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   and  ı = pitch angle

3. Both bending stress and contact stress should be checked for all bevel gears regardless of lubrication, as either type of stress may be limiting. The subject of contact stresses in bevel gears is an Involved subject for which the reader is referred to the references.

20.5.7 Design Procedure- Worm Gears—The design of worm-gear drives involves consideration of a rumber of factors, which do not arise in the design of spur and helical gears. These include the stresses associated with the theoretical line contact between the teeth of the worm and gear - and the wear associated with the relatively high sliding velocities at the tooth interface. Plastic worm gears meshing with either with  a plastic worm or a metal worm have been used. In either case the load-carrying capacity of the combination is substantially less than that of metal gears and worms. For design calculations, which are the scope of this discussion, the reader is referred to the references.

3.6 Operating Temperature

As a general guideline plastic gears should be used only for temperatures below 250^oF, as their load carrying capacity decreases with temperature. The actual recommended maximum temperature can be considerably below 2500^o F, depending upon the application. Limiting factors include the nature of the lubrication, loads, speeds, thermal expansion, nature of operation (continuous or intermittent) and the material properties of the plastics involved.
The combination of a plastic and a metal gear improves heat dissipation. If space permits, the plastic
can be proportioned so as to maximize the rate of heat transferred to its surroundings.
In order to  estimate the operating temperature limit it is recommended that the bending stress and
contact stress can  be calculated, taking into account the reduction in tensile strength and elastic moduli with temperature (Figures 1.53, 1.54).

20.7 Effect of Part Shrinkage on Gear Design

The nature of the part and the molding operation have a significant effect on the molded gear. From the design point of view the most important effect is the shrinkage of the gear relative to the size of the mold cavity.
Gear shrinkage depends upon mold proportions, gear geometry, material, ambient temperature and
is  usually expressed in inches per inch. For example, if a plastic gear with a shrinkage rate of 0.022 in./in. has a pitch diameter of 2 inches while in the mold, the pitch diameter after molding will be reduced by  (2)(0.22)"  or 0.44" and becomes 1.956" after it leaves the mold. Depending upon the
material and the molding process shrinkage rates ranging from about 0.OO1in./in. to 0.030 in/in, occur in (see Tablet 1.38 and Fig.1.61). Sometimes shrinkage rates are expressed as a percentage. 
For example a shrinkage rate of 0.0025 in/in, can be stated as a 0.25% shrinkage rate.