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Vibration analysis of cycloidal propeller blade during ship maneuvering

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Abstract

Marine cycloidal propeller (MCP) is well known for its maneuvering capability. It has unique kinematics. During operation, for each rotation of the propeller disc, each one of the blades undergoes one oscillation. There is phase angle between the oscillations of different blades. The face and back of the propeller blade interchange during each oscillation. These characteristics distinguish it from a typical screw propeller. In a screw propeller, the face and back of the propeller do not interchange and the blade pitch remains constant during each propeller revolution. Due to above reasons, the blades of cycloidal propellers are subjected to higher fluctuation in the loading. This causes fatigue loading on the blade and load variation on the prime mover. Therefore, during cycloidal propeller design, fatigue and load variation on the blade needs to be investigated. In this paper, structural dynamics of a cycloidal propeller blade during maneuvering conditions is investigated. The maneuvering conditions considered are bollard pull (towing), crash stop, cruising, crabbing, turning and zigzag (Planar Motion Mechanism). For analysis, the blade is considered as a thick plate. Variation of plate thickness and asymmetric support characteristics to account for aerofoil section and stock support are considered. Nonlinear finite element method is used for structural analysis. For computing the hydrodynamic load, a simple model is used. The analysis gives a good insight into the vibration characteristics of the cycloidal propeller blade.

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Abbreviations

\(a_{{Bi\left\{ S \right\}}}\) :

Acceleration of a single cycloidal propeller blade

\(C_{{i\{ S\} }}^{^{\prime}}\) :

Effective sway inflow velocity to a single cycloidal propeller blade

\(C.F_{{i\left\{ S \right\}}}\) :

Centrifugal force acting on a single cycloidal propeller blade

\(D_{{i\left\{ S \right\}}}\) :

Drag force acting on a single cycloidal propeller blade

\(D_{P}\) :

Diameter of propeller (2*\(R\))

\(e_{{1\left\{ S \right\}}}\) :

Eccentricity for generating x-direction force for starboard cycloidal propeller

\(e_{{2\left\{ S \right\}}}\) :

Eccentricity for generating y-direction force for starboard cycloidal propeller

\(F_{{i\left\{ S \right\}}}\) :

Force along ship’s Y-axis due to single cycloidal propeller blade

\(F_{{zbi\left\{ S \right\}}}\) :

Total vertical force acting on the bearing of a single cycloidal propeller blade

\(F_{{zD\left\{ S \right\}}}\) :

Total vertical force acting on the bearing of a single cycloidal propeller unit

\(I_{B}\) :

Moment of inertia of single cycloidal propeller blade

\(I_{D}\) :

Moment of inertia of a single unit of cycloidal propeller

\(I_{z}\) :

Moment of inertia of the ship about \(z\) axis

\(J_{z}\) :

Added mass moment of inertia of ship with respect to \(z\) axis

\(K_{SX} , \, K_{SY}\) :

Steering force coefficient along ship’s x- and y axis

\(L_{B}\) :

Length of blade

\(L_{{i\left\{ S \right\}}}\) :

Lift force acting on a single cycloidal propeller blade

\(m\) :

Mass of the ship

\(m_{x} , \, m_{y}\) :

Added mass of ship along x- and y axis

\(N_{H}\) :

Hydrodynamic yaw moment acting at midship

\(N_{P}\) :

Hydrodynamic yaw moment due to twin cycloidal propeller acting at midship

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

Added mass moment of inertia of ship due to sway velocity

\(N.F_{{i\left\{ S \right\}}}\) :

Force acting normal to chord on a single cycloidal propeller blade

\(p\) :

Roll rate of the ship

\(Q_{{Bi\left\{ S \right\}}}\) :

Hydrodynamic torque acting on the stock of a cycloidal propeller blade

\(Q_{{BFD\left\{ S \right\}}}\) :

Bearing friction torque acting on disc of port/ starboard cycloidal propeller

\(Q_{{BFi\left\{ S \right\}}}\) :

