Optimized gearbox design - Wind Power Generation and Wind Turbine Design - page 511

Figure 1: Simple wheel and pinion.
In its simplest form, a fi xed ratio gear comprises a pinion with a smaller number
of teeth meshing with a wheel having a larger number of teeth whose respective
axes are parallel.
The difference in tooth numbers then determines the ratio between the respec-
tive speeds of pinion and wheel; e.g. a 100-tooth wheel will drive a 20-tooth pinion
at fi ve times its own speed. As shown in Fig. 1, the wheel and pinion rotate in
opposite directions.
To provide a constant velocity ratio, the respective teeth must have the same
precise circular pitch and a geometric shape which enables the torque to be transmit-
ted from one tooth to the next by a slide/roll mechanism which ensures a constant
circumferential velocity. The universally chosen tooth form is an involute whose
properties are clearly described in any gearing text book. While toothed gearing is
very simple in principle, it is very diffi cult to implement in practice. Torque is trans-
mitted as a normal load between the mating teeth .but even if they are geometrically
perfect, this load creates surface and bending defl ections which in effect create pitch
errors that vary with torque. In addition, misalignments occur due to associated
defl ections in the shafts, bearings, mountings, casings, etc. which support the
gears. It becomes even more diffi cult when the gearbox is subjected to externally
generated forces due to the variable nature of the wind. All these effects create
unacceptable mal-distribution of tooth load across the face width of the gears.
Figure 2 shows the pitch circles of a pinion and wheel which contact one another
at a pitch point on the line joining their respective centres. The pitch line passing
through this point is tangential to the pitch circles and therefore, crosses the centre
line at right angles. The circumference of the respective pitch circles is equal to
their tooth numbers multiplied by the common circular pitch. As shown, the path
of contact between the mating gears is a straight line common tangent to their
respective base circles from which the involute tooth fl anks are generated. This
passes through the pitch point at an angle to the pitch line known as the pressure
angle (usually 20°). Its length is determined by the distance between the two points
where the respective tooth tip diameters cut across the common tangent. For con-
tinuity of transmission the normal distance between successive tooth fl anks (the
base pitch) has to be less than this length by a factor known as the contact ratio.
For most standard gears this varies between 1.4 and 1.7. Thus, at the beginning and