HOME PAGE
And F1 can be separated into components Fu and Fs on the pitch surface:
                                   (16-14)
So far, the equations are identical to the convex case. However, differences exist in the signs for equation terms. On the axial surface, F1 and Fs can be resolved into axial and radial subcomponents. Note the sign differences.
                         (16-15)
The above can be manipulated to yield:
     (16-16)
   Let a pair of spiral bevel gears have a shaft angle S =90º, a pressure angle an = 20º, and a spiral angle bm = 35º. If the tangential force, Fu to the central portion of the tooth face is 100, the axial thrust force, Fa, and radial force, Fr have the relationship shown in Table 16-4.
   The value of axial force, Fa, of a spiral bevel gear, from Table 16-4, could become negative. At that point, there are forces tending to push the two gears together. If there is any axial play in the bearing, it may lead to the undesirable condition of the mesh having no backlash. Therefore, it is important to pay particular attention to axial plays. From Table 16-4(2), we understand that axial thrust force, Fa changes from positive to negative in the range of teeth ratio from 1.5 to 2.0 when a gear carries force on the convex side. The precise turning point of axial thrust force, Fa, is at the teeth ratio z1 / z2 = 1.57357.
Table 16-4    Values of Axial Thrust Force, Fa and Radial Force, Fr
(1) Pinion
Meshing Tooth Face Ratio of Number of Teeth Z2
                                       Z1
1.0 1.5 2.0 2.5 3.0 4.0 5.0

Concave Side
of Tooth

 80.9
-18.1		 82.9
-1.9		 82.5
8.4		 81.5
15.2		 80.5
20.0		 78.7
26.1		 77.4
29.8

Convex Side
of Tooth

 -18.1
80.9		 -33.6
75.8		 -42.8
71.1		 -48.5
67.3		 -52.4
64.3		 -57.2
60.1		 -59.9
57.3
(2) Gear
Meshing Tooth Face Ratio of Number of Teeth Z2
                                       Z1
1.0 1.5 2.0 2.5 3.0 4.0 5.0

Concave Side
of Tooth

 80.9
-18.1		 75.8
-33.6		 71.1
-42.8		 67.3
-48.5		 64.3
-52.4		 60.1
-57.2		 57.3
-59.9

Convex Side
of Tooth

 -18.1
80.9		 -1.9
82.9		 8.4
82.5		 15.2
81.5		 20.0
80.5		 26.1
78.7		 29.8
77.4

    Figure 16-10 describes the forces for a pair of spiral bevel gears with shaft angle S = 90º, pressure angle an = 20º, spiral angle bm = 35º and the teeth ratio, u, ranging from 1 to 1 .57357.
    Figure 16-11 expresses the forces of another pair of spiral bevel gears taken with the teeth ratio equal to or larger than 1 .57357.

398