Gear Undercut & Profile Shift

Determine the minimum teeth Zmin to avoid undercut and the minimum profile shift coefficient x₀ and shift amount Lₜ for low-tooth-count gears.

Inputs

Formula

Zmin = 2ha*/sin²α; x0 = ha*(Zmin−Z)/Zmin; Lt = x0·m
根切区齿数过少时齿根出现根切,削弱强度
Gear Undercut & Profile Shift schematic

How to use

  1. Fill in Teeth Z, Pressure angle α, Addendum coeff. ha*, Module m in the Inputs section (watch the unit on each field).
  2. Click Calculate; the tool evaluates the formula shown above.
  3. Read Min teeth Zmin, Min shift x₀, Shift amount Lt, Undercut (1=yes) in the results area.
Formula notesMin teeth z_min ≈ 2·h_a* / sin²α. With α=20°, h_a*=1 → z_min≈17; fewer teeth cause undercut at the root.