4.1 Mass and centre of gravity
The engines were weighed with 4 load cells to obtain weight and centre of gravity for increasing accuracy of the mass elements in WinRemo rigid body simulation model. The load cells were set between the engine block and the transportation rails. The weight readings were obtained separately from the different load cells and the distance of the load cells to the engine block corners were measured with a calliper and a measuring tape. To get accurate results the measurements were repeated three times. The engine was lifted between the measurements and the load cells were moved to slightly different locations on the transportations rails before the engine was lowered again. The total mass and the centre of gravity were calculated from the results. Weight of the lifting tool and any other extra weight were reduced, and missing parts were added in the calcula- tions. In the Appendix D is presented weight calculation sheet of W8V31DF engine. In the Figure 31 is a photo of engine being weighed.
Figure 31. W8V31DF engine weighed with load cells between the engine and the transportation rails.
4.2 Modelling of rigid body modes with WinRemo
Mass elements for the engine with flywheel, flexible mount feet, power output shaft and flexible coupling are placed to the coordinate system. Stiffness elements are created for the resilient mounts, the flexible coupling, and the exhaust bellows. Stiffness properties for the flexible mounts are obtained from earlier measurements and experience along with measured values given by the manufacturer. According to Wärtsilä experiments, the dynamic stiffness values are difficult to obtain because different results have been got with the same flexible elements as seen in the Figure 32.
Figure 32. Dynamic stiffness values of XK-34X55/915 resilient mount loaded with W8V31 engine, according to vibration measurements. The striped bar and red bar are dynamic and static stiffnesses provided by the manufacturer. [14]
As a stiffness element there can be added an element with linear or non-linear behaviour.
A linear element has only parameters of static stiffness to the three directions and dy- namic coefficient that is a ratio of dynamic stiffness to static stiffness. It can be also entered the dynamic stiffness as static stiffness and set dynamic coefficient to 1 if only dynamic behaviour is to be considered. For a non-linear stiffness element, it is entered vertical load-deflection curve, vertical load-dynamic coefficient curve and stiffness-de- flection curves to the x, y, and z directions. For all the curves maximum 5 points can be entered.
Marine solutions vibration group provided the initial models of engines in WinRemo with inertia properties from earlier measurement experience. The models are modified with
the installation specific data and measured weight and transversal and longitudinal cen- tre of gravities. Inertia properties have been constructed with Modal Model Method matching the calculated rigid body modes to the measured experimentally changing in- ertia properties in WinRemo.
4.2.1 Engine W8V31DF
The initial model for the W8V31DF is made by the Marine solution vibration group. The mass element of separate flywheel and vibration damper is removed from the model as mass values of the engine with flywheel and damper are obtained as the weighing re- sults. The mass elements for the flexible mount feet are left in place as they were not mounted at the weighing. Mass properties of the flexible coupling is changed to match the Rato R+ G3E20 damper model along with PTO axle that were used in the test run installation.
For the flexible mounts, it is tried both non-linear XK-34X55/915 model found from the stiffness element library and dynamic stiffness values according to the Figure 32 as linear stiffness element. The dynamic stiffness values in the figure are measured while mount is preloaded by W8V31 engine. For the non-linear element the dynamic coefficient was changed to 1.9 that corresponds the ratio in the Figure 32, and also gave the best results compared to the measurements. The stiffness elements are rotated in WinRemo, and calculations are done for each 3 flexible mount configurations. The stiffness elements of the used exhaust bellow and flexible coupling are found from the WinRemo library.
The visual model, entered values and calculation results for the W8V31DF engine are in Appendix B. To this point the model is accurate enough to connect the natural frequen- cies to the measurement results. The calculated rigid body natural frequencies are pre- sented later in the Results section.
4.2.2 Engines W16V31 and W12V31
Modelling of the W16V31 and W12V31 engines were done similar way as the W8V31DF.
The used flexible mounts are same type. Initial models are made by Marine solutions vibration group. Weighing result for W16V31 engine is for different similar engine of the same project. Mass properties of the flexible coupling is changed to match the CX-186 damper model along with long PTO axle that were used in the test run installation.
4.3 Engine excitations
As a result of excitation calculation with the Dynex software, the main excitations for the 8-, 16-, and 12-cylinder engines are shown in the Table 3. All the engines have large internal bending moments to vertical and transversal directions at the orders 1 and 2.
The 8-cylinder engine has the oscillating forces to the vertical and horizontal directions zeroed with DOB > 100 %, and the engine then has external pitching and yawing couples at the order 1. The half orders are internal torsion moments due to the gas forces. At the firing frequency (order 2) the torsion moments are in-phase, and the engine has external rolling excitation. Orders 4 and 6 rolling are its higher harmonics.
The 16-cylinder engine is well balanced in terms of external mass forces. At the firing frequency, at the order 4 the engine has external rolling excitation from gas forces. At the order 8 there is the second harmonic of it. At the half orders the gas forces cause internal torsional excitations.
The 12-cylinder engine also is well balanced in terms of external mass forces. At the firing frequency, at the order 3 the engine has external rolling excitation from gas forces that is largely balanced by rolling couple from the mass forces to the opposite direction.
At the order 6 there is higher harmonic of the rolling couple from the gas forces. At the half orders the gas forces cause internal torsion excitations. More detailed excitation calculation results are in Appendix A.
Table 3. The main engine excitations of the 8-, 16- and 12-cylinder engines obtained with Dynex calculation software. At the “internal bending” row V indicates vertical and T transversal bending.
Amplitude (kNm)
Order W8V31DF W16V31 W12V31 Excitation type
0.5 77 136 42
Internal torsion
1.5 72 47 136
2.5 32 21 18
4.5 11 20 22
5.5 13 9 7.5
6.5 11 7 5.8
7.5 12 12
1 259V 77H 366V, 108T 448V, 132T
Internal bending
2 38V 21H 154V, 85T 67V, 37T
1 75 Pitching couple
1 75 Yawing couple
2 17 (firing)
Rolling couple
3 17 (firing)
4 11 22 (firing)
6 23 34
8 17