Timken Super Precision Bearings for Machine Tool Applications

A
ENGINEERING
Worm Gear
Tangential force
F tG =
or
=
F tG =
Thrust force
F aG =
=
(1.91 x 10 7 ) H (newtons)
D pG n G
(1.26 x 10 5 ) H (pounds-force)
F tW
tan
D pG n G
(1.91 x 10 7 ) H (newtons)
D pW n W
(1.26 x 10 5 ) H (pounds-force)
D pW n W
Separating force
F sG =
F tW sin
cos sin + μ cos
Where:
= tan -1
or
= tan -1
and
=
Metric system
D
(
pG
m D pW )
L
(
H
π D pW )
cos – μ tan
cos + μ cot
μ (1) = (5.34 x 10 -7 ) V r
3 + 0.146 - 0.103
V r
0.09
V r =
Inch system
D pW n W
(1.91 x 10 4 ) cos
(meters per second)
μ (1) = (7 x 10 -14 ) V r
3 + 0.235 - 0.103
V r
0.09
V r =
D pW n W
3.82 cos
(feet per minute)
(1) Approximate coefficient of friction for the 0.015 to 15 m/s (3 to 3000 ft/min) rubbing
velocity range.
Double Enveloping Worm Gearing
Worm
Tangential force
F tW =
=
Thrust force
F aW = 0.98 F tG
Separating force
F sW =
Worm Gear
Tangential force
F tG =
or
=
F tG =
=
Thrust force
F aG =
=
Separating force
F sG =
Where:
D mW
(1.91 x 10 7 ) H (newtons)
D mW n W
(1.26 x 10 5 ) H (pounds-force)
D mW n W
0.98 F tG tan
cos
(1.91 x 10 7 ) H m (newtons)
D pG n W
(1.26 x 10 5 ) H m (pounds-force)
D pG n W
(1.91 x 10 7 ) H (newtons)
D pG n G
(1.26 x 10 5 ) H (pounds-force)
D pG n G
(1.91 x 10 7 ) H (newtons)
D mW n W
(1.26 x 10 5 ) H (pounds-force)
D mW n W
0.98 F tG tan
cos
= efficiency (refer to manufacturer’s catalog)
= 2d c -0.98 D pG
Lead angle at center of worm:
( ) ( D pW
)
= tan -1 DpG = tan -1 L
m D pW
Use this value for F tG for bearing loading
calculations on worm gear shaft. For torque
calculations, use the following F tG equations.
Use this value for
calculating torque in
subsequent gears and
shafts. For bearing
loading calculations,
use the equation for F aW.
40 TIMKEN MACHINE TOOL CATALOG