GUIDELINES ON SHAFTING ALIGNMENT phần 6 docx

10.2 Discontinuity in Slope of Total Deflection Curve over Entire Length of Shafting Line Figure 10.4 is a close-up view of the deflection of the aft engine part of the structure obtaine

Fig 10.3 FE model integrated main engine structure with hull used to calculate the displacement at each bearing support point

10.2 Discontinuity in Slope of Total Deflection Curve over Entire Length of Shafting Line

Figure 10.4 is a close-up view of the deflection of the aft engine part of the structure obtained from the model shown in Fig 10.3 As can be seen from the result, while the deflection curve of the top of the double bottom beneath the shafting line is quite smooth, there is clearly a discontinuity at the aft engine end where the deflection curve consists of the point on the top of the double bottom in the shaft portion and the supporting points of the engine bearing in the engine portion of the double bottom

3.00 3.50 4.00 4.50 5.00

6000 8000

10000 12000

14000 16000

18000

Distance from foremost main bearing (mm)

Bearing Line

Aftermost end of the engine

structure

Fig 10.4 FEM results showing discontinuity between slopes of deflection curves of

double bottom and main bearing centers

A discontinuity in the slope of the total deflection curve over the entire shafting line could cause adverse effects on bearing reactions Fig 10.5 shows two sets of bearing heights that differ from each other only in the presence of a slope continuity at the longitudinal boundary between the hull and engine structures While the deflection in the engine portion of the curve in red smoothly joins the deflection in the shaft portion of the curve, the slope of the curve representing the engine portion of the deflection in blue is discontinuous at the longitudinal boundary between the hull and engine structures The bearing reaction forces are calculated for the two sets of bearing offsets, and are shown in Fig 10.6 The shafting model used in this calculation is the same

as that used in previous chapters

46

As can be seen from the results shown in Fig 10.6, the bearing reactions will change significantly if the discontinuity in the slope of the deflection curve exists despite the magnitude of the total hog that remains unchanged In this example, the first aftmost engine bearing becomes overloaded and the second aftmost engine bearing becomes loaded in the wrong direction

Therefore, it is desirable to ascertain whether there is any discontinuity in the slope of the deflection curve, using an integarated engine-hull FE model

Then let's consider why such a discontinuity in the slope of deflection cuve is generated As mentioned before in section 10.1.1, a smooth curve in an elastic body will remain smooth after the body is deformed This can be explained by the fact that the deflection curve at the center line on the double bottom top plate is relatively smooth, as shown in Fig 10.6 It can be easily understood that when assuming there is a straight line directly beneath the double bottom top, then the sraight line will become a smooth curve after hull deformation

Bearing reaction force (kgf), (-) Upward and (+) Downward -200000

-150000

-100000

-50000

0

50000

Bearing number

Original Smooth deflection Deflection with breaking point

Fig 10.6 The effect of slope discontinuity to bearing reactions

continuity at the longitudinal boundary between the hull and engine structures

Fig 10.5 Two sets of bearing heights that differ from each other only in slope

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

Bearing location, distance from left end (mm)

Original offset (mm) Final smooth offset Smooth hull deflection (mm) Straight engine portion Final breaking offset Quadratic polynomial (Smooth hull deflection)

Furthermore, the deflection line of the center line on the top plate of the double bottom will also become a smooth line, neglecting small local deformations between the double bottom top plate and the assumed straight line

On the other hand, the deflection at the supporting points of the engine bearings in the engine portion of the line can not be regarded as coming from the same straight line as the center line on the top plate of the double bottom, as shown in Fig 10.7 While the change in offsets of the intermediate bearing and stern tube bearings comes from the center line on the top plate of the double bottom, the change in offsets of the engine bearings comes from the engine seating lines on the top plate of the double bottom It is noted from the FE analysis results that the displacemet of the top plate of the double bottom varies in the transverse direction, although the magnitude of the fluctuation depends on the location of the cross section Therefore, the discontinuity in the slope of the deflection curve is considered to arise from these variations in displacement in the transverse direction

Fig 10.7 Illustration showing how the slope discontinuity is developed

Schematic sectional deflection curve of the top plate of the double bottom showing variation over the width

Center line on the top plate of the double bottom

Engine seating lines on the top plate of the double bottom Shafting line

10.3 Determination of Final Bearing Offsets in Shafting Installation

Based on the background described above, the final bearing offsets in a shafting installation should be determined so that the shafting alignment can meet all relavent requirements, even after adding both static and dynamic changes in bearing offsets to it

