Journal bearing performance under starved lubrication

Tribology International 33 (2000) 259–264www.elsevier.com/locate/triboint

Journal bearing performance under starved lubrication

Masato Tanaka*

Department of Mechanical Engineering and Engineering Synthesis, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Abstract

The hydrodynamic performance of a journal bearing under starved lubrication conditions is studied theoretically and experimen-tally. When lubricant is supplied to a journal bearing from an oil groove at an insufficient oil flow rate, the hydrodynamic oil filmcannot cover the full width of the bearing at the inlet of the convergent bearing clearance, and the covered width increases graduallywith the decrease in film thickness in the circumferential direction. This phenomenon affects the static and dynamic performanceof the journal bearing. The oil film boundary in the bearing clearance is calculated numerically for a constant load and a constantspeed under the assumption of laminar, iso-viscous lubrication. Measurements are in good agreement with predictions. Some morecalculations of journal centre loci are given. 2000 Elsevier Science Ltd. All rights reserved.

Keywords:Hydrodynamic lubrication; Starved lubrication; Journal bearing

1. Introduction

Hydrodynamic journal bearings are usually supposedto be operated under fully flooded lubrication, and per-formance is analysed with the assumption that a lubri-cant is supplied to the film inlet at a sufficient flow rate.

However, some bearings have to be operated understarved conditions. One of the possible reasons is a mal-function of the lubricating system which would decreasethe oil flow rate due to clogging up of the oil filter, anoil leak from a loosened pipe joint or partial loss of oilpump capacity.

Another reason is the recent introduction of spot lubri-cation into high speed tilting pad journal bearings. Con-ventional bearings of this type are usually operated underfully flooded lubrication because the pad chamber is fullof pressurised oil. This is achieved by means of the flowresistance of the annular clearances of ring seals at bothends of the chamber. This configuration guarantees highservice reliability in operation, but with increases inshaft speed, the pad surface temperature tends toincrease dangerously because hot oil does not flow outof the chamber rapidly but stays inside longer, thusincreasing the pad surface temperature. Consequently,high speed operation of journal bearings needs different

* Tel.: +81-3-5841-6373; fax:+81-3-3818-0835.E-mail address:[email protected] (M. Tanaka).

0301-679X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S0301-679X(00 )00040-2

lubrication or different oil feeding methods to decreasethe operating temperatures of bearing pads and to gainsome safety margin against bearing seizure.

Spot lubrication is one such method. The ring seals atboth ends of the pad chamber are removed, and lubricantis fed under pressure through nozzles placed in thespaces between adjacent pads. Cold new lubricant canreach the hot surface of the moving journal directly, andhot oil discharged from under the pads can flow out ofthe pad chamber freely without any restriction. Thismethod was shown to make a large contribution todecreasing pad surface temperature and increasing thesafety margin of high speed tilting pad journal bear-ings [1].

However, this method has one shortcoming; only partof the lubricant discharged from the trailing edge of eachpad recirculates and comes into the clearance of the nextpad, and a considerable part of the discharged oil flowsout of the chamber. On the other hand, the oil flow rateneeded for flooded lubrication increases with increasedshaft speed. Eventually the flow rate needed exceeds thesupply rate. Consequently such bearings have to be oper-ated under starved lubrication conditions, and designengineers need to know the hydrodynamic performanceof a starved journal bearing.

Some theoretical work [2,3] was reported on thisproblem, but to the best knowledge of the author com-parison with experimental results has not been reported.

This paper shows a theoretical analysis of oil film for-

260 M. Tanaka / Tribology International 33 (2000) 259–264

mation and the hydrodynamic performance of a full cir-cular journal bearing under starved lubrication con-ditions, and compares the predictions withmeasurements.

2. Test rig

Fig. 1 shows a schematic of the test rig used. A rigidshaft is supported in two rolling element bearings and isdriven at up to 1500 rpm by a variable speed electricmotor. A test bearing is supported at one end of the shaft.The test bearing is made of transparent plastics toobserve the behaviour of the oil film in the clearance.The nominal diameter and the length are 45 and 30 mm,respectively. The mean radial clearance is 90µm. Thebearing has one oil groove. Its circumferential and axiallength are 4 and 24 mm, respectively.

Lubricant oil is supplied through a hole into thegroove from outside at controlled flow rates. Static loadsare applied to the bearing by means of dead weights.The behaviour of the oil film in the clearance can beobserved and also recorded by means of a video-camerarecording system. The displacement of the bearing rela-tive to the shaft is measured by means of two gap sen-sors.

Fig. 1. Schematic of test rig.

3. Theoretical analysis

3.1. Starved film model

Preliminary experiments gave lots of information onoil film behaviour in the bearing clearance. Fig. 2 showsa schematic model of lubricant flow on a developed lub-ricating plane of a full circular journal bearing with anoil groove at the position of the maximum clearance.Under starved conditions, lubricant flowing out of thegroove cannot cover the full bearing width at the grooveposition, and the covered width increases gradually withthe decrease in film thickness in the circumferentialdirection. With the aid of recirculating oil flow near bothends, the oil film can eventually cover the full bearingwidth, resulting in the flooded lubrication condition. Upto this point, the bearing is starved. The oil film rupturessomewhere downstream in the divergent clearance, andoil flow is divided into two streams near both ends.Between the position of the oil groove and this rupturepoint, axial oil leakage flow takes place due to pressuredeveloped in the film.

Compared with flooded lubrication, the hydrodynamicoil film becomes thinner and also covers less area of thelubricating plane, resulting in a higher journal eccen-tricity ratio under a constant load and shaft speed.Consequently the static and dynamic characteristics ofthe oil film change from those under flooded lubri-cation conditions.

First of all, the oil film extent on the lubricating planeshould be obtained, then oil film force can be calculatedfor the starved oil film.

3.2. Basic equations

The laminar, iso-viscous Reynolds Equation (Eq. (1))is assumed to be applicable to the oil film.

∂∂xSh3

m∂p∂xD1

∂∂zSh3

m∂p∂zD56U

∂h∂x

(1)

where x and z are the coordinates of the lubricatingplane,h is the oil film thickness,U is the journal surfacespeed,m is the lubricant viscosity andp is the oil filmpressure.

This equation is made discrete by means of the finitedifference method, and is solved numerically for thepressure.

Eqs. (2) and (3) give the oil film velocities in the cir-cumferential and axial directions:

u5Uyh

2y(h−y)

2m∂p∂x

(2)

w52y(h−y)

2m∂p∂z

(3)

wherey is the coordinate for the film thickness direction.

261M. Tanaka / Tribology International 33 (2000) 259–264

Fig. 2. Oil film model.

Eq. (2) is integrated with respect toy from 0 to h andalso with respect toz across the width where the oilfilm exists, then the oil flow rate in the circumferentialdirection is given as follows:

q(x)5EEh

0

u dy dz5ESUh2

2h3

12m∂p∂xDdz (4)

Eq. (3) is integrated with respect toy from 0 toh andalso with respect tox along the circumferential lengthwhere positive oil film pressure exists, then the axial oilflow rate is given as follows:

qout(x)52EEh

0

2w|z=0

dy dx5Eh3

6m∂p∂z|

z=0

dx (5)

3.3. Equilibrium under starved lubrication

When a bearing load and a journal speed are givenunder flooded lubrication conditions, the eccentricity

ratio and the attitude angle of the journal at its equilib-rium can be obtained by repeatedly solving Eq. (1) withthe film thickness being modified. On the other hand,under starved conditions, oil film forces are dependenton the supplied oil flow rate and the shape of the oilfilm formed in the clearance. Consequently the solutionsare obtained by coupling Eqs. (1), (4) and (5).

The following assumptions are adopted in the calcu-lations.

1. The oil film is symmetric with respect to thecentreline of the bearing.

2. No side leakage takes place downstream of the cir-cumferential position where oil film rupture takesplace, and the oil recirculates to the groove position.

3. Recirculating oil flows into the clearance near theends of the bearing, and newly supplied oil spreadsout from the central part of the bearing.

Equilibrium can be determined to be reached when thethree- dimensional oil film shape is obtained which bal-ances the oil film force with given load under givenspeed and oil supply rate.


Fig. 3. Oil film formation (measured) (W=5 kgf, Q=30 ml/min,N=250 rpm).


4. Results and discussion

4.1. Oil film formation

Figs. 3–5 show the measurements of two-dimensionaloil film formation with constant load (5 kg) and constantoil supply rate (30 ml/min) and also with journal speedvarying from 250 to 1500 rpm. Observations were con-centrated on the 180° part downstream from the oil


Fig. 6. Oil film formation (calculated) (W=5 kgf, Q=30 ml/min,N=250 rpm).


groove to investigate the boundary between the starvedand complete oil films.

Under flooded conditions, an axially complete oil filmshould be found to start from the horizontal coordinateq=0° (oil groove position), but under starved conditionsthe oil film at q=0° is found to split into three separatestreams which finally merge into one complete film.With increase in shaft speed, the partial oil film isstretched in the circumferential direction, and the startingpoint of the axially complete film region is found tomove gradually downstream, shrinking its area. Similarresults were obtained for other loads and oil supply rates.

Figs. 6–8 show theoretical predictions of the oil filmformation corresponding to the measurements shown in


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Figs. 3–5. Predictions are found to be in fairly goodagreement with measurements.

Fig. 9 shows the variations of journal eccentricity ratioe and the circumferential angleqboundof the axially com-plete film position with shaft speed as the main variableand oil supply rate as a parameter under constant loadof 10 kgf. The journal eccentricity ratio increases withdecrease in oil supply rate and also shaft speed. The axi-ally complete film starts further downstream withincreases in shaft speed and with decreases in supply oilflow rate.

Fig. 10 shows theoretical predictions corresponding tothe measurements shown in Fig. 9. The predictedqbound

agree fairly well with the measurements, but the pre-dicted eccentricity ratios do not agree with the measure-ments quantitatively. This implies the difficulty of meas-uring the eccentricity ratio accurately.

Fig. 11 shows calculated journal eccentricity ratios forvarious supply oil flow rates. The results were obtainedfor a different journal bearing (D=45 mm, L=45 mm,C=80 µm) which would be used to investigate the effectof the starved lubrication on the stability of the rotor inthe bearing. Journal eccentricity ratio decreases with theincrease in Sommerfeld number, but with lower oil flowrates (starved conditions) the journal centre peels off theflooded condition line at larger eccentricity ratio.

Fig. 9. Variation ofe andqbound with speed (measured) (W=10 kgf).

Fig. 10. Variation ofe andqboundwith speed (calculated) (W=10 kgf).

Fig. 11. Journal centre loci.


5. Conclusions

Oil film formation and journal eccentricity ratio in afull circular journal bearing were analysed theoreticallyand experimentally under starved lubrication conditions,and the following conclusions were derived.

1. Under starved conditions, the oil film cannot coverthe full bearing width at the inlet of the convergentclearance, and the axially complete oil film startsdownstream from this point.

2. Oil flow rate, journal speed and bearing load affectthe circumferential angle of the start of the axiallycomplete oil film in the bearing clearance.

3. Under starved conditions journal eccentricity ratio isdifferent from that under flooded conditions, which

inevitably change the oil film shape at equilibrium,resulting in the change of the static and dynamiccharacteristics of the oil film.

References

[1] Tanaka M. Thermohydrodynamic performance of a tilting padjournal bearing with spot lubrication. ASME Trans J Tribol1991;113(3):615–9.

[2] Artiles A, Heshmat H. Analysis of starved journal bearings includ-ing temperature and cavitation effects. ASME Trans J Tribol1985;107(1):1–13.

[3] Bonneau D, Frene J. Film formation and flow characteristics atthe inlet of a starved contact—theoretical study. ASME Trans JLubrication Technol 1982;105(2):173–86.

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Journal bearing performance under starved lubrication