Since the industrial revolution, manufactured surfaces have required analysis to help control metal removal processes like turning, grinding, milling, and more. When both process and analysis are performed correctly, manufacturers can produce surfaces that perform their intended functions reliably and efficiently.

Engineers want to quantify the tool mark, or roughness of the surface, to ensure reproducibility of desired characteristics of such surfaces on the production floor.


Engineers want to quantify the roughness of the surface to ensure reproducibility of desired characteristics.

In controlling the characteristics of a surface the first focus was on controlling the peaks of a surface.

An incredible diversity exists among the industries requiring specific surface finish parameters.

Historically one of the first parameters measured and defined is Roughness Average (Ra), which each surface contains as a signature of its manufacturing process. In many cases Ra is very good either by itself or in combination with other parameters to monitor somewhat stable and proven processes reliably. Being a statistical parameter, Ra is very forgiving towards surface flaws but can indicate changes in the overall roughness of a surface. Its representation of a true surface characteristic is unfortunately weak and it is not sensitive to peaks and valleys.

In order to better understand the above surface finish patterns, researchers began searching for ways to study the total surface profile of physical characteristics beyond the Ra signature. This would allow them to better understand the manufacturing process and reveal the desired functional characteristics that would allow development of numerical parameters capable of specifying and producing a desired profile.

In the 1930s, Abbot and Firestone developed the “Bearing Area Curve,” or material distribution curve, to graphically show the distribution of material vs. air on a given surface.

By analyzing the material distribution, the observer is able to better understand how the air to material relationship (material ratio) of a surface changes depending on the depth of penetration into the material. Ideal bearing surfaces, or high wearing surfaces, will generally feature a very high material ratio towards the top of the surface.

In the process of observing this surface behavior, a simple parameter was developed called Rmr (formally known as tp). Rmr is capable of displaying the material ratio based on a “percentage to depth” or “depth to percentage” ratio. Even the best surfaces wear in quickly, i.e. the top peaks wear in quickly, usually within the first few interactions with another surface. In order to compensate for this “break in” of a surface, a small add-on to the material ratio parameter had to be developed. Today, this is used by manufacturers to specify a small material ratio—typically between 0% and 5% of the surface, as an off-set to the cutting line that defines Rmr all in an effort to stabilize representation of the parameter.

Many manufacturing processes can be improved by defining specific parameters to control the production processes. This makes it virtually impossible to visually inspect the bearing area curve. To alleviate this issue, process engineers started to define several Rmr values a single area curve. This has helped to describe the shape change of the curve over the depth much more efficiently than a single call-out is capable of. One parameter that was found to be helpful in this area was the RδC, or RdC (formally known as Htp). RdC represents the distance between two Rmr lines, or values.

In controlling the characteristics of a surface the first focus was on controlling the peaks of a surface. As many surfaces will require lubrication in their interaction, manufacturers discovered that not only controlling the peaks in the surface (smoothing the top surface) contribute to the materials performance, but that additional valleys in the surface would provide for oil retention and therefore lubricity of the surface.

Using the bearing area curve to specify surface finish function, designers have developed various different numeric surface parameters in an attempt to communicate surface attributes to manufacturers. Almost every product sold today contains surfaces that are critical to product success and longevity.

Previously we focused on the significance of both the peaks and valleys of a surface. When both of these surface elements are removed, all that remains is the center part of the roughness—its core. The core of the roughness and its relationship to the overall surface depth can reveal a great deal about the characteristics of a surface. Once this “core” attribute was identified it became necessary to numerically describe its surface attributes and the Rk family of parameters was born. Rk, or Core Roughness, focuses on the change of the material ratio within the surface and is calculated over the bearing area curve. Rk represents the distance the surface requires to “gain” 40% material ratio the fastest. Mathematically a slope line representing 40% material is moved along the material distribution curve and fixed where it experiences the smallest slope.

Once the core roughness has been determined, we are left with a peak portion of the roughness (Rpk*) and a valley portion of the roughness (Rvk*). Both values have an “*” as they are technically a reduced valley and peak height induced from wear (or break in) of the surface.

Both of the above surfaces have Ra values of 2.4 µm. The 1st surface has a fairly high Rk value of 8.2 µm. This means the surface essentially needs a long time to change its material ratio. The resulting peak roughness (Rpk) and valley roughness (Rvk) are small. This surface is equally distributed and generally speaking does not have the best wear characteristics. The second surface has a very small Rk value of 1.9 µm and also displays a small peak roughness of 0.9 µm. This means that after a short distance into the surface there is a significant material ratio available to resist wear. A high Rvk value indicates that there are valleys available to hold oil—hence we are looking at surface with good wear and oil retention capabilities.

Industry Examples

Here are several examples of industries that have benefited from bearing area curve derived parameters:

An industry that has found obvious benefits in adopting these techniques is engine manufacturers. Using the bearing ratio principle, cylinder bore and piston ring surfaces have been optimized for longevity and durability. This has led to a large reduction in the break-in period for new engines, by using a plateau honing technique to prepare surfaces for future wear better. Combined with overall tighter tolerance control and surface finish optimization, service intervals are extending further and further away; don’t be surprised to see better than 10,000 mile service requirements for oil changes on the horizon.

Another example of this exists within the tire industry. In order to dramatically increase the wear life of tire tread, carbon black was added to the tire compound. To be effective, the carbon black needed to be integrated into the compound without agglomerations. To accomplish this, a surface finish instrument with special software traced the finished product which allowed a dispersion index to be calculated to provide numeric control over the manufacturing process.

An unlikely industry to see any benefits might be the cosmetics companies. However, the cosmetics industry needed to provide evidence that its products actually improve skin conditions. To accomplish this, silicon replicas of various skin types are manufactured and then analyzed using specialized surface tracing systems before and after application of the skin cream.

As you can see, an incredible diversity exists among the industries requiring specific surface finish parameters. One common thread, throughout all of these examples, is that the study of the surface profile pointed the way to identifying the parameters needed to control generation of these critical surfaces.

 Since all of the deflections and error sources, both internal and external to the machine tool, present themselves on the surface of the machined part it is important to isolate and determine error sources in order to minimize them. Manufacturers can isolate and minimize surface component tool marks simply by adjusting the machine tool.