Design of roller and rolling contact bearings.ppt

Design of bearing

1. Design of roller contact bearings

2. Session outline
Terminologies
•AdvantagesandDisadvantages
Failurecriterion
Designofrollercontactbearings
Tutorialproblems

3. Bearings-Applications

4. Bearings-Applications

5. BEARINGS -DEFINITION
•Bearingisamechanicalelementthatpermitsrelativemotion
betweentwoparts,suchastheshaftandthehousing,with
minimumfriction
•Themostimportantcriteriontoclassifythebearingsisthetype
offrictionbetweentheshaftandthebearingsurface

6. BEARINGS -DEFINITION
•Dependinguponthetypeoffriction,bearingsareclassifiedintotwo
maingroups—slidingcontactbearingsandrollingcontactbearings

7. BEARINGS -FUNCTIONS
•Thebearingensuresfreerotationoftheshaftortheaxlewith
minimumfriction
•Thebearingsupportstheshaftortheaxleandholdsitinthe
correctposition
•Thebearingtakesuptheforcesthatactontheshaftortheaxle
andtransmitsthemtotheframeorthefoundation

8. ROLLING CONTACT BEARINGS
•Rollingcontactbearingsarealsocalledantifrictionbearingsor
simplyballbearings.
•Rollingelements,suchasballsorrollers,areintroduced
betweenthesurfacesthatareinrelativemotion
•Inthistypeofbearing,slidingfrictionisreplacedbyrolling
friction

9. ROLLING CONTACT BEARINGS -
APPLICATIONS
•Machinetoolspindles
•Automobilefrontandrearaxles
•Gearboxes
•Smallsizeelectricmotors
•Ropesheaves,cranehooksandhoistingdrums

10. ROLLING CONTACT
BEARINGS-PARTS
•Arollingcontactbearingconsistsoffourparts-innerandouter
races,arollingelementlikeball,rollerorneedleandacage
whichholdstherollingelementstogetherandspacesthem
evenlyaroundtheperipheryoftheshaft

11. ROLLING CONTACT
BEARINGS-PARTS

12. ROLLING CONTACT
BEARINGS-PARTS

13. ROLLING CONTACT
BEARINGS-TYPES
Dependinguponthetypeofrollingelement,thebearingsare
classifiedas
•Ballbearing
•Cylindricalrollerbearing
•Taperrollerbearingand
•Needlebearing

14. ROLLING CONTACT
BEARINGS-TYPES

15. ROLLING CONTACT
BEARINGS-TYPES
Dependinguponthedirectionofload,thebearingsarealso
classifiedas
•Radialbearing
•Thrustbearing

16. DEEP GROOVE BALL
BEARINGS
•Inthistypeofbearing,theradiusoftheballisslightlyless
thantheradiiofcurvatureofthegroovesintheraces
•Kinematically,thisgivesapointcontactbetweentheballs
andtheraces
•Therefore,theballsandtheracesmayrollfreelywithoutany
sliding

17. DEEP GROOVE BALL
BEARINGS

18. DEEP GROOVE BALL
BEARINGS-ADVANTAGES
•Duetorelativelylargesizeoftheballs,deepgrooveball
bearinghashighloadcarryingcapacity
•Deepgrooveballbearingtakesloadsintheradialaswellas
axialdirection
•Duetopointcontactbetweentheballsandraces,frictional
lossandtheresultanttemperatureriseislessinthisbearing
•Deepgrooveballbearinggenerateslessnoiseduetopoint
contact

19. DEEP GROOVE BALL
BEARINGS-ADVANTAGES
•Deepgrooveballbearingsareavailablewithborediameters
fromafewmillimetersto400millimeters

20. DEEP GROOVE BALL
BEARINGS-DISADVANTAGES
•Deepgrooveballbearingisnotself-aligning
•Accuratealignmentbetweenaxesoftheshaftandthehousing
boreisrequired
•Deepgrooveballbearinghaspoorrigiditycomparedwith
rollerbearing

21. CYLINDRICAL ROLLER
BEARING
•Whenmaximumloadcarryingcapacityisrequiredinagiven
space,thepointcontactinballbearingisreplacedbytheline
contactofrollerbearing
•Acylindricalrollerbearingconsistsofrelativelyshortrollers
thatarepositionedandguidedbythecage

