Elastic Shaft Alignment
(ESA)
April 2015
Rule Note
NR 592 DT R01 E
Marine & Offshore Division
92571 Neuilly sur Seine Cedex – France
Tel: + 33 (0)1 55 24 70 00 – Fax: + 33 (0)1 55 24 70 25
Website: http://www.veristar.com
Email: [email protected]
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BV Mod. Ad. ME 545 L - 7 January 2013
RULE NOTE NR 592
NR 592
Elastic Shaft Alignment
(ESA)
SECTION 1
GENERAL
SECTION 2
ELASTIC SHAFT ALIGNMENT (ESA)
APPENDIX 1
SHAFT ALIGNMENT CALCULATION METHODS
DRAFT March 2015
Section 1
General
1
Introduction
1.1
1.2
2
General
Additional service feature ESA
Additional class notation ESA
Maintenance of ESA notation
6
Documentation to be submitted
Elastic Shaft Alignment (ESA)
1
Overall methodology
1.1
1.2
2
3
4
12
Input data and assumptions
Alignment analysis
13
Input data and assumptions
Alignment analysis
Alignment procedure
6.1
6.2
6.3
6.4
10
Hull deformations
Hull flexibility matrix
Line shafting stiffness matrix
Running calculations
5.1
5.2
6
Structural Finite Element model
Line shafting
Bearings
Static calculations
4.1
4.2
5
8
Preliminary calculations
3.1
3.2
3.3
7
General
Calculations
Models
2.1
2.2
2.3
2
5
Documentation
3.1
Section 2
Objective
Definitions
Application
2.1
2.2
2.3
2.4
3
5
15
General
Ship in dry-dock
Ship afloat
Sea trials
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Appendix 1 Shaft Alignment Calculation Methods
1
General
1.1
2
Introduction
Methodology
2.1
2.2
2.3
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16
16
Hertz contact theory
Oil film calculation
Global equations
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NR 592, Sec 1
SECTION 1
1
1.1
GENERAL
2.1.3 The present Rule Note does not apply to ships
designed with azimuthal thrusters or non conventional shaft
lines intended for main propulsion.
Introduction
Objective
1.1.1 The objective of the present Rule Note is to provide
specific requirements and methodology for shaft alignment
assessment onboard large ships.
1.1.2 Large ships may experience significant hull deformations due to their loading conditions. Moreover, most of
these ships have a high powered propulsion plant with large
diameter shafts fitted in strengthened aft structure. Ship
designers have therefore to integrate the two conflicting
parameters being shaft line stiffness and hull flexibility.
1.1.3 The present Rule Note provides guidelines for calculations in view of hull deflection, aft steelwork elasticity, oil
film behaviour and shaft bearing stiffness as well as the
related requirements.
1.2
1.2.2 Elastic Shaft Alignment (ESA) means the iterative calculation method for shaft alignment described in this Rule
Note.
1.2.3 FE stands for Finite Element.
1.2.4 Sea swell is defined as global regular and long period
waves not created by local weather conditions.
2.1
Application
a) Ships of all types having propulsion power per shaft line
greater than or equal to 30 MW
b) Container ships having propulsion power per shaft line
greater than or equal to 15 MW
c) Liquefied gas carriers having propulsion power per shaft
line greater than or equal to 10 MW.
2.2.2 In case of specific shafting arrangements not covered
by [2.2.1], the Society may require calculations in compliance with the requirements detailed in Sec 2.
Additional class notation ESA
2.3.1 On a voluntary application from interested parties,
ships other than those covered by the scope defined in [2.2]
may be granted with additional class notation ESA, provided that requirements of the present Rule Note are fulfilled. In that case, the applicability of ESA notation is to be
considered on a case by case basis.
2.4
Maintenance of ESA notation
2.4.1 Additional service feature or additional class notation
ESA is definitively assigned to a ship under the following
conditions:
a) the applicable requirements of this Rule Note are fulfilled
b) the onboard shaft alignment is demonstrated to match
system description and input parameters listed in the
approved calculation report.
General
2.1.1 Ships complying with the requirements of the present
Rule Note can be granted with additional service feature or
additional class notation ESA, as defined respectively in
[2.2] and [2.3].
2.1.2 The present Rule Note applies for ships fitted with oil
lubricated shaft line bearings only.
