EHL film thickness is determined by
the viscosity and pressure-viscosity coefficient
of the lubricant in the inlet region.
For gears, the lubricant that is entrained
into the inlet is molecularly attached to
the surfaces of the pinion and wheel teeth
and consists of thin boundary layers that
immediately take on the bulk surface
temperatures of the pinion and wheel
teeth. Consequently, EHL film thickness
is determined by the equilibrium bulk
surface temperatures of the pinion and
wheel teeth in the inlet region before the
lubricant reaches the Hertzian region.
Bulk surface temperature. When the
pinion and wheel are running under a
given load, the surfaces of the pinion and
wheel teeth are heated by the sliding friction
between the gear teeth and gradually
increase in temperature until finally
reaching the equilibrium bulk surface
temperatures after many revolutions.
Inlet shear heating. In a fully flooded
EHL contact, only a fraction of the
lubricant can pass through the contact.
Therefore, some of the lubricant is rejected
and reverse flow occurs in the inlet.
Furthermore, if there is sliding in addition
to rolling, heat is generated by shearing
of the lubricant. Churning and shearing
generate heat that increases the lubricant
temperature above the average bulk surface temperatures. Therefore, the temperature
that controls lubricant viscosity and
EHL film thickness is the temperature
of the lubricant in the inlet. Empirical
equations are available to correct calculations
of isothermal EHL film thickness to
account for inlet shear heating.
Starvation. To form full EHL film
thickness, the inlet region must be fully
flooded. However, the inlet region might
be starved of lubricant if the lubricant
supply is inadequate, if very high speed
causes fling off of the lubricant, or both.
Under these conditions, EHL film thickness
might be reduced. Empirical equations
are available to correct calculations
of isothermal EHL film thickness to
account for lubricant starvation.
The Hertzian region. By the time the
lubricant enters the Hertzian region,
its viscosity has increased by a factor of
1,000 and it is trapped in the contact.
At maximum Hertzian pressures typical
in gears and rolling element bearings,
the lubricant undergoes a phase transition
into a solid glassy state. From this
point on the lubricant no longer behaves
as a Newtonian fluid, and it can be considered
a pseudo-solid. In the Hertzian
region the surfaces of the bodies are parallel
and separated by the central film
thickness that has an essentially constant
thickness. The film within the Hertzian
region is extremely stiff; therefore if the
load increases, the bodies deform more
than the central film thickness decreases.
Consequently, EHL contacts are relatively
insensitive to changes in load and
the main effect of increasing load is to
deform the surfaces, which increases the
area of the Hertzian region, but does little
to alter the shape of the inlet zone
where the EHL film is formed. Bottom
line, increasing load leaves the film thickness
virtually unchanged.
Sliding within the Hertzian region.
Sliding friction within the EHL film
increases the bulk temperature of the gear
teeth from a cold start by accumulating
heat from each tooth engagement.
The bulk temperature of the gear teeth
increases until the heat input is equal to
the heat loss to the surroundings. Once
the bulk temperature reaches equilibrium,
there is no further change in gear
tooth bulk surface temperature — unless
the operating conditions change. The
heat input is confined to the immediate
area of the Hertzian region and its duration
is only a fraction of a millisecond
long. Consequently, the heat produced by
frictional heating within the EHL film is
removed by conduction through the film
into the tooth surfaces, and by convection
as the hot oil exits the outlet region.
Due to the short contact time the heat
penetrates only a shallow distance into
the gear teeth and is rapidly dissipated.
Consequently, as the contact point moves
on, the heat input disappears immediately
and the surface temperature of the gear
teeth returns promptly to the equilibrium
bulk temperature. After one revolution
of the gear, a particular point on the gear
flank comes into engagement with essentially
the same bulk temperature as the
previous engagement. Although frictional
heating does not directly alter the film
thickness within the Hertzian region, any
increase of the bulk surface temperatures
due to frictional heating indirectly reduces
film thickness by decreasing the viscosity
of the lubricant in the inlet region.
The sliding is significant because it
generates traction forces that result in
energy losses. If the lubricant behaved
like a Newtonian fluid, the high viscosity
would lead to extremely high traction
force. Fortunately, however, when subjected
to high shear stresses the lubricant
behaves like a plastic pseudo-solid with
limited shear strength that is characterized
by its traction coefficient. The bulk
surface temperatures are controlled by
heat generated in the Hertzian region and
the temperatures can vary significantly,
depending on the molecular structure
of the lubricant base stock, which influences
a lubricant’s solidification pressure,
shear strength, and traction coefficient.
Furthermore, depending on anti-wear
and anti-scuff additives that may be in
the lubricant, the sliding and heat generate
boundary tribofilms that help to prevent
adhesive wear.
Shear thinning. Lubricants containing
high molecular weight polymers, which
are additives known as a viscosity index
(VI) improvers, may lose viscosity under
the high shear rates that occur in the
Hertzian region and reduce the EHL film
thickness. This is known as shear thinning.
The outlet region. As the lubricant
leaves the Hertzian zone, film pressure
tends to boost the lubricant flow toward
the outlet region. The amount of lubricant
within the contact is controlled by
the inlet and continuity of flow can only
be maintained if there is a local restriction
in the outflow, which causes a constriction
to form at the outlet. This is the
position where the minimum film thickness
occurs. A sharp spike is generated in
the film pressure next to the constriction
on the upstream side. The pressure drops
abruptly to atmospheric pressure downstream
of the spike and the lubricant viscosity
returns to its atmospheric viscosity.
Consequently, the contact pressure
between the surfaces is negligible in the
area of the minimum film thickness. The
divergent region of the outlet generates
negative pressure that causes dissolved
gases in the lubricant to come out of solution.
This ruptures the lubricant film,
which cavitates and forms a wavy wake
that consists of separate lubricant streamers
intermixed with air.