22. CYLINDRICAL ROLLER
BEARING

23. CYLINDRICAL ROLLER
BEARING-ADVANTAGES
•Duetolinecontactbetweenrollersandraces,theradialload
carryingcapacityofthecylindricalrollerbearingisveryhigh
•Cylindricalrollerbearingismorerigidthanballbearing
•Thecoefficientoffrictionislowandfrictionallossislessin
high-speedapplications

24. CYLINDRICAL ROLLER
BEARING-DISADVANTAGES
•Ingeneral,cylindricalrollerbearingcannottakethrustload
•Cylindricalrollerbearingisnotself-aligning
•Itcannottoleratemisalignment
•Itneedsprecisealignmentbetweenaxesoftheshaftandthe
boreofthehousing
•Cylindricalrollerbearinggeneratesmorenoise

25. ANGULAR CONTACT BEARING
•Inangularcontactbearing,thegroovesininnerandouter
racesaresoshapedthatthelineofreactionatthecontact
betweenballsandracesmakesananglewiththeaxisofthe
bearing
•Thisreactionhastwocomponents-radialandaxial
•Therefore,angularcontactbearingcantakeradialandthrust
loads

26. ANGULAR CONTACT BEARING

27. ANGULAR CONTACT
BEARING-ADVANTAGES
•Angularcontactbearingcantakebothradialandthrust
loads
•Inangularcontactbearing,onesideofthegrooveintheouter
raceiscutawaytopermittheinsertionoflargernumberof
ballsthanthatofdeepgrooveballbearing.Thispermitsthe
bearingtocarryrelativelylargeaxialandradialloads.
Therefore,theloadcarryingcapacityofangularcontact
bearingismorethanthatofdeepgrooveballbearing

28. ANGULAR CONTACT
BEARING-DISADVANTAGES
•Twobearingsarerequiredtotakethrustloadinboth
directions
•Theangularcontactbearingmustbemountedwithoutaxial
play
•Theangularcontactbearingrequiresinitialpre-loading

29. SELF-ALIGNING BEARINGS
•Theself-aligningballbearingconsistsoftworowsofballs,
whichrollonacommonsphericalsurfaceintheouterrace
•Inthiscase,theassemblyoftheshaft,theinnerraceandthe
ballswithcagecanfreelyrollandadjustitselftotheangular
misalignmentoftheshaft
•Thereissimilararrangementinthesphericalrollerbearing,
whereballsarereplacedbytworowsofsphericalrollers,
whichrunonacommonsphericalsurfaceintheouterrace

30. SELF-ALIGNING BEARINGS
•Comparedwiththeselfaligningballbearing,thespherical
rollerbearingcancarryrelativelyhighradialandthrustloads
•Bothtypesofself-aligningbearingpermitminorangular
misalignmentoftheshaftrelativetothehousing
•Theyarethereforeparticularlysuitableforapplications
wheremisalignmentcanariseduetoerrorsinmountingor
duetodeflectionoftheshaft
Theyareusedinagriculturalmachinery,ventilators,and
railwayaxle-boxes

31. SELF-ALIGNING BEARINGS

32. TAPER ROLLER BEARING
•Thetaperrollerbearingconsistsofrollingelementsinthe
formofafrustumofcone
•Theyarearrangedinsuchawaythattheaxesofindividual
rollingelementsintersectinacommonapexpointontheaxis
ofthebearing
•Intaperrollerbearing,thelineofresultantreactionthrough
therollingelementsmakesananglewiththeaxisofthe
bearing

33. TAPER ROLLER BEARING
•Therefore,taperrollerbearingcancarrybothradialand
axialloads
•Taperrollerbearinghasseparableconstruction
•Theouterringiscalled‘cup’andtheinnerringiscalled
‘cone’
•Thecupisseparablefromtheremainderassemblyofthe
bearingelementsincludingtherollers,cageandthecone

34. TAPER ROLLER BEARING

35. TAPER ROLLER BEARING -
ADVANTAGES
•Taperrollerbearingcantakeheavyradialandthrustloads
•Taperrollerbearinghasmorerigidity
•Taperrollerbearingcanbeeasilyassembledand
disassembledduetoseparableparts

36. TAPER ROLLER BEARING -
DISADVANTAGES
•Itisnecessarytousetwotaperrollerbearingsontheshaftto
balancetheaxialforce
•Itisnecessarytoadjusttheaxialpositionofthebearingwith
pre-load
•Thisisessentialtocoincidetheapexoftheconewiththe
commonapexoftherollingelements
•Taperrollerbearingcannottoleratemisalignmentbetween
theaxesoftheshaftandthehousingbore
•Taperrollerbearingsarecostly

37. SELECTION OF BEARING -
TYPE
•Forlowandmediumradialloads,ballbearingsareused,
whereasforheavyloadsandlargeshaftdiameters,roller
bearingsareselected
•Self-aligningballbearingsandsphericalrollerbearingsare
usedinapplicationswhereamisalignmentbetweentheaxesof
theshaftandhousingislikelytoexist
•Thrustballbearingsareusedformediumthrustloads
whereasforheavythrustloads,cylindricalrollerthrust
bearingsarerecommended

38. SELECTION OF BEARING -
TYPE
•Deepgrooveballbearings,angularcontactbearingsand
sphericalrollerbearingsaresuitableinapplicationswherethe
loadactingonthebearingconsistsoftwocomponents-radial
andthrust
•Themaximumpermissiblespeedoftheshaftdependsupon
thetemperatureriseinthebearing.Forhighspeed
applications,deepgrooveballbearings,angularcontact
bearingsandcylindricalrollerbearingsarerecommended

39. SELECTION OF BEARING -
TYPE
•Doublerowcylindricalrollerbearingsortaperroller
bearingsareusedundertheseconditions.Thelineofcontact
inthesebearings,ascomparedwiththepointofcontactinball
bearings,improvestherigidityofthesystem
•Noisebecomesthecriterionofselectioninapplicationslike
householdappliances.Forsuchapplications,deepgrooveball
bearingsarerecommended

40. STATIC LOAD CARRYING
CAPACITY
•Staticloadisdefinedastheloadactingonthebearingwhen
theshaftisstationary
•Itproducespermanentdeformationinballsandraces,which
increaseswithincreasingload
•Thestaticloadcarryingcapacityofabearingisdefinedas
thestaticloadwhichcorrespondstoatotalpermanent
deformationofballsandraces,atthemostheavilystressed
pointofcontact,equalto0.0001oftheballdiameter

41. STRIBECK’S EQUATION
Stribeck’sequationgivesthestaticloadcapacityofbearing.It
isbasedonthefollowingassumptions:
(i)Theracesarerigidandretaintheircircularshape
(ii)Theballsareequallyspaced
(iii)Theballsintheupperhalfdonotsupportanyload

42. DYNAMIC LOAD CARRYING
CAPACITY
•Thelifeofaballbearingislimitedbythefatiguefailureat
thesurfacesofballsandraces
•Thedynamicloadcarryingcapacityofthebearingis,
therefore,basedonthefatiguelifeofthebearing
•Thelifeofanindividualballbearingisdefinedasthenumber
ofrevolutions(orhoursofserviceatsomegivenconstant
speed),whichthebearingrunsbeforethefirstevidenceof
fatiguecrackinballsorraces

43. DYNAMIC LOAD CARRYING
CAPACITY
•Theratinglifeofagroupofapparentlyidenticalball
bearingsisdefinedasthenumberofrevolutionsthat90%of
thebearingswillcompleteorexceedbeforethefirstevidence
offatiguecrack
•Thedynamicloadcarryingcapacityofabearingisdefinedas
theradialloadinradialbearings(orthrustloadinthrust
bearings)thatcanbecarriedforaminimumlifeofonemillion
revolutions

44. EQUIVALENT BEARING LOAD
•Inactualapplications,theforceactingonthebearinghastwo
components—radialandthrust
•Itisthereforenecessarytoconvertthetwocomponents
actingonthebearingintoasinglehypotheticalload,fulfilling
theconditionsappliedtothedynamicloadcarryingcapacity
•Thenthehypotheticalloadcanbecomparedwiththe
dynamicloadcapacity

45. EQUIVALENT BEARING LOAD
Theequivalentdynamicloadisdefinedastheconstantradial
loadinradialbearings(orthrustloadinthrustbearings),
whichifappliedtothebearingwouldgivesamelifeasthat
whichthebearingwillattainunderactualconditionofforces
Theexpressionfortheequivalentdynamicloadis
P = XVF
r+ YF
a
P = equivalent dynamic load (N)
Fr = radial load (N)
Fa = axial or thrust load (N)
V = race-rotation factor
X =radial factor
Y = thrust factor

46. LOAD-LIFE RELATIONSHIP
The relationship between the dynamic load carrying capacity,
the equivalent dynamic load, and the bearing life is given by
L
10= rated bearing life (in million revolutions)
C = dynamic load capacity (N), and
p = 3 (for ball bearings)
p = 10/3 (for roller bearings)
For all types of ball bearings -C = P ( L
10)
1/3
For all types of roller bearings-C = P ( L
10)
0.3L
10=(
P
C
)
p