DRAFT March 2015
Additional service feature ESA
2.2.1 Additional service feature ESA is to be assigned to
new ships falling into one of the following categories:
2.3
Definitions
1.2.1 NR467 Rules for the Classification of Steel Ships is
hereafter referred to as "Rules for Steel Ships" in this Rule
Note.
2
2.2
2.4.2 If a modification implemented onboard a ship
granted with ESA notation has an influence on the input
parameters or values of the requested results listed in Sec 2
of this Rule Note, ESA notation may be suspended until a
detailed description of the performed actions and an
updated calculation report showing compliance with applicable requirement are submitted to, and approved by, the
Society.
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NR 592, Sec 1
3
3.1
Documentation
Table 1 : Data to be submitted
N°
Documentation to be submitted
3.1.1 A calculation report is to be submitted for approval. It
is to contain items listed in Tab 1.
The Society may require additional drawings or documentation if deemed necessary.
3.1.2 Details of input parameters to be considered and
required technical data within the scope of ESA notation are
listed in Sec 2.
6
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Item
1
General description of calculation method
2
Assumptions
3
List of investigated calculation conditions
4
Input parameters
5
Detailed results
6
Conclusions
7
Shaft line model
8
Hull flexibility matrix
9
Hull relative deformations
10
View of complete ship FE model
11
Detailed views of FE model of aft part of ship structure
12
Detailed alignment procedure (see Sec 2, [6])
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NR 592, Sec 2
SECTION 2
1
ELASTIC SHAFT ALIGNMENT (ESA)
Overall methodology
1.1
1.1.1
1.1.3 Vibration
These elastic alignment calculations could be supplemented by a global whirling calculation of line shafting and
ship structure which are connected through the oil film stiffness and damping.
General
Scope and objective of shaft alignment
Shaft alignment for main propulsion of ships mainly refers
to rigid and low speed parts of their line shafting. Studied
systems therefore depend on propulsion type installed
onboard. Tab 1 presents common main propulsion types
found on large ships and related shaft alignment scope.
Stern bearings machining and alignment, as well as other
bearing offsets, are to be optimized in order to reach the
most favourable load distribution for relevant operating
conditions.
Prime mover or gearbox is to be positioned to get acceptable loads on each support, and to anticipate thermal
expansion and hull deformation effects.
Table 1 : Propulsion types
and shaft alignment systems
Propulsion type
Direct drive
installation
Geared drive
installation
Prime mover
Alignment system
Low-speed
diesel/gas engine
from propeller
to crankshaft
Electric motor
from propeller
to rotor shaft
Medium-speed
diesel/gas engine
Steam/gas turbine
from propeller
to main gearbox
output shaft
Electric motor
1.1.2
Definitions
a) Elastic alignment calculations consider the relevant line
shafting system and its supports (see [1.1.1]). For each
declared operating condition, the offsets of supports and
the loading of the line shafting are investigated.
b) Offsets are the initial vertical and horizontal positions of
a bearing fixed by the alignment procedure and modified by the flexibility of the structure, the loading deformations and the thermal expansion.
c) The equilibrium of flexible beam elements subjected to
the external forces and supported by bearings is calculated in three dimensions. This means that vertical and
horizontal displacements are coupled.
d) These elastic alignment calculations to be submitted are
necessary to optimize the aft stern tube bearing slope
and the partial slope, if needed. It should be possible to
ensure correct oil film build-up by investigating shaft
location with respect to the oil grooves for declared running conditions.
DRAFT March 2015
The scope of the present Rule Note does not cover vibratory
assessment of ship design and its propulsion line(s).
The Society may require the above whirling calculation on
a case by case basis.
1.2
Calculations
1.2.1 Required input parameters
The conditions of calculation should be as close as possible
to the real operating conditions. The following input parameters are to be considered:
• deformations of the ship structure with respect to the
declared loading conditions of the ship: light ship, ballast, full load, etc. (see [3.1])
• aft hull structure flexibility matrix calculated in way of
each supporting point (see [3.2])
• propeller hydrodynamic efforts (forces and moments) in
vertical and transverse directions in straight course
• thermal expansion of supports (seat, sleeve, antifriction
material)
• deformation of prime mover or gearbox foundation: in
case of low-speed engine, pre-sag of main bearings is to
be considered.
1.2.2 Additional input parameters
Additional parameters could be considered for more precise calculations:
• deformation of ship structure with respect to the sea
swell
• propeller hydrodynamic efforts in turning conditions,
including rudder effects
• temperature effects on lubrication, by a calculation of
local and global dissipation.
