Input Parameters
11.5 Helical gears – bending stress. 11.6 Helical gears – contact stress. 11.7 Crossed helical gears. 11.7.1 Tips for crossed helical gear design. 11.1 HELICAL GEARS – an introduction. In spur gears Fig.11.1 dealt earlier, the teeth are parallel to the axis whereas in helical gears Fig.11.2 the teeth are inclined to the axis. To find more information on gear strength calculations, please refer to the technical reference, in the section “Bending Strength of Spur and Helical Gears”.
Gear type - according to the position of root and head cone
Gear ratio and tooth numbers
Pressure angle (the angle of tool profile) αt
Helix angle βm
Axis angle Σ
Tangential module on outer cone met (for metric calculation)
Tangential Diametral Pitch on outer cone Pet (for English units)
Note: Module and Diametral Pitch are reciprocal values.
Unit addendum height ha*
![Gear Gear](http://www.sdp-si.com/resources/elements-of-metric-gear-technology/images/Table6-3.jpg)
Unit clearance c*
Unit dedendum fillet rf*
Facewidths b1, b2
Unit correction x = x1 = - x2
Unit change of tooth thickness xt = xt1 = - xt2
Auxiliary Geometric Calculations
Design According to the Strength Calculation
Design of Face Width
Calculated parameters
Normal Pressure Angle in Middle Plane
tg αnm = tg αt cos βm |
Pitch angle
Outside pitch diameter
de1,2 = met z1,2 |
Outside length of surface line on pitch cone
Length of surface line on the mean cone
Rm = Re - 0.5 b |
Relative face width
Tangential module on the mean cone
Normal module on the mean cone
Mean pitch diameter
dm1,2 = mmt z1,2 |
Equivalent number of teeth
Ekvivalent pitch diameter
Ekvivalent base diameter
Ekvivalent outside diameter
dva1,2 = dv1,2 + 2 hae1,2 mmt / met |
Ekvivalent center distance
Virtual gear ratio
Virtual number of teeth
Virtual pitch diameter
Virtual base diameter
Virtual outside diameter
dan1,2 = dn1,2 + 2 hae1,2 mmt / met |
Virtual helix angle at the base cylinder
Virtual center distance
an = 0.5 (dn1 + dn2) |
Dedendum reduction
k1,2 = 0.02 (17 - zn1,2) for k > 0 the dedendum shortening is done |
Addendum
Dedendum
hfe1,2 = met (ha* + c* - x1,2) |
Outside diameter
Root diameter
dfe1,2 = de1,2 - 2hfe1,2 cos δ1,2) |
Outside diameter at small end
Vertex distance
A1,2 = Re cos δ1,2 - hae1,2 sin δ1,2 |
Outside bevel angle
Cutting angle
Tooth thickness (measured normally on the pitch diameter)
Chordal facewidth (normal)
ske1,2 = se1,2 cos2αt |
Addendum height above the chord
![Helical Gear Formulas Helical Gear Formulas](http://images.books24x7.com/bookimages/id_27514/fig23_01.jpg)
Unit addendum width (measured normally)
where: |
Operating width of gears
Factor of mesh duration
εγ = εα + εβ |
Minimum correction without tapering
Minimum correction without undercut
Minimum correction without undercut
Helix angle at end
sinβe = sinβm Rm/Re |
Normal pressure angle at end