Continued from HANSA 10/2010
6. Typical excitations of the nozzled thruster
6.1 Main static and dynamic force
components acting[ds_preview] on the azimuthing thruster
For the strength calculation of the ship structure the max. values of the static components of Fx, Fy, Fz and Mx, Mz are used in combination. My is ignored because of low relative magnitude.
Schottel supplies these values with the document »forces and moments« on request of designer or yard (page 29).
For that purpose the resulting values of bending moment, steering torque and horizontal force are usually transformed to the coordinates of the centre of the thruster well top flange.
So the values can be directly used for strength calculation of the ship structure.
For the modal analysis of the thruster in the structure either a reduced pendulum model or a complete 3D-thruster model is used. As long as a fair margin to resonances is achieved the modal analysis is the sufficient dynamic calculation.
For the forced damped vibration calculation of the submerged thruster in the ship structure the dynamic components of Fx, Fy, Fz and Mx are used.
Mz is ignored additionally to My because of the very high damping of the steering gears which results in negligible magnitude as well. Forced damped calculation is only used to check the effect of unavoidable resonances.
6.2 Exemplary static and dynamic forces of the 4-bladed nozzled thruster
For design purposes some standardised values for the a.m. force and moment components can be used for the 4-bladed nozzled thruster. It has to be considered that these values are only valid for thrusters with nozzle with typical design data for tug application!
Table 1 gives some standard values that can be used to make own calculations on such installations. The values are related to the centre of the lower gear box (section point of propeller and azimuth axis) and can act in any 360° rotated direction.
It has to be kept in mind, that most values are considerably dependent on e.g. motor torque, steering angle and ship speed and can therefore deviate from the above given values in practise. As a coincidental example the diagram in Fig. 52 shows some measured values of the relative dynamic side force component Fy,dyn at a ship speed of ab. 9 kn. This may illustrate, that the a.m. dynamic forces can be transiently exceeded under dynamic steering operation at higher ship speed. All the values above are thumb values which are good enough for basic design. In case of problems with resonances a more detailed view of the individual problem needs to be made!
7. Integration of the thruster into the ship construction
7.1 Calculations with detailed and reduced models
In Chapter 4.3 (Fig. 16) and 5.1 (Figs. 21 & 22) the modal behaviour of the thruster in the ship structure is already shown.
Further it is explained that the thruster can be reduced to a simplified pendulum model given to the customer which can then be used for strength calculation of the structure and for modal analysis of the thruster in the hull.
The dummy pendulum is built-up as a 3D-mass (including the mass and inertia properties of the underwater parts of the thruster) placed on the end of a beam element with different bending stiffnesses in the two pendulum directions (so it has the same properties as the thruster steering column).
This 3D mass plus beam is fixed to a circular plate representing the mass and membrane stiffness of the non-azimuthing part of the thruster. The diametre of the circular plate corresponds to the inner diametre of the thruster well in the ship. Thus the dummy pendulum fits into the ship structural model.
The comparative calculation on page 30 (Fig. 53–56) example of an exactly modeled thruster unit and its dummy pendulum model in a ship structure may invite yards and designers to make more regular use of this kind of calculation.
The results of the reduced and simplified models normally meet the results of the much more extensive high-resolution models by few percent only (for the rather low frequencies that are examined here).
In the example on page 30 with a very stiff integration of the thruster the first pendulum frequency (1st Eigenmode) of the thruster in the structure is ab. 40 Hz. The 1st and second propeller blade excitation frequency of the propeller (rotating at 230 rpm) is 15,3 resp. 30,6 Hz which means the excitation frequency is ab. 25 % lower than the first Eigenmode of the thruster. So in this case everything is fine.
If the safety margin is very small and the propeller blade excitation is close to an Eigenmode in the speed range of 80–120 % of the nominal speed measures should be taken to prevent excessive vibrations and the consequential reduction of component lifetimes.
The example in Fig.57 on page 30 of a forced damped vibration calculation of a thruster pair in the structure shows the system response close to the resonance.
In this case of a large thruster the pendulum frequency of 12,5 Hz is excited by the 1st propeller blade frequency of 12,1 Hz at nominal speed. The dynamic thrust component is applied with ab. 8 % of the nominal thrust.
The vertical vibration component that can be measured on the thruster foundation is calculated as svert = 0,2 mm which corresponds to a vibration velocity of ab. 15 mm/s.
Of course this is not critical from the strength point of view, but the resulting vibration load will be unfavourable for thruster component lifetime and comfort onboard.
7.2 Evaluation of the results
The comparison in Fig. 57 shows the minor deviations of the reduced models’ results against the detailed calculation. Same as for the shaft line vibrations a certain »clean« speed range especially around nominal speed is the design goal.
Classification societies do not have strict assignments whether or not a structural resonance is accepted because this is clearly dependent on what excitation magnitude hits what mode with what damping and what is finally the vibration amplitude of these coactions.
