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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.”

Areal Material Ratio Curve and evaluation of mr. Note that the profiles is shown above for simplicity. When evaluating the 3D (Areal) parameters the analysis applies to the complete 3D dataset.

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.

Two surfaces with the same Sa but 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%.

Example of Void, Dale Void and Core Void volumes. Note: The units for the Vv(mr), Vv(p) and Vvc(p,q) are um3/um2 - the void volume normalized by the cross sectional area of the measurement area. The peak offsets and valley offsets are applied prior to analysis.

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.

Note: The units for the Vv(mr), Vv(p) and Vvc(p,q) are µm3/µm2 - the void volume normalized by the cross sectional area of the measurement area. The peak offsets and valley offsets are applied prior to analysis.

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.

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