Table 12-4 shows experimentally determined load
factors,
K,
fatigue strengths,
Sc
,
and strength factors for a number of materials running either against
themselves or against hardened tool steel.[26] See the original reference for a
complete listing, as some materials were omitted here due to lack of space. Two
different loading modes are also addressed in separate sections of the table:
pure rolling, and rolling with 9% sliding. The first column of the table
defines the material. In each section, the next two columns give the
K
value
and the surface fatigue strength at 1
E
8 cycles as tested. The next two columns
contain strength factors
and 
, which represent the slope and intercept of
the S-N diagram (on log-log coordinates) for the
surface fatigue strength of the material as determined by regression on large
amounts of test data. These factors can be used in the equation of the
statistically fitted S-N line to find the expected cycle life N for
the applied
stress
level.
The
K
values in Table 12-4 can be used directly in
equation 12.25d to calculate an allowable load
F
for
the selected material at 1
E
8 cycles of stress. For other desired design
cycle lives, first calculate the largest negative (compressive) radial stress
for your design from the appropriate equations as defined in the preceding
sections. Then calculate
K
from equation 12.25e and use it and the values
of
and from Table 12-4 to find the value of N for
the application from equation 12.26. Since there is no endurance limit for
surface fatigue loading, we can expect pitting to begin after approximately N stress
cycles at the level of nominal stress contained in your calculated K factor.
Alternatively,
a desired number of cycles
N
can be chosen and an allowable design stress
level
z
for
a chosen material computed from equations 12.25e and 12.26. A safety factor can
be applied either by selecting a material with a longer cycle life than
required for the application or by sizing the parts to have a stress level
below the calculated allowable stress level for a necessary number of cycles.
The
strength values in Table 12-4 were obtained using rollers in contact,
lubricated with a light mineral oil of 280-320 SSU at 100
°
F. The
researchers report that “an orderly transition occurs from pitting fatigue to
abrasive wear as percent sliding is increased.” Pitting failures were observed
under as high as 300% sliding on some cast irons, and abrasive wear was seen at
as low as 9% sliding on hardened steels under high stress. They also note that
the addition of oxide coatings, fortified (EP) lubricants, or lead as an alloy
ing element all reduced tangential stress levels and increased fatigue life or
allowable % sliding.
The
addition of phosphate coatings to the surfaces reduced sparking and flashing of
lubricant, reduced the friction coefficient, and also increased fatigue life.
They saw evidence of pitting starting both at the surface under high % sliding
and below the surface in pure rolling or low-percent-sliding situations.[26]
Increased sliding percentages reduce fatigue life but not linearly. Figure
12-26 shows some
S-N
curves (from reference 26) for three materials
with various percentages of sliding.
The
speed of stress cycling only affected nonmetallic materials, wherein friction
heat blistered or yielded the material. A material’s stiffness is a factor,
however. Lowermodulus materials reduce the contact stress because their larger
deflections increase the contact-patch area. Cast iron on cast iron had longer
life than cast iron on hardened steel. The free graphite in cast iron also
makes it a good choice in contact situations, as it acts to retard adhesion as
well as being a dry lubricant, though the lower grades of CI have strengths too
low to be useful in this situation. Nodular iron in its harder forms may be a
better choice. Hardness of a material was not found to correlate closely with
its surface endurance. Some softer steels performed better than some harder
ones.[26]
Typical
curves showing load-life relationships for common gear and cam materials.
Curves in (
a
) are for 100-70-30 nodular iron (HB 240-260)
and class 45 gray cast iron (HB 220-240), both materials running on carbon tool
steels (HRC 60-62). Curves in (
b
) are for continuous-cast bronze running on
hardened steel. Curves in (
c
) are for heat-treated 4150 steel running
against the same material, but phosphate coated. In all charts, 9% sliding
velocity is 54 fpm; 42.8% sliding velocity is 221 fpm.
FIGURE 12-26
Load-life
curves for some combinations of materials in combined rolling and sliding
Source: R. A. Morrison, “Load/Life Curves for Gear and Cam Materials,” Machine
Design, vol. 40, pp. 102–108, Aug. 1, 1968, A Penton Publication, Cleveland,
Ohio, with permission
EXAMPLE 12-5
Finding
the Safety Factor in Surface Fatigue.
Problem:
Choose a material
to provide 10 years of life for the cam and roller follower in Example 12-4.
Given:
The stresses
are as shown in Example 12-4. The roller follower is turning at 4 000 rpm.
Assumptions:
There
is 9% sliding combined with rolling. The roller follower is made from HRC 60-62
tool steel. The cam can be of any suitable material from Table 12-4. The
machine will operate 3 shifts/day for 345 days/year.
Solution:
1
Calculate the required cycle life from the given data:
2
The maximum normal stress calculated in Example 12-4 is 56 858 psi compressive.
Its
K
factor can be calculated from equation 12.25d
(p. 381). The previously calculated material constants
m
1
and
m
2 are needed:
3
A trial material must be selected from Table 12-4 (pp. 382–383). With a
K
this
low, virtually any of the steels or ductile irons can probably be used. We will
try the Nodular iron, Gr. 80-60-03, h-t HB 207-241 (#18 in part 1 of the
table), since it is running against a hardened tool-steel roller. The slope and
intercept factors of this steel for rolling with 9% sliding are
4
These are used in equation 12.26 (p. 381) along with the value of K from
equation (c) above to find the number of cycles that can be expected at this
load before pitting begins.
5
A safety factor against pitting can now be calculated from the ratio of the
projected cycle life and the desired number of cycles.
Copyright 2004, Industrial
Press, Inc., New York, NY