Developments in Bearing

Simulation

Simon White – Product Manager

28/09/16

Advanced Roller Contact and Journal

Bearing Analysis

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© Copyright 2016

Agenda

• New Advanced Roller Contact Model

• New Journal Bearing Model

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• Bearings are a key aspect of drivetrain design and analysis

• Romax is at the forefront of bearing technology and has continuously developed an industry leading bearing analysis methodology which incorporates

o Fully coupled driveline flexibility in order to calculate loads and misalignments

o State of the art 6 DOF non linear bearing models

o Advanced analytical fatigue life methods

o Preload, thermal expansion and fit

o Flexible bearing raceways

Bearing Analysis in RomaxDesigner

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Romax Bearing Contact Analysis

• Ball and roller contacts are

very small, high

compressive stress regions.

• These contact problems

are very difficult to solve -

highly non-linear and

often extremely sensitive

• Hertzian contact analysis

using Finite Element

Analysis is impractical due

to extraordinary mesh

refinement required in

contact regions.

• Romax developed bearing

contact models are

analytical rather than FE

based

• Models are parametric

• Run times are extremely

fast

• Results more accurate than

can practically be achieved

using conventional FE

• Can be used within a whole

system model

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RomaxDESIGNER Flexible Bearings

• System/Component flexibility can be crucial in

predicting loads and durability

• Finite Element flexible bearing analysis within a

parametric, rapid system model are a key benefit of

RomaxDESIGNER

• Accurate prediction of deformations of bearings,

shafts and housings enables to prediction of the load

distribution between the rolling elements

• This allows accurate prediction of the load and

misalignment of the most heavily loaded roller

• The current contact stress analysis is then able to

predict stress levels and also the onset of edge contact

Rigid bearing

Flexible

bearing

Edge Contact

10% stress reduction

RomaxDesigner Contact

Model Developments

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Limitations of current contact model

• The current RomaxDESIGNER 14.7 Advanced

contact model is fast and accurate for typical

bearing contact analysis

• Main limitation of model is that it cannot

handle large discontinuities (eg edge contact)

and results may be truncated

• Difficult to ascertain the severity of edge

loading

Actual stress levels

Predicted stress

levels (peak missed)

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© Copyright 2016

New Contact Model – Commercial Drivers

• Certain bearings operate at the limits of their design and can

be subject to undesirable edge loading

• It is possible for a bearing to show signs of edge loading

without failing

• It is important to be able to assess the severity of edge

loading especially in existing applications

• Romax clients have requested a computational method to

better predict the magnitude of edge stresses to better predict

bearing life under extreme conditions

• The methodology needed to be easy to setup and runtimes

many orders of magnitude quicker than a full FE analysis

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Challenge in the prediction of edge stresses

• Accurately modelling all aspects of bearing

contact remains a real challenge

• Most bearing contact models are either based on

the thin-strip theory or Love’s half-space model.

• Thin-strip theory discretises the roller/raceway

into a number of uncoupled strips,

o Coupling is important to predict edge stresses.

• Love’s half-space model assumes that the

contacting surfaces stretch up to infinity along the

contact length and depth.

o Coupling included but this method cannot be used to

predict edge stresses of finite objects.

Only strips which are in

contact deflect

Strips outside the contact

do not deflect at all

because of the absence of

any coupling between

neighbouring strips.

Elastic material

Thin-strip model

Elastic half-space

Infinite Infinite

Infinite

Love’s half-space

model

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A new contact model to predict the edge stresses

• The R&D team at Romax have developed a new mathematical model to predict the

contact of two elastic bodies.

• The key features of the new model are:

o It is based on quarter-space theory, so can predict stresses of bodies with finite dimensions;

o It considers the coupling between contact strips;

o It does not assume that material is elastic up to infinity along the depth of the contact and uses

an elastic limit;

o It is capable of predicting stresses near the edges of contact bodies.

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© Copyright 2016

Formulation of the new quarter space contact

modelStep 1: Love’s half-space formulation

Surface displacement is a continuous function, meaning coupling between

different points/strips located within the contact region can be derived.

