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**2 D (Profile) Stylus Parameters**

**Stylus (X,Y) (Ra, Rt, Rz)****Stylus (X,Y) Rk, Rpk, Rvk****Stylus (X,Y) Δq****Stylus (X,Y) λq****Stylus (X,Y) Pc****Stylus (X,Y) Rsm****Stylus X to Stylus Y Ratios**

Once 3D data is acquired, a number of surface calculations are performed simulating the measurement of the surface with a 2D stylus profiling device. The 3D data is considered as a series of profiles in parallel along the X and Y axes. Each profile is filtered according to the ANSI/ASME B46.1 Standard, with short wavelength and long wavelength cutoffs. A filtered profile may consist of multiple sampling lengths (typically equal to the long wavelength cutoff). The total length of a filtered profile is termed the Evaluation Length. For the WYKO data, there is typically only 1 cutoff length and thus the cutoff length equals the Evaluation Length. However, some application may result in multiple cutoff lengths (i.e. sampling lengths) per evaluation length. After filtering, the various surface texture parameters are evaluated for each profile. Finally, the average value for a given surface texture parameter is then found over all the profiles considered.

Typically, over 400 profiles are analyzed per 3D image in both the X and Y directions. The figure below demonstrates how a turned surface would appear after the various Stylus X and Stylus Y filters are applied prior to the evaluation of the individual profile.

**Stylus X
Ra, Stylus X Rt, Stylus X Rz**, **Stylus Y Ra, Stylus
Y Rt, Stylus Y Rz**

**Stylus X Ra **and **Stylus Y Ra , **the
Average Roughness Along X and the Average Roughness Along Y, are
found from the integral of the profiles along the respective directions:

**Stylus (X, Y) Rt**, the Maximum Profiler
Height Along (X,Y),
is determined from the difference between the highest peak and lowest
valley found along the __evaluation__ length.

**Stylus (X,Y) Rz, **the Average
Maximum Profiler Height Along (X,Y), is derived from the
average, over all cutoff lengths (i.e. sampling lengths), of the difference
between the highest peak and lowest valley. Note, if the evaluation length
equals the sampling length then the Stylus (X.Y) Rt and Stylus (X,Y) Rz
values are equal.

Note that the value reported in the database is
the average of all **Stylus (X,Y)** **Ra**, **Rt**, **Rz** values
found over the 400+ profiles that comprise the 3D surface in the relevant
direction.

Application

**Stylus (X,Y)** (**Ra**, **Rt**, **Rz)** may
be useful in understanding any directionally dependent surface texture function.
For example, a surface used for sealing may require a larger roughness average
along the leak path direction (e.g. the X direction) and lower roughness average
perpendicular (e.g. the Y direction) to the leak path for proper seal engagement.

**Stylus
(X, Y) Rk**, Rpk, Rvk

The **Stylus (X, Y) Rk** parameters, are derived
from the bearing ratio curve based on the
ISO 13565-2:1996 standard. For each profile, a bearing area curve is generated
by simulating a horizontal line moving through the profile from the top
down, evaluating the percentage of contact the line would make with the surface
at each level.

From the bearing area curve, **Stylus (X,Y) Rpk, **the Reduced
Peak Height Along (X,Y), is found from a measure of the peak height above the core roughness. **Stylus
(X,Y) Rvk, **the Reduced Valley Depths Along (X, Y), is found from a measure of the valley depths below the core roughness. **Stylus (X, Y) Rk**, the Core Roughness Along (X, Y), is a measure of the core (peak to valley) roughness of the surface with the major peaks and valleys (established by **Stylus (X, Y) Rpk** and **Stylus (X, Y) Rvk ** removed.

Note that each profile in the X and Y directions are evaluated individually and the resulting average of a given parameter is reported.

Application

A high **Stylus (X, Y) Rpk** implies
a surface composed of high peaks providing small initial contact area and
thus high areas of contact stress when the surface is contacted. **Stylus
(X, Y) Rpk** may
represent the nominal height of the material that may be removed during
a running-in operation. **Stylus (X, Y) Rvk**
is a measure of the valley depths below the core roughness and may be related
to lubricant retention and debris entrapment.
By comparing the various parameters
along the different directions (X vs. Y) one may also assess the uniformity
of the surface peak and valley distributions relative to a particular
direction of interest. **Stylus (X, Y) Rk** is
a measure of the nominal roughness (peak to valley) and may be used to
replace parameters such as **Stylus (X, Y)** **Ra**, **Stylus
(X, Y) Rt**, or **Stylus (X, Y)** **Rz** when
anomalous peaks or valleys may adversely affect the repeatability of these
parameters.

