elastic shaft alignment (esa)

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

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BV Mod. Ad. ME 545 L - 7 January 2013

MARINE & OFFSHORE DIVISIONGENERAL CONDITIONS

RULE NOTE NR 592

NR 592Elastic 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 5

1.1 Objective1.2 Definitions

2 Application 5

2.1 General2.2 Additional service feature ESA2.3 Additional class notation ESA2.4 Maintenance of ESA notation

3 Documentation 6

3.1 Documentation to be submitted

Section 2 Elastic Shaft Alignment (ESA)

1 Overall methodology 7

1.1 General1.2 Calculations

2 Models 8

2.1 Structural Finite Element model2.2 Line shafting2.3 Bearings

3 Preliminary calculations 10

3.1 Hull deformations3.2 Hull flexibility matrix3.3 Line shafting stiffness matrix

4 Static calculations 12

4.1 Input data and assumptions4.2 Alignment analysis

5 Running calculations 13

5.1 Input data and assumptions5.2 Alignment analysis

6 Alignment procedure 15

6.1 General6.2 Ship in dry-dock6.3 Ship afloat6.4 Sea trials

2 Bureau Veritas DRAFT March 2015

Appendix 1 Shaft Alignment Calculation Methods

1 General 16

1.1 Introduction

2 Methodology 16

2.1 Hertz contact theory2.2 Oil film calculation2.3 Global equations

DRAFT March 2015 Bureau Veritas 3

NR 592, Sec 1

SECTION 1 GENERAL

1 Introduction

1.1 Objective

1.1.1 The objective of the present Rule Note is to providespecific requirements and methodology for shaft alignmentassessment onboard large ships.

1.1.2 Large ships may experience significant hull deforma-tions due to their loading conditions. Moreover, most ofthese ships have a high powered propulsion plant with largediameter shafts fitted in strengthened aft structure. Shipdesigners have therefore to integrate the two conflictingparameters being shaft line stiffness and hull flexibility.

1.1.3 The present Rule Note provides guidelines for calcu-lations in view of hull deflection, aft steelwork elasticity, oilfilm behaviour and shaft bearing stiffness as well as therelated requirements.

1.2 Definitions

1.2.1 NR467 Rules for the Classification of Steel Ships ishereafter referred to as "Rules for Steel Ships" in this RuleNote.

1.2.2 Elastic Shaft Alignment (ESA) means the iterative cal-culation method for shaft alignment described in this RuleNote.

1.2.3 FE stands for Finite Element.

1.2.4 Sea swell is defined as global regular and long periodwaves not created by local weather conditions.

2 Application

2.1 General

2.1.1 Ships complying with the requirements of the presentRule Note can be granted with additional service feature oradditional class notation ESA, as defined respectively in[2.2] and [2.3].

2.1.2 The present Rule Note applies for ships fitted with oillubricated shaft line bearings only.

2.1.3 The present Rule Note does not apply to shipsdesigned with azimuthal thrusters or non conventional shaftlines intended for main propulsion.

2.2 Additional service feature ESA

2.2.1 Additional service feature ESA is to be assigned tonew ships falling into one of the following categories:

a) Ships of all types having propulsion power per shaft linegreater than or equal to 30 MW

b) Container ships having propulsion power per shaft linegreater than or equal to 15 MW

c) Liquefied gas carriers having propulsion power per shaftline greater than or equal to 10 MW.

2.2.2 In case of specific shafting arrangements not coveredby [2.2.1], the Society may require calculations in compli-ance with the requirements detailed in Sec 2.

2.3 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, pro-vided that requirements of the present Rule Note are ful-filled. In that case, the applicability of ESA notation is to beconsidered on a case by case basis.

2.4 Maintenance of ESA notation

2.4.1 Additional service feature or additional class notationESA is definitively assigned to a ship under the followingconditions:

a) the applicable requirements of this Rule Note are ful-filled

b) the onboard shaft alignment is demonstrated to matchsystem description and input parameters listed in theapproved calculation report.

2.4.2 If a modification implemented onboard a shipgranted with ESA notation has an influence on the inputparameters or values of the requested results listed in Sec 2of this Rule Note, ESA notation may be suspended until adetailed description of the performed actions and anupdated calculation report showing compliance with appli-cable requirement are submitted to, and approved by, theSociety.


