PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 0 0.5 1 1.5 10000 15000 20000 25000 30000 Distance from aftmost bulkhead in engine room （mm） Relative displacement （mm） Model B Model B+M/E Fig. 7.11 A detailed view of relative displacements on d ouble bottom tank top within the engine portion of the shafting line. As can be seen from Fig. 7.10, there is a slight difference between the relative displacements in Model B and Model B+M/E. This difference is attributable to the engine seating portion of the shafting line and it was hardly seen in other portions. In addition, as Fig. 7.11 also shows, the magnitude of the deflection in Model B+M/E clearly decreased at the engine seating portion of the shafting line. Namely, the difference in the relative displacements is caused by increases in the double bottom stiffness due to the integration of the main engine. Although the change of the relative displacement is only about 0.2 mm, it should never be disregarded because engine alignments of recent large diesel engines are very sensitive to even small changes in bearing offsets. Therefore, a reliable analysis can only be obtained by integrating a structural model of the main engine and the ship. 36 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 8. Prediction of Thermal Deformation of Engine Bedplate 8.1 Temperature of Engine Structure in Running Condition In the running condition, the upper structure of engine, which is located close to the combustion chambers has, in pri n cipal, a higher temperature than lower structures such as the bedplate, although the exact value depends on the size and output of the engine size. Figure 8.1 shows the approximate temperature ranges of the cylinder block, frame (column), and bedplate for a large-sized engine. FRAME 40~50℃ BED PLATE 40~50℃ CYLINDER BLOCK 80~90℃ Fig. 8.1 An exam ple of the distribution of the temperature in an engine structure in the running condition. 8.2 Thermal Deformation of Engine Bedplate Although thermal deformation of the engine structure will occur three dimensionally , only vertical displacement, however, will affect shafting alignment. Further, vertical displacement can be decomposed into parallel translation and hogging deformation, which will be explained later. The parallel rise in height of all bearing positions is caused mainly by the rise of the average temperature of the engine bedplate. On the other hand, hogging deformation is caused by a relatively larger longitudinal expansion of the upper parts of the engine structure, including the cylinder block, due to the higher temperature of these parts compared with the lower structural parts. The parallel rise of the bearing offsets which has less effect than hogging deformation on shafting alignment has already been taken into consideration during shafting alignment calculation at some shipyards. There have been few examples to permit sufficient consideration of the effect of hogging deformation on shafting alignment due to the difficulty in estimating the extent of such hogging deformation, despite such effect being evident from calculation results. 8.2.1 Parallel Rise of B earing Of fsets Caused by Thermal Expansion The parallel rise of bearing offsets is the result of a uniform rise in height in the vertical direction at each bearing position caused by an increase in the temperature of the engine bedplate. The parallel rise can be easily calculated after the distribution of the temperature in the bedplate is known. The amount of parallel rise in height, Δh, can be calculated by Eq. (8.1), where the temperature of the bedplate can be regarded as linearly distributed in the vertical direction. 37 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE Fig. 8.4 shows the calculated results of an example using a FE model of an engine structure, giving a temperature increase of 15 o C from bottom to top and allowing the structure to deform freely. In this example, a maximum hogging deformation of about 0.1 mm was calculated. For specific engines, however, it is necessary to use more accurate temperature distribution data and constraints from the hull structure. Fig. 8.4 FE model of an engine structure showing hogging displacement at the main bearing center arising from thermal expansion. Thus, in this sense, it is better to consider the effect of the constra i nts of the hull even in cases where data on separate engine hogging is available from the manufacturer. The most accurate method to determine the hogging deflection of an engine bedplate caused by thermal expansion is onboard measurement. This consists of measuring the relative deflections that occurs from cold to warm (hot) condition under given draught (loading) conditions. 