Chapter 11 Rolling Contact Bearings - الصفحات...
Transcript of Chapter 11 Rolling Contact Bearings - الصفحات...
Chapter 11
Rolling Contact
Bearings
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Chapter Outline
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Overview
The term rolling bearing is used to describe
class of bearing in which the main load is
transferred through elements in rolling contact
rather than in sliding contact.
Rolling Contact Bearings – load is
transferred through rolling elements such as
balls, straight and tapered cylinders and
spherical rollers.
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Overview
Frictional characteristics of a rolling bearing are
affected by:
Load
Speed
Operating viscosity of lubricant
Bearings are manufactured to take:
Pure radial loads
Pure thrust loads
Combination of the two kinds of loads
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Bearing Types
Figure 11–1:
Nomenclature of a
ball bearing
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Bearing Types Figure 11–2: Various types of ball bearings
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Bearing Types 11/14/2013 8:13 PM
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Self aligning Thrust
Bearing Types
will take radial load as well as
some thrust load.
Balls are inserted into the
grooves by moving the inner
ring to an eccentric position.
Balls are separated after
loading, and the separator is
then inserted.
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Use of a filling notch in inner and outer rings
enables a greater number of balls to be inserted,
thus increasing the load capacity.
Thrust capacity is decreased
Bearing Types
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Filling Notch
Bearing Types
Angular-contact bearing provides a greater
thrust capacity.
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Angular Contact
Bearing Types
Figure 11–3: Types of
roller bearings
a. straight roller
b. spherical roller,
thrust
c. tapered roller, Thrust
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Straight roller Spherical roller
Bearing Types
Figure 11–3: Types of roller bearings
d. Needle
e. Tapered roller
f. Steep-angle tapered roller
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Needle Type
Tapered roller
Bearing Types
Figure 11–3: Types of roller bearings
Straight roller bearings will carry a
greater radial load than ball bearings
of same size because of greater
contact area.
A slight misalignment will cause rollers
to skew and get out of line.
Straight roller bearings will not take
thrust loads.
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Bearing Types
Figure 11–3: Types of roller
bearings
Spherical-roller thrust bearing is
useful where heavy loads and
misalignment occur.
The spherical elements have the
advantage of increasing their
contact area as the load is
increased.
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Bearing Types
Figure 11–3: Types of roller bearings
Needle bearings are very useful where radial
space is limited.
They have a high load capacity when separators
are used
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Needle Type
11–2 Bearing Life
When ball or roller of rolling-contact
bearings rolls, contact stresses occur on:
inner ring
rolling element
outer ring
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11–2 Bearing Life
Common life measures:
Number of revolutions of inner ring (outer
ring stationary) until first tangible
evidence of fatigue
Number of hours of use at a standard
angular speed until first tangible
evidence of fatigue
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11–2 Bearing Life
Fatigue failure consists of spalling of the
load carrying surfaces
American Bearing Manufacturers
Association (ABMA) standard: failure
criterion is the first evidence of fatigue
Timken Fatigue criterion: spalling or
pitting of an area of 0.01 in2
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11–2 Bearing Life The rating life of a group of nominally identical
ball or roller bearings is defined as number of
revolutions (or hours at a constant speed) that
90% of a group of bearings will achieve or
exceed before failure criterion develops.
Minimum life, L10 life, and B10 life are also used
as synonyms for rating life.
Rating life is the 10th percentile location of the
bearing group’s revolutions-to-failure distribution.
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11–2 Bearing Life
Median life is the 50th percentile life of a
group of bearings.
Median life is between 4 & 5 times L10 life.
Most commonly used rating life is 106 revs
Timken Company is rating its bearings at
3000 hours at 500 rpm (90×106 revs)
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11–3 Bearing Load Life at
Rated Reliability
When nominally identical groups are
tested to the life-failure criterion at
different loads, the data are plotted
on a graph as depicted in Fig. 11–4.
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a = 3 for ball bearings
a = 10/3 for roller bearings (cylindrical and tapered roller)
11–3 Bearing Load Life at
Rated Reliability
Catalog load rating = radial load that causes
10% of a group of bearings to fail at bearing
manufacturer’s rating life.
