GUIDELINES ON SHAFTING ALIGNMENT phần 5 ppsx

7.11 A detailed view of relative displacements on double bottom tank top within the engine portion of the shafting line.. 7.11 also shows, the magnitude of the deflection in Model B+M/E

0.5

1

1.5

Distance from aftmost bulkhead in engine room （mm）

Model B　 Model B+M/E

Fig 7.11 A detailed view of relative displacements on double 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

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 principal, 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 example 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 Bearing Offsets 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

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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 15oC 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 constraints 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

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9 Dynamic Components of Hull Deflection

9.1 Dynamic Hull Deflection Related to Ship Motions

9.1.1 Hull Deflection due to Ship motion

A dynamic component in the hull deflection was detected during the onboard measurement 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

Time

0.058 Hz

0.45 Hz 0.91 Hz

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

PART A GUIDELINES ON SHAFTING ALIGNMENT TAKING INTO ACCOUNT VARIATION IN BEARING OFFSETS WHILE IN SERVICE

12 s

Time

0.068 Hz

0.46 Hz

0.96 Hz

Frequency (Hz)

(a) Time history

(b) Power spectrum

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 Deflection

The magnitude of the above mentioned 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

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-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (S)

5Ch 8Ch 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)

Hog1 Sag1 Hog2 Sag2

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Fig 9.4 Dynamic relative displacement over the span between the aft end of the engine and the fore stern tube bearing

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-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (S)

-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)

Hog1

Hog2

9.2 Deformation due to Thrust

Another factor likely to cause hull deflection while in service is thrust 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

Sag2

Thrust

Fig 9.5 FE model subjected to thrust

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

0 5000

10000 15000

20000 25000

30000 35000

Distance from foremost main bearing (mm)

Without thrust

1.0

Fig 9.6 Absolute displacements of cases with and without thrust

With - Without

0

0.1

0.2

0.3

0.4

0 5000

10000 15000

20000 25000

30000 35000

Distance from foremost main bearing (mm)

Fig 9.7 Relative displacement of the case with thrust to the case without thrust

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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 calculated, 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 points, 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

(a)

(b)

(c)

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)

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 displacement 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 mesh size In such a case, a polynomial of the 3rd to 6th degree fitted to the data could be used in the shafting alignment, considering the deflection curve of a cantilever beam with non-uniform loads

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