Referring to Figure 2-4, the tangent to the two base circles is the line of contact, or line-of-action in gear vernacular. Where this line crosses the line-of-centers establishes the pitch point, P. This in turn sets the size of the pitch circles or as commonly called, pitch diameters The ratio of the pitch diameters gives the velocity ratio:
Velocity ratio of gear 2
to gear 1 is:
i = d1
(2-1)
d2
25 Pitch And Module
Essential to prescribing gear geometry is the size, or spacing of the teeth along the pitch circle. This is termed pitch, and there are two basic
Circular pitch - A naturally conceived linear measure along the pitch circle of the tooth spacing. Referring to Figure 2-5, it is the linear distance (measured along the pitch circle arc) between corresponding points of adjacent teeth. It is equal to the pitch-circle circumference divided the number of teeth:
p=circular pitch
= Pitch Circle Circumference = pd
(2-2)
number
of teeth
z
Module - Metric gearing uses the quantity
module m in place of the American inch unit, diametral pitch. The module
is the length of pitch diameter per tooth. Thus:
m = d
(2-3)
z
Relation of pitches: From the geometry that
defines the two pitches, that shown that module and circular pitch are
related by the expression:
P = p
(2-4)
m
This relationship is simple to remember and permits an easy
transformation from one to the other.
Diametral pitch Pd is widely used in England and
America to resent the tooth size. The relation between diametral pitch and
m = 25.4 (2-5)
Pd
2.6 Module Sizes And Standards
Module m represents the size of involute gear tooth. The unit of module is mm. Module is converted to circular pitch p, by the factor ,p.
p = pm (2-6)
Table 2-1 is extracted from JIS B 1701-1973 which defines the tooth profile and dimensions of involute gears. It divides the standard module into three series. Figure 2-6 shows the comparative size of various rack teeth.
| Table 2-1 Standard Values of Module unit: mm | ||||||||||||
|
||||||||||||
| Note:
The preferred choices are in the series order beginning with 1. |
Circular pitch, p, is also used to represent tooth size when a
special desired spacing is wanted, such as to get an integral feed in a
mechanism. In this case, a circular pitch is chosen that is an integer or
a special fractional value. This is often the choice in designing position
control systems. Another particular usage is the drive of printing plates
to provide a given feed.
Most involute gear teeth have the standard whole depth
and a standard pressure angle a
= 20º. Figure 2-7 shows the tooth profile of a whole depth
standard rack tooth arid mating gear. It has an addendum of ha
= 1m and dedendum hf ³
1 .25m. If tooth depth is shorter than whole depth it is called a stub
tooth and it deeper than whole depth it is a "high" depth tooth.
The most widely used stub tooth has an addendum ha
= 0.8m and dedendum hf = 1 m. Stub teeth have more strength
than a whole depth gear, but contact ratio is reduced. On the other hand,
a high depth tooth can increase contact ratio, but weakens the tooth.
In the standard involute gear, pitch p times the number
of teeth becomes the length of pitch circle:
