sliding and rolling contact bearings
3,420 views
136 slides
Mar 17, 2022
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About This Presentation
sliding and rolling contact bearings
Slide Content
UNIT I
PART A : SLIDING CONTACT BEARINGS
PART A : SLIDING CONTACT BEARINGS
INTRODUCTION
Abearingisamachineelementwhichsupportanothermoving
machineelement(knownasjournal).Itpermitsarelativemotion
betweenthecontactsurfacesofthemembers,whilecarryingthe
load.Alittleconsiderationwillshowthatduetotherelativemotion
betweenthecontactsurfaces,acertainamountofpoweriswasted
inovercomingfrictionalresistanceandiftherubbingsurfacesarein
directcontact,therewillberapidwear.Inordertoreducefrictional
resistanceandwearandinsomecasestocarryawaytheheat
generated,alayeroffluid(knownaslubricant)maybeprovided.
Thelubricantusedtoseparatethejournalandbearingisusuallya
mineraloilrefinedfrompetroleum,butvegetableoils,siliconoils,
greasesetc.,maybeused.
Abearingisamachineelementwhichsupportanothermoving
machineelement(knownasjournal).Itpermitsarelativemotion
betweenthecontactsurfacesofthemembers,whilecarryingthe
load.Alittleconsiderationwillshowthatduetotherelativemotion
betweenthecontactsurfaces,acertainamountofpoweriswasted
inovercomingfrictionalresistanceandiftherubbingsurfacesarein
directcontact,therewillberapidwear.Inordertoreducefrictional
resistanceandwearandinsomecasestocarryawaytheheat
generated,alayeroffluid(knownaslubricant)maybeprovided.
Thelubricantusedtoseparatethejournalandbearingisusuallya
mineraloilrefinedfrompetroleum,butvegetableoils,siliconoils,
greasesetc.,maybeused.
Functions of the bearing
The bearing ensures free rotation of the shaft
or the axle with minimum friction.
The bearing supports the shaft or the axle and
holds it in the correct position.
The bearing takes up the forces that act on
the shaft or the axle and transmits them to the
frame or the foundation.
The bearing ensures free rotation of the shaft
or the axle with minimum friction.
The bearing supports the shaft or the axle and
holds it in the correct position.
The bearing takes up the forces that act on
the shaft or the axle and transmits them to the
frame or the foundation.
Applications of Sliding contact bearings
crankshaft bearings in petrol and diesel
engines;
centrifugal pumps;
large size electric motors;
steam and gas turbines; and
concrete mixers, rope conveyors and
marine installations
crankshaft bearings in petrol and diesel
engines;
centrifugal pumps;
large size electric motors;
steam and gas turbines; and
concrete mixers, rope conveyors and
marine installations
Classification of Bearings
Though the bearings may be classified in many ways,yet the following
are important from the subject point ofview.
1. Depending upon the direction of load to be supported. The bearings
under this group areclassified as:
(a) Radial bearings, and (b) Thrust bearings.
In radial bearings, the load acts perpendicular to the direction of
motion of the moving elementas shown in Fig. (a) and (b).
In thrust bearings,the load acts along the axis of rotation as shown in
fig(c).
Note: These bearings may move in either of the directions as shown in
Fig.
Though the bearings may be classified in many ways,yet the following
are important from the subject point ofview.
1. Depending upon the direction of load to be supported. The bearings
under this group areclassified as:
(a) Radial bearings, and (b) Thrust bearings.
In radial bearings, the load acts perpendicular to the direction of
motion of the moving elementas shown in Fig. (a) and (b).
In thrust bearings,the load acts along the axis of rotation as shown in
fig(c).
Note: These bearings may move in either of the directions as shown in
Fig.
Radial and Thrust Bearings
2. Depending upon the nature of contact. The bearings under this
group are classified as :
(a) Sliding contact bearings, and (b) Rolling contact bearings.
In sliding contact bearings, as shown in Fig. (a), the sliding takes
placealong the surfacesof contact between the moving element
and the fixed element. The sliding contact bearings are alsoknown
as plain bearings.
In rolling contact bearings, as shown in Fig.(b), the steel balls or
rollers, are interposedbetween the moving and fixed elements.
The balls offer rolling friction at two points for each ball orroller.
group are classified as :
(a) Sliding contact bearings, and (b) Rolling contact bearings.
In sliding contact bearings, as shown in Fig. (a), the sliding takes
placealong the surfacesof contact between the moving element
and the fixed element. The sliding contact bearings are alsoknown
as plain bearings.
In rolling contact bearings, as shown in Fig.(b), the steel balls or
rollers, are interposedbetween the moving and fixed elements.
The balls offer rolling friction at two points for each ball orroller.
Sliding and Rolling Contact Bearings
Types of Sliding Contact Bearings
The sliding contact bearings in which the sliding action is guided in a
straight line and carryingradial loads, as shown in Fig. (a), may be
called slipperorguidebearings. Such type of bearingsare usually
found in cross-head of steam engines.
The sliding contact bearings in which the sliding action is along the
circumference of a circle oran arc of a circle and carrying radial loads
are known as journalorsleevebearings.When the angleof contact
of the bearing with the journal is 360°as shown in Fig.(a), then the
bearing is calleda fulljournalbearing. This type of bearing is
commonly used in industrial machinery to accommodatebearing
loads in any radial direction.
The sliding contact bearings in which the sliding action is guided in a
straight line and carryingradial loads, as shown in Fig. (a), may be
called slipperorguidebearings. Such type of bearingsare usually
found in cross-head of steam engines.
The sliding contact bearings in which the sliding action is along the
circumference of a circle oran arc of a circle and carrying radial loads
are known as journalorsleevebearings.When the angleof contact
of the bearing with the journal is 360°as shown in Fig.(a), then the
bearing is calleda fulljournalbearing. This type of bearing is
commonly used in industrial machinery to accommodatebearing
loads in any radial direction.
Journal or Sleeve Bearing
When the angle of contact of the bearing with the journal is
120°, as shown in Fig. (b), thenthe bearing is said to be partial
journalbearing. This type of bearing has less friction than full
journal bearing, but it can be used only where the load is always
in one direction. The most commonapplication of the partial
journal bearings is found in rail road car axles. The full and partial
journalbearings may be called as clearancebearingsbecause
the diameter of the journal is less than that ofbearing.
120°, as shown in Fig. (b), thenthe bearing is said to be partial
journalbearing. This type of bearing has less friction than full
journal bearing, but it can be used only where the load is always
in one direction. The most commonapplication of the partial
journal bearings is found in rail road car axles. The full and partial
journalbearings may be called as clearancebearingsbecause
the diameter of the journal is less than that ofbearing.
When a partial journal bearing has no clearance i.e. the diameters
of the journal and bearing areequal, then the bearing is called a
fittedbearing, as shown in Fig. (c).
The sliding contact bearings, according to the thickness of layer of
the lubricant between thebearing and the journal, may also be
classified as follows :
1. Thickfilmbearings. The thick film bearings are those in which
the working surfaces arecompletely separated from each other by
the lubricant. Such type of bearings are also calledas
hydrodynamic lubricated bearings.
of the journal and bearing areequal, then the bearing is called a
fittedbearing, as shown in Fig. (c).
