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Surface roughness, often shortened to roughness, is a component of
surface finish (surface texture). It is quantified by the deviations in the direction of the
normal vector
In geometry, a normal is an object such as a line, ray, or vector that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the (infinite) line perpendicular to the tangent line to the curve at ...
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. In
surface metrology
Surface metrology is the measurement of small-scale features on surfaces, and is a branch of metrology. Surface primary form, surface fractality, and surface finish (including surface roughness) are the parameters most commonly associated with th ...
, 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. In
tribology
Tribology is the science and engineering of interacting surfaces in relative Motion (physics), motion. It includes the study and application of the principles of friction, lubrication and wear. Tribology is highly interdisciplinary, drawing on m ...
, rough surfaces usually
wear
Wear is the damaging, gradual removal or deformation of material at solid surfaces. Causes of wear can be mechanical (e.g., erosion) or chemical (e.g., corrosion). The study of wear and related processes is referred to as tribology.
Wear in m ...
more quickly and have higher
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
coefficients than smooth surfaces. Roughness is often a good predictor of the performance of a mechanical component, since irregularities on the surface may form nucleation sites for cracks or corrosion. On the other hand, roughness may promote
adhesion
Adhesion is the tendency of dissimilar particles or surfaces to cling to one another ( cohesion refers to the tendency of similar or identical particles/surfaces to cling to one another).
The forces that cause adhesion and cohesion can be ...
. Generally speaking, rather than scale specific descriptors, cross-scale descriptors such as
surface fractality provide more meaningful predictions of mechanical interactions at surfaces including
contact stiffness and
static friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
.
Although a high roughness value is often undesirable, it can be difficult and expensive to control in
manufacturing
Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to a r ...
. For example, it is difficult and expensive to control surface roughness of
fused deposition modelling
Fused filament fabrication (FFF), also known as fused deposition modeling (with the trademarked acronym FDM), or called ''filament freeform fabrication'', is a 3D printing process that uses a continuous filament of a thermoplastic material. Filam ...
(FDM) manufactured parts. Decreasing the roughness of a surface usually increases its manufacturing cost. 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 roughness), but more generally a
surface profile measurement
A profilometer is a measuring instrument used to measure a surface's profile, in order to quantify its roughness. Critical dimensions as step, curvature, flatness are computed from the surface topography.
While the historical notion of a pro ...
is made with a
profilometer
A profilometer is a measuring instrument used to measure a surface's profile, in order to quantify its roughness. Critical dimensions as step, curvature, flatness are computed from the surface topography.
While the historical notion of a pro ...
. These can be of the contact variety (typically a diamond stylus) or optical (e.g.: a white light
interferometer
Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber op ...
or
laser scanning confocal microscope).
However, controlled roughness can often be desirable. For example, a gloss surface can be too shiny to the eye and too slippery to the finger (a touchpad is a good example) so a controlled roughness is required. This is a case where both amplitude and frequency are very important.
Parameters
A roughness value can either be calculated on a profile (line) or on a surface (area). The profile roughness parameter (
,
, ...) are more common. The area roughness parameters (
,
, ...) give more significant values.
Profile roughness parameters
![Roughness rus](https://upload.wikimedia.org/wikipedia/commons/3/32/Roughness_rus.png)
The profile roughness parameters are included in BS EN ISO 4287:2000 British standard, identical with the ISO 4287:1997 standard.
[BS EN ISO 4287:2000, Geometrical product specification (GPS). Surface texture. Profile method. Terms, definitions and surface texture parameters] The standard is based on the ″M″ (mean line) system.
There are many different roughness parameters in use, but
is by far the most common, though this is often for historical reasons and 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 in the French automotive industry. The MOTIF method provides a graphical evaluation of a surface profile without filtering waviness from roughness. A ''motif'' consists of the portion of a profile between two peaks and the final combinations of these motifs eliminate ″insignificant″ peaks and retains ″significant″ ones. Please note that
is a dimensional unit that can be
micrometer Micrometer can mean:
* Micrometer (device), used for accurate measurements by means of a calibrated screw
* American spelling of micrometre
The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...
or
microinch.
