Page 269 - Analysis and Design of Machine Elements

Wormgear Drives
coefficients of friction, sufficient strength and enough durability. A hardened ground 247
steel worm and a nonferrous wormgear are a good combination to reduce friction
and wear.
As a general rule of thumb, worms are usually made of medium carbon steel or alloy
steel. For high speeds and heavy loads, alloy steels carburized or quenched to a hardness
of 56–62 HRC are used. For low speeds and light loads, medium carbon steels that are
heat treated to a hardness of 220–300 HBW are preferred.
Bronzes are the most common nonferrous metals used for wormgears. Bronze wor-
mgears are able to wear-in and thus increase contact area [5]. The low elasticity modulus
of bronzes provides greater tooth deflection and improves load sharing between teeth.
Bronze gears also have good corrosion and wear resistance and low friction coefficients.
Typically used bronzes for wormgears are phosphor or tin bronze, lead bronze and alu-
minium iron bronze [1, 2, 6]. Most bronzes are cast, but wrought forms are also available.
The choice of bronzes needs to take into account sliding velocity. If the sliding velocity
is high, cast tin bronze, lead bronze, is recommended. If the sliding velocity is medium
−1
(≤6ms ) and load is heavy, cast aluminium–iron bronze is better. For low speeds and
light loads, grey cast irons could be selected.

9.4.3 Allowable Stresses
9.4.3.1 Allowable Contact Stresses
If wormgears are made of bronze with strength limits less than 300 MPa, the main failure
mode will be contact fatigue. The allowable contact stress is decided by [6]

[ ]= K HN [ ] ′ (9.27)
H
H
7
′
The basic allowable contact stresses [ ] at N = 10 is obtained from Table 9.2.
H
At other numbers of cycles, contact life factor K is introduced by [4]
HN
√ 7
8 10
K HN = (9.28)
N
5
5
7
7
When N > 25 × 10 ,use N = 25 × 10 and when N < 2.6 × 10 ,use N = 2.6 × 10 .
The number of cycles is calculated by
N = 60 jn L (9.29)
2 h
where n is the rotational speed of the wormgear, L is design life in hours and j is the
2 h
number of meshings of a wormgear tooth per revolution.
If wormgears are made of grey cast iron or high strength bronze, the load carrying
capacity of wormgear drive is decided by surface strength against scuffing. Due to limi-
ted data, a tentative contact calculation is used instead. The allowablecontact stresses are
selected from Figure 9.7, considering both mating worm hardness and sliding velocities.
9.4.3.2 Allowable Bending Stresses
Similar to the allowable contact stress, the allowable bending stress is obtained from
[ ]= K [ ] ′ (9.30)
FN
F
F
where bending life factor is [4]
√
9 10 6
K = (9.31)
FN
N