## Controlling Roughness on Short Surfaces

Roughness control is important on many surfaces. Unfortunately, some of these surfaces can be relatively short – making it difficult to perform a “traditional” roughness measurement.

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**A traditional roughness measurement**

A default roughness measurement is based on analyzing 5 sampling lengths (whereby a sampling length is equal to the roughness cutoff wavelength). See “3 Steps to Understanding Surface Texture” for more on the roughness cutoff wavelength. These 5 sampling lengths along a surface are referred to as the “evaluation length.” Thus, for a typical filter cutoff of 0.8 mm, the default evaluation length is 4.0 mm

In an actual measurement there is often the need for the tracing length to be longer than the desired evaluation length. This is often said to be related to the acceleration and deceleration of the instrument as it starts and stops. This isn’t necessarily the case with today’s instruments. With modern instruments, the first data point and the last data point are considered as “good points” and the acceleration/deceleration occurs outside this zone. With today’s instruments, the extra length at the ends is related to the filtering process.

Let’s consider the Gaussian filter as a weighted moving average.

As can be seen in this (above) figure, the middle of the Gaussian filter does not reach the ends of the profile. Thus, we need “extra” length on each end of the desired evaluation length. Some instruments require an extra full cutoff of data on each end of the profile for the Gaussian filter. Other instruments require an extra half cutoff on each end for a Gaussian filter.

For a typical 0.8 mm filter and the desire to achieve a default 4.0 mm evaluation length we have:

For a 1 cutoff discard on each end: 5.6 mm is the required tracing length

For a ½ cutoff discard on each end: 4.8 mm is the required tracing length

**What if my surface isn’t that long?**

__Option 1: Use a different kind of filter__

One option is to switch to a filter type that doesn’t require discarding. In Digital Metrology’s OmniSurf software we have the options of “spline” and “robust” filters. These filters return the full length of data after filtering… with no discarding at the ends as shown here:

Thus, with OmniSurf’s spline or robust filters, a 4.0 mm evaluation can be achieved with a 4.0 mm tracing length.

In many cases, a spline filter can be used in place of the Gaussian with only minimal differences in computed roughness parameters. These differences are typically well within the measurement uncertainty of the system.

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__Option 2: Use fewer sampling lengths__

The default evaluation based on 5 sampling lengths is simply that… a default. We can always use a non-default approach which doesn’t involve 5 sampling lengths. Ideally this would be noted on the drawing or the measurement report. If the surface is long enough to support two sampling lengths, then simply report the roughness value for the two available sampling lengths. If only one sampling length of surface is available, then report the roughness for the one sampling length.

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__Option 3: Use all available length__

OmniSurf’s parameter calculations do not partition the profile into sampling lengths. Calculations occur over the entire length of filtered data. (NOTE: OmniSurf does use sampling lengths for RzDIN, RzJIS, Rpm and Rvm as these parameters require partitioning).

Using all available data (particularly with spline or robust filtering) can be a useful approach for short surfaces. In fact, OmniSurf can compute roughness parameters on less than a full sampling length. This truly means that any length of data can be used with any filter.

__Option 4: Use all available length with no filtering__

If the available surface length is less than one sampling length, simply levelling the data has nearly the same effect as filtering. Thus, for a surface length less than one sampling length, we can often replace the roughness “R” parameters (e.g. Ra) with Primary “P” parameters (e.g. Pa).

**CAUTION: Don’t do this…**

One (bad) approach for dealing with short surfaces is to choose a shorter filter cutoff to achieve the 5 sampling lengths on the surface. This can be very dangerous as changing the cutoff wavelength changes the definition of “roughness”.

Let’s look at a small land that has been milled:

The highlighted zone in the above graph is 2.25 mm wide. This is not enough length for a traditional, 5 sampling length analysis with a typical 0.8 mm cutoff wavelength. Thus, some people might be inclined to shorten the filter cutoff to achieve 5 sampling lengths. Here’s what happens on this surface if we shorten the filter cutoff from 0.8 mm down to the next standard cutoff wavelength: 0.25 mm.

This (above) example should be a great reminder that a change in the filter cutoff fundamentally changes the definition of roughness. The computed “Ra” value is cut in half with the reduction of the cutoff wavelength.

There are many ways to handle short surfaces. Four good options are presented above. One thing that should not be done is shorten the filter cutoff.

For more information, contact Digital Metrology today!