C10: catalog load rating
If manufacturer’s rating life is 106 rev,
Catalog load rating is often referred to as:
Basic Dynamic Load Rating
Basic Load Rating
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11–3 Bearing Load Life at
Rated Reliability
Radial load that would be necessary to cause
failure at such a low life would be
unrealistically high.
Thus, Basic Load Rating should be viewed as
a reference value, and not as an actual load
to be achieved by a bearing.
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11–3 Bearing Load Life at
Rated Reliability
In selecting a bearing for a given application,
it is necessary to relate desired load & life
requirements to catalog load rating
corresponding to catalog rating life.
Units of LR and LD are revolutions
Subscripts R & D stand for Rated & Desired
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11–3 Bearing Load Life at
Rated Reliability
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EXAMPLE 11–1
Consider SKF, which rates its bearings for 1 million
revolutions. If you desire a life of 5000 h at 1725 rpm
with a load of 400 lbf with a reliability of 90%, for which
catalog rating would you search in an SKF catalog?
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1–12 Reliability
Reliability: probability of survival of the
design’s function
Reliability method of design is one in which:
We obtain distribution of stresses &
distribution of strengths
Relate these two in order to achieve an
acceptable success rate
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1–12 Reliability
The statistical measure of the probability
that a mechanical element will not fail in
use is called the reliability of that element.
pf is probability of failure, given by number
of instances of failures per total number of
possible instances.
0 ≤ R ≤ 1.
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1–12 Reliability
R = 0.90: there is a 90 % chance that the
part will perform its proper function without
failure
Failure of 6 parts out of every 1000
manufactured might be considered an
acceptable failure rate for a certain class of
products. This represents a reliability of
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1–12 Reliability
Consider a shaft with two bearings having
reliabilities of 95 % & 98 %.
The overall reliability of the shaft system is
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Example Select a deep groove ball bearing for a desired life of 5000 hours at
1725 rpm with 90% reliability. The bearing radial load is 400 lb.
Mechanical Engineering Dept.
32
Bearing Reliability
If a machine is assembled with 4
bearings, each having a reliability of
90%, then reliability of the system is
(.9)4 = 0.65
Select bearings with higher than 90%
reliability
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Bearing Reliability
The distribution of bearing failure can be best approximated
by two and three parameter Weibull distribution.
C10 is catalog basic dynamic load rating @ LR hours of life at
speed of nR rpm
C10
Ken Youssefi 34
Example Select a deep groove ball bearing for a desired life of 5000 hours at 1725
rpm with 99% reliability. The bearing radial load is 400 lb.
C10 = 14.3 kN 30 mm Bore deep groove bearing For 90% reliability
Use 99% reliability, R = .99
= 23.7 kN
Select a 35 mm
bearing instead
of 30 mm for
90% reliability
11–6 Combined Radial and Thrust Loading
Fa = axial thrust load
Fr = radial load
Fe = equivalent radial load that does the same
damage as the combined radial & thrust loads
together
V = rotation factor
V = 1 when inner ring rotates
V = 1.2 when outer ring rotates
Two dimensionless groups: Fe/V Fr and Fa/V Fr
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11–6 Combined Radial and Thrust Loading
e is defined by the intersection
of the two lines.
Equations for the two lines
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Figure 11–6: relationship of
dimensionless group Fe/(VFr) & Fa/(VFr)
11–6 Combined Radial and Thrust Loading
X & Y factors depend upon geometry & construction of
specific bearing.
Table 11–1: representative values of X1, Y1, X2, and Y2 as
a function of e, which in turn is a function of Fa/C0
C0 = basic static load rating
Load that will produce a total permanent deformation in
the raceway and rolling element at any contact point of
0.0001 times diameter of the rolling element
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11–6 Combined Radial and Thrust Loading Table 11–1: Equivalent Radial Load Factors for Ball Bearings
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11–6 Combined Radial and Thrust Loading Table 11–2: Dimensions & Load Ratings for Single-Row 02-Series
Deep-Groove and Angular-Contact Ball Bearings
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11–6 Combined Radial and Thrust Loading
The rotation factor V is intended to correct for the
rotating ring conditions.
