In August of 2011 I made a presentation to our sales team on how we had incorporated the new ISO Geometrical Product Specifications into our operating software for all of our form tester products. I thought the presentation went well—I was clear and precise, and the material wasn’t too complex. I expected everyone would be embracing the new options now offered in the software. However, at the end, several people looked puzzled. “Yeah, but,” summed up one of the participants, “what are these new standards good for? Who will use them?”

It’s an interesting question, and a very important one. To understand that, we must first understand the reasoning behind these new standards and the new parameters they offer us the opportunity to use. In fact it is just that, the “opportunity,” which is the key to understanding these standards. These standards give us the potential to specify form tolerances on parts in new ways that may be beneficial to the function of a component. The new ISO Standards for Roundness (12181), Cylindricity (12180), Straightness (12780) and Flatness (12781) can be seen as setting a stage for future development. The result of many years of discussion, they open a new window for form specifications and may have significant ramifications on how some companies specify, measure and manufacture parts.

## Determine the Mean

As for what they do, that is relatively straightforward. In the old days (which, for the purposes of this discussion, we will classify as pre-April 2011 when these standards were officially released), when we talked about any form characteristic, it was always in terms of a single number, derived from a maximum peak to valley value which deviated from an ideal geometric form. So if we looked at the roundness of something, we would take a roundness trace, collecting data as to how a surface varied around the circumference of something. To determine roundness, we would first determine some type of best-fit circle (the ideal geometric form) and then find the highest peak outside the best-fit circle and the lowest valley inside the best-fit circle. The sum total of those distances from the best-fit circle was the roundness value: it was defined, simply, as the maximum deviation from a perfect circle.

Now enter the new standards, which are just a little more complicated. Like all standards documents, the new ISO Geometrical product specifications spend a lot of time defining terms. But the most fundamental—and perhaps revolutionary—change these new standards make is to allow other options than simply the maximum deviation from an ideal geometric form to be specified. We still fit an ideal geometric form of some kind, but now we have the option of looking at parameters that would put tolerances on the peaks separately from the valleys, as well as other refinements to the total variation.

To understand how this is accomplished, let’s look at the world of surface metrology, which is where these parameters have some close cousins. In the world of roughness, for many decades we have calculated parameters by fitting a mean line through the measured profile, and then used the relationship between the profile points and the mean line to calculate all sorts of parameters. The most typical calculation we make is the average distance all the profile points are from the mean line, which is Ra. We can also get parameters such as the root mean square distance of the profile points, Rq, or the maximum peak height separated from valley depth, Rp and Rv, and so on. In surface metrology, a surface can be mathematically characterized in any number of different ways to assess its functionality. In fact, there are at present about a hundred parameters for assessing surface features defined in various international, national, and company internal standards.

It is exactly this desire to better characterize and define the allowable form errors on a surface so that these can be matched to the function of the surface that is driving this change in the form standards. Now, the ISO form standards haven’t gone as far as the roughness standards yet in generating a multitude of parameters, but they have made a start.

 Tech Tips These standards give us the potential to specify form tolerances on parts in new ways that may be beneficial to the function of a component. By utilizing new reference geometries, the standards specify new parameters for roundness, cylindricity, straightness and flatness. The most fundamental change these new standards make is to allow other options than simply the maximum deviation from an ideal geometric form to be specified.

To understand what they have done, let us first examine the process that is defined for calculating these parameters. In all types of form measurements the first step is to collect data on the surface in question. Usually this data is then filtered to remove any surface roughness present. Then the “reference geometry” is fitted to the profile. This is where the first new terminology and definitions are made in the standards. Finally, deviations of all types are calculated with respect to the reference geometry. This is the second, and biggest, area of new terminology and definitions.

In defining the new reference geometries, new terminology is given to the reference circles, cylinders, lines, and planes. The basic types of best-fit elements are the minimum zone, least squares, minimum circumscribed, or maximum inscribed. Each of these has been given specific abbreviations to represent them. The minimum zone is abbreviated as MZ, the least squares as LS, the minimum circumscribed as MC, and the maximum inscribed as MI. When we are talking about roundness, the reference geometry is a circle, which is abbreviated as CI. When talking about other geometries, such as a cylinder, line, or plane, the abbreviations are CY, LI, or PL respectively. Following these conventions, abbreviations would be combined to represent a minimum zone circle as MZCI, a maximum inscribed cylinder as MICY, or a least squares plane as LSPL. Both circles and cylinders can have all four types of reference geometries; however lines and planes can only have two, either MZ or LS.

