Undercut of involute gears | Minimum number of teeth | Calculation and derivation

This video takes a closer look at the so-called undercut of gears. This occurs when the number of teeth falls below a certain minimum number. The formula for calculating the minimum number of teeth is derived in this video.

From a manufacturing point of view, the undercut is due to the fact that with small gears, the cutting edges engage relatively deep into the gear and undermine the teeth. Such undermining of the tooth is also known as undercutting and leads to a weakening of the tooth. Undercuts should therefore always be avoided, which means that the number of teeth must not fall below a minimum.

With small gears, an undercut is also necessary from a functional point of view so that the gears can mesh properly. If there was no undercut on small gears, the teeth would interfere!

The undercut also shortens the length of the line of contact by cutting off part of the involute tooth profile. The teeth therefore lose contact with each other well before the actual end of engagement.

An undercut always occurs when the base circle touches the line of action within the line of contact! With a standard pressure angle of 20°, an undercut occurs below a number of teeth of 17. This minimum number of teeth is independent of the module!

THowever, it is possible to make gears with fewer than the theoretical minimum of 17 teeth - and without an undercut! To do this, however, the manufacturing process must be specially adapted with a so-called profile shift.

00:00 Introduction
00:18 Undercut due to the manufacturing process
01:14 Undercut due to the function
01:43 Influence of the undercut on the line of contact
02:57 Reference profile - line of action
04:34 Minimum number of teeth
06:07 Calculation (derivation) of the minimum number of teeth

[Martin]

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