Optimized gearbox design - Wind Power Generation and Wind Turbine Design - page 515

T
C= fdm (3 )

where m = module = d / N . Then,

TN

(4 )

2

fd =

C

where f , d and T are as before and N is the number of teeth.
By equating the surface and bending volumes derived as above, it is possible to
obtain a non-dimensional “optimum” number of pinion teeth based on the balance
of bending to surface criteria and the gear ratio viz. By comparing eqns (1) and (4),
it yields,

⎛ 1 ⎞ C

N= 1 + nK (5)

⎜ ⎟

⎝ ⎠

Since tooth number is unaffected by face width to diameter ratio or torque, it is
only necessary to choose a rounded down number compatible with the nearest
standard pitch and the required face width, diameter and ratio. Thus, root fi llet
stress is not usually a limiting criterion because the pitch is easily increased by
reducing the number of teeth. Nonetheless, there are big incentives for making
pitch as fi ne as possible.

1. A smaller pitch with bigger tooth numbers has a somewhat greater contact ratio

but a shorter path of contact and commensurately lower tooth sliding veloci-
ties. This improves effi ciency and reduces sliding losses and associated sur-
face related problems such as scuffi ng. It also reduces surface stress slightly by
increasing the relative radius at the chosen load point.
For a given load, the reduced bending moment on the root of a shorter tooth 2.

means a thinner rim is required for its support. This is very important in epicyclic
gears as described later.

For simplicity, the foregoing consideration of gear geometry is confi ned to spur
rather than helical gears. The latter also embody tip relief to mitigate pitch error
problems as the teeth enter and leave the contact zone. However, experience sug-
gests that although they are generally quieter than spurs, they are both subject to
the same problems associated with the effects of parasitic loads and defl ections
and the helix corrections required to compensate for them. Unfortunately, such
corrections only work for one condition. Attempts to cater for varying conditions
by crowning the teeth, inevitably lead to higher stresses.

3 G eartrains

It is not practical to have a single stage gearbox to provide a step-up ratio of 100:1.
In practice, such an overall ratio invariably requires three stages. To minimise size