As a general requirement Schottel advises to have the speed range of 80–120 % of nominal speed clean of resonances of the 3(6) main modes of the thruster(s) with the 1st and second blade harmonic.
When calculated with detailed models the clean range can be reduced. In any case the range between 90–110 % should be kept clean.
Resonances in the speed range of ab. 50–80 % of the nominal speed can often be accepted, because the relation of excitation and damping is good enough to deliver uncritical vibration amplitudes only.
For the example shown under 7.1 (Fig. 57) the calculation result and alternative solutions are displayed in the Campbell diagram on page 31. It can be seen, that there will be a problem with the 1st blade order hitting the 1st pendulum Eigenmode of the thruster in the longitudinal direction (see point a).
This will require either a stiffer connection of the thruster to the hull (»undercritical« design) with a potential shifting of the natural frequency to point b at ab.13,7 Hz (see also 4.1 Influence of connection stiffness) or alternatively the use of a 5-bladed propeller with consequently a 25 % higher excitation frequency (»overcritical« design) which will leave the resonance point at ab. 75 % of the nominal speed which can normally be accepted (see point c).
Point c is clearly outside the required resonance-free speed range of 80–120 % nominal speed.
Point b is inside this range but already higher than 110 % nominal speed which could be accepted under consideration of the high model accuracy.
The examples on page 31 (Fig. 58) may illustrate, that the examination of the dynamic behaviour of the thruster in the structure can have different calculation depths starting with a »first shot« done with a simplified pendulum model in a coarsely meshed hull model.
If resonances are found within a speed range of 80–120 % of the nominal speed constructive counter measured should be taken to solve the problem.
If resonances are unavoidable more detailed models to examine the modal behaviour or even a forced damped calculation can help to make a decision.
8. Summary
With its long experience in the development, design and construction of azimuth drives for the tug application Schottel today has methods and experts available to support any task of integration of the drive system into the ship.
The responsible project engineer in the sales department accompanies the project during the important order-entry-phase in which the most important technical questions are clarified within a short period of time of a few weeks. Within this period of time all order specific aspects of design are handled and corresponding calculations are made by mainly the technical branch of the order management department under assistance of the development departments of hydrodynamic, electrical, hydraulic and mechanical engineering.
From the technical point-of-view the order-entry-phase is closed with the release of the final and official installation drawing showing the drive system integrated into the hull and coupled to the motor.
Any relevant information from the customer side needs to be included beforehand!
For the fixation method of the thruster to the hull Schottel offers a number of three variants with individual advantages to be chosen by the customer. Different premises lead to the decision for either a welded connection, a bolted connection with O-ring sealing or a »rubber flange« installation with water beam cut rubber plates.
Any of these alternative solutions has its own specific advantages and disadvantages from the point of view of the customer, especially the yard that has to install the thruster properly.
All the 3 variants are furthermore possible with installation from »above« or »below« which influences the degrees of freedom for the construction above the thrusters and the maintenance possibilities.
Additionally to the main connection between thruster main flange and ship flange the radial webs of the thruster or even the bottom plate can be connected to the hull structure. This is to a lesser extend to gain strength but more regular to gain stiffness and to influence the modal behaviour of the thruster in the hull structure.
For the various installation methods design criteria and installation tolerances are given and hints to prevent problems were made.
For the shaft line the differences between the traditional arrangement with inclined solid steel shafts and cardan shafts and the modern straight designs with hollow shafts and compensation couplings are shown.
The design goal of using the lowest possible number of bearings and other components requiring maintenance is highlighted.
The most common problems of installation and operation of shaft lines like lubrication, vibration, insufficient foundation stiffness (including the special case of bulkhead bearings) and over- and under load mainly due to radial and axial displacements are explained and examples are given.
The effort of Schottel to reach a mostly standardised modular shafting system which nevertheless comprises solutions for all kind of installation is demonstrated.
The standard components used with their specific pros and cons and properties are addressed. The Schottel modular shafting system allows the order specific design of the shaft line considering questions of strength, lifetime and vibration safety of the drive train. To get a better overview on what is done and expected on both sides (supplier and customer) an overview over the standard scope of calculations and information exchanged is given.
By this it gets clearer to the parties involved what is expected from whom and what assumptions are made.
With regard to thruster dynamic in the ship structure the various force and moment components acting on the thruster are explained and thumb values are given that can be used for dimensioning and for the basic design.
Examples are given for the modal behaviour and for forced vibrations of the submerged thruster when excited by realistic dynamic load components.
Working with simplified models with reduced resolution is exemplary shown. Schottel offers forces and moments plus reduced thruster models to be used by the designer for the strength and vibration calculation of the thruster-hull system.
For further comments, questions and more detailed information please do not hesitate to contact:
Manfred Heer
