## What do you mean by “Roundness”?

Most of us that have been around surface metrology have had a reasonable grasp of the “filter cutoff” concept. In the case of surface texture there are long wavelengths that we call “waviness” and short wavelengths that we call “roughness”. The wavelength that separates these two regimes is called the “cutoff wavelength” and a filter is used to separate the profiles. (See the 3 Steps to Understanding Surface Texture for more on surface texture filtering.)

A recent addition to Digital Metrology’s OmniRound software gave some interesting insight into Gaussian filtering for roundness. This has been pretty eye-opening for many people and may surprise you. However, some of you many need some background first…

### But first some background…

In the case of roundness we don’t necessarily talk about “wavelengths” like we do in surface texture – instead we talk about “frequencies”. Roundness is a low-frequency “form” measurement so high frequency “roughness” effects are removed. Instead of a cutoff wavelength indicating how much high-frequency roughness to remove, we have a cutoff frequency expressed in terms of “undulations per revolution” or “upr”. An “undulation” can be thought of as a “wave”. In fact, in older documents we see the term “cycles per revolution” or “cpr”. In today’s world this term has become upr.

### So what frequencies do we include in roundness measurement?

Historically, the default roundness cutoff was 50 upr. This means that anything occurring less than 50 times per revolution is considered to be the “shape” of the surface. If it occurs more than 50 times, then it is considered to be in the roughness regime – not roundness. Recent ISO standards give cutoff recommendations based on the conversion of wavelengths to cutoff frequencies based on the circumference of the part. Ultimately, the designer needs to consider which frequencies are of interest and choose the cutoff accordingly. ISO and national standard propose the “preferred series” of cutoffs to be 5, 15, 50, 150, 500, 1500, etc. This way, the instrument manufacturers and users have a basic set to choose from. Check out a US Quarter at different cutoff frequencies (First row left-to-right: 5, 15, and 50 upr. Second row: 150 and 500 upr):

In the case of the quarter, a “default” 50 upr cutoff (rightmost graph on the top row) would not include serrations on the quarter in the roundness evaluation. By the way, if you don’t feel like counting them, there are 119 serrations.

Choosing a smaller cutoff value means that the data will be “smoothed” more. This smoothing occurs via a Gaussian filter which is a weighted moving average and the width of the moving average depends on the cutoff value.

### Brick walls and ripples

The Gaussian filter is not a perfect filter in terms of separating frequencies. For example, if you choose a 50 upr filter. It does not mean that you will get everything up to 50 upr and nothing beyond 50 upr. That kind of filter that give 100% of low frequencies and 0% of high frequencies is referred to as a brickwall filter and has this characteristic:

Unfortunately, the brick wall filter causes extra “ripples” to be put into the roundness data. These ripples are due to what’s called the “Gibbs Effect”. (You can Google it for more information.)

To get rid of these extra ripples, we need reduce the transmission at some of the lower frequencies and add some transmission at some of the higher frequencies. When we do this, it makes the transmission less “sharp”. The Gaussian filter is an “ideal filter” in that it has sharpest possible transmission while not adding any additional “ripples” to the profile. For you controls people, you can think of the Gaussian filter as “critically damped”.

Here’s how the Gaussian transmission characteristics look for some common cutoffs.

### Now this may surprise you…

The above transmission graph gives the impression that the Gaussian filter is pretty “sharp” in terms of its transmission. However, that graph is typically shown on a logarithmic x-axis. The latest version of OmniRound allows you to see the selected filter’s transmission right on top of the frequency content of your measured profile.

So let’s take what we’ve seen with the quarter (way at the top) and filter it with a typical 50 upr Gaussian filter (like we’ve just seen) and see what the filter transmission looks like.

The light blue curve on the “Harmonic Amplitudes” graph is the transmission characteristic for the selected, 50 upr Gaussian filter. This transmission doesn’t look very sharp but it is, in fact, what the Gaussian filter does whenever you are measuring roundness.

(NOTE: If you need a quick tutorial on the harmonic graph and what the bars mean, click over to the BrakeView website and check out the description at: http://www.BrakeView.com/Harmonics.html )

So the Gaussian isn’t a “sharp” as it appears on log paper. In fact as we look at the OmniRound screenshot above, we see that the transmission is very long and it includes frequencies almost all the way to the serrations. If you think that is interesting, check out what a 15-50 upr bandpass Gaussian filter’s transmission looks like:

In the case of the 15-50 bandpass, the most that any single frequency is transmitted is approximately only 75%!

