The displacement of the helical rack, i, for one rotation of the mating gear is the product of the radial pitch, Pt and number of teeth.
(6-13)According to the equations of Table 6-7, let radial pitch Pt = 8 mm and displacement i = 160 mm. The radial pitch and the displacement could be modified into integers, if the helix angle were chosen property.
In the axial system, the linear displacement of the helical rack, 1, for one turn of the helical gear equals the integral multiple of radial pitch.
i = p zm (6-14)
SECTION 7 SCREW GEAR OR CROSSED HELICAL GEAR MESHES
These helical gears are also known as spiral gears. They are true helical gears and only differ in their application for interconnecting skew shafts, such as in Figure 7-1. Screw gears can be designed to connect shafts at any angle, but in most applications the shafts are at right angles.
NOTES:
1. Helical gears of the same hand operate at right
angles.
2. Helical gears of opposite hand operate on
parallel shafts.
3. Bearing location indicates the direction of thrust.
7.1 Features
7.1.1 Helix Angle and Hands
The helix angles need not be the
same. However, their sum must equal the shaft angle:
b1
+ b2
= S
(7-1)
where b1
and b2
are the respective helix angles of the two gears, and S
is the shaft angle (the acute angle between the two shafts when viewed in
a direction paralleling a common perpendicular between the shafts).
Except for very small shaft angles, the helix hands are the same.
Because of the possibility of different helix angles for the gear pair, the radial modules may not be the same. However, the normal modules must always be identical.
7.1.3 Center Distance
The pitch diameter of a crossed-helical gear is given by Equation (6-7), and the center distance becomes:
(7-2)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:
velocity ratio = i = z1 (7-3)
z2
or, if pitch diameters are introduced, the relationship is:
i = z1 cosb2 (7-4)
z2 cos b1
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, mn1 mn2, are the same. Let a pair of screw gears have the shaft angle œ and helical angles b1 and b2:
(7-5)If the screw gears were profile shifted, the meshing would become a little more complex. Let bw1, bw2 represent the working pitch cylinder;
(7-6)
