamic memory effect is The frequency domain responses of other degrees of freedom and longitudinal force memory effect are the same, for other translational motions: The first-order coefficient A Y1 , second-order coefficient A Y2 , first-order phase Second-order phase The four parameters are fitted using the transverse viscous hydrodynamic force with memory effect measured by the pulse motion response experiment. The first-order coefficient A Z1 , second-order coefficient A Z2 , first-order phase Second-order phase The four parameters are fitted by using the vertical viscous hydrodynamic force with memory effect measured by the pulse motion response experiment; the frequency domain response of the lateral hydrodynamic memory effect is The frequency domain response of the vertical hydrodynamic memory effect is: For the rolling, pitching and yaw motion, the combined velocity increment in the time interval (τ0, τ0+dτ0) in the above method is The fitting equation is: Among them, p0 is the amplitude of the rolling angular velocity, and the first-order coefficient A K1 and the first-order phase The roll viscous hydrodynamic force with memory effect measured by the pulse motion response experiment is fitted, q0 is the roll angular velocity amplitude, and the first-order coefficient A is M1 and the first-order phase The pitch viscous hydrodynamic force with memory effect measured by the pulse motion response experiment is fitted, r0 is the roll angular velocity amplitude, and the first-order coefficient A is N1 and the first-order phase The bow roll viscous hydrodynamics with memory effect measured by the pulse motion response experiment are fitted; the frequency domain response of the rolling hydrodynamic memory effect is The frequency domain response of the pitch hydrodynamic memory effect is: The frequency domain response of bow hydrodynamic memory effect is: Step 4: Calculate the time domain response of the hydrodynamic memory effect Based on the hydrodynamic results of the pulse motion response experiment, the frequency domain response of the hydrodynamic memory effect at each motion frequency is calculated. The frequency domain response of the hydrodynamic memory effect is fitted by the least squares method to calculate the time domain response of the hydrodynamic memory effect. Taking the longitudinal force as an example, the inverse Fourier transform of equation (4) is: The time domain responses of other hydrodynamic memory effects are: Among them, F Y (k) is the real part of the Theodorsen function of the lateral force, F Z (k) is the real part of the Theodorsen function of the lateral force, F K (k) is the real part of the Theodorsen function of the lateral force, F M (k) is the real part of the Theodorsen function of the lateral force, F N (k) is the real part of the Theodorsen function of the lateral force; Step 5: Establish a 6-DOF ROV hydrodynamic model The complete six-DOF ROV viscous hydrodynamic model is: in is the dimensionless displacement of longitudinal motion, Transverse motion is dimensionless displacement, Vertical motion is dimensionless displacement, Rolling motion is dimensionless displacement, Pitch motion is dimensionless displacement, The yaw motion is dimensionless displacement, d is the increment, and the above formula needs to meet the following conditions: in is the forward motion longitudinal force response function, is the lateral force response function for forward motion, is the vertical force response function of the forward motion, is the roll moment response function for the forward motion, is the forward motion pitch moment response function, is the forward motion torque response function, is the longitudinal force response function of negative motion, is the lateral force response function for negative motion, is the vertical force response function of negative motion, is the negative motion rolling moment response function, is the negative pitch moment response function, is the negative motion turning moment response function, the positive and negative directions are defined in the body coordinate system, and the nonlinear hydrodynamic force F of the ROV with memory effect DY The model is:

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