CN118332944A - A modeling method for a six-degree-of-freedom ROV hydrodynamic model considering fluid memory effect - Google Patents

Abstract

The invention discloses a six-degree-of-freedom ROV hydrodynamic model taking fluid memory effect into consideration and a modeling method, wherein the method comprises the following five steps: step one, an ROV steady hydrodynamic model is established, and the inertia and viscous hydrodynamic coefficients of the ROV are calculated; step two, establishing an unsteady viscous hydrodynamic model; step three, calculating hydrodynamic memory effect frequency domain response, and carrying out frequency domain transformation on the unsteady viscous hydrodynamic model; step four, calculating hydrodynamic memory effect time domain response; and fifthly, establishing a six-degree-of-freedom ROV hydrodynamic model. The method establishes a six-degree-of-freedom ROV hydrodynamic model through an impulse motion response experiment, can calculate the hydrodynamic force which changes along with time and is influenced by the instantaneous motion of the ROV, can calculate the influence of the motion history of the ROV on the current hydrodynamic force, and is suitable for the hydrodynamic force of the ROV under continuous motion in the positive and negative directions of six degrees of freedom.

Description

A modeling method for a six-DOF ROV hydrodynamic model considering fluid memory effect

Technical Field

The invention relates to a modeling method of a six-degree-of-freedom ROV hydrodynamic model considering fluid memory effect, and belongs to the field of ships.

Background technique

Operational unmanned remote controlled submersibles in underwater robots. Cable remote controlled submersibles (ROVs) are mainly used to support drilling operations (marine engineering installation operations) and are applied to the entire process from the first drilling to completion. During drilling operations, ROVs will complete operations such as observing the seabed environment, installing well pipe seals, guides, guiding tools, and assisting drilling equipment to enter the well. ROVs are often used in underwater structure installation and disassembly operations to set or assemble seabed structures, including setting or pulling rigging, assisting in the traction and positioning of large underwater structures, moving heavy parts, laying and burying cables and pipelines, and assisting in the installation of sinking rafts. ROV is one of the important tools in marine resource development and exploration, and marine structure installation and maintenance operations. With the development of deep-sea oil and gas, the demand for installation, maintenance and disassembly operations of underwater structures in deepwater areas has gradually increased, and the role of operational-level ROVs in offshore operations has become increasingly important. Therefore, the dynamics of ROV operations are studied, and a six-degree-of-freedom ROV hydrodynamic model and modeling method considering the fluid memory effect are invented, which has important engineering significance for improving the safety of offshore operations and improving operational efficiency.

When a rigid body moves steadily in water, it is usually assumed that the hydrodynamic force and torque are uniquely determined by the disturbance of the steady motion at that moment. Based on this assumption, the "quasi-steady flow" hydrodynamic derivative is defined, and the motion is described using a linear or nonlinear equation with a constant coefficient. This method is widely used in the study of the motion, stability, and control of floating bodies and underwater robots, but it has defects in dealing with ROV hydrodynamics, because the shape of ROV is more complex than that of ships and submarines, the degree of freedom of motion is more, and it will not always be in a steady state of motion during underwater operations. In the unsteady motion of ROV, the hydrodynamic force includes the additional mass force related to acceleration, the drag related to the stern track, and the influence of viscosity. When sailing in deep water, there are complex flows, positive and negative vortices, and mixed flows on the stern and track of ROV. The intensity of these flows and the impact on hydrodynamics increase with the increase of Reynolds number. Therefore, the hydrodynamic force of ROV in deep water is related to the history of the previous movement, and there is a "memory effect" in hydrodynamics. 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 hydrodynamics with nonlinear, asymmetric and coupled characteristics. Therefore, it is of great academic value to invent a six-degree-of-freedom ROV hydrodynamic model and modeling method considering the fluid memory effect.

The existing ROV hydrodynamic model has the following deficiencies:

1. Although the ROV six-degree-of-freedom dynamic model has been established, the memory effect of the fluid cannot be considered. The existing ROV hydrodynamic model can calculate the change of hydrodynamic force over time and motion, but it cannot calculate the lag effect of motion history on the magnitude and phase of hydrodynamic force;

2. The existing ROV hydrodynamic model only expresses the asymmetry and nonlinearity of ROV hydrodynamics as unequal hydrodynamic coefficients in different motion directions, and cannot express the influence of motion history and fluid memory effect on the asymmetry and nonlinearity of ROV hydrodynamics.