The sliding contact bearings, according to the thickness of layer of
the lubricant between thebearing and the journal, may also be
classified as follows :
1. Thickfilmbearings. The thick film bearings are those in which
the working surfaces arecompletely separated from each other by
the lubricant. Such type of bearings are also calledas
hydrodynamic lubricated bearings.
2. Thinfilmbearings. The thin film bearings are those in which,
although lubricant is present,the working surfaces partially
contact each other atleast part of the time. Such type of bearings
are also called boundary lubricated bearings.
3. Zerofilmbearings. The zero film bearings are those which
operate without any lubricantpresent.
4. Hydrostaticorexternallypressurizedlubricatedbearings. The
hydrostatic bearings are thosewhich can support steady loads
without any relative motion between the journal and the bearing.
This is achieved by forcing externally pressurized lubricant between
the members.
although lubricant is present,the working surfaces partially
contact each other atleast part of the time. Such type of bearings
are also called boundary lubricated bearings.
3. Zerofilmbearings. The zero film bearings are those which
operate without any lubricantpresent.
4. Hydrostaticorexternallypressurizedlubricatedbearings. The
hydrostatic bearings are thosewhich can support steady loads
without any relative motion between the journal and the bearing.
This is achieved by forcing externally pressurized lubricant between
the members.
Terms used in Hydrodynamic Journal Bearing
A hydrodynamic journal bearing is shown in Fig., in which O is the centre of the
journaland O′ is the centre of the bearing.
Let D = Diameter of the bearing,
d = Diameter of the journal,
and
l = Length of the bearing.
The following terms used in hydrodynamic journalbearing are important from
the subject point of view :
A hydrodynamic journal bearing is shown in Fig., in which O is the centre of the
journaland O′ is the centre of the bearing.
Let D = Diameter of the bearing,
d = Diameter of the journal,
and
l = Length of the bearing.
The following terms used in hydrodynamic journalbearing are important from
the subject point of view :
1.Diametralclearance. It the difference between thediameters
of the bearing and the journal. Mathematically,diametral
clearance,
c = D –d
Note : The diametral clearance (c) in a bearing should be small
enough to produce the necessary velocity gradient, so that the
pressure built up will support the load. Also thesmall clearance
has the advantage of decreasing side leakage. However, the
allowance must be made for manufacturing tolerances in the
journal and bushing. A commonly used clearance inindustrial
machines is 0.025 mmper cm of journal diameter.
of the bearing and the journal. Mathematically,diametral
clearance,
c = D –d
Note : The diametral clearance (c) in a bearing should be small
enough to produce the necessary velocity gradient, so that the
pressure built up will support the load. Also thesmall clearance
has the advantage of decreasing side leakage. However, the
allowance must be made for manufacturing tolerances in the
journal and bushing. A commonly used clearance inindustrial
machines is 0.025 mmper cm of journal diameter.
Bearing Characteristic Number andBearing
Modulus forJournal Bearings
Modulus forJournal Bearings
The factor ZN / p is termed as bearing characteristic number and is a
dimensionless number.The variation of coefficient of friction with the
operating values of bearing characteristic number(ZN / p) as obtained by
McKee brothers (S.A. McKee and T.R. McKee) in an actual test of friction is
shown in Fig. The factor ZN/p helps to predict the performance of a bearing.
The part of the curve PQrepresents the region of thick filmlubrication.
Between Q and R, theviscosity (Z) or the speed (N) areso low, or the
pressure ( p) is sogreat that their combination ZN / pwill reduce the film
thickness so thatpartial metal to metal contact willresult. The thin film or
boundarylubrication or imperfect lubricationexists between R and S on the
curve.This is the region where thviscosity of the lubricant ceases tobe a
measure of frictioncharacteristics but the oiliness of thelubricant is effective
in preventingcomplete metal to metal contact andseizure of the parts.
dimensionless number.The variation of coefficient of friction with the
operating values of bearing characteristic number(ZN / p) as obtained by
McKee brothers (S.A. McKee and T.R. McKee) in an actual test of friction is
shown in Fig. The factor ZN/p helps to predict the performance of a bearing.
The part of the curve PQrepresents the region of thick filmlubrication.
Between Q and R, theviscosity (Z) or the speed (N) areso low, or the
pressure ( p) is sogreat that their combination ZN / pwill reduce the film
thickness so thatpartial metal to metal contact willresult. The thin film or
boundarylubrication or imperfect lubricationexists between R and S on the
curve.This is the region where thviscosity of the lubricant ceases tobe a
measure of frictioncharacteristics but the oiliness of thelubricant is effective
in preventingcomplete metal to metal contact andseizure of the parts.
It may be noted that the partPQ of the curve represents stableoperating
conditions, since fromany point of stability, a decrease in viscosity (Z) will
reduce ZN / p. This will result in a decrease incoefficient of friction (μ) followed
by a lowering of bearing temperature that will raise the viscosity(Z ).
From Fig. we see that the minimum amount of friction occurs at A and at this
point the value of ZN / p is known as bearing modulus which is denoted by K.
The bearing should not beoperated at this value of bearing modulus, becausea
slight decrease in speed or slight increase inpressure will break the oil film and
make the journalto operate with metal to metal contact. This willresult in high
friction, wear and heating. In orderto prevent such conditions, the bearing
should bedesigned for a value of ZN / p at least three timesthe minimum value
of bearing modulus (K). If thebearing is subjected to large fluctuations of load
and heavy impacts, the value of ZN / p = 15 K maybe used.
conditions, since fromany point of stability, a decrease in viscosity (Z) will
reduce ZN / p. This will result in a decrease incoefficient of friction (μ) followed
by a lowering of bearing temperature that will raise the viscosity(Z ).
From Fig. we see that the minimum amount of friction occurs at A and at this
point the value of ZN / p is known as bearing modulus which is denoted by K.
The bearing should not beoperated at this value of bearing modulus, becausea
slight decrease in speed or slight increase inpressure will break the oil film and
make the journalto operate with metal to metal contact. This willresult in high
friction, wear and heating. In orderto prevent such conditions, the bearing
should bedesigned for a value of ZN / p at least three timesthe minimum value
of bearing modulus (K). If thebearing is subjected to large fluctuations of load
and heavy impacts, the value of ZN / p = 15 K maybe used.
From above, it is concluded that when thevalue of ZN / p is
greater than K, then the bearingwill operate with thick film
lubrication or underhydrodynamic conditions. On the other
hand, whenthe value of ZN / p is less than K, then the oil
filmwill rupture and there is a metal to metal contact.
greater than K, then the bearingwill operate with thick film
lubrication or underhydrodynamic conditions. On the other
hand, whenthe value of ZN / p is less than K, then the oil
filmwill rupture and there is a metal to metal contact.
Coefficient of Friction for JournalBearings
In order to determine the coefficient of friction for well lubricated full
journal bearings,the following empirical relation established by McKee
based on the experimental data, may beused.
In order to determine the coefficient of friction for well lubricated full
journal bearings,the following empirical relation established by McKee
based on the experimental data, may beused.
Critical Pressure of the Journal Bearing
Sommerfeld Number
The heat generated in a bearing is due to the fluid friction and
friction of the parts havingrelative motion. Mathematically, heat
generated in a bearing,
Qg = μ.W.V N-m/s or J/s or watts ...(i)
where μ = Coefficient of friction,
W = Load on the bearing in N,
= Pressure on the bearing in N/mm
2
×Projected area of the
bearingin mm
2
= p (l ×d),
V = Rubbing velocity in m/s = πd.N/60 , d is in metres, and
N = Speed of the journal in r.p.m.