Therefore, specifically, the first step is to determine the bearing offsets as in usual practice Then the next step is to re-calculate the shafting alignment taking into account the predicted changes in bearing offset to check whether the alignment still meets the relevant requirements If the re-calculated result is satisfactory, then the initially obtained bearing offsets can be set as the final parameters for the shafting installation If the re-calculated result is not satisfactory, then the initially obtained bearing offsets should be readjusted until the relevant requirements are met

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11 Confirmation of Bearing Reactions

11.1 Jack-up Method

The Jack-up method is a method in which the reaction of a bearing in question is measured from the jack load that is set as close to the bearing as possible through a separately determined modification factor (see Fig 11.1) The jack load is estimated from the relationship between the jack load and the jack displacement which is recorded during the jack up and jack down process In the jack up test, the dial gauge used to measure the jack displacement should be properly secured so that it is affected by neither the rise of the shaft nor the deformation

of the floor plate

Hydraulic jack Dial gauge

Fig 11.1 Jack-up measurement of the bearing load

11.1.1 Theoretical Jack up Process

The jack up process can be theoretically simulated through calculation It is demonstrated using a shafting model shown in Fig 11.2 The simulation is performed by calculating the relationship between the lift up and the reaction at the jack point The main steps in the simulation are as follows

500 mm

Jack

Fig 11.2 A shafting model used to demonstrate the theoretical jack-up process

- An additional supporting point is generated by setting the jack directly under the shaft at a point 500 mm

away from the intermediate bearing of which the reaction to be measured The reaction of this newly added supporting point is, however, zero at this point

- The jack is gradually lifted, in increments of 0.002 mm in this case, until the bearing load becomes zero The total lift is 0.01587 mm in this case

- Because the bearing has been completely unloaded, it is no longer a supporting point Therefore, the calculation described below is performed using the beam model without the supporting point as shown in Fig 11.3 Since the number of supporting points is reduced by one, the relationship between the jack lift and the jack load (the slope) is also changed The result of the simulation is shown in Fig 11.4

500 mm

Jack

Fig 11.3 A state where the load of the bearing in question is just becoming zero

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

Jack load (kgf)

Intermediate bearing loaded Intermediate bearing unloaded Linear extrapolation (Intermediate bearing unloaded)

P0

R'J

RJ

Fig 11.4 Theoretically calculated jack-up result of the shafting model

Point P0 in the above figure represents a state in which the reaction of the intermediate bearing has just become zero The jack load at this point is represented by R'J By fitting the relationship between the jack lift and the jack load after this point to a linear curve and then extrapolating the line to where the jack lift is zero, the jack load when the jack lift is zero, Rj, can be obtained This load from which the bearing load is usually calculated is, in other words, the jack load when the jack is being set and the bearing in question is removed

50

In this example,

kgf '

R J=244885

kgf

R J =24450

11.1.2 Determination of Bearing Load from Jack up Test

The bearing load RB can be calculated from the obtained jack load RB J using the following equation (11.1)

J

R = × (11.1) where, C is the correction factor calculated as follows:

BJ

BB I

I

where,

IBB: The reaction influence number of the bearing when the jack is regarded as a supporting point

IBJ: The reaction influence number of the bearing to the jack supporting point

In order to better understand the jack up method，Eq (11.1) is derived below Figure 11.5 shows three important states during the jack up process using the calculated shafting lines

Fig 11.5 Deflection curves of the shaft line at three important states during the jack-up process

State 1： The initial state, at this point the reaction of the bearing is RB The jack is set underneath the shaft

but the jack load remains zero This state is represented by the solid black line in Fig 11.5

State 2： After gradually lifting the jack up by a lift of δ, the bearing load becomes zero while the bearing

remains in contact with the shaft This state is represented by the solid red line in Fig 11.5 At this point the jack load is R'J

State 3： Supposing that the bearing has been removed at State 2, the jack is lowered by an amount δ back to the

original setting position This state is represented by the dotted red line in Fig 11.5 During this

process the bearing supporting point is supposed to have lowered by an amount h At this point the

jack load is RJ

State 4： Supposing that the bearing has been set again at the supporting point, the bearing is lifted by an

amount h, until the jack load becomes zero During this process the jack, of course, remains in

contact with the shaft The bearing load at this point is exactly the load RB that is to be measured

In other words, state 4 is identical to state 1

In the process of transition from state 3 to state 4, the change in the bearing and jack loads can be expressed as follows:

Bearing: 0 + IBBh = RB B Jack: RJ＋IBJh = 0 Therefore，

J BJ

BB

I

I

Since the reaction influence numbers for the shafting model shown in Fig 11.5 are:

IBJ = -1538261 (kgf/mm)

IBB = 1535661 (kgf/mm) Therefore, the jack correction factor is:

9983

0.

