T-30
SECTION 3 DETAILS OF INVOLUTE GEARING
3.1 Pressure Angle
The pressure angle is defined as the angle between the line-of-action (common tangent to the
base circles in Figures 2-3 and 2-4) and a perpendicular to the line-of-centers. See Figure 3-1.
From the geometry of these figures, it is obvious that the pressure angle varies (slightly) as the center
distance of a gear pair is altered. The base circle is related to the pressure angle and pitch diameter
by the equation:
db = d cosa
(3-1)
where d and a are the standard values, or alternately:
db = d' cosa'
(3-2)
where d' and a' are the exact operating values.
The basic formula shows that the larger the pressure angle the smaller the base circle. Thus, for
standard gears, 14.5° pressure angle gears have base circles much nearer to the roots of teeth than
20°
gears. It is for this reason that 14.5° gears encounter greater undercutting problems than 20°
gears. This is further elaborated on in SECTION 4.3.
Fig. 3-1 Definition of Pressure Angle
3.2 Proper Meshing And Contact Ratio
Figure 3-2 shows a pair of standard gears meshing together. The contact point of the two
involutes, as Figure 3-2 shows, slides along the common tangent of the two base circles as rotation
occurs. The common tangent is called the line-of-contact, or line-of-action.
A pair of gears can only mesh correctly if the pitches and the pressure angles are the same.
Pitch comparison can be module (m), circular (p), or base (pb).
That the pressure angles must be identical becomes obvious from the following equation for
base pitch:
pb = p m cosa
(3-3)
Base Circle
Base Circle
Line-of-Centers
Pressure Angle
a
Line-of-Action
(Common Tangent)