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, the scan can be evaluated to make sure there are no obvious glitches that skew the values.
Because it may not be obvious to many users what each of the measurements really mean, a simulation tool allows a user to adjust key parameters, visualizing how surfaces which are obviously different to the human eye are differentiated by the measurements. For example,
fails 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
followed by additional characters in the subscript. The subscript identifies the formula that was used, and the
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,
is the arithmetic average of the roughness profile,
is the arithmetic average of the unfiltered raw profile, and
is the arithmetic average of the 3D roughness.
Each of the formulas listed in the tables assume 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 value of filtered roughness profile determined from deviations about the center line within the evaluation length and
is the
range
Range may refer to:
Geography
* Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra)
** Mountain range, a group of mountains bordered by lowlands
* Range, a term used to i ...
of the collected roughness data points.
The arithmetic average roughness,
, is the most widely used one-dimensional roughness parameter.
Here is a common conversion table with also roughness grade numbers:
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
Turning is a machining process in which a cutting tool, typically a non-rotary tool bit, describes a helix toolpath by moving more or less linearly while the workpiece rotates.
Usually the term "turning" is reserved for the generation of ...
on a
lathe
A lathe () is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, and turning, with tools that are applied to the workpiece to c ...
.
Other "frequency" parameters are S
m,
a and
q. S
m is the mean spacing between peaks. Just as with real mountains it is important to define a "peak". For S
m 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 a statistical analysis of pairs of measurements can be performed (e.g.: R
z and
a or R
a and Sm) to find the strongest correlation.
Common conversions:
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.
Fractal theory
The mathematician
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...
has pointed out the connection between surface roughness and
fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...
.
The description provided by a
fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
at the microroughness level may allow the control of the material properties and the type of the occurring chip formation. But fractals cannot provide a full-scale representation of a typical machined surface affected by tool feed marks; it ignores the geometry of the cutting edge. (J. Paulo Davim, 2010, ''op.cit''.). Fractal descriptors of surfaces have an important role to play in correlating physical surface properties with surface structure. Across multiple fields, connecting physical, electrical and mechanical behavior with conventional surface descriptors of roughness or slope has been challenging. By employing measures of surface fractality together with measures of roughness or surface shape, certain interfacial phenomena including contact mechanics, friction and electrical contact resistance, can be better interpreted with respect to surface structure.
Areal roughness parameters
Areal roughness parameters are defined in the ISO 25178 series. The resulting values are Sa, Sq, Sz,... Many optical measurement instruments are able to measure the surface roughness over an area. Area measurements are also possible with contact measurement systems. Multiple, closely spaced 2D scans are taken of the target area. These are then digitally stitched together using relevant software, resulting in a 3D image and accompanying areal roughness parameters.
Soil-surface roughness
Soil-surface roughness (SSR) refers to the vertical variations present in the micro- and macro-relief of a soil surface, as well as their stochastic distribution. There are four distinct classes of SSR, each one of them representing a characteristic vertical length scale; the first class includes microrelief variations from individual soil grains to aggregates on the order of 0.053–2.0 mm; the second class consists of variations due to soil clods ranging between 2 and 100 mm; the third class of soil surface roughness is systematic elevation differences due to tillage, referred to as oriented roughness (OR), ranging between 100 and 300 mm; the fourth class includes planar curvature, or macro-scale topographic features.
The two first classes account for the so-called microroughness, which has been shown to be largely influenced on an event and seasonal timescale by rainfall and tillage, respectively. Microroughness is most commonly quantified by means of the Random Roughness, which is essentially the standard deviation of bed surface elevation data around the mean elevation, after correction for slope using the best-fit plane and removal of tillage effects in the individual height readings. Rainfall impact can lead to either a decay or increase in microroughnesss, depending upon initial microroughness conditions and soil properties. On rough soil surfaces, the action of rainsplash detachment tends to smoothen the edges of soil surface roughness, leading to an overall decrease in RR. However, a recent study which examined the response of smooth soil surfaces on rainfall showed that RR can considerably increase for low initial microroughness length scales in the order of 0 – 5 mm. It was also shown that the increase or decrease is consistent among various SSR indices.