1.2.3 Calculation methods
The following calculation principles may be applied for
elastic alignment studies:
• In static conditions: bearing reactions may be calculated
with the Hertz contact theory.
• In running conditions: bearing reactions may be calculated by integration of the oil film pressure which is
given by the Reynold’s equations for a journal bearing.
Guidance on these two methods is given in App 1.
Other possible methods may be considered by the Society
on a case by case basis.
Submitted report should precisely detail calculation process
and the assumptions made.
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NR 592, Sec 2
1.2.4
Assessment
Assessment of the alignment conditions is based on
approval of the output results listed in Tab 2, evaluated
against the criteria listed in Tab 4 and Tab 6.
In addition, results are to be in compliance with the applicable manufacturer limits.
For new ships, guidance on alignment procedure is given in
Article [6].
Table 2 : Results to be submitted
In static conditions:
In running conditions:
Shaft location inside bearings
Squeezing of anti-friction
material (for information)
Oil film thickness
2
2.1.1
The terms of the hull flexibility matrix are to be calculated
at each shaft line support (see [3.2]). For that purpose, the
system is to be limited to the aft part of the ship.
b) Longitudinal secondary stiffeners are to be modeled in
order to ensure a sufficiently refined mesh of the ship
structure. As a consequence, standard size of the finite
elements used is to be based on the secondary stiffener
spacing.
c) The structural model should be built on the basis of the
following criteria:
Structural Finite Element model
General
• Webs of primary members are to be modeled with at
least three elements on their height
Structural FE model of the ship under study is to be used for
preliminary calculations necessary to perform elastic alignment analysis:
• Plating between two primary supporting members is
to be modeled with at least two element stripes
• hull deformations (see [3.1])
• The ratio between the longer side and the shorter
side of the elements is to be less than 3 in the areas
expected to be highly stressed
• hull flexibility matrix (see [3.2]).
2.1.2
Drawings
• Holes for the passage of ordinary stiffeners may be
disregarded.
The FE model is to be performed using at least the following
drawings:
d) Cast part of bossing as well as forward stern tube bush
steelwork should be modeled with solid elements
(8 nodes bricks), as shown on Fig 3.
• structural parts
• steelwork of engine room and double bottom (if any).
2.1.3
Model for hull flexibility matrix
a) Nodes should be restrained in displacement and rotation in way of the forward transverse section.
Models
2.1
2.1.4
FE model is to be precisely refined and developed according to the following guidelines:
Reaction distribution along effective length of aft bush bearing
Oil film pressure
Requirements for calculations of hull deformations are
given in [3.1].
The FE model to be used may be extracted from the model
of the whole ship. It should extend from the aft end up to
the forward watertight bulkhead of the engine room.
Reaction distribution between shaft bearings
Static contact pressure on
anti-friction material
A view of ship FE model for each relevant loading condition
is to be submitted, as shown in Fig 1.
Model for hull deformations
In order to compute hull deflections according to the relevant ship loading conditions, a complete ship FE model is to
be used.
In addition to loading influence, hull deformations due to
sea swell may be also considered.
e) Longitudinal position of the equivalent supporting
points (see [2.3]) is to be exactly the same on the line
shafting and on the structure.
Views of aft hull structure FE model showing modeling
details are to be submitted. See examples shown on Fig 2
and Fig 3.
Figure 1 : Complete ship FE model
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NR 592, Sec 2
Figure 2 : Aft hull structure FE model
Figure 3 : Stern bossing details
2.2
External loads on shafts are to be considered. The following
efforts are listed for reference:
Line shafting
2.2.1 General
The shaft line model is to be based on the exact geometry
and characteristics of shafts and masses which are part of
the mechanical system defined in Tab 1.
2.2.2 Shafts
Shafts are to be modeled using circular or conical beam elements.
For installations directly driven by low-speed diesel/gas
engines, the crankshaft equivalent beam model is to be
used when the exact stiffness matrix of crankshaft is not
available.
Local masses (i.e. propeller, wheels, gears, couplings, etc)
are to be considered in addition to the shaft weight.
Where applicable, buoyancy effects on shaft sections operating in water or oil are to be included in the model.
DRAFT March 2015
• geared installations: tooth forces and moments in each
direction
• direct coupled low-speed engines: chain forces, cylinder weights.
2.2.3 Propeller
Propeller should be modeled by application of additional
mass on shaft model, in way of propeller centre of gravity.
