T-150
SECTION 17 STRENGTH AND DURABILITY OF GEARS
The strength of gears is generally expressed in terms of bending strength and surface durability.
These are independent criteria which can have differing criticalness, although usually both are
important.
Discussions in this section are based upon equations published in the literature of the Japanese
Gear Manufacturer Association (JGMA). Reference is made to the following JGMA specifications:
Specifications of JGMA:
JGMA 401-01 Bending Strength Formula of Spur Gears and Helical Gears
JGMA 402-01 Surface Durability Formula of Spur Gears and Helical Gears
JGMA 403-01 Bending Strength Formula of Bevel Gears
JGMA 404-01 Surface Durability Formula of Bevel Gears
JGMA 405-01 The Strength Formula of Worm Gears
Generally, bending strength and durability specifications are applied to spur and helical gears
(including double helical and internal gears) used in industrial machines in the following range:
Module:
m
1.5 to 25 mm
Pitch Diameter:
d
25 to 3200 mm
Tangential Speed: v
less than 25 m/sec
Rotating Speed:
n
less than 3600 rpm
Conversion Formulas: Power, Torque and Force
Gear strength and durability relate to the power and forces to be transmitted. Thus, the
equations that relate tangential force at the pitch circle, Ft (kgf), power, P (kw), and torque, T
(kgf×m) are basic to the calculations. The relations are as follows:
102P 1.95 x 106P 2000T
Ft = ––––– = –––––––––––– = ––––––
(17-1)
v dw n dw
Ftv 10–6
P = –––– = ––––– Ftdwn
(17-2)
102 1.95
Ftdw 974P
T = ––––– = ––––––
(17-3)
2000 n
where: v
: Tangential Speed of Working Pitch Circle (m/sec)
dwn
v
= ––––––
19100
dw : Working Pitch Diameter (mm)
n
: Rotating Speed (rpm)
17.1 Bending Strength Of Spur And Helical Gears
In order to confirm an acceptable safe bending strength, it is necessary to analyze the
applied tangential force at the working pitch circle, Ft, vs. allowable force, Ft lim. This is
stated as:
Ft £ Ft lim
(17-4)
