Helical gear calculator (normal system, center distance, contact ratio)
From normal module, helix angle, teeth and profile shift: transverse module and pressure angle, diameters, center distance and contact ratios (transverse and overlap).
Mesh
Gear 1
Gear 2
mt = mn/cosβ αt = atan(tanαn/cosβ) d = z·mt
invαwt = 2tanαn(xn1 + xn2)/(z1 + z2) + invαt
y = (z1 + z2)/(2cosβ) × (cosαt/cosαwt − 1) a = ((z1 + z2)/(2cosβ) + y)mn
εβ = b·sinβ/(π·mn)
Left: tooth traces (helices) seen from the side; their slope at the height of the axis is the helix angle β. Right: the reference cylinder unrolled. Measured square to the tooth trace is the normal plane (mn), square to the axis the transverse plane (mt). pn = pt × cos β, so mt = mn ÷ cos β (drawn with β = 30°).
Printed from Kezuriba (kezuriba.net/en/gears/helical/)
✎Notes
- These are the formulas for the normal system (the same cutters as spur gears can be used). They do not apply to gears designed in the transverse system.
- Two meshing helical gears have opposite hands (right-hand and left-hand).
The formulas follow the published technical data listed below and have been checked against the worked examples in those sources. For design or inspection, confirm against your drawing and the standards.