Mode shapes

Viewing the animations formed from ODS FRF data at the nominal speed, shows the vibration shape change on an order according to the flexible element configuration, de- pending on whether there is a rigid body mode at the order or not. The shape of the motion is changing to completely different by just changing the direction of the flexible elements, which shifts the natural frequencies by changing the stiffness properties. The

engine excitations are completely similar with all the configurations. In the Table 7 are presented the mode shapes of different flexible mount configurations at the first 4 half orders.

Table 7. Engine block operating deflection shapes recognized from the animations, at first two orders and half orders at nominal speed, full load.

Frequency

(Hz) order default 90 deg 0 deg

6.25 0.5 Block torsion,

yawing Block torsion Block torsion, yawing

12.5 1 Vertical and

horizontal bending, rolling

Vertical and

horizontal bending Rolling

18.75 1.5 Block torsion Rolling Block torsion

25 2 Vertical and hori-

zontal bending.

Block torsion in driving end.

Vertical and hori- zontal bending.

Block torsion in driving end.

Vertical and hori- zontal bending.

Block torsion in driving end.

The rolling mode was measured to be at 14.5 Hz with the default mounting configuration.

The operating deflection shape at the order 1 (12.5 Hz) is mainly vertical and horizontal bending, also a little bit of rolling. With the 90-degree configuration, while the rolling mode is at 17.5 Hz, the shape is only the bending, not rolling at all. With the 0-degree configu- ration the rolling mode is at 12.4 Hz, just on the order 1, and the rolling motion is clearly dominating. Screenshots from the ODS animations are presented in the Figure 36 – Figure 38.

Figure 36. Default mount configuration operating deflection shape at the order 1 (12.5 Hz). Bending shape is dominating. A little bit of rolling is also noticeable. The rolling mode is on 14.5 Hz with the default configuration.

Figure 37. 90-degree mount configuration operating deflection shape at the order 1 (12.5 Hz). Bending shape is dominating. No signs of rolling. Rolling mode is on 17.5 Hz with the 90-degree configuration.

Figure 38. 0-degree mount configuration operating deflection shape at the order 1 (12.5 Hz). Rolling shape is dominating. Rolling mode is on 12.4 Hz with the 0-degree configuration.

In the Table 8 there are shown the vibration amplitudes at the order 1 with the different flexible element configurations. It can be seen from the table that the 0-degree configu- ration that has the rolling mode on the order 1 has the highest amplitude, and the 90- degree configuration where the rolling mode is furthest from the order 1 has the lowest amplitude. The table also shows ratio of 0-degree configuration amplitude to 90-degree configuration amplitude that is considered as gain between the excitation and the rigid body vibration in resonance. It is obvious the rolling mode at 12.4 Hz is excited at the order 1 with the 0-degree configuration although the shape of excitation is different, and according to lumped mass theory the internal bending shouldn’t excite the rigid body mode.

Table 8. Order 1 amplitude of vibration (mm/s) with the different flexible mount con- figurations, measured from the engine block corners. 0-degree configuration that has rolling mode on the order 1, has the highest amplitude. 90-degree configuration has the mode furthest from the order 1. The rightmost column has ratio of amplitudes at 0-degree to 90-degree configuration, which is considered as gain between the excitation and the rigid body vibration.

Meas.pt Direction default 90-deg 0-deg Gain

A1 L 1.4 0.4 0.7 1.8

T 1.3 1.6 0.9 0.6

V 3.3 3.0 5.4 1.8

A3 L 1.5 1.8 0.7 0.4

T 3.5 2.8 6.5 2.3

V 2.6 2.4 4.0 1.7

C1 L 1.6 1.0 1.3 1.3

T 0.9 0.3 3.1 10.3

V 2.8 2.1 5.6 2.7

C3 L 1.7 1.9 1.0 0.5

T 5.4 2.0 9.2 4.6

V 1.6 1.8 4.0 2.2

As mentioned, with the 90-degree configuration the rolling mode is at 17.5 Hz that is near to the order 1.5. The same thing happens when looking at the order 1.5 vibration; the rolling mode shape is dominating with the 90-degree configuration. With the other con- figurations the dominating shape is the torsion caused by gas forces. The torsional force must excite the rolling mode. Screenshots of the animations of the order 1.5 deflection shapes are in the Figure 39 - Figure 41.

Figure 39. Default mount configuration operating deflection shape at the order 1.5 (18.75 Hz). Torsion shape is dominating. Rolling mode is on 14.5 Hz with the default configuration.

Figure 40. 90-degree mount configuration operating deflection shape at the order 1.5 (18.75 Hz). Rolling shape is dominating. Rolling mode is on 17.5 Hz with the 90-degree configuration.

Figure 41. 0-degree mount configuration operating deflection shape at the order 1.5 (18.75 Hz). Rolling shape is dominating. Rolling mode is on 12.4 Hz with the 0-degree configuration.

The Table 9 shows order 1.5 vibration amplitudes on the engine block corners with the flexible element configurations. The 90-degree configuration that has rolling mode on order 1.5, now has the highest amplitude. The table also shows ratio of 90-degree con- figuration amplitude to 0-degree configuration amplitude, that is considered as gain be- tween the excitation and the rigid body vibration in resonance.

Table 9. Order 1.5 amplitude of vibration (mm/s) with the different flexible mount con- figurations, measured from the engine block corners. The 90-degree configuration that has rolling mode on order 1.5, has the highest amplitude. The rightmost column has ratio of amplitudes at 90-degree to 0-degree configuration, which is considered as gain be- tween the excitation and the rigid body vibration.

