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19.2 Metric Design Equations
Some of the gear design equations are dimensionless and are derived from geometric proportions and relationships. These equations will not be affected by the use of metric units as opposed to inch units since the units cancel. lt is important, however, that the same units are used consistently throughout.  When this is not the case the problem of metriflcation can be approached in two steps. The first step is to express the present inch-base units in metrics and to modify the constants and coefficients accordingly. This procedure will yield results expressed in the form presently used in engineering practice in industrialized metric countries.

The second step is to express these results in Si units which differ slightly from the conventional metric units. Thls is true for stress calculations but does not affect gear dimensioning.

Metrification in the U.S. is taking place at a time when the SI (International System of Units) has been adopted in most metric countties, but its use has not spread to the practical design engineering profession. For. these countries, transition to the SI system represents a change which is accompanied by a degree of reluctance. The standardization related to transition to metrics in the U.S. is expected to introduce the SI units as well, in a single step.

lf we concentrate on the large number of equations which are independent of the system of measuring units, there will be no problem with metrification. Most of the kinematic design equations that appear American gear texts. and are associated with inch-system gears, are suitable for use with metric gear dimensions, provided that a proper substitution of module (in) is made for-pitch.

For equations involving diametral pitch:

we find that for equations involving circular pitch:

P_c  is replaced by _{p     m}                                      (66)
                          _25.4

Note: When converting between metric module and the inch diametral pitch, the conversion factor and relationship can be remembered from the simple product of the two pitch measures:

m * P_{d  = 25.4}

By this means, all geometric and all kinematic equations involving pitch parameters can be used. However, by the above, conversion results are still given in inch measurements. Thus, this is a way to adapt the metric module to kinematic design equations given in inch units.

Basic kinematic and geometric design equations for spur gears in both metric module and inch  diametral-pitch forms are given in table 1.35. These equations show the essence of using the modules versus inch diametral pitch.

Some equations which are identical in both systems are:

1. Over-pins measurements.
2. Relationship between tooth thicknesses at different radii from gear center.
3. Long and short addendum equations.
4. Profile-shifted gear-design equations: i.e., enlarged gear teeth, non-standard center distance