47. LOAD-LIFE RELATIONSHIP
The relationship between life in million revolutions and life in
working hours is given by
L
10h= rated bearing life (hours)
n = speed of rotation (rpm)L
10=
10
6
60nL
10h

48. SELECTION OF BEARING LIFE
Bearing life for wheel applications

49. SELECTION OF BEARING LIFE
Bearing life for industrial applications

50. LOAD FACTOR

51. SELECTION OF BEARING FROM
MANUFACTURER’S CATALOGUE
(i)Calculatetheradialandaxialforcesactingonthebearing
anddeterminethediameteroftheshaftwherethebearingisto
befitted.
(ii)Selectthetypeofbearingforthegivenapplication.
(iii)DeterminethevaluesofXandY,theradialandthrustfactors,
fromthecatalogue.

52. SELECTION OF BEARING FROM
MANUFACTURER’S CATALOGUE
(i)Calculatetheradialandaxialforcesactingonthebearing
anddeterminethediameteroftheshaftwherethebearingisto
befitted.
(ii)Selectthetypeofbearingforthegivenapplication.
(iii)DeterminethevaluesofXandY,theradialandthrustfactors,
fromthecatalogue.

53. SELECTION OF BEARING FROM
MANUFACTURER’S CATALOGUE
(iv)Calculatetheequivalentdynamicloadfromtheequation.
P = XF
r+ YF
a
(v)Makeadecisionabouttheexpectedbearinglifeandexpress
thelifeL
10inmillionrevolutions.
(vi)Calculatethedynamicloadcapacityfromtheequation
C=P(L
10)
1/3

54. DIMENSION SERIES OF
BEARING

55. DIMENSION SERIES OF
BEARING
(i)Thelasttwodigitsindicatetheborediameterofthebearing
inmm(borediameterdividedy5).Forexample,XX07indicates
abearingof35mmborediameter.
(ii)Thethirddigitfromtherightindicatestheseriesofthe
bearing.Thenumbersusedtoindicatetheseriesareasfollows:
Extralightseries–1Lightseries–2Mediumseries–3
Heavyseries–4Forexample,X307indicatesamedium
seriesbearingwithaborediameterof35mm.

56. DIMENSION SERIES OF
BEARING
(iii)Thefourthdigitandsometimesfifthdigitfromtheright
specifiesthetypeofrollingcontactbearing.Forexample,the
digit6indicatesdeepgrooveballbearings

57. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Inaparticularapplication,theradialloadactingonaball
bearingis5kNandtheexpectedlifefor90%ofthebearingsis
8000h.Calculatethedynamicloadcarryingcapacityofthe
bearing,whentheshaftrotatesat1450rpm.
Given:
F
r=5kN
L
10h=8000h
n=1450rpm

58. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Bearinglife(L
10):L
10=
10
6
60nL
10h
=
10
6
60(1450)(8000)
L
10=696millionrevolutions

59. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Dynamicloadcapacity:
Since the bearing is subjected to purely radial load,
P = F
r= 5000 NC=P(L
10)
3
1
=(5000)(696)
3
1
C=44310.48N

60. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Ataperrollerbearinghasadynamicloadcapacityof26kN.The
desiredlifefor90%ofthebearingsis8000handthespeedis
300rpm.Calculatetheequivalentradialloadthatthebearing
cancarry.
Given :
C=26kN
L
10h=8000h
n=300rpm

61. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Bearinglife(L
10):L
10=
10
6
60nL
10h
=
10
6
60(300)(8000)
L
10=144millionrevolutions

62. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentradialload:C=P(L
10
)
p
1
=P(L
10
)
(10/3)
1
C=P(L
10)
(10)
3
=P(L
10)
0.3
P=
(L
10)
0.3
C
=
(144)
0.3
26000
P=5854.16N
Since the bearing is subjected to purely radial load,
Fr = P = 5854.16 N

63. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Asingle-rowdeepgrooveballbearingissubjectedtoaradialforceof
8kNandathrustforceof3kN.Theshaftrotatesat1200rpm.The
expectedlifeL
10hofthebearingis20000h.Theminimum
acceptablediameteroftheshaftis75mm.Selectasuitableball
bearingforthisapplication.

64. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Given:
F
r=8kN
F
a=3kN
L
10h=20000hr
n=1200rpm
d=75mm

65. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
XandYfactors:
Whenthebearingissubjectedtoradialaswellasaxialload,the
valuesofXandYfactorsareobtainedfromTablebytrialand
errorprocedure.
Itisobserved,thatvaluesofXareconstantandthevaluesofY
varyonlyincasewhen,Fr
Fa
2e

66. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
XandYfactors:
Inthiscase,thevalueofYvariesfrom1.0to2.0.Wewillassume
theaveragevalue1.5asthefirsttrialvalueforthefactorY.
X=0.56
Y=1.5
F
r=8000N
F
a=3000N

67. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentbearingload:
P=XF
r+YF
a=0.56(8000)+1.5(3000)=8980NL
10=
10
6
60nL
10h
=
10
6
60(1200)(20000)
L
10=1440millionrevolutions

68. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSDynamicloadcapacity:C=P(L
10)
3
1
=(8980)(1440)
3
1
C=101406.04N

69. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSBearing selection:
FromTable,itisobservedthatfortheshaftof75mmdiameter,
BearingNo.6315(C=112000)issuitablefortheabovedata.
Forthisbearing,C
o=72000NFr
Fa
=
8000
3000
=0.375
Fco
Fa
=
72000
3000
=0.04167

70. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSBearing selection:
e=0.24(approximately)Fr
Fa
=
8000
3000
=0.375
Fco
Fa
=
72000
3000
=0.04167 Fr
Fa
2e

71. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSBearing selection:
ThevalueofYisobtainedbylinearinterpolationY=1.8-
0.07-0.04
1.8-1.6
x(0.04167-0.04)
Y=1.79
and
X=0.56

72. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Dynamicloadcapacity:
P=XF
r+YF
a=0.56(8000)+1.79(3000)=9850NC=P(L
10)
3
1
=(9850)(1440)
3
1
C=111230.46N

73. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSSelectionofbearing:
BearingNo.6315(C=112000)issuitablefortheabove
application

74. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Asingle-rowdeepgrooveballbearingNo.6002issubjectedtoan
axialthrustof1000Nandaradialloadof2200N.Findtheexpected
lifethat50%ofthebearingswillcompleteunderthiscondition.

75. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Given:
F
a=1000N
F
r=2200N
Bearing=No.6002

76. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
XandYfactors:
ThecapacitiesofbearingNo.6002are,C
o=2500NandC=
5590NFr
Fa
2e Fr
Fa
=
2200
1000
=0.455
Fco
Fa
=
2500
1000
=0.4

77. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSBearing selection:
ThevalueofYisobtainedbylinearinterpolationY=1.2-
0.5-0.25
1.2-1.0
x(0.4-0.25)
Y=1.08
and
X=0.56

78. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Dynamicloadcapacity:
P=XF
r+YF
a=0.56(2200)+1.08(1000)=2312NC=P(L
10)
3
1
5590=(2312)(L
10
)
3
1
L
10=14.13millionrevolutions

79. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Bearinglife(L
50):
Itcanbeprovedthatthelife(L50),which50%ofthebearings
willcompleteorexceed,isapproximatelyfivetimesthelifeL10
which90%ofthebearingswillcompleteorexceed
L
50= 5L
10= 5 (14.13) = 70.65 million rev.

80. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Atransmissionshaftrotatingat720rpmandtransmitting
powerfromthepulleyPtothespurgearGisshowninFigure.
Thebelttensionsandthegeartoothforcesareasfollows:
P
1=498NP
2=166NP
t=497NP
r=181N.Theweightofthe
pulleyis100N.ThediameteroftheshaftatbearingsB
1andB
2
is10mmand20mmrespectively.Theloadfactoris2.5andthe
expectedlifefor90%ofthebearingsis8000h.Selectsinglerow
deepgrooveballbearingsatB
1andB
2.

81. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

82. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Given:
n=720rpm
d
1=10mm
d
2=20mm
L
10h=8000h
loadfactor=2.5

83. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

84. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

85. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

86. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

87. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

88. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

89. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

90. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

91. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

92. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

93. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

94. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

95. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

96. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

97. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

98. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

99. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

100. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

101. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

102. DESIGN FOR CYCLIC LOADS
AND SPEEDS
Incertainapplications,ballbearingsaresubjectedtocyclic
loadsandspeeds.Asanexample,consideraballbearing
operatingunderthefollowingconditions:
(i)radialload2500Nat700rpmfor25%ofthetime,
(ii)radialload5000Nat900rpmfor50%ofthetime,and
(iii)radialload1000Nat750rpmfortheremaining25%ofthe
time.

