Profile shift of involute gears | avoiding undercut | derivation

With a profile shift, the tool profile is shifted outwards by a certain amount during gear manufacturing. As the profile shift increases, an undercut decreases and can even be avoided completely.
A profile shift is used when an undercut is to be avoided, tooth stability is to be increased or the center distance is to be adjusted.
A positive profile shift leads to an increase in the root and tip circle, to a wider tooth root and, at the same time, to a narrower tooth tip. In addition, the tooth thickness on the reference pitch circle increases and the tooth space width decreases accordingly. The surface pressure is reduced by the part of the involute tooth profile that is further out.
Both the base circle diameter and the reference pitch circle diameter do not change with a profile shift. With a negative profile shift, the effects mentioned are exactly the opposite. Due to the many positive effects, a positive profile shift is generally recommended.
00:00 Introduction
00:29 Profile shift
00:55 Influence of the profile shift on the shape of the tooth profile
01:44 Pitch point
02:31 Standard reference pitch circle
03:27 Profile shift coefficient
04:06 Calculation of tip and root circle diameter
05:04 Increase of tooth thickness
06:32 Tip shortening
07:59 Calculation of the tooth (tip) thickness
09:20 Center distance
10:22 V-Plus- und V-Minus-gear
10:50 Operating pressure angle and line of contact
11:29 Calculation of the profile shift coefficient to avoid undercutting
12:50 Derivation of the profile shift coefficient
14:51 Hertzian contact stress
15:28 Summary

[@gowthammurali1224]

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