Page 230 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
208
Helix angle,
A helix angle is specified for each helical gear design. Although a large helix angle
benefits smooth and quiet operation, it may induce a large thrust load. A typical range
∘
∘
of ahelix angleisfrom8 to 20 .
Face width factor,
d
Increasing face width reduces both bending stress and contact stresses and improves
surface durability. However, the face width is normally not greater than the pitch
diameter of pinion, as a wide face width increases possibility of misalignment and
uneven load distribution along the gear teeth. The face width of pinion and gear can
be obtained from
⎧ b = d
d 1
⎪
⎨ b = b (8.87)
2
⎪ b = b +(5 ∼ 10)mm
⎩ 1
The selection of face width factor relates closely to how a gear is supported by
d
bearings. For symmetric, asymmetric and cantilever support, face width factor
d
is selected from the ranges of 0.9–1.4, 0.7–1.15 and 0.4–0.6, respectively [5]. Small
values are for the design where both gears have hardness greater than 350HBW,
while large values for at least one gear has hardness less than 350HBW.
8.6.6.3 Design by Gear Strength

(1) Design by gear teeth surface strength
After the initial values of design variables have been selected, the design process
can proceed by applying loads and speeds imposed by design specifications to the
specific design until both contact fatigue strength and bending fatigue strength are
satisfied.
The diameter of pinion that is directly related to the gear size is determined to satisfy
the requirement of surface contact strength against pitting. A larger pitch diam-
eter usually leads to reduced contact stresses and improved surface durability but
increased pitch line velocity, while a small pitch diameter may result in too few teeth
to avoid interference. The smallest acceptable pinion diameter can be used as the
first choice to keep the design compact.
(2) Design by gear teeth bending strength
The module that directly relates to tooth size is determined by satisfying bending
strength requirement. A large module results in larger teeth and generates lower
bending stresses. A standard acceptable value of module should be used to facilitate
manufacturing and reduce cost.
(3) Design by both gear teeth surface strength and gear teeth bending strength
More often, gears are designed by both tooth surface fatigue strength ≤ [ ]and
H H
bending fatigue strength ≤ [ ] regardless of tooth surface hardness. A trial load
F F
factor K (usually K = l.2–1.4) is used to calculate trial pitch diameter d (or trial
t t 1t
module m ). Then use d to calculate pitch line velocity, determine dynamic factor
nt 1t
K , transverse load factor K and face load factor K to obtain load factor K.Ifthere
v a