Surface roughness

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. Surface structure plays a key role in governing contact mechanics, Surface structure is often closely related to the friction and wear properties of a surface. A surface with a higher fractal dimension, large Ra value, or a positive Rsk, 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. == 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 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 Ra 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 Ra. 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 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 Ra 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, Ra 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 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 n ordered, equally spaced points along the trace, and y_i is the vertical distance from the mean line to the i^\text{th} 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, Ra is the arithmetic average value of filtered roughness profile determined from deviations about the center line within the evaluation length and Rt is the range of the collected roughness data points. The arithmetic average roughness, Ra, is the most widely used one-dimensional roughness parameter. Here is a common conversion table with 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 on a lathe. Other "frequency" parameters are Sm, \lambdaa and \lambdaq. 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 \lambdaa and the root mean square wavelength \lambdaq are derived from \Deltaa. 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.: Rz and \lambdaa or Ra and Sm) to find the strongest correlation. 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 has pointed out the connection between surface roughness and fractal dimension. 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 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. ==See also==