Surface Texture - Profile Parameters


Surface texture of mechanical components has been checked over 80 years in order to improve performances of manufactured products. The first roughness testers recorded surface heights using a stylus tip in contact with the surface and a traverse unit. The measured profile was drawn on a carbon paper and a value of roughness was given on a galvanometer. For a long time, only one parameter was known and used, under the name Ra (Roughness average) or CLA (Center Line Average) or even AA (Arithmetic Average). Then came RMS or Rq, Rz and Rmax, and later many more parameters; so many in fact that Pr Whitehouse eventually wrote his famous paper about parameter rash [WHITEHOUSE 1982].

Today, profile parameters and areal parameters are defined in a handful of international standards that sometimes have local variations due to national or sectorial standards. Profile parameters are separated into three groups depending on the type of profile from which they are calculated: P parameters are calculated on the Primary Profile; R parameters are calculated on the roughness profile; and W parameters are calculated on the waviness profile.

Sampling length vs Evaluation length

In order to overcome problems arising in the early profilometers, such as noise or repeatability, some parameters are meant to be calculated on profile segments (sampling lengths) and then averaged. The sampling length is usually defined as the cut-off length (λc) of the filter used to separate roughness and waviness. For example, using a cut-off length of 0.8 mm and 5 sampling lengths, parameters will be estimated on each segments (Ra1, Ra2, ., Ra5) and the parameter value will be given as the mean of these estimated values. Other parameters are defined and calculated on the evaluation length which usually is the profile length after filtering. Details are given in [ISO 4288].

Note that the same parameters calculated according to ASME B46.1 are not averaged and are calculated on the evaluation length. Their value slightly differ from the parameters calculated according ISO.


Sampling length = 2,5 mm

ISO 4287 - Profile method - Terms, definitions and surface texture parameters

This is the master standard for profile parameters in the ISO GPS system. It defines terms and provides definitions for common parameters. Below, definitions given for Rx are also valid for Px and Wx.

Amplitude parameters

Rt, total height of the profile: height between the deepest valley and the highest peak on the evaluation length.

Rp, maximum profile peak height: height of the highest peak from the mean line, defined on the sampling length.

Rv, maximum profile valley depth: depth of the deepest valley from the mean line, defined on the sampling length.

Rz, maximum height of the profile: defined on the sampling length: this parameter is frequently used to check whether the profile has protruding peaks that might affect static or sliding contact function.

Ra, arithmetic mean deviation of the assessed profile: defined on the sampling length. Ra is used as a global evaluation of the roughness amplitude on a profile. It does not say anything on the spatial frequency of the irregularities or the shape of the profile. Ra is meaningful for random surface roughness (stochastic) machined with tools that do not leave marks on the surface, such as sand blasting, milling, polishing

Rq, root mean square deviation of the assessed profile: corresponds to the standard deviation of the height distribution, defined on the sampling length. Rq provides the same information as Ra.

Rsk, skewness of the assessed profile: asymmetry of the height distribution, defined on the sampling length. This parameter is important as it gives information on the morphology of the surface texture. Positive values correspond to high peaks spread on a regular surface (distribution skewed towards bottom) while negative values are found on surfaces with pores and scratches (distribution skewed towards top). It is therefore interesting when contact or lubrication functions are required. However, this parameter does not give any information on the absolute height of the profile, contrary to Ra.

Rku, kurtosis of the assessed profile: sharpness of the height distribution, defined on the sampling length.

Rc, mean height of profile elements: defined on the evaluation length. This parameter can be calculated on surfaces having texture cells or grains. It is similar to the motif parameter R found in ISO 12085 and, in that sense, it should be considered as a feature parameter (see ISO 25178).

Spatial parameters

RSm, mean spacing of profile elements, defined on the evaluation length*. This parameter is interesting on surfaces having periodic or pseudo-periodic motifs, such as turned or structured surfaces. In these cases, RSm will approximate their spacing. RSm is meaningless on random surface texture.
* Initially defined on the sampling length, it is now recommended to calculate it on the evaluation length.

