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Fundamental research on the maneuverability of the underwater vehicle having thrust vectoring system

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Abstract

This report aims to present maneuverability of an underwater vehicle with a thrust vectoring system. So far, the thrust vectoring system has been applied in the products of Bluefin Robotics, and its equipment makes possible to eliminate the protrude control fins. It is also capable of contributing the better maintenance and handling in actual operation. In this paper, at first, captive model tests and free running model tests in towing tank are extensively conducted for the model having thrust vectoring system, and then used mathematical model of the thrust vectoring inspired by the azimuthing propeller model of the surface ships is correlated. As a result, the tank test results show that although the thrust vectoring system in this research generates larger rudder forces at lower speed range, there exists the directional instability due to the low slenderness and the elimination of the aft control surface. In addition, the numerical consideration using an optimal control theory shows that the additional aft fins on the shroud of thrust vectoring system well contribute directional stability and controllability over a wide speed range.

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Abbreviations

B :

Buoyancy [N]

D P :

Propeller diameter [m]

Drag:

Resistance [N]

F T x :

x Directional force due to thruster [N]

F Ty :

y Directional force due to thruster [N]

F Tz :

z Directional force due to thruster [N]

g :

Gravitational acceleration [N]

I yy :

Moment of inertia in pitch [kg m2]

I zz :

Moment of inertia in yaw [kg m2]

J :

Advance coefficient of thruster

J y :

Advance coefficient of thruster in y direction

J z :

Advance coefficient of thruster in z direction

K Tx :

Thrust coefficient of thruster in x direction

K Ty :

Thrust coefficient of thruster in y direction

K Tz :

Thrust coefficient of thruster in z direction

L :

Model Length [m]

L h :

Yaw moment lever due to thruster [m]

L v :

Pitch moment lever due to thruster [m]

m :

Ship mass [kg]

M q :

Derivative of pitch moment with respect to pitch angular velocity

\(M_{{\dot{q}}}\) :

Derivative of pitch moment with respect to pitch angular acceleration

M T :

Pitch moment due to thruster [N m]

M w :

Derivative of pitch moment with respect to heave velocity

M www :

Derivative of pitch moment with respect to cubic heave velocity

\(M_{{\dot{w}}}\) :

Derivative of pitch moment with respect to heave acceleration

n :

Propeller revolution number [1/s]

n max :

Maximum propeller revolution number [1/s]

N r :

Derivative of yaw moment with respect to yaw angular velocity

\(N_{{\dot{r}}}\) :

Derivative of yaw moment with respect to yaw angular acceleration

N v :

Derivative of yaw moment with respect to sway velocity

\(N_{{\dot{v}}}\) :

Derivative of yaw moment with respect to sway acceleration

N T :

Yaw moment due to thruster [N m]

q :

Pitch angular velocity [1/s]

r :

Yaw angular velocity [1/s]

S :

Wetted surface area [m2]

t :

Time [s]

t f :

Final time [s]

T x :

x Directional force due to thruster in thruster-fixed coordinate system [N]

T y :

y Directional force due to thruster in thruster-fixed coordinate system [N]

T z :

z Directional force due to thruster in thruster-fixed coordinate system [N]

u :

Surge speed [m/s]

V :

Ship speed [m/s]

v :

Sway speed [m/s]

w :

Heave speed [m/s]

x :

x Directional position [m]

x 0 :

Initial longitudinal position of a model [m]

x G :

Longitudinal position of center of gravity [m]

\(X_{{\dot{u}}}\) :

Derivative of surge force with respect to surge acceleration

X vv :

Derivative of surge force with respect to squared sway velocity

X ww :

Derivative of surge force with respect to squared heave velocity

X q :

Derivative of surge force with respect to pitch angular velocity

\(X_{{\dot{q}}}\) :

Derivative of surge force with respect to pitch angular acceleration

\(X_{{\delta_{f} \delta_{f} }}\) :

Derivative of surge force with respect to squared dive fin

y :

y Directional position [m]

y 0 :

Initial lateral position of a model [m]

Y v :

Derivative of sway force with respect to sway velocity

\(Y_{{\dot{v}}}\) :

Derivative of sway force with respect to sway acceleration

Y r :

Derivative of sway force with respect to yaw angular velocity

\(Y_{{\dot{r}}}\) :

Derivative of sway force with respect to yaw angular acceleration

z :

z Directional position [m]

z B :

Vertical position of center of buoyancy [m]

z G :

Vertical position of center of gravity [m]

Z q :

Derivative of heave force with respect to pitch angular velocity

\(Z_{{\dot{q}}}\) :

Derivative of heave force with respect to pitch angular acceleration

Z w :

Derivative of heave force with respect to heave velocity

Z www :

Derivative of heave force with respect to cubic heave velocity

\(Z_{{\dot{w}}}\) :

Derivative of heave force with respect to heave acceleration

\(Z_{{\delta_{\alpha } }}\) :

Derivative of heave force with respect to aft control surface

δ f :

Dive fin angle

δ h :

Horizontal angle of thruster

δ max :

Maximum angle of thruster

δ v :

Vertical angle of thruster

δ α :

Aft control surface angle

∇:

Volume [\({\text{m}}^{ 3}\)]

κ yy :

Radius of gyration in pitch [m]

\(\theta\) :

Pitch angle

ρ :

Water density

ω :

Frequency of motion [1/s]

ψ :

Yaw angle

\(\psi_{{t_{f} }}\) :

Yaw angle at final time

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Acknowledgements

The authors are grateful to Mr. Minoru Atsumi, Mr. Makoto Okubo, Mr. Noriyuki Yokoyama, Mr. Hidetake Mashiko and Mr. Naofumi Yamato at Meguro basin in NSRC, for their assistance in the model tests. I would like to thank Dr. Kazuyuki Yamakita and Mr. Shinya Matsumoto for their support and encouragement. Further, the authors are also grateful to Mr. Izumi Sekizaki from Izumi Sokki Co. Ltd. and Mr. Ryosaku Kusume from Sanshin Seisakusyo Co. Ltd.

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Author notes

  1. Atsuo Maki

    Present address: Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka, 565-0971, Japan

Authors and Affiliations

  1. Naval Systems Research Center, Acquisition, Technology & Logistics Agency, Ministry of Defense, 2-2-1 Nakameguro, Meguro, Tokyo, 153-8630, Japan

    Atsuo Maki, Tatsuhiro Tsutsumoto & Yoshiki Miyauchi

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  1. Atsuo Maki
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  2. Tatsuhiro Tsutsumoto
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  3. Yoshiki Miyauchi
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Correspondence to Atsuo Maki.

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Maki, A., Tsutsumoto, T. & Miyauchi, Y. Fundamental research on the maneuverability of the underwater vehicle having thrust vectoring system. J Mar Sci Technol 23, 495–506 (2018). https://doi.org/10.1007/s00773-017-0487-1

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