PSI - Issue 68

Alen Marijančević et al. / Procedia Structural Integrity 68 (2025) 1203 – 1207 A. Marijancˇevic´ et al. / Structural Integrity Procedia 00 (2024) 000–000

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pass through the BSR. In both cases, additional attention should be paid to the lifetime assessment. It is generally considered, according to DNV-CG-0038 - Class Guideline, that when determining load carrying capacity for shafts for marine applications, axial stresses can be ignored. The most important are torsional stresses and, in certain cases, flexural stresses. While torsional vibrations Senjanovic´ et al. (2019) are often attributed to fatigue, there are studies that consider bending vibrations caused by sailing in heavy seas Braut et al. (2023). The torsional vibrations of the marine propulsion shaft line are thoroughly examined in this work, and then flexural vibrations are coupled in order to examine how this a ff ects the overall vibrational response and the calculation of the intermediate shaft’s fatigue life.

2. Materials and methods

In this study, a low-speed two-stroke engine with a direct-coupled, fixed-pitch propeller setup is considered. Main engine characteristics are given in Table 1. It is equipped with a torsional vibration damper (TVD) on the free side of the engine crankshaft. Propeller has 5 blades and outer diameter of 7.15 m. Lengths of intermediate and propeller shafts are 7.21 and 6.69 meters respectively. The torsional excitation of the propulsion shaft by the engine is defined by tangential pressure harmonics. The first two harmonics of lateral forces, bending, and torsional moments excite the shaft line at the propeller..

Table 1: Main engine and propeller characteristics.

Parameter

Value

Unit

Engine type

B&W5G60ME-C9.2

No. of cylinders

5

Firing order

14325

6

Max. continuous output Max. continuous speed

8500

kW rpm mm mm mm

77

Cylinder bore

600

Stroke

2790 6278 2790

Reciprocating mass

Stroke

kg / cyl.

Ratio of connecting rod

0.5

2.1. Propulsion shaft FE model

In this study, two models are considered. The first includes only torsional degrees of freedom and has a total of 13 nodes. In the second model, the complexity of the model was increased by introducing additional nodes in order to be able to introduce bearing positions and characterization. The second model therefore has 27 nodes. In addition to torsional degrees, lateral degrees of freedom were also introduced. Campbell diagram, shown in Fig. 1(a), is obtained using first model. It gives information that critical speed, excited with 5th harmonic, is to be expected at 45 rpm. Therefore Barred Speed Range (BSR) can be defined as the range in between 40 and 51 rpm. To verify this figures additionally a steady state torsional vibration analysis is performed. The shear stress at the intermediate shaft can be seen in Fig. 1(b).

2.2. Torsional - lateral coupled vibration

In order to analyze the influence of flexural vibrations and the corresponding load cycles on the total life span due to dominant torsional vibrations, torsional and flexural degrees of freedom are included in the second model. Every bearing is modeled with direct lateral sti ff ness and damping coe ffi cient. Lumped masses previously used in torsional model need to be recalculated because in this model shaft line posses its own mass. Coupling between torsional and lateral DOF is introduced defining propeller added mass and damping matrices Eq. (1) Carlton (2018).