Worm gears are widely used in
industrial settings and in automobile gear boxes. This worm gear design
tutorial will discuss the basics of the worm gear box design calculation using
the AGMA empirical formula.
A worm gear box must
contain a worm and a mating gear (helical gear) and normally the axis of the
worm is perpendicular to the axis of the gear. Look at the picture below:
Where,
D1 Pitch Diameter of Worm
D2 Pitch Diameter of Gear
C Centre to Centre Distance
between the Worm and the Gear
This worm gear design tutorial will
discuss up to the selection of the module and pitch and the calculation of the
number of teeth, pitch circle diameter and centre to centre distance between
the worm and gear. We will use the AGMA formulae for doing the calculations.
Design calculations of the other aspects of the worm gear will be discussed in
a subsequent part of the tutorial.
○ The axial pitch of the worm and the circular
pitch of the gear must be same for a mating worm and gear. We will use the
term Pitch (P) for both the pitch in this tutorial.
○ Also, the module of the worm as well as the gear
must be equal for a mating worm and gear.
○ Now, lets say we have the following design
input:
Speed of the Worm (N1) = 20 RPM
Speed of the Gear (N2) = 4 RPM
○ And, we have to find out the Module (m),
Pitch (P), Number of helix of Worm (T1), Number of teeth of Gear (T2), Pitch
circle diameter of Worm (D1), Pitch circle diameter of Gear (D2), Centre to
centre distance(C).
○ Select the suitable module and its corresponding
pitch from the following AGMA specified table:
Module m (in MM)
- Pitch P (in MM)
2 -------------------------6.238
2.5 ---------------------- 7.854
3.15 --------------------- 9.896
4 ------------------------- 12.566
5 ------------------------- 15.708
6.3 ----------------------- 19.792
8 -------------------------- 25.133
10 ------------------------- 31.416
12.5 ----------------------- 39.27
16 -------------------------- 50.625
20 -------------------------- 62.832
○ Say, we are going ahead with the Module as
2 and the Pitch as 6.238.
○ Use the following gear design equation:
N1/N2 = T2/T1
And, we will get:
T2 = 5 * T1
.Eqn.1
○ Now use the following AGMA empirical formula:
T1 + T2 > 40
Eqn.2
○ By using the two equations (Eqn.1 &
Eqn.2), we will get the approximate values of
T1 = 7 and T2 = 35
○ Calculate the pitch circle diameter of the worm
(D1) by using the below AGMA empirical formula:
D1 = 2.4 P + 1.1 = 16.0712 mm
○ The following AGMA empirical formula to be used
for calculating the pitch circle diameter of the gear (D2):
D2 = T2*P/3.14 = 69.53185 mm
○ Now, we can calculate the centre to centre
distance (C) by the following equation:
C = (D1 + D2)/2 = 42.80152 mm
○ The below empirical formula is the cross check
for the correctness of the whole design calculation:
(C^0.875)/2 <= D1 <=
(C^0.875)/1.07
Observe that our D1 value
is falling in the range.
The worm gear box design calculation
explained here uses the AGMA empirical formulas.