Page 228 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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limits, Hlim and bending endurance limits, of commonlyusedgearmaterials for
Flim
a medium material quality grade. General design practice would use the data below
the average, that is, between MQ (medium quality) and ML (low quality). The bending
endurance limits of a completely reverse stress are 70% of the unidirectional value [16].
When design lives required are different from those in the tests, endurance limits
obtained from the tests may be modified by multiplying life factors K HN for contact
stress and K FN forbendingstressThenumberofloadcyclesiscalculatedbythe same
equation for both contact and bending stress, as
N = 60njL (8.84)
h
where N is the number of load cycles; L is design life in hours; n is rotational speed of
h
gearsinrpm and j is the number of gear teeth meshing per revolution.
Thus, the allowable contact stress corresponding to the design life and safety factor is
calculated by
K HN H lim

[ ]= (8.85)
H
S
H
where
K HN –life factor for contact stress. It accounts for the actual number of contact stress
7
cycles different from 5 × 10 cycles when the data were produced for the contact
endurance limits. The life factor for contact stress K varies from 0.85 to 1.6,
HN
depending on the actual number of contact stress cycles, materials and heat
treatments.
S –safety factor for contact strength. Since gears can still operate even after surface
H
failure gives a noise warning, safety factors are selected within a range of 0.85–1.6
corresponding to reliabilities from low to high. The usual selection is S = 1.0.
H
The allowable bending stress corresponding to the design life and safety factor is cal-
culated in a way similar to that of allowable contact stress, as
K
FN F lim
[ ]= Y (8.86)
F ST
S
F
where
K – life factor for bending stress, which is used to adjust bending endurance limit
FN
6
to a life other than 3 × 10 cycles when the data were produced for the bending
endurance limits. The life factor for bending stress varies from 0.85 to 2.5,
depending on the actual number of bending stress cycles, materials and heat
treatments.
Y ST – stress correction factor for testing gears, usually select Y ST = 2.
S F – safety factor for bending strength. Since tooth breakage is sudden and
catastrophic, resulting in the end service of a transmission system, safety factors
are usually selected in a range from 1.25 to 1.5; larger than the safety factor
against pitting.
Life factors for contact or bending stress are selected according to the actual number
of stress cycles, materials and heat treatments. The smaller the actual number of stress
cycles and the harder the materials, the greater the life factor that can be used. For a
higher number of cycles or for critical applications where the tolerance for pitting and
tooth wear is minimal, the average or below the average value is used for most cases to
ensure a conservative design. Detailed data for life factors can be found in references
[9, 14, 15].