T-58
7.1.3 Center Distance
The pitch diameter of a crossed-helical gear is given by Equation (6-7), and the
center distance becomes:
mn z1 z2
a = –––– (–––––– +––––––)
(7-2)
2 cosb1 cosb2
Again, it is possible to adjust the center distance by manipulating the helix angle. However,
helix angles of both gears must be altered consistently in accordance with Equation (7-1).
7.1.4 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:
z1
velocity ratio = i = –––
(7-3)
z2
or, if pitch diameters are introduced, the relationship is:
z1 cosb2
i = ––––––––
(7-4)
z2 cosb1
7.2 Screw Gear Calculations
Two screw gears can only mesh together under the conditions that normal modules
(mn1) and (mn2) and normal pressure angles (an1, an2) are the same. Let a pair of screw
gears have the shaft angle S and helical angles b1 and b2:
If they have the same hands, then:
ü
S = b1 + b 2
ï
ý
(7-5)
If they have the opposite hands, then:
ï
S = b1 – b 2, or S = b2 – b1
þ
If the screw gears were profile shifted, the meshing would become a little more complex.
Let bw1, bw2 represent the working pitch cylinder;
If they have the same hands, then:
ü
S = bw1 + bw2
ï
ý
(7-6)
If they have the opposite hands, then:
ï
S = bw1 – bw2, or S = bw2 – b w1
þ
Fig. 7-2 Screw Gears of Nonparallel and Nonintersecting Axes
S
b1
b2
b1
b2
S
Gear 1
(Right-Hand) (Left-Hand)
Gear 2
(Right-Hand)