39 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 9. Dynamic Components of Hull Deflection 9.1 Dynamic Hull Deflec tion Related to Ship Motions 9.1.1 Hull Deflection d ue to Ship motion A dynamic component in the hull deflection was detected during the onboard meas urement conducted of the subject VLCC by the Society. This is the first time that such a phenomenon could be confirmed by virtue of a measurement system capable of measuring hull deflections automatically and continuously. Figure 9.1 and 9.2 show the time history and power spectrum of the measured hull deflection beside the main engine in both the stop and full speed condition, respectively. The waves in the sea area where the measurements were carried out were comparatively high due to the effects of a typhoon during the time when the measurements were taken. As can be seen from these results, the dominant periodic variation in hull deflection has a frequency of about of 0.06 Hz, while the frequency in full speed condition was a little higher than in the stop condition. The amplitude of the variations in the full speed condition is much greater than in the stop condition. Such periodic fluctuation in hull deflection is considered to be related to the ship motions of pitching and heaving in waves because of its lowness of frequency. Because the resonance frequencies of the undesired lateral and axial vibration of the tightened steel strip are much higher than the frequencies of ship motions, it was unlikely that the strip could have been affected by such ship motions. The subsequent two peaks in the power spectrum diagrams at frequencies of around 0.45 and 0.9 Hz are considered to represent two and three-noded vertical hull vibration respectively. It is, however, negligible in comparison to the variation in deflection due to rigid ship motions. In addition, it is confirmed that the variation of deflection due to rigid ship motions is hardly affected by loading condition and would not appear when the sea is calm, for example, in a protected area in close to shore. 13 s Displacement Time 0.058 Hz 0.45 Hz 0.91 Hz Power spectru m Frequency (Hz) (a) Time history (b) Power spectrum Fig. 9.1 Time history of displacement at the longitudinal middle of the engine and its power spectrum when the ship was in stop condition. 40 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 12 s Time Displacement 0.068 Hz 0.46 Hz 0.96 Hz Power spectru m Frequency (Hz) (a) Time history (b) Power spectru m Fig. 9.2 Time history of displacement at the longitudinal middle of the engine and its power spectrum when the ship was at a full speed of about 18 knots. 9.1.2 Magnitude of Ship Motion Induced Hull D eflection The magnitude of the above m entioned ship motion induced hull deflection will vary , depending on sea conditions, size and speed of the ship, and other factors. In the example of the VLCC on which the measurements discussed here were carried out, the amplitude of the maximum displacement is 0.3 mm in shafting portion of the measurement line and 0.2 mm in engine side portion of the measurement line, respectively. This maximum displacement is almost equivalent to half of the displacement caused by a difference of about 10 m in draught, which is about 0.6 mm. Figures 9.3 and 9.4 show the fluctuations of the measured displacements in the engine side portion and the shafting portion of the measurement line. This is the first time for such a dynamic component in deflection to be detected because of the measurement system's ability to measure continuously and to such a high degree of precision. The dynamic component could be a main contributory factor to the shafting alignment related engine bearing failures reported so far. Fig. 9.3 Dynamic relative displacement over the length of the engine. -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 30 40 50 60 70 80 90 Time (S) Displacement (mm) 5Ch 6Ch 8Ch 9Ch 10Ch -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -2000 0 2000 4000 6000 8000 10000 12000 Location (mm) Displacement (mm) Hog1 Sag1 Hog2 Sag2 41 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE Fig. 9.4 Dynamic relative displacement over the span between the aft end of the engine and the fore stern tube bearing. -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 30 40 50 60 70 80 90 Time (S) Di -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -2000 0 2000 4000 6000 8000 10000 12000 Location (mm) Displacement (mm) Hog1 2Ch 3Ch 4Ch Sag1 Hog2 9.2 Deformation due to Thrust Another factor likely to cause hull deflection while in service is thru st. To verify this, a FE model subjected to thrust corresponding to normal navigation condition was developed, as shown in Fig. 9.5. The calculated result from the FE model is shown in Fig. 9.6 and Fig. 9.7. Figure 9.6 shows the absolute hull deflections with and without thrust, while Fig. 9.7 shows the differences between the two conditions, i.e., the relative deflection from the stop condition to normal navigation condition. As can be seen from Fig. 9.7, thrust will cause a hogging deflection as there is an increase in draught. This effect, however, can be ignored in design, because it is very minimal, being only 0.2 mm over the entire span from the propeller to the fore side of the engine in the VLCC case. splacem m) Sag2 ent (m Thrus t Fig. 9.5 FE model subjected to thrust. 