The factor of 1.2 for outer-ring rotation is simply an
acknowledgment that the fatigue life is reduced under
these conditions.
For Self-aligning bearings, V = 1 for rotation of either
ring.
Straight or cylindrical roller bearings will take no axial
load, or very little, the Y factor is always zero.
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11–6 Combined Radial and Thrust Loading
ABMA has established standard boundary dimensions
for bearings, which define bearing bore, outside
diameter (OD), width, and fillet sizes on the shaft and
housing shoulders.
The basic plan covers all ball and straight roller bearings
in metric sizes.
For a given bore, there is an assortment of widths &
outside diameters.
For a particular outside diameter, one can usually find a
variety of bearings having different bores and widths.
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11–6 Combined Radial and Thrust Loading
Basic ABMA plan is illustrated in Fig. 11–7
Bearings are identified by a two-digit number called the
dimension-series code
1st number = width series, 0, 1, 2, 3, 4, 5, and 6
2nd number = diameter series (outside) 8, 9, 0, 1, 2, 3, 4
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11–6 Combined Radial and Thrust Loading
Figure 11–7: Basic ABMA plan for boundary dimensions.
Apply to ball bearings, straight roller bearings, and
spherical roller bearings, but not to inch series ball
bearings or tapered roller bearings.
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11–6 Combined Radial and Thrust Loading
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Figure 11–8: Shaft & housing
shoulder diameters dS & dH
should be adequate to ensure
good bearing support
11–6 Combined Radial and Thrust Loading
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Table 11–3: Dimensions & Basic Load Ratings for Cylindrical Roller
Bearings
11–6 Combined Radial and Thrust Loading
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Table 11–4: Bearing-Life Recommendations for Various
Classes of Machinery
11–6 Combined Radial and Thrust Loading
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Table 11–5: Load-Application Factors
Use the load-application factors to increase the
equivalent load before selecting a bearing
EXAMPLE 11–4 An SKF 6210 angular-contact ball bearing has an axial load Fa of 400
lbf & a radial load Fr of 500 lbf applied with the outer ring stationary.
The basic static load rating C0 is 4450 lbf & the basic load rating C10 is
7900 lbf. Estimate the life at a speed of 720 rpm.
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11–8 Selection of Ball &
Cylindrical Roller Bearings
EXAMPLE 11–7: The second shaft on a parallel-shaft 25-hp foundry
crane speed reducer contains a helical gear with a pitch diameter of
8.08 in. Helical gears transmit components of force in the tangential,
radial, and axial directions. The components of the gear force
transmitted to the second shaft are shown in Fig. 11–12, at point A.
The bearing reactions at C and D, assuming simple-supports, are also
shown. A ball bearing is to be selected for location C to accept the
thrust, and a cylindrical roller bearing is to be utilized at location D. The
life goal of the speed reducer is 10 kh, with a reliability factor for the
ensemble of all four bearings (both shafts) to equal or exceed 0.96 for
the Weibull parameters of Ex. 11–3. The application factor is to be 1.2.
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EXAMPLE 11–7
af =1.2
T = 595(4.04) = 2404 lbf · in
FrD =
FrC =
R =
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EXAMPLE 11–7 11/14/2013 8:13 PM
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C10 = af =
Choose a 02-25 mm series, or a 03-25 mm series cylindrical roller bearing
from Table 11–3.
(b) The ball bearing at C involves a thrust component. Assuming Fa/(V Fr) > e,
1 Choose Y2 from Table 11–1.
2 Find C10
3 Identify a suitable bearing from Table 11–2, note C0.
4 Using Fa/C0 enter Table 11–1 to obtain a new value of Y2.
5 Find C10.
6 If the same bearing is obtained, stop.
7 If not, take next bearing and go to step 4.
EXAMPLE 11–7 11/14/2013 8:13 PM
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As a first approximation, take the middle entry from Table 11–1:
X2 = 0.56 Y2 = 1.63.
