n13_helical_gears
page 1 of 3
MOTOR
X
Wa
Z

Wt
TOP VIEW
Wr
Wr

Wa
Wt

Y
Y
X
MOTOR
Z
J

K
DRIVER
LJ =
2 inch
LK =
3 inch
SIDE VIEW
FRONT VIEW
d = 4 inch
18 HP
 = 20° pressure angle
r = 2 inch
250 rpm
desire 108 rotations
 250 rev  min
250 rpm = 

 min  60 sec
 2 rad 

 = 26.18 rad/sec
 rev 
P=T
 sec  550 ft .lbf

T = P /  = 18 HP
 26.18 rad  HP. sec
T = Wt r
Wt = T / r = 2269 lbf
Wr = Wt tan  = 825.8 lbf
 = 30° helix angle
 12 in 

 = 4538 in.lbf
 ft 
Wa = Wt tan  = 1310 lbf
n13_helical_gears
MOTOR
page 2 of 3
FXJ
FXK
X
Z
Wa
FZJ
FZK

Wt
TOP VIEW
Wr
Wr

Wa
Y
X
MOTOR
FYJ
FXJ
Wt

FYK
FXK
J
Y
Z

K
DRIVER
LJ =
2 inch
LK =
3 inch
SIDE VIEW
FRONT VIEW
TOP VIEW
 M Y about J
 Wt L J   FZK L J  L K   0
CCW positive
FZK = +907.6 lbf
TOP VIEW
 M Y about K CCW positive
 Wt L K   FZJ L J  L K   0
FZJ = +1361.4 lbf
FRONT VIEW
 M Z about J CCW positive
 Wr L J   Wa r   FYK L J  L K   0
FYK = -193.7 lbf
FRONT VIEW
 M Z about K
 Wr L K   Wa r   FYJ L J  L K   0
CCW positive
FYJ = +1019.5 lbf
n13_helical_gears
page 3 of 3
FJ _ RADIAL  FYJ  FZJ = 1701 lbf
2
2
FK _ RADIAL  FYK  FZK = 928 lbf
2
2
assume worst case - Wa acts on bearing J
ball bearing selection
Fr = 1701 lbf
P = X V Fr + Y Fa
V=1
try
desire L10 = 100 for 100x106 rev
Fa = 1310 lbf
inner race rotating
Eq. 11.22a
Fig. 11-24
X=1
L10 = (C / P)3
Y=0
P = Fr = 1701 lbf
Eq. 11.20a
CDESIRED = P (L10)1/3 = 1701 lbf (100)1/3 = 7895 lbf
try
6309 bearing
Fa / C0 = 0.1955
C = 9150 lbf
C0 = 6700 lbf
interpolate e = 0.3493
Fa / (V Fr) = 0.7701 > e
X = 0.56
P = X V Fr + Y Fa = 2620 lbf
Fig. 11-23
Fig. 11-24
interpolate Y = 1.273
Fig. 11-24
Eq. 11.22a
CDESIRED = P (L10)1/3 = 2620 lbf (100)1/3 = 12,161 lbf
try
6311 bearing
Fa / C0 = 0.131
C = 12,900 lbf
interpolate e = 0.314
Fa / (V Fr) = 0.7701 > e
X = 0.56
P = X V Fr + Y Fa = 2788 lbf
C0 = 10,000 lbf
Fig. 11-23
Fig. 11-24
interpolate Y = 1.401
Fig. 11-24
Eq. 11.22a
CDESIRED = P (L10)1/3 = 2788 lbf (100)1/3 = 12,940 lbf
probably OK
6311 bearing
C = 12,900 lbf
very close to CDESIRED