Hybrid parameters

Rdq, root mean square slope of the assessed profile, defined on the sampling length. Rdq is a first approach to surface complexity. A low value is found on smooth surfaces while higher values can be found on rough surfaces having microroughness.

RPc, peak count number. Was introduced in Amendment 1. Provides the density of peaks per unit of length.

Functional parameters

Rmr, material ratio at a given depth. This parameter gives the percentage of material cut at a given depth from the top of the profile. The reference may also be taken from the center line or another reference height (c0).

Rdc, profile section height between two material ratios. A stable value of roughness height can be evaluated using Rdc(2%-98%) if outliers are present on the surface. This calculation excludes the highest peaks that will be worn out and the deepest valleys that will be filled in. In the automotive industry, the material height removed during running-in can be assessed with Rdc(1%-33%) and the void volume used for lubricant pockets can be assessed with Rdc(25%-99%).


Material ratio calculated on the Abbott-Firestone curve.
Rmr at 2 ┬Ám below the highest peak is 10%.


Section height between 5% and 95% of material ratio is 6,5 µm.

ISO 12085 - Profile method - Motifs parameters

This standard is the international version of a French standard established by CNOMO, a consortium involving PSA Peugeot Citroen and Renault, during the 80s and 90s. The method is based upon a graphical segmentation of the profile into motifs that are then quantified in height and width. The originality and advantage of this method is the correlation that was established between parameter values and functional requirements, due to a vast measurement campaign that characterized more than 40 000 components. It is commonly called the French motifs method or R&W parameters.

Today, these parameters are less used but the conclusions regarding the relationship between function and specification remain important and can be used with other parameters.


Roughness motifs

Motifs are defined on a profile as a peak-valley-peak trio and are detected by a special segmentation method. The main part of the algorithm is a combination procedure based upon four conditions and controlled by a limit A. The combinations merge small and insignificant motifs into larger ones. At the end of the procedure, significant motifs are quantified with parameters.

Roughness parameters

R, mean depth of roughness motifs

AR, mean spacing of roughness motifs

Rx, maximum depth of roughness motifs

Then an upper envelope is calculated by joining roughness motifs peaks by line segments, and the segmentation procedure is repeated on this envelope using two limits A and B. Then waviness parameters are calculated.

Waviness parameters

W, mean depth of waviness motifs

AW, mean spacing of waviness motifs

Wx, maximum depth of waviness motifs

Wte, Amplitude of the upper envelope

These parameters are part of the 2D Automotive module.


Upper envelope and Waviness motifs


Recommended motifs parameters in specification,
for each type of function

The drawback of this method is its instability as it is based on conditions instead of mathematical basis. There is a work in progress to adapt the watershed segmentation to profiles and replace the combination rules by a Wolf pruning. This new motifs method should be described in ISO 16610, probably in part 45 and will be derived from the areal segmentation method used in areal feature parameters. The correlation between the two methods is discussed in [BLATEYRON 2004]

ISO 13565-2 and ISO 13565-3 - Profile method - Surfaces having stratified functional properties

This series of standards are specially aimed at characterizing stratified surface texture produced by a two-step manufacturing process such as honing-polishing machining. The first part of this standard series, ISO 13565-1, defines a special double-pass filter that provides a sort of robustness against deep holes that are common in stratified surfaces. This filter is now superceded by the Gaussian Regression filter defined in ISO 16610-31. Part 2 defines a set of parameters called Rk parameters that are derived from a graphical construction on the Abbott-Firestone curve. Rk parameters should be calculated only if the Abbott curve has a S-shape, otherwise the graphical construction may fail and parameter values will be meaningless.

Parameters of ISO 13565-2

Rk, core roughness depth

Rpk, reduced peak height. This parameter is used to characterize protruding peaks that might be eliminated during function.

Rvk, reduced valley depth. This parameters is used to characterize valleys that will retain lubricant or worn-out materials.

