By the mid-1800s, the general form of rail and wheel had developed into something very similar to
those in use today (Figure 34.3) but it was late in the 19th century when Hertz (1896) developed the first
scientific description of the wheel/rail contact. Hertz developed an analysis method to describe the elastic
contact of glass lenses but, following its publication, it was found that it could also be used to describe
contacts within rolling element bearings, between gear teeth, and between rails and wheels (Johnson,
1985). Hertzian contacts between three-dimensionally curved bodies have an elliptical form, and pressure
within this contact region varies with an elliptical distribution (Figure 34.4). The distribution is described
by Equation 34.1, in which
p0
is the maximum pressure within the contact,
a
and
b
are the semi-axes of
the contact patch, and
x
and
y
are coordinates with their origin in the plane of the contact and at its center.
By the mid-1800s, the general form of rail and wheel had developed into something very similar to
those in use today (Figure 34.3) but it was late in the 19th century when Hertz (1896) developed the first
scientific description of the wheel/rail contact. Hertz developed an analysis method to describe the elastic
contact of glass lenses but, following its publication, it was found that it could also be used to describe
contacts within rolling element bearings, between gear teeth, and between rails and wheels (Johnson,
1985). Hertzian contacts between three-dimensionally curved bodies have an elliptical form, and pressure
within this contact region varies with an elliptical distribution (Figure 34.4). The distribution is described
by Equation 34.1, in which
p0
is the maximum pressure within the contact,
a
and
b
are the semi-axes of
the contact patch, and
x
and
y
are coordinates with their origin in the plane of the contact and at its center.
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