NR 592, Sec 1

3 Documentation

3.1 Documentation to be submitted

3.1.1 A calculation report is to be submitted for approval. Itis to contain items listed in Tab 1.The Society may require additional drawings or documenta-tion if deemed necessary.

3.1.2 Details of input parameters to be considered andrequired technical data within the scope of ESA notation arelisted in Sec 2.

Table 1 : Data to be submitted

N° 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])


NR 592, Sec 2

SECTION 2 ELASTIC SHAFT ALIGNMENT (ESA)

1 Overall methodology

1.1 General

1.1.1 Scope and objective of shaft alignment

Shaft alignment for main propulsion of ships mainly refersto rigid and low speed parts of their line shafting. Studiedsystems therefore depend on propulsion type installedonboard. Tab 1 presents common main propulsion typesfound on large ships and related shaft alignment scope.

Stern bearings machining and alignment, as well as otherbearing offsets, are to be optimized in order to reach themost favourable load distribution for relevant operatingconditions.

Prime mover or gearbox is to be positioned to get accept-able loads on each support, and to anticipate thermalexpansion and hull deformation effects.

Table 1 : Propulsion types and shaft alignment systems

1.1.2 Definitions

a) Elastic alignment calculations consider the relevant lineshafting system and its supports (see [1.1.1]). For eachdeclared operating condition, the offsets of supports andthe loading of the line shafting are investigated.

b) Offsets are the initial vertical and horizontal positions ofa bearing fixed by the alignment procedure and modi-fied by the flexibility of the structure, the loading defor-mations and the thermal expansion.

c) The equilibrium of flexible beam elements subjected tothe external forces and supported by bearings is calcu-lated in three dimensions. This means that vertical andhorizontal displacements are coupled.

d) These elastic alignment calculations to be submitted arenecessary to optimize the aft stern tube bearing slopeand the partial slope, if needed. It should be possible toensure correct oil film build-up by investigating shaftlocation with respect to the oil grooves for declared run-ning conditions.

1.1.3 VibrationThese elastic alignment calculations could be supple-mented by a global whirling calculation of line shafting andship structure which are connected through the oil film stiff-ness and damping.

The scope of the present Rule Note does not cover vibratoryassessment of ship design and its propulsion line(s).

The Society may require the above whirling calculation ona case by case basis.

1.2 Calculations

1.2.1 Required input parametersThe conditions of calculation should be as close as possibleto the real operating conditions. The following input param-eters are to be considered:• deformations of the ship structure with respect to the

declared loading conditions of the ship: light ship, bal-last, full load, etc. (see [3.1])

• aft hull structure flexibility matrix calculated in way ofeach supporting point (see [3.2])

• propeller hydrodynamic efforts (forces and moments) invertical and transverse directions in straight course

• thermal expansion of supports (seat, sleeve, antifrictionmaterial)

• deformation of prime mover or gearbox foundation: incase of low-speed engine, pre-sag of main bearings is tobe considered.

1.2.2 Additional input parametersAdditional parameters could be considered for more pre-cise 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 methodsThe following calculation principles may be applied forelastic alignment studies:• In static conditions: bearing reactions may be calculated

with the Hertz contact theory.• In running conditions: bearing reactions may be calcu-

lated by integration of the oil film pressure which isgiven 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 Societyon a case by case basis.

Submitted report should precisely detail calculation processand the assumptions made.

Propulsion type Prime mover Alignment system

Direct drive installation

Low-speed diesel/gas engine

from propeller to crankshaft

Electric motorfrom propeller to rotor shaft

Geared drive installation

Medium-speed diesel/gas engine from propeller

to main gearbox output shaft

Steam/gas turbine

Electric motor


NR 592, Sec 2

1.2.4 Assessment

Assessment of the alignment conditions is based onapproval of the output results listed in Tab 2, evaluatedagainst the criteria listed in Tab 4 and Tab 6.

In addition, results are to be in compliance with the appli-cable manufacturer limits.

For new ships, guidance on alignment procedure is given inArticle [6].

Table 2 : Results to be submitted

2 Models

2.1 Structural Finite Element model

2.1.1 General

Structural FE model of the ship under study is to be used forpreliminary calculations necessary to perform elastic align-ment analysis:

• hull deformations (see [3.1])

• hull flexibility matrix (see [3.2]).

