Page 229 - Analysis and Design of Machine Elements

8.6.5 Design Criteria Gear Drives 207
As mentioned before, the two most likely potential failure modes governing a typical
gear design are bending fatigue failure at tooth root fillets and surface fatigue failure
at the tooth surface. To ensure the proposed design configuration is acceptable, both
bending stress and contact stress must be less than corresponding allowable stresses.
For enclosed soft tooth surface gears, pitting is the most common failure mode. To
provide adequate performance for pitting resistance, contact stress should not exceed
H
theallowablecontact stress [ ]. Thus the gear should first be designed by ≤ [ ].
H H H
Then, failure by tooth breakage should be prevented by ensuring that bending stress
F
less than or at most equal to the allowable bending stress [ ].
F
For enclosed hard tooth surface gears, tooth breakage is a common failure phe-
nomenon. Surface durability is equally important as gear teeth may experience
numerous cycles of stresses. In order to provide adequate performance for both
strengths, the gear teeth should be first designed according to ≤[ ] and then
F
F
checked by ≤[ ].
H H
For open gearings, wear happens before tooth breakage. The design approach is there-
fore similar to bending strength analysis, except 70–80% of the allowable bending stress
is selected to consider wear effects.
8.6.6 Design Procedure and Guidelines
Gear design, like other design procedures, involves a series of approximations and iter-
ations. Besides, the standard values for modules and pressure angle, plus limitation on
tooth number, impose additional constraints. The following subsections provide the
design procedure and guidelines to design a safe and long-lasting gear drive. Design
cases are presented in Section 8.6.7.

8.6.6.1 Select Gear Type, Materials, Accuracy Grades, Heat Treatments
and Manufacturing Methods
The selection of gear type, materials, accuracy grade and manufacturing process for a
particular design scenario depends largely on many factors, including the gear layout,
the transmitted power, the rotational speed, noise limitation and cost constraints.
High alloy steel with high surface hardness usually results in a compact design but
at a high cost. Also, higher quality and tighter tolerance gears with ground or shaved
teeth improve load sharing, reduce dynamic loads and consequently lower stresses and
improve surface durability, but also cost is high [3]. Therefore, compromise is indis-
pensable while making design decisions. Moreover, because of its size, the possibility of
undercut and more frequent contact, a pinion usually uses better and more expensive
materials than gears.

8.6.6.2 Initial Selection of Design Variables
The number of teeth of a pinion, z 1
Generally speaking, gears with more teeth tend to run more smoothly and quietly than
gears with fewer teeth. However, the number of pinion teeth should be as small as
possible to keep a transmission system compact. But the possibility of interference or
undercut is great with fewer teeth. For enclosed gearings, the number of pinion teeth
is initially selected as z = 20–40, while for open gearings, it is selected as z = 17–20.
1 1
The number of teeth of the meshing gear can be obtained by z = uz .
1
2