Summary of the invention

Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a modeling method for a six-degree-of-freedom ROV hydrodynamic model taking into account the fluid memory effect, which can take into account the influence of motion history, the hydrodynamic amplitude and phase changes caused by the fluid memory effect, and can also calculate the fluid memory effect affected by the motion history during the ROV changing its heading.

Technical solution: To solve the above technical problems, the present invention provides a six-degree-of-freedom ROV hydrodynamic model and modeling method considering the fluid memory effect. The hydrodynamic model includes five steps, namely: establishing a steady 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.

The ROV steady hydrodynamic model is established, the body coordinate system and fixed coordinate system of the ROV are established, and the inertial and viscous hydrodynamic coefficients of the ROV are measured through conventional submersible planar motion mechanism experiments, wherein the viscous hydrodynamic coefficient is divided into coefficients of the positive and negative motion directions of each degree of freedom in the body coordinate system.

The ROV unsteady hydrodynamic model is established according to the law that the hydrodynamic force is proportional to the square of the velocity and according to the system pulse and response relationship to establish an unsteady hydrodynamic model related to the ROV motion trajectory, hydrodynamic coefficient and velocity.

The hydrodynamic memory effect frequency domain response is to perform frequency domain transformation on the unsteady hydrodynamic model, and calculate the hydrodynamic memory effect frequency domain response based on the ROV viscous hydrodynamics affected by the fluid memory effect obtained in the pulse motion response experiment.

The pulse motion response experiment measures the hydrodynamic force of the ROV by means of a single degree of freedom oscillating ROV in a steady flow, and measures the unsteady viscous hydrodynamic force of the ROV affected by the fluid memory effect by combining the inertial hydrodynamic coefficient obtained by calculating the additional mass and the viscous hydrodynamic coefficient.

The time domain response of the hydrodynamic memory effect is obtained by performing a pseudo-frequency domain transformation on the frequency domain response of the hydrodynamic memory effect to obtain the time domain response of the single-degree-of-freedom hydrodynamic memory effect.

The six-degree-of-freedom ROV hydrodynamic model is established, and based on the time-domain response of the hydrodynamic memory effect, a time-domain response model of the hydrodynamic memory effect considering the reentry motion and hydrodynamic asymmetry is established, and a six-degree-of-freedom ROV hydrodynamic model considering the fluid memory effect is established.

A six-degree-of-freedom ROV hydrodynamic model and modeling method considering fluid memory effect of the present invention comprises the following steps:

Step 1: Establish ROV steady-state hydrodynamic model

1. Establish ROV coordinate system

Define the fixed coordinate system Ox ₀ y ₀ z ₀ and the body coordinate system G-xyz. Both coordinate systems are right-handed coordinate systems, with the origin O fixed at a point on the earth, the Oz ₀ axis along the direction of gravity, Ox ₀ pointing to the north, and Oy ₀ pointing 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 is ρ, the length of ROV is L, and the acceleration due to gravity is g.

2. Establish a steady hydrodynamic model

Where _FST represents the hydrodynamic force of 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 pitching 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 are measured by the existing conventional submersible planar motion mechanism experiment, where the viscous hydrodynamic coefficient is divided into the coefficients of the positive and negative motion directions of each degree of freedom in the body coordinate system.

Step 2: Establishing the ROV unsteady viscous hydrodynamic model

1. Impulse motion response experiment

The impulse motion response experiment is intended to measure nonlinear hydrodynamic forces with memory effects. To generate nonlinear hydrodynamic forces, a large velocity relative to the flow is required. The impulse motion response experiment described in the present invention uses a small amplitude vibration table, and a high relative velocity of convection is used to meet the requirements for the occurrence of nonlinear hydrodynamic forces. The ROV in the present invention oscillates along the direction of the water flow. If the force in the opposite direction is measured, the ROV needs to be rotated 180 degrees and reinstalled. In the pulse motion response experiment, the relative velocity to the flow is used as the velocity of the ROV. The motion equation of the 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 motions 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 roll, pitch, and bow velocities are the same as the roll, pure pitch, and pure bow 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 coordinate system, a is the motion amplitude, ω is the motion frequency, t is the time, positive and negative motion means that each translational degree of freedom moves along the positive and negative directions of its body coordinates respectively, and positive and negative motion in the rotational degree of freedom means that the ROV moves along the positive and negative directions of the body coordinates in the longitudinal direction of the body coordinates respectively.