Buoyancy effect in water is to be considered.
Depending on the considered ship loading condition, propeller mass is to be adapted, taking into account the exact
immersion ratio.
Mean values of hydrodynamic propeller efforts are to be
applied in each relevant operating condition, in vertical and
transverse directions.
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NR 592, Sec 2
2.3
2.3.1
3
Bearings
Preliminary calculations
General
For hull flexibility matrix calculation, bearings are to be
modeled with supporting points connected to the structure
(see [3.2]).
3.1
For elastic shaft alignment calculation, line shafting model
should include the following bearing particulars:
Calculation of hull steel work deformation is required for
determination of the relative displacements of the line shafting supports as a function of loading and operating conditions.
• effective contact length
• oil groove angular location
3.1.1
Hull deformations
General
• clearances
• mechanical properties of sleeve and anti-friction materials
3.1.2
• machining of slope and partial slope, if any.
Calculations are to be performed using the FE model of the
whole ship, as mentioned in [2.1.3].
Axial location of supporting points should match exactly for
FE model and shaft line model.
2.3.2
Aft bush bearing
The aftermost bearing is to be modeled with at least five
supporting points in order to have detailed results at each
section of the bearing.
The aft bearing is to be considered as a long bearing for the
chosen elasto-hydrodynamic calculation method.
2.3.3
Other bearings
Each other bearing (forward bush, intermediate bearings,
gearbox or main engine bearings) is to be modeled with one
or more supporting points.
Principle
Since practical alignment operations are generally performed in light ship condition, relative deformations
between light ship and any relevant operating conditions
(ballast and full load in particular) are to be calculated in
order to add the corresponding relative displacements of
bearings to their initial offset values for alignment analysis.
The hull relative displacements previously defined are to be
obtained at each supporting point. Moreover, values are to
be computed according to the reference line defined by the
aftermost support (aft end of stern bush) and the forward
most support of the shaft line, as shown on Fig 4.
Figure 4 : Hull deformations
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DRAFT March 2015
NR 592, Sec 2
3.1.3
i
Deformations due to sea swell
In addition to the deformations of hull structure as a function of loading conditions (see [3.1.2]), the deformations of
hull structure due to sea swell could be included in elastic
alignment calculations, based on the following requirements:
• i = 1: first load case defined by a unit force
applied on the first support in transverse
direction
• i = 2: second load case defined by a unit
force applied on the first support in vertical
direction
a) Influence of sea waves caused by local wind should not
be considered.
b) Sea swell wave characteristics are to be defined for maximizing the double-bottom relative deformation in way
of shaft line supports. Wave parameters (direction,
height H and wave length λ) are to be chosen as follows:
• i = 3: third load case defined by a unit force
applied on the second support in transverse
direction.
j
• Couple (H, λ) is to be physically realistic (i.e: the
wave should not break with the chosen values).
c) Loading due to wave defined by (H,λ) should be
applied, considering two sinusoidal equivalent profiles:
maximum pressure (wave crest) and low pressure (wave
trough) located in way of the aft peak.
d) Relative displacements of shaft supporting points
between the two load cases defined in item c) are to be
considered in elastic alignment calculations as additional bearing offsets included in vector Ub0 (see definition in App 1). The calculated displacements due to sea
swell are to be given at the same points where hull displacements due to ship loading have been calculated
(see [3.1.2]).
3.2.1
Hull flexibility matrix
Definition
In way of supports, the displacements in transverse and vertical directions induced by a transverse or vertical unit force
applied on one support determine a line of the flexibility
matrix.
The flexibility matrix may be written as follows:
⋯ d 1, Tj d 1, Vj
⋱ ⋮
⋮
⋯ d i, Tj d i, Vj
⋱ ⋮
⋮
⋯ d 2n, Tj d 2n, Vj
: Transverse displacement of support j due to
load case i
di, Vj
: Vertical displacement of support j due to load
case i.
The hull flexibility matrix size is to be 2n x 2n.
3.2.3
Data to be submitted
The following data are to be submitted, in electronic format,
as attachment to the calculation report:
• hull flexibility matrix
3.3
General
d 1, T1 d 1, V1
⋮
⋮
d i, T1 d i, V1
⋮
⋮
d 2n, T1 d 2n, V1
di, Tj
• coordinates of the supporting points considered for calculation of the hull flexibility matrix.
The hull flexibility matrix is to be calculated with the model
of aft hull structure described in [2.1.4].