Practical effects
Surface structure plays a key role in governing
contact mechanics
Contact mechanics is the study of the deformation of solids that touch each other at one or more points.Johnson, K. L, 1985, Contact mechanics, Cambridge University Press.Popov, Valentin L., 2010, ''Contact Mechanics and Friction. Physical Pri ...
,
that is to say the mechanical behavior exhibited at an interface between two solid objects as they approach each other and transition from conditions of non-contact to full contact. In particular,
normal contact stiffness
Normal contact stiffness is a physical quantity related to the generalized force displacement behavior of rough surfaces in contact with a rigid body or a second similar rough surface. Rough surfaces can be seen as consisting of large numbers o ...
is governed predominantly by asperity structures (roughness, surface slope and fractality) and material properties.
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.
Surface structure is often closely related to the friction and wear properties of a surface.
A surface with a higher
fractal dimension
In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...
, large
value, or a positive
, will usually have somewhat higher friction and wear quickly. The peaks in the roughness profile are not always the points of contact. The form and waviness (i.e. both amplitude and frequency) must also be considered.
See also
*
Discontinuity (Geotechnical engineering)
*
Rugosity
Rugosity, ''f''r, is a measure of small-scale variations of amplitude in the height of a surface,
:f_ = A_/A_
where ''A''r is the real (true, actual) surface area and ''A''g is the geometric surface area. Utility
Rugosity calculations are comm ...
*
Normal contact stiffness
Normal contact stiffness is a physical quantity related to the generalized force displacement behavior of rough surfaces in contact with a rigid body or a second similar rough surface. Rough surfaces can be seen as consisting of large numbers o ...
*
Surface finish
Surface finish, also known as surface texture or surface topography, is the nature of a surface as defined by the three characteristics of lay, surface roughness, and waviness.. It comprises the small, local deviations of a surface from the perf ...
*
Surface metrology
Surface metrology is the measurement of small-scale features on surfaces, and is a branch of metrology. Surface primary form, surface fractality, and surface finish (including surface roughness) are the parameters most commonly associated with th ...
* Surface roughness measurement
ISO 25178
ISO 25178: Geometrical Product Specifications (GPS) – Surface texture: areal is an International Organization for Standardization collection of international standards relating to the analysis of 3D areal surface texture.
Structure of the stan ...
*
Waviness
Waviness is the measurement of the more widely spaced component of surface texture. It is a broader view of roughness because it is more strictly defined as "the irregularities whose spacing is greater than the roughness sampling length". It can ...
*
Asperity (materials science)
In materials science, asperity, defined as "unevenness of surface, roughness, ruggedness" (from the Latin ''asper''—"rough"), has implications (for example) in physics and seismology. Smooth surfaces, even those polished to a mirror finish, a ...
References
External links
Surface Metrology Guide
Online calculator to convert roughness parameters Ra and Rz* Enache, Ştefănuţă, La qualité des surfaces usinées (Transl.: Quality of machined surfaces).Dunod, Paris, 1972, 343 pp.
* Husu, A.P., Vitenberg, Iu., R., Palmov, V. A., Sherohovatost poverhnostei (Teoretiko-veroiatnostnii podhod) (Transl.: Surface roughness (theoretical-probabilistic approach)), Izdatelstvo "Nauka", Moskva, 1975, 342 pp.
* Davim, J. Paulo, Surface Integrity in Machining, Springer-Verlag London Limited 2010,
* Whitehouse, D. Handbook of Surface Metrology, Institute of Physics Publishing for Rank Taylor-Hobson Co., Bristol 1996
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Tribology
Metalworking terminology
Mechanical engineering