2. ROV viscous hydrodynamic model affected by fluid memory effect

ROV viscous hydrodynamic model:

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 , roll moment K ₂ , pitch moment M ₂ , and bow moment N ₂ , and F _DY is the nonlinear hydrodynamic force with memory effect measured by the pulse motion response experiment.

Consider the growth process of ROV from rest to uniform motion at speed U in a certain direction. The pulse motion starts from the origin of the fixed coordinate system. At this time, the dimensionless displacement of ROV is Where U is the velocity of any one of the six degrees of freedom, and t is time. The total velocity increment of the motion in the time interval (τ ₀ ,τ ₀ +dτ ₀ ) is Where τ ₀ is the initial dimensionless displacement of any interval, dτ ₀ represents the increment of dimensionless displacement in the interval, and dU represents the velocity increment in the interval. When dτ ₀ is small enough, the motion of the ROV can be considered as a step motion, and the increment of the unsteady viscous hydrodynamic force F _2i (where i = X, Y, Z, K, M, N, representing longitudinal force X ₂ , lateral force Y ₂ , vertical force Z ₂ , rolling moment K ₂ , pitching moment M ₂ , and yaw moment N ₂ ) in this process is expressed as:

where dF _2i is the unsteady viscous hydrodynamic increment, F′ _UUi 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 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 bow moment response function Φ _N ). According to the superposition principle and Duhamet integral, the function F _2i (τ) of the unsteady viscous hydrodynamic force per unit time interval of any time history with respect to the dimensionless displacement can be obtained:

If τ = 0 at the beginning of ROV motion, the unsteady viscous hydrodynamic model is simplified to:

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:

Where i = X, Y, Z, K, M, N.

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

Defining dimensionless frequency Then the aωcos(ωt) term of all motion velocities in step 2 becomes aωe ^jkτ . Taking the positive oscillation motion as an example, u＝ _UC +aωe ^jkτ . When the small disturbance ε approaches 0, there is a limit:

Where j represents a 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, and G _X is the imaginary part of the Theodorsen function. The Fourier transform of the above formula is:

Substituting equation (2) into equation (1), we consider And take the real part:

The above formula is used to fit the longitudinal viscous hydrodynamic force with memory effect measured by the pulse motion response experiment to obtain the first-order coefficient A _X1 , the second-order coefficient A _X2 , and the first-order phase Second-order phase

consider Then the frequency domain response of the longitudinal hydrodynamic memory effect is The frequency domain response of the other degrees of freedom is the same as that of the longitudinal force memory effect. For other translational motions:

The first-order coefficient A _Y1 , the second-order coefficient A _Y2 , and the first-order phase Second-order phase The four parameters are obtained by fitting the transverse viscous hydrodynamic force with memory effect measured by the pulse motion response experiment: the first-order coefficient A _Z1 , the second-order coefficient A _Z2 , and the 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 (τ ₀ ,τ ₀ +dτ ₀ ) in the above method is Fitting equation:

Where p ₀ is the roll angular velocity amplitude, the first-order coefficient A _K1 and the first-order phase The roll viscous hydrodynamic force with memory effect measured by the impulse motion response experiment is fitted, _q0 is the roll angular velocity amplitude, the first-order coefficient A _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, the first-order coefficient A _N1 and the first-order phase The frequency domain response of the bow roll viscous hydrodynamics with memory effect measured by the pulse motion response experiment is obtained by fitting. 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, and 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 (3) is:

The time domain responses of other hydrodynamic memory effects are:

Step 5: Establish a 6-DOF ROV hydrodynamic model

Nonlinear hydrodynamics with memory effect:

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, and d is the increment. The above formula needs to meet the following conditions:

in is the longitudinal force response function of the forward motion, 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 roll moment response function, is the negative motion pitch moment response function, is the negative motion turning moment response function. The positive and negative directions are defined in the body coordinate system.

