Surface roughness, often shortened to roughness, is a component of surface texture. It is quantified
by the vertical deviations of a real surface from its ideal form. If these deviations are
large, the surface is rough; if they are small, the surface is smooth. Roughness is typically
considered to be the high-frequency, short-wavelength component of a measured surface. However,
in practice it is often necessary to know both the amplitude and frequency to ensure
that a surface is fit for a purpose. Roughness plays an important role in determining
how a real object will interact with its environment. Rough surfaces usually wear more quickly and
have higher friction coefficients than smooth surfaces. Roughness is often a good predictor
of the performance of a mechanical component, since irregularities in the surface may form
nucleation sites for cracks or corrosion. On the other hand, roughness may promote adhesion.
Although roughness is often undesirable, it is difficult and expensive to control in manufacturing.
Decreasing the roughness of a surface will usually increase exponentially its manufacturing
costs. This often results in a trade-off between the manufacturing cost of a component and
its performance in application. Roughness can be measured by manual comparison
against a "surface roughness comparator", a sample of known surface roughnesses, but
more generally a Surface profile measurement is made with a profilometer that can be contact
or optical. However, controlled roughness can often be
desirable. For example, a gloss surface can be too shiny to the eye and too slippy to
the finger so a controlled roughness is required. This is a case where both amplitude and frequency
are important.
Parameters A roughness value can either be calculated
on a profile or on a surface. The profile roughness parameter are more common. The area
roughness parameters give more significant values.
Profile roughness parameters Each of the roughness parameters is calculated
using a formula for describing the surface. Although these parameters are generally considered
to be "well known" a standard reference describing each in detail is Surfaces and their Measurement.
There are many different roughness parameters in use, but is by far the most common though
this is often for historical reasons not for particular merit as the early roughness meters
could only measure . Other common parameters include , , and . Some parameters are used
only in certain industries or within certain countries. For example, the family of parameters
is used mainly for cylinder bore linings, and the Motif parameters are used primarily
within France. Since these parameters reduce all of the information
in a profile to a single number, great care must be taken in applying and interpreting
them. Small changes in how the raw profile data is filtered, how the mean line is calculated,
and the physics of the measurement can greatly affect the calculated parameter. With modern
digital equipment it makes sense to look at the scan and make sure there aren't some obvious
glitches that are skewing the values - and if there are, to re-measure.
Because it is not obvious to many users what each of the measurements really means, it
is helpful to have a simulation tool that lets you "play" with key parameters and see
how well surfaces which are obviously different to the human eye are differentiated by the
measures. It is clear, for example that would fail to distinguish between two surfaces where
one is composed of peaks on an otherwise smooth surface and the other is composed of troughs
of the same amplitude. Such tools can be found in app format.
By convention every 2D roughness parameter is a capital R followed by additional characters
in the subscript. The subscript identifies the formula that was used, and the R means
that the formula was applied to a 2D roughness profile. Different capital letters imply that
the formula was applied to a different profile. For example, Ra is the arithmetic average
of the roughness profile, Pa is the arithmetic average of the unfiltered raw profile, and
Sa is the arithmetic average of the 3D roughness. Each of the formulas listed in the tables
assumes that the roughness profile has been filtered from the raw profile data and the
mean line has been calculated. The roughness profile contains ordered, equally spaced points
along the trace, and is the vertical distance from the mean line to the data point. Height
is assumed to be positive in the up direction, away from the bulk material.
Amplitude parameters Amplitude parameters characterize the surface
based on the vertical deviations of the roughness profile from the mean line. Many of them are
closely related to the parameters found in statistics for characterizing population samples.
For example, is the arithmetic average of the absolute values and Rt is the range of
the collected roughness data points. The roughness average, , is the most widely
used one-dimensional roughness parameter. Slope, spacing, and counting parameters
Slope parameters describe characteristics of the slope of the roughness profile. Spacing
and counting parameters describe how often the profile crosses certain thresholds. These
parameters are often used to describe repetitive roughness profiles, such as those produced
by turning on a lathe. Other "frequency" parameters are Sm, a and
q. Sm is the mean spacing between peaks. Just as with real mountains it is important to
define a "peak". For Sm the surface must have dipped below the mean surface before rising
again to a new peak. The average wavelength a and the root mean square wavelength q are
derived from a. When trying to understand a surface that depends on both amplitude and
frequency it is not obvious which pair of metrics optimally describes the balance, so
it is a good idea to do a statistical analysis of pairs of measurements to find the strongest
correlation. Bearing ratio curve parameters
These parameters are based on the bearing ratio curve This includes the Rk family of
parameters.
Fractal theory The mathematician Benoît Mandelbrot has pointed
out the connection between surface roughness and fractal dimension.
Areal roughness parameters Areal roughness parameters are defined in
the ISO 25178 series. The resulting values are Sa, Sq, Sz,... . At the moment many optical
measurement instruments are able to measure the surface roughness over an area.
Practical effects In terms of engineering surfaces, roughness
is considered to be detrimental to part performance. As a consequence, most manufacturing prints
establish an upper limit on roughness, but not a lower limit. An exception is in cylinder
bores where oil is retained in the surface profile and a minimum roughness is required.
Roughness is often closely related to the friction and wear properties of a surface.
A surface with a large value, or a positive , will usually have high friction and wear
quickly. The peaks in the roughness profile are not always the points of contact. The
form and waviness must also be considered. It affects the productivity of wind generation
farms. See also
Discontinuity Rugosity
Surface finish Surface metrology
Surface roughness measurement ISO 25178 Waviness
References ^ Whitehouse, David. Surfaces and their Measurement.
Boston: Butterworth-Heinemann. ISBN 978-0080972015. ^ Abbott, Steven. "SPE". AbbottApps. Steven
Abbott TCNF Ltd. Retrieved January 13, 2014. ^ a b c d Degarmo, E. Paul; Black, J --~~~~--~~~~--~~~~.; Kohser,
Ronald A., Materials and Processes in Manufacturing, Wiley, p. 223, ISBN 0-471-65653-4.
^ Den Outer, A.; Kaashoek, J.F.; Hack, H.R.G.K.. "Difficulties of using continuous fractal
theory for discontinuity surfaces". International Journal of Rock Mechanics and Mining Science
& Geomechanics Abstracts 32: 3–9. doi:10.1016/0148-9062(94)00025-X.
External links Surface Metrology Guide
Roughness terminology Ra and Rz description
Surface Roughness Review and Equations SPE