The document discusses key terminology used in gear design such as pitch circle, base circle, addendum, dedendum, and pressure angle. It also summarizes Lewis bending equation assumptions and the AGMA standards process for spur and helical gear design. This includes calculating torque, tangential load, pitch line velocity, bending stress factors, contact stress, and comparing bending and wear safety factors. The procedure involves inputting parameters, selecting materials, calculating sizes, stresses, and iterating the design if limits are not satisfied.

1. Gears

2. Basic
Terminology

3.  Pitch Circle : It is curve of intersection of pitch surface of
revolution and the plane of rotation. It is imaginary circle that rolls
without sleeping
 Base Circle : It is an imaginary circle from which the involute curve
of tooth is generated.
 Addendum : It is radial distance between pitch and addendum
circle. It indicates height of tooth above pitch circle.
 Dedendum : It indicates depth of tooth below pitch circle.
 Pressure angle : It is angle between line of action and common
tangent to pitch circles.
 Line of action : It is common tangent to the base circles of
matting gears.
 Module : It is ratio of pitch circle diameter to number of teeth.
Basic
Terminology

4. Lewis Bending
Equation
 In the Lewis equation certain assumptions were made.
 Gear was considered as a cantilever beam will load applied at the lip
and is uniformly distributed over the entire face width.
 Radial force effects are neglected.
 Tooth sliding friction, and stress concentration due to abrupt changes
in area were also neglected.
 Hence, we get a relation between the load F, bending stress B, tooth pitch
p, tooth width b and lewis form factor y (value can be taken from
machine design handbook), as
 B= F/bpy
 This was only for static loading conditions which are not so in working in
case of gears instead dynamic loading is acting. Stress concentration at
tooth fillet can also be not ignored. Also the load isn't concentrated on the
tip. It is distributed between the teeth in single pair contact much below
the gear tooth tip.
 Since Bending stress depends on no. of factors including pitch line
velocity, contact ratio,fatigue stress concentration, Moment of inertia of
the gears and attached rotating members.
 So Lewis equation was modified

5. Surface
Durability-
HertzTheory
 Unusually high contact stresses may occur when a load is applied
over a small area of contact. Practical examples include contact of
a wheel and a rail, valve cams and tappets, in rolling bearings and
mating gear teeth.
 Hertz’s analysis of contact stress involves the following set of
assumptions:
1. The surfaces are smooth and frictionless.
2. The contact area is small compared to the size of the bodies.
3. The bodies are isotropic and elastic.

6. Surface
Durability-
HertzTheory

7. AGMA
 AGMA stands forAmerican Gear ManufacturingAssociation
 Design – Spur and Helical gear according to AGMA standards.
1. AGMA 901 : A Rational Procedure for the Preliminary Design of
MinimumVolume Gears
2. AGMA 913 : Method for Specifying the Geometry of Spur and
Helical Gears
 To simplify calculation and chart viewing, we have assumed 20°
pressure angle and full-depth teeth.
 From the following slides we have mentioned the AGMA
procedure which we’ll be following for gear designing.

8. AGMA
SpurGear
Bending
1.
where
 dp- Diameter of Pitch Circle
 Np- No. ofTeeth
 Pd- Diameteral Pitch
2.
where
 V – Pitch LineVelocity
 d – Gear Diameter
 n - Gear Speed
3.
where
 Wt –TangentialTransmitted Load
 H - Power

9. AGMA
SpurGear
Bending
4.
where

10. AGMA
SpurGear
Bending where Qv is the quality number, which ahs value ranging from 3 to 7
for commercial-quality gears and 8 to 12 for precision quality.
For simplicity, assuming there is no detrimental size effect and
taking Ks = 1.

11. AGMA
SpurGear
Bending

12. AGMA
SpurGear
Bending

13. AGMA
SpurGear
Bending
For the value of J

14. AGMA
SpurGear
Bending
5. Allowable Stress
where

15. AGMA
SpurGear
Bending
 Taking KT = 1, assuming temperature to be less then 120℃.

16. AGMA
SpurGear
Wear
 The analysis of wear was done by Earle Buckingham. It based on Hertz
theory of contact stresses.

17. AGMA
SpurGear
Wear

18. AGMA
SpurGear
Wear
 Wt, Ko, Kv, Ks and Km values will be same as in for bending .
 Cf = 1

19. AGMA
SpurGear
Wear

20. AGMA
SpurGear
Wear
 For simplicity, we are assuming that gear and pinion are made of
same material. Hence, the value of CH = 1.
 Assuming the temperature to be less than 121 ℃. Hence, KT = 1.
 KR is same as in bending.
 When deciding whether bending or wear is the threat to
function, we compare SF and S²H.

21. Procedure
 Input parameters on which gear has to be designed which are
input speed, gear ratio, the power to be transmitted, the life of
the gear, teeth on pinion and gear and other working condition.
 Select the suitable material for gear for the given working
condition. Generally material of the pinion is harder than the
gear as it is subjected to rigorous loading than gear. Standards
for material are given in the literature survey.
 We will choose the involute profile of the teeth as it always
satisfies the law of gearing. Also, a slight change in center
distance will have no effect on the shape of the involute.
 Pressure angle is limited to 20° as it is most widely used and
increasing pressure angle improves the tooth strength but
shortens the duration of contact. Decreasing pressure angle
requires more number of teeth on the pinion to avoid
undercutting. The 20° pressure angle is a good compromise for
most of the power transmission as well as precision gearboxes.
 The condition of interference and backlash must be kept in
mind.

22. Procedure
 Based on the input parameter, the diameter of gear and pinion
and input torque is to be calculated.
 Then from input torque, the value of output torque and from
output torque and pinion diameter, the tangential load is to be
calculated.

23. Procedure
 From pinion diameter, pitch line velocity is calculated.
 Using Tangential load, pitch line velocity and other input
parameters bending stress factors are computed which are life
cycles, design factors, bending stress, velocity factor, elasticity
coefficients, and allowable bending stress.
 From pitch line velocity and input parameters, contact stress
can be calculated which are life cycles, design factors, velocity
factor, contact stress geometry factors per gear mesh and
contact stress calculation per gear stage.

24. Procedure
 If both conditions satisfy end the process.
 Otherwise reiterate.

25. References
 We’ve referred the following standard textbooks for
understanding the concept and the procedure of gear designing:
 Design of Machine Elements byV.B. Bhandari, 4th Ed
 Shigley’s Mechanical Engineering Design, 9th Ed
 Design of Machinery by Robert L Norton, 2nd Ed
We have used Shigley for procedure because it’s designing is based
on AGMA. For understanding we’ve used US system, while coding
we’ll make changes according to the SI units.