3.2.2
: Index for the considered support (j ∈ [1, n]). For
each support j, two columns are built for transverse and vertical displacements (column
indexes Tj and Vj).
Each term of the hull flexibility matrix is noted as follows:
• Only head sea condition should be investigated.
3.2
: Row index for the load case reference
(i ∈ [1, 2n]). For instance:
3.3.1
Line shafting stiffness matrix
General
Stiffness matrix of line shafting is to be computed, and
reduced if necessary, in way of the supporting points, for
vertical and transverse directions, with a suitable calculation method which should be specified in the submitted
report.
The supporting points considered in this calculation shall
match the supporting points considered in calculation of
the hull flexibility matrix (see [3.2]).
The line shafting stiffness matrix size is to be 2n x 2n.
⋯ d 1, Tn d 1, Vn
⋱
⋮
⋮
⋯ d i, Vn d i, Vn
⋱
⋮
⋮
⋯ d 2n, Tn d 2n, Vn
Influence coefficients are defined as vertical and transverse
variations of the reactions on the supporting points when a
unit displacement is successively applied to each point in
vertical and transverse directions. Calculation of these coefficients is based on the line shafting stiffness matrix.
where:
3.3.2
d
: Displacement in transverse or vertical direction
n
: Total number of supporting points
DRAFT March 2015
Data to be submitted
Table of the influence coefficients is to be submitted for
information.
Bureau Veritas
11
NR 592, Sec 2
4
Static calculations
4.1
4.1.2 Input data
The input data listed in Tab 3 are to be considered for calculation of the static alignment.
Input data and assumptions
4.1.1
4.2
General
The aim of static alignment calculations is to check that the
parameters are adjusted in order to reduce the risk of failure
or excessive wear down in stopped, start-up and slow down
conditions.
Alignment analysis
4.2.1 Methodology
The analysis should be performed with the models
described in Article [2] and the input data listed in [4.1].
An acceptable method is described in App 1.
Bearing offsets and stern bush machining data are to be
optimized at design stage for static conditions.
4.2.2 Output data
For the relevant calculation cases, the results to be submitted for the approval of static calculations are the following:
• maximum contact pressure on each bearing
• distribution of reactions
• squeezing of anti-friction layer
• shaft deflection and slope
• shaft bending moment
• shaft shear force
• shaft bending stress.
Since shaft alignment operations are performed in static
condition, the corresponding calculations are to be made as
accurately as possible, in compliance with the requirements
listed in [4.2]. Static reactions measured by load tests are to
be used for the correlation between calculations and measurements.
The relevant static cases are to be investigated, considering
the possible combination of the following influence parameters:
• ship’s loading condition
4.2.3 Acceptance criteria
The submitted results are to comply with the acceptance
criteria listed in Tab 4.
• ambient temperature in engine room (cold/warm)
• shaft line bolting (connected/opened).
Table 3 : Input data for a static alignment calculation
Input data
No
Calculation data
1
Initial squeezing of antifriction material
Bearings
2
Offsets of supports taking into account thermal expansion, pre-sag and structural deformation (1)
3
Effective length (2)
4
Diameters of shell sleeves and antifriction material layer
5
Young’s modulus and Poisson’s ratio of shell and antifriction material layer
Shafts
6
Outer and inner diameters of shafts in way of supporting points
7
Young’s modulus and Poisson’s ratio of shafts in way of supporting points
8
Stiffness matrix of shaft line in way of supporting points (3)
General
9
External forces and moments (4)
10
Flexibility matrix of steel work (5)
(1)
(2)
(3)
(4)
(5)
12
Hull structural deformations are to be calculated according to [3.1].
Effective length is the active part of the bearing, e.g. chamfers are not considered.
Stiffness matrix of shafts is to be calculated according to [3.2].
External loads listed in [2.2] are to be included.
Flexibility matrix is to be calculated according to [3.2].
Bureau Veritas
DRAFT March 2015
NR 592, Sec 2
Table 4 : Acceptance criteria for static alignment calculations
N°
Result
Limit
1
Maximum local pressure on stern bushes, PB
PB < 110 bars
2
Bearing loads (1)
Reaction values and distribution are to be within the applicable manufacturers’ requirements
Antifriction material type
Specific pressure on stern bushes, PS (2)
3
White metal
Others
PS < 0,8 MPa
PS < 0,6 MPa
4
Mean relative shaft slope in aftmost bearing, θS (3)
The relative slope between shaft and stern bush inner axes is to be less
than the ratio of radial clearance divided by the bearing effective length
5
Shaft bending stress and moment
Calculated bending stress and moment are to be in compliance with the
manufacturers’ requirements
(1)
(2)
For static conditions, recommended load distribution on aft bush bearing is: 2/3 of reaction on aft part, 1/3 on forward part.
