Is Average Roughness (Ra) Enough When Measuring Surface Quality?

Being able to quantify a surface finish is both a complex and necessary task. While surface topography relates to a three-dimensional property, the most accepted surface measurement parameter is average roughness (Ra), a two-dimensional parameter. Ra is relatively simple to quantify and can be measured against historical data but does little to describe potential functionality or the subtle nuances inherent in a surface.

This article explores the implications of using 3D parameters to deliver a more in-depth understanding regarding surface finish and performance, including two case studies where the use of 3D parameters influenced the design and development of high-performance surfaces.

Evolution from R Parameters to S Parameters

First developed in the 1930s, stylus-based techniques were introduced to measure surface finish. For stylus measurements, a sharp or rounded tip is traced along the surface with its vertical deflection correlating to sample heights.

Data from stylus measurements are then quantified using various R parameters, such as 2D descriptors, including Ra, Rp (maximum peak height), Rv (maximum valley depth), Rt (total height), Rq (root-mean-square roughness), Rz (average of maximum peaks and minimum valleys), among others.

Figure 1. Some of the parameters used to describe surfaces in 2D. Image Credit: Bruker Nano Surfaces and Metrology

In the late 1900s, optical profiling was developed as a 3D surface measurement technique. Through refining this technique, fast, large-area topographical analysis via areal data collection and multi-frame stitching was brought in. These 3D datasets exposed many more details regarding the texture of a surface compared to a 2D trace, and Ra became an deficient quantitative descriptor. Originally, adjustments were made, and Ra was simply modified to be a 3D equivalent of average surface roughness (Sa), but this left out key information regarding surface height variation details and texture specifics that 3D datasets are able to encapsulate.

Table 1. Some of the many parameters used to describe surfaces in 3D. Source: Bruker Nano Surfaces and Metrology

The S parameters (Table 1) were conceptualized in the 1990s, and were initially categorized into four main categories: amplitude, spatial, hybrid, and functional. These parameters are able to depict a surface with greater accuracy than just 2D parameters, painting a quantitative picture of micro-roughness, waviness, wearability, lubricant retention capacity, texture direction, etc. Using the S parameters, engineers and process designers are able to better understand their surfaces and can consequently design surfaces with an improved focus on functionality.

Figure 2. Bearing area curve, with Spk*–peak height, Svk*–valley depth, A1–peak cross-sectional area, A2–valley cross-sectional area, Mr1–material ratio 1, and Mr2–material ratio 2. Image Credit: Bruker Nano Surfaces and Metrology

Alternatively, surface texture can also be understood and represented by the bearing area curve (BAC, also referred to as a bearing ratio curve or an Abbott-Firestone curve). The BAC, displayed in Figure 2, is the collective probability density function of height for a surface profile line. That profile may derive from either a single trace (for 2D data) or an average over several traces (for 3D data). This Abbott curve is also applied for the evolution of the 3D volume parameters for characterizing fluids, such as Sci (core fluid retention index) and Svi (valley retention index).

Persistence and Weaknesses of Ra

Today, surface finish is still typically described using only an Ra value, despite its incapacity to describe the subtlety of real surfaces. This ongoing attachment to Ra is largely due to two leading factors: ease of low-cost 2D measurements with a stylus profilometer, and easy access to historical data for Ra.

While it does have some merits as a general surface texture guideline, Ra is too generalized to accurately describe a surface’s real variations or functional nature. For instance, a surface with sharp spikes and deep pits or one with a broad isotropy may produce the same Ra value.

Figure 3. Four very different surfaces all with Ra = 0.4 μm (16 μin), finished by (a) grinding, (b) horizontal milling, (c) reaming, and (d) vertical milling. Image Credit: Bruker Nano Surfaces and Metrology

In Figure 3, there are four surfaces shown each with the same Ra for various finishing steps, each of which creates visually distinct surfaces that would perform very differently from each other in terms of function. Ra calculated from a single trace (or even multiple) cannot distinguish between these surfaces and cannot offer much information about their functionality, while S parameters has the capacity to do both.

Figure 4. Plot showing Ra, Sds, and Std for the four samples in Figure 2. There were four variants of Ra: as-advertised, as-certified, independentlyverified, and WLI data–calculated. Connecting lines are simply a guide for the eye, following the same parameter across samples. Image Credit: Bruker Nano Surfaces and Metrology

The surfaces from Figure 3 were assessed using (1) a number of stylus-collected Ra measurements, and (2) Bruker’s white-light interferometry (WLI) to determine S parameters and conduct a stylus analysis that relates back to stylus measurements. Ra and S-parameter results are plotted in Figure 4.

