the structural design of large grinding mills with reference to shell mounted bearings

8/2/2019 The Structural Design of Large Grinding Mills With Reference to Shell Mounted Bearings

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The structural design of large grinding m ills,w ith reference to shell-mounted bearingsby D . A . FENTON*, P. Eng. (V isitor)

SYNOPSIST he paper outlines the advantages of shell-m ounted grinding m ills over m ills having a conventional trunnion-s up po rte d s he ll.The growing use of larger mills in the past decade has led to a significant num ber of mechanical and structuralfailures, the m ost com mon being those at the junction of the head and the shell. Larger m ill diam eters favour the useo f s he ll-moun te d b ea rin gs .T he elim inatio n o f castin gs, w hich hav e an inh eren t w eakn ess to frac ture, m ak es th e shell-su pp orte d m ill lig hterand stronger than a conventional m ill of the sam e shell thickness.

SAMEVATTINGDie referaat behandel in hooftrekke die voordele van rompgemonteerde breekmeule bo meule met 'n kon-vensionele rom p w at deur 'n d ratap g esteun w ord.D ie toenem ende gebruik van groter m eule gedurende die afgelope dekade het 'n beduidende aantal m eganiese enstrukturele falings tot gevolg gehad, meestal by die aansluiting van die kop by die rom p. Groter m euldiametersbevorder die gebruik van rom pgem onteerde laers.D ie uitskakeling van gietstukke w at 'n inherente neiging het om te breek, m aak die rom pgesteunde m eulligter ensterker as 'n konvensionele m eul m et dieselfde rom pdikte.

IntroductionThe diam eter and sizes of grinding m ills have increJSedsteadily in the past few years. Many small m ills have

run for long periods of time with low rates of failule, butthere have been a significant number of failures inm ill shells and heads, some of which have been analysedby the author. Many structural failures have occurred,but they have not been well documented: data onhigh-cycle fatigue is sparse; scale effect can be trulyrepresented only by a full-size machine; and long timeto failure, changes in the conditions of the charge,liner wear, ball or rod size, and thermal effects makedocum entation difficult. In w et-m illing, stress corrosionis a significant factor in the fatigue life of the machine.Design of a Conventional M ill

The head of a conventional mill is illustrated inFig. 1. O ff-setting of the head-shell junction from thebearing reaction means that fully reversed rotatingbending stresses are induced in the head and head-shelljunction.

The dotted curve represents the neutral axis N-A ofthe section resisting the rotating bending stresses. Thevalue of K show n in the small-scale diagram representsthe ratio of m inimum stress divided by maximumstress, and K = -1 represents the worst conditions forfatigue damage. This situation is inherent in thetrunnion-m ounted ball m ill.

Membrane stresses are illustrated in Fig. 2. Thesestresses are high when compared with the rotatingbending stresses in Fig. 1, but they are unidirectional innature and are not so damaging as a fully reversed stress.

In Figure 2a, the overall bending stresses are com-bined; that is, the rotating bending due to the offset ofbearing reaction in Fig. 1 is combined with the bendingof the shell between the bearing supports, behaving as ashort beam. The local stress due to the impact of the

*A erofall M ills L im ited, M ississau ga , C an ada.34

charge to centrifugal and inertia forces is shown inFig.2b.

The nature of these stresses is a local curved-platebending stress, the distribution of which is illustratedin Fig. 3. The value K =0 ratio of minimum stress tomaximum stress gives these stresses a unidirectionalproperty that is not so damaging in fatigue as is thefully reversed stress represented by K = -1. Themagnitude of the local stress, however, can be muchgreater than the overall stress and must be accountedfor in large-diam eter m ills w ith short lengths (length-to-diameter ratios of less than 2).

W hen the above stresses are combined, the effect is toproduce concentrations of stress near the junction of thehead and shell, which have resulted in many failures inmills. The thickness distribution is also a factor of headfailures. The evaluation of correct thickness distributionis complex owing to the conflicting requirements offatigue (to bring the stress level down) and fracturecriteria, which require the thickness of the cast materialto be a minimum (owing to the propagation of cracks).

The following are disadvantages of conventional m illdesign :(a) heavy head sections, susceptible to fractures or

fatigue failures, involving high cost,(b) high concentrations of stress where the rigid headjoins the compliant shell,

(c) restriction of relatively small trunnion diameters,reducing the throughput of the mill, and

(d) relatively high frictional losses in hydrostatic sleevebearings, representing some 7 to 9 per cent of them ill horsep ow er supp ly.