From Table 11–2, angular-contact bearing 02-60 mm has C10 = 55.9 kN. C0
is 35.5 kN.
which makes e from Table 11–1 approximately 0.24. Now Fa/[V Fr ] = 344/[(1)
464.4] = 0.74, which is greater than 0.24, so we find Y2 by interpolation:
EXAMPLE 11–7 11/14/2013 8:13 PM
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From Table 11–2 an angular contact bearing 02-65 mm has C10 =
63.7 kN and C0 of 41.5 kN.
making e approximately 0.23. Now from before, Fa/V Fr = 0.74, which is
greater than 0.23. We find Y2 again by interpolation:
EXAMPLE 11–7 11/14/2013 8:13 PM
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From Table 11–2 an angular-contact 02-65 mm
is still selected, so the iteration is complete
11–9 Selection of Tapered
Roller Bearings
Components of a tapered roller bearing:
1. Cone (inner ring)
2. Cup (outer ring)
3. Tapered rollers
4. Cage (spacer-retainer)
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11–9 Selection of Tapered
Roller Bearings
Assembled bearing consists of two separable
parts:
1. Cone assembly: cone, rollers, and cage
2. Cup
Bearings can be: single-row, two row, four-
row, and thrust-bearing assemblies
Auxiliary components such as spacers and
closures can be used
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11–9 Selection
of Tapered
Roller Bearings
Figure 11–13:
Nomenclature of a
tapered roller bearing.
G = location of effective
load center; use this
point to estimate radial
bearing load
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11–9 Selection of Tapered
Roller Bearings Even when an external thrust load is not
present, radial Cup load will induce a thrust
reaction within bearing because of taper.
To avoid separation of the races & rollers, this
thrust must be resisted by an equal and
opposite force.
One way of generating this force is to always
use at least two tapered roller bearings on a
shaft.
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11–9 Selection
of Tapered
Roller Bearings
Direct & indirect
mounting involve space
and compactness
needed or desired, but
with same system
stability
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Indirect mounting
Direct mounting
11–9 Selection of
Tapered Roller Bearings
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Figure 11–15: Catalog entry of single-row
straight-bore Timken roller bearings, in part.
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11–9 Selection of Tapered
Roller Bearings A radial load on a tapered roller bearing will
induce a thrust reaction.
The load zone includes about half the rollers
and subtends an angle of approximately 180◦.
Fi = induced thrust load from a radial load with
a 180◦ load zone, Timken provides the equation
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11–9 Selection of Tapered
Roller Bearings K factor is geometry specific = ratio of radial
load rating to thrust load rating
K can be first approximated with 1.5 for a radial
bearing and 0.75 for a steep angle bearing in
the preliminary selection process.
After a possible bearing is identified, exact
value of K for each bearing can be found in
bearing catalog.
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11–9 Selection of Tapered Roller
Bearings
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Figure 11–16: Direct-mounted tapered roller bearings,
showing radial, induced thrust, and external thrust
loads.
11–9 Selection of Tapered
Roller Bearings
FrA & FrB = radial loads, applied at
effective force centers GA & GB.
FiA & FiB = induced loads due to effect of
radial loads
Fae = externally applied thrust load on
shaft
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11–9 Selection of Tapered
Roller Bearings Fe = X V Fr + Y Fa
Timken recommends using X = 0.4 & V = 1 for
all cases, and using the K factor for the specific
bearing for Y. This gives an equation of the form
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11–9 Selection of Tapered
Roller Bearings Fa is net axial load carried by bearing due to
combination of induced axial load from the
other bearing & external axial load.
Only one of the bearings will carry the net axial
load. Which one it is depends on:
1. Direction the bearings are mounted
2. Relative magnitudes of induced loads
3. Direction of external load
4. Whether shaft or housing is the moving part
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11–9 Selection of Tapered
Roller Bearings First, determine visually which bearing is being
“squeezed” by the external thrust load, and
label it as bearing A.
Label the other bearing as bearing B.
If there is no external thrust, then either bearing
can arbitrarily be labeled as bearing A.