### So what do we do with this?

I know that this is supposed to be a 60-second tutorial and I know I’ve run way over that time limit. But hopefully this is a quick “reality check” for those of you involved in the specification and measurement of roundness.

There is much more that we can talk about in terms of understanding roundness, harmonics, filter types, bandpass analysis and how these relate to making your parts work better.

Or for help on roundness specification and measurement send an email to: info@digitalmetrology.com

## 3 Steps to Understanding Surface Texture

A common question in surface measurement is “I have a surface finish specification.  Where do I begin?” or “I’m new to the field of surface measurement.  What do I need to know?”  With that in mind, this tutorial is provided to help you “hit the high points” of surface measurement (no pun intended).

### Measuring Surfaces

Surfaces are comprised of many “shapes”. We call the long wavelength shapes: “waviness” and the short wavelength features: “roughness”. The measurement of surfaces involves producing numbers to describe these shapes.

By the way, the blue profile in the top graph is referred to as the “primary” profile.

In general, the term “surface texture” refers to the primary profile, roughness, waviness and other surface attributes such as the direction of the surface features (also referred to as the “lay” of the surface). The term “surface finish” typically refers to the “roughness” aspects of the surface – ignoring the shape and underlying waviness. Be careful when dealing with only the “surface finish” as many functional problems are related to waviness as well.

### The picture is pretty, but how do we do it?

Surface measurement can be understood through the use of 3 fundamental topics:

• Fitting
• Filtering
• Analysis

Since I’ve only got 45 seconds left, we’d better get started…

### 1. Fitting

The first step in dealing with surface finish or surface “texture” is removing the underlying “shape”. In many cases the surface to be measured is tilted relative to the measuring device. In other cases, the surface may be nominally curved. In either case, the underlying geometry must be removed. This involves the “fitting” of a geometric reference such as a line or an arc and then looking at the wiggles (residuals) above and below the reference geometry.

The raw data from the probe is shown in the top (gray) profile. Superimposed on the raw data is a least squares line. In this case the least squares line is used to remove the tilt from the profile. The residuals (above and below the line) make up the blue (primary) profile.

Note: a small filter is sometimes used to remove noise from the primary profile. This filter is called the “short wavelength filter” but that’s another topic for another day.

### 2. Filtering

Once the geometry has been removed we need to separate the waviness and the roughness. This is the most critical aspect of surface measurement and yet it is probably the least understood.

Filtering surface profiles involves running a “smoothing” filter through the primary data. The amount of smoothing is based on a “filter cutoff wavelength”. The “cutoff wavelength” is the wavelength that separates roughness from waviness. Shorter wavelengths fall into the roughness profile and longer wavelengths appear in the waviness profile.

A “Gaussian” filter is recommended in ASME and ISO standards. Gaussian filters are based on passing a Gaussian, weighted average through the primary profile – resulting in the waviness profile. The roughness profile is made up of all of the peaks and valleys (residuals) above and below the waviness profile.

Changing the filter cutoff value (which changes the amount of “averaging” and “smoothing”) can have a huge impact on the measurement of roughness and waviness. Choosing a smaller cutoff value will result in smaller roughness values… even though the real surface could be very rough. The filter cutoff provides the means for defining “what I am calling roughness”.

The following graphic presents the same surface with two different filter cutoffs. The roughness profile on the bottom left gives twice the “average roughness” (Ra) value of the profile on the bottom right.

There is a table of “standard” cutoff values (along with selection recommendations) in ASME B46.1-2002 as well as ISO 4288-1996. This information is also provided in OmniSurf’s help system.

### 3. Analysis

OK – I know it. This is much more than 60 seconds. But there was a lot of good stuff to talk about.

Once we’ve separated things into roughness and waviness profiles we need to come up with numbers to describe them. After all, pictures are great, but engineers love numbers. The simplest of parameters is the “total” height of a given profile. This is the “peak-to-valley” height of the profile. For the primary profile the total, peak-to-valley height is designated: “Pt”. For the waviness profile it is “Wt” and for the roughness profile it is “Rt”. (The first letter always designates the profile.)

Unfortunately, the old adage “you get what you pay for” holds true here. The parameters, Pt and Rt are often quite unstable since they can be influenced by dirt, vibration and other things that are “outside the normal statistics” of the surface. On the other hand, the peak-to-valley waviness, Wt, is considerably more stable as it is based on only the long wavelengths and effects such as dirt are “smoothed out”.

Regarding roughness parameters, hundreds of parameters have been proposed. We won’t go into all of them here because, after all, we have gone well past our 60 seconds.