Item (d), the hydrostatic sleeve bearing, requiressustained high pressure to maintain lift and so retainthe oil film . The power required to maintain the highpressure is about 4 per cent of the mill horsepowersupply. The frictional characteristics of the long ski-likeshoe, and the fact that the motion of the journal opposesthe pumping action of the lifting fluid along one half ofthe shoe length, give rise to boundary friction of betw een

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3 and 5 per cent of the m ill horsepow er supply. In total,the loss of horsepower is between 7 and 9 per cent of thetotal horsepow er. A s m ills increase in size, the deflectionof the journal causes problems in the oil-film wedge(oil film is wiped), leading to higher pum ping capacitiesto maintain lift.

f -:t!!MzB = FUNCTION OFR AD IU S & FIX IT YM= BENDING M OMENTZ = SECTION MODULUSR = B EARING R EACT ION

-----N.

F UL L R EVER SA L

MO:oFig. I-Rotating bending stresses in the head of a con-ventional m ill

Fig. 2aOVERALL BEN DIN G STRESSDISTRIBUTION

1R

Fig.:.!b

M EM BR AN E ST RE SSDISTRIBUTION

Fig. 2-Distribution of stress in the bearings of a conventionalmill

Shell-supported Ball M illsThe shell-supported ball m ill and the conventional m ill

are illustrated in Fig. 3.T he fu nc tio n W is complex in nature and depends on

the f ol low ing:(a) the mass of the mill shell,(b) the mass of the lining (a variable subject to wear),(c) the ball or rod size (affecting the impact pressure),(d) inertia and impact pressure (a function of liner w ear),(e) disposition of the charge along the m ill,(f) a variable impact zone as the mill rotates, and(g ) scale effect.

T he fu nc tio n C is a dimensionless constant and variesw ith the geometry and constraint of the shell section.The value of C varies between 0,4 and 0,75.

It is evident that the shell-supported mill requiresless space than does the conventional m ill, and thedistance between the bearing reactions is less than thatof a conventional m ill with the same working length.Thus, the bending moment and rotating bending stressesare less for the shell-supported mill of identical shellthickness.

The distribution of membrane and rotating 'bendingstress is shown in Fig. 4. The dotted curves reflect theeffect of reinforcing round manholes and the localthickening of the shell due to stiffness requirements ofthe journal. The thickening of the shell reduces themembrane stresses and improves the fatigue life of thestructure.Fig. 5 illustrates the stresses and geometry of the jour-nal. T he bending stresses refer to circumferen tial bending ,

CONVENTIONAL MILL D ISTRIBUTION OF IJl ~x__.1\,b

t: ~lnl['

uff

DISTRIBUTIONOF s THROUGH

SHELL TH ICKNESS

SH ELL - SU PP OR TED M ILLFU LL REVERSA LVERY 1,,2 REVOLUTION+ - I = MIY

M= !!(x-x2)2 TW = F unction 0 1In ertia &Pressure

+~ k=O- UNIDIRECTIONALSTRESS s "Co b212D = Shor t s id e0 1 S he llt "Thickness 01ShellC = Fun ct io n o lG eo .met ry & Fixi tyP = Pressure

Fig. 3-Stresses in a conventional m ill and a shell-supportedmillJO URNA L O F TH E SOU TH A FR IC AN INS TITU TE O F M IN IN G AND MET ALLU RGY SEPTEMBER 1976 35


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D ISTR IBUTED LOADw LB/IN \--

Vi~

SHOENo.1 ~ ~SHOE No.2 -

BENDINGSTRESSLB/IN 2BENDING STRESS

tIEXTEN T OF RE I NFORC'.E DMANHOLES/ JOUR-NA LE XTE NT O FUNREINFORCEDPERIPHERALHOLEMEMBRANESTRESSLB/,IN2

Fig. 4-Distribution of overall bending stress and membranestress in a shell-supported mill

INNER FACE

A

OUTER FACEBEND ING STRESS D ISTR IBU TIONFOR CURVED BEAM

and the distribution of these is shown. Fatigue con-siderations are the criteria for the design. The bendingstresses are fully reversed twice in each revolution of themill. The shear stresses also vary round the journalcircum ference, and the local distribution is illustrated.A2 an d T2 refer to the effective length of the journaland its thickness.

A4 an d T4 refer to the depth and thickness of thevestigial head. The torsional shears are generated by thethrust force F and the offset of the shoe pressure fromthe shear centre of the structure. N-A on the diagramrefers to the neutral axis of the curved beam.

The deflection of the journal is compensated for bythe rotation of the shoes to conform to the motion ofthe journal, and journal deflections will not interferewith the -thickness of the oil film.

It should be noted that the closeness of the welds to theneutral axis of the curved beam is an advantageousdesign feature. When the curved beam is analyzed fortorsional and flexural shears, particular attention beingpaid to the analysis of the welds and shell structure forfatigue design, the following are apparent. The rigidconstraint requirement for hydrostatic bearings iselim inated since the bearing shoes are radially adjustable,and benefit is derived from the fabricated sections.Local bending of the shell must be allowed for, and it isdesirable for a gear flange to be mounted where themembrane s tr es se s a re low.

B.M.DISTRIBUTIONAROUNDSHELL

T4GEOMETRY FORTORSIONALSHEAR

A4 DISTRIBUTION

A2

Fig. 5- The stresses and geometry of the journal in a shell-supported mill

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The analysis shows the advantages of the shell-supported ball m ill to be as follows:(a) relatively light head structure,(b) low stress levels at previous critical sections of the

shell,(c) possibility of large openings in the feed and dischargeend of the mill,(d) significant space saving feature due to elim inationof trunnions, and(e) very low frictional losses in the hydrodynamicbearings, representing 1 to 1,5 per cent of the millh orse pow er sup ply .

Fati~ue in Shell Desi~nThe stress reversibility factor and typical fatigue

stress are illustrated in Fig. 6. The full line represents2 X 106 cycles, and the dotted curve represents limitingstresses for twenty years' continuous running for atypical ball m ill 6 m in diameter. In the determ inationof safe levels of working stress, a number of factors areconsidered, including stress raisers, type of stress,torsional and flexural shears, rotating bending stress,m embrane stress, and com binations of these.

The statistical nature of the fatigue data is significant.A wide scatter of results means that, for long life andto ensure low probability of failure, the maximumstresses permitted should not be based on a medianvalue of the data but rather on the lower lim it of thescatter.T ypically, 1,4 X 108 cycles for tw enty years' continuousrunning of a 6 m-diameter ball m ill is a measure of thenumber of cycles required. Many mills have failed in

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STRESSLB/ IN 2X 1,000

20

10

0 104 105

less than five years of operation, som e of them becauseof w eakness in the design features m entioned.P ivoted-sh oe H ydrodynam ic Bearin~s

The Aerofall bearing utilizes four pivoted hydro-dynamic shoes, the short discrete lengths of shoe per-m itting true hydrodynamic action. The shoes aresupported on spherical pivots in such a manner thatthey can rock freely in all directions and are radiallyadjustable to conform to the shape of the journal.The larger the diameter of the mill the better are thehydrodynamic characteristics. These features make theshell-supported m ill a reality.

The computer facility at Aerofall has made rapidoptimizations possible for shell structure, bearingdesign, m ass analysis, and inertia characteristics so thatmotors can be matched to the mill.Fig. 7 illustrates, in carpet form , the distribution ofshoe-aspect ratio for various pressures and shoe lengths.The data were obtained from the mill inertia character-istics, and the viscosity, kinematic, and thermal con-ditions of the oil. The aspect ratio is given by B/L, an dthe minimum thickness of the oil film is denoted by Ho.

The lim it in pressure on the shoe is consistent with theaverage bearing pressures to sustain an oil film . Thelimit in shoe length is the physical limitation of thebearing shoes consistent with the geometry of thebearing.

It is seen that there is a reduction in minimumthickness of oil film with decreasing values of B/L. Thechoice of a nearby 'square shoe with a relatively thickminimum oil film is desirable. A long ski-type of shoe,

20 YEARSaCONT INUOUSRUNNING LIFE SPAN FOR BALL MILL\

-- -- ----- -----10 6CYCLES 108 10907

- LIM IT OF SCATTER-- DESIGN LIM IT TO PRODUCEHIGH SURVIVAL RATEFig. 6-Stress versus number of cycles for mild steel

JO URNA L O F T HE SOU TH A FR IC AN IN STIT UT E O F M IN IN G AND METALL URGY SEPTEMBER 1976 37


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... LIMITON Ho.)OO3

40 0 DESIGN PRESSURE

SELECTED SHOE

SHOE PRESSUREIb/in2 B~=180 0

600

tLIM IT FORSHOE LENGTH50 55 60L SHOE LENGTH in

200

30 35 40 45F ig . 7- T he distribu tion o f shoe-asp ect ra tio

MIN .O IL F ILMTHICKNESS

tO08 , ,,,, "-" "-........'....... -- -- -- --

IN'010

,006

.,004

,002.

