1. SURFACE STRESSES
• Mating gear have a
combination of rolling
and sliding at their
interface. The stresses
at tooth surface are
dynamic Hertzian
contact stresses in
combined rolling and
sliding.
• The surface stresses in
the gear teeth were
investigated by
Buckingham who
recognized that two
cylinders having the
same radius of
curvature as the gear
teeth at the pitch
point and radially
loaded in rolling
contact.

2. SURFACE STRESSES
• Where Wt is tangential
load or force.
• D is the pitch diameter of
the two gears in mesh. F is
the face width. I is the
dimensionless surface
geometry factor for
pitting resistance.
• Cp is an elastic
coefficient that
accounts for differences
in the gear and pinion
material constants.

3. SURFACE STRESSES
• The factors Ca , Cm ,
Cv and Cs are equal
respectively to Ka, Km,
Kv and Ks.
• Surface geometry factor
I: This factor takes into
account the radii of
curvature of the gear
teeth and pressure
angle.
ρp and ρg are radii of
curvature of the pinion
and gear . The radii of the
curvature of the teeth are
calculated from the mesh
geometry.

4. SURFACE STRESSES
• Elastic Coefficient
Cp: The elastic
coefficient
accounts for
differences in tooth
materials.
• Ep and Eg are
moduli of elasticity
for pinion and
gear.Ѵp and Ѵg are the
Poisson’s ratios.

5. SURFACE STRESSES
• Surface Finish
Factor Cf: It is used
to account for
unusually rough
surface finishes on
gear teeth. For the
conventional
methods of gear
Cf be set to 1.

6. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
• EXAMPLE:
• Determine the surface
stresses in the gear
teeth of the 3-gear
train containing a
pinion, an idler and
gear. The transmitted
load on the gear teeth
is 432 lb. The pinion has
14 teeth , a 25˚ pressure
angle , and pd = 6.
• The idler has 17 teeth
and gear has 49 teeth.
Pinion speed is 2500
rpm. Face width is 2
inches.
• Assumptions: The teeth
are standard AGMA full
depth profiles. The load
and source are both
uniform in nature. A
quality index of 6 will
be used. All gears are
made of steel with Ѵ =
0.28.

7. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
• •

8. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
• •

9. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
• •

10. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
• •

11. SURFACE STRESSES ANALYSIS OF SPUR
GEAR TRAIN
•

12. MATERIAL STRENGTHS
• Since both of the gear failure modes involve fatigue
loading, material fatigue strength data are needed,
both for bending stresses and for surface contact
stresses. Test data for fatigue strengths of most gear
materials have been compiled by AGMA.
• AGMA BENDING FATIGUE –STRENGTHS FOR GAER
MATERIALS:
• The published AGMA data for both bending and
surface- strengths are in effect, partially corrected
fatigue strengths, since they are generated
appropriately sized parts having the same
geometry, surface finish etc.

13. •

14. • LIFE FACTOR KL:
• Since the test data are for a life of 1E7 cycles. A
shorter or longer cycle life will require
modification of the bending fatigue strength
based on the S – N relationship for the material.
The number of load cycles in this case is defined
as the number of mesh contacts.
• Figure shows the S – N curves for the bending
fatigue strength of steels having several different
tensile strengths as defined by their Brinell
hardness numbers. Curve fitted equations are
also shown in the figure for each S – N line. These
equations can be used to compute the
appropriate KL factor for a required number of
load cycles N.

16. • The upper portion of the shaded zone can be
used for commercial applications. The lower
portion of the shaded zone is typically used for
critical service applications where little pitting
and tooth wear is permissible and where smooth
ness of operation and low vibration levels are
required.
• TEMPERATUE FACTOR KT:
• The lubricant temperature is reasonable measure
of gear temperature. For steel materials in oil
temperatures up to about 250ºF, KT can be set to
1. For higher temperature KT can be estimated
from

17. •

20. •

21. • SURFACE – LIFE FACTOR CL :
• Since the test data are for a life of 1E7 cycles. A
shorter or longer cycle life will require
modification of the bending fatigue strength
based on the S – N relationship for the material.
The number of load cycles in this case is defined
as the number of mesh contacts.
• Figure shows the S – N curves for the surface
fatigue strength of steels having several different
tensile strengths as defined by their Brinell
hardness numbers. Curve fitted equations are
also shown in the figure for each S – N lines. These
equations can be used to compute the
appropriate CL factor for a required number of
load cycles N.

23. • The upper portion of the shaded zone can be
used for commercial applications. The lower
portion of the shaded zone is typically used for
critical service applications where little pitting
and tooth wear is permissible and where smooth
ness of operation and low vibration levels are
required.
• HARDNESS RATIO FACTOR CH: This factor is a
function of the gear ratio and relative hardness of
pinion and gear, CH is always 1.0. CH is only
applied to the gear- tooth strength. Two formulas
for its calculation are suggested in the standard.

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