103. DESIGN FOR CYCLIC LOADS
AND SPEEDS
•Underthesecircumstances,itisnecessarytoconsiderthe
completeworkcyclewhilefindingoutthedynamicloadcapacity
ofthebearing
•Theprocedureconsistsofdividingtheworkcycleintoa
numberofelements,duringwhichtheoperatingconditionsof
loadandspeedareconstant

104. DESIGN FOR CYCLIC LOADS
AND SPEEDS
IfP
eistheequivalentloadforthecompleteworkcycle,thelife
consumedbytheworkcycleisgivenby,Pe=[
N
1+N
2+..
N
1
P
1
3
+N
2
P
2
3
+...
]
3

105. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGSAsingle-rowdeepgrooveballbearinghasadynamicload
capacityof40500Nandoperatesonthefollowingworkcycle:
(i)radialloadof5000Nat500rpmfor25%ofthetime;
(ii)radialloadof10000Nat700rpmfor50%ofthetime;and
(iii)radialloadof7000Nat400rpmfortheremaining25%of
thetime.
Calculatetheexpectedlifeofthebearinginhours

106. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentloadforcompleteworkcycle:

107. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentloadforcompleteworkcycle:Pe=[
N
1+N
2+N
3
N
1P
1
3
+N
2P
2
3
+N
3P
3
3
]
3
=[
125+350+100
125(5000)
3
[phone])
3
+100(7000)
3
]
3
Pe=8860.6N L
10=(
P
C
)
p

108. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Bearinglife(L
10h):L
10=(
P
C
)
p
=(
8860.6
40500
)
3
L
10=95.51millionrevolutions
L
10h=
60n
L
10(10
6
)
=
60(575)
95.51(10
6
)
L
10h=2768.45hours

109. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

110. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

111. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

112. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

113. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS

114. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Asingle-rowdeepgrooveballbearingisusedtosupportthelay
shaftofafourspeedautomobilegearbox.Itissubjectedtothe
followingloadsinrespectivespeedratios:

115. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Thelayshaftisfixedtotheengineshaftandrotatesat1750rpm.
Thestaticanddynamicloadcarryingcapacitiesofthebearing
are11600and17600Nrespectively.Thebearingisexpectedto
beinusefor4000hoursofoperation.Findoutthereliability
withwhichthelifecouldbeexpected.

116. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Given:
n=1750rpm
C
o=11600N
C=17600N
L
h=4000h

117. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentloadforcompleteworkcycle:
N1+N2+N3+N4=1750rpmN
1=
100
1
(1750)=17.5rpm
N
2=
100
3
(1750)=52.5rpm
N
3=
100
21
(1750)=367.5rpm
N
4=
100
75
(1750)=1312.5rpm

118. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Firstgear:Fr
Fa
2e Fr
Fa
=
4000
3250
=0.8125
Fco
Fa
=
11600
3250
=0.28 Y=1.2-
0.5-0.25
1.2-1.0
x(0.28-0.25)
Y=1.176
and
X=0.56

119. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Firstgear:
P
1=XF
r+YF
a=0.56(4000)+1.176(3250)=6062N
Secondgear:Fr
Fa
1e Fr
Fa
=
2750
500
=0.182
Fco
Fa
=
11600
500
=0.0431
P
2=F
r=2750N

120. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Thirdgear:Fr
Fa
1e Fr
Fa
=
2750
50
=0.0182
Fco
Fa
=
11600
50
=0.00431
P
3= F
r= 2750 N
Fourthgear:
P
4=0

121. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Equivalentloadforcompleteworkcycle:Pe=[
N
1+N
2+N
3+N
4
N
1P
1
3
+N
2P
2
3
+N
3P
3
3
+N
4P
4
3
]
3
=[
125+350+100+0
17.5(6062)
3
+52.5(2750)
3
+367.5(2750)
3
+0
]
3
Pe=1932.67N L
10=(
P
C
)
p

122. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
BearinglifeL
10andL:L
10=(
P
C
)
p
=(
1932.67
17600
)
3
L
10=755.2millionrevolutions
L
h=
60n
L(10
6
)
4000=
60(1750)
L(10
6
)
L=420millionrevolutions

123. TUTORIAL PROBLEMS -
ROLLING CONTACT
BEARINGS
Reliabilityofbearing:L10
L
=[
loge
p10
1
loge
p
1
]
b
1
755.2
420
=[
loge
0.90
1
loge
p
1
]
1.17
1
p=0.9483=94.83%

124. THANK YOU