How are Ra and Sa calculated?


#1

Could someone detail how Ra and Sa are computed in ProfilmOnline?

I obtain very small values of these two parameters for very wavy surfaces and can’t find precisely how Ra and Sa are computed. I am aware of the general formula but am looking for more details.

For the line roughness, is the filter (spline/gaussian) always applied to the data before computing the different roughness parameters? Is the line profile then segmented and Ra calculated for each segment and then averaged? If yes, how are these segments defined and how can I modify that? What does “Cutoff Length” and “Number of samples” define?

Similarly, what is the treatment applied prior to Sa calculation?

Thank you!


#2

Answers to your questions:

For line roughness, a filter is always applied. The profile is segmented and Ra for each segment is computed and averaged. The length of each segment is equal to the cutoff length. You can therefore modify the segment length by clicking the settings gear icon at the top-right corner of the Line Roughness analysis results panel, and then setting the Cutoff length in the Roughness Settings dialog. If you select Max samples, the application will use every segment. If you select User specified and enter n (a number), the application will use the first n segments.

There is no treatment applied prior to calculation of Sa – You should apply operators yourself as described below.

Detailed Description for Ra, Sa:

Ra and Sa are defined and computed according to international standards.

Ra is defined by ISO 4287. According to this standard, the profile is first filtered using a cutoff length (λc) to extract the roughness profile (and remove the waviness).

The filtered length is then subdivided into “samples” or segments, each having a sample length equal to the cutoff length. Ra is defined as the average of the Ra values calculated within each of the samples.

In ProfilmOnline you can specify Cutoff Length and specify the Number of Samples or use the maximum possible that will fit within the filtered length.

Sa is defined by ISO 25178. This calculation does not apply filters, nor segment and average over regions. Sa is calculated over the entire surface. You can read an overview of ISO 25178 at the following link:
Wikipedia ISO 25178

To calculate roughness using Sa, you should first remove the underlying form using the Flatten operator (the standard calls this applying an F-Operator) to obtain what’s described in the standard as an S-F surface. Then use the Filter operator, configured to output the Roughness image (the standard calls this applying an L-Filter) to obtain what’s described in the standard as the S-L surface. When used this way, the Filter operator removes the largest scale elements from the surface. You would then calculate Sa using Area Roughness Analysis. Please see the Wikipedia article for definitions of each of these terms.


#3

Thanks a lot, this is really helpful!