Abstract. 1 Introduction

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1 Consideration of medium-speed four-stroke engines in ship vibration analyses I. Asmussen, A. Muller-Schmerl GermanischerLloyd, P.O. Box , 20416Hamburg, Germany Abstract Vibration problems were recently observed on some ships equipped with medium-speed diesel engines. Measurements revealed in these cases resonance condition between ignition frequency and H-type vibrations of the engines. As a consequence the excitation forces transmitted from the engines to the foundations were drastically magnified. A procedure is described how the natural frequency of the corresponding H-type modes can be predicted at the design stage. The procedure is demonstrated on the example of three vessels. The results obtained theoretically are verified by measurements. Generally, it was found that the calculated natural frequencies of the H-modes are in very good agreement with the measured values. It is shown that reliable results can only be obtained by considering the stiffness of the engine housing. Following this approach a tool has been developed to predict the natural frequency of the H- type mode shape of a medium-speed engine with a high degree of accuracy. In case of danger of resonance, proposals can be given to detune the system, either by mounting the engine full- or semi-resiliently, or by changing the stiffness of the foundation. 1 Introduction As a result of the steady increase in mean effective and firing pressures of medium-speed four-stroke engines, as well as of optimized structures vibration problems have been observed during operation. In these cases measurements revealed resonance proximity between the firing frequency and the transverse vibration mode of the engine on its foundation, the so-called H-type vibration. Despite the fact that this resonance results in forces introduced into the hull

2 368 Marine Technology and Transportation being significantly magnified dynamically, present dimensioning practice is restricted to avoiding resonance of local structures. As it is extremely costly to change the vibration behaviour of the engine/foundation once the vessel is in service, a procedure has been developed for assessing the risk of resonance at the design stage using the finite element (FE) technique. During the past few years comprehensive research work has been carried out with the aim to realistically simulating the introduction of forces into the hull, by integrating the engine into the FE model of the hull. This has, however, been done for slow-speed two-stroke engines only [1] - [3]. 2 Typical vibration modes of medium-speed engines The combustion forces occurring during ignition play a dominant role as excitation source coming from medium-speed four-stroke engines. Due to these forces, transferred through the crank gear, transversal and vertical forces act on the engine structure and excite the typical engine vibration modes: the transverse vibration about the longitudinal axis (H-type mode), the torsional vibration about the vertical axis (X-type mode) as well as the longitudinal vibration about the transversal axis (L-type mode). While the longitudinal vibration may be excited by vertical forces, the H-type and X-type vibrations are predominantly caused by the transverse guide forces. Fig. 1 shows schematically the combustion forces resulting in the typical engine excitation moments. guide forces H-moment guide forces X-moment vertical forces L-moment Figure 1: Excitation forces and moments of engines, It is of particular significance that the H-moment occurring at the firing frequency is an external moment, which is fully - or dynamically magnified - introduced into the foundation. The X- and L-moments, on the other hand, are internal moments, which act externally only through the deformation of the engine casing. Contrary to slow-speed engines severe L-type and X-type excitations occur very rarely with medium-speed engines. Therefore, H-type vibrations are of particular interest for this type of engine.

3 Marine Technology and Transportation Procedure for assessing the H-type transverse vibration mode of the engine/foundation system In view of the large number of influence parameters it is not possible to offer a solution in form of estimating formulae. As outlined below, it is also impossible to consider the engine or the ship's foundation as isolated systems, i.e. to neglect their interactions. Therefore, a practical procedure is described to predict the transverse natural frequency of the engine/foundation with the aid of a simple, three-dimensional FE model. The FE model as well as the calculated H-mode vibration of the engine/foundation of one of the three ships, which were selected to demonstrate the procedure here are shown in Fig. 2. Figure 2: FE model and calculated H-type mode of the engine/foundation. 3.1 Engine idealization For the idealization of the engine all components characterizing the global stiffness are modelled by plane stress elements of equivalent stiffness and mass distribution. Components, which have an insignificant effect upon the overall engine stiffness are only accounted for with respect to their masses. The masses are partly realized by auxiliary truss elements on the engine's periphery or by increasing the density of the surrounding elements. A realistic idealization of the complicated cast housing, an exact realization of the mass moments of inertia as well as a correct modelling of the engine width in conformity with the foundation are of particular significance with regard to the accuracy of the results obtained. 3.2 Foundation idealization By numerous variant calculations it has been possible to verify that, normally, only the double bottom in way of the engine room has to be idealized. It is sufficient to consider the essential structures, such as top plate, inner bottom, shell,