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11–9 Selection of Tapered
Roller Bearings Figure 11–17: Examples of determining which
bearing carries the external thrust load. In each
case, the compressed bearing is labeled as
bearing A.
a. External thrust applied to rotating shaft
b. External thrust applied to rotating cylinder
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11–9 Selection of Tapered Roller Bearings
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Figure 11–17
11–9 Selection of Tapered
Roller Bearings Second, determine which bearing actually
carries the net axial load.
If induced thrust FiA from bearing A happens to
be larger than the combination of external
thrust & thrust induced by bearing B, then
bearing B will carry the net thrust load.
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11–9 Selection of Tapered
Roller Bearings
If equivalent radial load is ever less than original
radial load, then original radial load should be
used.
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EXAMPLE 11–8
The shaft depicted in Fig. 11–18a carries a helical gear
with a tangential force of 3980 N, a radial force of 1770 N,
and a thrust force of 1690 N at the pitch cylinder with
directions shown. The pitch diameter of the gear is 200
mm. The shaft runs at a speed of 800 rpm, and the span
(effective spread) between the direct-mount bearings is
150 mm. The design life is to be 5000 h and an application
factor of 1 is appropriate. If the reliability of the bearing set
is to be 0.99, select suitable single-row tapered roller
Timken bearings.
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EXAMPLE 11–8
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Find reactions at A & B
Trial 1: With direct
mounting of bearings
and application of
external thrust to shaft,
the squeezed bearing
is bearing A.
EXAMPLE 11–8
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Using K of 1.5 as initial guess for each bearing, the
induced loads from the bearings are
Since FiA is clearly less than FiB + Fae, bearing A carries
the net thrust load, and Eq. (11–16) is applicable.
RD=
EXAMPLE 11–8
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From Fig. 11–15, tentatively select type TS 15100 cone
and 15245 cup, which will work: KA = 1.67, C10 = 12
100 N.
For bearing B, from Eq. (11–7), the catalog entry C10
should equal or exceed
Tentatively select the bearing identical to bearing A,
which will work: KB = 1.67, C10 = 12 100 N.
EXAMPLE 11–8
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Trial 2: Repeat the process with KA = KB = 1.67 from
tentative bearing selection.
For bearing A, from Eq. (11–7) the corrected catalog
entry C10 should equal or exceed
EXAMPLE 11–8
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Select cone and cup 15100 and 15245, respectively, for
both bearing A and B.
Effective load center is located at a = −5.8 mm, that is,
5.8 mm into the cup from the back.
The shoulder-to-shoulder dimension = 150 − 2(5.8) =
138.4 mm
11–11 Lubrication
If relative velocity of sliding surfaces is
high enough, then lubricant action is
hydrodynamic
Elastohydrodynamic lubrication (EHD) =
phenomenon that occurs when a
lubricant is introduced between surfaces
that are in pure rolling contact.
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11–11 Lubrication
When a lubricant is trapped between two
surfaces in rolling contact, a tremendous
increase in pressure within the lubricant
film occurs.
Viscosity is exponentially related to
pressure,
A very large increase in viscosity occurs in
the lubricant that is trapped between the
surfaces
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11–11 Lubrication
Purposes of an antifriction-bearing
lubricant:
1. Provide a film of lubricant between
sliding & rolling surfaces
2. Help distribute & dissipate heat
3. Prevent corrosion of bearing surfaces
4. Protect the parts from entrance of
foreign matter
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Use Grease When Use Oil When
Temperature ≤ 93°C Temperatures are high
Speed is low Speed is high
Unusual protection is
required from entrance of
foreign matter
Oil tight seals are readily
employed
Simple bearing enclosures
are desired
Bearing type is not
suitable for grease
lubrication
Operation for long periods
without attention is desired
Bearing is lubricated from
a central supply
11–11 Lubrication 11/14/2013 8:13 PM
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11–12 Mounting and Enclosure
The housing bore & shaft outside diameter
must be held to very close limits.
One of the bearings usually has the added
function of positioning or axially locating
the shaft.
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11–12 Mounting and Enclosure
Figure 11–20: A common bearing mounting. Outer
ring of right-hand bearing floats in the housing.
