Figure 1. Demonstration of the measurement of Ra. Source: Michigan Metrology

When measuring surface roughness, typically the average roughness, Ra, is specified. Ra is a measure of the average of the absolute value of the variation of the surface texture profile about a best-fit mean line. A typical specification for Ra may be 16 microinches, or 0.4 micrometers.

Figure 1. Demonstration of the measurement of Ra. Source: Michigan Metrology
The measure of Ra is expressed in units of length because it is a measure of the absolute value of the area under the profile-relative to a mean line-averaged over the length of the profile.

Figure 1. Demonstration of the measurement of Ra. Source: Michigan Metrology
Along with specifying the surface roughness with Ra, one must establish the cutoff lengths used to measure the surface. A specification of Ra alone is inadequate because measurement with different cutoff lengths may result in differences in the measured Ra values.

Figure 2A demonstrates the measurement of surface profile without filtering being comprised of many different spatial wavelengths. Source: Michigan Metrology
A surface profile is composed of a spectrum of different spatial wavelength components of various amplitudes. The measured profile will consist of a “filtered” version of the true profile because the instrument will be physically limited in sensing the finest spaced features. The longer wavelength structure detected will be limited by the physical extent of the region measured. After it is measured, the resulting raw profile is further filtered by electronics or software algorithms to precisely limit the spatial wavelengths comprising the measured profile.

Figure 2B demonstrates the measurement of surface profile with only a 0.8-millimeter long wave cutoff applied, resulting in the elimination of the “wavy-like” structures. Source: Michigan Metrology
A typical long wave cutoff, lc, for roughness is 0.8 millimeter, which means a 0.8-millimeter spatial wavelength component that is 1 micrometer peak to valley will be measured as 0.5 micrometer peak to valley after being filtered. Spatial wavelength components longer than 0.8 millimeter are further attenuated prior to the evaluation of Ra.

In addition to specifying the long wave cutoff, a short wave cutoff, ls, must be specified. Typically, the ratio of the long wave cutoff to the short wave cutoff is 100:1. Thus an 8-micrometer short wave cutoff may go along with a 0.8-millimeter long wave cutoff to establish a typical measurement bandwidth.

Figure 2C demonstrates the measurement of surface profile with only an 8-micrometer short wave cutoff applied, which results in the finer spaced structures being attenuated. Source: Michigan Metrology
A short wave cutoff of 8 micrometers means that an 8-micrometer spatial wavelength component that is 0.1 micrometer peak to valley will be measured as 0.05 micrometer peak to valley after being filtered. Spatial wavelength components of less than 8 micrometers are further attenuated prior to the evaluation of Ra.

Per ASME B46.1-1995 (p. 36), a standard on surface texture specification, the long wave cutoff length, lc, must be specified on all drawings. Per ISO 1302-2002 (p. 9), a standard on surface texture, the long wave cutoff length, lc, and the short wave cutoff length, ls, must be specified on all drawings.

Figure 2D demonstrates the measurement of surface profile with both long wave cutoffs and short wave cutoffs applied. Applying both the 0.8-millimeter long wave cutoff and the 8-micrometer short wave cutoff results in this “band limited” profile. Source: Michigan Metrology
The determination of the appropriate cutoff is application specific. Typically, the critical area of interaction with mating components, material properties and the scale of physical phenomena being considered are some of the elements that contribute to the selection of correct measurement cutoff lengths.

Per ISO 1302-2002, the proper specification on a drawing for a surface with a maximum Ra of 4 micrometers with a long wave cutoff of 0.8 millimeter and a short wave cutoff of 8 micrometers is described in Figure 3. Source: Michigan Metrology
Note that in some applications it may be necessary to specify a surface with a set of different cutoff lengths to control surface function. Per ISO 1302-2002, the proper specification on a drawing for a surface with a maximum Ra of 4 micrometers with a long wave cutoff of 0.8 millimeter and a short wave cutoff of 8 micrometers is described in Figure 3.

## Tech Tips

• Along with specifying the surface roughness with average roughness, Ra, one must establish the cutoff lengths used to measure the surface.

• A typical long wave cutoff, lc, for roughness is 0.8 millimeter, which means a 0.8-millimeter spatial wavelength component that is 1 micrometer peak to valley will be measured as 0.5 micrometer peak to valley after being filtered.

• In addition to specifying the long wave cutoff, a short wave cutoff, ls, must be specified. Typically, the ratio of the long wave cutoff to the short wave cutoff is 100:1.