4 370 Marine Technology and Transportation longitudinal and transverse girders etc.. In order to estimate the effect of the adjacent structures, the model is rigidly supported at the forward and aft engine room bulkheads in the global directions as well as vertically at the points of connection of the shell and the frames. The masses of tank contents and hydrodynamic masses are in most cases negligible. It is, however, emphasized that the ship model simplifications described are admissible only, if it is ensured that the natural frequency of the basic double bottom vibration mode occurs considerably above the H-type eigenfrequency. 4 Application of the procedure to three example ships Following the principles as outlined, corresponding analyses were performed for three example vessels and compared with measurements. The ships were chosen such as to clearly illustrate the effect of different engine and foundation structures upon the H-type frequencies. In this context, it has to be noted that ships 2 and 3 are equipped with the same engine, i.e. the effect of the foundation structure upon the frequency will become particularly obvious. 4.1 Calculation of natural vibrations In a first step the H-type transverse mode of the engines supported on an infinitely rigid foundation was calculated: Table 1: H-Type eigenfrequencies of engines with infinitely rigid foundation eigenfrequency (cps) engine 1 engine Using a very detailed FE model, the manufacturer of engine 1 calculated the corresponding mode at 41 cps also. It becomes obvious that the simple engine model is well suited to calculate the H-type transverse eigenfrequency, but offers only limited information on the exact mode shape because of simplifications with regard to modelling of partial vibration systems such as the turbocharger, for instance. In a next step the H-type transverse eigenfrequencies of the engines as mounted on the hull foundations were calculated, see results in table 2. A calculated H-type vibration mode of one example ship can be seen in Fig. 2. Table 2: Measured and calculated H-type transverse eigenfrequencies ship 1 ship 2 ship 3 measured eigenfrequency (cps) calculated eigenfrequency (cps)

5 Marine Technology and Transportation 371 An important factor in the assessment of new procedures is the verification of the calculated values by measurements. The left side of table 2 gives the eigenfrequencies, determined by extensive measurements conducted by the engine manufacturer and Germanischer Lloyd. Fig. 3 shows the transverse amplitude measured on the upper edge of the cylinder crankcase as a function of the firing frequency. The resonance frequency obtained from the calculation is drawn into the measured response curve, showing good agreement frequency [cps] Figure 3: Measured response function at ignition frequency. A notable fact, in view of the very similar vibration behaviour of the engines with infinitely rigid support, see table 1, is the remarkable frequency difference of the engines support on foundations of finite stiffness (25 to 34 cps). This is due to the different foundation stiffnesses. The pronounced frequency decrease in case of flexible foundations clearly shows the significance of the integrated consideration of engine and foundation. With respect to the engine stiffness, the transverse vibration behaviour proves to be very sensitive as well. Variant calculations for the three ships with the engine being modelled as a rigid body, showed an increase in frequencies in the range of 20 % to 70 %, depending on the foundation stiffness. A simplified idealization of the engine as an infmitly rigid body is therefore not possible. 4.2 Calculation of forced vibrations An attempt was also made to calculate the response of the engine using the mode superposition method [4]. The evaluation of measured resonance curves, see fig. 3 for example, made it possible to estimate a damping factor. For the transverse bending vibration of the main engine a modal damping of 6 % could be assessed following the theory given in [5]. The response (velocity peak

6 372 Marine Technology and Transportation values) was determined on the upper edge of the crankcase at mid engine due to excitation by the H-moment. Table 3: Comparison of calculated and measured amplitudes ship 1 ship 2 ship 3 \ velocity amp itude (mm/s) in rescmance at IVICR calculated measured 11 5 calculated measured The fact that the largest deviations occur at the resonance frequency indicates that the damping factor used in the calculation was somewhat too small. However, the results do show that the procedure described is suitable to also estimate the magnitude of engine vibrations excited at firing frequency. 5 Countermeasures in case of resonance proximity A comparison of the calculated eigenfrequency with the firing frequency reveals a possible risk of resonance. In resonance proximity the forces introduced into the foundation and thus into the ship may be magnified dynamically 6 to 9 times. In case of an excitation frequency/eigenfrequency ratio of 0.7 < fexc/^eig. < 1.3 it is, therefore, recommended to initiate countermeasures in order to detune the engine/foundation system. Possible measures with respect to the recommended frequency ranges of a low-vibration design are shown schematically in Fig. 4. Here the transfer function of a one degree of freedom (H-type motion of engine) system is plotted. 05 to X undercritical design engine rigidly supported on stiff foundation overcritical design enginerigidlysupported on weak foundation or engine mounted semi-resiliently engine mounted full-resiliently 1 1/2 excitation frequency / eigenfrequency Figure 4: Possible countermeasures to detune engine/foundation vibrations.

