2. INTRODUCTION
• Pitting is a surface fatigue resulting from
repetitions of high contact stress
• Hertzian contact stress, with tooth bending and
shearing are produced when gear meshes
• Deciding parameter in finding the dimensions of
gear
• The spur gear with higher module is the best
choice for transmitting large power between the
parallel shafts
3. CONTACT STRESS
• beside contact pressure, sliding velocity,
viscosity of lubricant as well as other factors
such as frictional forces, contact stresses also
influence the formation of pits on the tooth
• calculating gear contact stresses use Hertzs
equations, which were originally derived for
contact between two cylinders
4. Hertz Contact Stress
• Contact failure in gears is predicted by
comparing the calculated Hertz contact stress
to experimentally determined value
• problems frequently occurs when two
members with curved surfaces are deformed
when pressed against one another giving rise
to an area of contact under compressive
stresses
5. the area of contact under load is a narrow
rectangle of width B and length L the stress
distribution pattern is elliptical across the width
*Ali RaadHassan, “Contact Stress Analysis of Spur Gear Teeth Pair”, World Academy of Science, Engineering and
Technology 58, 2009.
6. The value of contact pressure is given by
Pc max =
4𝐹
𝜋𝐵𝐿
Where B =
8𝐹
𝜋𝐿
×
1−𝜗12
𝐸1
+
1−𝜗22
𝐸2
1
𝐷1
+
1
𝐷2
F – applied force
1, 2 are poison’s ratio of 2 materials of cylinders
D1,D2 are respective diameters
E1. E2 are respective young’s modulus
Assuming 1=2=0.3
We can write the contact pressure as
* Bharat Gupta, Mr. Abhishek Choubey, Mr. Gautam V. Varde, “Contact Stress Analysis of Spur Gear”, International Journal of
Engineering Research & Technology (IJERT), Vol. 1 Issue 4, June – 2012.
7. Pc max = 0.35 ×
𝐹
𝐿
×
1
𝑅1
+
1
𝑅2
1
𝑅1
+
1
𝑅2
• The Hertz equations discussed so far can be used to
calculate the contact stresses in case of tooth
surfaces of two mating spur gears
• Though an approximation, the contact aspects of
such gears can be taken to be equivalent to those of
cylinders having the same radii of curvature at the
contact point as the load transmitting gears have.
• Radius of curvature changes continuously in case of
an involutes curve
* Bharat Gupta, Mr. Abhishek Choubey, Mr. Gautam V. Varde, “Contact Stress Analysis of Spur Gear”, International Journal of
Engineering Research & Technology (IJERT), Vol. 1 Issue 4, June – 2012.
8. Now by using following equations for gears
F=
Ft
cos 𝛼
L=b
R1 = (d1×sinα)/2
R2 = (d2×sinα)/2
Where, Ft is tangential force
b is tooth width
R1 &R2 radii of curvature at pitch point
d1 & d2 are pitch circle dia of the gears
* Bharat Gupta, Mr. Abhishek Choubey, Mr. Gautam V. Varde, “Contact Stress Analysis of Spur Gear”, International Journal of
Engineering Research & Technology (IJERT), Vol. 1 Issue 4, June – 2012.
9. To simplify the equation of contact pressure is written
as
Pp = ym ×yp
Ft
𝑏×𝑑1
×
𝑢+1
𝑢
Allowable Pp=
Pp
𝑓𝑜𝑠
U=
𝑑2
𝑑1
ym is material coefficient
ym = 0.35 × 𝐸
yp is pitch point coefficient
yp =
1
cos 𝛼+tan 𝛼𝑤
* Bharat Gupta, Mr. Abhishek Choubey, Mr. Gautam V. Varde, “Contact Stress Analysis of Spur Gear”, International Journal of
Engineering Research & Technology (IJERT), Vol. 1 Issue 4, June – 2012.
10. MODELING OF SPUR GEAR
• Solid Works CAD software is used
• The method of gear tooth geometry and parametric
modeling is as follow,
Determining the basic parameter
Determining the geometric parameter
The characteristic parameter
• to establish precise involute gear profile curve, the
parameter equation of the standard involutes
curves
X=rbsin- rbcos
y=rbcos+rbsin and z=0
11. • In order to get the correct assembly in Solid Works:
• The axes of pinion and gear must be parallel to each other and the
center distance of two gears must be equal to the sum of the two
pitch circles radius of gear.
• And at the same time, the tooth surface contact of pinion and
gear must be tangential to the point of contact.
The main dimension and parameters for standard 20⁰, full depth
involute spur gear are,
27. CONLUSION AND FUTURE WORK
• These results reveal that Maximum allowable
Contact Pressure decreases with increase in
module.
• Both analytical and ANSYS results follow same
trend i.e. contact pressure decreases with
increase in module.
• And finally we observed the factor of safety is
also increased with increasing the module
28. FUTURE SCOPE
• Applying gear coatings gives decreased values
of Contact stresses in mating gears.
• Coating thickness should be chosen carefully
in order to avoid problems like jamming,
creation of uneven surfaces, etc
29. References
• Ali RaadHassan, “Contact Stress Analysis of Spur Gear Teeth Pair”, World Academy
of Science, Engineering and Technology 58, 2009.
• Bharat Gupta, Mr. Abhishek Choubey, Mr. Gautam V. Varde, “Contact Stress
Analysis of Spur Gear”, International Journal of Engineering Research & Technology
(IJERT), Vol. 1 Issue 4, June – 2012.
• Ramalingam Gurumani, Subramaniam Shanmugam,”Modeling and Contact
Analysisof Crowned Spur Gear Teeth”, Engineering MECHANICS, Vol. 18, 2011.
• Sushil Kumar Tiwari, Upendra Kumar Joshi,” Stress Analysis of Mating Involute Spur
Gear Teeth” International Journal of Engineering Research & Technology (IJERT),
Vol. 1 Issue 9, November- 2011.
• Vivek Karaveer, Ashish Mogrekar and T. Preman Reynold Joseph, “Modeling and
Finite Element Analysis of Spur Gear” International Journal of Current Engineering
and Technology, Vol.3,No.5(Dec- 2013)