Beneficial effects: Compared with the prior art, the advantages are:

1. The hydrodynamic force calculated by the six-degree-of-freedom ROV hydrodynamic model of the present invention not only changes with time and is affected by the instantaneous motion of the ROV, but also can calculate the influence of the motion history of the ROV on the current hydrodynamic force. Compared with the hydrodynamic model widely used in the field of ships, the hydrodynamic model of the present invention calculates the hydrodynamic amplitude and phase under the periodic motion of the ROV more accurately, and the nonlinear expression of the hydrodynamic force is more realistic.

2. The frequency domain response of the hydrodynamic memory effect of the present invention is calculated using the results of the pulse motion response experiment. The ROV is driven by a small amplitude motion mechanism to perform simple harmonic motion along the flow direction, and the nonlinear hydrodynamic force is obtained by increasing the relative speed. Different from the widely used planar motion mechanism experiment in the field of ships to measure the hydrodynamic force on both sides of the heading, by changing the installation direction of the ROV, the pulse motion response experiment can obtain the hydrodynamic force only along any flow direction, which is suitable for establishing an asymmetric hydrodynamic model related to the direction, and the hydrodynamic force measured by this method can take into account the influence of the fluid memory effect on the amplitude and phase of the nonlinear hydrodynamic force.

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 force of each degree-of-freedom ROV under continuous motion in the positive and negative directions. The six-degree-of-freedom ROV hydrodynamic model of the present invention takes into account the impact of the ROV changing direction process on the hydrodynamic force, and can express the impact of the motion history on the asymmetry of the ROV hydrodynamic force.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of the ROV coordinate system.

Figure 2 is a schematic diagram of the impulse response motion, (a) positive surge velocity, (b) negative surge velocity, (c) positive sway velocity, (d) negative sway velocity, (e) positive heave velocity, (f) negative heave velocity, (g) positive roll velocity, (h) negative roll velocity, (i) positive pitch velocity, (j) negative pitch velocity, (k) positive bow velocity, and (l) negative bow velocity.

FIG3 shows the viscous hydrodynamic force measured by the pulse motion experiment, the viscous hydrodynamic force measured by the positive longitudinal sway (a), the viscous hydrodynamic force measured by the positive transverse sway (b), the viscous hydrodynamic force measured by the positive vertical sway (c), and the legend (d).

FIG4 is the frequency domain response of the hydrodynamic memory effect, positive longitudinal swell (a), negative longitudinal swell (b), positive/negative longitudinal swell (c), negative longitudinal swell (d), positive longitudinal swell (e), and negative longitudinal swell (f).

Figure 5 shows the time domain response of the hydrodynamic memory effect, including the longitudinal sway response function (a), the transverse sway response function (b), and the heave sway response function (c).

Fig. 6 is the result of calculation using the six-DOF ROV hydrodynamic model considering the fluid memory effect; positive longitudinal sway (a1) 0.942 rad/s, (a2) 1.571 rad/s, (a3) 2.199 rad/s, (a4) 2.827 rad/s; positive transverse sway (b1) 0.942 rad/s, (b2) 1.571 rad/s, (b3) 2.199 rad/s, (b4) 2.827 rad/s; positive vertical sway (c1) 0.942 rad/s, (c2) 1.571 rad/s, (c3) 2.199 rad/s, (c4) 2.827 rad/s; (d) legend.

FIG. 7 is a flow chart of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

In order to verify the effectiveness and effect of the method of the present invention, the present invention is further described below by taking an operating-level ROV as an example. The example includes the following steps, as shown in FIG7 :

Step 1: Establish ROV steady-state hydrodynamic model

1. Establish ROV coordinate system

Define the fixed coordinate system Ox ₀ y ₀ z ₀ and the body coordinate system G-xyz as shown in Figure 1. Both coordinate systems are right-handed coordinate systems, with the origin O fixed at a point on the earth and the Oz ₀ axis 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 coordinate system; define the surge, sway, heave accelerations and roll, pitch and yaw angular rates The density of water is ρ, the length of ROV is L, and the acceleration due to gravity is g.

2. Establish a steady hydrodynamic model

Where _FST represents the hydrodynamic force of 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 pitching 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 through conventional submersible planar motion mechanism experiments.

Step 2: Establishing the ROV unsteady viscous hydrodynamic model

1. Impulse motion response experiment

The impulse motion response experiment is designed to measure nonlinear hydrodynamic forces with memory effects. To generate nonlinear hydrodynamic forces, a large velocity relative to the water flow is required.