I

I C BJ

BB =

−

=

In addition, RJ is 24450 kgf as mentioned in 11.1.1, thus the bearing load RB is obtained as follows: B

kgf 24408 24450

.

This result completely agrees with that directly calculated using the beam model described earlier

The bearing load can also be expressed in Eq (11.2), if we consider the process of transition from state 1 to state 2 in the same way as above

JJ

JB

I

I

52

where,

IJJ: The reaction influence number of the jack when the jack is regarded as a supporting point

IJB: The reaction influence number of the jack to the baring

Equation (11.2) theoretically leads to the same result as that obtained from Eq (11.1) In practice, however, R'J is difficult to determine accurately from the measured relationship between the jack lift and jack load, because the real jack load-lift curve will form a loop referred to as an hysteresis curve due to the unavoidable friction in the hydraulic jack Equation (11.2) is thus less used in practice

11.1.3 Analysis Method of Jack up Recording Curves

The hydraulic pressure is higher in the lifting process than in the lowering process for a given external load, because friction between the cylinder and the rod is unavoidable Due to this reason, a loop called an hysteresis curve is generated during the jack up and jack down process as schematically shown in Fig 11.6 To eliminate the effect of the friction, the middle line of the loop should be used to determine the jack load

2

D I J

R R

Jack load

Increasing Decreasing

Average line

RD RJ RI

Fig 11.6 Hysteresis curve of actual jack-up result due to unavoidable friction in hydraulic jack

It is important to confirm the sudden change, known as 'break point', that appears in the slope of the jack load-lift curve The break point comes about because the number of the supporting points in the shafting decreases by one when the bearing load becomes zero If such a break point does not appear and the jack load-lift curve looks like that shown in Fig 11.7, there is a high possibility that the bearing load is nearly zero at the original position

Jack load

Increasing Decreasing

Fig 11.7 Jack-up result showing no break point is a sign that the bearing being unloaded

As noted above, the break point comes about because the number of the supporting points in the shafting decreases by one when the bearing load becomes zero The load of the bearing immediately next to the jack first becomes zero and the first break point appears When the jack continues to rise, then another bearing close

to the jack will also become unloaded and the slope of the jack load-lift curve will become steeper, as shown in Fig 11.8 If the jack continues to rise further, at some point, the upper clearance of the nearest bearing to the jack will finally disappear, causing a downward bearing reaction, and slope of the jack lift-load curve will suddenly decrease Therefore, in order to avoid excessive jack up, it is important to finish the jack-up test as soon as sufficient data for determining RJ has been gathered, after the first break point has appeared

Jack load

No bearing unloaded

First bearing unloaded

Second bearing unloaded

Shaft touched first bearing upper limit

Fig 11.8 Each slope in the jack-up result corresponds to a different shafting model

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11.2 Gauge Method

11.2.1 Mechanism of Gauge Method

The bending moment along the shafting will change when the reactions of the bearings change due to the change

in the bearing offsets Since the change in bending moment at any cross section is linearly proportional to the change in bearing offsets or bearing reactions, the change in bearing offsets or bearing reactions can be reversely calculated from the change in bending moment at several cross sections which are measured

Supposing that the No 4，No 5 and No 6 bearings in Fig 11.9 rise by 1.0 mm, respectively, the change in the bending moment at cross sections 10,000 mm, 17,000 and 18,000 mm from the left end, respectively, is calculated and shown in Table 11.1 These values are called moment influence numbers, and the matrix composed of these moment influence numbers as its elements is referred to as the moment influence number matrix

No.1 No.2 No.3 No.4 No.5 No.6

M 1 M 2 M 3

Fig 11.9 A shafting model for demonstrating gauge method Table 11.1 Bending Moment Influence Number Matrix

Offset (mm) Moment (kgf-mm) δ 4 (1mm) δ 5 (1mm) δ 6 (1mm)

Therefore, the relationship between the change in bending moment and the change in bearing offsets can be given in Eq (11.4)

-28154234 17284736 -12732321

5815648 44923370 -43329799

δ4 δ5 δ6

M1 M2 M3