# roughness

The roughness (also roughness , out of date roughness ) is a term from surface physics that describes the unevenness of the surface height. There are different calculation methods for the quantitative characterization of the roughness, each of which takes different characteristics of the surface into account. The surface roughness can be influenced by polishing , roller burnishing , grinding , lapping , honing , pickling , sandblasting , bristle blasting , etching , steaming or corrosion .

The term roughness also refers to a third to fifth order deviation in shape in technical surfaces according to DIN 4760 . The roughness of a technical surface is specified in the surface information in the technical drawing .

Roughness is particularly important in technology, for example on technical sliding or visible surfaces. The available measuring devices can be divided into three categories:

• Manual methods. This includes the rugotest . However, this is not covered by the chain of GPS standards.
• Profile-based methods. These include profile methods
• Area-based methods. This includes, among other things, optically extensive measuring methods.

In the case of optical profile and area-based methods, there are numerous measuring methods to choose from. These include confocal microscopy , conoscopic holography , focus variation or white light interferometry .

## Roughness parameters on the profile

In everyday life, basically three roughness specifications are used, which are usually given in the unit micrometer (µm).

• The mean roughness value , represented by the symbol , indicates the mean distance of a measuring point - on the surface - to the center line. The center line intersects the actual profile within the reference section in such a way that the sum of the profile deviations in a plane parallel to the center line is distributed over the length of the measuring section.${\ displaystyle R _ {\ mathrm {a}}}$ The mean roughness corresponds to the arithmetic mean of the absolute deviation from the mean line. It is calculated in two dimensions as follows:
${\ displaystyle R _ {\ mathrm {a}} = {\ frac {1} {M \, N}} \, \ sum _ {m = 1} ^ {M} \ sum _ {n = 1} ^ {N } \ left \ vert z \ left (x_ {m}, y_ {n} \ right) - \ left \ langle z \ right \ rangle \ right \ vert}$ where the mean is through
${\ displaystyle \ left \ langle z \ right \ rangle = {\ frac {1} {M \, N}} \ sum _ {m = 1} ^ {M} \ sum _ {n = 1} ^ {N} z \ left (x_ {m}, y_ {n} \ right)}$ is calculated.
The mean roughness (in one dimension) is somewhat easier to imagine than the height of the rectangle, which has the same length as the section to be examined and the same area as the area between the reference height and profile.
• The so-called quadratic roughness (English rms-roughness or root-mean-squared roughness : root of the mean square) is calculated from the mean of the deviation squares and corresponds to the " quadratic mean "
${\ displaystyle R_ {q} = {\ sqrt {{\ frac {1} {M \, N}} \, \ sum _ {m = 1} ^ {M} \ sum _ {n = 1} ^ {N } \ left (z \ left (x_ {m}, y_ {n} \ right) - \ left \ langle z \ right \ rangle \ right) ^ {2}}}}$ • The so-called mean roughness depth (also ten point height), previously represented by the symbol (up to DIN EN ISO 4287: 1984), has now been deleted as an ISO parameter (from DIN EN ISO 4287: 1997). The averaged roughness can still be output by older measuring devices and is determined as follows. ${\ displaystyle R_ {z}}$ • A defined measuring section on the surface of the workpiece is divided into seven individual measuring sections, with the middle five measuring sections being the same size. The evaluation is only carried out over these five measuring sections, since the Gaussian filter to be used requires half a single measuring section for pre-run and post-run, or a convolution has a not negligible run-in and run-out behavior.
• The difference between the maximum and minimum value is determined for each of these individual measuring sections of the profile.
• The mean value is formed from the five individual roughness values ​​thus obtained .

This characteristic value should not be confused with the roughness depths or . is defined as the difference between the maximum and minimum value of the profile ( ) in relation to the total measuring section, i.e. the five individual measuring sections in the normal case. is the largest of the five individual roughness depths. The GPS chain of standards also provides for other measurement constellations. ${\ displaystyle R _ {\ mathrm {t}}}$ ${\ displaystyle R _ {\ mathrm {max}}}$ ${\ displaystyle R _ {\ mathrm {t}}}$ ${\ displaystyle R _ {\ mathrm {p}} -R _ {\ mathrm {v}}}$ ${\ displaystyle R _ {\ mathrm {max}}}$ ## Roughness parameters on the surface

The roughness on the surface is standardized in ISO 25178 . In the meantime (as of 2009) there are optical measuring devices that measure surface roughness parameters.