1.1 Experimental equipment

The 3D printed model of the ROV with a scale ratio of 1:4 is 0.732m long, 0.41m wide and 0.45m high. The model test follows the Froude similarity law. The model test is carried out in a nonlinear wave tank, which is 40m long, 4m wide and 1.8m deep. A set of rectifiers is set along the channel, with the front and rear ends more than 15L away from the ROV model. After rectification, it flows into a 2-meter-wide waterway (working area) composed of deflection plates and wave tank side walls.

The incoming flow velocity is measured by a Doppler velocimeter, which is set at a distance of 3m 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 work area and is used to install measuring equipment such as a six-degree-of-freedom vibration table, accelerometers, dynamometers, struts, and ROV models. The two horizontal accelerometers have a range of g = 9.81m/ ^s2 and a resolution of 3× ^10-5g . The dynamometer is a six-component balance with a measurement range of 600N and 50Nm.

1.2 Experimental methods

The impulse motion response experiment of the present invention uses a small amplitude vibration table, and the ROV in the present invention oscillates along the direction of the water flow through a high relative velocity of convection to meet the requirements of nonlinear hydrodynamics. If the force in the opposite direction is measured, the ROV needs to be rotated 180 degrees and reinstalled. In the pulse motion response experiment, the relative velocity to the flow is used as the velocity of the ROV, as shown in Figure 2. The motion equation of the 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 motions 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 roll, pitch, and bow velocities are the same as the roll, pure pitch, and pure bow 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 coordinate system, a is the motion amplitude, ω is the motion frequency, t is the time, positive and negative motion means that each translational degree of freedom moves along the positive and negative directions of its body coordinates respectively, and positive and negative motion in the rotational degree of freedom means that the ROV moves along the positive and negative directions of the body coordinates in the longitudinal direction of the body coordinates respectively.

The defined ROV motion speed is realized by the six-degree-of-freedom vibration table, and the ROV direction is changed by changing the relative position between the strut and the dynamometer. At the beginning of the experiment, the water pump flow speed is observed through the Doppler velocimeter results, and the water pump power is adjusted to make the speed reach 0.4m/s. Input the ROV motion amplitude, frequency and phase, center the six-degree-of-freedom vibration table and keep it still. After the flow rate stabilizes, start the movement. Observe the accelerometer measurement results, and collect the dynamometer results F _DY after the acceleration amplitude stabilizes, including longitudinal force, lateral force, vertical force, roll moment, pitch moment, and bow moment. After all the force measurement results are stable in amplitude and more than 5 cycles, stop the six-degree-of-freedom vibration table movement and center it, and save the force measurement results. After the flow rate stabilizes to 0.4m/s again and the acceleration result stabilizes to 0, enter the new motion frequency and repeat the experiment. After all frequencies in one direction are measured, stop the six-degree-of-freedom vibration table and the water pump. After the water level is calm, adjust the ROV direction. Repeat the above process to measure the hydrodynamic forces in other directions.

1.3 Experimental conditions

Flow rate: 0.4m/s

Amplitude: 0.03m

Frequency: 0.1~0.5Hz, interval 0.05Hz.

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

2. ROV viscous hydrodynamic model affected by fluid memory effect

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 , roll moment K ₂ , pitch moment M ₂ , and bow moment N ₂ , and F _DY is the nonlinear hydrodynamic force with memory effect measured by the pulse motion response experiment, as shown in FIG4 .

Consider the growth process of ROV from rest to uniform motion at speed U in a certain direction. The pulse motion starts from the origin of the fixed coordinate system. At this time, the dimensionless displacement of ROV is Where t is time. The total velocity increment in the time interval (τ ₀ ,τ ₀ +dτ ₀ ) is Where τ ₀ is the initial dimensionless displacement of any interval, dτ ₀ represents the increment of dimensionless displacement in the interval, and dU represents the velocity increment in the interval. When dτ ₀ is small enough, the motion of the ROV can be considered as a step motion, and the increment of the unsteady viscous hydrodynamic force F _2i (where i = X, Y, Z, K, M, N, representing longitudinal force X ₂ , lateral force Y ₂ , vertical force Z ₂ , rolling moment K ₂ , pitching moment M ₂ , and yaw moment N ₂ ) in this process is expressed as:

where dF _2i is the unsteady viscous hydrodynamic increment, F′ _UUi 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 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 bow moment response function Φ _N ). According to the superposition principle and Duhamet integral, the function F _2i (τ) of the unsteady viscous hydrodynamic force per unit time interval of any time history with respect to the dimensionless displacement can be obtained:

If τ＝0 when the ROV starts moving, the above equation can be simplified to:

Where U ₀ is the initial velocity of the ROV. 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

Defining dimensionless frequency Then the aωcos(ωt) term of all motion velocities in step 2 becomes aωe ^ikτ . Taking the positive oscillation motion as an example, u＝ _UC +aωe ^ikτ . When the small disturbance ε approaches 0, there is a limit:

Where i represents a 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, and G _X is the imaginary part of the Theodorsen function. The Fourier transform of the above formula is:

F _X = 1, k → 0

F _X = 0, k → + ∞

(6)

Substituting equation (2) into equation (1), we consider And take the real part:

Where A _X1 is the first-order coefficient of the _X2 experimental results fitted using the above formula, and A _X2 is the second-order coefficient. is the first-order phase, is the second-order phase. The four parameters are fitted using the longitudinal viscous hydrodynamic force with memory effect measured by the pulse motion response experiment. In the present invention, the experimental data is first low-pass filtered, and the 0 phase moment of the pulse motion is determined according to the acceleration sensor data. τ in each group of experiments is calculated according to the flow velocity, k is calculated according to each group of motion frequency, and a fitting equation is established. Relatively stable force measurement data of more than 5 cycles is used, and the least squares method is used to ensure that the error between the fitting result and the experimental result is minimized, and all coefficients and phases are calculated.

consider Then the frequency domain response of the longitudinal hydrodynamic memory effect is The frequency domain response of other degrees of freedom is the same as that of the longitudinal force memory effect. It should be noted that for the rolling, pitching and bowing motions, the combined velocity increment in the time interval (τ ₀ ,τ ₀ +dτ ₀ ) in the above method is The frequency domain response of the hydrodynamic memory effect is shown in Figure 4.

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, and 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 (3) is:

The time domain responses of other hydrodynamic memory effects are:

Step 5: Establish a 6-DOF ROV hydrodynamic model

Nonlinear hydrodynamics of ROV affected by fluid memory effect

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, and d is the increment. The above formula needs to meet the following conditions:

in is the longitudinal force response function of the forward motion, 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 roll moment response function, is the negative motion pitch moment response function, is the negative motion turning moment response function. The positive and negative directions are defined in the body coordinate system.

The time domain response of the hydrodynamic memory effect is shown in Figure 5. The hydrodynamic results are shown in Figure 6. Under low frequency conditions, the hydrodynamic estimates of the model of the present invention and the existing model are both very good. When the frequency is 0.942rad/s, the relative error of the calculated results is within 5%. As the frequency increases, there is a significant difference between the existing model results and the measured results. The hydrodynamic amplitude of the existing model is smaller than the measured result. The phase of the existing model is earlier than the measurement. In most cases at higher frequencies, the relative error of the hydrodynamic force of the model of the present invention is still less than 5%. The peak values of the hydrodynamic force of the model of the present invention and the measured hydrodynamic force appear in one cycle at basically the same time. Therefore, the model of the present invention can better estimate the delay of the force amplitude and phase caused by the memory effect than the existing model.

The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims (1)

1. A method of modeling a six degree of freedom ROV hydrodynamic model that takes into account fluid memory effects, comprising the steps of:

step one: establishing ROV steady hydrodynamic model

(1) Establishing an ROV coordinate system

Defining a fixed coordinate system O-x ₀y₀z₀ and a satellite coordinate system G-xyz, wherein the two coordinate systems are right-hand coordinate systems, an origin O is fixed on any point on the earth, an Oz ₀ axis is along the gravity direction, ox ₀ points to north, oy ₀ points to east, the origin G is fixed on the gravity center of the ROV, gx and Gy axes point to the head and starboard of the ROV model respectively, and heave, pitch and yaw angular velocities (p, q, r) and heave, heave and heave velocities (u, v, w) are defined in the satellite coordinate systems; definition of heave, heave accelerationAnd roll, pitch and yaw angular velocitiesDensity ρ of water, length L of ROV, gravitational acceleration g;

