Surface roughness
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Surface roughness often shortened to roughness, is a component of surface texture. It is quantified by the deviations in the direction of the normal vector 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, roughness is typically considered to be the highfrequency, shortwavelength 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, 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 on the surface may form nucleation sites for cracks or corrosion. On the other hand, roughness may promote adhesion. Generally speaking, rather than scale specific descriptors, crossscale descriptors such as surface fractality provide more meaningful predictions of mechanical interactions at surfaces including contact stiffness ^{[1]} and static friction.^{[2]}
Although a high roughness value is often undesirable, it can be difficult and expensive to control in manufacturing. For example, it is difficult and expensive to control surface roughness of fused deposition modelling (FDM) manufactured parts.^{[3]} Decreasing the roughness of a surface usually increases its manufacturing cost. This often results in a tradeoff 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 is made with a profilometer. These can be of the contact variety (typically a diamond stylus) or optical (e.g.: a white light interferometer 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.
Contents
Parameters
A roughness value can either be calculated on a profile (line) or on a surface (area). The profile roughness parameter (Ra, Rq,...) are more common. The area roughness parameters (Sa, Sq,...) give more significant values.
Profile roughness parameters
Each of the roughness parameters are calculated using a formula for describing the surface. Standard references that describe each in detail are Surfaces and their Measurement.^{[4]}
The profile roughness parameters are included in BS EN ISO 4287:2000 British standard, identical with the ISO 4287:1997 standard.^{[5]} 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.^{[6]} 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 R_{a} is a dimensional unit that can be micrometer 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.^{[7]}
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 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 R_{t} is the range of the collected roughness data points.
The arithmetic average roughness, , is the most widely used onedimensional roughness parameter.
Parameter  Description  Formula 

R_{a},^{[8]} R_{aa}, R_{yni}  arithmetical mean deviation of the assessed profile  ^{[8]} 
R_{q}, R_{RMS}^{[8]}  root mean squared  ^{[8]} 
R_{v}  maximum valley depth  
R_{p}  maximum peak height  
R_{t}, R_{y}  Maximum Height of the Profile  
R_{sk}  skewness  
R_{ku}  kurtosis  
R_{zDIN}, R_{tm}  average distance between the highest peak and lowest valley in each sampling length, ASME Y14.36M  1996 Surface Texture Symbols  , where is the number of sampling lengths, and is for the sampling length. 
R_{zJIS}  Japanese Industrial Standard for , based on the five highest peaks and lowest valleys over the entire sampling length.  , where and are the highest peak, and lowest valley respectively. 
Here is a common conversion table with also roughness grade numbers:
Roughness N
ISO Grade Numbers 
Roughness values Ra
micrometers (µm) 
Roughness values Ra
microinches (µin.) 
RMS 
CLA (µin.)
Center Line Avg. 
Rt
Roughness (µm) 

N12  50  2000  2200  2000  200 
N11  25  1000  1100  1000  100 
N10  12.5  500  550  500  50 
N9  6.3  250  275  250  25 
N8  3.2  125  137.5  125  13 
N7  1.6  63  69.3  63  8 
N6  0.8  32  35.2  32  4 
N5  0.4  16  17.6  16  2 
N4  0.2  8  8.8  8  1.2 
N3  0.1  4  4.4  4  0.8 
N2  0.05  2  2.2  2  0.5 
N1  0.025  1  1.1  1  0.3 
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 

R_{dq}, R_{$\Delta$q}  the RMS of the profile within the sampling length  
R_{da}, R_{$\Delta$a}  the average absolute slope of the profile within the sampling length  
where delta i is calculated according to ASME B46.1 and is a 5th order Savitzky–Golay smoothing filter 
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 AbbottFirestone 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.^{[9]} The description provided by a fractal 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 fullscale 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.).
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.
Soilsurface roughness
Soilsurface roughness (SSR) refers to the vertical variations present in the micro and macrorelief 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 macroscale topographic features^{[10]}.
The two first classes account for the socalled 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 bestfit plane and removal of tillage effects in the individual height readings.^{[11]} Rainfall impact can lead to either a decay or increase in microroughnesss, depending upon initial microroughness conditions and soil properties.^{[12]} 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 ^{[13]}.
Practical effects
Surface structure plays a key role in governing contact mechanics,^{[1]} 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 noncontact to full contact. In particular, normal contact stiffness 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.^{[14]}
Surface structure is often closely related to the friction and wear properties of a surface.^{[2]} A surface with a higher fractal dimension, 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
 Normal contact stiffness
 Surface finish
 Surface metrology
 Surface roughness measurement ISO 25178
 Waviness
References
 ^ ^{a} ^{b} Zhai, C.; Gan, Y.; Hanaor, D.; Proust, G.; Retraint, D. (2016). "The Role of Surface Structure in Normal Contact Stiffness" (PDF). Experimental Mechanics. 56 (3): 359–368. doi:10.1007/s1134001501070.
 ^ ^{a} ^{b} Hanaor, D.; Gan, Y.; Einav, I. (2016). "Static friction at fractal interfaces". Tribology International. 93: 229–238.
 ^ http://manufacturingscience.asmedigitalcollection.asme.org/article.aspx?articleid=2475087
 ^ Whitehouse, David (2012). Surfaces and their Measurement. Boston: ButterworthHeinemann. ISBN 9780080972015.
 ^ BS EN ISO 4287:2000, Geometrical product specification (GPS). Surface texture. Profile method. Terms, definitions and surface texture parameters
 ^ Dietzsch M., Papenfluss K., Hartmann, T. The MOTIF method (ISO 12085: 1996) A suitable description for functional, manufactural and metrological requirements, International Journal of Machine Tools and Manufacture, 1998, 38, No 56, pp. 625632
 ^ Abbott, Steven. "SPE (Surface Profile Explorer)". AbbottApps. Steven Abbott TCNF Ltd. Retrieved January 13, 2014.
 ^ ^{a} ^{b} ^{c} ^{d} Degarmo, E. Paul; Black, J.; Kohser, Ronald A. (2003), Materials and Processes in Manufacturing (9th ed.), Wiley, p. 223, ISBN 0471656534.
 ^ Den Outer, A.; Kaashoek, J.F.; Hack, H.R.G.K. (1995). "Difficulties of using continuous fractal theory for discontinuity surfaces". International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts. 32 (1): 3–9. doi:10.1016/01489062(94)00025X.
 ^ Römkens, M.J.M; Helming, K; Prasad, S.N. "Soil erosion under different rainfall intensities, surface roughness, and soil water regimes". CATENA. 46 (2–3): 103–123. doi:10.1016/s03418162(01)001618.
 ^ Allmaras, R. R. (1966). Total Porosity and Random Roughness of the Interrow Zone as Influenced by Tillage. Agricultural Research Service, U.S. Department of Agriculture.
 ^ K. N. Potter; Potter, K. N. (1990). "SOIL PROPERTIES EFFECT ON RANDOM ROUGHNESS DECAY BY RAINFALL". Transactions of the ASAE. 33 (6): 1889–1892. doi:10.13031/2013.31554.
 ^ Abban, B. K. B.; Papanicolaou, A. N. (.; Giannopoulos, C. P.; Dermisis, D. C.; Wacha, K. M.; Wilson, C. G.; Elhakeem, M. (20170928). "Quantifying the changes of soil surface microroughness due to rainfall impact on a smooth surface". Nonlin. Processes Geophys. 24 (3): 569–579. doi:10.5194/npg245692017. ISSN 16077946.
 ^ http://www.enginebuildermag.com/2000/09/cylinderboresurfacefinishes/
External links
Wikimedia Commons has media related to Surface roughness. 
Look up surface roughness in Wiktionary, the free dictionary. 
 Surface Metrology Guide
 Roughness terminology
 Ra and Rz description
 Surface Roughness (Finish) Review and Equations
 SPE (Surface Profile Explorer)
 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 (Teoretikoveroiatnostnii podhod) (Transl.: Surface roughness (theoreticalprobabilistic approach)), Izdatelstvo "Nauka", Moskva, 1975, 342 pp.
 Davim, J. Paulo, Surface Integrity in Machining, SpringerVerlag London Limited 2010, ISBN 9781848828735
 Whitehouse, D. Handbook of Surface Metrology, Institute of Physics Publishing for Rank TaylorHobson Co.,Bristol 1996
 Strength of materials RS.kurmi