2.1.2 Drawings

The FE model is to be performed using at least the followingdrawings:

• structural parts

• steelwork of engine room and double bottom (if any).

2.1.3 Model for hull deformations

In order to compute hull deflections according to the rele-vant ship loading conditions, a complete ship FE model is tobe used.

In addition to loading influence, hull deformations due tosea swell may be also considered.

A view of ship FE model for each relevant loading conditionis to be submitted, as shown in Fig 1.

Requirements for calculations of hull deformations aregiven in [3.1].

2.1.4 Model for hull flexibility matrix

The terms of the hull flexibility matrix are to be calculatedat each shaft line support (see [3.2]). For that purpose, thesystem is to be limited to the aft part of the ship.

The FE model to be used may be extracted from the modelof the whole ship. It should extend from the aft end up tothe forward watertight bulkhead of the engine room.

FE model is to be precisely refined and developed accord-ing to the following guidelines:

a) Nodes should be restrained in displacement and rota-tion in way of the forward transverse section.

b) Longitudinal secondary stiffeners are to be modeled inorder to ensure a sufficiently refined mesh of the shipstructure. As a consequence, standard size of the finiteelements used is to be based on the secondary stiffenerspacing.

c) The structural model should be built on the basis of thefollowing criteria:

• Webs of primary members are to be modeled with atleast three elements on their height

• Plating between two primary supporting members isto be modeled with at least two element stripes

• The ratio between the longer side and the shorterside of the elements is to be less than 3 in the areasexpected to be highly stressed

• Holes for the passage of ordinary stiffeners may bedisregarded.

d) Cast part of bossing as well as forward stern tube bushsteelwork should be modeled with solid elements(8 nodes bricks), as shown on Fig 3.

e) Longitudinal position of the equivalent supportingpoints (see [2.3]) is to be exactly the same on the lineshafting and on the structure.

Views of aft hull structure FE model showing modelingdetails are to be submitted. See examples shown on Fig 2and Fig 3.

Figure 1 : Complete ship FE model

In static conditions: In running conditions:

Reaction distribution between shaft bearings

Reaction distribution along effective length of aft bush bearing

Shaft location inside bearings

Static contact pressure on anti-friction material

Oil film pressure

Squeezing of anti-friction material (for information)

Oil film thickness


NR 592, Sec 2

Figure 2 : Aft hull structure FE model

Figure 3 : Stern bossing details

2.2 Line shafting

2.2.1 GeneralThe shaft line model is to be based on the exact geometryand characteristics of shafts and masses which are part ofthe mechanical system defined in Tab 1.

2.2.2 ShaftsShafts are to be modeled using circular or conical beam ele-ments.

For installations directly driven by low-speed diesel/gasengines, the crankshaft equivalent beam model is to beused when the exact stiffness matrix of crankshaft is notavailable.

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 oper-ating in water or oil are to be included in the model.

External loads on shafts are to be considered. The followingefforts are listed for reference:

• geared installations: tooth forces and moments in eachdirection

• direct coupled low-speed engines: chain forces, cylin-der weights.

2.2.3 PropellerPropeller should be modeled by application of additionalmass 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, pro-peller mass is to be adapted, taking into account the exactimmersion ratio.

Mean values of hydrodynamic propeller efforts are to beapplied in each relevant operating condition, in vertical andtransverse directions.


NR 592, Sec 2

2.3 Bearings

2.3.1 General

For hull flexibility matrix calculation, bearings are to bemodeled with supporting points connected to the structure(see [3.2]).

For elastic shaft alignment calculation, line shafting modelshould include the following bearing particulars:

• effective contact length

• oil groove angular location

• clearances

• mechanical properties of sleeve and anti-friction materials

• machining of slope and partial slope, if any.

Axial location of supporting points should match exactly forFE model and shaft line model.

2.3.2 Aft bush bearing

The aftermost bearing is to be modeled with at least fivesupporting points in order to have detailed results at eachsection of the bearing.

The aft bearing is to be considered as a long bearing for thechosen 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 oneor more supporting points.

3 Preliminary calculations

3.1 Hull deformations

3.1.1 General

Calculation of hull steel work deformation is required fordetermination of the relative displacements of the line shaft-ing supports as a function of loading and operating condi-tions.

3.1.2 Principle

Calculations are to be performed using the FE model of thewhole ship, as mentioned in [2.1.3].