Heat Generated in a Journal Bearing
friction of the parts havingrelative motion. Mathematically, heat
generated in a bearing,
Qg = μ.W.V N-m/s or J/s or watts ...(i)
where μ = Coefficient of friction,
W = Load on the bearing in N,
= Pressure on the bearing in N/mm
2
×Projected area of the
bearingin mm
2
= p (l ×d),
V = Rubbing velocity in m/s = πd.N/60 , d is in metres, and
N = Speed of the journal in r.p.m.
Heat Generated in a Journal Bearing
Design a journal bearing for a centrifugalpump from the
following data :Load on thejournal = 20 000 N; Speed of the
journal = 900r.p.m.; Type of oil is SAE 10, forwhich the
absolute viscosity at 55°C = 0.017 kg / m-s;Ambient
temperature of oil = 15.5°C ;Maximumbearing pressure for
the pump = 1.5 N / mm
2
.Calculate also mass of the lubricating
oil required for artificial cooling, ifrise of temperatureof oil be
limited to 10°C.Heat dissipation coefficient = 1232 W/m
2
/°C.
following data :Load on thejournal = 20 000 N; Speed of the
journal = 900r.p.m.; Type of oil is SAE 10, forwhich the
absolute viscosity at 55°C = 0.017 kg / m-s;Ambient
temperature of oil = 15.5°C ;Maximumbearing pressure for
the pump = 1.5 N / mm
2
.Calculate also mass of the lubricating
oil required for artificial cooling, ifrise of temperatureof oil be
limited to 10°C.Heat dissipation coefficient = 1232 W/m
2
/°C.
The load on the journal bearing is 150 kNdue to turbine
shaft of 300 mmdiameter running at 1800 r.p.m.
Determine the following :
1. Length of the bearing if the allowable bearing pressure
is 1.6 N/mm
2
, and
2. Amount of heat to be removed by the lubricant per
minute if the bearing temperature is 60°C and viscosity of
the oil at 60°C is 0.02 kg/m-s and the bearing clearance is
0.25 mm.
shaft of 300 mmdiameter running at 1800 r.p.m.
Determine the following :
1. Length of the bearing if the allowable bearing pressure
is 1.6 N/mm
2
, and
2. Amount of heat to be removed by the lubricant per
minute if the bearing temperature is 60°C and viscosity of
the oil at 60°C is 0.02 kg/m-s and the bearing clearance is
0.25 mm.
A full journal bearing of 50 mm diameter and 100 mm long has a
bearingpressure of 1.4 N/mm
2
. The speed of the journal is 900
r.p.m. and the ratio of journal diameter to thediametral clearance
is 1000. The bearing is lubricated with oil whose absolute viscosity
at theoperating temperature of 75°C may be taken as 0.011 kg/m-
s. The room temperature is 35°C. Find :
1. The amount of artificial cooling required, and 2.The mass of the
lubricating oil required, if the difference between the outlet and
inlettemperature of the oil is 10°C. Take specificheat of the oil as
1850 J / kg / °C.
bearingpressure of 1.4 N/mm
2
. The speed of the journal is 900
r.p.m. and the ratio of journal diameter to thediametral clearance
is 1000. The bearing is lubricated with oil whose absolute viscosity
at theoperating temperature of 75°C may be taken as 0.011 kg/m-
s. The room temperature is 35°C. Find :
1. The amount of artificial cooling required, and 2.The mass of the
lubricating oil required, if the difference between the outlet and
inlettemperature of the oil is 10°C. Take specificheat of the oil as
1850 J / kg / °C.
A150mmdiametershaftsupportingaloadof10kN
hasaspeedof1500r.p.m.Theshaftrunsinabearing
whoselengthis1.5timestheshaftdiameter.Ifthe
diametralclearanceofthebearingis0.15mmandthe
absoluteviscosityoftheoilattheoperating
temperatureis0.011kg/m-s,findthepowerwastedin
friction.
hasaspeedof1500r.p.m.Theshaftrunsinabearing
whoselengthis1.5timestheshaftdiameter.Ifthe
diametralclearanceofthebearingis0.15mmandthe
absoluteviscosityoftheoilattheoperating
temperatureis0.011kg/m-s,findthepowerwastedin
friction.
A80mmlongjournalbearingsupportsaloadof2800N
ona50mmdiametershaft.Thebearinghasaradial
clearanceof0.05mmandtheviscosityoftheoilis0.021
kg/m-sattheoperatingtemperature.Ifthebearingis
capableofdissipating80J/s,determinethemaximum
safespeed.
ona50mmdiametershaft.Thebearinghasaradial
clearanceof0.05mmandtheviscosityoftheoilis0.021
kg/m-sattheoperatingtemperature.Ifthebearingis
capableofdissipating80J/s,determinethemaximum
safespeed.
Ajournalbearing60mmisdiameterand90mmlong
runsat450r.p.m.Theoilusedforhydrodynamic
lubricationhasabsoluteviscosityof0.06kg/m-s.Ifthe
diametralclearanceis0.1mm,findthesafeloadonthe
bearing.
runsat450r.p.m.Theoilusedforhydrodynamic
lubricationhasabsoluteviscosityof0.06kg/m-s.Ifthe
diametralclearanceis0.1mm,findthesafeloadonthe
bearing.
Assignment Problems
1.Themainbearingofasteamengineis100mmindiameterand
175mmlong.Thebearingsupportsaloadof28kNat250r.p.m.If
theratioofthediametralclearancetothediameteris0.001andthe
absoluteviscosityofthelubricatingoilis0.015kg/m-s,find:1.The
coefficientoffriction;and2.Theheatgeneratedatthebearingdue
tofriction.[Ans.0.00277;101.5J/s]
2.Ajournalbearingisproposedforasteamengine.Theloadonthe
journalis3kN,diameter50mm,length75mm,speed1600r.p.m.,
diametralclearance0.001mm,ambienttemperature15.5°C.Oil
SAE10isusedandthefilmtemperatureis60°C.Determinetheheat
generatedandheatdissipated.TakeabsoluteviscosityofSAE10at
60°C=0.014kg/m-s.[Ans.141.3J/s;25J/s]
1.Themainbearingofasteamengineis100mmindiameterand
175mmlong.Thebearingsupportsaloadof28kNat250r.p.m.If
theratioofthediametralclearancetothediameteris0.001andthe
absoluteviscosityofthelubricatingoilis0.015kg/m-s,find:1.The
coefficientoffriction;and2.Theheatgeneratedatthebearingdue
tofriction.[Ans.0.00277;101.5J/s]
2.Ajournalbearingisproposedforasteamengine.Theloadonthe
journalis3kN,diameter50mm,length75mm,speed1600r.p.m.,
diametralclearance0.001mm,ambienttemperature15.5°C.Oil
SAE10isusedandthefilmtemperatureis60°C.Determinetheheat
generatedandheatdissipated.TakeabsoluteviscosityofSAE10at
60°C=0.014kg/m-s.[Ans.141.3J/s;25J/s]
3.A100mmlongand60mmdiameterjournalbearing
supportsaloadof2500Nat600r.p.m.Iftheroom
temperatureis20°C,whatshouldbetheviscosityofoiltolimit
thebearingsurfacetemperatureto60°C?Thediametral
clearanceis0.06mmandtheenergydissipationcoefficient
basedonprojectedareaofbearingis210W/m2/°C.[Ans.
