Surfaces and Contact Mechanics, Part One, Page 10

We move now to a different scale, the microscopic scale. This is the scale on which most contact mechanics involves; and the perspective we get from measuring surface deviations from some nominal line (or plane, in three dimensions) is the field of surface profilometry. Using contact or non-contact methods, one can measure these deviations and produce a profile, or representation, of the surface. The analysis of surface profiles (in two dimensions) began in the 1950's. Profilometer traces of nominally smooth surfaces at the macroscopic scale showed that they are very rough at the microscopic scale. Statistical parameters obtained from these traces are still used extensively in science and industry to characterize a surface. In this lecture we will consider the definitions and standards that have been enacted for analysis of two-dimensional surface data. The next lecture concerns recent extensions of that analysis into three-dimensional data sets.

The following is taken directly from references [9 and 10, and references therein] unless otherwise noted.

Definitions

ASME B46.1-1995 [9] outlines methods in the analysis of surface roughness, waviness, and lay. This standard is used in most commercially available software capable of analyzing two-dimensional surface profile data. Roughness is defined as the finer irregularities of the surface texture that usually result from the inherent action of some production process, such as machining or wear. Roughness features are typically in the submicron to 10-(m range. Waviness can be defined as the more widely spaced component of the surface texture. Roughness may be considered to be superimposed on the wavy surface. Lay is defined as the predominant direction of the surface pattern, ordinarily determined by the production method used. Figure 53 [9] schematically illustrates these concepts.

Figure 53. The concepts of surface roughness, waviness, and lay are illustrated schematically.

Macroscopically, surfaces are machined to have some desired geometry, whether it's flat or curved. Figure 54 [9] shows how surface profiles deviate from that desired, or nominal, geometry

Figure 54. The difference between a nominal surface and a measured surface profile is illustrated.

When a surface profile is presented, it's important to recognize the difference in the horizontal and vertical scales. For example, the horizontal distance may be in millimeters while the vertical distance may be in micrometers, a difference of three orders of magnitude. When magnified, what is originally seen as a sharp peak becomes a gentle, rolling hill (Figure 55).

Figure 55. Recognizing the difference in the aspect ratio between the scales is important when looking at profile data.

The measurement and analysis of surface profile data is illustrated schematically as follows:

Figure 56. The profile data handling process is illustrated.

To separate the waviness and roughness information from the raw profile data, one of three filtering methods may be used: Gaussian, RC, and Adjacent averagaing. The link below is for a "pdf" file that explains these techniques. You will need to have Adobe Acrobat Reader 3.0 minimum installed on your computer and your web browser to view the file.

Filtering Methods (filter.pdf)

Figure 57.

Figure 58.

There are three lengths that are defined in profilometry: traversing length, evaluation length, and sampling length. The traversing length (or trace length) is the distance over which the stylus moved and the data acquisition system recorded the movements. The standards developed by professional committees arbitrarily decided to discard a length of data on each end of the traversing length, with the length remaining being the evaluation length. The data contained within the evaluation length is used for calculating statistical parameters. For some surface statistical parameters, information is taken from smaller, equally divided segments (usually five) called sampling lengths. Figure 59 illustrates the three lengths discussed.

Figure 59.

There are numerous statistical parameters that may be calculated from the profilometry data. The most common parameters calculated from the roughness profile are R_a and R_q, the average roughness deviation and the root-mean-square (rms) roughness deviation, respectively. The calculation of these parameters is shown in Figure 60.

Figure 60.

A point of caution: surfaces can be very different and produce the same R_a value. These statistical parameters should not be used to completely describe and evaluate surfaces, but rather should be combined with other surface techniques to provide a better understanding of a given surface.

Figure 61 is a table showing the R_a values obtained from surfaces prepared by a spectrum of different methods. The horizontal scale step-size is a factor of two reduction with each step left to right.

Figure 61.

The actual profilometry data is made up of discontinuous steps in the x direction. Four the CAFS profilometer (Mahr Perthometer System), trace length is divided into 8064 points. This determines the horizontal resolution. For example, if the trace length is 10 mm, the data points are separated by 1.24 mm. The vertical axis resolution is determined by the deflection limit of the stylus cartridge of the profilometer. One such probe has a limit of +/- 250 mm relative to an arbitrary zero height on the surface. This scale is then divided into 2¹⁶ = 65536 steps providing a maximum resolution of 7 nm. Of course, mechanical and thermal noise within the measurement environment limit the true resolution. Figure 62a illustrates the discontinuous nature of profile data. Each data point is labeled z_i and separated by some horizontal step-size d₀. Figure 62b shows three other roughness parameters that are sometimes used. R_t is the vertical distance from the highest point within the evaluation length to the lowest point. R_p is the vertical distance from the highest point within the evaluation length to the mean line. R_v is the vertical distance from the mean line to the lowest point within the evaluation length.

Figure 62.

An important piece of information with regard to surfaces, especially to contact mechanics, is the peak-height distribution (also known as, the amplitude density function). The peak height distribution is the number of heights within the profile versus the profile height with respect to the mean line. Surfaces that are truly random would have a Gaussian peak height distribution, but many surfaces do not. Figure 63a shows how such a distribution is generated. Figure 63b shows a roughness parameter R_sk, the skewness, where
(36)

Figure 63. Part (a) illustrates the construction of the peak height distribution (amplitude density function). Part (b) shows profiles that lead to various values of the skewness.

A roughness parameter that indicates the shape of the peak height distribution (in terms of width and height) is the kurtosis, R_ku, given by
(37)

Figure 64 illustrates some profiles that lead to various values of the kurtosis. The ideal Gaussian would have a kurtosis of 3. The triangle profile is not very typical. Most profiles that have a kurtosis of less than three would be vary broad with a smaller maximum than would be observed in the ideal case.

Figure 64.

Another method for evaluating surface in terms of contact will be by looking at the amount of material present for various depths from the maximum peak height. To do this, we define the profile bearing length as the sum of the lengths shown as b_i in Figure 65.

Figure 65. The profile bearing length is defined as the sum of the lengths indicated in this drawing as b_i.

The profile bearing length ratio, t_p, is defined as the profile bearing length divided by the evaluation length, L.