Specific pressure PS (in MPa) is defined as follows:
RV
P S = ------------------L eff ⋅ D O
where:
RV
: Total vertical reaction on the considered bearing, in N
Leff
: Effective length of the considered bearing, in mm
DO
: Outer diameter of shaft in way of the considered bearing, in mm.
Mean relative shaft slope is defined as the difference between the slope values calculated at ending nodes of the considered bearing.
(3)
5
Running calculations
5.1
5.1.1
5.2
Alignment analysis
5.2.1
Input data and assumptions
Methodology
The analysis should be performed with the models
described in Article [2] and the input data listed in [5.1].
General
The aim of running alignment calculations is to check that
the parameters are adjusted in order to reduce the risk of oil
film break-up or excessive pressure on the antifriction material when the ship is sailing.
A proposed method is described in App 1.
Figure 5 : Scale of shaft location severity zone
Bearing offsets, stern bush machining data and oil groove
location are to be optimized at design stage for running
conditions.
Z
0.4
Calculations in straight course are to be performed as
defined in [5.2] for each relevant operating condition. The
following influence parameters are to be considered to
define the calculation cases:
• ship’s loading condition
Y
• ambient engine room temperature (cold/warm)
0.4
0.3
• shaft speed (low/mid/maximum).
5.1.2
0.2
!
0.1
#
0.2
"
0.1
0.1
0.2
0.3
8
0.4
$ 0.1
%
As specified in [1.2.2], turning phases are generally critical
for the oil film and bearing behaviour. If realistic propeller
effort values are available for those conditions, it is recommended to perform the corresponding calculations.
0.3
!
& 0.2
0.3
'
'
0.4
Input data
The input data listed in Tab 5 are to be considered for the
alignment calculation in running conditions.
DRAFT March 2015
y and z axes refer to bearing radial clearance, in mm.
Bureau Veritas
13
NR 592, Sec 2
5.2.2
•
•
•
•
•
Output data
For each relevant calculation case, the results to be submitted for approval of the elastic calculations are the following:
• maximum local oil film pressure
• relative position of shaft centres with respect to oil
grooves
squeezing of anti-friction layer
shaft deflection and slope
shaft bending moment
shaft shear force
shaft bending stress.
5.2.3 Acceptance criteria
The submitted results are to comply with the acceptance
criteria listed in Tab 6.
• minimum oil film thickness
• distribution of reactions
Table 5 : Input data for an alignment calculation in running conditions
Input data
No
Calculation data
1
Initial position of shaft in its bearings
Bearings
2
Offsets of supports taking into account thermal expansion, pre-sag and structural deformation (1)
3
Effective length (2)
4
Diameters of shell sleeves and antifriction material layer
5
Young’s modulus and Poisson’s ratio of shell and antifriction material layer
Shafts
6
Outer and inner diameters of shafts in way of supporting points
7
Young’s modulus and Poisson’s ratio of shafts in way of supporting points
8
Stiffness matrix of shaft line in way of supporting points (3)
General
9
Oil viscosity
10
Rotational speed of shafts
11
External forces and moments (4)
12
Flexibility matrix of steel work (5)
(1)
(2)
(3)
(4)
(5)
Hull structural deformations are to be calculated according to [3.1].
Effective length is the active part of the bearing, e.g. chamfers are not considered.
Stiffness matrix of shafts is to be calculated according to [3.2].
External loads listed in [2.2] are to be included.
Flexibility matrix is to be calculated according to [3.2].
Table 6 : Acceptance criteria for alignment calculations in running conditions
N°
Result
Limit
1
Maximum local oil film pressure, PO
PO < 80 bars
2
Bearing loads
Reaction values and distribution are to be within the applicable manufacturers’ requirements
3
Specific pressure on stern bushes, PS (1)
Antifriction material type
Other
PS < 0,8 MPa
PS < 0,6 MPa
4
Shaft position in aft bush with respect to oil
grooves
The shaft centre is to be located in safe areas (see Fig 5)
Zone 0 is forbidden, zone 10 is optimum
5
Minimum oil film thickness, hmin
hmin > 30 µm
6
Mean relative shaft slope, θS (1)
The relative slope between shaft and stern bush inner axes is to be less
than the ratio of radial clearance divided by the bearing effective length
7
Shaft bending stress and moment
Calculated bending stress and moment are to be in compliance with the
manufacturers’ requirements
(1)
14
White metal
See definitions in Tab 4.
