4/7/2022

ROLLING CONTACT BEARINGS

• Bearing Nomenclature and Definitions

• Bearing Types
• Bearing Life
• Combined Radial and Thrust Loading
• Selection of Radial and Cylindrical Roller
Bearings

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Shigley’s Mechanical Engineering Design

Applications of Rolling Contact Bearing

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Images of Rolling Contact Bearing

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Shigley’s Mechanical Engineering Design

Images of Rolling Contact Bearing Cont’d

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Nomenclature of a Ball Bearing

General Motors Corp. Used with

permission, GM Media Archives.

Fig. 11–1
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Shigley’s Mechanical Engineering Design

Types of Ball Bearings

Fig. 11–2
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Types of Roller Bearings

Straight Cylindrical Spherical Roller, thrust Tapered roller, thrust

Fig. 11–3
Needle Tapered roller Steep-angle tapered roller
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Shigley’s Mechanical Engineering Design

Bearing Life Definitions

 Bearing Failure: Spalling or pitting of an area of 0.01 in2
 Life: Number of revolutions (or hours @ given speed) required for
failure.
◦ For one bearing
 Rating Life: Life required for 10% of sample to fail (Reliability of
90%)
◦ For a group of bearings
◦ Also called Minimum Life or L10 Life
 Median Life: Average life required for 50% of sample to fail.
◦ For many groups of bearings
◦ Also called Average Life or Average Median Life
◦ Median Life is typically 4 or 5 times the L10 Life

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Load Rating Definitions

 Catalog Load Rating, C10: Constant radial load that causes 10%
of a group of bearings to fail at the bearing manufacturer’s
rating life.
◦ Depends on type, geometry, accuracy of fabrication, and
material of bearing
◦ Also called Basic Dynamic Load Rating, and Basic Dynamic
Capacity
 Basic Load Rating, C: A catalog load rating based on a rating life
of 106 revolutions of the inner ring.
◦ The radial load that would be necessary to cause failure at such a
low life is unrealistically high.
◦ The Basic Load Rating is a reference value.

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Shigley’s Mechanical Engineering Design

Load Rating Definitions

 Static Load Rating, Co:

Static radial load which corresponds to a permanent deformation of
rolling element and race at the most heavily stressed contact of
0.0001d.
◦ d = diameter of roller
◦ Used to check for permanent deformation
◦ Used in combining radial and thrust loads into an equivalent
radial load
 Equivalent Radial Load, Fe:
Constant stationary load applied to bearing with rotating inner ring
which gives the same life as actual load and rotation conditions.

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Load-Life Relationship
 Nominally identical groups of bearings are tested to the life-failure
criterion at different loads.
 A plot of load vs. life on log-log scale is approximately linear.
 Using a regression equation
to represent the line,

◦ a = 3 for ball bearings

◦ a = 10/3 for roller bearings
(cylindrical and tapered
roller)

Fig. 11–4
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Shigley’s Mechanical Engineering Design

Load-Life Relationship
 Applying Eq. (11–1) to two load-life conditions,

 Denoting condition 1 with R for catalog rating conditions, and

condition 2 with D for the desired design conditions,

 The units of L are revolutions. If life is given in hours at a given

speed n in rev/min, applying a conversion of 60 min/h,

 Solving Eq. (a) for FR, which is just another notation for the
catalog load rating,

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Load-Life Relationship

 The desired design load FD and life LD come from the problem
statement.
 The rated life LR will be stated by the specific bearing
manufacturer. Many catalogs rate at LR = 106 revolutions.
 The catalog load rating C10 is used to find a suitable bearing in
the catalog.

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Shigley’s Mechanical Engineering Design

Load-Life Relationship

 It is often convenient to define a dimensionless multiple of rating

life

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Dimension-Series Code
 ABMA standardized dimension-series code represents the relative
size of the boundary dimensions of the bearing cross section for
metric bearings.
 Two digit series number
 First digit designates the width series
 Second digit designates the diameter series
 Specific dimensions are tabulated in catalogs under a specific
series

Fig. 11–7
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Shigley’s Mechanical Engineering Design

Representative Catalog Data for Ball Bearings (Table 11–2)

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Representative Catalog Data for Cylindrical Roller Bearings

(Table 11–3)

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Shigley’s Mechanical Engineering Design

Example

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Combined Radial and Thrust Loading

 When ball bearings carry both an
axial thrust load Fa and a radial
load Fr, an equivalent radial load
Fe that does the same damage is
used.
 A plot of Fe/(VFr) vs. Fa /(VFr) is
obtained experimentally.
 V is a rotation factor to account for
the difference in ball rotations for
outer ring rotation vs. inner ring
rotation.
◦ V = 1 for inner ring rotation
◦ V = 1.2 for outer ring rotation
 Set FD = Fe
Fig. 11–6
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Shigley’s Mechanical Engineering Design

Combined Radial and Thrust Loading

 The data can be approximated by
two straight lines

 X is the ordinate intercept and Y is

the slope
 Basically indicates that Fe equals
Fr for smaller ratios of Fa/Fr, then
begins to rise when Fa/Fr exceeds
some amount e

Fig. 11–6
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Combined Radial and Thrust Loading

 It is common to express the two
equations as a single equation

where
i = 1 when Fa /(VFr) ≤ e
i = 2 when Fa /(VFr) > e

 X and Y factors depend on geometry

and construction of the specific
bearing.

