Tribology International 36 (2003) 807–814www.elsevier.com/locate/triboint

D. Markin, D.M.C. McCarthy∗, S.B. GlavatskihDivision of Machine Elements, Lulea University of Technology, 971 87 Lulea, Sweden

Abstract

Keywords: Tilting-pad bearings; Synthetic oil; Finite-element method; PTFE

1. Introduction

Thrust bearings are a major component in the turbineassemblies of hydroelectric power stations. Friction inthe oil film separating bearing thrust surfaces and theshaft contributes a considerable amount to power losses,reducing the efficiency of the power plant. Through theintroduction of synthetic oils to replace existing mineraloils, these losses can be reduced. It has been shown thatester base oil ISO VG46 can be an efficient substitutefor mineral oil ISO VG68 in medium sized pivoted-padthrust bearings[1]. In large spring-supported thrust bear-ings, thermal deformations are greater, so additionaltheoretical analysis is required before such recommen-dations can be made.

Substantial amounts of oil are used for lubrication andcooling purposes in such large spring-supported bear-ings, potentially posing a considerable risk to theenvironment should they be released, whether throughaccident or system failure, into the waterways. Certainsynthetic oils, having minimum adverse environmental

∗ Corresponding author. Tel.:+46-920-492-854; fax:+46-920-491-047.

E-mail address: donald.mccarthy@mt.luth.se (D.M.C.McCarthy).

0301-679X/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0301-679X(03)00097-5

impact whilst retaining the essential properties for lubri-cation and cooling, can provide an attractive alternativeto commonly used mineral oils.

The objective of this study is therefore to develop aworking finite-element method (FEM) model of theentire shaft and bearing assembly that can be applied tothrust bearing analysis. In doing so, the influences ofbearing design and oil type on the operating character-istics can be charted and the capabilities of the softwareassessed. Two different bearing types, spherical pivotand spring-supported, are investigated in this study. Theaddition of pad facing materials to the thrust surfacesprovides an extra factor influencing the performance inthe case of the spring-supported bearing.

2. Modelling

In this study, analysis of bearing operations is madethrough carrying out simulations on models createdusing commercially available FEM software[2]. FEMis useful since more complicated, 3D model geometriescan be generated than is the case with FDM. Althoughthere are a number of software packages available, wechose this particular option in order to assess its effec-tiveness in this application.

A FEM approach to simulation ofhydrodynamic-pad thrustbearing assemblies

Finite-element method (FEM) modelling is applied to analysis of the performance of hydrodynamic-pad thrust bearingassemblies. A 3D model of the bearing assembly that includes the bearing pad and shaft is used to assess the influence of operatingconditions on bearing parameters such as temperature and oil film distributions across the pads. The model is first applied to theinvestigation of a spherically pivoted-pad. Through comparison with results from experiments carried out on just such a bearing,good correlation between the model and experimental results is found for maximum oil film temperature, pressure distribution andthickness. The model is then applied to the examination of a bearing having spring-supported babbitt pads. The effect of differentoil types on a spring-supported thrust bearing is analysed. Further application of the model to investigate the same spring-supportedpad, this time with a resilient surface coating, is discussed. 2003 Elsevier Ltd. All rights reserved.

808 D. Markin et al. / Tribology International 36 (2003) 807–814

Nomenclature

a thermal expansion coefficient (K�1)l heat flow per unit area (W m�2 K�1)k thermal conductivity (W m�1 K�1)m viscosity (mPas)h3 oil film thickness at outlet (µm)Tbath oil bath temperature (°C)n Poisson’s ratio (–)H convection coefficient (W m�2 K�1)Hc convection coefficient at trailing edge, outer corner (W m�2 K�1)y hot oil carry over fraction (–)cv specific heat per unit volume (J m�3 K�1)cm specific heat per unit mass (J kg�1 K�1)QV

in oil flow at the inlet node (m3 s�1)QV

out oil flow at the outlet node (m3 s�1)QV

R reservoir oil flow to inlet node (m3 s�1)E Young’s modulus (Nm�2)r density (kg m�3)Tin, TR, Tout temperatures at the inlet, reservoir and outlet nodes (°C)

In the first stage, the model of the pivot-mounted padis created in order to establish whether it is possible toaccurately describe a tilting-pad thrust bearing using thissoftware. Calibration of the model is carried out throughcomparison with experimental data recorded during testsreported in Ref. [1], including information relating to theuse of four different oils. A second model is created toinvestigate a large bearing with spring-supported pads.This model allows for the inclusion of a surface facing.Actual pad dimensions are given in Table 1.

Both models are simplified through rotational sym-metry to permit concentration on only one individualthrust pad. The bearing pad and the shaft segment aremodelled by means of 3D solid elements, making allow-ance for thermal and mechanical deformations in bothcomponents. The temperatures calculated are used fordetermination of the thermal displacements and stresses.

A 2D film element is used for representation of theoil film. Calculated values belong to the fictitious “mid-surface” plane located halfway between the top and bot-

Table 1Dimensional details of the two pad types

Support Outer Inner No. of Pad Padtype radius radius pads angle (°) thickness

(mm) (mm) (mm)

Spherical 114.3 57.15 6 50 28.58pivot, 60%offsetSpring 475 312.5 12 23.5 61support

tom surfaces of the film. This “mid-surface” is com-prised of fictitious nodes having pressure and tempera-ture values associated with the nearest pair of top andbottom surface nodes. The mid-surface temperatures aredetermined through a discrete form of the oil filmenergy equation.

Using a discrete form of the Reynolds equation, press-ure is calculated based upon the surface velocity speci-fied for the film top surface, pressure boundary con-ditions, the deformed film thickness and the temperatureand pressure dependent viscosity. The pressure boundaryconditions for a film surface are specified so that thepressure around the oil film edges is equal to zero. Noconsideration is made for any squeeze effect due tomotion in the normal direction. The pressure distributionand the specified surface velocity determine the shearstresses and the volume flow of the oil. A calculationflow chart illustrating data exchange during simulationof a bearing is shown in Fig. 1. The film element isconsidered to be non-linear and full Newtonian equilib-rium iterations are always performed. Each iteration con-sists of calculation of the increments in pressure, tem-perature and displacement. The applied force/momenttolerances govern the convergence since a small changein pressure or temperature usually means a relativelylarge change in forces and moments.

Boundary conditions for the convective heat flow aredefined by specifying the temperature distribution overthe oil film inlet. The inlet node temperature is foundusing the following equation [3]:

Tin �cRQV

RTR � coutyQVoutTout

cinQVin

(1)

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Fig. 1. Data flow chart.

y is the portion of the volume flow at the outlet nodesthat is carried over to the flow at the inlet nodes. Theremaining portion of the inlet flow is taken from the res-ervoir node. This has to be specified within the model.The film element transports heat by means of conductionin the transverse direction driven by the temperature dif-ference between the top and bottom surface nodes andthe fictitious mid-surface nodes. The heat conducted tothe top and bottom surfaces is transported further byconduction within the pad and the shaft adjacent to theoil film.

Since the film element is 2D, verification of the codeis required. Due to availability of a complete set ofexperimental data for a pivoted-pad bearing, the firstmodel prepared is for this type. The entire modelassembly is shown in Fig. 2.

The body of the pad consists of several blocks. Thisallows for setting of various characteristics such as ther-mal boundary conditions on pad surfaces for differentparts of the pad. An irregular mesh is used in order toachieve better coincidence between the pad geometryand node location. Thermal boundary conditions set forthe pad include heat transfer by convection to the ambi-ent medium and the surrounding oil and air temperatures.

The model geometry differs somewhat from that ofthe actual pad in order to permit simplification of themodel through reduction of the number of nodes andelements. However, the area of the bearing load carryingsurface has remained unaltered. In the model, the lackof material at the outer corners of the underside (in-cuts)is not considered. Such an omission does not signifi-cantly affect stress or temperature distributions withinthe pad because deficiencies are located in non-criticalregions having low values for temperature and pressure.

Fig. 3 shows an example of the “contour map” output

Fig. 2. Model assembly.

from the model illustrating distribution of temperaturewithin the pad.

Since the pivot contact area is small and can beassumed to be a point, the spherical pivot is modelledas a single point located on the underside face of thepad. The angle of inclination of the pad is free to changein all directions.

The spring-supported pad model is built in the sameway as for the pivoted-pad bearing. An isotropic,thermo-elastic steel material is used for the pad and the

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Fig. 3. Temperature distribution in the pad at 1500 rpm, 2.0 MPawith mineral oil ISO VG46.

shaft segment. An additional layer added on the top ofthe pad simulates the 2 mm thick facing.

The software package used does not allow for hand-ling of cavitation or sub-ambient pressures in the simula-tions. Hence it was not possible to simulate such amaterial as PTFE. However, it was possible to investi-gate the effect of a resilient material, having the samethermal properties as PTFE, on the bearing operatingcharacteristics. The properties of this resilient materialare shown in Table 2. More details are available else-where [4].

3. Results and discussion

3.1. Pivoted-pad bearing

A typical load–speed combination for the pivoted-padbearing (1 MPa at 1500 rpm) is chosen in order to ident-ify thermal boundary conditions such as convectioncoefficients, hot oil carry over factor and oil bath tem-perature. The “ tuning” procedure includes variation ofthese parameters in order to find the best correspondencebetween experimental and theoretical values. Experi-mental data referred to in this study were obtained frombearings mounted in a test rig as described in Ref. [5].

The value of H for the pad is varied between 100 and500 W m�2 K�1 whereas, for the outer corner near the

Table 2Material properties

Parameter E (Nm�2) n a (×10�6 K�1) k (W m�1 K�1) cm (J kg�1 K�1)

Steel (pad backing and 2.1 × 1011 0.3 12 47 500shaft)Babbitt 5.2 × 1010 0.3 23 55 ~230Resilient material 5.0 × 109 0.3 170 0.24 1050

trailing edge, Hc is varied between 100 and 1000 W m�2

K�1. The value for y is taken in the range 0.7–0.9 andTbath in the range 50–60 °C.

Other conditions applied include the oil flow rate tothe bearing being kept constant, as is the temperaturevalue for oil supplied to the bearing in the oil bath, main-tained at 50 °C for all simulations. Similarly, ISO VG46mineral oil is used in all simulations. The characteristicsof this oil are shown in Table 3.

Increasing Hc gives a lower rate of circumferentialtemperature rise through the diminution of temperatureat the trailing edge. Tbath and y have an equal effect ontemperature levels: a decrease in their values gives lowercalculated temperatures. y has a more pronouncedinfluence on film temperatures.

The best agreement for calculated and measured tem-perature distribution is observed for the following com-bination of the calibration variables: Tbath 50 °C; H 100W m�2 K�1; Hc 500 W m�2 K�1; y 0.9. These valuesare then used in other simulations.

Computed and measured temperature results are plot-ted in Fig. 4. Tmid is the theoretical and T4, T5 and T6

are the experimental temperatures at the pad mid-width.In the experiments, thermocouples were positionedapproximately 3 mm below the pad working surface.Theoretical temperatures are shown for the correspond-ing plane. T75/75 and T10 are, respectively, the theoreticaland experimental temperature at the 75/75 location. Thisis defined as a point at 75% of the radial width from theinner radii of the pad at a position, circumferentially,75% around from the inlet edge. An additional tempera-ture, Toil is included in the diagrams. This theoreticaltemperature describes thermal conditions along the padradial centre line, at the interface between the oil filmand the pad. Some deviation between simulated andexperimental temperature values is still visible,especially at the leading edge.

All simulations showed relatively good agreementbetween theoretical and experimental values for oil filmthickness. Calculated values for power loss are lowerthan the experimental values. This is explained by thefact that estimation of churning losses is not included inthe model. Fig. 5 shows variation in h3 and bearingpower loss for the compete bearing for different loadcombinations at 1500 rpm.

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Table 3Oil characteristics

At 40 °C ISO VG46 mineral ISO VG46 PAO ISO VG46 ester ISO VG68 mineral

r 855 819 906 861m 39.5 39.8 42.7 60.7cv (×106) 1.74 1.82 1.87 1.74k 0.13 0.145 0.173 0.13

Fig. 4. Temperature profiles at 1500 rpm/2.0 MPa.

Fig. 5. Power loss/minimum film thickness at 1500 rpm.

Fig. 6 shows oil film pressure distributions in the cir-cumferential direction at the 25% and 75% positions ofthe pad width, measured radially from the pad innerradius. Pressure profiles are well predicted by the model

Fig. 6. Pressure profile for different oils at 1500 rpm/2.0 MPa.

therefore only one load case is considered in order toillustrate this.

To verify against experimental findings and TEHDresults [1] of how oil type affects bearing operating para-meters, simulations are carried out for two load cases,0.5 and 2.0 MPa, and two rotation speeds, 1500 and3000 rpm. Properties of the oil used are shown inTable 3.

Fig. 7 shows temperature variations for different oilsfor a shaft speed of 1500 rpm and specific bearing loadof 2 MPa. The results show similar temperature distri-butions with oil type as in the experiments. Ester baseoil VG46 gives slightly higher temperatures than poly-α-olefin (PAO) oil VG46 and mineral oil VG46, whichhave approximately similar temperature profiles. Thehighest temperature is observed for mineral oil VG68.

Theoretical power loss and minimum film thicknessfor a complete bearing with different oils at a shaft speedof 1500 rpm and two bearing loads are shown in Fig. 8.The tendency is the same as in the experiments. Com-parison of calculated and measured data show that vari-ations as well as absolute values of h3 are well predictedby the current model.

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Fig. 7. Temperature profile for different oils at 1500 rpm/2.0 MPa.

Fig. 8. Power loss and minimum film thickness for different oils at1500 rpm.

3.2. Spring-supported pad

The influence of pad facing is the first thing to beexamined. Oil used in this instance is mineral oil ISOVG46. Operating conditions are assumed as follows:specific bearing load 3.8 MPa, rotational speed 600 rpm.Additionally, thermal conditions are: Tbath = 55 °C, y= 0.9, H = Hc = 100 W m�2 K�1. The value of H forshaft surfaces exposed to air is assumed to be 10 W m�2

K�1 [6]. It is further assumed that the temperature ofair coming into contact with the shaft inside the bearinghousing is the same as that of Tbath.

Results of simulations for bearings with facings areshown in Fig. 9. From these, it can be seen thatmaximum film temperature for the resilient material is7.2 °C higher than that for babbitt. Additional resultsshow that maximum temperature of the pad backingdecreases from 104.2 to 68.4 °C. This is an importantfeature since thermal deformations of the pad arereduced, consequently increasing bearing load capacity.

The lower maximum pressure provides an additionalimprovement. A decrease in maximum film pressure by10% indicates that the allowable maximum bearing loadcan be increased. Calculated power loss for the resilientmaterial facing is 41.1 kW, 2.5 kW less than that for thebabbitted bearing. An increase in oil film temperatureand a corresponding decrease in power loss areexplained by lower heat conductivity of the resilientmaterial. Minimum film thickness is only slightlydecreased, by 0.9 µm, an acceptable result. Similar datawere reported in Ref. [7] for a spring-supported PTFEcomposite faced bearing. The same film thickness and30% lower maximum pressure were measured in thePTFE composite bearing compared to the babbitted bear-ing. It can therefore be assumed that a further reductionin Young’s modulus can provide lower maximum press-ure whilst retaining the same film thickness.

No significant difference in bearing operating para-meters is observed either for pads with babbitt facing orthose without any facing material. The differences in oilfilm temperature and thickness are within 1 °C and 0.4µm, respectively.

In addition to the utilisation of a resilient facing, bear-ing performance may be further improved by choosingsynthetic oils. The same oils are used in these simula-tions as in the case with the pivoted-pad bearing. Tbath

is taken to be equal to 35 °C. The data obtained areassembled in Table 4. Analysis of the results shows thatvariation in minimum oil film thickness and power losswith oil type is the same as in the pivoted-pad bearing.There is only a small difference in calculated minimumfilm thickness for ester base oil VG46 and mineral oilVG68.

It should be noted that figures for power loss quotedin Table 4 relate purely to shearing losses and do notmake allowance for churning as this was not includedin the models. It is known that churning losses dependon the viscosity of the oil in the oil bath: higher viscosityleads to higher losses and vice versa. If churning is fac-tored in to the results given in Table 4 for shearingpower losses, then the total losses for the oils will differnoticeably. Hence total losses will be lower for the oilswith lower viscosity grade. Film thickness is also oftenan important factor when assessing the suitability of oils,primarily from the point of view of bearing safety. Esterbase oil provides a thicker oil film than mineral or PAOoils of similar viscosity grade. Therefore the ester baseoil can thus be judged to be an efficient replacement forthe mineral oil of higher viscosity grade.

4. Conclusions

A working FEM model of the entire shaft and bearingassembly has been developed and applied to thrust bear-ing analysis. Thermal and mechanical deformations in

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Fig. 9. Distribution of temperature and pressure (same parameters in both cases).

Table 4Results for different oils

Tbath=35 °C, y=0.9 ISO VG46 mineral ISO VG46 PAO ISO VG46 ester ISO VG68 mineral

Maximum film pressure (MPa) 10.86 10.85 10.85 10.38Minimum film thickness (µm) 25 26 28 30Maximum film temperature (°C) 92.1 92.4 93.6 92.0Maximum facing temperature (°C) 88.6 89.0 90.4 87.7Maximum pad backing temperature (°C) 87.2 87.7 89.0 86.4Power loss (kW) 52.8 56.4 61.2 62.4

the bearing assembly as a whole were allowed for.Results from the simulation showed general agreementwith those for the experiments. However, in order toincrease the accuracy and capabilities of the model, 3Dtreatment of the film element is necessary together withtaking cavitation into account. Based on the resultsobtained, the following conclusions can be drawn:

FEM simulations show that ester base oil VG46 canefficiently replace mineral oil VG68 in middle and largesized tilting-pad thrust bearings without sacrificing bear-ing safety. However, additional tests are required forother bearing designs or for centrally pivoted-pads.

Utilisation of a resilient facing in large spring-supportedbearings allows noticeable improvement in the bearingperformance. Compared to babbitted bearings, maximumfilm pressure and power loss are reduced whilst mini-mum film thickness remains essentially the same. Inaddition, the pad backing temperature is much lower,leading to lower pad thermal crowning and ultimatelyhigher load carrying capacity. The introduction of a bab-bitt pad facing in the FEM model has negligible effecton operating parameters.

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Acknowledgements

This research was supported financially by the Swed-ish Institute (Svenska Institutet) through the provisionof a scholarship to D. Markin and by Alstom Power.Additional assistance from Gunnar Larsson at SOLVIAEngineering AB and Tomas Arvidsson at Alstom Poweris also gratefully acknowledged.

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