## Discussion of the roughness parameters

As can be seen in simplified form for one dimension in Figure 1, the mean roughness and the quadratic roughness are only dependent on the absolute deviation of the height from the mean value, but not on the distribution of the height values ​​over the area. For example, the mean roughness in images A, C and D and , while the values ​​for image B are calculated and calculated. ${\ displaystyle R _ {\ mathrm {a}} = 2}$ ${\ displaystyle R_ {q} = 4}$ ${\ displaystyle R _ {\ mathrm {a}} = 1}$ ${\ displaystyle R_ {q} = 1}$ In mechanical engineering, there are solutions in the GPS standard chain for the above problem. The characteristic values ​​from the Abbott curve and the amplitude-density curve, as well as the difference between waviness and roughness, should be listed here. For example, the roughness of a workpiece says something about the quality of the tool, while the waviness says something about the quality of the machine. So it often happens that the roughness requirements are extremely increased in the case of quality problems, but the waviness causing the problem is "filtered out" during the roughness measurement . The GPS chain of standards defines all noise parameters also as ripple parameters. The only difference is the respective cut-off frequency. Waviness parameters are identified with the prefix "W".

${\ displaystyle R _ {\ mathrm {a}}}$ and are therefore unsuitable for making statements about the spatial frequency of the bumps. The first thing to do is to determine the wavelength of the critical structures. This shows whether “P”, “R” or “W” parameters are to be specified. Then it must be decided whether the critical corner points can be seen from the profile, the Abbott curve or the amplitude-density curve. Only then does it make sense to specify a measured value for quality assurance. ${\ displaystyle R_ {q}}$ ## Procedure for paper

There are various test methods to determine the roughness or smoothness of paper . Most of the test methods used today attempt to characterize the smoothness of the print under a defined contact pressure. For this purpose, air is often used as an aid, which flows between a reference surface and the paper surface under defined conditions. With Bekk the reference surface is a ground glass plate, with Bendtsen and Parker Print Surf a flat metal ring face.

### Optical test methods

Newer measuring methods work with optical methods. The advantages of these methods are the non-destructive measurement and the evaluation of more complex parameters of the surface and the volume, as defined in ISO 25178 , for example . Optical processes are limited to the properties of the surface. In the case of air flow processes, a flow through the paper can lead to a falsification of the roughness values.

### Air flow method

• The smoothness according to Bekk
• The smoothness according to Bendtsen
• The Parker Print Surf smoothness

#### Smoothness according to Bekk

• Application range: approx. 2–5 s
• Measuring area: 10 cm²
• Pressure on sample: 100 kPa

Three different measuring ranges are possible:

• A: 10 to 600 s with a large vacuum container, pressure drop from 507 to 480 mbar, measured time = GL (Bekk) s
• B:> 300 s (according to A) with a small vacuum container, pressure drop from 507 to 480 mbar, measured time × 10 = GL (Bekk) s
• C: <20 s (according to A) with a large vacuum container, pressure drop from 507 to 293 mbar, measured time: 10 = GL (Bekk) s

#### Bendtsen roughness / smoothness

The Bendtsen roughness is the air flow rate that passes between the measuring ring of the measuring head of the Bendtsen device and the sample surface and that occurs at a specified overpressure.

• Measuring range: 10 to 3000 ml / min
• Measuring area: 100 × 0.15 mm ring-shaped
• Pressure on the sample: 10 N / cm² (= 100 kPa)
• Differential pressure: (15 ± 0.2) mbar

#### Parker Print Surf (PPS) roughness / smoothness

The PPS roughness is also one of the air flow measurement methods and is very widespread in the printing paper industry .

• Measuring area: 98 mm × 51 µm (ring-shaped)
• Pressure on sample: (6.2 ± 0.1) kPa
• Sample support: hard rubber plate

The devices are calibrated by appropriately accredited experts . Ring tests are carried out within the paper industry in order to be able to compare the devices with one another and to determine suitable calibration intervals.