Undercut (Gear)
Undercut is the unintended removal of material at the tooth root that occurs when the cutting tool penetrates the tooth material during the manufacture of involute gearing. It primarily occurs with small tooth counts, weakens the tooth root, and impairs the gear mesh.
Cause and Minimum Tooth Count
For involute gearing, the risk of undercut depends on the pressure angle and the number of teeth. At a standard pressure angle of 20°, the theoretical minimum tooth count is z_min = 17. Gears with fewer teeth are undercut during hobbing or gear shaping: the tool reference profile exceeds the involute at the root and removes material. The undercut eliminates part of the involute tooth flank, reduces the contact ratio, and weakens the root cross-section.
Remedies: Profile Shift and Tooth Count Selection
The most effective way to avoid undercut is to apply a positive profile shift (x > 0). The tool reference profile is shifted radially outward so that it no longer undercuts the involute region. Alternatively, a higher tooth count (z ≥ 17) can be chosen. For very small tooth counts (z = 5...10), as found in pin gears or worm wheels, a substantial profile shift is required. A larger pressure angle of 25° reduces the minimum tooth count to approximately z_min = 12.
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