Since practical alignment operations are generally per-formed in light ship condition, relative deformationsbetween light ship and any relevant operating conditions(ballast and full load in particular) are to be calculated inorder to add the corresponding relative displacements ofbearings to their initial offset values for alignment analysis.

The hull relative displacements previously defined are to beobtained at each supporting point. Moreover, values are tobe computed according to the reference line defined by theaftermost support (aft end of stern bush) and the forwardmost support of the shaft line, as shown on Fig 4.

Figure 4 : Hull deformations


NR 592, Sec 2

3.1.3 Deformations due to sea swell

In addition to the deformations of hull structure as a func-tion of loading conditions (see [3.1.2]), the deformations ofhull structure due to sea swell could be included in elasticalignment calculations, based on the following require-ments:

a) Influence of sea waves caused by local wind should notbe considered.

b) Sea swell wave characteristics are to be defined for max-imizing the double-bottom relative deformation in wayof shaft line supports. Wave parameters (direction,height H and wave length λ) are to be chosen as fol-lows:

• Couple (H, λ) is to be physically realistic (i.e: thewave should not break with the chosen values).

• Only head sea condition should be investigated.

c) Loading due to wave defined by (H,λ) should beapplied, considering two sinusoidal equivalent profiles:maximum pressure (wave crest) and low pressure (wavetrough) located in way of the aft peak.

d) Relative displacements of shaft supporting pointsbetween the two load cases defined in item c) are to beconsidered in elastic alignment calculations as addi-tional bearing offsets included in vector Ub

0 (see defini-tion in App 1). The calculated displacements due to seaswell are to be given at the same points where hull dis-placements due to ship loading have been calculated(see [3.1.2]).

3.2 Hull flexibility matrix

3.2.1 General

The hull flexibility matrix is to be calculated with the modelof aft hull structure described in [2.1.4].

3.2.2 Definition

In way of supports, the displacements in transverse and ver-tical directions induced by a transverse or vertical unit forceapplied on one support determine a line of the flexibilitymatrix.

The flexibility matrix may be written as follows:

where:

d : Displacement in transverse or vertical direction

n : Total number of supporting points

i : Row index for the load case reference(i ∈ [1, 2n]). For instance:

• i = 1: first load case defined by a unit forceapplied on the first support in transversedirection

• i = 2: second load case defined by a unitforce applied on the first support in verticaldirection

• i = 3: third load case defined by a unit forceapplied on the second support in transversedirection.

j : Index for the considered support (j ∈ [1, n]). Foreach support j, two columns are built for trans-verse and vertical displacements (columnindexes Tj and Vj).

Each term of the hull flexibility matrix is noted as follows:

di, Tj : Transverse displacement of support j due toload case i

di, Vj : Vertical displacement of support j due to loadcase 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

• coordinates of the supporting points considered for cal-culation of the hull flexibility matrix.

3.3 Line shafting stiffness matrix

3.3.1 General

Stiffness matrix of line shafting is to be computed, andreduced if necessary, in way of the supporting points, forvertical and transverse directions, with a suitable calcula-tion method which should be specified in the submittedreport.

The supporting points considered in this calculation shallmatch the supporting points considered in calculation ofthe hull flexibility matrix (see [3.2]).

The line shafting stiffness matrix size is to be 2n x 2n.

Influence coefficients are defined as vertical and transversevariations of the reactions on the supporting points when aunit displacement is successively applied to each point invertical and transverse directions. Calculation of these coef-ficients is based on the line shafting stiffness matrix.


Table of the influence coefficients is to be submitted forinformation.

d1 T1, d1 V1, ⋯ d1 Tj, d1 Vj, ⋯ d1 Tn, d1 Vn,⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ ⋮di T1, di V1, ⋯ di Tj, di Vj, ⋯ di Vn, di Vn,⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ ⋮d2n T1, d2n V1, ⋯ d2n Tj, d2n Vj, ⋯ d2n Tn, d2n Vn,


NR 592, Sec 2

4 Static calculations

4.1 Input data and assumptions

4.1.1 General

The aim of static alignment calculations is to check that theparameters are adjusted in order to reduce the risk of failureor excessive wear down in stopped, start-up and slow downconditions.

Bearing offsets and stern bush machining data are to beoptimized at design stage for static conditions.

