Surface roughness

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 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, 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, cross-scale descriptors such as surface fractality provide more meaningful predictions of mechanical interactions at surfaces including contact stiffness and static friction.
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. 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 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.
Parameters.
A roughness value can either be calculated on a profile (line) or on a surface (area). The profile roughness parameter (formula_1, formula_2, ...) are more common. The area roughness parameters (formula_3, formula_4, ...) give more significant values.
Profile roughness parameters.
 The profile roughness parameters are included in BS EN ISO 4287:2000 British standard, identical with the ISO 4287:1997 standard. The standard is based on the ″M″ (mean line) system.
There are many different roughness parameters in use, but formula_1 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 formula_1. Other common parameters include formula_7, formula_2, and formula_9. Some parameters are used only in certain industries or within certain countries. For example, the formula_10 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 formula_1 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, formula_1 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 formula_13 followed by additional characters in the subscript. The subscript identifies the formula that was used, and the formula_13 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, formula_1 is the arithmetic average of the roughness profile, formula_16 is the arithmetic average of the unfiltered raw profile, and formula_3 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 formula_18 ordered, equally spaced points along the trace, and formula_19 is the vertical distance from the mean line to the formula_20 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, formula_1 is the arithmetic average value of filtered roughness profile determined from deviations about the center line within the evaluation length and formula_22 is the range of the collected roughness data points.
The arithmetic average roughness, formula_1, is the most widely used one-dimensional roughness parameter.
! Parameter !! Description !! Formula

