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     5.9.3 Center Distance — The pitch diameter of a crossed-helical gear is given by equation 30, and the center distance becomes:
       C =    1   (   N₁    +     N₂  )                                                                         (34)
              2P_dn     cos y₁      cos y₂    

      Again it is possible to adjust the center distance by manipulating the helix angle. However, both gear helix angles must be altered consistently in accordance with equation 33.
      5.9.4 Velocity ratio — Unlike spur and parallel shaft helical meshes the velocity ratio (gear ratio) cannot be determined from the ratio of pitch diameters, since these can be altered by juggling of helix angles. The speed ratio can be determined only from the number of teeth as follows:
           velocity ratio Z = N₁                                                                                 (35)
                                     N₂
or if pitch diameters are introduced the relationship is:
            Z =   D₁ cos y₁                                                                                        (36)
                    D₂ cos y₂

5.10 Axial Thrust of Helical Gears   

In both parallel-shaft and crossed shaft applications helical gears develop an axial thrust load. This is a useless force that loads gear teeth and bearings and must accordingly be considered in the housing and bearing design. In some special instrument designs this thrust load can be utilized to actuate face clutches, provide a friction drag, or other special purpose. The magnitude of the thrust load depends on the helix angle and is given by the expression:

W_T =W^t tany                                                                                                       (37)

where:

W_T = axial thrust load
W^t = transmitted load

     The direction of the thrust load is related to the hand of the gear and the direction of rotation. This is depicted in Figure 1.29. When the helix angle is larger than about 20°, the use of double helical gears with opposite hands (Figure 1 .30b) or herringbone gears (Figure 1.30a) is worth considering.

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