Since shaft alignment operations are performed in staticcondition, the corresponding calculations are to be made asaccurately as possible, in compliance with the requirementslisted in [4.2]. Static reactions measured by load tests are tobe used for the correlation between calculations and mea-surements.

The relevant static cases are to be investigated, consideringthe possible combination of the following influence param-eters:

• ship’s loading condition

• ambient temperature in engine room (cold/warm)

• shaft line bolting (connected/opened).

4.1.2 Input dataThe input data listed in Tab 3 are to be considered for calcu-lation of the static alignment.

4.2 Alignment analysis

4.2.1 MethodologyThe analysis should be performed with the modelsdescribed in Article [2] and the input data listed in [4.1].

An acceptable method is described in App 1.

4.2.2 Output dataFor the relevant calculation cases, the results to be submit-ted 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.

4.2.3 Acceptance criteriaThe submitted results are to comply with the acceptancecriteria listed in Tab 4.

Table 3 : Input data for a static alignment calculation

No Input data

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) Hull structural deformations are to be calculated according to [3.1].(2) Effective length is the active part of the bearing, e.g. chamfers are not considered.(3) Stiffness matrix of shafts is to be calculated according to [3.2].(4) External loads listed in [2.2] are to be included.(5) Flexibility matrix is to be calculated according to [3.2].


NR 592, Sec 2

Table 4 : Acceptance criteria for static alignment calculations

5 Running calculations

5.1 Input data and assumptions

5.1.1 General

The aim of running alignment calculations is to check thatthe parameters are adjusted in order to reduce the risk of oilfilm break-up or excessive pressure on the antifriction mate-rial when the ship is sailing.

Bearing offsets, stern bush machining data and oil groovelocation are to be optimized at design stage for runningconditions.

Calculations in straight course are to be performed asdefined in [5.2] for each relevant operating condition. Thefollowing influence parameters are to be considered todefine the calculation cases:

• ship’s loading condition

• ambient engine room temperature (cold/warm)

• shaft speed (low/mid/maximum).

As specified in [1.2.2], turning phases are generally criticalfor the oil film and bearing behaviour. If realistic propellereffort values are available for those conditions, it is recom-mended to perform the corresponding calculations.

5.1.2 Input data

The input data listed in Tab 5 are to be considered for thealignment calculation in running conditions.

5.2 Alignment analysis

5.2.1 Methodology

The analysis should be performed with the modelsdescribed in Article [2] and the input data listed in [5.1].

A proposed method is described in App 1.

Figure 5 : Scale of shaft location severity zone

y and z axes refer to bearing radial clearance, in mm.

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 manu-facturers’ requirements

3 Specific pressure on stern bushes, PS (2)

Antifriction material type

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 lessthan the ratio of radial clearance divided by the bearing effective length

5 Shaft bending stress and momentCalculated bending stress and moment are to be in compliance with themanufacturers’ requirements

(1) For static conditions, recommended load distribution on aft bush bearing is: 2/3 of reaction on aft part, 1/3 on forward part.(2) Specific pressure PS (in MPa) is defined as follows:

where:RV : Total vertical reaction on the considered bearing, in NLeff : Effective length of the considered bearing, in mmDO : Outer diameter of shaft in way of the considered bearing, in mm.

(3) Mean relative shaft slope is defined as the difference between the slope values calculated at ending nodes of the considered bearing.

PSRV

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NR 592, Sec 2

5.2.2 Output data

For each relevant calculation case, the results to be submit-ted for approval of the elastic calculations are the following:

• maximum local oil film pressure

• relative position of shaft centres with respect to oilgrooves

• minimum oil film thickness

• distribution of reactions

• squeezing of anti-friction layer• shaft deflection and slope• shaft bending moment• shaft shear force• shaft bending stress.

5.2.3 Acceptance criteriaThe submitted results are to comply with the acceptancecriteria listed in Tab 6.

Table 5 : Input data for an alignment calculation in running conditions

Table 6 : Acceptance criteria for alignment calculations in running conditions

No Input data

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) Hull structural deformations are to be calculated according to [3.1].(2) Effective length is the active part of the bearing, e.g. chamfers are not considered.(3) Stiffness matrix of shafts is to be calculated according to [3.2].(4) External loads listed in [2.2] are to be included.(5) Flexibility matrix is to be calculated according to [3.2].

