Page 31 - Gear Technology Solutions

The amounts of loss and gain are different due to the tooth thickness taper
which results in different angles b cv and b cx (Figure 17). The two formulas at
the top right and the bottom left in Figure 17 represent the vertical and
horizontal components of the close-up diagram. The upper formula represents
the vertical component of the cutter radius vector and contains the first
unknown d cv/d cx. The lower formula represents the horizontal component of the
cutter radius vector and contains also d/d cx plus the second unknown x2/x1
cv
(compare with the graphic in Figure 17). If the two formulas are squared and
then added together, a quadratic equation with the solution of the following
form delivers the lost and gained distances x2/x1.
________________________________________________________
x1 = {2RW•cos(b cx) – √ [2RW•cos(b cx)]² - 4[cos(b cx)•DED1/2•sin(b cx)]² } / (2cos(b cx))

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x2 = {2RW•cos(b cv) – √ [2RW•cos(b cv)]² - 4[cos(b cv)•DED1/2•sin(b cv)]² } / (2cos(b cv))

The final solution of the normal chordal tooth thickness calculation has the
form:

Normal Chordal Tooth Thickness =
(Transverse Chordal Thickness +x1 – x2) * cos(b )

In case of face hobbing, the cutter radius is not perpendicular to the flank
surface. The angular discrepancy is equal to the cutter blade offset angle d W
which is considered in the applet THKDATA in order to assure correct results
also in case of face hobbing.

For the calculation of straight bevel gear tooth thicknesses, the curvature in
flank line direction is set equal to the length crowning created by the cutter dish
angle. With this approach, all bevel gear tooth thicknesses can be converted
with the same set of equations and with the same accuracy.

1.10 Measurement of the actual Tooth Thickness Deviation

The tooth thickness will be measured according to the strategy described in
this manual. This means that no updated CMM software is required to be able
to apply the new approach. An updated version of the UNICAL software is
sufficient. If the requirement of a bevel gear manufacturer is the measurement
and recording of the real normal chordal tooth thickness, then the new
approach already tells before the first measurement the precise normal chordal
tooth thickness as output in the Dimension-Sheet. The results from the CMM
define tooth thickness deviation in length unit normal to the flank surface. If

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