5.4 Equivalent Spur Gear
The true involute pitch and involute geometry of a helical gear is that in the plane of rotation. However, in the normal plane, looking at one tooth, there is a resemblance to an involute tooth of a pitch corresponding to the normal pitch. However, the shape of the tooth corresponds to a spur gear of a larger number of teeth, the exact value depending on the magnitude of the helix angle.
| The geometric basis of deriving the
number of teeth in this equivalent tooth form spur gear is given in Figure 1.27. The
result of the transposed geometry is an equivalent number of teeth given as: NV = N (28) cosły This equivalent number is also called a virtual number because this spur gear is imaginary. The value of this number is its use in determining helical tooth strength. |
|
5.5 Pressure Angle
Although strictly speaking, pressure angle exists
only for a gear pair, a nominal pressure angle can be considered for an individual gear.
For the helical gear there is a normal pressure angle as well as the usual pressure angle
in the plane of rotation. Figure 1.28 shows their relationship, which is expressed as:
tan f = tan fn
(29)
cos
y
5.6 Importance of Normal Plane Geometry
Because of the nature of tooth generation with a rack-type hob, a single tool can generate helical gears at all helix angles as well as spur gears. However, this means the normal pitch is the common denominator, and usually is taken as a standard value. Since the true involute features are in the transverse plane, they will differ from the standard normal values. Hence, there is a real need for relating parameters in the two reference planes.
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