0.0183kg/m-s]
supportsaloadof2500Nat600r.p.m.Iftheroom
temperatureis20°C,whatshouldbetheviscosityofoiltolimit
thebearingsurfacetemperatureto60°C?Thediametral
clearanceis0.06mmandtheenergydissipationcoefficient
basedonprojectedareaofbearingis210W/m2/°C.[Ans.
0.0183kg/m-s]
Objective Type Questions
PART B
ROLLING CONTACT BEARINGS
ROLLING CONTACT BEARINGS
INTRODUCTION
Inrollingcontactbearings,thecontactbetweenthebearing
surfacesisrollinginsteadofslidingasinslidingcontact
bearings.
Wehavealreadydiscussedthattheordinaryslidingbearing
startsfromrestwithpracticallymetal-to-metalcontactand
hasahighcoefficientoffriction.
Itisanoutstandingadvantageofarollingcontactbearing
overaslidingbearingthatithasalowstartingfriction.
Duetothislowfrictionofferedbyrollingcontactbearings,
thesearecalledantifrictionbearings.
Inrollingcontactbearings,thecontactbetweenthebearing
surfacesisrollinginsteadofslidingasinslidingcontact
bearings.
Wehavealreadydiscussedthattheordinaryslidingbearing
startsfromrestwithpracticallymetal-to-metalcontactand
hasahighcoefficientoffriction.
Itisanoutstandingadvantageofarollingcontactbearing
overaslidingbearingthatithasalowstartingfriction.
Duetothislowfrictionofferedbyrollingcontactbearings,
thesearecalledantifrictionbearings.
Advantages and Disadvantages ofRolling Contact
Bearings Over SlidingContact Bearings
Advantages
1.Lowstartingandrunningfrictionexceptatveryhighspeeds.
2.Abilitytowithstandmomentaryshockloads.
3.Accuracyofshaftalignment.
4.Lowcostofmaintenance,asnolubricationisrequiredwhileinservice.
5. Small overall dimensions.
6. Reliability of service.
7. Easy to mount and erect.
8. Cleanliness.
Bearings Over SlidingContact Bearings
Advantages
1.Lowstartingandrunningfrictionexceptatveryhighspeeds.
2.Abilitytowithstandmomentaryshockloads.
3.Accuracyofshaftalignment.
4.Lowcostofmaintenance,asnolubricationisrequiredwhileinservice.
5. Small overall dimensions.
6. Reliability of service.
7. Easy to mount and erect.
8. Cleanliness.
Disadvantages (or) Limitations:
1. More noisy at very high speeds.
2. Low resistance to shock loading.
3. More initial cost.
4. Design of bearing housing complicated.
1. More noisy at very high speeds.
2. Low resistance to shock loading.
3. More initial cost.
4. Design of bearing housing complicated.
Applications of Rolling contact bearings:
machine tool spindles;
automobile front and rear axles;
gear boxes;
small size electric motors; and
rope sheaves, crane hooks and hoisting
drums.
machine tool spindles;
automobile front and rear axles;
gear boxes;
small size electric motors; and
rope sheaves, crane hooks and hoisting
drums.
Types of Rolling Contact Bearings
Followingarethetwotypesofrollingcontact
bearings:
1.Ballbearings,and
2.Rollerbearings.
Followingarethetwotypesofrollingcontact
bearings:
1.Ballbearings,and
2.Rollerbearings.
Theballandrollerbearingsconsistofaninnerracewhichis
mountedontheshaftorjournalandanouterracewhichiscarried
bythehousingorcasing.
Inbetweentheinnerandouterrace,thereareballsorrollersas
showninFigures.
Anumberofballsorrollersareusedandtheseareheldat
properdistancesbyretainerssothattheydonottoucheachother.
Theretainersarethinstripsandisusuallyintwopartswhichare
assembledaftertheballshavebeenproperlyspaced.
Theballbearingsareusedforlightloadsandtherollerbearings
areusedforheavierloads.
mountedontheshaftorjournalandanouterracewhichiscarried
bythehousingorcasing.
Inbetweentheinnerandouterrace,thereareballsorrollersas
showninFigures.
Anumberofballsorrollersareusedandtheseareheldat
properdistancesbyretainerssothattheydonottoucheachother.
Theretainersarethinstripsandisusuallyintwopartswhichare
assembledaftertheballshavebeenproperlyspaced.
Theballbearingsareusedforlightloadsandtherollerbearings
areusedforheavierloads.
The rolling contact bearings, depending upon
the load to be carried, are classified as :
(a) Radial bearings, and (b) Thrust bearings.
Types of Radial Ball Bearings
the load to be carried, are classified as :
(a) Radial bearings, and (b) Thrust bearings.
Types of Radial Ball Bearings
1.Singlerowdeepgroovebearing.Asinglerowdeep
groovebearingisshowninFig.(a).
Duringassemblyofthisbearing,theracesareoffsetand
themaximumnumberofballsareplacedbetweenthe
races.Theracesarethencentredandtheballsare
symmetricallylocatedbytheuseofaretainerorcage.The
deepgrooveballbearingsareusedduetotheirhighload
carryingcapacityandsuitabilityforhighrunningspeeds.
Theloadcarryingcapacityofaballbearingisrelatedto
thesizeandnumberoftheballs.
groovebearingisshowninFig.(a).
Duringassemblyofthisbearing,theracesareoffsetand
themaximumnumberofballsareplacedbetweenthe
races.Theracesarethencentredandtheballsare
symmetricallylocatedbytheuseofaretainerorcage.The
deepgrooveballbearingsareusedduetotheirhighload
carryingcapacityandsuitabilityforhighrunningspeeds.
Theloadcarryingcapacityofaballbearingisrelatedto
thesizeandnumberoftheballs.
2.Fillingnotchbearing.Afillingnotchbearingisshownin
Fig(b).Thesebearingshavenotchesintheinnerandouter
raceswhichpermitmoreballstobeinsertedthanina
deepgrooveballbearings.Thenotchesdonotextendto
thebottomoftheracewayandthereforetheballs
insertedthroughthenotchesmustbeforcedinposition.
Sincethistypeofbearingcontainslargernumberofballs
thanacorrespondingunnotchedone,thereforeithasa
largerbearingloadcapacity.
Fig(b).Thesebearingshavenotchesintheinnerandouter
raceswhichpermitmoreballstobeinsertedthanina
deepgrooveballbearings.Thenotchesdonotextendto
thebottomoftheracewayandthereforetheballs
insertedthroughthenotchesmustbeforcedinposition.
Sincethistypeofbearingcontainslargernumberofballs
thanacorrespondingunnotchedone,thereforeithasa
largerbearingloadcapacity.
3.Angularcontactbearing:
AnangularcontactbearingisshowninFig.(c).These
bearingshaveonesideoftheouterracecutawayto
permittheinsertionofmoreballsthaninadeepgroove
bearingbutwithouthavinganotchcutintobothraces.
Thispermitsthebearingtocarryarelativelylargeaxial
loadinonedirectionwhilealsocarryingarelativelylarge
radialload.
Theangularcontactbearingsareusuallyusedinpairsso
thatthrustloadsmaybecarriedineitherdirection.
