## One-Dimensional Roughness Parameters

Standardized one-dimensional roughness parameters can be evaluated with the Roughness tool.

The one-dimensional texture is split into waviness (the low-frequency components defining the overall shape) and roughness (the high-frequency components) at the cut-off frequency. This frequency is specified in the units of the Nyquist frequency, that is value 1.0 corresponds to the Nyquist frequency. It is also displayed as the corresponding real-space wavelength.

In the following formulas we assume the mean value of rj is zero, i.e. it holds

### Roughness Amplitude Parameters

Roughness Average Ra

Standards: ASME B46.1-1995, ASME B46.1-1985, ISO 4287-1997, ISO 4287/1-1997.

Arithmetical mean deviation. The average deviation of all points roughness profile from a mean line over the evaluation length

An older means of specifying a range for Ra is RHR. This is a symbol on a drawing specifying a minimum and maximum value for Ra.

Root Mean Square Roughness Rq

Standards: ASME B46.1-1995, ISO 4287-1997, ISO 4287/1-1997.

The average of the measured height deviations taken within the evaluation length and measured from the mean line

Maximum Height of the Profile Rt

Standards: ASME B46.1-1995, ISO 4287-1997.

Maximum peak-to-peak-valley height. The absolute value between the highest and lowest peaks

Maximum Profile Valley Depth Rv, Rm

Standards: ASME B46.1-1995, ASME B46.1-1985, ISO 4287-1997, ISO 4287/1-1997.

Lowest valley. This is the depth of the deepest valley in the roughness profile over the evaluation length

Maximum Profile Peak Height Rp

Standards: ASME B46.1-1995, ASME B46.1-1985, ISO 4287-1997, ISO 4287/1-1997.

Highest peak. This is the height of the highest peak in the roughness profile over the evaluation length

Average Maximum Height of the Profile Rtm

Standards: ASME B46.1-1995, ISO 4287-1997.

Mean peak-to-valley roughness. It is determined by the difference between the highest peak ant the lowest valley within multiple samples in the evaluation length

where Rvm and Rpm are defined below.

For profile data it is based on five sample lengths (m = 5). The number of samples corresponds with the ISO standard.

Average Maximum Profile Valley Depth Rvm

Standards: ISO 4287-1997.

The mean valley depth based on one peak per sampling length. The single deepest valley is found in five sampling lengths (m = 5) and then averaged

where

Average Maximum Profile Peak Height Rpm

Standards: ISO 4287-1997.

The mean peak height based on one peak per sampling length. The single highest peak is found in five sampling lengths (m = 5) and then averaged

where

Base roughness depth R3z

Standards: ISO 4287-1997.

The distance between the third highest peak and the third lowest valley. A peak is a portion of the surface above the mean line crossings.

Base roughness profile depth R3zISO

Standards: ISO 4287-1997.

The height of the third highest peak from the third lowest valley per sampling length. The base roughness depth is found in five sampling lengths and then averaged.

Ten-point height Rz

Standards: ISO 4287-1997

The average absolute value of the five highest peaks and the five lowest valleys over the evaluation length.

Average peak-to-valley profile roughness RzISO

Standards: ISO 4287-1997.

The average peak-to-valley roughness based on one peak and one valley per sampling length. The single largest deviation is found in five sampling lengths and then averaged. It is identical to Rtm.

Standards: ISO 4287-1997.

The amplitude distribution function is a probability function that gives the probability that a profile of the surface has a certain height z at any position x.

The Bearing Ratio Curve BRC

Standards: ISO 4287-1997.

The Bearing Ratio Curve is related to the ADF, it is the corresponding cumulative probability distribution and sees much greater use in surface finish. The bearing ratio curve is the integral (from the top down) of the ADF.

Skewness Rsk

Standards: ISO 4287-1997.

Skewness is a parameter that describes the shape of the ADF. Skewness is a simple measure of the asymmetry of the ADF, or, equivalently, it measures the symmetry of the variation of a profile about its mean line

Kurtosis Rku

Standards: ISO 4287-1997.

Kurtosis is the ADF shape parameter considered. Kurtosis relates to the uniformity of the ADF or, equivalently, to the spikiness of the profile.

Swedish height H

Height difference between two predefined lines. The upper line exposes 5 % of the surface and the lower line exposes 90 %. In other words it is the difference between 95th and 10th height distribution percentiles. H is less sensitive to data spikes than Rt.