The most common roughness parameter is the average roughness, Ra. Many years ago this parameter was referred to as the “arithmetic average” (AA) or the “centerline average” (CLA). Today we designate it “Ra” to be consistent with all of the rest of the parameters.

The average roughness (Ra) reports the “average distance between the surface and the meanline” looking at all of the points along the profile.

For example, if a surface has heights and depths as follows, it will give an Ra value of 3.33 (in units of height such as microinches or micrometers):

Since the average roughness (Ra) is simply the “average distance” from the meanline, peaks and valleys are treated the same way.  So several profiles can all have the same Ra value:

Second to Ra, in terms of popularity is the “average peak-to-valley roughness” or “ten-point roughness”, designated Rz.  Rz has different definitions based on the standard that you are working with.  However there are two basic definitions: one used in German (DIN) standards (which is in today’s ASME and ISO standards) and one used in Japanese (JIS) standards which was used in older ASME and ISO standards.  There is no time left to discuss these in great detail, but it can be said that the DIN approach uses one peak and one valley in each sampling length, whereby the JIS approach uses 5 peaks and 5 valleys in each sampling length.  As a result the DIN values are always equal to or higher than the JIS values.  Be sure that you know which one you are using!

### There is a lot more to talk about (but we’re out of time!)

That’s why Digital Metrology offers on-site training for surface texture specification, measurement and analysis.

## Can I do R&R Studies on my surface Finish Gage/Gauge?

In recent years, one of the most commonly asked questions in surface measurement is “How do I do R&R studies for my surface finish instruments?”

Perhaps a better question should be “Should I use an R&R study when dealing with surface finish?” In many cases, the answer should be a strong “No!” In other cases, the answer could be “Maybe, but be very careful.”

Repeatability and Reproducibility (R&R) studies are used in the assessment of many measurement systems… in many cases these studies can be quite useful in determining an appropriate method or instrument. However, this may not necessarily be the case in surface finish measurement.

### Better may not always be better!

For a simple measurement devices, such as a calipers or micrometers, the measurement is static and one-dimensional. If the device has good repeatability, it can be adjusted to give good accuracy and then the device is deemed acceptable. In the case of dynamic or measurements such as surface finish measurement (including roughness, waviness and profile), better repeatability may not mean a better gage. For example, a relatively “dead” instrument may repeat very well, but the measured values are meaningless as the instrument doesn’t have the ability to detect the actual surface features. Furthermore, the values produced by surface finish instruments cannot be “adjusted for accuracy by shifting the zero point” as is the case with one-dimensional instruments. If the surface finish instrument measures too low for a given surface, it may not measure too low on a different surface.

If you want the best possible repeatability – just unplug the gage! If you want to determine how good your instrument is you need a better method.

### The surface is your enemy

When performing a traditional R&R study, one of the assumptions is that you can measure the same thing multiple times.  Unfortunately, this is nearly impossible in surface measurement – particularly in profile (stylus-based) measurements.  In these measurements, the stylus tip interacts with the surface in a path that is on the order of one micrometer wide.  To place the stylus in exactly the same position for repeat measurements is nearly impossible.  Furthermore, the first measurement may have actually changed (e.g. scratched) the surface through the stylus contact pressure.  Typically, a surface texture R&R study provides an indication of the repeatability of the fixturing – not the performance of your instrument!

### So what is the answer?

A better approach to assessing an instruments performance comes through the use of an uncertainty analysis. Don’t let the scare you, it is not that difficult. Uncertainty analysis gives the answer to the question “How wrong can my result be?” Look at your watch right now. Go ahead, I’ll wait. Is the time correct? Probably not. How wrong do you think it is? That’s an uncertainty estimate.

To determine the uncertainty of a roughness instrument, we can look at the factors that can influence you measurement. (This is very similar to the Failure Mode and Effect Analysis (FMEA) used in manufacturing). In surface texture measurement these may include factors such as: (in no particular order)

• Traceability / Masters
Is a micron on the graph really a micron?
• Linearity
Do I get the same answer at different probe positions?
• Noise
Is that signal really the surface?
• Frequency Response
Can I see all wavelengths – long and short?
• Datum Straightness
Is that waviness really in my part?
• Software and Math
Is 2+2 really equal to 4.00001 ?

Digital Metrology has extensive experience in surface texture uncertainty analysis along with a set of test standards and procedures related to each of these error sources. Once quantified, these error sources can be combined to give an estimated measurement uncertainty for your particular instrument and measurement application. Coupling this instrument uncertainty with the “in-part variation” is useful in determining the number of measurements and the impact on process capability parameters such as Cpk. Most of the time, these have revealed very interesting results.