From Wikipedia, the free encyclopedia
Roughness is a measure of the texture of a surface. 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 (see surface metrology).
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 (see
tribology). 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.
Although roughness is usually 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.
Principle of a contacting stylus instrument profilometer:
A cantilever is holding a small tip that is sliding
along the horizontal direction over the object's
surface. Following the profile the cantilever is moving
vertically. The vertical position is recorded as the
measured profile shown in light green.Roughness
may be measured using contact or non-contact methods.
Contact methods involve dragging a measurement stylus
across the surface; these instruments include
profilometers. Non-contact methods include
interferometry, confocal microscopy, electrical
capacitance and electron microscopy.
Sketch depicting how a probe stylus travels over a
surface.For 2D measurements, the probe usually traces
along a straight line on a flat surface or in a circular
arc around a cylindrical surface. The length of the path
that it traces is called the measurement length. The
wavelength of the lowest frequency filter that will be
used to analyze the data is usually defined as the
sampling length. Most standards recommend that the
measurement length should be at least seven times longer
than the sampling length, and according to the Nyquist–Shannon
sampling theorem it should be at least ten times longer
than the wavelength of interesting features. The
assessment length or evaluation length is the length of
data that will be used for analysis. Commonly one
sampling length is discarded from each end of the
For 3D measurements, the probe is commanded to scan over
a 2D area on the surface. The spacing between data
points may not be the same in both directions.
In some cases, the physics of the measuring instrument
may have a large effect on the data. This is especially
true when measuring very smooth surfaces. For contact
measurements, most obvious problem is that the stylus
may scratch the measured surface. Another problem is
that the stylus may be too blunt to reach the bottom of
deep valleys and it may round the tips of sharp peaks.
In this case the probe is a physical filter that limits
the accuracy of the instrument.
There are also limitations for non-contact instruments.
For example instruments that rely on optical
interference cannot resolve features that are less than
some fraction of the frequency of their operating
wavelength. This limitation can make it difficult to
accurately measure roughness even on common objects,
since the interesting features may be well below the
wavelength of light. The wavelength of red light is
about 650 nm, while the Ra of a ground shaft might be
In the past, surface finish was usually analyzed by
hand. The roughness trace would be plotted on graph
paper, and an experienced machinist decided what data to
ignore and where to place the mean line. Today, the
measured data is stored on a computer, and analyzed
using methods from signal analysis and statistics.
The first step of roughness analysis is often to filter
the raw measurement data to remove very high frequency
data since it can often be attributed to vibrations or
debris on the part surface. Next, the data is separated
into roughness, waviness and form. This can be
accomplished using reference lines, envelope methods,
digital filters, fractals or other techniques. Finally
the data is summarized using one or more of the
roughness parameters, or a graph.
Illustration of the effect of different form removal
techniques on surface finish analysis.
Plots showing how filter cutoff frequency affects the
separation between waviness and roughness.
Illustration showing how the raw profile from a surface
finish trace is decomposed into a primary profile, form,
waviness and roughness.
Illustration showing the effect of using different
filters to separate a surface finish trace into waviness
In the United States, surface finish is usually
specified based on the ASME Y14.36M-1996 standard. Other
standards also exist, including ISO 1302:2001.
Illustration of how to specify surface finish on a
Example surface finish lay patterns.A lay pattern is a
repetitive impression created on the surface of a part.
It is often representative of a specific manufacturing
operation. A product designer may specify a lay pattern
on a part because the directionality the lay affects the
part's function. Unless otherwise specified, roughness
is measured perpendicular to the lay.
Each of the roughness parameters is calculated using a
formula for describing the surface.
There are many different roughness parameters in use,
but Ra is by far the most common. Other common
parameters include Rz, Rq, and Rsk. Some parameters are
used only in certain industries or within certain
countries. For example, the Rk 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.
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
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 n ordered, equally spaced
points along the trace, and yi is the vertical distance
from the mean line to the ith data point. Height is
assumed to be positive in the up direction, away from
the bulk material.
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, Ra is the arithmetic
average of the absolute values and Rt is the range of
the collected roughness data points.
The amplitude parameters are by far the most common
surface roughness parameters found in the United States
on mechanical engineering drawings and in technical
literature. Part of the reason for their popularity is
that they are straightforward to calculate using a
Parameter Description Formula
Ra, Raa, Ryni arithmetic average of absolute values
Rq, RRMS root mean squared
Rv maximum valley depth Rv = miniyi
Rp maximum peak height Rp = maxiyi
Rt Maximum Height of the Profile Rt = Rp − Rv
RzDIN, Rtm average distance between the highest peak and
lowest valley in each sampling length, ASME Y14.36M -
1996 Surface Texture Symbols , where s is the number of
sampling lengths, and Rti is Rt for the ith sampling
RzJIS Japanese Industrial Standard for Rz, based on the
five highest peaks and lowest valleys over the entire
sampling length. , where Rpi Rvi are the ith highest
peak, and lowest valley respectively.
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.
Parameter Description Formula
Rdq, R?q the RMS slope of the profile within the
Bearing Ratio Curve Parameters
These parameters are based on the bearing ratio curve
(also known as the Abbott-Firestone curve.) This
includes the Rk family of parameters.
Sketches depicting surfaces with negative and positive
skew. The roughness trace is on the left, the amplitude
distribution curve is in the middle, and the bearing
area curve (Abbott-Firestone curve) is on the right.
 Fractal theory
The mathematician Benoît Mandelbrot has pointed out the
connection between surface roughness and fractal
In most cases, 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.
It can be difficult to quantify the relationship between
roughness and part performance because there are so many
different ways to characterize the surface.
Roughness is often closely related to the friction and
wear properties of a surface. A surface with a large Ra
value, or a positive Rsk, will usually have high
friction and wear quickly.
Deep valleys in the roughness profile are also important
to tribology because they may act as lubricant
The peaks in the roughness profile are not always the
points of contact. The form and waviness must also be
Many factors contribute to the surface roughness in
manufacturing. When molding or forming a surface, the
impression of the mold or die on the part is usually the
principle factor in the surface roughness. In machining,
and abrasive processes the interaction of the cutting
edges and the microstructure of the material being cut
both contribute to the roughness.
Just as different manufacturing processes produce parts
at various tolerances, they are also capable of
different roughnesses. Generally these two
characteristics are linked: manufacturing processes that
are dimensionally precise create surfaces with low
roughness. In other words, if a process can manufacture
parts to a narrow dimensional tolerance, the parts will
not be very rough.
Surface finishes produced by common manufacturing
In general, the cost of manufacturing a surface
increases greatly as the roughness tolerance decreases.
International Roughness Index (IRI) - a dimensionless
quantity used for measuring road roughness and proposed
as a world standard by the World Bank. Typically IRI is
presented as an average value over 20 m, 100 m, 400 m, 1
mile etc. IRI is not an excellent indicator on ride
quality. Consider two 10 cm high and arc-shaped traffic
calming speed bumps, one "spinebreaker" being 1 m long
and the other being as much as 10 m long and thus too
smooth for calming city traffic. Both give an IRI20 of
about 8 mm/m. Not being able to distinguish between two
bumps that obviously give dramatically different ride
quality, one can really question IRI as a pavement
Manning's n-value - used by geologists to characterise