There Is a Sieve in Your Roughness Gage

For analysis purposes, filters are used to separate wavelengths into roughness and waviness. The cutoff value functions like a sieve to separate these wavelengths.

This column commonly emphasizes the following: the importance of surface finish; the importance of using the correct equipment to indicate that target specs are met after a machining operation; and the different methods used to trace a probe across a surface to gather data and analyze the surface. We have also learned that a surface generated on a part is the result of many controllable and uncontrollable inputs.
What I haven’t written much about are the holes in surface finish gaging equipment.
Before we discuss that, let’s go back and review how a typical surface is generated on a lathe or turning center. As the part turns in the spindle, a tool drags against it to embed the most basic roughness foundation. The movement of the tool is the result of its motion relative to the machine ways. Out-of-straightness conditions will be passed onto the part. Vibrations from the spindle, the coolant pump and the press down the aisle, along with various other environmental conditions, can be localized to the turning center. In the end, all influence the total profile of the part. As such, they influence how the surface will perform.
If the surface is not performing as specified, or the surface is not what it’s specified to be, an analysis needs to be conducted. To begin analyzing the surface, the appropriate surface or waviness parameter must be selected, along with the correct setting for making the measurement.
Modern tracing methods move a standardized conical diamond across the surface in a controlled manner using a skidded or skidless drive. Traces are normally made 90 degrees to the lay or in the predominant direction of the surface pattern.
Filters separate the different waveforms that are part of the surface’s total profile. Before starting though, it is necessary to understand the two basic features of a waveform: wavelength and amplitude. The total profile consists of multiple wavelengths and amplitudes superimposed on one another. When sampling a surface and collecting data, the surface data is filtered in several ways. For instance, the diamond radius and the skid on a skidded instrument filter the data by mechanical means.
Other filters are used to separate wavelengths into roughness and waviness for analysis purposes. The short wavelengths are generally considered roughness, and the longer ones are waviness forms. The user must select the cutoff (or filter), which is the setting used to separate the profile into the component wavelength bands of roughness and waviness.
The cutoff value is the longest nominal wavelength to be included in roughness. Wavelengths longer than the roughness cutoff are included in waviness. These are the “holes” discussed above: The cutoff value functions like a sieve.
The sieve analogy simplifies the explanation of filters in surface metrology. A random mixed pile of sand, gravel and stones is put onto the sieve. The mesh of the sieve acts like a wavelength separator. The small sand particles that pass through the mesh are like roughness. The larger gravel that does not pass through is like waviness. Stones larger than gravel are errors of form, which also do not pass through the mesh.

Cutoff setting is critical, and cutoff lengths are set forth in national and international standards. When analyzing roughness, the selected cutoff must be short enough to exclude long wavelengths (waviness). These cutoff lengths are defined by ASME and ISO standards. When reviewing the drawing of a part and surface specifications, the surface call out must specify the cutoff value for a surface finish specification in order for the drawing to be consistent with ASME.