Introduction to Gear technologies0 pages

1.3.4 Conversion
For those wishing to ease themselves into working with
metric gears
by looking at them in terms of familiar inch gearing relationships
and mathematics, Table 1-5 is offered as a means to make a quick
comparison.
Table 1-5 Spur Gear Design Formulas
To Obtain From Known Use This Formula*
Pitch Diameter Module D = mN
Circular Pitch Module
Pc = mp = D p
N
Module Diametral Pitch
m = 25.4
Pd
Number of Teeth Module and Pitch Diameter N = D
m
Addendum Module a = m
Dedendum Module b = 1.25m
Outside Diameter Module and Pitch Diameter or Number of
Teeth
Do = D + 2m = m (N + 2)
Root Diameter Pitch Diameter and Module DR= D - 2.5m
Base Circle Diameter Pitch Diameter and Pressure Angle Db = D cos f
Base Pitch Module and Pressure Angle Pb = m p cos f
Tooth Thickness at Standard Pitch
Diameter Module
Tstd = p m
2
Center Distance Module and Number of Teeth
C = m (N1 + N2)
2
Contact Ratio Outside Radii, Base Circle Radii Center
Distance, Pressure Angle
mp=(1Ro-1Rb)½+(2Ro-2Rb)½-Csinf
m p cos f
Backlash (linear) Change in Center Distance B = 2(DC)tan f
Backlash (linear) Change in Tooth Thickness B = DT
Backlash (linear) Along Line-of-action Linear Backlash Along Pitch Circle BLA = B cos f
Backlash, Angular Linear Backlash aB = 6880 B (arc minutes)
D
Mm. No. of Teeth for No Undercutting Pressure Angle
Nc = 2
sin²f
* All linear dimensions in millimeters
Symbols per Table 1-4
SECTION 2 INTRODUCTION TO GEAR TECHNOLOGY
This section presents a technical coverage of gear
fundamentals. It is intended as a broad coverage written in a
manner that is easy to follow and to understand by anyone
interested in knowing how gear systems function. Since gearing
involves specialty components, it is expected that not all
designers and engineers possess or have been exposed to every
aspect of this subject. However, for proper use of gear
components and design of gear systems it is essential to have a
minimum understanding of
gear basics and a reference source for details.
For those to whom this is their first encounter with gear
component it is suggested this technical treatise be read in the
order presented so as to obtain a logical development of the
subject. Subsequently, and for those already familiar with
gears, this material can be used selectively in random access as
a design reference.
335
Catalog Q410