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Figure 16-6 contains the directions of forces acting on a straight bevel gear mesh. In the meshing of a pair of straight bevel gears with shaft angle S = 90º, all the forces have relations as per Equations (16-8)
               (16-8)

16.4 Forces In A Spiral Bevel Gear Mesh

Spiral gear teeth have convex and concave sides. Depending on which surface the force is acting on, the direction and magnitude changes. They differ depending upon which is the driver and which is the driven. Figure 16-7 presents the profile orientations of right- and left-hand spiral teeth. If the profile of the driving gear is convex, then the profile of the driven gear must be concave. Table 16-3 presents the concave/convex relationships.

Table 16-3 Concave and Convex Sides of a 
                   Spiral Bevel Gear Mesh
Right-Hand Gear as Drive Gear
Rotational Direction of Drive Gear  
Right-Hand Drive Gear left Hand Driven Gear
Clockwise Convex Concave
Counterclockwise Concave Convex
Left-Hand Gear as Drive Gear
Rotational Direction of Drive Gear Meshing Tooth Face
left Hand Driven Gear Right-Hand Drive Gear
Clockwise Concave Convex
Counterclockwise Convex Concave
NOTE: The rotational direction of a bevel gear is defined as the direction one sees viewed along the axis from the back cone to the apex.
16.4.1 Tooth Forces on a Convex Side Profile
   The transmission force, Fn can be resolved into components F1, and Ft as (see Figure 16-8):
               (16-9)
Then F1 can be resolved into components Fu and Fs:
               (16-10)
       

On the axial surface, Ft, and Fs can be resolved into axial and radial subcomponents.
           (16-11)
     By substitution and manipulation. we obtain:
(16-12)

16.4.2 Tooth Forces on a Concave Side Profile
  
On the surface which is normal to the tooth profile at the central portion of the tooth, the transmission force, Fn can be split into F1 and Ft, as (see Figure 16-9):
                         (16-13)

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