T-110
Table 11-2 Equations for Contact Ratio for a Bevel Gear Pair
11.3 Contact Ratio For Nonparallel And Nonintersecting Axes Pairs, e
This group pertains to screw gearing and worm gearing. The equations are
approximations by considering the worm and worm gear mesh in the plane perpendicular
to worm gear axis and likening it to spur gear and rack mesh. Table 11-3 presents these
equations.
Table 11-3 Equations for Contact Ratio of Nonparallel and Nonintersecting Meshes
Example of worm mesh:
mx = 3
an = 20°
zw = 2
z2 = 30
d1 = 44
d2 = 90
g
= 7.76517°
ax = 20.17024°
ha1 = 3
dth= 96
db2 = 84.48050
e = 1.8066
11.4 Axial (Overlap) Contact Ratio, eb
Helical gears and spiral bevel gears have an overlap of tooth action in the axial
direction. This overlap adds to the contact ratio. This is in contrast to spur gears which
Item
Equation for Contact Ratio
Symbol
Back Cone Distance
Base Circle Radius of an
Equivalent Spur Gear
Outside Radius of an
Equivalent Spur Gear
Contact Ratio
d
–––––
2cosd
Straight Bevel Gear Spiral Bevel Gear
Rv cosa
Rv cosat
Rv + ha
Straight Bevel Gear
–––––––––– ––––––––––
Ö
Rva1
2
– Rvb1
2
+
Ö
Rva2
2
– Rvb2
2
– (Rv1 + Rv2)sina
–––––––––––––––––––––––––––––––––––––––––
pmcosa
Spiral Bevel Gear
–––––––––– ––––––––––
Ö
Rva1
2
– Rvb1
2
+
Ö
Rva2
2
– Rvb2
2
– (Rv1 + Rv2)sinat
–––––––––––––––––––––––––––––––––––––––––
pmcosat
Rv
Rvb
Rva
ea
Type of Gear Mesh
Equation of Contact Ratio, e
db1 cosat1 db2 cosat2
–––––––––––– –––––––––––– a – –––––––– – ––––––––
da1
2
db1
2
da2
2
db2
2
2 2
Ö
(–––) – (–––) +
Ö
(–––) – (–––) – ––––––––––––––––––––––
2 2 2 2 sinan
––––––––––––––––––––––––––––––––––––––––––––––––––––
pmncosan
–––––––––––––
ha1 – xx2mx dth
2
db2
2
d2
––––––––– +
Ö
(–––) – (–––) – ––– sin
ax
sinax
2 2 2
–––––––––––––––––––––––––––––––––––
pmxcosax
Screw Gear a
Screw Gear b
Worm
a
Worm Gear b
