Page 459 - Wind Energy Handbook

GEARBOX 433

7.4.7 Gear arrangements

Parallel axis gears may be arranged in one of two ways in each gear stage. The
simplest arrangement within a stage consists of two external gears meshing with
each other and is commonly referred to as ‘parallel shaft’. The alternative ‘epicyclic’
arrangement consists of a ring of planet gears mounted on a planet carrier and
meshing with a sun gear on the inside and an annulus gear on the outside. The sun
and planets are external gears and the annulus is an internal gear as its teeth are on
the inside. Usually either the annulus or planet carrier are held fixed, but the gear
ratio is larger if the annulus is fixed.
The epicyclic arrangement allows the load to be shared out between the planets,
reducing the load at any one gear interface. Consequently the gears and gearbox
can be made smaller and lighter, at the cost of increased complexity. The scope for
material savings are greatest in the input stages of the gear train, so it is common to
use the epicyclic arrangement for the first two stages and the parallel shaft
arrangement for the output stage. A further advantage of epicyclic gearboxes is
greater efficiency as a result of the reduced sliding that takes place between the
annulus and planet teeth.
The derivation of the optimum gear ratio in a series of parallel shaft stages is
fairly straightforward and is described below. Equation (7.47) for tooth bending
stress can be modified as follows

F t h 6(h=m) 6z 1 (h=m)
ó B ¼ K S ¼ F t K S ¼ F t K S (7:47a)
1 bt 2 bm(t=m) 2 bd 1 (t=m) 2
6

where m is the module, defined as d 1 =z 1 for spur gears and z 1 is the number of
pinion teeth. If the ratios h=m and t=m are treated as constants, then the bending
stress is proportional to the number of teeth for a given size of gear. Hence the
design of the gears is governed by contact stress because, in principle, the bending
stress can always be reduced by reducing the number of pinion teeth. Thus, based
on Equation (7.46), the permitted tangential force, F t , is proportional to bd 1 u=(u þ 1)
so that the permitted low-speed shaft torque, T LSS ¼ F t d 2 =2 is given by

2
T LSS / d 2 bd 1 u=(u þ 1) ¼ bd =(u þ 1) (7:51)
2
Hence the volumes of the low-speed shaft gear wheel and the meshing pinion can
2
be expressed as V 2 ¼ kT LSS (u þ 1), where k is a constant, and V 1 ¼ V 2 =u respec-
tively. These can be used to derive an expression for the volume of gears in a drive
train with an infinite number of stages each with the same ratio. It is found that the
total gear volume is a minimum for a gear stage ratio of 2.9, but increases by only
10 percent when the ratio drops to 2.1 or rises to 4.3.
The gear teeth of parallel shaft gear stages are only loaded in one direction, so the
permitted alternating bending stress in fatigue, ó alt , is modified to account for the
non-zero mean value in accordance with the Goodman relation: