NBSM 73-196 (d)

Surface Finish, Friction and Wear;

The Need for More Than One Parameter

Dennis A. Swyt

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

May 3, 1973

Final Report

X

*

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

NBSIR 73-196

SURFACE FINISH, FRICTION AND WEAR;

THE NEED FOR MORE THAN ONE PARAMETER

Dennis A. Swyt

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

May 3, 1973

Final Report

U. S. DEPARTMENT OF COMMERCE, Fre<|erick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

SURFACE FINISH, FRICTION AND WEAR;

THE NEED FOR MORE THAN ONE PARAMETER

Introduction

Friction and wear are familiarly known to be complex phenomena

dependent upon the mechanical and chemical properties of the surfaces

in contact and the lubricant used to separate them. In order to manufacture equipment with predictable lifetimes and performance characteristics under loads, it has become necessary to evaluate a multitude of

these material properties. The topography, or surface finish, of parts

has been seen to strongly influence among other things, frictional forces,

the load carrying capacity of gears, the dynamics of lubricational properties, and the wear lifetimes of bonded solid lubricants. However, it

has become clear that single parameter characterization of surface

finish (e.g. by means of AA or RMS roughness values) is an inadequate

means of describing surface finish and its functional relation to friction and wear.

The purpose of this report is to consider in a very elementary way

the cause of this inadequacy and to briefly consider some of the presently

implementable alternatives.

Specification of Roughness

At present, the most common specification of surface finish is by

means of an AA roughness value, usually coupled with a description of
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the process by which the surface is finally formed, e.g., by milling,

grinding, etc. The AA roughness is derived from a two-dimensional

profile of the surface generated by a stylus instrument. Recent litera^

ture in surface finish demonstrates a growing awareness of the great

difficulty of succintly characterizing a given profile once a valid one

is obtained. While AA values can be obtained with a reasonable degree

of accuracy and repeatability, they cannot be correlated very well with

product function and reliability, (although an inverse relation with

cost has been revealed). Thus, when an engineer calls for a finer

finish, he may not be sure of the effect on lubrication properties

or load carrying capacity of a gear.

Since the limitations of using only one parameter (AA) are

known, other means of characterizing surfaces via profiles have

been attempted. Bearing area curves, maximum peak heights, average .

peak-to-valley distances, or peak height densities have been specified and commercial instruments are available for their measurements.

Some indication will not be given as to why these parameters are

prone to the same type of difficulties as AA values, namely insensitivity to and inability to distinguish different types of surface

structure. In a later section some more useful "second parameters"

will be discussed.

The limitations of a Single Parameter

In Figure 1 are shown seven profiles, more or less physically

realizable and associated with different formation processes. The

first two are complex, with some repetitive structure, and are reminiscent of profiles of milled or ground surfaces. The next two are
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almost purely sinusoidal, differing, however, in wavelength. Although

machining of such surfaces would be difficult, there are on the market

surface roughness standards produced by photo-etching of light interference patterns that have such profiles. The fifth profile corresponds

to the triangular waveform of another type of surface roughness standard.

The last two profiles are highly idealized and correspond to surfaces

having repetitive grooves and ridges, respectively. The significance

of these profiles lies in the fact that, although they vary widely in

character, they could all have the same AA roughness value. To see

why this is possible consider the following exercise which involves

only a minimum amount of sleight-of-hand.

A Game with Numbers

Figure 2 shows a collection of fifty digits, consisting of. five

each of the numbers one through ten. Some standard mathematical

quantities are associated with this collection, some of which are

indicated in Figure 3. The average (or mean) value is the sum of

all the digits, divided by the number of digits; the average deviation

from the mean is the sum of the absolute values of the differences

between each digit and the mean, divided by the number of digits;

finally, the standard, or root mean square deviation from the mean,

which is the square root of the sum of the squares of the differences

of each number from the mean, usually divided by one less than the

total number of values. The range of the numbers is the difference

between the highest and lowest.
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There may also be associated with the collection some type of

distribution curve. Figure 4 shows the number of times each digit

appears and the graph shows the fraction of the total number of

digits which have values less than a given digit.

Now consider what a profile instrument does when it measures

some characteristic of a profile. It effectively associates some

number, an ordinate, with the vertical displacement of the stylus

and then performs by analog circuitry some mathematical operation.

Figure 5 shows the relation between the mathematician's and the

surface metrologists ' s names for a given parameter. The average

corresponds to the centerline; the average deviation to the AA

(or CLA) roughness; the standard deviation to the RMS roughness,

the range to the maximum peak-to-valley distance over an interval,

and the distribution to the bearing area curve. Figure 6 shows diagramatically what these parameters correspond to on a profile.

The Sleight of Hand

By taking our original collection of fifty numbers and representing each number as a line on a bar graph, one can construct

64 ^ any number of profiles (about 10 for fifty numbers) . Five are

shown in Figure 7. The first is merely to indicate the constituent

numbers. The next four are, however, realizable surface profiles

with striking and significantly different characters. It should

be remembered that all these profiles are made up of the same fifty

ordinates and, therefore, have identical center lines, AA, RMS and
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maximum peak-to-valley parameters as well as Identical bearing area

curves. The point to be made is that these parameters are measures

of ordinate height only and are by nature insensitive to the ordering

or sequential alignment of the heights involved. Further, this insensitivity is not due to instrument design or implementation. (As an

aside, the variations shown in the Figure could very well fall within

the band pass characteristics of an averaging meter, AA or RMS, and

not be greatly effected by the cut-off setting)

There are, however, mathematical tools for analyzing profiles

which taken into account the ordering of the profile ordinates.

Instruments for this type of analysis are commercially available;

some involve software programmed computer analysis, others have

hardware which perform similar functions. Such instrumentation

tends to be quite expensive and the original analysis time-consuming

and sophisticated. With these disclaimers in mind, let us, just for

fun, consider what auto-correlation and frequency spectrum analysis

can tell about surface roughness.

Auto-Correlations and Frequency Spectra

In Figure 8 are shown the mathematical definitions of the

auto-correlation function (ACF) and the frequency spectrum (FS)

Suffice it to say that the ACF is the sum of the products of a

function and the same function a given interval away; and that

the FS yields the coefficients (amplitudes) of the spatial frequencies which comprise the surface profile. Note that the results

of these calculations are not single numbers, but functions which

may be presented in graphical form.
-6-

Figure 9 shows some simple profiles and their corresponding ACF

and FS functions. It is obvious that the periodic nature of the

profiles is immediately revealed, although in different ways, by

the two functions. The first three profiles in Figure 10 correspond

more closely to realistic surfaces. The first is like a fine ground

surface, the second like machined surfaces. The value of the ACF

in these cases lies in the facts that it yields the RMS directly

and also qualitatively indicates the nature of the surface variations, differentiating between random and periodic components.

In Figure 11 are shown some of the results of one study of

real surfaces wherein the peak height distribution, ACF and FS

functions were computed. The problem with these higher order functions is that while they can differentiate types of surfaces, some

means must be devised to associate index numbers with them and to

relate these index numbers to product performance.

The Average Wavelength 'Parameter

A "wavelength-conscious" parameter which may be easily

measured and describes in some degree roughness peak spacings has

been suggested. The function being averages is the derivative

(the instantaneous slope) of the profile; such an average may be

done on an AA or RMS basis as indicated in Figure 12. The relation

between the average wavelength and the RS for some real surfaces

is shown in Figure 13. The parameter has the advantage that it

may be measured by existing AA (or RMS) averaging instruments with

only minor modifications or supplemental circuitry.
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Summary of Parameter Characteristics

A table summarizing the characteristics of the surface parameters

discussed above Is given In Figure 14. The list Is not meant to be

Inclusive but rather to point out that when measuring surfaces, one

should be critically aware of what a measured parameter does (and

does not) tell him about a surface.

As indicated, a topographical map is just so much raw data;

it can be displayed to give a qualitative image or numerically

analyzed. A profile is a two dimensional cross section of a surface;

how well it represents the entire surface is a problem to contend

with. Given a profile, the six index numbers and five functions are

some of the means by which a profile can be analyzed. The profile

details to which these parameters are sensitive are indicated; the

degree to which these single parameter Indices (or those which may

come to be associated with the functions) are related to final product

operation is another question.

Conclusion

In conclusion, it should be emphasized that carefully measured

AA values may validly characterize one aspect of surface texture.

Further, if AA specifications for surface finish are accompanied by

a specification of the final process by which the surface if formed,

control is placed over some of the other aspects which AA values

do not reflect. However, in order that the periodic and random

nature of a surface can be quantitatively described, new tools

must be developed and evaluated.
-8-

Higher order mathematical descriptions of surfaces, achieved

through computer analysis of profiles, may be a necessary and, in

the long run, economical means of analyzing surface topography and

relating it to product function and reliability. At present such

analysis is practical only in a research environment and achievable

at relatively high cost. However, it is likely that in the future

blueprints will need to specify much more about a surface finish

than one number can tell.
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Flgure Credits

Boundary Lubrication: An Appraisal of World Literature, ASME

Research Connnittee on Lubrication, F. F. Ling, et al., eds.,

1969, p. 9 (Figure 1).

Federal Scientific Corp., Tech. Notes on Ubiguitous Analyzer and

Spectrum Analyzers. (Figures 9 -10).

The Properties and Metrology of Surfaces, IME Conference Proceedings,

Vol. 182, part 3K, 1967-68, p. 118-119 (Figure 11).

Measurement and Control, Vol. 5, March 1972, p. 98 (Figure 13).
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FORM NBS.114A n-71)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 73 196

2. Gov't Accession No.

4. TITLE AND SUBTITLE

SURFACE FINISH, FRICTION AND WEAR: THE NEED FOR MORE THAN

ONE PARAMETER

7. AUTHOR(S)

Dr. Dennis A. Swyt

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BLTIEAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

12, Spoasoring Organization Name and Address

Same

3. Recipient's Accession No.

5. Publication Date

6. Performing Organization Code

8. Performing Organization

j NBSIR 73-196 [ 10. Project/Taslc/Work Unit No. '

11. Contract/Grant No.

13. Type of Report & Period Covered

Final

14, Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Surface finish is most conmonly described by an arithmetic average (AA) value,

often coupled with a description of the process by which the surface is finally

formed. Since the insensitivity of the AA parameter to the periodic nature of

surface structure is well known, many supplemental "second" parameters have been

suggested. This short paper gives an indication of the basis for the insensitivity

of the AA parameter to periodic structure and considers briefly some "wave length

conscious" parameters (e»g, , average wavelength and correlation lengths) which

may be useful in supplementing the basic AA value for a more complete description

of surface finish.

17. KEY WORDS (Alphabetical order, separated by semicolons)

AA roughness; surface autocorrelation; surface finish; surface finish average wave'

length; surface periodicity.

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'•^76-191*