MR1 and MR2: material ratio delimiting the core area.

Other parameters such as A1 and A2, Rpk* or Rvk* can also be calculated for specific use.

These parameters are part of the 2D Automotive module.


Graphical construction of Rk parameters

Parameters of ISO 13565-3

This standard is specilized in the characterisation of stratified vertical random components such as a valley texture with a fine plateau texture superimposed. Here again, these parameters should be calculated only on surfaces that comply with this description.

Rpq, Plateau Root Mean Square roughness

Rvq, Valley Root Mean Square roughness

Rmq, Material ratio at plateau-to-valley transition

These parameters can be also calculated on the primary profile, as Ppq, Pvq and Pmq.

These parameters are part of the 2D Automotive module.

Other standards

ASME B46.1

This standard today is more in line with ISO standards than the previous versions, except for some differences. The main difference is about sampling length and averaged parameters. In ASME, all profile parameters are defined and calculated on the evaluation length.

VDA 2006

This standard from the German automotive industry collects parameters defined in ISO 4287 and ISO 13565 and introduces several rules that differ from ISO. The main difference concerns the use of microroughness filter λs that is prohibited here. It also reintroduces the parameter Rmax that was once part of ISO 4287 and is a good complement to Rz.

VDA 2007

This standard defines special parameters for the evaluation of periodic surfaces, especially in the field of mating surfaces. It is usually referred to as Dominant waviness. It defines three parameters calculated after a special zero bandpass filter:

WDSm, horizontal waviness

WDc, mean height of waviness profile elements

WDt, total waviness profile height

These parameters are part of the 2D Automotive module.

Daimler MBN 31 007-7

This internal standard provides methods and parameters to analyze lead-reduced dynamic sealing surfaces. It is referred to as Lead or Twist analysis. The following parameters are calculated:

DG, number of threads

Dt, lead depth

DP, period length

DF, theoretical supply cross section

DFu, DF per turn

DLu, contact length

Dγ, lead angle

DSγ, offset lead angle

This standard is available in the Lead (Twist) Analysis module.

Daimler MBN 31 007-12

This internal standard defines one parameter to caracterize the waviness profile:

Wst, maximum absolute height difference of the waviness profile


MountainsMap offers several options to comply to these standards. ISO parameters are all available in MountainsMap but sometimes as an option (such as the 2D Automotive Module). ASME B46.1 is offered as a family in the Parameter study. VDA 2006 can be implemented by disabling the microroughness option in the Preferences. VDA2007 and MBN 31 007-12 are part of the Automotive Module (in version 7.3 and above). The Daimler Lead method is available as a separate Lead (Twist) Analysis Module.

See also MountainsMap Profile and 2D Advanced Surface Texture.


Towards a complete revision of profile standards

New structure

In fall 2012, the WG16 group of ISO TC 213 decided to start revising profile standards in order to align them with the ISO 25178 structure and concepts. Basically, the new structure will consist of at least three parts:

  • Part 1 - Drawing indications. Will incorporate the content of ISO 1302, plus new symbols.
  • Part 2 - Definitions and parameters. Will include definitions of all parameters, from ISO 4287, ISO 12085 and ISO 13565, plus several new parameters.
  • Part 3 - Specification operators. Will define default values, and units of parameters.

In August 2016, the project was officially registered under the reference: ISO 21920.

At this stage, there is no plan to describe instruments characteristics or calibration as this was included in ISO 25178 parts 60x and 70x, as well as parts 7x for material measures and softgauges.

Time frame

Principles have been discussed in 2013 at the Helsinki meeting and a first draft of Part 2 was established by a task force within the group. The first official New Work Item Proposal was issued to Geneva Central Secretariat in Fall 2016. Publication is not expected before 2018-2019. After the publication of this 3-parts standard, the old profile standards will be cancelled (ISO 1302, 4287, 4288, 12085, 13565-2, 13565-3)

ISO 1302 ISO 4287

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