AnangularcontactbearingisshowninFig.(c).These
bearingshaveonesideoftheouterracecutawayto
permittheinsertionofmoreballsthaninadeepgroove
bearingbutwithouthavinganotchcutintobothraces.
Thispermitsthebearingtocarryarelativelylargeaxial
loadinonedirectionwhilealsocarryingarelativelylarge
radialload.
Theangularcontactbearingsareusuallyusedinpairsso
thatthrustloadsmaybecarriedineitherdirection.
4.Doublerowbearing:
AdoublerowbearingisshowninFig.(d).These
bearingsmaybemadewithradialorangularcontact
betweentheballsandraces.
Thedoublerowbearingisappreciablynarrower
thantwosinglerowbearings.
Theloadcapacityofsuchbearingsisslightlyless
thantwicethatofasinglerowbearing.
AdoublerowbearingisshowninFig.(d).These
bearingsmaybemadewithradialorangularcontact
betweentheballsandraces.
Thedoublerowbearingisappreciablynarrower
thantwosinglerowbearings.
Theloadcapacityofsuchbearingsisslightlyless
thantwicethatofasinglerowbearing.
5.Self-aligningbearing.Aself-aligningbearingisshownin
Fig.(e).Thesebearingspermitshaftdeflectionswithin2-3
degrees.Itmaybenotedthatnormalclearanceinaball
bearingaretoosmalltoaccommodateanyappreciable
misalignmentoftheshaftrelativetothehousing.Iftheunit
isassembledwithshaftmisalignmentpresent,thenthe
bearingwillbesubjectedtoaloadthatmaybeinexcessof
thedesignvalueandprematurefailuremayoccur.
Followingarethetwotypesofself-aligningbearings:
(a)Externallyself-aligningbearing,and(b)Internallyself-
aligningbearing.
Fig.(e).Thesebearingspermitshaftdeflectionswithin2-3
degrees.Itmaybenotedthatnormalclearanceinaball
bearingaretoosmalltoaccommodateanyappreciable
misalignmentoftheshaftrelativetothehousing.Iftheunit
isassembledwithshaftmisalignmentpresent,thenthe
bearingwillbesubjectedtoaloadthatmaybeinexcessof
thedesignvalueandprematurefailuremayoccur.
Followingarethetwotypesofself-aligningbearings:
(a)Externallyself-aligningbearing,and(b)Internallyself-
aligningbearing.
Inanexternallyself-aligningbearing,theoutside
diameteroftheouterraceisgroundtoasphericalsurface
whichfitsinamatingsphericalsurfaceinahousing,as
showninFig.(e).
Incaseofinternallyself-aligningbearing,theinner
surfaceoftheouterraceisgroundtoasphericalsurface.
Consequently,theouterracemaybedisplacedthrougha
smallanglewithoutinterferingwiththenormaloperationof
thebearing.
Theinternallyself-aligningballbearingisinterchangeable
withotherballbearings.
diameteroftheouterraceisgroundtoasphericalsurface
whichfitsinamatingsphericalsurfaceinahousing,as
showninFig.(e).
Incaseofinternallyself-aligningbearing,theinner
surfaceoftheouterraceisgroundtoasphericalsurface.
Consequently,theouterracemaybedisplacedthrougha
smallanglewithoutinterferingwiththenormaloperationof
thebearing.
Theinternallyself-aligningballbearingisinterchangeable
withotherballbearings.
Standard Dimensions andDesignations of
Ball Bearings
Ball Bearings
Thedimensionsthathavebeenstandardisedonan
internationalbasisareshowninFig..Thesedimensionsarea
functionofthebearingboreandtheseriesofbearing.The
standarddimensionsaregiveninmillimetres.Thereisno
standardforthesizeandnumberofsteelballs.
Thebearingsaredesignatedbyanumber.Ingeneral,the
numberconsistsofatleastthreedigits.Additionaldigitsor
lettersareusedtoindicatespecialfeaturese.g.deepgroove,
fillingnotchetc.Thelastthreedigitsgivetheseriesandthe
boreofthebearing.Thelasttwodigitsfrom04onwards,
whenmultipliedby5,givetheborediameterinmillimetres.
Thethirdfromthelastdigitdesignatestheseriesofthe
bearing.
internationalbasisareshowninFig..Thesedimensionsarea
functionofthebearingboreandtheseriesofbearing.The
standarddimensionsaregiveninmillimetres.Thereisno
standardforthesizeandnumberofsteelballs.
Thebearingsaredesignatedbyanumber.Ingeneral,the
numberconsistsofatleastthreedigits.Additionaldigitsor
lettersareusedtoindicatespecialfeaturese.g.deepgroove,
fillingnotchetc.Thelastthreedigitsgivetheseriesandthe
boreofthebearing.Thelasttwodigitsfrom04onwards,
whenmultipliedby5,givetheborediameterinmillimetres.
Thethirdfromthelastdigitdesignatestheseriesofthe
bearing.
Themostcommonballbearingsareavailableinfour
seriesasfollows:
1.Extralight(100),
2.Light(200),
3.Medium(300),
4.Heavy(400)
seriesasfollows:
1.Extralight(100),
2.Light(200),
3.Medium(300),
4.Heavy(400)
Notes:1.Ifabearingisdesignatedbythenumber305,
itmeansthatthebearingisofmediumserieswhose
boreis05×5,i.e.,25mm.
2.Theextralightandlightseriesareusedwherethe
loadsaremoderateandshaftsizesarecomparatively
largeandalsowhereavailablespaceislimited.
3.Themediumserieshasacapacity30to40percent
overthelightseries.
4.Theheavyserieshas20to30percentcapacityover
themediumseries.Thisseriesisnotusedextensivelyin
industrialapplications.
itmeansthatthebearingisofmediumserieswhose
boreis05×5,i.e.,25mm.
2.Theextralightandlightseriesareusedwherethe
loadsaremoderateandshaftsizesarecomparatively
largeandalsowhereavailablespaceislimited.
3.Themediumserieshasacapacity30to40percent
overthelightseries.
4.Theheavyserieshas20to30percentcapacityover
themediumseries.Thisseriesisnotusedextensivelyin
industrialapplications.
Types of Roller Bearings
1.Cylindricalrollerbearings.Acylindricalrollerbearingis
showninFig.(a).Thesebearingshaveshortrollersguided
inacage.Thesebearingsarerelativelyrigidagainstradial
motionandhavethelowestcoefficientoffrictionofany
formofheavydutyrolling-contactbearings.Suchtypeof
bearingsareusedinhighspeedservice.
showninFig.(a).Thesebearingshaveshortrollersguided
inacage.Thesebearingsarerelativelyrigidagainstradial
motionandhavethelowestcoefficientoffrictionofany
formofheavydutyrolling-contactbearings.Suchtypeof
bearingsareusedinhighspeedservice.
2.Sphericalrollerbearings.Asphericalrollerbearingis
showninFig.(b).Thesebearingsareself-aligning
bearings.Theself-aligningfeatureisachievedby
grindingoneoftheracesintheformofsphere.These
bearingscannormallytolerateangularmisalignmentin
theorderof±11/2°andwhenusedwithadoublerow
ofrollers,thesecancarrythrustloadsineither
direction.
showninFig.(b).Thesebearingsareself-aligning
bearings.Theself-aligningfeatureisachievedby
grindingoneoftheracesintheformofsphere.These
bearingscannormallytolerateangularmisalignmentin
theorderof±11/2°andwhenusedwithadoublerow
ofrollers,thesecancarrythrustloadsineither
direction.
3.Needlerollerbearings.Aneedlerollerbearingis
showninFig.(c).Thesebearingsarerelativelyslender
andcompletelyfillthespacesothatneitheracagenora
retainerisneeded.Thesebearingsareusedwhenheavy
loadsaretobecarriedwithanoscillatorymotion,e.g.
pistonpinbearingsinheavydutydieselengines,where
thereversalofmotiontendstokeeptherollersincorrect
alignment.
showninFig.(c).Thesebearingsarerelativelyslender
andcompletelyfillthespacesothatneitheracagenora
retainerisneeded.Thesebearingsareusedwhenheavy
loadsaretobecarriedwithanoscillatorymotion,e.g.
pistonpinbearingsinheavydutydieselengines,where
thereversalofmotiontendstokeeptherollersincorrect
alignment.
4.Taperedrollerbearings.Ataperedrollerbearingis
showninFig.(d).Therollersandracewaysofthese
bearingsaretruncatedconeswhoseelementsintersect
atacommonpoint.Suchtypeofbearingscancarry
bothradialandthrustloads.Thesebearingsare
availableinvariouscombinationsasdoublerow
bearingsandwithdifferentconeanglesforusewith
differentrelativemagnitudesofradialandthrustloads.
showninFig.(d).Therollersandracewaysofthese
bearingsaretruncatedconeswhoseelementsintersect
atacommonpoint.Suchtypeofbearingscancarry
bothradialandthrustloads.Thesebearingsare
availableinvariouscombinationsasdoublerow
bearingsandwithdifferentconeanglesforusewith
differentrelativemagnitudesofradialandthrustloads.
DYNAMIC LOAD CARRYING CAPACITY
Thelifeofaballbearingislimitedbythefatigue
failureatthesurfacesofballsandraces.
Thedynamicloadcarryingcapacityofthebearing
is,therefore,basedonthefatiguelifeofthebearing.
Thelifeofanindividualballbearingisdefinedasthe
numberofrevolutions(orhoursofserviceatsome
givenconstantspeed),whichthebearingruns
beforethefirstevidenceoffatiguecrackinballsor
races.
Thelifeofaballbearingislimitedbythefatigue
failureatthesurfacesofballsandraces.
Thedynamicloadcarryingcapacityofthebearing
is,therefore,basedonthefatiguelifeofthebearing.
Thelifeofanindividualballbearingisdefinedasthe
numberofrevolutions(orhoursofserviceatsome
givenconstantspeed),whichthebearingruns
beforethefirstevidenceoffatiguecrackinballsor
races.
EQUIVALENT BEARING LOAD
Theequivalentdynamicloadisdefinedastheconstantradial
loadinradialbearings(orthrustloadinthrustbearings),whichif
appliedtothebearingwouldgivesamelifeasthatwhichthe
bearingwillattainunderactualconditionofforces.
Theexpressionfortheequivalentdynamicloadiswrittenas,
P=XVFr+YFa
where,
P=equivalentdynamicload(N)
Fr=radialload(N)
Fa=axialorthrustload(N)
V=race-rotationfactor
XandYareradialandthrustfactorsrespectivelyandtheirvalues
aregiveninthemanufacturer’scatalogues.
Theequivalentdynamicloadisdefinedastheconstantradial
loadinradialbearings(orthrustloadinthrustbearings),whichif
appliedtothebearingwouldgivesamelifeasthatwhichthe
bearingwillattainunderactualconditionofforces.
Theexpressionfortheequivalentdynamicloadiswrittenas,
P=XVFr+YFa
where,
P=equivalentdynamicload(N)
Fr=radialload(N)
Fa=axialorthrustload(N)
V=race-rotationfactor
XandYareradialandthrustfactorsrespectivelyandtheirvalues
aregiveninthemanufacturer’scatalogues.
Assuming V as unity, the general equation for equivalent
dynamic load is given by,
P = XFr+ Yfa
When the bearing is subjected to pure radial load Fr ,
P = Fr (Fa= 0)
When the bearing is subjected to pure thrust load Fa,
P = Fa(Fr = 0)
dynamic load is given by,
P = XFr+ Yfa
When the bearing is subjected to pure radial load Fr ,
P = Fr (Fa= 0)
When the bearing is subjected to pure thrust load Fa,
P = Fa(Fr = 0)
LOAD-LIFE RELATIONSHIP
The relationship between the dynamic load carrying capacity,
the equivalent dynamic load, and the bearing life is given by,
L10 = (C/P)^p
where,
L10 = rated bearing life (in million revolutions)
C = dynamic load capacity (N), and
p = 3 (for ball bearings)
p = 10/3 (for roller bearings)
The relationship between the dynamic load carrying capacity,
the equivalent dynamic load, and the bearing life is given by,
L10 = (C/P)^p
where,
L10 = rated bearing life (in million revolutions)
C = dynamic load capacity (N), and
p = 3 (for ball bearings)
p = 10/3 (for roller bearings)
Life of a Bearing
Thelifeofanindividualball(orroller)bearingmaybe
definedasthenumberofrevolutions(orhoursatsome
givenconstantspeed)whichthebearingrunsbeforethe
firstevidenceoffatiguedevelopsinthematerialofoneof
theringsoranyoftherollingelements.
Thelifeofanindividualball(orroller)bearingmaybe
definedasthenumberofrevolutions(orhoursatsome
givenconstantspeed)whichthebearingrunsbeforethe
firstevidenceoffatiguedevelopsinthematerialofoneof
theringsoranyoftherollingelements.
Life of a Bearing
Theratinglifeofagroupofapparentlyidentical
ballorrollerbearingsisdefinedasthenumber
ofrevolutions(orhoursatsomegivenconstant
speed)that90percentofagroupofbearings
willcompleteorexceedbeforethefirst
evidenceoffatiguedevelops(i.e.only10per
centofagroupofbearingsfailduetofatigue).
Theratinglifeofagroupofapparentlyidentical
ballorrollerbearingsisdefinedasthenumber
ofrevolutions(orhoursatsomegivenconstant
speed)that90percentofagroupofbearings
willcompleteorexceedbeforethefirst
evidenceoffatiguedevelops(i.e.only10per
centofagroupofbearingsfailduetofatigue).
Thetermminimumlifeisalsousedtodenotetherating
life.
Ithasbeenfoundthatthelifewhich50percentofagroup
ofbearingswillcompleteorexceedisapproximately5times
thelifewhich90percentofthebearingswillcompleteor
exceed.
Inotherwords,wemaysaythattheaveragelifeofa
bearingis5timestheratinglife(orminimumlife).
Itmaybenotedthatthelongestlifeofasinglebearingis
seldomlongerthanthe4timestheaveragelifeandthe
maximumlifeofasinglebearingisabout30to50timesthe
minimumlife.
life.
Ithasbeenfoundthatthelifewhich50percentofagroup
ofbearingswillcompleteorexceedisapproximately5times
thelifewhich90percentofthebearingswillcompleteor
exceed.
Inotherwords,wemaysaythattheaveragelifeofa
bearingis5timestheratinglife(orminimumlife).
