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**3D Functional Parameters **

**mr (Material Ratio)****Smr(c) Areal Material Ratio****Sdc(mr) Inverse Areal Material Ratio****Spk, Sk, Svk, SMr1, SMr2****Spk/Sk, Svk/Sk, Spk/Svk****Sxp (p,q) (Peak Extreme Height)****Vv(mr), Vvv(p), Vvc(p,q)****Vm(mr), Vmp(p), Vmc(p,q)**

mr (Material Ratio)

The Material Ratio, **mr**,
is the ratio of the intersecting area of a plane (i.e. parallel to the
mean plane) passing through the surface at a given height to the cross
sectional area of the evaluation region. The **Areal
Material Ratio** **Curve** (*aka* **Bearing
Area Curve** or **Abbot Firestone Curve**) is established
by evaluating **mr** at various levels from the highest peak
to the lowest valley.

Prior to establishing the Areal Material
Ratio Curve, a certain percentage of the peak points (i.e., the **Peak
Offset**)
and valley points (i.e., the **Valley Offset**) are eliminated
to minimize the effects of outliers. Typically
the Peak Offset and Valley Offset are set to 1%, unless otherwise specified. **mr** is
also referred to as “**Percent Data Cut**.”

Smr(c) (Areal Material Ratio)

The Areal Material Ratio, **Smr(c)** is
the ratio (expressed as a percentage) of the cross sectional area of the
surface at a height (c) relative to the evaluation cross sectional area.
The height (c) may be measured from the best fitting least squares mean
plane or as a depth down from the maximum point of the Areal Material Ratio
Curve.

Application

**Smr(c)** may used to determine
the amount of bearing area remaining after a certain depth of material
is removed from the surface. A typical application may be in the specification
of engine cylinder bore surfaces prior to running-in. Typically a cylinder
bore may be honed to produce a pattern consisting of a plateau-like surface
upon which are superimposed fine peaked structures. The fine peaked structure
is provided to augment final running-in/seating of the sliding piston rings.
Thus a specification for a surface may be **Smr(0.5µm) > 40%,** measured
from the Max Value Areal Material Ratio curve with 1% peak and 1% valley
offsets. This specification would be developed based on experiments that
determine, for example, that running-in typically removes the top 0.5µm
of the surface heights before surface stabilization.

Sdc(mr) (Inverse Areal Material Ratio)

The Inverse Areal Material ratio, **Sdc(mr)** is
the height , **c**, which gives the specified material
ratio, **mr**. The height ** c** may be measured
from the best fitting least squares mean plane or as a depth down from
the maximum point of the Areal Material Ratio Curve.

Application

**Sdc(mr)** might
be used to assure that an optimum crevice volume is produced for a sealing
surface to allow for some lubricant entrapment (to prevent running dry)
but not be too deep to prevent leakage. For example, a specification such
as -0.4 um <Sdc(100%)<-0.8 µm with a 1% peak and 1% valley offset,
measured from the mean plane, would assure that the bottom 50% or the surface
would extend at least 0.4 um below the mean plane but
no greater than 0.8µm.

Spk (Reduced Peak Height), Sk (Core Roughness Depth), Svk (Reduced Valley Depth), SMr1 (Peak Material Portion), SMr2 (Peak Valley Portion)

The parameters **Spk**, **Sk**, **Svk**, **SMr1**,
and **SMr2** are all derived from the Areal Material Ratio curve
based on the
ISO 13565-2:1996 standard. The Reduced Peak Height, **Spk**, is
a measure of the peak height above the core roughness. The Core Roughness Depth, **Sk**, is
a measure of the “core” roughness
(peak-to-valley) of the surface with the predominant peaks and valleys removed.
The Reduced Valley Depth, **Svk**, is
a measure of the valley depth below the core roughness. **SMr1**,
the Peak Material Portion, indicates
the percentage of material that comprises the peak structures associated with **Spk**. The
Valley Material Portion, **SMr2**, relates
to the percentage (i.e., 100%-**SMr2**)
of the measurement area that comprises the deeper valley structures associated
with **Svk**.

Application

A large **Spk** implies a surface composed of high peaks providing
small initial contact area and thus high areas of contact stress (force/area)
when the surface is contacted. Thus **Spk** may represent the
nominal height of the material that may be removed during a running-in operation.
Consistent with **Spk**, **SMr1** represents the
percentage of the surface that may be removed during running-in. **Sk** represents
the core roughness of the surface over which a load may be distributed after
the surface has been run-in. **Svk** is a measure of the valley
depths below the core roughness and may be related to lubricant retention
and debris entrapment. **Sk** is a measure of the nominal roughness
(peak to valley) and may be used to replace parameters such as **Sz** when
anomalous peaks or valleys may adversely affect the measurement.

Spk/Sk (Reduced Peak Height to Core Ratio), Svk/Sk (Reduced Valley Depth to Core Ratio), Spk/Svk (Reduced Peak Height to Reduced Valley Depth Ratio)

The ratios of the various areal material
ratio parameters **Spk/Sk** , the Reduced Peak Height to Core
Ratio, **Svk/Sk**, the Reduced Valley Depth to Core Ratio, and **Spk/Svk**,
the Reduced Peak Height to Reduced Valley Depth Ratio may be helpful in
further understanding the nature of a particular surface texture. In some
instances, two surfaces with indistinguishable roughness average (**Sa**)
may be easily distinguished by a ratio such as **Spk/Sk**. For
example a surface with high peaks as opposed to a surface with deep valleys
may have the same **Sa** but
with vastly
different **Spk/Sk** values.

Application

By considering the ratios such as **Spk/Sk**, **Svk/Sk** and **Spk/Svk** one
may determine quantitatively the dominance of peak structures relative
to valley structures. In typical tribological applications such as seals and
bearings these ratios may be useful in differentiating surfaces that have similar
surface roughness as measured by **Sa**. The ratios may be further
thought of as a measure of the texture amplitude distribution normalized by the
overall roughness magnitude and thus may be used to characterize the texture
amplitude symmetry.

Sxp (p,q) Peak Extreme Height

The Peak Extreme Height, **Sxp
(p,q)**, is a measure of the difference in heights on the
surface from the areal material ratio value of “p” and the
areal material ratio of “q”. The default value for “p” is
97.5% and the default value
for “q” is 50%.

Application

Assuming a surface was worn or modified such that the
resulting material area was 50%, **Sxp** (97.5%, 50%) indicates the depth of
the remaining material to the lowest regions of the texture. Thus **Sxp **(97.5%,50%)
may be used to determine the depth of material available after 50% or the
surface has either been removed or deformed to a plateau-like structure.
By changing the values of “p” and “q”, **Sxp** (p,q)
may be used to control other aspects of the texture.

As another example, **Sxp** (90%, 10%) may
be used to control the overall “peak-to
valley” height of the surface by not accounting for the top 10%
of the surface which may likely be easily deformed/worn and the bottom
10% which may be easily filled in during initial surface interactions.

Vv(mr) (Void Volume), Vvv(p) (Dale Void Volume), Vvc(p,q) (Core Void Volume)

**Vv(mr), **the Void Volume**, ** is
the volume of space bounded by the surface texture from a plane at a
height corresponding to a chosen “**mr**” value
to the lowest valley. “**mr**” may be set to
any value from 0% to 100%.

**Vvv(p)**, the Dale Void Volume, is
the volume of space bounded by the surface texture from a plane at a
height corresponding to a material ratio (mr) level, “**p**” to
the lowest valley. The default value for “**p**” is
80% but may be changed as needed.

**Vvc(p,q)**, The Core Void Volume**, **is
the volume of space bounded by the texture at heights corresponding
to the material ratio values of “**p**” and “**q**”.
The default value for “**p**” is 10% and the
default value for “**q**” is 80%.

Application

**Vv(mr)**, **Vvv(p)** and **Vvc(p,q)** all
indicate a measure of the void volume provided by the surface between various
heights as established by the chosen material ratio(s) values. Thus
these three void volume parameters indicate how much fluid would fill the
surface (normalized to the measurement area) between the chosen material
ratio values. For example, a **Vv(25%)** = 0.5 µm3/µm2 in (note
how the units µm3/µm2 reduce to µm) that a 0.5 µm
thick film over the measurement area would provide the same volume of fluid
as needed to fill the measured surface from a height corresponding to mr=25%
to the lowest valley.

The void volume parameters are useful when considering
fluid flow, coating applications and debris entrapment. A new surface may
be specified by **Vv(0%)** which
would indicate the total initial void volume provided by the texture. The
Core Void Volume , **Vvc,** may be useful to establish how
much core space is available once a surface has been run-in resulting in
decreased peak heights . The Dale Void Volume, **Vvv(p)** may
be useful in indicating the potential remaining volume after significant
wear of a surface has resulted.

Vm(mr) (Material Volume) , Vmp(p) (Peak Material Volume), Vmc(p,q) (Core Material Volume)

**Vm(mr)**, the Material Volume**, ** is
the volume of material comprising the surface from the height corresponding
to **mr** to the highest peak of the surface. “**mr**” may
be set to any value from 0% to 100%.

**Vmp(p)****,
the Peak Material Volume,** is
the volume of material comprising the surface from the height corresponding
to a material ratio level, “**p**”, to the highest
peak. The default value for “**p**” is 10% but
may be changed as needed.

**Vmc(p,q)****,
the Core Material Volume, is the **volume of material comprising
the texture between heights corresponding to the material ratio values
of “**p**” and “**q**”.
The default value for “**p**” is 10% and the
default value for “**q**” is 80% but may be
changed as needed.

Application

**Vm(mr)**, **Vmp(p)** and **Vmc(p,q)** all
indicate a measure of the material forming the surface at the various heights
down from the highest peak of surface or between various heights as defined
for Vmc(p,q).

For example, a **Vm(10%)** =0.35µm3/µm2
would indicate (note how the units µm3/µm2 reduce to µm) that a layer 0.35µm
thick of material over the measured cross section would account for all
the material from the highest peak to the 10% point on the bearing area
curve.

The various Material Volume parameters are useful to
understand how much material may be worn away for a given depth of the
bearing curve (i.e. **Vmp(p)**) and how much material is available for load
support once the top levels of a surfaces are worn away (i.e. **Vmc(p,q)**). For
sealing applications, **Vmp(p)** may provide insight into the amount of material
available for seal engagement whereas **Vvc(p.q)** (see above) may then provide
information about the resulting void volume for fluid entrapment or leakage.