7 Marine Technology and Transportation 373 The individual measures can be: 5.1 Varying the foundation stiffness Frequency variation in case of a rigidly mounted engine can possibly be achieved by modifying the foundation design. An effective undercritical design of a foundation realizing a safety margin of 30 % requires high, stiff foundations. It appears appropriate only for engines with relatively low firing frequencies. For engines with higher firing frequencies an overcritical design may be more appropriate. The foundations will then be of a more elastic construction, so that after passing the resonance a condition with low amplitudes will occur. However, this method has also its limitations. Apart from possible strength problems and classification requirements to be observed, it has to be ensured that the next higher vibration modes will not enter into the excitation frequency range. 5.2 Engine mounted full-resiliently An alternative method is to support the main engine elastically on spring elements, with a view to significantly detune the system of engine and foundation. A frequency ratio fexcaeig. ^ the range between 2 and 4 is to be aimed at, so that the magnitude of the forces introduced into the ship will fall drastically below the static values (vibration isolation). However, the amplitudes at the engine may increase considerably, so that the connections to other components have to be installed elastically. 5.3 Engine mounted semi-resiliently Another alternative is to use a semi-resilient support of the engine [6], see Fig. 5. Compared with the a full-resilient support, it is not so effective, but less costly. By fitting semi-elastic elements it is possible to decrease the natural frequency of the H-mode and hence to reduce the forces transferred to the foundation in the order of the static values. Elastic connections are, as a rule, generally not necessary. Figure 5: Principle of a semi-resilient mounting. / engine bedplate semi-resilient element shock fast top plate ship's foundation The countermeasures finally to be chosen for detuning the vibration system depend on the individual case.

8 374 Marine Technology and Transportation It is pointed out that the procedure to calculate the natural frequency of the H-mode described can be applied for full-resiliently and semi-resiliently mounted systems as well. For these cases the stiffness effects of the elastic or of the semi-elastic supporting elements have to be taken into account. In the FE models the supporting elements were simulated by beam elements with corresponding vertical and horizontal stiffness values. For the calculation of the vibrations of a full-resiliently supported engine the foundation normally need not be included in the model. Due to the considerable difference in stiffness of the foundation and the elastic supporting elements, the elasticity of the foundation can be neglected. The stiffness ratio between foundation and elastic elements should, however, be at least 10. For the calculation of semi-elastically supported engines this simplification is not possible. With reference to ship 1 as described in chapter 2.1, two sister ships were provided with semi-resilient supports (ship la with non-optimized, ship Ib with optimized elements). Both versions were calculated with the aid of the procedure described. A comparison of the calculated H-type eigenfrequencies with values obtained by measurements performed by the engine manufacturer confirms the reliability of the method. Table 4: Measured and calculated H-type transverse eigenfrequencies for semi-resiliently supported engines. ship la ship Ib measured frequency (Hz) calculated frequency (Hz) References 1. Mumm, H. & Asmussen, I. Simulation of low-speed main engine excitation forces in global vibration analyses, Proceedings of the International Conference on Noise & Vibration in the Marine Environment, London, U.K., Meinke, K.-D. Qualitative analysis of the coupled vibrations of main engine and ship hull, Schiffbauforschung 26, 1987 (in German). 3. Donath, G. & Bryndum, L. Vibrations onboard ships induced by the propulsion plant, Handbuch der Werften, Vol. XIX, 1988 (in German). 4. Clough, R. & Penzien, J. Dynamic of Structures, Mac Graw Hill, Nashif, A.D., Jones, D.I.G., Henderson, J.P. Vibration Damping, John Wiley & Sons, Lausch, W. Semi-resilient engine mounting system from MAN B&W, Diesel Gas Turbine Worldwide, U.S.A., 1991.

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