Stylus XΔq, Stylus YΔq

**Stylus (X, Y) Δq** is
the Root Mean Square Slope Along (X,Y). The **Stylus X ****Δq** and **Stylus
Y ****Δq** calculations find the rms (standard
deviation) of the profile slope given by:

From Fourier analysis, the surface texture is composed of a series of sine waves in all directions with different spatial frequencies (i.e. 1 /spatial wavelength) and amplitudes. The power spectrum is a measure of the amplitude of each sine wave for a particular spatial frequency, along a given direction. Thus for a 3D surface, the power spectrum would be displayed as a “3D” function in which the X and Y axes represent the various spatial frequencies for a given direction. The amplitude of the power spectrum (displayed on the Z axis) represents the amplitude of the sine wave at a particular spatial frequency direction. The angular power spectrum is found by integrating the amplitudes of each component sine wave as a function of angle.

The figures below demonstrate a crosshatched surface, the power spectral density of the surface and the angular power spectral density function.

Application

The **Δq** measurements along the X and
Y directions provides a quantitative assessment of the rate of change of
the surface heights over the profile length. Since the slope values are
squared prior to integration, the polarity (i.e. positive or negative)
of the slope is lost in the calculation. The **Δq** measurements
may be useful in applications where a machining process is producing parts
with nominally correct amplitude parameters (e.g. **Ra**)
but has other functional or process problems. For machining operations,
parameters associated with the materials or machine setup may be manifested
in significant changes in the surface slopes, easily measured by **Δq**.
The wetting characteristics of a surface and the surface area of a texture
may be related to **Δq.**

Stylus Xλq, Stylus Yλq

**Stylus (X ,Y) λq** ,
the Root Mean Square (rms) Profile Wavelength Along (X, Y), is a measure
of the dominant spatial wavelength that comprises the surface weighted
by the amplitude of the various spatial components. The evaluation of these
parameters stems from Fourier analysis of the surface texture resulting
in the following:

Application

The **λq** measurements along the X and Y directions provide a quantitative measure of the key spatial wavelengths that comprise the texture in the respective directions. A surface that
has a high amplitude long wavelength wavy structure on which are superimposed small amplitude short wavelength texture features will have a **λq** representative of the long wavelength structure. However, as the amplitude of the shorter wavelength structure begins to approach that of the long wavelength structure,
the measured **λq** will seek a value somewhere between the long wavelength and short wavelength values. **λq** is used when tool feed rates are under investigation and as a further means to differentiate surfaces/processes that yield similar amplitude parameters (e.g. **Ra**) but function differently. **λq** may be related to the appearance of a surface and also the real area of contact between loaded components.

Stylus X Pc, Stylus Y Pc

**Stylus (X,Y) Pc** the Peak
Density Along (X,Y), measures the number of peaks per unit length
in the X and Y directions respectively. A peak is defined as when the
profile intersects consecutively a lower and upper boundary level set
at a height above and depth below the mean line, equal to **Ra,** for
the profile being analyzed.

Application

**Stylus X Pc **and **Stylus Y Pc** are
useful parameters for assessing the peak density (e.g. peaks/mm) along
a given direction. Applications involved in coating a surface, or when
fluid leakage/retention are of issue may make use of the **Pc** parameters
to optimize the surface texture design. Sometimes the combination of parameters
such as **Rz** with **Pc** will yield additional
information about the spacing and depth of dominant surface features that
may affect

the function of a component.

Stylus X Rsm, Stylus Y Rsm

**S****tylus (X,Y) Rsm, **the
Mean Profile Spacing Along (X,Y), * *is a measure of the average
length between points along the profile which cross the mean line with
the same slope direction. For a profile element to be considered, the feature
must extend above and below the mean line by more than 10% of Rz and be
spaced apart from a previous feature by at least 1% of the sampling length.

Application

**Stylus X Rsm **and **Stylus
Y Rsm** are used to understand the dominant width of features
and thus may be useful in understanding chanels for fluid flow and void
space for coating coverage applications. Depending on the material properties,
closer spaced texture (i.e. small Rsm) may be more prone to plastic deformation
upon contact than wider spaced (i.e. large **Rsm**) features.

S**tylus
X Ra/Stylus Y Ra, Stylus X Rz/Stylus Y Rz,
Stylus X Δq/Stylus Y Δq,
Stylus X λq/Stylus Yλq,
Stylus X Pc/ Stylus Y Pc**

The various **Stylus X/Stylus Y** ratios
are found by dividing the corresponding Stylus X parameter(e.g. **Stylus X Ra**) by the corresponding Stylus
Y Parameter (e.g. **Stylus Y Ra**). Thus the various ratios are
unitless quantities.

Application

The ratio of the various Stylus X and Stylus Y parameters
demonstrates the spatial isotropy of the surface texture. For example,
the lathe-turned

surface (Figure A) has a high degree of anisotropy and thus the ratio of **Stylus
X Ra/Stylus Y Ra** is greater than 1.00. A shot peened isotropic
surface will tend to have Stylus X & Y ratios of about 1.00. The ratios
may be used to assess the ability for a given surface finishing operation to
remove remnants of a previous operation. The ratios may also be used to uncover
any dominant surface directional paths that may contribute to fluid leakage.