20 40 60 80 100 120 140 160 180 200TEMP. OFFig. 8- The effect of temperature on the m inimum thickness of oil film

38 SEPTEMBER 1976 JO URNA L O F TH E SOU TH A FR IC AN IN ST ITU TE O F M IN IN G AND MET ALLU RGY


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FRICTIONH O R S E P O W E R1400

1200

HYDRODYNAMIC~G20080 100 1100

H Y D R O S T A T I C BEARING

~120 13 0 140 150 160 170

TEM P. ofFig. 9-Friction characteristics of hydrostatic and hydrodynamic bearings

c haracte rized by B/L ~O,5, would give low oil-filmth ic kn esse s a nd g re ate r p ossib ility o f film b re ak down andh ig h b ou nd ary friction . T his w ould b e c haracte ristic of ah yd ro sta tic sle ev e b ea rin g w ith h ea vy lo ad /d iame te r.F ig . 8 shows th e effec t o f tempe rature on th e m in im umo il-film th ick ness. T herm al b ala nce must be ob tain ed b yc oolin g m eth od s if sh ell tem peratures rea ch hig h values.Fig. 9 illustrates the friction characteristics of thehydrostatic and hydrodynamic bearings for a large-diameter ball m ill. Long ski-type shoes that havehydrodynam ic action have friction characteristics be-tween the two extremes. This is because the shoe

efficiency is less than that of a hydrodynam ic bearingand a higher leakage rate. R eference to Fig. 7 show s thelim it of such shoes when applied to shells of largediameter.ConclusionThe conflicting requirements of fatigue stress versuscycles to failure, and the growth of fracture cracks

versus cycles to failure, pose a problem to the designer.By the elim ination of one of the requirements, e.g., thefracture criteria (elim ination of thick heavy castingswith relatively small trunnions and inherent stressconcentration factors), the designer of shell-supportedball m ills has one less possible failure to consider at thed es ig n s ta ge .Statistical data on the high-cycle fatigue of m ild-steel

structures are very sparse at the present time. Small.scale fatigue tests are not representative but can be

used as a guide, particularly with the range of thescatter band. However, field failures of full-scalestructures are the best guide to representative stressesin d esig n.Failures in large grinding mills have happenedfrequently. Although defects in materials and work.manship can be blamed for some of the failures, manyof the features contributing to failures are incorporatedat the design stage.The hydrodynamic pivoted-shoe bearing hassignificant advantages structurally, as well as in utility,

over the hydrostatic sleeve bearing, or over small-diameter bearings with long ski-type shoes that havehydrodynamic characteristics. The capital cost of thehydrodynamic bearing is secondary after a few yearsrunning.BibliographyBLODGETT , O . W . Desig n of w eldm en ts. The James F. LincolnA rc We ld in g F ou nd atio n.CO RNFO RD, A. S. The design of grinding m ills for m echanicalreliability. Birmingham (Alabama), S.M .E., 18th to 20thO ct., 1 972 .FREUD EN TH AL, A. M . Statistical m ethods in fatigue. ASMEh an db oo k m eta ls e ng in ee rin g d esig n, 2nd edition, 1965.F ULLER, D . Theory and practice of lubrication for engineers.HAVARD, D. G., W ILLIAM S, D . P., and ToPPER, T. H . Bi-axialfatigue of m ild steel data synthesis and interpretation. OntarioHyd ro R es ea rc h Qu ar te rly , vol. 27, no. 2, second quarter 1975.ROARK, R. J., and YOUNG, W . C. F orm ulas for stress and strain.1975.S.A.E. Fatig ue d es ig n h an db oo k.TIMOSHENKO,S. Theory of rods, plates and shells.V ON SCHRAMM, R. Mill trunnion bearings with hydrostaticlubrication. Zement-Kalk-Gips, 12th N ov., 1974. (In G erm an).