With guidelines linking the same parameter across samples on the plot, the included certified values of Ra are highly close to all four fingernail standard samples (near horizontal lines at Ra=400 µm). However, all other measurements diverge from these provided values of Ra.

An independent certification and WLI stylus analysis calculated Ra values (which are based on an average over an area) demonstrate close correlation with one another, only straying for the vertical milling sample where the stylus measurement location remained unknown.

For further information on these measurements and how Bruker’s Vision64^® software can enable stylus analysis of WLI areal data, see Bruker’s Application Note 558, “Correlating Advanced 3D Optical Profiling Surface Measurements to Traceable Standards”.

The two S parameters plotted from WLI measurements (summit density Sds and structure angle Std) shown in Figure 4 exhibit clear differences between the samples in contrast to Ra. In particular, vertical milling displayed a much greater Std (as a result of the angle of the dominant surface structure) and lower Sds (due to the lower summits per unit area) when compared to the other three finishing steps.

It is clear to see that single- or multiple-trace Ra does not offer a full overview of the differences between these surfaces. Averaging Ra over a greater area begins to explain some of the variations, while introducing an analysis of S parameters promotes greater understanding both of differences and of what those differences could actually mean in terms of functionality.

Case Study 1: Determining a Source of Corrosion

Ra is not always considered an effective quality screen or sufficient measure for development and problem solving. At Masco Corporation, Research & Development, the average roughness specification of incoming ASTM 366 coil steel stock was conforming to an average of 20 to 70 microinches, but corrosion of a considerable portion of the stock was brought about after a series of cold working and surface treatment processes.

Figure 5. Surfaces of ASTM 366 coil steel stock that either tended to rust (right) or not to rust (left). Courtesy of John Finch, Terry Chuhran, and Daryl Wilusz,
Masco Corporation.

Surface analysis was conducted on the incoming stock to identify the source of the rust. Figure 5 displays 3D optical profiler plots of the various stock surfaces that determined what was considered either acceptable or rust-prone final parts.

The rust-prone stock exhibits several deep valleys, whereas the acceptable stock is more isotropic. Of the S parameters, skewness (Ssk) and valley depth (Sv) were found to closely correspond with the tendency toward corrosion.

Figure 6. Bearing ratio analysis of the two surfaces in Figure 5. The stock that eventually corroded showed a greater percentage of valleys deeper than 2 μm. Image Credit: Bruker Nano Surfaces and Metrology

In Figure 6, a BAC was plotted for both types of stock, signaling the percentage of the surface that falls above or below a particular depth. These curves quantified the percentage of valley area that typically resulted in corrosion. From this data, it was established that the deeper valley structure held processing solutions and did not rinse or dry properly, resulting in flash rusting. A ratio of parameters taken from the bearing area analysis was a supreme indicator of the incoming stock’s tendency to rust.

Case Study 2: Using 3D Parameters to Engineer a Surface

Engineering new parts' surfaces requires more than just a Ra value for good functionality. Steel Parts's new clutch plate design required optimal friction and wear performance parameters. After numerous plate designs with known performance characteristics were evaluated (Figure 7), it was identified that skewness and kurtosis corresponded well with wear and friction, as did various other combinatorial parameters. These parameters were used to effectively develop and control a successful novel manufacturing process that ensured the performance of parts demonstrated consistency.

Figure 7. Experimental clutch plate designs whose performances were connected to certain S parameters. Courtesy of John Riggle, Steel Parts.

Conclusion

Progress made in 3D measurement techniques, such as optical profiling, have brought about advancements that have allowed engineers, process designers, and quality control professionals to gain more control through access to an improved toolkit for describing surfaces.

Table 2. Standards with definitions and usage guidelines for surface parameters. Source: Bruker Nano Surfaces and Metrology

3D parameters can differentiate surface shape and determine functionality. A careful surface design study creates a more in-depth understanding of functional characteristics and a process that is easier to control to ultimately improve surface performance. For more details, definitions, and usage guidelines for surface parameters, see the standards illustrated in Table 2.

This information has been sourced, reviewed and adapted from materials provided by Bruker Nano Surfaces and Metrology.

For more information on this source, please visit Bruker Nano Surfaces and Metrology.