However, the formulation assumes that the length of the contacting body is

infinite.

Therefore when applied to finite contacting bodies, there would be incorrect

compressive and shear stress acting on the two free surfaces

This means, surface displacement at a point near the edge (point a) is

exactly same as the displacement at a point near the centre of the body

(point b).

Using the quarter-space theory allows the correct modelling of

free surfaces that are free of any compressive and shear stress.

This is a more realistic representation of the contacting body

with finite dimensions.

As a result, the displacement near the edge is more than the

displacement near the centre of the body. This is because the

edges are softer than the material in the centre.

Step 2: Moving from half space to quarter space formulation

Free

surfaceFree

surface

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© Copyright 2016

• The new Romax contact model has been validated against FE and Hertz theory for a

range of different geometries

• Note: FE solve time 1 hour, Romax algorythm solve time 0.2 sec

Validation of Model

40

mm

Ø 10 mm

Applied forces: 5 kN and

20 kN

Ø 10 mm

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© Copyright 2016

Validation of Model - Results

• Areas under both FE and new contact-model curves give the correct applied load.

• In the FE model, the number of nodes across contact width is insufficient (cannot further refine

mesh), which leads to higher contact width and higher peak stress compared to the true solution.

Theoretical

solution for

infinite length

roller

Insufficient

points for FE

model

Edge effects

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Application of the new contact model to predict roller-edge

stresses for wind turbine bearing

• When implemented in RomaxDesigner, the new contact can successfully predict

edge stresses

Peak stress at the edge of the roller

predicted by the new contact model.

Peak stress no

longer truncated

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© Copyright 2016

Consideration of Yielding

• If deformation is considered to be elastic, then peak

predicted stresses can be seen to exceed the yield

limit of the bearing material

• A yield factor can be specified which uses the

material UTS to calculate a contact stress yield limit

• When this value is reached within a strip, that strip is

unable to support further load and therefore the

neighbouring strips have to support the load

• Yielding will propagate until the load is supported and no more strips exceed the yield limit

or until the entire roller has yielded

• Depth of yield and yield width are reported, warnings and failure messages are generated

depending on level of yielding

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© Copyright 2016

Applications

• Can be used as default contact model (Requires advanced details)

• Applicable to both Bearing and Drivetrain manufacturers

o Design and assess roller profile modifications

o Assess different designs from different suppliers

o Give insight into cause of issues

o Allow sensitivity studies to be performed

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Proprietary Bearing Catalogue

• A key requirement for manufacturers wanting to use the

advanced bearing modules is being able to include

advanced and internal bearing data

• Suppliers are normally unwilling to share this data as it is

considered proprietary

• However the RomaxDESIGNER proprietary bearing

database allows suppliers to provide this geometry in an

encrypted form therefore hiding all advanced geometry

from the customer

• If both the manufacturer and supplier have

RomaxDESIGNER then model data, loads and

proprietary bearing data can all be shared with obvious

benefits

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© Copyright 2016

Contact Model Summary

• Romax has developed a new mathematical model to predict the contact of elastic solids of

arbitrary shapes and finite dimensions.

• The model is based on novel techniques and is unique to Romax Software

• The model is verified against finite-element analysis, analytical models and literature

• The model is accurate, fast, robust and easy to setup

• The model is successfully able to predict contact stresses for complicated profiles

• The model is designed to be used within RomaxDESIGNER/WIND using the full system

model and flexible bearings for the highest level of accuracy

• New model released with RomaxDESIGNER/WIND (R17 AR1)

RomaxDesigner Journal

Bearing Developments

Slide 22CONFIDENTIAL

© Copyright 2016

Journal/Sleeve Bearings

• Oil lubricated full fluid film journal bearings consist of a shaft or

journal which rotates freely in a supporting metal sleeve or

shell.

• There are no rolling elements in these bearings. Their design

and construction may be relatively simple, but the theory and

operation of these bearings can be complex

• Various numerical and analytical methods exist to allow the

design and analysis of these bearings

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© Copyright 2016

Current RomaxDesigner Journal Bearing Capability

• Currently the released versions of RomaxDesigner (RxD) do not include any

predictive journal bearing analysis capability

• Journal bearings can usually be represented using stiffness or clearance bearings but

this approach has an number of key limitations

o Stiffness is user defined and must be calculated using a standalone external code

o The stiffness will only be approximate as the real bearing behaviour is highly non-linear

o Cross coupled stiffness terms are not included

• Romax are currently working to develop a range of multi fidelity journal bearing

solutions for RomaxDesigner

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© Copyright 2016

Level 1 – Analytical Plain Bearing Model

• Analytical approximation of Reynolds equation

for journal bearings

• Valid for wide range of bearing aspect ratios

• Suitable for simulation of rigid plain bearings

only (no holes, groves or distortions)

• Rapid analysis within a Romax static simulation

• Pressure profile, film thickness, stiffness…

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Level 2 - Rigid Hydrodynamic Model (RHD)

• Numerical model using Finite difference

formulation

• Suitable for the simulation of Rigid bearings

only

• Allows the inclusion of grooves and holes

Oil feed

holes

Min film

thickness240

degrees

60 degrees

Oil feed holes

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Level 3 - Elastohydrodynamic (EHD) and Thermo-Elastohydrodynamic (TEHD) Model

• Similar formulation to RHD

• EHD Considers deflection of shaft and

housing

o Model connects to condensed FE structures

o Iterative solution to obtain load and distortion

• TEHD model considers heat flux between

the bearing and the structure

• Option to enable cavitation prediction

when using dynamic simulation

Cavitation zone

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Verification against published data

The code has been verified for a 2 groove journal bearing against the simulation methods by

Elrod and Fesanghary et. al.

Elrod, H. G. (1981). A cavitation algorithm. Journal of Lubrication Technology, 103(3), 350-354.

Fesanghary, M., & Khonsari, M. M. (2011). A modification of the switch function in the Elrod cavitation algorithm. Journal of Tribology, 133(2),

024501.

Published

resultsPresent

numerical

method results

GrooveGroove

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© Copyright 2016

Verification against published data: Part 2

The code has been verified against the results published by Chun and Lalas for a journal

bearing with half-circumferential groove.

Chun, S. M., & Lalas, D. P. (1992). Parametric study of inlet oil temperature and pressure for a half-circumferential grooved journal

bearing. Tribology transactions, 35(2), 213-224.

Reported maximum oil pressure = 6.5

MPa

Calculated maximum oil pressure = 6.65

MPa

Error in the maximum pressure prediction is 2.3%

However, the mesh density of the published data is not fine

enough to resolve the peak pressure.

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Verification against published data: Part 3Cavitation boundary (film reformation and collapse) has been validated against the experimental results by Lundholm (1969) and verified against the simulation results of Kumar and Booker (1991).

Lundholm G. The circumferential groove journal bearing considering cavitation and dynamic stability. Acta Polytechnica Scandinavica , 1969, volume 42.

Kumar, A., & Booker, J. F. (1991). A finite element cavitation algorithm: application/validation. Journal of tribology, 113(2), 255-260

Case I: Oil viscosity = 0.115 Pa.s

Inlet pressure = 0.098 MPa

Speed = 1500 rpm

Output

parameter

Experiment

(Lundholm)

Simulation

(Kumar &

Booker)

Simulation

(Romax)

Eccentricity

ratio

0.8 0.79 0.78

Peak pressure

(MPa)

- 1.14 1.07

Attitude

angle

(degrees)

- 40.7 40.9

Full film zoneCavitation

zone

Oil groove

--- Experimental cavitation zone (Lundholm)

● Simulated cavitation zone (Kumar & Booker)

Simulation results (Romax)

Film collapse Film reformation

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© Copyright 2016

Summary

• Suite of Jounal Bearings currently in developmentRxD

• Will allow basic and detailed analysis of journal bearings within

RomaxDesigner

o Accurate boundary conditions

o Improved system accuracy

• Initial results looking very promising

• Analytical and RHD models will be released with R17, the others will

follow soon after