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5.2 Fundamental of Helical Teeth

In tho piano of rotation the helical gear tooth is involute and all of the relationships govorning spur gears apply to the helical. However, tho axial twist of the teeth introduces a holix anglo. Since the helix angle varies from the base of the tooth to the outside radnjs, the helix angle, w~ is detned as the angle between the tangent to the helicoidal tooth at the intersection of the pitch cylinder and the tooth profile, and an element of the pitch cylinder. See Figure 1.24.
      The direction of the helical twist is designated as either left or right. The direction is defined by the right-hand rule.

5.3 Helical Gear Relationships

For helical gears there are two related pitches: one in the plane of rotation and the other in a plane normal to the tooth. In addition there is an axial pitch. These are defined and related as follows: Referring to Figure 1.25, the two circular pitches are related as follows:

       P_cn = P_c cos y = normal circular pitch                                                  (25)

     The normal circular pitch is less than the transverse or circular pitch in the plane of rotation, the ratio between the two being equal to the cosine of the helix angle. Consistent with this, the normal diametral pitch is greater than the transverse pitch:

P_dn =   P_d     = normal diametral pitch                                                           (26)
          cos y

        The axial pitch of a helical gear is the distance between corresponding points of adjacent teeth measured parallel to the gears axis—see Figure 1.26. Axial pitch, p1. is related to circular pitch by the expressions: 

P_a = P_c cot y =  P_cn  = axial pitch                                                                 (27)
                          sin y

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