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3 Understanding Ease-Off

3.1 Where did the term “Ease-Off” originate from?

Ease-Off is a term which was created in the late 1970’s at the WZL of RWTH-
Aachen University by the two scientists Schriefer and Neupert [1, 2]. During a
visit of The Gleason Works in 1976, Schriefer and Neupert heard the term
“mismatch”, and they asked Theodore J. Krenzer for an explanation [3]. The
explanation was that with mismatch there was more ease-off between the
flanks (from the conjugate surface) to prevent edge contact and provide a lo-
calized contact bearing. Until then the term ease-off was used as a verb. The
earliest quote was found dating from 1945 made by Ernest Wildhaber [4].
When Schriefer and Neupert returned back to Germany, a new verb: Ease-Off
was created and is today the common term for the flank surface crowning or
mismatch graphic.

3.2 It Begins with the Roll Simulation

The results of the manufacturing simulation are that the surfaces of the pinion
and gear teeth are described as points and normal vectors of surface grids.
Those surfaces are the basis for several analyses. For the roll simulation, the
pinion flanks with their coordinate system XRI-YRI-ZRI are located in the cor-
rect relative position to the ring gear flanks with their coordinate system XRA-
YRA-ZRA. This relative position is defined by the shaft offset vector TT and the
shaft angle S. The signified blanks of pinion and ring gear are shown in Fig-
ure 1. In the present example, the shaft angle is 90° and the TT vector is equal
to zero, which defines a spiral bevel gearset without hypoid offset. In order to
evaluate the properties of the gearset under load with deflected gear box hous-
ing, it is possible to use shaft angles that deviate from 90° together with any
offset vector TT. The results of a roll simulation are Ease-Off, tooth contact
pattern and motion transmission error. In order to correlate those results in a
meaningful way with the tooth flanks of the evaluated gearset, the flank projec-
tion into the plane ZRA-YRA (points A-B-C and D) is defined as presentation
plane (Figure 1). The Ease-Off is a three-dimensional graphic of the flank de-
viations from a conjugate pair. It is calculated by rolling the pinion flank “into”
the gear coordinate system according to the Gearing Law, resulting in a virtual
gear flank which is conjugate to the actual pinion flank. This conjugate gear
flank will then be compared to the present gear flank, where all differences in
arc length are plotted point by point in ordinate direction into the Ease-Off
graphic [4].

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