N° Result Limit

1 Maximum local oil film pressure, PO PO < 80 bars

2 Bearing loadsReaction values and distribution are to be within the applicable manu-facturers’ requirements

3 Specific pressure on stern bushes, PS (1)

Antifriction material type

White metal Other

PS < 0,8 MPa PS < 0,6 MPa

4Shaft 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 lessthan the ratio of radial clearance divided by the bearing effective length

7 Shaft bending stress and momentCalculated bending stress and moment are to be in compliance with themanufacturers’ requirements

(1) See definitions in Tab 4.


NR 592, Sec 2

6 Alignment procedure

6.1 General


The detailed shaft alignment procedure should be submittedfor approval. It should include the corresponding calcula-tions and description of each step that will be performedonboard: sightings, shaft installation fitting procedure andapplied measurement tolerances.

The final report of measurements performed onboard show-ing compliance with the approved alignment procedure isto be submitted to the Society.

6.1.2 Propeller immersion

For the calculation cases corresponding to the alignmentoperations, the propeller immersion is to be adjusted inrelation to the foreseen ship loading condition during theseoperations.

6.1.3 Recommendations

Sub-articles [6.2] and [6.3] are recommendations aboutshaft alignment procedure, including measurement stepsand related tolerance.

These recommendations are only guidance to designers andshipyards.

6.2 Ship in dry-dock

6.2.1 Ambient conditions

Relative alignment of stern bushes should be carried outwhen weldings of the neighbouring steel work of the aft-body of the ship are completed.

As far as possible, laser or optical centering checks shouldbe performed at night in order to avoid undesirable light ortemperature disturbance.

6.2.2 Sightings

Once the sloping and fitting of stern bushes have beenrealised, exact position of their centres should be preciselychecked by optical or laser sightings. Measured vertical andhorizontal offsets of stern bushes should be in accordancewith the theoretical alignment. Maximum deviationbetween measurements and optimized offsets should betypically 0,05 mm or less.

6.2.3 Gearbox/prime mover prepositioning

In addition to stern bushes centering, preliminary position-ing 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 cen-tre should be measured and adjusted if necessary, accord-ing to the values determined by elastic alignment study.

6.3 Ship afloat

6.3.1 Floating conditions

Final alignment operations should be performed with theship afloat in order to take into account the hull deforma-tions due to the hydrostatic pressure. The following stepsshould be performed in floating conditions:

• intermediate bearing positioning

• prime mover positioning

• shaft bolting

• load tests.

6.3.2 Positioning of bearings

Position of the intermediate bearings and prime mover/gear-box should be adjusted by an accurate method.

If gap/sag method is used to adjust the shaft bearings, therequirements hereafter should be followed:

• gap/sag values should be calculated and submitted inthe calculation report

• tolerance for gap/sag attained onboard should be typi-cally within a range of 0,05 mm or less compared to thecalculated values.

6.3.3 Bearings load tests

After shaft bolting, final load checkings should be per-formed on the accessible bearings with jack-up test method.If applicable, it should be applied on:

• forward bush

• intermediate bearings

• aft gearbox bearings (journal type only)

• three aftmost main engine bearings.

Calculation of correction factors and jacking procedureshould be submitted in the report.

6.4 Sea trials

6.4.1 Test procedure

For running-in of stern bearings, the relevant ship operatingconditions should be tested, including the followingcourses:

• straight

• zigzag

• turning.

Test sequences should be sufficiently spaced in time inorder to permit necessary dissipation of heat generated bythe succession of severe loadings, thus avoiding overheatingof stern bearings.

6.4.2 Monitoring

The following points should be monitored during sea trials:

• lubricating oil flows

• bearing temperatures

• vibration signs (noises, unusual vibrations in engineroom, etc).


NR 592, App 1

APPENDIX 1 SHAFT ALIGNMENT CALCULATION METHODS

1 General

1.1 Introduction

1.1.1 The objective of this Appendix is to give generalguidelines on an acceptable method for elastic alignmentcalculations in static and running conditions.

2 Methodology

2.1 Hertz contact theory

2.1.1 When the shaft line is laying on bearings withoutrotation, the Hertz contact theory is applicable to describethe characteristics of the contact: stiffness, reaction, lengthof contact, maximum pressure, squeezing.

This calculation is a part of the global resolution of equilib-rium (see [2.3]).

2.1.2 The Hertz contact theory is considering a cylinder ina finite length cylindrical socket with a load applied on thecylinder. The Hertz law leads to the maximum static pres-sure and reaction in the contact basing on the mechanicalproperties as well as the geometry of the cylinder and thesocket.

2.1.3 For the application of the Hertz theory on shaft align-ment calculations, the cylinder is the shaft and the socket isthe bearing at the supporting point. The displacement of theshaft inside the bearing is known (see Fig 1) and the contactpressure and the load have to be calculated considering thatit 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 ofoil is induced by its viscosity and the shaft speed creates alift of the shaft. There is no more contact between the shaftand the bearing: the oil film is built-up. The calculation ofthis oil film is to be carried-out on the basis of two equa-tions:

• a hydrodynamic differential equation which determinesthe behaviour of a thin and viscous fluid (Reynoldsequation)

• a geometric equation which determines the height ofthe oil film according to the relative position betweenthe deformed journal of the shaft and its machined pro-file.

These equations lead to the characteristics of the oil film:stiffness, reactions, oil pressure, damping.

This calculation is a part of the global resolution of equilib-rium (see [2.3]).

2.2.2 For the application of the oil film theory on the shaftalignment calculation, the initial shaft displacement insidethe bearing is known (see Fig 2) and the load has to be cal-culated by integration of pressure along the bearing circum-ference.

2.3 Global equations

2.3.1 The global equations are based on the quasi-staticequilibrium of the shaft with the structure, the bearings andthe external forces.

The aim is to reach, by an iterative process, the equilibriumposition of the shaft line inside the bearings and to obtain,with a final Hertz or oil film calculation, the characteristicsof the shaft behaviour in bearings (see Fig 3).

2.3.2 The equations are to take into account the mechani-cal parameters of all bearings. The problem is then reducedin way of the supporting points.

2.3.3 General equilibrium equation may be written as fol-lows:

where:

[K] : Global stiffness matrix, being a combination ofthe following partial matrices:

[Ks] : Shaft line stiffness matrix, see Sec 2,[3.3]

[Ksb] : Stiffness matrix of contact in staticcontact or running oil lubricatedcontact, see [2.1] and [2.2] respec-tively

[Eh] : Hull flexibility matrix as defined inSec 2, [3.2]

U : Vector of displacements, including the follow-ing components, see Fig 1 and Fig 2:

Ub0 : Vector of initial bearing centre posi-

tion with reference to shaft centre(without gravity), depending on theloading condition, temperature andalignment procedure

Us : Vector of shaft centre displacementsin way of the supporting points rela-tively to the reference line

Usb : Vector of shaft centre relative dis-placements in way of the supports

Bsb : Vector considering the non-linearity of the con-tact conditions:

where Fsb is the contact force vector

K[ ] U Bsb Fext+ +⋅ 0=

Bsb Fsb Ksb[ ] Usb⋅( )–=


NR 592, App 1

Fext : External load vector, including gravity and otherexternal efforts (propeller, engine, gearing),reduced in way of the supports. See Sec 2, [2.2].

2.3.4 The resolution of this equation is based on an itera-tive process using an initial displacement Usb

0 close to theequilibrium solution in order to calculate the main contactcharacteristics: Ksb

0, Fsb0 and Bsb

0.

Then a calculation of the global equation, see Fig 3, deter-mines vector Usb

1.

2.3.5 The convergence criteria for this iterative process iscalculated using the maximum absolute difference betweenthe terms Usb

i and Usbi+1. This value is to be less than

0,001 mm.

Figure 1 : Bearing and shaft equilibrium in static condition

Figure 2 : Bearing and shaft equilibrium in running condition

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NR 592, App 1

Figure 3 : Flow chart of iterative process

Resolution of Hertz formulaOil film calculation

Resolution of the signal globalequilibrium equation

Usb1 = Usb0

Resolution of Hertz formulaCalculation of oil film parameters

Usbi = Usbi+1

Fext , Ub0, Ks , Eh Fsbi, Ksbi, Bsbi

Ubi+1

No

Yes

Usbn = Usbi+1

Convergence criteria reachedMax (Usbi+1 - Usbi) < 0,001 mm


elastic shaft alignment (esa)

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