(2) Setting up a steady hydrodynamic model

Where F _ST denotes the steady hydrodynamic force of the ROV,For the inertial hydrodynamic coefficient of the heave motion,For the coefficient of inertial hydrodynamic of the swaying motion,For the coefficient of heave motion inertia hydrodynamic,Is the inertial hydrodynamic coefficient of the roll motion,Is the inertial hydrodynamic coefficient of the pitching motion,The inertial hydrodynamic coefficient of the bow swing motion; longitudinal viscous hydrodynamic coefficientComprising positive direction coefficientsAnd negative direction coefficientCoefficient of transverse viscous hydrodynamic forceComprising positive direction coefficientsAnd negative direction coefficientVertical viscous hydrodynamic coefficientComprising positive direction coefficientsAnd negative direction coefficientRoll viscosity hydrodynamic coefficientComprising positive direction coefficientsAnd negative direction coefficientHydrodynamic coefficient of pitch viscosityComprising positive direction coefficientsAnd negative direction coefficientHydrodynamic coefficient of bow-shake viscosityComprising positive direction coefficientsAnd negative direction coefficientThe inertia and viscous hydrodynamic coefficients of the ROV are measured through a conventional submersible plane motion mechanism experiment, wherein the viscous hydrodynamic coefficients are divided into coefficients of positive and negative two motion directions of each degree of freedom in a satellite coordinate system;

Step two: establishing ROV unsteady viscous hydrodynamic model

Wherein F ₂ is ROV viscous hydrodynamic force affected by fluid memory effect, including longitudinal force X ₂, transverse force Y ₂, vertical force Z ₂, roll moment K ₂, pitch moment M ₂, and yaw moment N ₂;

The increment of unsteady viscous hydrodynamic force F _2i is expressed as:

Where τ is the dimensionless displacement, τ ₀ is the beginning dimensionless displacement of any interval, U is any speed function in ROV speed, dU represents the speed increment, dF _2i is the unsteady viscous hydrodynamic increment, F _U′_Ui is the viscous hydrodynamic coefficient, where i=X, Y, Z, K, M, N represent the longitudinal viscous hydrodynamic coefficients, respectively Comprising positive direction coefficientsAnd negative direction coefficientCoefficient of transverse viscous hydrodynamic forceComprising positive direction coefficientsAnd negative direction coefficientVertical viscous hydrodynamic coefficientComprising positive direction coefficientsAnd negative direction coefficientRoll viscosity hydrodynamic coefficientComprising positive direction coefficientsAnd negative direction coefficientHydrodynamic coefficient of pitch viscosityComprising positive direction coefficientsAnd negative direction coefficientHydrodynamic coefficient of bow-shake viscosityComprising positive direction coefficientsAnd negative direction coefficientΦ _i is a response function, and represents a longitudinal force response function Φ _X, a transverse force response function Φ _Y, a vertical force response function Φ _Z, a rolling moment response function Φ _K, a pitching moment response function Φ _M and a rolling moment response function Φ _N respectively, and according to the superposition principle and Duhamet integration, a function F _2i (τ) of unsteady viscous hydrodynamic force relative to dimensionless displacement in a unit time interval of any time interval can be obtained:

If τ=0 at the beginning of the ROV motion, the above equation is reduced to:

Where U ₀ is the initial velocity of the ROV, which is the combined velocity of the flow and the velocity of the ROV motion, if the initial velocity of the ROV is 0 at τ <0, then the above equation is reduced to:

step three: calculating hydrodynamic memory effect frequency domain response

The equation of motion of an ROV in a satellite coordinate system is: for forward motion, the longitudinal speed u=uc+aωcos (ωt), the transverse speed v=uc+aωcos (ωt), the vertical speed w=uc+aωcos (ωt), the roll, pitch, yaw speed is the same as the roll, pure pitch, pure yaw motion in the submersible planar motion mechanism experiment; for negative motion, the longitudinal velocity u= -Uc-aωcos (ωt), the lateral velocity v= -Uc-aωcos (ωt), the vertical velocity w= -Uc-aωcos (ωt), the dimensionless frequency is definedUc is a velocity constant, a is a motion amplitude, ω is a motion frequency, then taking the positive direction heave motion as example u=u _C+aωe^jkτ, there is a limit when the small disturbance epsilon approaches 0:

Where j represents a complex number, Φ _X is a longitudinal hydrodynamic response function, C _X is a Theodorsen function of longitudinal hydrodynamic, A _X is the magnitude of the Theodorsen function,As the argument of Theodorsen function, F _X is the real part of Theodorsen function, G _X is the imaginary part of Theodorsen function, fourier transforming the above equation to:

Substituting formula (3) into formula (2) is considered And taking the real part, the longitudinal force X ₂ is expressed as:

Wherein the first-order coefficient A _X1, the second-order coefficient A _X2 and the first-order phase Second order phaseFitting four parameters by adopting longitudinal viscous hydrodynamic force with memory effect, which is measured by an impulse motion response experiment;

Consider The longitudinal hydrodynamic memory effect frequency domain response is thenOther degrees of freedom are the same as the longitudinal force memory effect frequency domain response for other translational movements:

Wherein the first-order coefficient A _Y1, the second-order coefficient A _Y2 and the first-order phase Second order phaseThe four parameters are obtained by fitting transverse viscous hydrodynamic force with memory effect, which is measured by an impulse motion response experiment, and the first-order coefficient A _Z1, the second-order coefficient A _Z2 and the first-order phase are obtainedSecond order phaseThe four parameters are obtained by fitting vertical viscous hydrodynamic force with memory effect, which is measured by an impulse motion response experiment. The response of the transverse hydrodynamic memory effect frequency domain is thatThe frequency domain response of the vertical hydrodynamic memory effect is that

For roll and pitch yaw motions, the increment of the motion closing speed in the time interval (tau ₀,τ₀+dτ₀) in the method isThe fitting equation is:

Wherein p ₀ is the amplitude of the roll angular velocity, the first-order coefficient A _K1 and the first-order phase The rolling viscous hydrodynamic force with the memory effect, which is measured by adopting an impulse motion response experiment, is obtained by fitting, q ₀ is the amplitude of the rolling angular velocity, the first-order coefficient A _M1 and the first-order phaseThe pitching viscous hydrodynamic force with the memory effect, which is measured by adopting an impulse motion response experiment, is obtained by fitting, r ₀ is the amplitude of the rolling angular velocity, the first-order coefficient A _N1 and the first-order phaseAnd fitting by adopting a bow-swing viscous hydrodynamic force with a memory effect, which is measured by an impulse motion response experiment. The response of the rolling hydrodynamic memory effect frequency domain is thatThe domain response of the pitching hydrodynamic memory effect is thatThe bow-sway hydrodynamic memory effect frequency domain response is that

Step four: calculating hydrodynamic memory effect time domain response

Based on the hydrodynamic results of the impulse motion response experiment, calculating hydrodynamic memory effect frequency domain response under each motion frequency, fitting the hydrodynamic memory effect frequency domain response by a least square method, and using the method for calculating hydrodynamic memory effect time domain response, taking longitudinal force as an example, performing inverse Fourier transform on the formula (4) is as follows:

other hydrodynamic memory effect time domain responses are:

Wherein 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, and F _N (k) is the real part of the Theodorsen function of the lateral force;

step five: establishing a six-degree-of-freedom ROV hydrodynamic model

The complete six-degree-of-freedom ROV viscous hydrodynamic model is:

Wherein the method comprises the steps of For a dimensionless displacement of the longitudinal movement,The transverse movement is free from dimensional displacement,The vertical movement has no dimensional displacement,The roll motion is dimensionless in displacement,The pitching motion is free from dimensional displacement,The bow movement is dimensionless displacement, d is an increment, and the above formula needs to meet the following conditions:

Wherein the method comprises the steps of As a forward motion longitudinal force response function,As a forward motion transverse force response function,As a forward motion vertical force response function,As a forward motion roll moment response function,As a forward motion pitching moment response function,As a forward motion turning moment response function,As a function of the longitudinal force response for negative motion,As a negative-going motion transverse force response function,As a negative motion vertical force response function,As a negative-going motion roll moment response function,As a negative-going motion pitch moment response function,For a negative motion turning moment response function, positive and negative directions are defined under a satellite coordinate system, and a model of the nonlinear hydrodynamic force F _DY with the memory effect of the ROV is as follows: