Proceedings of the Institution of Mechanical Engineers-1955-Kettleborough-746-65.pdf

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Proceedings of the Institution of Mechanical

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DOI: 10.1243/PIME_PROC_1955_169_075_02

1955 169: 746Proceedings of the Institution of Mechanical EngineersC. F. Kettleborough, B. R. Dudley, E. Baildon and C. F. Kettleborough

ExperimentCorrelation between Theory an

Experimental Results: Part II

Micheli Bearing Lubrication* : Part I

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746

Michell Bearing LubricationPart I-Experimental ResultsBy C.F. Kettleborough, B.Eng., Ph.D. (Associate Member).f-,B. R. Dudley, B.Sc. (Eng.) (Graduate)$,and E. Baildon, M.Sc. (Eng.) (Associate Member)

Part 11-Correlation Between Theory and ExperimentBy c.F. Kettleborough, B.Eng., h.D. (Associate Member)

An experimental investigation into the operation of tilting-pad thrust bearings has been carriedout. The following experimental determinations have been made : film pressure distributions, filmgeometry, friction characteristics, and temperature distributions for a range of speeds, loads, operatingtemperatures (that is, viscosity), and pivot positions. An attempt has been made to correlate theseresults with existing theories.

I N T R O D U C T I O NA complete systematic investigation into thrust bearings doesnot seem to have been carried out. Some work has already beendone by von Freudenreich (1917, 1933, 1941), Gibson (1919),Newbigin (1913, 1922), Morgan, Muskat, and Reed (1940),and Cameron (1949)1/.

Th e opportunity to carry out systematic work at the Universityof Sheffield was provided when a prototype experimentalmachine was presented to the University.Nomenclature.

Friction force.Film ratio.Film thickness (see Fig, 2a). (Suffixes: i inlet; o outlet;R outer radius; r inner radius.)Measured displacements of tilting pad. (Suffures :o outletside; i inlet side; c central.)Length of pad at inner radius.Mean length of pad.Rotational speeds.Load per unit area.Inner radius.Total load per pad.Viscosity.Circumferential tilt angle.Angular position of centre of pressure or applied load fromoutlet edge.Angle subtended by the pad.Coefficient of friction.Angular velocity.Film thickness criterion =(Ho/Lro) ( /Zw)f.Friction criterion = ( p / r o ) (W /Zw)+ .

In the correlation between theory and experiment Boswallsand Christophersons notations have been retained (Boswall1928; Christopherson 1941).Other notation is introduced as required.In the parameter ZNIP, Z is the mean oil viscosity in poise,The M S . of this paper was received at the Institution on 1st March* Based on a thesis presented for the degree of Ph.D., Universityf Senior Lecturer, University of Melbourne, Australia.$ Lecturer, School of Applied Mechanics, University of Sheffield.s Lecturer in Mechanical Engineering, University of Sheffield./I An alphabetical list of references is given in the Appendix.

N is the speed in r.p.m., and P the load in lb. per sq. in.1954.of Sheffield, by C. F. Kettleborough.

E X P E R I M E N T A L A P P A R A T U SThe apparatus is basically a prototype experimental machinepresented to the University of Sheffield where it has beensuitably adapted and equipped for the investigations under-taken.Th e functional part of the apparatus is shown in Fig. 1. Th eshaft 4 carries a flexibly-mounted thrust ring 9 the plane faces ofwhich rotate between two sets of stationary Michell sector-shaped pads. Th e two sets, each consisting of six pads, are freelymounted on the end flanges of the casing 6 which is supportedconcentrically with the axis of the shaft and which is attachedto a frame 1. This whole assembly has limited rotational free-dom about the axis of the shaft but movement is restrained by aloaded torque arm used for the measurement of the total fric-tional torque acting on the pads. The enclosed casing 6 is filledwith oil, and fresh oil at controlled temperature is circulated

through it.Each sector pad in the right-hand set is independently loadedin the direction parallel to the shaft axis by means of a hydrauliccylinder and piston, the end of which is formed to a sphericalshape where it bears on the outer face of the pad. These thrustloads are transmitted through the collar to the six other reactionpads, each of which bears against a spherical-ended plug held ina bush which, in turn, is held in a flange located in the innercover of the casing. Each pad thus possesses freedom for tiltingabout a point pivot. Moreover, by angular adjustment ofeccentrically-bored bushes which contain, and locate withia thecasing covers, the stems of the loading cylinders and the reactionpivot plugs, it is possible to adjust the position of each pointpivot relatively to the pad. These bushes are graduated at 5-deg.intervals. This arrangement enables each pad to be pivoted atthe symmetrical point 7, Fig. 2a, or at points lying on either oftwo concentric circles of radii 0.05 and 0.10 inch. Seven actualpivot positions, specified in Fig. 2a, were used in the experi-ments.The sector pads, made of gunmetal and each having a bearingarea of 0.9196 sq. in., are detailed in Fig. 2b. On the edges ofeach bearing sector is constructed a kite-shaped flange throughwhich pass two pins to provide peripheral location of the padaround the thrust collar, Th e flange face, moreover, provides adatum surface from which measurements of film geometry aremade. For this purpose three plungers are arranged so that theirends bear at A, B, and C, on the flanges of one pad, and thepositions of these plungers when the pad makes metal-to-metalcontact with the thrust collar, relative to their positions when thepad is floating on an oil film, are measured by means of Talymingauges; or by dial gauges when the movements are relativelylarge.Each of the directly-loaded pads has five oil pressure search-holes 0.028 inch in diameter drilled on the working face. Of

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M I C H E L L B E A R I N G L U B R I C A T I O N 747these, one 'common' hole occupies the same relative position oneach pad, but all others are differently positioned so that thecombination for the six pads gives a mesh di stribution of twenty-five pressure holes over the whole lubricating film. Moreover,this mesh is so arranged that for given operating conditions, thepressures at fifty different relative positions in the film may beobserved, twenty-five being obtained with each direction of

10

1.2.3.4.5.6.7 .8.9.10.

M IUa Diagrammatic sketch of h4ichell thrust test machine.

b Details of experimental thrust bearing.Swinging frame.Supporting casting.Rear cover of thrust end.Shaft.Ball bearings.Thrust casing.Shaft locating sleeve.Thrust casing cover.Runner ring.Bonded rubber sleeve.

11. Reaction pad.12 . Loaded pad.13. Loading piston.14 . Hydraulic cylinder.15 . Eccentric bush.16. Pressure search valve.17. Centre-lineof pressure search18 . Deflexion piston.19. Mercury manometer.

pipe connexions.

Fig. 1. Michell Thru st Bearingrotation. A comparison of the observed pressures at the 'corn-mon' holes in the six pads shows whether or no t they are allworking under the same conditions. A typically drilled pad isshown in Fig. 2c , and an actual pad with pipes attached inFig. 3. The location of the pressure search-holes are shown inFig. 6.Each pressure search-hole in the pad is connected by aflexible looped pipe to t he fr ont cover and-thence by pipe andvalve to a common manifold (Fig. Ib ) fittedwith a pressure gauge.This manifold may be put in direct communication with anyone particular search hole when all other holes are isolated fromit by closed valves. Two manifolds, one wth thirty and the

I z . R9" \CENTRE LINEOF PAD

a Pivot positionsand film-thickness symbols.POSITIONS OF DEFLEXION, M E A S U T D S

Ib Details of tiltmg pad.

c Typical pad drilled for pressure search-holes.Fig. 2 . Defining Pivot Positions, Film-thickness Symbols,and Tilting Pad Details



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748 M I C H E L L B E A R I N G L U B R I C A T I O Norher with five connexions, are available for use with six padsor with one pad respectively.In the oil supply and circulatory system, an oil pump suppliesoil under pressure through temperature-control equipment tothe loading cylinders. The bulk oil flow passes through apressure-reducing valve to the main-bearing casing whence theoil is returned to the sump. The rate of oil flow through thecasing may be regulated by opening a bypass valve. This reducesthe oil flow through the bearing casing by allowing some of thebulk oil to return directly from the main to the oil sump. Anauxiliary hand-pump connected into the search-hole pressure

Fig. 3. Small Experimental DetailsLoaded pads d t h pressure tappings.Eccentric bushes.Reaction pad fitted with thermocouples.

manifold enables the pressure at any one search hole to beboosted to facilitate the observation offilm pressure readings.The distribution of temperature at the working surfaces ofthe pads is observed by means of a series of cotton, enamelled,copper-constantan thermocouples (28 gauge) fitted into holesdrilled through each of the six reaction pads. Combination ofthe observations gives a pattern of the temperature distributionover the whole working surface, and a t the same time the tem-peratures at two positions which are common to all the six padsmay be compared between the different pads.E X P E R I M E N TA I, T E C H N I Q U E S AND R E U , T S

Pressure Measurement. Initial investigations showed thatwhen the pressure manifold was put in communication withone search hole, the time taken for the oil pressure to riseand reach a steady value depended on the search-hole positionwithin the bearing casing. For holes in the pad at the highestpoint of the bearing periphery, the time taken was only afew minutes; for holes in lower peripheral positions, thetime taken was longer; and for holes in the lowest pad, nochange of oil pressure could be detected even after about2 hours. Further investigation showed that the only sig-nificant condition which varied within the casing was that ofthe oil itself, which was found to be more aerated in the lowerpart of the casing where the oil entered than nearer the oil exitin the upper part of the casing.Investigation of the time rate-of-change of manifold pressurefollowing the opening of a search-hole connexion showed thatthe pressure-time relation has the characteristic form of thecurve A in Fig. 4, although the scale of the time base varies withth e position of the search hole within the bearing. T he total timetaken for pressure stabilization is reduced if the manifold pres-sure is boosted by means of the hand-pump when a particularsearch hole is opened. This preloading eliminates the earlyportion of the pressure-time characteristic in which the rate ofpressure rise is small and modifies the pressure-time charac-teristic 10 the typical forms shown by curves B to F in Fig. 4.

This boosting device facilitated further experiments in whichit was found that the film pressures observed at the six commonholes had appreciably different values. Though the pads wereequally loaded, they were not operating with identical film con-ditions. For this reason and also in order to obtain closer controlof the temperature of the oil passing under the pads, it wasfound expedient to operate the bearing using only one pair ofpads at a time, that is, one pressure search-pad with its directlyopposite reaction pad. To obtain representative observations ofthe oil film temperature, thermocouples were inserted in holesdrilled through the reaction pad in mid-radial positions nearthe inlet and outlet edges, the hot junctions being cut level withthe surface of the pad. The average of the two indicated tem-peratures was taken as the representative temperature of the oilfilm. The two pads were placed a t the top peripheral position ofthe bearing where pressure Observations were most quicklyobtained and oil aeration was least. The six search-hole padswere successively inserted at this position, and in this way com-plete pressure distribution observations for various operatingconditions were obtained.

0 10 20 30 40TIME AFTER OPENING VALVE-MINUTESFig. 4. Oil-film-pressure Against Ti n e Curves for DifferentSearch HolesTest s were made to investigate the extent to which the loopedoil-pressure pipes which connect the pads to the casing cover,offered restraint to the tilting of the pads. A method of assem-bling the pads in position and then softening the copper pipeswas developed, and this interference was reduced to a satisfactoryminimum.

For each set of operating con-ditions, fifty pressure observations were made. Of these, twenty-five were obtained with one direction of bearing rotation; thepivot position was then changed over to the symmetrical pointon the opposite side of the sector centre-line-the direction ofrotation was reversed and twenty-five more pressure observationswere made.When the full set of fifty observations were placed on onediagram, however, imperfect correlation of the two half setsexisted owing to slight differences in the working conditionswith the two directions of rotation. Hence, when plotting pres-sure curves and contours, it was, in general, expedient to basethe diagrams primarily on one set of wenty-five observations,

Film Pressure Observations.



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M I C H E L L B E A R I N G L U B R I C A T I O N2o01

Figure a /+ Speed,

749

Applied1 Load,lb. ZNlPlb. per Applied Experi-sq. ln mental

a On bearing surface.0 200OIL FILM PR ES SU R E - L B . P E R SQ. IN.

56a6b6c6d

c Circumferential.n

0.40 2,700 73 67 64 19.10.40 1,495 142 130 124 7.430.40 1,495 142 130 125 7.43*0.50 1,495 227 208 - 3.420.50 1,495 142 130 136 7.43

6 Radial. d Along sections parallel to inlet edge.Fig. 5, Oil-film-pressure Distributions

m Position of applied load. + Calculated centre of pressure from experimental pressure distribution.though valuable help was obtained from the other set in fixingthe contours in the region of the film where rapid changes ofpressure gradient take place.In analysing the pressure observations, allowance was, ofcourse, made for the effect of the pressure of the oil in thebearing casing both on the film pressures and on the hydraulicpiston load.

TABLE. DATA OR TYPICALRESSUREISTRIBUTIONS

* Large oil flow, remainder s m a l l oil flow.Thirty-five complete experimental pressure distributions wereobtained for different conditions of speed, temperature, pivotposition, load, and rate of oil f low. Table 1gives the leading data

for typical pressure distributions for which the detailed observa-tions are shown graphically in Figs. 5 and 6.The pressures obtained are set out at the mesh points of thetypical contour diagrams of these figures, and the six pressuresobserved at common hole positions are also given for com-parison. For further analysis of these results, the curves ofpressure distribution along the five radial lines and along thefive circumferential arcs of the mesh were constructed as at band c in Fig. 5. The area enclosed by the curve of film pressureplotted with reference to a circumferential arc of the film is ameasure of the intensity of film loading per unit radial width ofthe pad at that particular arc. These loading rates were deter-mined for the circumferential arcs of the mesh together with anumber of intermediate arcs, and they were then plotted on abase which corresponds to the radial width of the pad as at b inFig. 5. Th e area enclosed by this curve of radial loading rate,which is a measure of the film pressure resultant, was thendetermined. For the particular conditions investigated, theintegrals of the film pressures obtained in this way were found todiffer from the actual loads applied to the pad by between 4 and10 per cent.T o determine the centre of film pressure, which shouldcoincide with the point at which the pad is actually pivoted, itwas necessary to make two integrations of the first moments ofthe film pressures, and those moments were conveniently takenabout (1) either the inlet or the outlet edge of the pad, and



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750 M IC H E L L B E A R I N G L U B R I C A T I O N

a Small flow through casing.

b Large f low through casing.

463 463480 49 444 1 501C

dFig. 6. Typical Film-pressure Distributions

Figures on contours refer to film pressure in lb. per sq. in.Position of applied load.

+ Calculated centre of pressure from experimental pressure distribution.(2) the point of intersection of the produced inlet and outletedges of the pad. For integration (1) the moments about theedge of the pad of rates of film-pressure loading along a numberof !ines parallel to the edge such as those indicated in Fig. 5aand plotted as in Fig. 5d were computed, and integrated to deter-mine the distance of the centre of pressure from that edge.Integration (2) carried out in a similar way was facilitatedbecause the rates of film loading along a number of circular arcswere already known. The positions of the centres of pressuredetermined in this way, were found to be reasonably close tothe actual pivot positions.

It is notable that with given operating conditions, the film-pressure distributions were affected by the rates of oil flowthrough the bearing casing. This is shown, for example, by a

comparison of the two sets of observations plotted in Fig. 6aand b which were both obtained with identical operating con-ditions except for the rate of oil flow through the casing. Thecentre of pressure is displaced towards the outer radius by theincreased flow.Occasionally, a recorded film pressure was incompatible withthe general distribution and was neglected, as, for example,along circumferential direction E in Fig. 5c . This unknownpressure must be the same on both circumferential and radialdistributions.Fig- 6c shows a typical pressure distribution when pivoted sothat 914 =0-50 and offset towards the outer radius. Thepressure contours have been displaced towards the outerperiphery, and this restores equilibrium about the pivot poin: .



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M I C H E L L B E A R I N G L U B R I C A T I O N 751To generate these higher pressures the film thickness is con-siderably reduced at the outer periphery-this was confirmedby film thickness determinations.Fig. 6d shows the pressure distributions for radial offset pivotposition 4 for each direction of rotation but otherwise identicaloperating conditions of load, speed, and viscosity. The integratedload was little affected by the contour differences.It was noted that the greater the operating temperature, thehigher the maximum film pressures recorded. Oil-film-pressuredistributions were also obtained when the tilting pads werepivoted on the inlet side.

For measurements of filmgeometry, three rods pass through the outer cover of thebearing casing and rest with their spherically-formed ends incontact a t A, B, and C with the flange of the piston-loaded sec-tor pad (Fig. 2b). When observations are to be made, the loadingpiston for the pad is subjected to hydraulic pressure whilst the

Measurement of Film Geometry.

a

1

Fig. 7. Illustrating Measured Movement of Rods ActuatingDeflexion-measuring Gaugesa Position of components with thrust ring stationary.b Position of components under load with thrust ring moving in

thrust ring is stationary, so that the working aces of both thepiston-loaded and the mating reaction pads are brought asnear as possible into metal-to-metal contact with the thrust ring.The axial position of the measuring rods relative to the casingis observed. The bearing is then set in operation under par-ticular conditions of working; he formation of oil films beneathboth the loaded and reaction pads causes axial displacement ofthe measuring rods; and the new positions of the rods relative

direction shown.

to the casing are observed. The relative displacement of themeasuring rods at A, B, and C due to the change from static torunning conditions, are determined, and they are denoted byho, hi, and h, respectively. Computation of the film thicknessesfrom these observations is subject to the assumptions (1) thatthe thickness of the residual oil films which exist under the staticconditions are negligible compared with those of the operativefilms, (2) that the geometry of the film beneath both pads isidentical, and ( 3 ) that there is no deformation of either the padsor their surrounding flanges.In these circumstances, in changing from static to runningconditions, the formation of active oil films causes an axialdisplacement T (in Fig. 7) of the thrust ring relative to thecasing, that is, the distance between the face of the reactionpad at the pivot point and the relevant working face of thethrust collar increases by an amount T . Hence, the pivot pointof the piston-loaded pad is similarly displaced a distance Trelative to the corresponding working face of the thrust ring.Th e displacements to , i , and r s of the measuring rods due tothe tilting of the thrust pad, are related to the known totaldisplacements ho, hi, and h, by the equationsho = o + T, hi = i+ T, nd hc = tc+ T

From the plan positions of the measuring points A, B, and Cin relation to the pivot point, it is possible to express the dis-placement T of the pivot point relative to the thrust ring interms of the three relative displacements to , ti, and rc of themeasuring rods. Hence the above three equations become solubleand, when the values of to, t i , and tc are obtained, the thicknessof the film is easily determined. I n particular, it was found con-venient to compute the thicknesses of the oil film at the four mid-boundary points and at the four corners of the film. The valuesobtained are referred to by the H symbols set a t the appropriatedpoints in Fig. 2a.In the equipment initially used for observing the smalldisplacements of the measuring rods, the ends of these rods wereattached to a rubber diaphragm, the deflexion of which forcedmercury along a capillary tube. The diaphragm was laterreplaced advantageously by a lapped piston (Fig. l b ) . Thisequipment, however, was in turn replaced by Talymin gauges.Th e operation of the pick-up units of these gauges depends on achange of electrical inductance brought about by the movementagainst a light spring pressure of the pick-up plunger. Thesepick-up units were mounted on the outer cover of the bearingcasing and actuated by the horizontal piston-headed rods bearingon the pad flange. The range of the instruments extends up to0.003 inch and, when the displacements to be measured exceededthis range, the gauges were replaced by mechanical dial gaugescalibrated in 0.0001-inch units. When a large oil flow was passedthrough the thrus t casing the pressure therein increased. Underthese conditions a light spring W B dded just to overcome theoil pressure so that the measuring rods lightly touched thepad flanges.When these measuring instruments were in use, three pairs ofpads were assembled in the thrust casing and spaced 120 deg.apart in order to apply three-point loading to the thrust ring.Before systematic observations were taken, the thrust ring wasmachined to ensure that the working faces were plane and parallelto a high degree of accuracy, and the faces of the pads were alsoscraped and lapped to a satisfactory plane finish. Even so, whenthe thrust ring was rotated slowly, small variations in the gaugereadings were observed. Hence, in observing the static positionsof each of the three measuring rods, the mean value of four gaugereadings taken with the thrust ring in positions spaced 90 deg.apart was obtained.When the shaft was rotated at working speed, the gaugepointers oscillated over a small range with a frequency which wasfound stroboscopically to be equal to the speed of the shaft.Separate experiments in which the gauges recorded the displace-ment of the free end of a vibrating cantilever spring, however,confirmed that the mean position of the vibrating pointer corre-sponds to the mean position of the end of the cantilever.Experiments were carried out with the bearing operating atconstant speed, and observations were made with various loadsand oil temperatures. This procedure was continued for a numberof different operating speeds.



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752 M I C H E L L B E A R I N G L U B R I C A T I O NExperiments with successively one, two, and three measuringinstruments in position, indicated that the spring pressure ofthe pick-up units did not affect the running oil film thickness.Film Thickness Observations. Film thickness observationswere taken for all seven pivot positions at five different speedsranging from 485 to 2,700 r.p.m., and for various loads and tem-peratures. Under conditions of point pivoting, the tilting padhas complete freedom to tilt in both the circumferential andradial directions (Fig. 8) . With the approximately mid-radial

are shown plotted against the criterion ZN/P, in Figs. 9-12.Of these pivot positions, No. 1which had an arc ratio =0.4probably corresponds closely with pivot positions actuallyadopted in practice.A tendency was observed for higher speeds of the bearing to

4 Q 12 i0 24Fig. 10. Film Geometry for Pivot Position 1, g /$ =0.40

Speed, 870 r.p.m.

" IZ N / P

IiIVz

J'Fig. 8. Tilting Behaviour of Pads

Arrows point in the approximate direction of greatestfilm convergencepivot positions (that is, positions 1,5,7,6,3) the radial tilt corn-ponent was small compared with the circumferential component.In pivot positions 1 and 3, the radial component of the tilt

With the pivot on the line of pad symmetry but radially offsetas a t positions 2 and 4, however, the radial tilt component wasgreater than the circumferential component. The films also

o.ooiofor pivot position indicated. v)DY$+0.0005z

underwent reversal above a certain value of ZN/P. 3converged radially towards the boundary arc nearer to the pivot, 0 2 4 6 8 10 12 14 16 18 20but further investigation would be required to establish this asan invariable effect of radially offset pivoting.of the computed film thicknessesH , thefilm ratio Hj/Ho,and the circumferential tilt component angle OL

ZN/PRepresentative Fig. 1 .Minimum Film Thickness for Each Pivot PositionN =485 .p.m.

1 I/+ =0.40;Hop2 !/+ =0.50; Hop4 g/+ =0.50; Ho,.5 814 =0.45;HoR==HorfiHo.6 814 =0.55; Hop7 I/ + =0.50; HoR =HOT=Ho.

3 el + =0.60;Hop

Numbers 1-7 refer to pivot positions.8

6Qd4 a2

1

a - ; I I I I , 00 6 I1 1's 14 30 36 42 54Z N / P

Fig. 9. Experimental Values of Hi and Ho,$14 =0.40 Fig. 12. Oil-film Thicknesses, Film Ratio, and CircumferentialTilt Angle for e/+ =0.40 and N =2,700 r.p.m.o 2,700. 0 2,000. + 1,495. x 1,OOO. 0 870. 485. 0 H i. Tilt angle a. -- ilHo. Ho.Speed, r.p.m. .



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M I C H E L L B E A R I N G L U B R I C A T I O N 753produce slightly thicker films for the same value of ZNIP andthis to some extent accounts for the scatter of the experimentalpoints shown in Fig. 9. Th e film thickness at the mid-boundanpoints and corners of the film for pivot position 1 and a bearingspeed of 870 r.p.m. are shown in Fig. 10, and they are repre-sentative of the observations made at all other speeds with thesame pivot position.In all circumstances there was a continuous increase in thethickness of the film as conditions of bearing operation werechanged to give greater values of ZNIP.The minimum thickness of the film is a major considerationin bearing design, so that a margin of safety against metal-to-metal contact may be provided. The values of the minimumfilm thickness, which in general occurs at one corner of the film,for the various pivot positions and an operating speed of 485r.p.m. are plotted in Fig. 11. For pivot positions 1,5,6,7, and 3,these values are closely representative of the mean film thicknessalong the whole outlet edge of the pad but with pivot positions 2and 4, for which the principal tilt of the pad was directed roughlydiagonally from corner to corner, the film thickness variedappreciably along the outlet edge. These results show thatwithin the range of the experiments, optimum minimum filmthickness conditions are obtained when the pad is pivoted mid-radiallyat positions for which the arc ratiohasvalues lying betweenabout 0.45 and0.50. When the pivot is set at mid-radial positionsoutside this range, the minimum film thickness is reduced toan extent which is appreciably greater for positions such as3 and 6 on the inlet side than for positions such as 1 on the outletside. Pivoting of the pad with radial offset from the centre isshown to result in extreme thinning of the film at one corner.Fig. 12 gives typical experiment values derived for Ho and Hifor a speed of 2,700 r.p.m. and for values of ZN}P up to 54.From these curves the mean film ratio (=Hi /Ho )and the meanangle of tilt [=%(%- )] are derived and plotted.obtained

L m .By plotting logarithmically, the following relations wereZN 0-71Ho =0.156(j;-)

ZN 0-54Hi =0 . 9 2 ( 7 )For all pivot positions 1, 5, 7, 6, and 3 respectively the filmratio decreased as ZN/P increased. For pivoting centrally onthe outlet side the film ratio was greater the higher the speed;for pivoting on the inlet side the opposite was the case.In he theory of the plane rectangular slider bearing in whichside leakage and viscosity changes are neglected, it is shown thatfor a given position of the transverse line pivot within the outlethalf of the pad, the film thickness ratio H;/Hohas a given andinvariable value independently of other operating conditions ofthe bearing. The numerical values of the film ratio for pivot

positions corresponding to &/c$ =0.40,0.45, and 0.50are 2-80,1.66, and I .O respectively. The corresponding experimentalvalues of the film ratio HJHo are shown in Fig. 13, and theextent to which these curves depart from the above values is ameasure of the actual deviation caused by side leakage, changesin viscosity, sector shaping of the pad, and the influence ofsurface profile (Raimondi and Boyd 1953), from the results pre-dicted by this theory. At small values of ZNjP the differencesare appreciable but with higher values of the criterion, agreementprogressively becomes closer.Though the values of the film ratio Hi/Ho diminish forprogressively higher values of ZNjP, the observations in generalshow that the angle cc of pad tilt in the circumferential directionbecomes greater as the value of ZNIP is increased. For givenoperating conditions, the tilt angle cc was relatively large whenthe pad was pivoted a t position 1; as small with pivot positionson the inlet side of the pad; and had its minimum value withcentral pivoting at position 7. For the mid-radial positions thefilm ratio Hi/Ho s also a minimum at this point (Fig. 13).Fig. 13 b shows the mean outlet oil film thickness (Ho)or eachof the five mid-radial pivot positions and illustrates that theoptimum pivot position is in the range 0.45-0.50. Th e value ofHo ecreases for other pivot positions, especially on the inlet

side. Fig. 13b is in qualitative agreement with theoretical pre-dictions but why the slope is a minimum for central pivoting isdifficult to understand.The above theory excludes the possibility of load-carryingfilms being formed beneath the pad when it is pivoted a t thecentre and at positions within the inlet half of the pad. When thetheory is modified, however, to take account of viscosity changesin accordance with a simple approximate law, it is shown, as for

I I I I II .0015zIsU

go.00 05 c.0005ZuI-

CL

t,c308 160 I 2 ---+--210

ZN/Pa Film ratio HJHO. b Outlet film thickness.

Fig. 13. For Different Pivot PositionsSpeed, 485 r.p.m.

example by Boswall (192S), that hydrodynamic film operationis possible when the range of pivot positions is extended into theinlet half of the pad. This theoretical conclusion is confirmedby the experimental results obtained with pivoting at positions7, 6, and 3.All the above results were taken with the oil-bypass valve open.When more oil was passed through the thrust casing, by closingthe oil-bypass valve, the oil film thickness was increased by upto 10 per cent.When the experimental apparatus

is in operation the torque which acts on the floating casing andwhich is balanced by a calibrated torque arm, is due to the com-bined action of (1) the hydrodynamic friction forces which thepressure films exert on the working faces of the pads, and (2 )dragforces exerted on the inner surfaces of the casing by the movingoil contained within it. The torque due to (2) was determinedby operating the bearing with the pads unloaded; the appro-priate load was then applied to the pads and the combined torquewas observed; and finally the torque due to (1) was obtained bydifference.Values of the nominal coefficient of friction p =F/ for thepads were computed, where W is the total load acting on eachpad and F is an equivalent friction force assumed to act tan-gentially on the working face of the pad at the same distance fromthe shaft axis as the pivot, and which has a moment about theshaft axis equal to that of the actual film tractive forces actingon the pad. For the pivot at position 1, values of the friction

Friction Characteristics.



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754 M I C H E L L B E A R I N G L U B R I C A T I O N

Pivot position375124

_-

Z y rFig. 14. Friction Characteristics when Pivoted at 814 =0.40---- Moving surface (theoretical).--- Stationary (theoretical).Experimental.

coefficient for the viscous traction on both the moving andstationary surfaces of the bearing have been calculated inaccordance with Boswalls theoretical treatment of the sector-shaped pad in which allowance is made for side leakage but notfor changes in viscosity nor for the effects of any radial com-

814 k n0.0061 0.4400054 0460.0043 0 0.500.45 0.0041 0.480.40 0.0039 045

0.50 0.0052 0450.50 0.0045 0.51

0.60.55 -I--

ponent of tilt of the pad. These results are shown graphically inFig. 14. Since the total tangential force which tends to moveeach pad includes both the viscous traction on the inchedsurface and the small resolved component of the pressureresultant acting on that face, which together equal the viscoustraction on the moving surface, the experimental results are tobe compared with the upper of the two theoretical lines. Thescatter of the experimental points does not appear to bear anysystematic relation to the different speeds a t which the observa-tions were made.For all pivot positions the relations between p and the para-meter ZN/P were straight lines when plotted logarithmicallpsuch that p =k ( Z N / P ) = .The values of K and n are given inTable 2 . Within the experimental range the pad friction is

TABLE. VALUESF k AND n

a After 2 minutes. c After 29 minutes.

d After 50 minutes.After 8 minut-s.Fig. 15. Experimental Temperature Distributions as Bearing Warms Up

Speed, 2,700 r.p.m. Load, 433 b. per sq. in. 8/4=0-40.



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MICHELL BEARING LUBRICATION 75 5

129132132133130

shown to have minimum values when the pad is pivoted atposition 1 for which 3 / $ =0-40, and progressively increasedvalues when the pivot is moved successively to positions nearerthe inlet edge.On closing the oil-bypass valve, to pass all the oil through thebearing, the friction decreased for all pivot positions.

Surface Temperature Distributions. Each pad was drilled tocarry six, seven, or eight thermocouples arranged to give a com-plete temperature distribution. For each pad the thermocoupleswere situated o n given radial and circumferential lines so thaterrors could be more easily detected. Also, the couples were SOplaced that on reversing the direction of rotation the number oftemperature points was doubled. Thirty thermocouple stationswere provided but owing to the pivot, not all these could beused for any one distribution. As for pressure distributions, itwas expedient to base the temperature distributions on one setof observations. Owing to difficulties in securing thermocouplesto the actual edges of the pads, boundary temperatures were

0.90.90.850800.65

Fig. 16. Temperature Conditions Along CircumferentialCentre-line

obtained from thermocouples fixed in holes drilled through thepads as near the edges as possible.Thermocouples showed that the rear face of the pad, and justbeyond the outlet edge were approximately at the bulk oil tem-perature. T he bearing surface was lapped and scraped before andafter fixing the thermocouples in position with plastic metal andsolder. Calibration was done with the thermocouples in position.T o obtain better temperature control one pair of pads in the topposition was used. In analysing results the best smooth tem-perature contours were drawn. Peculiar kinks have no meaningunder these experimental conditions.The important variables are speed, load, pivot position, andinlet temperature. According to theory, for a film of given thick-ness and taper the speed and inlet temperature have no effecton the temperature increase between inlet and outlet edge j theimportant factors are the applied load and the pivot position.Fig. 15 shows successive temperature distributions as thebearing temperature increases at a speed of 2,700 r.p.m. j Fig. 16shows the temperature along the circumferential centre-he.Several general trends for all temperature distributions areillustrated. It is obvious that raising the oil inlet temperaturereduces the measured temperature variation as well as raises thegeneral level of the temperature. Th e measured maximum tem-perature occurs just within the outlet edge. This is due to thelarge amount of cooling performed by the oil around the padboundaries,

Higher temperatures are recorded towards the outer periphery,due to the increased length of the pa th the oil has to traverse.Further experimental distributions confirmed that the speedhas a much greater effect on the mean temperature rise than th eload. At a speed of 485 r.p.m. the maximum temperature varia-uon was only 2 deg. F. for loads of 142 and 433 lb. per sq. in.;lncreasing the speed to 2,700 r.p.m. produced a temperaturechange of 19 deg. F. (Fig. 15). (Inle t temperature 110 deg. F.)TABLE. EFFECTF PIVOTOSITION

Posiuon oftemperature,deg. F. temperature*0.400.450.500.550.60

* Defined as fractional angular position from inlet edge.The effect of pivot position is illustrated in Table 3 for aspeed of 2,700 r.p.m., a load of 433 lb. per sq. in. and an inlettemperature of 110 deg. F. There is relatively little differencein the maximum recorded temperature but the position of the

Fig. 17. Experimental Temperature Distribution for Offsetfter 2 minutes.-- fter 8 minutes. ---- - -- After 29 minutes.---- fter 50 minutes. - Pivot Position 2at SAGE on March 10, 2013pme.sagepub.comDownloaded from


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756 MICHELL BEARING LUBRICATIONmaximum temperature moved towards the centre of the pad.This was confirmed at other speeds.Similar results were obtained with the pivoting at an offsetposition such as No. 2 . The main difference is that theobserved area of maximum temperature is much nearer the outerperiphery. This is because the oil film is thinnest at the outerperiphery and hence the heat produced there is greater than forthe mid-radial pivots. Also, the maximum temperature is some5 deg. F. greater than for a pad pivoted at, say, position 7 andoperating under the same conditions. This is also due to thethinner oil film under which offset pivoted pads operate. Fig. 17shows a typical distribution.

PART 11-CORRELATION BETWEEN THEORYAND EXPERIMENT

The theoretical determination of the essential operatingcharacteristics of a hydrodynamically-lubricated bearing is basedon the solution of Reynolds equation for two-dimensional flow.For the sector-shaped pad the equation isa[z.h3 a]+p .-[-h3 . . g]= 6wr2;fieh . (1)ar ZThis equation has been solved by Boswall (1928), Skinner

(1938), Christopherson (1941), and Wood (1949). Boswall andWood assumed that the filmthickness was a linear function ofthe angle subtended by the pad, thus assuming a warped surfacefor the pad. Christopherson's solution is the most general, inwhich the film geometry and viscosity need not be simplified.Kingsbury (1931) used his electrical tank analogy to obtainmany results of practical importance.In solving the above equation, the important starting factoris the film ratio. This gives a non-dimensional pressure functionthe integration of which yields the operating characteristics suchas the filmthickness and friction criteria. Reynolds equation fortwo-dimensional flow for the sector-shaped pad and for constantviscosity have been solved using the theories of Boswall andChristopherson for several values of the film ratio. Followingjournal-bearing theory, the following non-dimensional criteriaare defined.Film thickness criterion is definedilm Thickness Criterion.as

According to BoswallAccording to Christopherson

A H = (6D)*8, =(6#)*{JJPe29RaRa@]*Friction criterion is definedriction Criterion.

According to Boswall

According to Christopherson

These criteria are plotted in Fig. 18, together with thefractional angular position of the centre of pressure from theoutlet edge. From these computationsjt is seen that the filmthickness criterion is a maximum when e/$ =0.41 andf =2.2as the pivot position moves towards the centre the friction

0.43

0.40

A H

0 3 5

0.32I

Fig. 18. Theoretical Values for Sector PadAH.el$ .A p for moving surface.------ -- ----_ -_Ip for stationary surface.

a For =0.40.-- Solution after Boswall H = ( 0 , ) ._ _ - - Solution after Christopherson H = ( 0 l r l ) .Centreof pressure, Christopherson.+ Centre of pressure, Boswall.Position of applied load.

Film thickness constant under radial line passing through pivotposiuon.

b For offset pivot position 2.Fig. 19. Pressure Distribution



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M I C H E L L B E A R I N Gcriterion increases rapidly, the film ratio decreases to unity andthe film thickness decreases to zero; he friction criteria reacha minimum value when the film ratio is between 3.0 and 4.0;the oil-flow criteria show that as the film ratio increases thequantity of oil flowing across the outlet edge increases muchless than that flowing into the pad, that is, the side leakageincreases (these criteria are not shown).The pressure distribution corresponding to Fig. 6a is shownin Fig. 19a (dotted line). This has been computed byChristophersons relaxation theory, allowing for complete radialand circumferential tilt, but for constant viscosity, the non-dimensional film thicknesses being determined from the experi-mental values for the same value of ZNIP. The computed centreof pressure is nearer the outlet edge than the actual pivotposition; this is to be expected as a constant viscosity has beenassumed. The pressure in the oil film is directly proportionalto the viscosity; as the viscosity decreases while the oil passesbetween the bearing surface, the pressure generated is corre-spondingly decreased, the resultant effect being to cause thecentre of pressure to move towards the inlet edge.Th e particular film geometry of Fig. 19awas chosen becausethe film thickness was constant under a radial line passingthrough the pivot point. The full lines in Fig. 19a show thepressure distribution assuming the film thickness is a linearfunction of the angle subtended by the pad, the non-dimensionalfilm thickness H at inlet and outlet being that shown at theradial centre-line of Fig. 19a;H is also shown at the four corners.It seems that there is a considerable variation of H as illustrated,and the most noticeable effect is to cause the top left-hand comerto carry more load.The actual experimental distribution operates with higherfilm pressures owing to the decrease in viscosity, and henceoil pressures towards the outlet boundaries are reduced.Th e value of the outlet film thickness criterion is as follows:

(1) After Christopherson; h =f Blrl)=0.390.(2) After Boswall; h =f 0,) only =0.388.(3) Experimentally =0.270.Fig. 19b shows a typical relaxed pressure distribution (assum-ing constant viscosity) for the radial offset pivot position. Thenon-dimensional values of H were obtained from actuallymeasured film thickness. The computed centre of pressure is at

some distance from the actual pivot position but this is due toneglecting viscosity variation which is particularly large nearthe area of maximum pressure for offset pivoting.

L U B R I C A T I O N 757The following conclusions can be drawn:(1) Outlet film thickness. The constant viscosity solutiongives a slightly greater value for the outlet film thickness.(2) Inlet film thickness. The constant viscosity solutiongives a low value of the inlet film thickness.(3) Film ratio. When the viscosity varies the film ratioincreases. The pressure built up under a slider bearing is dueto the viscosity of the oil. As the viscosity decreases from inletto outlet, the viscosity at the outlet side is less effective increating a pressure within the film and thus would tend tomove the centre of pressure towards the inlet side. As thepivot position is fixed this movement is counteracted by theslope of the pad increasing.(4) Coefficient of friction. The use of a constant meanviscosity gives a value higher than when the viscosity varies.

Effect of Variable Viscosity. A qualitative picture can beobtained by considering the simple flat slider with no sideleakage, for which operating charts are available. Those due toNorton (1942) are used here.W o r k e dExample. Assume, for simplicity, a pad 1 inch square,pivoted so that X/L=0.40, mean temperature 92 deg. F. givinga mean viscosity of 1 poise; surface speed 27.8 ft. per sec. andapplied load 400 lb. First the problem is solved assuming aconstant viscosity, that is, b = 1. Using Nortons equations(Norton1942)and figures in the following order-equation (64),Fig. 39, Fig. 38, equation (41), equation (73) and the viscositytemperature curve for the oil used, the results are : ilm ratio 2.8,minimum film thickness 0,00134 inch, and oil temperature rise22.9 deg. F. With the given oil undergoing a temperature riseof 22.9 deg. F. and having a mean viscosity of 1 poise at 92 deg. F.,the inlet and outlet viscosities are found to be 1.35 poises (at83 deg. F.) and 0.65 poise (at 106 deg. F.). Hence the viscosityratio b =2-08.Th e process is repeated with b =2.08, resultingin the values, film ratio 3.6,minimum film thickness0-00133 nch,and oil temperature rise 20 deg. F. For greater accuracy, theprocess could be repeated using a temperature rise of 20 deg. F.instead of 22-9 deg. F.-the method being one of successiveapproximation. However, a further trial is hardly justified.By taking a number of combinations of the mean temperature,speed, and applied load-similar to conditions in the laboratory-Fig. 20 was obtained. The value of 2 in the variable ZU/P sthe mean viscosity in poise. The peripheral speeds were takento be the mean speedsof 2,700 and 500 r.p.m.

U/PFig. 20. Theoretical Values of Film Ratio, Inlet Film Thickness,and Coefficient of Friction for Tilting Slider, but NeglectingSide Leakage Speed, 2,700 r.p.m.-_----- peed, 500 r.p.m.---Iased on constant mean viscosity.

From an examination of Fig. 20 it might appear that thedivergence from the constant viscosity results is due to speed.However, it is well known that, according to the theory, thetemperature rise of the oil passing through the bearing dependsonly on the applied load. For any given value of ZlJlP, if U sincreased, P must also be increased for a given value of Z . Anincrease of P causes a greater temperature rise and hence agreater viscosity change, resulting in the divergence discussedabove. The curve for the outlet film thickness has not beenplotted as the difference was so very small-for a given value ofZlJlP, an increase in speed caused a slight decrease in the outletfilm thickness.These qualitative results serve to explain the observed factsthat thicker oil films are associated with higher speeds, the a mratio (Hi/Ho)of the pad decreases as ZN/P increases (initiallyvery rapidly), the film ratio is greater for higher speeds and alwaysgreater than that value based on a constant viscosity. However,there was no speed effect observed for the friction curves butthis is probably due to the very small variation with speed shownin Fig. 20. Theory and experiment differ as to the speed effecton the outlet filmthickness.



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758 M I C H E L L B E A R I N G L U B q I C A T I O NComparison of Theoretical and Experimental Film ThicknessCriteria. In theory, for any given pivot position, these criteriaeach have a unique value. Fig. 21 shows tlie plot of thesetheoretical criteria, which fall on a single curve, the corre-sponding centre of pressure being located by an arrow. Experi-mental criteria curves for all mid-radial pivot positions and for aspeed of 485 r.p.m. are also given in Fig. 21. The latter have been

" - I " I1 1 i+ i . - i--L_--A---L 1

3 4A/l FRICTION CRITERION

Fig. 21. Experimental and Theoretical Friction and FilmThickness Criteria

Experimental for N =485 r.p.m._ _ - _ Theoretical.

calculated from the Ho/(ZN/P) nd p/ (ZN/P) raphs, Ho andp being read off at identical values of ZNIP. In all cases theexperimental film thickness criteria are less than the theoreticalvalues and reach a maximum in the region 0.45 to 0.50; d,decreases and moves farther away from the theoretical line asZN/P decreases, that is, as the effect of variable viscosityincreases. The friction criterion progressively increases as thepivot moves towards the inlet edge; here is approximate agree-&/$-+ t i O , A , +0, and 5 p --f m; xperimental results showthat pivoting on the inlet side is possible but with increasedfriction and reduced minimum film thickness.Typical experimental values of the criteria for two pivotpositions are shown in Fig. 22; corresponding values of ZN/Pare given. Larger values of5 , are associated with higher speeds.Further criteria for two values of ZNIP are shown in Fin. 23.

C O M B I N E D C O N C L U S I O N SThe experimental results confirm that fluid film lubricationexists for pivot positions not only in the conventional positionbut also for central pivoting and pivoting on the inlet side of thepad. Experiments show that the film thickness readings lie onseparate curves for each speed; his has been shown to be due tovariable viscosity. The operating pivot position for these experi-ments for maximum minimum film thickness is in the regione/$ =0.45 to 0.50 ; this compares with the value 614 =0.40 to0.42 adoptedjn practice. For minimum friction the pivot should

be placed at el $ =0.40 (for these experimental conditions); thefriction increases as the pivot moves towards the inlet edge.

0-30

Fig. 22. Experimental Friction and Film Thickness CriteriaN =2,000 r.p.m.N =485 r.p.m.-- - --- - Z N I P decreasing in direction of arrow.

Limitations to existing lubrication theory in simplifying theviscosity changes render impossible an exact comparisonbetween theory a nd experiment. T he effects of variable viscosityhave been illustrated.Typical experimental pressure and temperature distributionshave been discussed.Unusual effects are caused by increasing the flow of oilthrough the bearing case: the film thickness increases, thefriction decreases; nd the pressure contours move towards theouter radius.

A H

I I I2.5 3.0 3.5O C2.0

A P0

Fig. 23. Experimental Values of Friction and Film ThicknessCriteria for Speeds of 2.000 and 485 r.p.m. and Values ofZN/P of 4 and 16, Theoretical.---- peed, 2,000 r.p.m.Speed, 485 r.p.m.



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M I C H E L L B E A R I N G L U B R I C A T I O N 759ACKNOWLEDGEMENTS

Th e authors wish to acknowledge the help and facilities ofthe Michell Thrust Bearing Co., Ltd., in particular for theexperimental equipment. The work described here was carriedout during the period 1947-50 at the University of Sheffieldunder the general direction of Professor H. W. Swift, head ofthe Departments of Engineering, to whom many thanks areextended for continual interest and advice.

A P P E N D I XB IB L IO G R A P H Y

BOSWALL,.0. 1928 Theory of Film Lubrication (Long--mans, Green, London). -CAMERON.. 1949 Proc. 1.Mech.E.. vol. 161. D. 73. TheSukace-roughness of Bearing-surfaces and ^its Relationto Oil-film Thickness a t Breakdown.CHRISTOPHERSON,. G. 1941 Proc. I.Mech.E., vol. 146,p. 126, A New Mathematical Method for the Solutionof Film Lubrication Problems.GIBSON,. H. 1919 Engineeritzg, vol. 107, p. 765, The MichellThrust Block.KINGSBURY,. 1931 Trans. A.S.M.E., vol. 53, APM-53-5,p. 59, OnProblems in the Theory of Fluid-film Lubrica-tion with an Experimental Method of Solution.MARTIN,H. M. 1920 Engineering, vol. 109, p. 233, TheTheory of the Michell Thrust Bearing.

MICHELL,A. G. M. 1905 Zeit. f i r Math. Physik, vol. 52,p. 123, The Lubrication of Plane Sliders.MORGAN,., MUSKAT,M., and REED,D. W. 1940 Jl. AppliedPhys., vol. 1I, p. 541, Studies in Lubrication.MUSKAT,M., MORGAN, ., and MERES,M. W. 1940 Jl.Applied Phys., vol. 11, p. 208, The Lubrication of PlaneSliders of Finite Width.NEWBIGIN,H. T. 1913-14 Proc. I.C.E.,vol. 196, p. 223, TheProblem of the Thrust Bearing.NORTON, . E. 1942 Lubrication (McGraw-Hill Book Co.,London and New York).RAIMONDI, . A., and BOYD, . 1953 The Influence ofSurfaceProfile on the Load Capacity of Thrust Bearings withCentrally Pivoted Pads. Presented at the AnnualMeetingof the A.S.M.E. New York, 29th November to 4thDecember. 1938 Jl. Applied Phys., vol. 9, p. 409, FilmLubrication of Finite Curved Surfaces.1921 Commonwealth Engineer (Australia), vol. 9,p. 115, Proposed Method for Solving Problems inLubrication. 1917 Brown Boveri Mitteilungen, pp. 3,35, 58,80, Moderne Drucklager.1933 Brown Boveri Review, July/August, p. 119, SomeRecent Results of Tests made with Segmental Bearings.1941 Brown Boveri Review, November, p. 366, SomeRecent Investigations into Segmental Thrust Bearings.1949 Phil . Mag. , vo1. 40, Pt. 1, p. 220, NewForm of the Solution of Reynolds Equation for theMichell Rectangular and Sector-shaped Pads.

1922 Engineering,vol. 114, p. 260, Lubrication Tests.

SKINNER, . M.STONE,W.

VONFREUDENREICX,.

WOOD, W. L.

CommunicationsDr. A . CAMERONMember) wrote that there was a constanttheoretical ratio between (Ho/L) and l /p which equalled&/All, in the authors notation. He would like to ask if that ratiowas constant experimentally, or how far it varied. If it wasconstant it gave a simple way of finding Ho.

Mr. J. A. COLE,M.Sc. (Associate Member), wrote that thethrust bearing had been rather neglected as the subject of experi-mental research in comparison with the journal bearing, and thepresent paper was therefore to be welcomed. The authors hadmade comprehensive measurements, many of a difficult nature,and had satisfactorily related them to existing theory, showing inparticular the necessity for taking into account variation ofviscosity along the film.Th e paper concentratedon he relation of experiment to theoryrather to the exclusion of design considerations, but the authorsmight have further information which would increase the valueof the investigation in that respect. As with the journal bearing,the great difficulty in design was the estimation of 2, the repre-sentative viscosity, which in the paper had apparently been basedon the mean of pad thermocouple readings at the mid-inlet andmid-outlet edges. It was normally calculated from a heat balancefor the bearing, all the friction loss being assumed to appear asheat in the outflowing oil. The authors, although noting theimportant influence of oil flow, particularly on film thickness andfriction loss, had given no figures for flow rates and had notmade it clear whichof the variables, oil flow rate, inlet tempera-ture, and supply pressure had been held constant during thetests. That information, and an indication of the variation of therepresentative temperature with applied conditions, would bevery helpful.Further, he would ask whether the detailed temperaturedistribution results had been examined to check the adequacy

of the chosen representative temperature and possibly to suggestwhere a single pad thermocouple might best be situated. Blok(1949)* had suggested that a single representative viscositysuitable for experimentally checking the theoretical relationbetween one set of variables, such as film thickness and Z N / P ,would prove unsuitable for another, such as friction and Z N lP .One set of pads in the test apparatus had been individually andtherefore equally loaded, but for the six reaction pads theequality of loading had been, as was common, dependent uponthe accuracy of construction of the machine. The authors hadmentioned that where the measurements had been made onmore than one pad, appreciable variations had been observed,and that suggested that load-equalizing devices could profitablybe generally used in practice, as indeed they were in the UnitedStates. In their absenceit might be desirable to keep the numberof pads down to three: there was, in any case, not a great dealof information available on the optimum numbers of pads.Th e observations of radial tilt in addition to circumferentialtilt, and its change of sign under certain conditions, wereinteresting. Similar effects had also been observed at M.E.R.L.(Barwell 1951-52)t during tests on thrust bearings at highersurface speeds, despite the fact that the pads had tilted on astep. Deformation of the step had permitted radial tilt to OCCLUIt would be interesting to have the authors data on the rela-tive friction losses due to pad friction and casing drag. At highspeeds the churning Iosses might be considerable, but someamelioration had been obtained at M.E.R.L. by the expedientof replacing the general oil supply to the casing by individualfeeds to a suitably designed edge-groove system in each pad,* BLOK,H. 949Proc. I.Mech.E., vol. 161, p. 66 , Communicationon paper by Cameron, A., and Wood, W. L.t BARWELL,. T. 1951-52 Trans. Inst. of Eng.and Shipbuilders inScotland, vol. 95, p. 64, Some Aspects of Research on Friction an dWear.



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760 C O M M U N I C A T I O N S O N MICHELL BEARING L U B R I C A T I O NMr.A. HILL, BSc. (Associate Member), wrote that the paperwas of particular value in that the authors had demonstrated thatthe film thickness, pressure distribution, and temperature risefor a given pivoted pad more or less agreed with the theoreticalpredictions.He used the words more or less because the theory was itselfvery far from being able to give a complete answer. Some of thedivergences from theory which the authors had recorded were ofeven greater interest than the agreements.Aeration of the oil had been mentioned early in the paper, andit was his impression that it was connected with the oil flow andthe bypass valve.There were repeated references to that bypass valve, the closingof which caused an increased flow of oil, resulting in, as recorded,a thicker film, less friction, and differing pressure and tempera-ture distribution.If a thrust pad were given all the oil it needed to form a film,surely that film would not increase because more oil was flowingpast Ihe pad. -The results sueaested that with the normal flow of oil in theexperiments, the-pads suffered from partial starvation and hadtherefore been unable to build up free films. When the flow wasincreased to the maximum, he asked whether the mean oil tem-peratures of inlet and outlet varied. Also whether the authorscould give any results for the full oil flow which could be com-pared directly with the published results. When the effect ofvariation of oil flow had been observed, he asked whether theauthors would say why the tests had been carried out a t thelower flow and not at the maximum.The authors had mentioned a tendency for variation in speedto affect the film thickness in spite of the overall value of Z N / Premaining constant. He himself had experienced similarbehaviour when using that criterion, although the possibility ofexperimental error had to be remembered. In Fig. 9, however,the results were sufficiently consistent to show a definite trendand they confirmed his opinion that as a criterion for com-parison of thrust-bearing results Z N / P , although it was simple,left much to be desired. He asked whether the authors wouldsuggest an improved criterion.As a suggestion he would tentatively put forward the form( Z N / P ) x ( D / L ) ,where D was the mean diameter of the padand L its mean circumferential length.On p. 755, he authors had stated According to theory, thespeed and inlet temperature have no effect on the temperatureincrease between the inlet and outlet edge; the important factorsare the applied load and the pivot position. That was verysurprising; and rather unconventional-he asked whether theauthors would give their reasons.He was relieved to see, however, that the experimental resultshad followed more conventional lines, the heat produced beingmore affected by speed than by load. So far as he was aware,that was the first time that the shape of the film had beenobtained experimentally for pivot positions placed towards theleading edge of the pad, although Michell had evaluated thecondition of a normal pad with reversed rotation. He hadestimated that the viscosity at exit would be half that at inlet.The curves in Fig. 13 were of particular interest, as was theminimum slope occurring at the centre pivoted position, NO. 7.To show the pad attitude for the condition ZW/P= 10,Fig. 24 had been made from Fig. 13.He thought that for pivot positions 0.5 to 0.6 and greater, astable film might be considered to be formed regardless of theviscosity characteristic of the fluid used, and the angle of tiltto be increased as the pivot position increased.As the pivot position was reduced from 0.5 to 0.4 or less,however, the mean film thickness decreased, resulting in anincreased rate of shear. The temperature rise across the face ofthe pad would increase correspondingly and the variation inviscosity would also increase. The centre of pressure wouldmove with the pivot, resulting in increased side leakage. Thecombination of those two actions was probably the cause of theincrease in the angle of tilt.If the pivot were moved still further, the angle of tilt woulddecrease again, since as the pivot position approached 0, the padangle would approach 0. He considered it very likely that thefilmwas unstable when the pivot was forward of the centre

position, and he would very much like to see a Nm pressuredistribution as given in Fig. 6 for a pivot position of 0.4, andasked whether the authors could provide that.Since the film formation depended in that case upon theviscosity-temperature relation of the fluid, it was perhapsfortunate that the Viscosity of ordinary lubricating oils decreasedrapidly as temperature rose.

LENGTH OF PA D O N MEAN DIAMETER-INCHFig. 24. Diagram of Pad Attitude for Various PivotPositions at ZN/P =10

Based on Fig. 13.Mr. J. L. JEFFERSON,.A. (Associate Member), Mr. P. M.HAILEY (Newcastle upon Tyne), and Mr. M. MILNE AssociateMember) wrote that the ingenious test rig and painstakingapproach to the problem had made a very welcome addition tothe all too scanty knowledge of pivoted pad behaviour.The limitations of the simple constant-viscosity hydro-dynamic theory had long been exposed by the successful use ofcentrally-pivoted pads and pads of negative eccentricity. Never-theless, the authors discovery that in regard to the film thick-ness, the central pivot was probably the best, came as a slight

surprise-albeit a pleasant one. According to Fig. 11, however,pads had operated with film thicknesses less than 3x 10-5 inch,which raised the question as to whether, in fact, minimum filmthickness was necessarily the best criterion of a good pad.From the operating engineers standpoint, of the non-dimen-sional parameter Z N / P , Z was often, and P almost always, indoubt. In those circumstances the coefficient of friction tendedto become meaningless and recourse must be made to some-thing more tangible-the power. There, perhaps, a quibblemight be made concerning the authors otherwise admirableexperimental technique, since the torque obtained by differencewas not necessarily the total absorbed by the thrust-some lossbeing found even with unloaded pads.In that connexion the curves shown in Fig. 25 might be ofinterest. They were taken from a series of experiments currentlybeing carried out at their works in which load capacity was thechief interest. The thrust block was of normal commercialturbine size and type, with line-pivoted pads loaded on one sideonly. The measured power curve had been derived from oil tem-perature rise (an admittedly crude procedure, but one the resultsin which were shown to be not too improbable by the drivingturbine powers). At high speeds (again, much in excess of the37.5 ft. per sec. maximum which the authors appeared to haveemployed) the power loss was much greater than that predictedby the simple constant-viscosity theory, viscosity being relatedto pad temperature, In fact,it seemed that there wasanadditionalchurning loss dependent on the cube of the speed. That loss,which was disregarded by the theory, and which would not bediscovered by the authors tests, could obviously be of supremeimportance at high speeds.Th e one-at-a-time insertion of pads for pressure distribu-tion measurements was a determined attempt to circumventdifficulties whose magnitude might be gauged from the valuesof minimum film thickness given in Fig. 11. The results had



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C O M M U N I C A T I O N S O N M I C H E L L B E A R I N G L U B R I C A T IO N 761justified the pains taken, but the practical problem of ensuringeven distribution from pad to pad was unlikely to fall readily toa frontal assault, and the effect of its neighbours on the pressuredistribution of any pad might clearly be considerable. Underextreme conditions premature failure might occur through theintractable behaviour of an abnormal pad.

Fig. 25. Variation of Power Loss with Speed for No LoadConditionOil inlet to block a t constant temperature. el 8 =0.45.

Th e reduction in measured friction, together with the shift ofpressure contours, due to increased oil flow was noted withinterest; it would be valuable if the authors would give thecorresponding changes in film thickness and surface temperaturedistribution. In their works tests a more disconcerting shift ofpressure contours (apparently with variation in load) had beenobserved.A single pressure tapping, situated at the mid-radiusopposite the line pivot, had been taken from each of two hori-zontally opposite working side pads and that seemingly im -probable phenomenon-which was rendered more likely by thefact that the process was reversible-was shown in Fig. 26.Some idea of the complexity of the subject was revealed bythe measurements of film thickness. Fig. 10 showed a reversal ofradial tilt at a value of ZNIP 11-5, hereas aD exactly opposite

s.G

- 0 260 400 600 860 1.600 I,iOO 1.400 1.600MEAN APPLIED PA D PRESSURE-LB. PE R SQ. IN.Fig. 26. Local Pad Pressure Against Mean Applied FadPressure

Oil inlet to block at constant temperature. 8/6=0.45.

tendency (H,+>H, as P increased) had been reported byBarwell (1951)*, who ascribed it to the effect of load alone on hishigh-speed rig. They wondered whether the authors had anydirect evidence that Z and ATcould also cause such reversal.In comparing a rise of 2 deg. F. at a speed of 484 r.p.m. withone of 19 deg. F. at a speed of 2,700 r.p.m. (p. 755) the authorshad adopted an inlet temperature of 110 deg. F.Unfortunately,that would appear from Fig. 15 to represent an unsteady con-dition which might invalidate the comparison. The theoreticalCOLLAR ROTATION

Fig. 27. Contours of Pad After FailureFigures denote depression in 1 l,OOO inch below datum.

Fig. 28. Pad from which Contours in Fig. 27 were Takencontention that only applied load and pivot position affectedthe temperature rise premised that the pads and collar wereperfect insulators; the fact that they were not might serve toexplain why the authors temperature rises were much lower thantheory would predict. If the collar acted as a thermal storehouse,that would also help to explain the evening out of temperaturecontours in Fig. 15.Higher temperatures had been observed towards the outerperiphery due to the increased length of the path. Radial tilt* BARWELL,. T. 1951-52 Trans. Inst. Eng. and Shipbuilders inScotland, vol. 95, p. 64, Some Aspects of Research on Friction andWear.at SAGE on March 10, 2013pme.sagepub.comDownloaded from


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762 COMMUNICATIONS ON MICHELL BEARING LUBRICATIONmight contribute to the unbalance of temperature, and it mightbe added that those temperatures were likely to be aggravatedby thermal distortion of the pad. In Fig. 27 were illustrated thegeometric contours of a pad, measured after failure, Since the padhad been initially nominally plane, those measurements gave someidea of its shape a t the time of failure (in that case at 2,255 Ib.per sq. in., 124 ft. per sec.). Fig. 28 showed the actual set ofpads from which that example had been taken, the pad i n ques-tion having been etched to show up surface cracks.

Dr. G. D. S. MACLELLAN, M.A. (Associate Member), wrotethat Fig. 14 indicated that the authors method of computingthe values of ZNIP and p suggested that the experimental resultsbore a closer relation to the theoretical value for p on thestationary surface than on he moving surface. No comment hadbeen made on that somewhat surprising result, although just theopposite was to be expected. Th e fact that the theoreticalp valuefor the stationary surface was shown in Fig. 14 to be less thanthat for the moving surface was presumably due to the neglectof the component of the normal force on the inclined stationarysurface which acted parallel to the plane of the moving surface.I n fact, the resultant force on each surface in a directionparallel to the plane of the moving surface was the same, and itwould have been preferable to omit from Fig. 14 the line for pon the stationary surface (theoretical).In that connexion it would be useful to know how the meaneffective oil temperature had been determined for evaluating Zin the quantity ZNIP. An apparatus very similar to thatdescribed by the authors had been presented to th e CambridgeUniversity Engineering Laboratory and had been used for someyears in an undergraduate experiment. Quite satisfactory agree-ment with theory had been found by using Camerons method(Cameron 1949) of allowing for a temperature rise under thepad, above the surrounding bulk oil temperature, determinedas a fraction of that which would be expected if all the frictionalwork were dissipated as heat in the oil.A U T H O R S R E P L I E S

Dr. C. F. KETTLEBOROUGH wrote, in reply to Dr. Cameron,that variations had been observed in the experimental values ofthe ratio &(=* 2). typical experimental curve whichshowed that variation and was based on results set out in Fig. 21,Part 11, was given in Fig. 29. As the value of ZNIP decreased,

0.05 I I I I I I0 4 8 12 16 10 24Z h/P

Fig. 29. Variation of the Non-dimensional ParameterA,/A, with ZNIPSpeed 48 5 r.p.m. Pivot position 1. e /$ =0.40._--- Constant theoretical value.Experimenral curve.

the experimental curve fell away from the theoretical value,owing presumably to the fact that the viscosity variation wasgreater as the load increased.

Dr. C. F. KETTLEBOROUGH,r. B. R. DUDLEY,nd Mr. E.BAILDON rote in reply to Mr. Cole that the rate of oil flowthrough the casing and the supply pressure had been maintainedconstant in the experiments. The flow rate was, in general,115 cu. cm. per min. at a pressure slightly above atmospheric.A few experiments had been carried out with the maximumavailable flow rate of 1,015 cu. cm. per min. at a pressure ofabout 12 lb. per sq. in. In the systematic experiments, the oiltemperature at inlet to the pad had been controlled at a numberof different values ranging between 90 and 160 deg. F.To obtain a representative temperature of the oil film beneaththe pad, two thermocouples had been fixed in holes drilled com-pletely through the pad, mid-radially, and near the inlet andoutlet edges. The junctions of the couples had been cut levelwith the working surface of the pad. The average value of thetwo indicated temperatures had been taken as the representativetemperature of the whole oil contained in the film and therepresentative viscosity 2 had been based upon it.The temperature distribution observations made had beenlimited in number and confined to mid-radial pivot positionsand off-set position 2. The mean value of the pad surface iilmviscosity had been taken as (1;Z A) /A where A was thetotal surface area of th e pad. Th at integration had been applied tothe available observations in order to compare the mean distribu-tion viscosity with that obtained from the average of the twothermocouples. The integration had been done graphically in amanner similar to that used for pressure distributions.For the lowest speed of 485 r.p.m., the maximum differencebetween the viscosity value, obtained from the two thermo-couples, and the mean distribution viscosity, as defined by theabove integral, had been found to be 4 per cent, and for a speedof 1,495 r.p.m. the maximum difference had been 6 per cent.At the highest speed of 2,700 r.p.m., however, whilst thedifferences in some cases had been within 5 per cent, they hadhad a maximum value of 20 per cent for mid-radial pivots and13 per cent for offset position 2. Th e viscosity value obtainedfrom the two thermocouples had been in general greater thanthe mean distribution viscosity of the oil in contact with thepad surface.Mr. Cole had raised the interesting question of the possibilityof obtaining a representative value of the oil-film viscosity bymeans of a single-pad thermocouple. The temperature distribu-tion observations obtained, however, had not encouraged hopesof that possibility. They had shown that for a given set ofoperating conditions, a closed isothermal contour could be foundfor the particular operative value of the mean distribution tem-perature of the surface film. A thermocouple placed anywhereon that contour would indicate that temperature. If any of theoperating conditions, say, speed, were changed, then the newisothermal contour (corresponding to a different representativetemperature) occupied a different position.In hat connexion, attention was directed to the limitations ofthe pad thermocouple which had i ts hot-junction level with thepad surface and therefore indicated the local temperature of thecontacting oil film. That film in particular was subjected to theinfluence of the temperature gradients through the pad.Appreciable temperature variations due to the differing ratesof shear existed throughout the thickness of the bulk oil con-tained in the film, he local temperature at any point of whichdiffered from that of the corresponding point in the surface film.It was therefore possible, at least for some operating conditions,that the mean surface-layer temperature differed substantiallyfrom the mean temperature of the bulk oil in the film on whichrepresentative viscosity would be more properly based. More-over, the unknown relation between those two temperatures waslikely to vary in a complex manner as conditions of pad operationchanged. That important relation could be investigated only bycomparing extensive and refined thermocouple observationswith mean oil-film temperatures obtained by heat balance or insome other way.In Fig. 30 were shown typical observations of the churningdrag torque acting on the floating casing. Tha t torque constitutedan appreciable fraction, up to 54 per cent, of the total torqueacting on the casing. They noted with interest that that



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A U T H O R S ' R E P L I E S O N M I C H E L L B E A R I N G L U B R I C A T I O N 763disadvantage of flooded casing lubrication b d een avoided atM.E.R.L. by the use of individual oil supplies LO each pad.In order to minimize non-uniform operatior, of the variouspads, a rubber ring (part 10, Fig. 1)had been bonded betweenthe inner periphery of the thrust collar and the out-r surface ofthe splined bush which had been mounted on the shaft. I n thatway the thrust collar had been given some degree of flexibiljtyrelative to the shaft. Consistent experimental results, however,had not been obtained from the pads when all six pairs had beenin operation at the same time. They agreed that more informationabout the effectiveness of load-equalizing devices and the opti-mum number of pads would be valuable.

I 1 I I I I

$2 O O 10 20 30 40Z N / PFig.30. Churning Torque on Casing

Pivot position 1. 8/+ =0.40.Speed 2,700 r.p.m. ---- peed 485 r.p.m.

In reply to Mr. Hill, the probable cause of the oil aerationwhich had occurred in the earlier part of the experimental workhad been cavitation at the pump suction. That inlet had beenmodified to give a larger entry area and subsequently aerationhad been practically eliminated and entirely absent with the oilat the higher temperatures. The oil had entered the bearingcasing at the bottom, always completely filled the casing andhad been withdrawn from the top.The normal rate of oil flow through the casing had been115 cu. cm. per min., and the operating characteristics of thepads had been found to be unchanged over a range of higher andlower rates of flow. At a very much later stage in the experiments,tests had been made with the bypass valve completely closed,the rate of flow through the casing being then increased to aboutnine times the normal flow rate and the oil pressure to about12 lb. per sq. in. The cause of the change in the operatingcharacteristics had not been discovered but the observed effectshad been frankly reported. They could not agree that 'partialstarvation' of oil supply to the pads took place under the lowerrate of oil supply to the bearing.Experimental results which showed the effect of the higherrate of oil flow on film thickness and friction were set out inFigs. 31 and 32.They agreed that the scatter of the experimental observationsshown in Fig. 9 drew attention to the imperfection (at leastapparent) of Z N / P as a basic criterion of pad performance. Inthat particular work, the effects of point pivoting as distinctfrom line pivoting might have played some part. They con-sidered, however, that a possibly important contributory factorto the scatter had been the use of a representative viscosity, Z,based on the temperature of the pad surfacefilm rather thanonthe mean temperature of the bulk film oil. The difference betweenthose temperatures might have varied appreciably when operat-ing conditions changed.The criterion Z N / P .D / L suggested by Mr. Hill would nothave affected the scatter of the observations shown in Fig. 9since D / L was constant for a given bearing.The statement on p. 755 had been based on the theory ofrectangular pads in which side leakage was neglected butviscosity changes were taken into account. If it were assumedthat all the work done in overcoming viscous traction of the oilappeared uniformly asheat in the oil, it could be shown that fora given operating position of the pad in relation to the movingsurface, the rise in temperature of the oil passing through the

film depended on ly on the load per unit of pad area. The observedmean temperature rise of the pad surface film (as distinct fromthat of the bulk oil passing through the film), however, had beenfound to be affected more by speed than by load.It was presumed that Mr. Hill's notation for pivot positionreferred to the fractionalangular distance of the pivot measuredfrom the inlet edge of the pad, in contrast with that used bythemselves which had been based on pivot distances from theoutlet edge. Using the latter notation, the experimental resultsof Fig. 13a showed that the film ratio HJHowas a minimum forcentral pivoting and, within the experimental range, had anincreased value as the pivot was moved away from the centre on

0.004IUz4 .003-:g50.002h8

0.001

0 4 8 I 2 16 20Z N / PFig. 31. Oil Film ThicknessSpeed 2,000 r.p.m. Pivot position 1. O/ + =0.40.---- ormal oil flow. Large oilflow.

I 2 3 4 5 6 7 8 9 1 0 15Z N / PFig. 32. Coefficient of Friction, p

Pivot position 1. 9/+ =0.40.---- ormal oil flow. Large oil flow.either side. Mr. Hill had drawn attention by Fig. 24 to the factthat for a value of ZN/P equal to 10, the tilt angle with centralpivoting was less than that for the other pivot positions. Thatwas also true for any other value of Z N / P for the experimentalobservations set out in Fig. 13a and b. A further point of interestin regard to central pivoting concerned the relatively high valuesof the film thickness Ho t the pad outlet edge which weregreater than those for the other pivot positions, with the excep-tion of =0.45 over part of the range-as shown in Fig. 13b.=0.5 and less onthe outlet side of the centre, a stable film would form and, forgiven operating conditions of load, speed, and oil viscosity, they

They agreed that for pivot positions



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764 A U T H O R S R E P L I E S ON MICHELL B E A R I N G L U B R I C A TI O Nwould expect the angle of pad tilt to be greater with pivots moredistant from the centre. Tha t was in agreement with the resultsshown in Fig. 13a and b.In the experiments with the pads pivoted within the inlethalf, the operating conditions of the films had been found to bejust as stable and steady as for pivot positions within the outlethalf. For the range of pivot positions which could be explored,namely, e/q!=0.5 to 0.6, no signs of instability of operationsuch as Mr. Hill considered might possibly arise, had beenobserved. Pressure, film thickness, and friction observations hadbeen made, and Fig. 33 showed pressure distribution contoursobserved for pivot position 814 =0.6.

I

L 5 2 307Fig. 33. Pressure Distribution with Pad Pivoted Forwardof Centre Position

Applied load 130 lb. Integral load 126 lb. Speed 1,495 r.p.m. Meantemperature 115 deg. F. Pivot position 3. 8/4 =0.6.Position of applied load.+ Cal.culated centre of pressure from experimental pressure distribu-

Th e extremely low values of minimum film thickness referredto by Mr. Jefferson, Mr. Hailey, and Mr. Milne applied moreparticularly to the two radially eccentric pivot positions 2 and 4and occurred at one of the corners of the pads. The measure-ments had not been made directly but had been deduced fromthe indications of the three measuring rods. I n a few cases, forvery low values of

Proceedings of the Institution of Mechanical Engineers-1955-Kettleborough-746-65.pdf

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