What's the difference between module and diametral pitch for rack and pinion drives?

Gear sizes are usually specified by one of two names:module or diameter pitch.Although both specifications define the dimensions of gear teeth,modules and diameter pitch are calculated differently,with modules(sometimes called metric pitch)being the metric size standard and diameter pitch being the imperial(in.)size method.

The standard modules for spur and helical gears are defined by ISO 54:1996 and indicate the pitch diameter(or pitch length of the straight rack)occupied by each tooth.The larger the module,the larger the gear teeth and the whole gear.

m = module(mm)

d = pitch diameter or pitch length(mm)

n = number of teeth

Module can also be found by dividing the circular pitch by pi(π).

m = module(mm)

p = circular pitch(mm)

The module of a gear can be found by dividing the pitch by pi (π).

To find the circular pitch of the gear,divide the circumference around the pitch circle(circumference=pi x pitch diameter)by the number of teeth.

p = circular pitch(mm)

d = pitch diameter(mm)

n = number of teeth

By removing the circular constant of pi(π),the module system simplifies the calculation of other gear parameters.Diameter pitch,on the other hand,represents the number of teeth per inch of pitch diameter.It is important to note that the tooth(and therefore gear)size is inversely proportional to the diameter pitch.In other words,larger diameter pitch means that there are more teeth per inch of pitch diameter,and therefore smaller.

DP = diametral pitch(1/in)

n = number of teeth

d = pitch diameter or pitch length(in)

With 10 teeth per inch,this is a 10DP rack.

Because it is based on imperial units,diameter pitch is primarily used in the United States.However,most high-precision rack and pinion drives(both in and out of the United States)use the module size designation.Modules and diameter pitch are opposite each other and are related by a 25.4 mm to inch conversion,where:

DP = diametral pitch(in)

m = module(mm)

Although modules and diameterl pitch are similar,mating gears of different size schemes cannot be used together or interchanged directly.In other words,the mating gear must have the same module(for example,m2 pinion with m2 rack)or the same diameter pitch(for example,12DP pinion with 12DP rack).

Note that these calculations apply to rack and pinion drives with positive(straight)teeth.For the version with helical teeth,there are two pitch measurements(normal and transverse),so there are two versions of the module and two versions of the diameter pitch.

Helical gears have normal pitch and transverse pitch,so modules need to be measured twice and diameter pitch twice.