Bureau Veritas
DRAFT March 2015
NR 592, Sec 2
6
Alignment procedure
6.3
6.3.1
6.1
6.1.1
General
Data to be submitted
The detailed shaft alignment procedure should be submitted
for approval. It should include the corresponding calculations and description of each step that will be performed
onboard: sightings, shaft installation fitting procedure and
applied measurement tolerances.
Ship afloat
Floating conditions
Final alignment operations should be performed with the
ship afloat in order to take into account the hull deformations due to the hydrostatic pressure. The following steps
should be performed in floating conditions:
• intermediate bearing positioning
• prime mover positioning
• shaft bolting
• load tests.
The final report of measurements performed onboard showing compliance with the approved alignment procedure is
to be submitted to the Society.
6.1.2
Propeller immersion
For the calculation cases corresponding to the alignment
operations, the propeller immersion is to be adjusted in
relation to the foreseen ship loading condition during these
operations.
6.1.3
Recommendations
Sub-articles [6.2] and [6.3] are recommendations about
shaft alignment procedure, including measurement steps
and related tolerance.
These recommendations are only guidance to designers and
shipyards.
6.2
6.2.1
Position of the intermediate bearings and prime mover/gearbox should be adjusted by an accurate method.
If gap/sag method is used to adjust the shaft bearings, the
requirements hereafter should be followed:
• gap/sag values should be calculated and submitted in
the calculation report
• tolerance for gap/sag attained onboard should be typically within a range of 0,05 mm or less compared to the
calculated values.
6.3.3
Bearings load tests
After shaft bolting, final load checkings should be performed on the accessible bearings with jack-up test method.
If applicable, it should be applied on:
• forward bush
• aft gearbox bearings (journal type only)
• three aftmost main engine bearings.
Ambient conditions
As far as possible, laser or optical centering checks should
be performed at night in order to avoid undesirable light or
temperature disturbance.
Sightings
Once the sloping and fitting of stern bushes have been
realised, exact position of their centres should be precisely
checked by optical or laser sightings. Measured vertical and
horizontal offsets of stern bushes should be in accordance
with the theoretical alignment. Maximum deviation
between measurements and optimized offsets should be
typically 0,05 mm or less.
6.2.3
Positioning of bearings
• intermediate bearings
Ship in dry-dock
Relative alignment of stern bushes should be carried out
when weldings of the neighbouring steel work of the aftbody of the ship are completed.
6.2.2
6.3.2
Calculation of correction factors and jacking procedure
should be submitted in the report.
6.4
6.4.1
Sea trials
Test procedure
For running-in of stern bearings, the relevant ship operating
conditions should be tested, including the following
courses:
• straight
• zigzag
• turning.
Test sequences should be sufficiently spaced in time in
order to permit necessary dissipation of heat generated by
the succession of severe loadings, thus avoiding overheating
of stern bearings.
Gearbox/prime mover prepositioning
In addition to stern bushes centering, preliminary positioning of gearbox or prime mover should be performed
(depending on the shaft alignment system, see [1.1.1]).
Vertical and transverse offsets of flywheel or gearwheel centre should be measured and adjusted if necessary, according to the values determined by elastic alignment study.
DRAFT March 2015
6.4.2
Monitoring
The following points should be monitored during sea trials:
• lubricating oil flows
• bearing temperatures
• vibration signs (noises, unusual vibrations in engine
room, etc).
Bureau Veritas
15
NR 592, App 1
APPENDIX 1
1
1.1
SHAFT ALIGNMENT CALCULATION METHODS
General
Introduction
1.1.1 The objective of this Appendix is to give general
guidelines on an acceptable method for elastic alignment
calculations in static and running conditions.
2
2.1
2.2.2 For the application of the oil film theory on the shaft
alignment calculation, the initial shaft displacement inside
the bearing is known (see Fig 2) and the load has to be calculated by integration of pressure along the bearing circumference.
2.3
2.3.1 The global equations are based on the quasi-static
equilibrium of the shaft with the structure, the bearings and
the external forces.