Bearing friction torque acting on the stock of a cycloidal propeller blade

\(Q_{E}\) :

Engine/ prime mover torque for port/ starboard cycloidal propeller

\(Q_{{EBi\left\{ S \right\}}}\) :

Total torque for pitching a single cycloidal propeller blade

\(Q_{{ED\left\{ S \right\}}}\) :

Torque required for rotating a unit of cycloidal propeller excluding blade torque

\(Q_{{HD\left\{ S \right\}}}\) :

Hydrodynamic torque acting on disc of port/ starboard cycloidal propeller

\(Q_{{HFD\left\{ S \right\}}}\) :

Hydrodynamic friction torque acting on disc of port/ starboard cycloidal propeller

\(r\) :

Yaw rate of ship

\(r_{b}\) :

Radius of a cycloidal propeller blade stock

\(T_{{i\left\{ S \right\}}}\) :

Force along ship’s X-axis due to single cycloidal propeller blade

\(T.F_{{i\left\{ S \right\}}}\) :

Force acting tangent to chord on a single cycloidal propeller blade

\(u\) :

Surge velocity of ship in \(x\) direction

\(u_{P}\) :

Circumferential velocity of the propeller blade

\(v\) :

Sway velocity of ship in \(y\) direction

\(\left( {V_{R} } \right)_{{{\text{Max}}}}\) :

Maximum effective inflow velocity to a propeller blade during a maneuver

\((x_{G} , \, y_{G} , \, z_{G} )\) :

Position of centre of gravity of ship from the origin \(O\)

\(X_{H}\) :

Bare hull hydrodynamic force in x direction at midship

\(X_{P}\) :

Hydrodynamic force due to twin MCP acting on ship in x direction

\(\dot{X}_{E} , \, \dot{Y}_{E}\) :

Ship velocity in earth coordinate system

\(Y_{H}\) :

Bare hull hydrodynamic force in y direction at midship

\(Y_{P}\) :

Hydrodynamic force due to twin MCP acting on ship in y direction

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

Added mass of ship in sway direction due to yaw motion

\(\alpha_{{Bi\left\{ S \right\}}}\) :

Angle of attack of ith blade of port/ starboard cycloidal propeller

\(\delta_{{i\left\{ S \right\}}}\) :

Pitch angle ith blade of port/ starboard cycloidal propeller

\(\theta_{{i\left\{ S \right\}}}\) :

Orbit angle of ith blade of port/ starboard cycloidal propeller

\(\mu\) :

Friction coefficient for the bearing (assumed to be same for all the bearings)

\(\rho_{W}\) :

Density of water

\(\phi_{{i\left\{ S \right\}}}\) :

Angle between line drawn from eccentricity point to normal to chord of cycloidal propeller blade and longitudinal axis of ship

\(\psi_{{Ri\left\{ S \right\}}}\) :

Inflow angle to ith blade of port/ starboard cycloidal propeller

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Authors and Affiliations

  1. Indian Register of Shipping, Mumbai, India

    J. Joseph Prabhu

  2. National Institute of Technology Calicut, Kozhikode, India

    Anil Kumar Dash

  3. Indian Institute of Technology Kharagpur, Kharagpur, India

    Vishwanath Nagarajan & Mohammed Rabius Sunny

  4. Ocean Engineering and Naval Architecture Department, IIT Kharagpur, Kharagpur, 721 302, West Bengal, India

    Vishwanath Nagarajan

Authors
  1. J. Joseph Prabhu
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  2. Anil Kumar Dash
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  3. Vishwanath Nagarajan
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  4. Mohammed Rabius Sunny
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Correspondence to Vishwanath Nagarajan.

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Prabhu, J.J., Dash, A.K., Nagarajan, V. et al. Vibration analysis of cycloidal propeller blade during ship maneuvering. J Mar Sci Technol 28, 44–71 (2023). https://doi.org/10.1007/s00773-022-00899-1

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