Depending upon the material and the molding process, shrinkage rates ranging from about 0.001 mm/mm to 0.030 mm/mm occur in plastic gears (see Table 18-1 and Figure 18-7). Sometimes shrinkage rates are expressed as a percentage. For example, a shrinkage rate
of 0.0025 mm/mm can be
stated as a 0.25% shrinkage rate.
The effect of shrinkage must be anticipated in the design of
the mold and requires expert knowledge. Accurate and specific treatment of
this phenomenon is a result of years of experience in building molds for
gears; hence, details go beyond the scope of this presentation.
In general, the final size of a molded gear is a result of
the following factors:
1. Plastic material being molded.
2. Injection pressure.
3. Injection temperature.
4. Injection hold time.
5. Mold cure time and mold temperature.
6. Configuration of part (presence of web, insert, spokes,
ribs, etc.).
7. Location, number and size of gates.
8. Treatment of part after molding.
From the above, it becomes obvious that
with the same mold - by changing molding parameters - parts of different
sizes can be produced.
The form of the gear tooth itself changes
as a result of shrinkage, irrespective of it shrinking away from the mold,
as shown in Figure 18-8. The resulting gear will be too thin at the
top and too thick at the
In order to obtain an idea of the effect of part shrinkage subsequent to molding, the following equations are presented where the primes refer to quantities after the shrinkage occurred:
cosa' = cos a (18-11)
1 + s*
m' = (1 - s*)m (18-12)
d' = zm' (18-13)
p' = pm' (18-14)
where: s* = shrinkage rate (mm/mm)
m = module
a = pressure angle
d = pitch diameter (mm)
p' = circular pitch (mm)
z = number of teeth
It follows that a hob generating the electrode for a cavity which will produce a post shrinkage standard gear would need to be of a nonstandard configuration.
Let us assume that an electrode is cut for a 20º pressure angle, module 1, 64 tooth gear which will be made of acetal (s* = 0.022) and will have 64 mm pitch diameter after molding.
cosa = cos a'(1 + s*)= 0.93969262 (1 + 0.022)
= 0.96036
therefore, a = 16º11' pressure angle
m= m = 1 = 1.0225
1 - s* 1-0.022
The pitch diameter of the electrode, therefore, will be:
d = zm = 64 x 1.0225 = 65.44mm
For the sake of simplicity, we are ignoring the correction which has to be made to compensate for the electrode gap which results in the cavity being larger than the electrode.
The shrinking process can give rise to residual stresses within the gear, especially if it has sections of different thicknesses. For this reason, a hubless gear is less likely to be warped than a gear with a hub.
If necessary, a gear can be annealed after molding in order to relieve residual stresses. However, since this adds another operation in the manufacturing of the gear, annealing should be considered only under the following circumstances:
1. If maximum dimensional stability is essential.
2. If the stresses in the gear would otherwise exceed the design limit.
3. If close tolerances and high-temperature operation makes annealing necessary.
Annealing adds a small amount of lubricant within the gear surface region. If the prior gear lubrication is marginal, this can be helpful.
18.6 Proper Use Of Plastic Gears
18.6.1 Backlash
Due to the thermal expansion of plastic gears, which is significantly greater than that of metal gears, and the effects of tolerances, one should make sure that meshing gears do not bind in the course of service. Several means are available for introducing backlash into the system. Perhaps the simplest is to enlarge center distance. Care must be taken, however, to ensure that the contact ratio remains adequate.
It is possible also to thin out the tooth profile during manufacturing, but this adds to the manufacturing cost and requires careful consideration of the tooth geometry.
To some extent, the flexibility of the bearings and clearances can compensate for thermal expansion. If a small change in center distance is necessary and feasible, it probably represents the best and least expensive compromise.
