Page 224 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
202
8.5.4.2 Bending Strength Analysis
To prevent tooth breakage, bending stress must satisfy
4KT 1
= Y Y ≤ [ ] (8.81)
F √ Fa Sa F
2
3 2
m z (1 − 0.5 ) 1 + u 2
1 R R
Equation (8.81) can be used for the design of bevel gear teeth, as
√
4KT 1 Y Y
Fa Sa
m ≥ 3 ⋅ (8.82)
√ [ ]
2 2
(1 − 0.5 ) z 1 + u 2 F
R R 1
The factors Y Fa and Y can be found by the virtual number of teeth z from Table 8.4.
sa
v
8.6 Design of Gear Drives
8.6.1 Introduction
In gear drive design, the provided design specifications include the transmitted power,
the rotational speeds of pinion and gear, or gear ratio, the operating conditions and
environment. The types of driving device and driven machine are also required for the
selection of application factors.
The design starts by deciding on the gear types and accuracy grades according to the
application. It also involves the selection of tentative materials and heat treatments, as

well as initial variables, like the number of teeth, helix angle and so on. Design must
satisfy two design criteria; that is, bending strength of gear teeth and pitting resistance
of tooth surface.
Gears can be designed in either order as long as both design criteria are satisfied.
Different design approaches are demonstrated in Section 8.6.7. Since information in the
problem statement is insufficient for solving the unknowns directly, trial and iteration
in the gear design process are unavoidable. There are usually a number of acceptable
designs and computer-aided design techniques, for example, iteratively running
developed design programs by a computer, are thus preferred to find an optimized
design.
The objective of gear design is to determine design variables, such as the module, the
number of teeth, face width, pitch diameters and so on to achieve smooth and quiet
operation with a compact, long life, low cost, good manufacturability gear drive. As
gears are in a power transmission system, they must be compatible with surrounding
elements, such as bearings, shafts, housing, driver and driven machines.

8.6.2 Materials and Heat Treatments
Gears can be made from a wide variety of materials to achieve properties required for the
application. Considering the general failure modes discussed in Section 8.2.3, candidate
gear materials should have good strength, especially fatigue strength, good resistance to
wear, surface fatigue and corrosion, high surface hardness and internal ductility, good
machinability and reasonable cost. Compromise is often necessary when selecting mate-
rials to satisfy some of incompatible requirements.