Itmaybenotedthatthelongestlifeofasinglebearingis
seldomlongerthanthe4timestheaveragelifeandthe
maximumlifeofasinglebearingisabout30to50timesthe
minimumlife.
Dynamic Load Rating for Rolling Contact
Bearings under VariableLoads
Bearings under VariableLoads
Reliability of a Bearing
Wehavealreadydiscussedinthepreviousarticlethatthe
ratinglifeisthelifethat90percentofagroupofidentical
bearingswillcompleteorexceedbeforethefirstevidenceof
fatiguedevelops.
Thereliability(R)isdefinedastheratioofthenumberof
bearingswhichhavesuccessfullycompletedLmillion
revolutionstothetotalnumberofbearingsundertest.
Sometimes,itbecomesnecessarytoselectabearinghavinga
reliabilityofmorethan90%.
AccordingtoWiebull,therelationbetweenthebearinglifeand
thereliabilityisgivenas
Wehavealreadydiscussedinthepreviousarticlethatthe
ratinglifeisthelifethat90percentofagroupofidentical
bearingswillcompleteorexceedbeforethefirstevidenceof
fatiguedevelops.
Thereliability(R)isdefinedastheratioofthenumberof
bearingswhichhavesuccessfullycompletedLmillion
revolutionstothetotalnumberofbearingsundertest.
Sometimes,itbecomesnecessarytoselectabearinghavinga
reliabilityofmorethan90%.
AccordingtoWiebull,therelationbetweenthebearinglifeand
thereliabilityisgivenas
Ashaftrotatingatconstantspeedissubjectedto
variableload.Thebearingssupportingtheshaft
aresubjectedtostationaryequivalentradialload
of3kNfor10percentoftime,2kNfor20percent
oftime,1kNfor30percentoftimeandnoload
forremainingtimeofcycle.Ifthetotallife
expectedforthebearingis20×10^6revolutions
at95percentreliability,calculatedynamicload
ratingoftheballbearing.
variableload.Thebearingssupportingtheshaft
aresubjectedtostationaryequivalentradialload
of3kNfor10percentoftime,2kNfor20percent
oftime,1kNfor30percentoftimeandnoload
forremainingtimeofcycle.Ifthetotallife
expectedforthebearingis20×10^6revolutions
at95percentreliability,calculatedynamicload
ratingoftheballbearing.
Therollingcontactballbearingaretobeselected
tosupporttheoverhungcountershaft.Theshaft
speedis720r.p.m.Thebearingsaretohave99%
reliabilitycorrespondingtoalifeof24,000hours.
Thebearingissubjectedtoanequivalentradial
loadof1kN.Considerlifeadjustmentfactorsfor
operatingconditionandmaterialas0.9and0.85
respectively.Findthebasicdynamicloadratingof
thebearingfrommanufacturer'scatalogue,
specifiedat90%reliability.
tosupporttheoverhungcountershaft.Theshaft
speedis720r.p.m.Thebearingsaretohave99%
reliabilitycorrespondingtoalifeof24,000hours.
Thebearingissubjectedtoanequivalentradial
loadof1kN.Considerlifeadjustmentfactorsfor
operatingconditionandmaterialas0.9and0.85
respectively.Findthebasicdynamicloadratingof
thebearingfrommanufacturer'scatalogue,
specifiedat90%reliability.
Solution:
Given data: N = 720 rpm, LH= 24,000 Hours, W = 1KN
We know that life of the bearing corresponding to 99% reliability,
L99= 60 N.LH= 60*720*24000 = 1036.8*10^6 rev
Let L90= life of the bearing corresponding to 90% reliability
Considering life adjustment factors for operating condition and material as
0.9 and 0.85 respectively, we have
Given data: N = 720 rpm, LH= 24,000 Hours, W = 1KN
We know that life of the bearing corresponding to 99% reliability,
L99= 60 N.LH= 60*720*24000 = 1036.8*10^6 rev
Let L90= life of the bearing corresponding to 90% reliability
Considering life adjustment factors for operating condition and material as
0.9 and 0.85 respectively, we have
Continued....
L90= L99/0.1026 = (1036.8*10^6 ) / 0.1026 = 10105 * 10^6 rev
We know that dynamic rate loading
(since k = 3 for ball bearing)
C = 21.62 KN Ans
L90= L99/0.1026 = (1036.8*10^6 ) / 0.1026 = 10105 * 10^6 rev
We know that dynamic rate loading
(since k = 3 for ball bearing)
C = 21.62 KN Ans
Selectasinglerowdeepgrooveballbearingfora
radialloadof4000Nandanaxialloadof5000N,
operatingataspeedof1600r.p.m.foranaverage
lifeof5yearsat10hoursperday.Assume
uniformandsteadyload.
radialloadof4000Nandanaxialloadof5000N,
operatingataspeedof1600r.p.m.foranaverage
lifeof5yearsat10hoursperday.Assume
uniformandsteadyload.
Solution:
Given data: WR= 4000 N, WA= 5000 N, N = 1600 rpm
Since average life of the bearing is 5 years 10 hours per
day, therefore life of the bearing in hours,
LH= 5*300*10 =15,000 hours
(Assuming 300 working days per year)
And life of the bearing in revolutions,
L= 60 N * LH= 60*1600*15,000 = 1440*10^6 rev
We know that basic dynamic equilantradial load,
W = X*V*WR+ Y*WA
Given data: WR= 4000 N, WA= 5000 N, N = 1600 rpm
Since average life of the bearing is 5 years 10 hours per
day, therefore life of the bearing in hours,
LH= 5*300*10 =15,000 hours
(Assuming 300 working days per year)
And life of the bearing in revolutions,
L= 60 N * LH= 60*1600*15,000 = 1440*10^6 rev
We know that basic dynamic equilantradial load,
W = X*V*WR+ Y*WA
Inordertodeterminetheradialloadfactor(X)andaxialload
factor(Y),werequireWA/WRandWA/C0.Sincethevalueofbasic
staticloadcapacity(C0)isnotknown,thereforeletustakeWA/C0
=0.5.
Nowfromtable27.4,wefindthatthevaluesofXandY
correspondingtoWA/C0=0.5andWA/WR=5000/4000=1.25
(whichisgreaterthane=0.44)are
X = 0.56 and Y = 1
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (0.56*1*4000 + 1*5000)= 7240 N
From table 27.5, we find that for uniform and steady load, the
service factor (Ks) is 1. Therefore the bearing should be selected
for,
W = 7240*1 = 7240 N
factor(Y),werequireWA/WRandWA/C0.Sincethevalueofbasic
staticloadcapacity(C0)isnotknown,thereforeletustakeWA/C0
=0.5.
Nowfromtable27.4,wefindthatthevaluesofXandY
correspondingtoWA/C0=0.5andWA/WR=5000/4000=1.25
(whichisgreaterthane=0.44)are
X = 0.56 and Y = 1
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (0.56*1*4000 + 1*5000)= 7240 N
From table 27.5, we find that for uniform and steady load, the
service factor (Ks) is 1. Therefore the bearing should be selected
for,
W = 7240*1 = 7240 N
We know that the basic dynamic load rating,
C = 81,760 N = 81.76 KN (k = 3 for ball bearings)
From table 27.6, let us select the bearing no. 315 which has the
following basic capacities
C0= 72 KN = 72,000 N, C = 90 KN = 90,000 N
Now WA/ C0= 5000/72,000 = 0.07
From table 27.4 the values of ‘X’ and ‘Y’ are X = 0.56 and Y = 1.6
Substitute in W = X*V*WR+ Y*WA
W = 0.56*1*4000 + 1.6*5000 = 10,240 N
Basic dynamic load rating
C = 115635 N = 115.63 KN
From table 27.6, let us select the bearing no. 319 having C = 120 KN, may be selected.
