Chapter 11
Chapter 11
Load-Life Relationship
Using a regression
equation to represent
the line,
◦ a = 3 for ball
bearings
◦ a = 10/3 for roller
bearings
(cylindrical and
tapered roller)
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.
It is often convenient to define a dimensionless multiple of rating life
Reliability vs. Life
Defining the life measure in dimensionless form as x = L/L10, the reliability is expressed with a
Weibull distribution as
1|Page
Chapter 11
Reliability vs. Life
Solving Eq. (11–4) for x yields
Relating Load, Life, and Reliability
Relating Load, Life, and Reliability
Along a constant load line ( AB), Eq. (11–4) applies:
Along a constant reliability contour ( BD), Eq. (11–2) applies:
Solving for xB,
2|Page
Chapter 11
Relating Load, Life, and Reliability
Catalog information is at point A, at coordinates C10 and
x10 =L10 /L10 =1, on the 0.90 reliability contour.
The design information is at point D, at coordinates FD and xD,
on the R=R D reliability contour.
The designer must move from point
D to point A via point B.
Fig. 11–5
24
Copyright © 2015 McGraw
-Hill Education. All rights reserved. No reproduction or distribution without the prior written fconsent
McGraw-Hill
o
Education.
Shigley’sMechanical Engineering Design
For two bearings on a shaft, R = RARB
If the bearings are to be identical, each bearing should have a reliability equal to the square root
of the total desired reliability RA=RB = √R.
3|Page
Chapter 11
Combined Radial and Thrust Loading
The data can be approximated by
Combined Radial and Thr
two straight lines
It is common to express the two
equations as a single equation
were
i = 1 when Fa /(VFr) ≤ e
i = 2 when Fa /(VFr) > e
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
Copyright © 2015 McGraw
-Hill Education. All rights reserved. No reproduction or distribution without the prior written fconsent
McGraw-Hill
o
Education.
Shigley’sMechanical Engineering Design
◦
V = 1 for inner ring rotation
◦
V = 1.2 for outer ring rotation
X and Y factors depend on geometry
36
and construction of the specific
bearing.
4|Page
Chapter 11
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
Variable Loading with Piecewise Constant Loading
45
Copyright © 2015 McGraw
-Hill Education. All rights reserved. No reproduction or distribution without the prior written fconsent
McGraw-Hill
o
Education.
Shigley’sMechanical Engineering Design
5|Page
Chapter 11
Variable Loading with Periodic Variation
Variable Loading with Piecewise Constant Loading
Fig. 11–11
50
Copyright © 2015 McGraw
-Hill Education. All rights reserved. No reproduction or distribution without the prior written fconsent
McGraw-Hill
o
Education.
Shigley’sMechanical Engineering Design
6|Page
0
