Module (gear)

Gear pair, example for a gear:
24 teeth, module 2 mm → pitch circle diameter 48 mm, tip diameter 52 mm, tooth pitch 6.28 mm. ${\displaystyle m=}$
${\displaystyle d=}$
${\displaystyle d_{k}=}$
${\displaystyle p=m\pi \approx }$

The module (plural modules ) or the diameter division is a measure of the size of the teeth of gears , namely the pitch circle diameter divided by the number of teeth : ${\displaystyle m}$ ${\displaystyle d}$ ${\displaystyle z}$

${\displaystyle m={\frac {d}{z}}}$.

Determining variables of the teeth, such as head and foot height, foot radius and head edge break, are specified relative to the module. In the unit of measurement used (usually mm ), their dimensions are rational . The tooth or circumference pitch , on the other hand, is irrational because of the irrational number of circles in the ratio of circumference and diameter: ${\displaystyle p}$ ${\displaystyle \pi }$

${\displaystyle p={\frac {U}{z}}={\frac {\pi d}{z}}=m\pi }$.

Only gears from the same module can be combined. In order to simplify the selection of matching gears and to be able to use standardized tools, preferred series are defined in DIN 780 :

Module in mm according to preferred series I according to DIN 780
0.05	0.06	0.08	0.1	0.12	0.16	0.2	0.25	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1	1.25
1.5	2	2.5	3	4th	5	6th	8th	10	12	16	20th	25th	32	40	50	60

Module in mm according to preferred series II according to DIN 780
0.055	0.07	0.09	0.11	0.14	0.18	0.22	0.28	0.35	0.45	0.55	0.65	0.75	0.85	0.95	1.125	1.375
1.75	2.25	2.75	3.5	4.5	5.5	7th	9	11	14th	18th	22nd	28	36	45	55	70

Row 1 is preferable to row 2.

In the field of Anglo-American system of measurement of the reciprocal value of the module has historically been given, in the unit 1 / inch respectively, and as "diametral pitch," Conversion: . Using the reciprocal value corresponds to specifying the thread pitch as the number of turns per inch of screw length. The “Diametral Pitch” is no longer exclusively used in favor of the module in countries with an Anglo-American measurement system. An intermediate step is the "English Module", a module in inches instead of mm. ${\displaystyle P_{\text{d}}={\frac {z}{d}},\,}$ ${\displaystyle m={\frac {25{,}4{\text{ mm/inch}}}{P_{\text{d}}}}}$

Types of module

The pitch is defined as the arc length on the pitch circle between equal points on two adjacent teeth. ${\displaystyle p}$

Normal module m _n

Module in normal section , a surface of the toothing perpendicular to the flank lines. The normal cut surface is spatially curved.

Front module m _t

Module in a face section , a surface perpendicular to the face of the wheel or the wheel axis. With straight-cut spur gears, the face cut is the same as the normal cut. In general, the above definition relates to this section. In the case of helical gears with a helix angle , the front module results in ${\displaystyle \beta }$

${\displaystyle m_{\text{t}}={\frac {m_{\text{n}}}{\cos \beta }}={\frac {p}{\pi }}={\frac {d}{z}}}$,

where for straight toothed gears and thus applies. ${\displaystyle \beta =0}$ ${\displaystyle m_{\text{t}}=m_{\text{n}}}$

Axial module m _x

Module in an axial section , a plane containing the wheel axis:

${\displaystyle m_{\text{x}}={\frac {m_{\text{n}}}{\sin \left|\beta \right|}}={\frac {m_{\text{t}}}{\tan \left|\beta \right|}}}$

The following applies to straight-toothed spur gears . The use of the axial module does not make sense here. ${\displaystyle \beta =0}$ ${\displaystyle m_{\text{n}}=m_{\text{t}}}$

Web links

• Design formula collection - methods and gears (accessed on January 7, 2020)
• Gear calculation (accessed on September 17, 2015)

Remarks