C = 81,760 N = 81.76 KN (k = 3 for ball bearings)
From table 27.6, let us select the bearing no. 315 which has the
following basic capacities
C0= 72 KN = 72,000 N, C = 90 KN = 90,000 N
Now WA/ C0= 5000/72,000 = 0.07
From table 27.4 the values of ‘X’ and ‘Y’ are X = 0.56 and Y = 1.6
Substitute in W = X*V*WR+ Y*WA
W = 0.56*1*4000 + 1.6*5000 = 10,240 N
Basic dynamic load rating
C = 115635 N = 115.63 KN
From table 27.6, let us select the bearing no. 319 having C = 120 KN, may be selected.
Asinglerowangularcontactballbearingnumber
310isusedforanaxialflowcompressor.The
bearingistocarryaradialloadof2500Nandan
axialorthrustloadof1500N.Assuminglight
shockload,determinetheratinglifeofthe
bearing.
310isusedforanaxialflowcompressor.The
bearingistocarryaradialloadof2500Nandan
axialorthrustloadof1500N.Assuminglight
shockload,determinetheratinglifeofthe
bearing.
Solution:
Given data: WR= 2500 N, WA= 1500 N
From table 27.4, we find that for single row angular contact ball
bearing, the values of radial factor (X) and thrust factor (Y) for
WA/WR= 1500 / 2500 = 0.6 are
X = 1 and Y = 0
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (1*1*2500 + 0*1500)= 2500 N
From table 27.5, we find that for light shock load, the service factor
(Ks) is 1.5. Therefore the design dynamic equilantload should be
taken as
W = 2500*1.5 = 3750 N
Given data: WR= 2500 N, WA= 1500 N
From table 27.4, we find that for single row angular contact ball
bearing, the values of radial factor (X) and thrust factor (Y) for
WA/WR= 1500 / 2500 = 0.6 are
X = 1 and Y = 0
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (1*1*2500 + 0*1500)= 2500 N
From table 27.5, we find that for light shock load, the service factor
(Ks) is 1.5. Therefore the design dynamic equilantload should be
taken as
W = 2500*1.5 = 3750 N
From table 27.5, we find that for a single row angular contact ball
bearing number 310, the basic dynamic capacity,
C = 53 KN = 53,000 N
We know that rating life of the bearing in revolutions,
L = 2823*10^6 rev (k = 3 for ball bearings)
bearing number 310, the basic dynamic capacity,
C = 53 KN = 53,000 N
We know that rating life of the bearing in revolutions,
L = 2823*10^6 rev (k = 3 for ball bearings)
Designaself-aligningballbearingforaradial
loadof7000Nandathrustloadof2100N.The
desiredlifeofthebearingis160millionsof
revolutionsat300r.p.m.Assumeuniformand
steadyload.
loadof7000Nandathrustloadof2100N.The
desiredlifeofthebearingis160millionsof
revolutionsat300r.p.m.Assumeuniformand
steadyload.
Solution:
Given data: WR= 7000 N, WA= 2100 N, L = 160*10^6 rev, N = 300 rpm
Fromtable27.4,wefindthatforself-aligningballbearing,
thevaluesofradialfactor(X)andthrustfactor(Y)for
WA/WR=2100/7000=0.3are
X = 0.65 and Y = 3.5
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (0.65*1*7000 + 3.5*2100)= 11,900 N
From table 27.5, we find that for uniform and steady load, the
service factor (Ks) is 1. Therefore the design dynamic equilant
load should be taken as
W = 11,900*1 = 11,900 N
Given data: WR= 7000 N, WA= 2100 N, L = 160*10^6 rev, N = 300 rpm
Fromtable27.4,wefindthatforself-aligningballbearing,
thevaluesofradialfactor(X)andthrustfactor(Y)for
WA/WR=2100/7000=0.3are
X = 0.65 and Y = 3.5
Since the rotational factor (V) for most of the bearings is 1,therefore
dynamic equivalent load,
W = X*V*WR+ Y*WA= (0.65*1*7000 + 3.5*2100)= 11,900 N
From table 27.5, we find that for uniform and steady load, the
service factor (Ks) is 1. Therefore the design dynamic equilant
load should be taken as
W = 11,900*1 = 11,900 N
We know that the basic dynamic load rating,
C = 64600 N = 64.6 KN (k = 3 for ball bearings)
From table 27.6 , let us select bearing number 219 having
C = 65.5 KN
C = 64600 N = 64.6 KN (k = 3 for ball bearings)
From table 27.6 , let us select bearing number 219 having
C = 65.5 KN
Table 27.4 –Slide 113-114
Table 27.5 –Slide 115
Table 27.6 –Slide 116-121
Table 27.5 –Slide 115
Table 27.6 –Slide 116-121
Assignment Problems
1.Theballbearingsaretobeselectedforan
applicationinwhichtheradialloadis2000Nduring
90percentofthetimeand8000Nduringthe
remaining10percent.Theshaftistorotateat150
r.p.m.Determinetheminimumvalueofthebasic
dynamicloadratingfor5000hoursofoperation
withnotmorethan10percentfailures.[Ans.13.8
kN]
1.Theballbearingsaretobeselectedforan
applicationinwhichtheradialloadis2000Nduring
90percentofthetimeand8000Nduringthe
remaining10percent.Theshaftistorotateat150
r.p.m.Determinetheminimumvalueofthebasic
dynamicloadratingfor5000hoursofoperation
withnotmorethan10percentfailures.[Ans.13.8
kN]
2.Aballbearingsubjectedtoaradialloadof5kNisexpected
tohavealifeof8000hoursat1450r.p.m.withareliabilityof
99%.Calculatethedynamicloadcapacityofthebearingso
thatitcanbeselectedfromthemanufacturer'scatalogue
basedonareliabilityof90%.[Ans.86.5kN]
3.Aballbearingsubjectedtoaradialloadof4000Nis
expectedtohaveasatisfactorylifeof12000hoursat720
r.p.m.withareliabilityof95%.Calculatethedynamicload
carryingcapacityofthebearing,sothatitcanbeselected
frommanufacturer'scataloguebasedon90%reliability.If
therearefoursuchbearingseachwithareliabilityof95%ina
system,whatisthereliabilityofthecompletesystem?
[Ans.39.5kN;81.45%]
tohavealifeof8000hoursat1450r.p.m.withareliabilityof
99%.Calculatethedynamicloadcapacityofthebearingso
thatitcanbeselectedfromthemanufacturer'scatalogue
basedonareliabilityof90%.[Ans.86.5kN]
3.Aballbearingsubjectedtoaradialloadof4000Nis
expectedtohaveasatisfactorylifeof12000hoursat720
r.p.m.withareliabilityof95%.Calculatethedynamicload
carryingcapacityofthebearing,sothatitcanbeselected
frommanufacturer'scataloguebasedon90%reliability.If
therearefoursuchbearingseachwithareliabilityof95%ina
system,whatisthereliabilityofthecompletesystem?
[Ans.39.5kN;81.45%]
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