Methodology
Hertz contact theory
2.1.1 When the shaft line is laying on bearings without
rotation, the Hertz contact theory is applicable to describe
the characteristics of the contact: stiffness, reaction, length
of contact, maximum pressure, squeezing.
This calculation is a part of the global resolution of equilibrium (see [2.3]).
2.1.2 The Hertz contact theory is considering a cylinder in
a finite length cylindrical socket with a load applied on the
cylinder. The Hertz law leads to the maximum static pressure and reaction in the contact basing on the mechanical
properties as well as the geometry of the cylinder and the
socket.
The aim is to reach, by an iterative process, the equilibrium
position of the shaft line inside the bearings and to obtain,
with a final Hertz or oil film calculation, the characteristics
of the shaft behaviour in bearings (see Fig 3).
2.3.2 The equations are to take into account the mechanical parameters of all bearings. The problem is then reduced
in way of the supporting points.
2.3.3 General equilibrium equation may be written as follows:
[ K ] ⋅ U + B sb + F ext = 0
where:
[K]
2.1.3 For the application of the Hertz theory on shaft alignment calculations, the cylinder is the shaft and the socket is
the bearing at the supporting point. The displacement of the
shaft inside the bearing is known (see Fig 1) and the contact
pressure and the load have to be calculated considering that
it has the same direction as the displacement Usb.
2.2
Oil film calculation
2.2.1 When the shaft rotates at a sufficient speed, a flow of
oil is induced by its viscosity and the shaft speed creates a
lift of the shaft. There is no more contact between the shaft
and the bearing: the oil film is built-up. The calculation of
this oil film is to be carried-out on the basis of two equations:
U
• a hydrodynamic differential equation which determines
the behaviour of a thin and viscous fluid (Reynolds
equation)
• a geometric equation which determines the height of
the oil film according to the relative position between
the deformed journal of the shaft and its machined profile.
These equations lead to the characteristics of the oil film:
stiffness, reactions, oil pressure, damping.
Bsb
This calculation is a part of the global resolution of equilibrium (see [2.3]).
16
Global equations
Bureau Veritas
: Global stiffness matrix, being a combination of
the following partial matrices:
[Ks]
: Shaft line stiffness matrix, see Sec 2,
[3.3]
[Ksb]
: Stiffness matrix of contact in static
contact or running oil lubricated
contact, see [2.1] and [2.2] respectively
[Eh]
: Hull flexibility matrix as defined in
Sec 2, [3.2]
: Vector of displacements, including the following components, see Fig 1 and Fig 2:
Ub0
: Vector of initial bearing centre position with reference to shaft centre
(without gravity), depending on the
loading condition, temperature and
alignment procedure
Us
: Vector of shaft centre displacements
in way of the supporting points relatively to the reference line
Usb
: Vector of shaft centre relative displacements in way of the supports
: Vector considering the non-linearity of the contact conditions:
B sb = F sb – ( [ K sb ] ⋅ U sb )
where Fsb is the contact force vector
DRAFT March 2015
NR 592, App 1
Fext
: External load vector, including gravity and other
external efforts (propeller, engine, gearing),
reduced in way of the supports. See Sec 2, [2.2].
Then a calculation of the global equation, see Fig 3, determines vector Usb1.
2.3.4 The resolution of this equation is based on an iterative process using an initial displacement Usb0 close to the
equilibrium solution in order to calculate the main contact
characteristics: Ksb0, Fsb0 and Bsb0.
2.3.5 The convergence criteria for this iterative process is
calculated using the maximum absolute difference between
the terms Usbi and Usbi+1. This value is to be less than
0,001 mm.
Figure 1 : Bearing and shaft equilibrium in static condition
Y
Ub o
Ub
Us
Usb
Z
Figure 2 : Bearing and shaft equilibrium in running condition
Y
Ubo
Ub
Us
Usb
Z
DRAFT March 2015
Bureau Veritas
17
NR 592, App 1
Figure 3 : Flow chart of iterative process
Usb1 = Usb0
Resolution of Hertz formula
Oil film calculation
Fext , Ub0, Ks , Eh
Usbi = Usbi+1
Fsbi, Ksbi, Bsbi
Resolution of the signal global
equilibrium equation
Ubi+1
Convergence criteria reached
Max (Usbi+1 - Usbi) < 0,001 mm
No
Yes
Usbn = Usbi+1
Resolution of Hertz formula
Calculation of oil film parameters
18
Bureau Veritas
DRAFT March 2015