Meas.pt. Direction default 90-deg 0-deg Gain

A1 L 0.7 0.7 0.8 0.9

T 0.3 0.6 0.3 2.0

V 0.9 1.5 0.9 1.7

A3 L 1.3 1.0 1.5 0.7

T 1.6 2.7 1.3 2.1

V 0.4 0.9 0.6 1.5

C1 L 0.8 0.8 0.8 1.0

T 0.2 1.3 0.2 6.5

V 0.5 2.0 0.3 6.7

C3 L 1.3 0.8 1.3 0.6

T 0.4 3.3 0.6 5.5

V 0.5 1.2 0.3 4.0

5.2 16-cylinder engine

Nominal speed ODS vibration measurements along with speed sweep and engine stop- ping measurements were performed for 16-cylinder V-engine W16V31 that is mounted to the fixing rail with 18 resilient mounts, 9 pcs per side. The mounts were the same type than with the 8-cylinder engine. The rigid body natural frequencies of the W16V31 engine measured with the speed sweep and engine stopping measurements along with the cal- culated modes are presented in the Table 10. The highest calculated engine excitations were shown earlier, in the Table 3Error! Reference source not found.. The Figure 42 shows ODS FRF graphs obtained with stopping measurement.

Table 10. The measured and calculated rigid body natural frequencies (Hz) of the flexibly mounted W16V31 engine. The measurement results are matching well with the calculations.

Mode shape Stopping Calculated

Longitudinal 11.99

Transversal 4.00 3.93

Vertical 8.63 8.53

Rolling 15.3 14.58

Pitching 4.75 4.76

Yawing 6.88 7.28

Figure 42. ODS FRF of the W16V31 obtained with engine stopping measurement.

The graph has data of each measurement points overlapped. Natural frequencies are seen in the graph as peaks. The highest amplitude peak that is rolling mode, is seen to be “unfinished” as there has not been an excitation at a frequency high enough. The mode is excited by the order 1 at the highest engine speed at the stopping. The true peak of the rolling mode is seen as small amplitude bump. The order 1.5 excitation doesn’t exist in the stopping because it is a gas force.

At the order 1 (12.5 Hz) the main excitations are internal bending moment with amplitude of 366 kNm to the vertical and 108 kNm to the horizontal direction (Table 3Error! Refer- ence source not found.). The engine is well balanced in terms of external forces. The dominating mode shape at the order 1 according to the ODS measurement is the block bending. There is no rigid body mode near to the order 1.

At the order 0.5 (6.25 Hz) the internal excitation is block torsion with amplitude of 136 kNm, but the mode shape is clearly yawing (Figure 43) as there is a yawing mode at 6.88 Hz. The block torsion is hardly seen from the animation. Yawing mode is excited, alt- hough the shape of the excitation is different. The question is how the force is transferring to excite the mode. The rest orders have mode shapes matching with the excitation shapes at the nominal speed as there were no rigid body modes close to them.

Figure 43. Operating deflection shape of the W16V31 at the order 0.5 (6.25 Hz) show- ing yawing rigid body motion. The yawing mode is at 6.88 Hz.

5.3 12-cylinder engine

Nominal speed ODS vibration measurements along with speed sweep and engine stop- ping measurements were performed for W12V31 engine that was mounted to the fixing rail with 14 resilient mounts, 7 pcs per side. The rigid body natural frequencies of the W16V31 engine measured with the speed sweep and engine stopping measurements along with the calculated ones are presented in the Table 11.

Table 11. The measured and calculated rigid body natural frequencies (Hz) of the flexibly mounted W12V31 engine.

Mode shape Stopping Sweep Calculated (long PTO)

Longitudinal 11.93

Transversal 3.88 3.88 3.71

Vertical 8.38 8.25 7.82

Rolling 17.3 17.0 17.14

Pitching 4.25 4.13 4.30

Yawing 6.88 6.75 8.57

The operating deflection shapes at the nominal speed according to animations are in the Table 12. The dominating shape at the order 1 is the block bending. There are no rigid body modes near to the order 1. At the order 0.5 the shape is a combination of pitching and yawing as there is a yawing mode near to the order. Also, the pitching mode is quite close but not very close to the order 0.5. The excitation at the order 0.5 is internal torsion.

The Figure 44 shows the deflection shape at the order 0.5. No other natural frequencies hit very close to the orders or half orders at the nominal speed.

Table 12. Operating deflection shapes of the flexibly mounted W12V31 engine at the nominal speed 750 rpm.

frequency order Shape

6.25 0.5 Pitching and yawing

12.5 1 Mainly vertical bending, some pitching 18.75 1.5 Block torsion

25 2 Block bending

31.25 2.5 Block torsion 37.5 3 Transversal bending

Figure 44. Operating deflection shape of the W12V31 at the order 0.5 (6.25 Hz). The engine is moving rigidly in shape of pitching and yawing. The pitching mode is at 4.25 Hz and yawing at 6.88 Hz.

In the Figure 45 are sweep measurement results with different engine loads. It is seen different amplitudes in pitching mode excited by the order 0.5. That confirms the assump- tion that the pitching mode is excited by the torsional excitation from the load dependent gas forces.

Figure 45. W12V31 sweep measurement FRF with 2 different engine loadings during the sweep. The order 0.5 torsion excitation sweeps the range from 3.9 Hz to 6.7 Hz.

Amplitude of the torsion excitation changes with the engine load as cylinder pressures change. That is seen as the change in pitching mode’s (4.13 Hz) amplitude. The ampli- tude of vibrations excited by mass forces remain the same.