Chapter 10 Helical gears
(斜齿圆柱齿轮）

10－2 Force on helical gear teeth
 Left hand helix and
right hand helix
(左旋和右旋）

Helical gear geometry
and forces

Force analysis of gear system
A gear train is composed of four helical gears with the shaft axes in a single
plane. The gears have a 20 normal pressure angle and a 15helix angle and
a normal module of mn=2mm .Gear 1is cut right-handed and has 16 teeth. The
gears on shaft b have 56 and 27 teeth respectively.. Gear 4 has 60 teeth. The
driver rotates at 970 rpm and transmits 5kW. a) Calculate the center distance
between shafts a,b and b,c. b) Calculate the pitch diameter of each gear.
C)indicate the Wt 、Wr and Wx on each gear of shaft b.
27T
LH
16T
RH
a
1
input
56T
LH
b
c
3
2
4
60T
RH

 The figure shows a gear train composed of a pair of straight bevel gears and
a pair of helical gears. Shaft a is the input shaft of the train and delivers 17kW
at a speed of 720 rpm. The bevel gears have a module of 5mm and a face
with of gear is 50mm. The helical gears have a normal module of 6mm.
 a)If the thrust forces on shaft b counteract , Indicate the hand of the helical
gears. b) . Indicate the Wt 、Wr and Wx on each gear of shaft b.
a
b
60T
c
25T
21T 84T

Example 10-1
A helical gear has a normal diametral pitch of 8,
a normal pressure angle of 20º 32 teeth, a face
width of 3.00 in, and a helix angle of 15º.
Compute the diametral pitch, the transverse
pressure angle, and the pitch diameter. If the
gear is rotating at 650 rpm while transmitting
7.50 hp, compute the pitch line speed, the
tangential force, the axial force, and the radial
force.

10-3 stresses in helical gear teeth
The bending stress:
where Ko = overload factor for bending strength
Ks = size factor for bending strength
Km = load distribution factor for bending
strength
KB = rim thickness factor
Kv= dynamic factor for bending strength
See bottom of page 399

10-4 pitting resistance for helical
gear teeth
 The contact stress
Where Cp= elastically coefficient (table 9-10)
I=geometry factor (table 10-1 10-2)
I
FD
K
K
K
K
W
Cp
Sc
P
V
m
S
O
t


10-5 design of helical gears
 A pair of helical gears for a milling machine
drive is to transmit 65 hp with a pinion speed of
3 450 rpm and a gear speed of 1 100 rpm. The
power is from an electric motor. Design the
gears.