42 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 0.0 2.0 3.0 4.0 5.0 6.0 7.0 05000100001500020000250003000035000 Distance from foremost main bearing (mm) splacement (mm) With thrust Without thrust 1.0 Di Fig. 9.6 Absolute displacements of cases with and without thrust. With - Without 0 0.1 0.2 0.3 0.4 05000100001500020000250003000035000 Distance from foremost main bearing (mm) Displacement (mm) Fig. 9.7 Relative displacement of the case with thrust to the case without thrust. 43 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 10. Determination of Final Bearing Offsets 10.1 Prediction of Relative Displacement over Entire Length of Shafting Line 10.1.1 Prediction of Relative Displacement over Entire Shafting Length by Measurements The change in bearing reaction forces due to variations in the bearing offsets can be calculate d, provided that the relative displacement to a reference straight line passing through both end bearing supporting points can be measured as shown in Fig. 10.1. However, only the displacements of the top of the bottom plating at shafting portion of a shafting line within the engine room and along side the main engine can be actually measured, as shown in Fig. 10.1(b). In order to recreate the entire relative displacement over the shafting span from these separately measured displacements, it is necessary to assume that all bearing supporting points are on a smooth curve. The 'smooth curve' mentioned here is defined as a curve whose differential function varies continuously from point to point along the curve. If this assumption is proved acceptable, the whole relative displacement can be recreated by joining these separately measured displace lines with the same slope at their joining points, as show in Fig. 10.1(c). In addition, as shown in the figure, the displacement within the stern tube is approximated as a straight line. It is noteworthy that the curves mentioned here are curves that join the bearing supporting p oints, and are not the shafting lines themselves. Actually measurable displacements Displacements necessary to calculate bearing reactions Fig. 10.1 Total displacement can be recreated by connecting separately measured displacements at shafting and engine portion of the shafting line, having the different displacement curves have the same slopes at each connecting points. (a) Original bearing support line. (b) Bearing support line after deformation. (c) Entire bearing support line recreated from separate sets of measured displacements. (a) (b) (c) 44 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE It can be is easily understood that all bearing supporting points will lie on a smooth curve, assuming that all bearing supporting points were initially on a straight line in an elastic body, as shown in Fig. 10.2. A straight line a-b in an elastic body will become a curve a'-b' after the elastic body is deformed under an external force or enforced restraints, as shown in Fig. 10.2(b). Since the derivative of displacement in the Y direction with respect to x denotes shear strain, the derivative must have a unique value at any point. Therefore, the displacement curve in the Y direction must be continuous and smooth. x y z a b (a) a' b ' (b) v a'- b ' x (c) Fig. 10.2 (a) A straight line a-b in an elastic body. (b) The line a-b becomes a curve a'-b ' after the body is deformed. (c) The curve a'-b' must be smooth and continuous, since the differential dv/dx represents shear strain. 10.1.2 Prediction of Relative Displacement over Entire Shafting Length by Calculations Another way other besides measurement to estimate the relative di splace ment over the entire shafting length is to use a FE model that integrates the engine structure with the hull structure, as shown in Fig. 10.3. Since the FEM can be used to estimate the entire relative displacement directly, there is no need to recreate the entire relative displacement from separately obtained displacements. Furthermore, once the FE model has been validated, it can be used to evaluate the potential effect of any structural alteration. Therefore, it is desirable to perform FE analysis as the circumstances permit. However, the bearing offsets obtained do not necessarily lie on a smooth line due to the mes h size. In such a case, a polynomial of the 3 rd to 6 th degree fitted to the data could be used in the shafting alignment, considering the deflection curve of a cantilever beam with non-uniform loads. 45 . deformation on shafting alignment has already been taken into consideration during shafting alignment calculation at some shipyards. There have been few examples to permit sufficient consideration. speed condition was a little higher than in the stop condition. The amplitude of the variations in the full speed condition is much greater than in the stop condition. Such periodic fluctuation. draught (loading) conditions. 39 PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE 9. Dynamic Components of Hull Deflection 9.1 Dynamic