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D is c u s s io n o f t h e p r e v io u s p a p e rE. N. H . MOLLOY*

The first 22-foot-diameter A erofall m ill was installedat Mangula in 1957. This was fitted with cast-irontrunnion'! located to the mill shell w ith 2-inch-diameterm ild-steel bolts. The cast-iron trunnion on the dischargeside started to crack in 1960, and this was accompaniedby frequent breakages of the 2-inch-diameter steelbolts. This occurred thirty-seven months after the com-m issioning of the mill.

The second 22-foot-diameter Aerofall m ill, installedin 1959, was fitted with the same trunnion'! and thesame size bolts as those used in the first m ill. The dis-charge trunnion developed cracks late in 1960, seventeenmonths after commissioning. As with the first m ill,.T he M essina (T vl) D evelopm ent Com pany, Johannesburg.

great difficulties were experienced w ith frequent break-ages of the 2-inch-diameter bolts.

Two changes were made in the design of the mills.New discharge trunnions made of cast steel tospecification ASTM/A27/65/35 were fitted, and the2-inch-diameter m ild-steel bolts were replaced withhigh-tensile bolts of 21 inch diameter. The cast-steeltrunnions have stood up well during the past thirteenyears, and failure of the bolts has been negligible. Thetrunnions are mounted on M ichell-type bearings, whichhave proved very efficient.

C om parisons w ith plants handling equivalent tonnageshave shown that the cost of dry grinding in the Aerofallm ills at Mangula is lower than that at concentratorsusing conventional crushing and grinding equipm ent.

O .F .S. BranchM inutes of the General Meeting held at the W elkomClub on W ednesday, 2nd June, 1976, at 4.00 p.m .M r G. J. C . Young (Chairman of the O.F.S. Branch)w as in the C hair. A lso present w ere:

Two Fe llows Mes srs Z . J . L omba rd (Comm itte e Member),D . A . Smith (C ommittee M em ber).Two Member s M essrs R. W . Im pey, D . 1. W atson.Fou r Assoc ia te s Messrs A . J. Johansen, W . F. deL ange, J. Scott, C . P . V isser.Two Graduat es Messrs A . P. S. Howard, P. S. W ent-worth.One S tudent M r D. A. Arnold.Thirty-two Visi tors.Tota l Present Forty-four.M r Y oung declared the M eeting open and extended aw elcom e to the m em bers and visitors present.ApologiesApologies for non-attendance were received fromB . J. D rysdale, J. Lorenzon, A . N . Shand, and L. V orster.M inutes of Previous General M eetingThe M inutes of the G eneral M eeting held on the 11thFebruary, 1976, w ere taken as read, and their adoption,proposed by M r D. A. Sm ith and seconded by M r Z. J.L omba rd , w as c arrie d.G eneral B usinessMr Young reported that Mr R. R. Perkin, HonorarySecretary of the O.F.S. Branch for the past two years,had recently been transferred to Johannesburg and hadhad to resign his office. On behalf of the Committee,

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Mr Young expressed his thanks to M r Perkin for thehard work that he had put into the local branch. M rA . R. Godfrey had been asked by the Chairman toperform the duties of Honorary Secretary until suchtime as a new Honorary Secretary could be appointed.Talks on N uclear InstrumentationM r Young introduced Mr J. W . Tongs and Mr J. G .Barnard of Texas Nuclear (S.A.) (Pty) Ltd, and calledon them to give a talk on the uses of nuclear in '!trument-a tio n in in du stry .

M r Tongs began by outlining the basics of radiationand nuclear energy, and how these were utilized innuclear mass meters and density meters. M r Barnardspoke about the problems involved in weighing and inthe calibration of mass meters. He outlined the way inwhich many of these problems could be overcome withthe use of nuclear instruments. A demonstration of theimportant features of the Texas Nuclear meter con-cluded the presentation, which attracted a lively dis-cussion.

Mr Young thanked Mr Tongs and Mr Barnard onbehalf of those present for their very interesting present-ation.Closure

The Chairman thanked members and visitors for theirattendance, and declared the M eeting closed at 7.00 p.m .He thanked Texas Nuclear (S.A .) (Pty) Ltd for verykindly providing the refreshments served after themeeting.

SEPTEM BER 1976 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY

the structural design of large grinding mills with reference to shell mounted bearings

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