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11–12 Mounting and Enclosure
Fig. 11–20: The function of shaft shoulder may
be performed by:
1. retaining rings
2. hub of a gear or pulley
3. spacing tubes or rings
The round nuts may be replaced by:
1. retaining rings
2. washers locked in position by screws
3. Cotters
4. taper pins
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11–12 Mounting and Enclosure
Fig. 11–20: The housing shoulder may be
replaced by:
1. a retaining ring
2. Outer ring of bearing may be grooved for a
retaining ring
3. a flanged outer ring may be used
4. Force against outer ring of the left-hand
bearing is usually applied by:
a. cover plate
b. retaining rings
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11–12 Mounting and Enclosure
Figure 11–21: An
alternative bearing
mounting to that in Fig.
11–20
Outer races are completely
retained.
If distance between
bearings is great,
temperature rise during
operation may expand the
shaft enough to destroy the
bearings.
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Figure 11–22: Two-bearing mountings
The effect of mounting is to preload the bearings
in an axial direction.
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Figure 11–23: Mounting
for a washing machine
spindle.
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11–12 Mounting and Enclosure
When maximum stiffness & resistance to shaft
misalignment is desired, pairs of angular
contact ball bearings are often used in an
arrangement called duplexing.
Bearings manufactured for duplex mounting
have their rings ground with an offset, so that
when a pair of bearings is tightly clamped
together, a preload is automatically established.
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Figure 11–24: Arrangements of angular ball
bearings
a. Duplex Face-to-face mounting, DF
b. Duplex Back to back mounting, DB
c. Duplex Tandem mounting, DT
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Figure 11–24: DF mounting
DF mounting, will take heavy radial loads and
thrust loads from either direction.
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Figure 11–24: DB mounting
DB mounting has the greatest aligning stiffness
Good for heavy radial loads thrust loads from
either direction.
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Figure 11–24: DT mounting
DT, is used where thrust is always in same
direction
A preload, if required, must be obtained in some
other manner
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Bearings are usually mounted with the rotating
ring a press fit.
The stationary ring is then mounted with a push
fit.
This permits the stationary ring to creep in its
mounting slightly, bringing new portions of the
ring into the load-bearing zone to equalize wear.
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Preloading
The object of preloading is to:
1. remove internal clearance
usually found in bearings
2. increase fatigue life
3. decrease shaft slope at the
bearing
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Preloading
Methods of Preloading straight roller bearings:
1. Mounting bearing on a tapered shaft or sleeve
to expand the inner ring
2. Using an interference fit for the outer ring
3. Purchasing a bearing with the outer ring
preshrunk over the rollers
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Preloading
Ball bearings are usually preloaded by the axial
load built in during assembly.
Bearings of Fig. 11–24a and b are preloaded in
assembly because of differences in widths of
the inner & outer rings.
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Alignment
Permissible misalignment in bearings depends
on:
Type of bearing
Geometric & material properties of specific bearing
In general, cylindrical & tapered roller bearings
require alignments that are closer than deep-
groove ball bearings.
Spherical ball bearings & self-aligning bearings
are the most forgiving.
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Alignmentm, Table 7–2: Typical Max Ranges for
Slopes & Transverse Deflections
Life of bearing decreases significantly when
misalignment exceeds allowable limits.
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Enclosures
To exclude dirt and foreign matter and to retain
the lubricant, bearing mountings must include a
seal.
Figure 11–26: Typical sealing methods
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Used with grease lubrication
when speeds are low
Rubbing surfaces should
have a high polish
Felt seals should be
protected from dirt by:
placing them in machined
grooves
using metal stampings as
shields
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Enclosures
An assembly consisting of
rubbing element and,
generally, a spring backing,
which are retained in a sheet-
metal jacket.
usually made by press fitting
them into a counter bored hole
in the bearing cover.
They should not be used for
high speeds
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Enclosures
Effective for high-speed
May be used with either oil or
grease.
At least three grooves should
be used, and they may be cut
on either bore or outside
diameter.
Clearance may vary from 0.010
to 0.040 in, depending upon
speed and temperature.
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3rd Exam
On Wednesday 20/11/2013 at
11:00
Tested Material: Chapter 11
Practice Problems: 14, 17, 19, 27, 28, 41
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