Fig. 11–6
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Shigley’s Mechanical Engineering Design

Equivalent Radial Load Factors for Ball Bearings

 X and Y for specific bearing obtained from bearing catalog.

 Table 11–1 gives representative values in a manner common to
many catalogs. Table 11–1

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Equivalent Radial Load Factors for Ball Bearings

Table 11–1

 X and Y are functions of e, which is a function of Fa/C0.

 C0 is the basic static load rating, which is tabulated in the catalog.
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Shigley’s Mechanical Engineering Design

Example 2

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Example 2 (continued)

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Shigley’s Mechanical Engineering Design

Bearing Life Recommendations (Table 11–4)

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Recommended Load Application Factors (Table 11–5)

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Shigley’s Mechanical Engineering Design

Assignment 2 - Problem 1
The shaft shown here rotates at 1500 rev/min. The bearings are to
have 60kh at a combined reliability of 90%. The belt in the loose
side of pulley A is 15 percent of the tension on the tight side.
Select deep groove bearings for use at O and E.
Use application factor of unity.

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Assignment 2 - Problem 2

An 02-Series single-row deep groove ball bearing

rotating at 400 rev/min is to be selected for the following
applications:

Radial Load = 8 kN
Axial Load = 2 kN
Design Life = 10 kh
Desired Reliability = 90%

Specify the smallest bore size that can satisfy the above conditions.

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Shigley’s Mechanical Engineering Design

Courtesy of The Timken Company.

Tapered Roller Bearings
 Two separable parts
◦ Cone assembly
 Cone (inner ring)
 Rollers
 Cage
◦ Cup (outer ring)
 Rollers are tapered so virtual
apex is on shaft centerline
 Taper allows for pure rolling
of angled rollers
 Distance a locates the
effective axial location for
force analysis Courtesy of The Timken company.

Fig. 11–13
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Tapered Roller Bearings

 Straight roller bearings can carry large radial loads, but no axial
load.
 Ball bearings can carry moderate radial loads, and small axial
loads.
 Tapered roller bearings rely on roller tipped at an angle to allow
them to carry large radial and large axial loads.
 Tapered roller bearings were popularized by the Timken Company.

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Shigley’s Mechanical Engineering Design

Mounting Directions of Tapered Roller Bearings

 Mount pairs in opposite
directions to counter the axial
loads
 Can be mounted in direct
mounting or indirect
mounting configurations
 For the same effective spread
ae, direct mounting requires
greater geometric spread ag
 For the same geometric
spread ag, direct mounting
provides smaller effect
spread ae
Courtesy of The Timken
Fig. 11–14 Company.

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Induced Thrust Load

 A radial load induces a thrust reaction due to the roller angle.

 K is ratio of radial load rating to thrust load rating

 K is dependent on specific bearing, and is tabulated in catalog

Fig. 11–16
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Shigley’s Mechanical Engineering Design

Equivalent Radial Load

 The equivalent radial load for tapered roller bearings is found in
similar form as before,

 Timken recommends X = 0.4 and Y = K

 Fa is the net axial load carried by the bearing, including induced

thrust load from the other bearing and the external axial load
carried by the bearing.
 Only one of the bearings will carry the external axial load

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Bearing Lubrication
 The purposes of bearing lubrication
◦ To provide a film of lubricant between the sliding and rolling
surfaces
◦ To help distribute and dissipate heat
◦ To prevent corrosion of the bearing surfaces
◦ To protect the parts from the entrance of foreign matter

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Bearing Lubrication
 Either oil or grease may be used, with each having advantages in
certain situations.

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Some Common Bearing Mounting Configurations

Fig. 11–20

Fig. 11–21

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Shigley’s Mechanical Engineering Design

Some Common Bearing Mounting Configurations

Fig. 11–22
Courtesy of The Timken Company.

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Some Common Bearing Mounting Configurations

Courtesy of The Timken Company.

Fig. 11–23

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Shigley’s Mechanical Engineering Design

Preloading

 Object of preloading
◦ Remove internal clearance
◦ Increase fatigue life
◦ Decrease shaft slope at bearing

Fig. 11–25

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Enclosures

 Common shaft seals to exclude dirt and retain lubricant

Fig. 11–26
General Motors Corp. Used with permission, GM Media Archives.

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