Page 217 - Analysis and Design of Machine Elements

Gear Drives
Let zone factor Z = √ 2cos b , which reflects the effect of profile curvature at pitch 195
H
sin t cos t
point on the contact stress. The transverse pressure angle can be obtained from
t
Eq. (8.36) and the helix angle at base circle from Eq. (8.37).
b
Contact ratio factor Z affects the effective length of contact line and consequently

the unit face width load. When < 1, contact ratio factor is calculated by [14]

√
4 −
Z = (1 − )+ (8.52)

3

When ≥ 1, use = 1tocalculate Z .

In a helical gear, the inclined contact line due to helix angle will also affect contact
stress on the tooth surface. The helix angle factor Z is introduced to account for this

effect. The helix angle factor Z is calculated by [14]

√
Z = cos (8.53)

We then have contact stress in a helical gear expressed as
√
KF t u ± 1
= Z Z Z Z ⋅ (8.54)
H H E
bd u
1
8.4.3.2 Contact Strength Analysis
For a design to be acceptable based on contact strength of helical gears, it must ensure

that
√
KF t u ± 1
= Z Z Z Z ⋅ ≤ [ ] (8.55)
E
H
H
H

bd 1 u
Let face width factor = b/d ;Eq. (8.55) canbeconverted to thedesignformula as
d
1
√
( ) 2
3 2KT 1 u ± 1 Z Z Z Z
E
H

d ≥ ⋅ (8.56)
1
u [ ]
d H
8.4.4 Tooth Bending Strength Analysis
Contrary to a spur gear whose teeth generally break near tooth root fillets, tooth
breakage in a helical gear frequently happens along an inclined line where high bending
stresses occur. The bending strength analysis is similar to that of a spur gear, with minor
modifications to account for geometrical differences between helical and spur gears.
8.4.4.1 Bending Stress Calculation
The approaches to the design evaluation of tooth bending strength of spur gears are
applicable to helical gears, yet a normal virtual spur gear is used. Besides, the effect of
contact ratio and helix angle are considered by introducing contact ratio factor Y and

helix angle factor Y . Thus, the maximum local bending stress in a helical gear tooth is

KF t
= Y Y Y Y (8.57)
F Fa Sa
bm n