Page 264 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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9.3 Load Carrying Capacities
The determination of load carrying capacity for wormgear drives is more complicated
than for other types of gear drives due to complex profile geometry. Besides, wor-
mgear drive capacity is often limited not only by fatigue strength but also by thermal
capacity.
However, since an Archimedean wormgear drive resembles the meshing of helical
gear and rack in the central plane, it is reasonable to predict contact and bending fatigue
strength similar to those for helical gears, with factors introduced to account for their
differences.

9.3.1 Tooth Surface Fatigue Strength Analysis

Usually, hardened steel worms operate with soft bronze wormgears. As worm threads
are inherently strong and robust, the surface fatigue strength analysis is only performed
on wormgear teeth.
Similar to other gearings, contact stress calculation on wormgears is carried out on
the basis that the stress at pitch point does not vary greatly from the maximum stress
at other points of engagement, but is more convenient to be determined. The contact
stress calculation starts with the Hertz formula,
√
√ ( 1 1 )
√ ±
√ KF
√ n • 1 2
Hmax = √ ( 2 2 )
L 1− 1−
1 + 2
E 1 E 2
where
K –loadfactor, K = K K K ;
A v
K – application factor. Since wormgear drives operate smoothly, low to moderate
A
values within the recommended range from Table 2.1 can be selected for worm
gearing design;
K – face load factor. For stable load, select K = 1.0; For shock and vibration load,

select K = 1.1–1.3 [6];

−1
K – dynamic factor. For pitch line velocity of a wormgear less than 3 m s ,select
v
K = l.0–1.1; otherwise, select K = 1.1–l.2;
v v
Z – elastic coefficient. For hardened steel worms mating with cast tin bronze,
E
cast aluminium bronze, cast irons and nodular cast iron, the elastic coefficients
−2 1/2
are selected as 155, 156, 162 and 181.4 (N mm ) , respectively [6].
F – normal force, calculated by Eq. (9.13);
n
, – radius of curvature at pitch point, mm; Since a wormgear drive resembles a
1 2
helical gear and rack at the central plane, =∞, ≈ d sin /2cos .
1
2
2
L – total contact length, mm.
After substituting these variables into Hertz formula, the contact stress at the mating
surface of the wormgear is estimated as [6]
√
9.4KT 2
= Z E 2 ≤ [ ] (9.15)
H
H
d d
1 2