By utilizing these new mean, or reference, geometries, the standards specify new parameters for roundness, cylindricity, straightness and flatness. In the world of roundness, for example, the old roundness, a total peak to valley specification is now called RONt, or roundness total. It is determined as the total value of the distance to the highest peak and the distance to the lowest valley from the reference circle. But the mean reference geometry concept also allows you to get those separately: mean to the peak is RONp, and mean to the valley is RONv, analogous to the Rp and Rv in the world of roughness. You can also get the root mean square distance of all profile points from the reference circle as RONq.

For straightness there are similar definitions so that the old straightness definition of maximum peak to valley is now called STRt, but the mean line to peak is also available as STRp and the mean line to valley is available as STRv, and the root mean square distance of all profile points from the mean line is STRq. With straightness there are some additional options such as the straightness of a surface element or axis of a cylinder. The straightness of the surface element is known as STRsg and the straightness of the axis is STRsa.

With 3-D components such as cylinders and planes the same types of parameters are available as well as a few additional ones. Examples of the additional parameters for a cylinder are CYLtt and CYLat, which are used to define the total taper and taper angle respectively. This allows not only a definition of how the form deviates in total from a perfect cylinder, CYLt, but also how it changes in diameter along the length.

## The Meaning of Mean

So what does this actually mean? That’s where things seem to get a bit complicated for many people. What it does not mean is that to use these new ISO specifications you now have to fundamentally change your product specs, but you can if you want to. You can specify RONt (or STRt, CYLt, FLTt) and get the exact same meaning that you used to get with the simple maximum peak to valley specifications. What’s powerful is what the new standards may mean theoretically for the function of the components you are designing or manufacturing.

For that, let’s look at the example of a hydraulic cylinder sliding back and forth through a seal. You could probably tolerate valleys in the surface of the cylinder (even though they might generate leakage) a lot more than you could tolerate peaks sticking up and gouging into the seal as the cylinder slides back and forth. So in addition to RONt, you might want to specify a peak value for RONp that is very tight, and give a little more room using RONv on the valleys.

This same type of functionality of the surface can already be assessed using existing surface roughness parameters. In the world of surface we found exactly what we expect in theory, that you’ve got to have some valleys to retain lubrication, but not too many to generate leakage. The same may be true to some extent with form. But what we don’t know yet is whether such a form specification would do the same job because form error is always on a longer wavelength scale than surface roughness. So even though specifying RONp or RONv might provide an even better indication of that sealing function, we don’t yet have much experience with how scalable these new specs are.

The same kind of considerations can be thought of in terms of flatness and seals: two flat surfaces on a fuel injector, or other high pressure hydraulic precision mating components, for example. In the world of roughness we have Ra, Rz, Rv, etc. All of them are roughness parameters, but some of them tell you more about the ability of a surface to seal high pressure and prevent leakage. Translate that into the world of form, and you may have an application for FLTv, FLTp, or FLTq.

These are the kinds of theoretical discussions the people who work with these standards have had for years. These first basic parameter extensions have the potential to really enhance the ability of a designer to specify what a part needs in terms of characteristics for its performance, or perhaps in order to give manufacturing a bit more room to work, to possibly make their process more economical but still assure the parts function well.

## Working in a Mean Dimension

One reason these types of parameters haven’t been used before is the simple Catch-22 that the standards haven’t existed before. But there are other concerns as well.

One is conceptual. It is very interesting that ISO has expanded the standards in a way that will allow people to specify 3-D shapes in ways that will hopefully correlate better with the functions of the 3-D surfaces they’re trying to control and manufacture. These new standards open the door to thinking more along the lines of the way components function in the intended application.

Will this catch on? It is hard to say. We are very used to thinking and working in two dimensions. In the world of roughness, most of the development work in the past century has been in 2-D: you drag a diamond in one trace across the surface and get a profile to work with. Only in recent years has there been movement into truly 3-D thinking. Even with form, we’re typically generating and controlling surfaces in the 3-D world but we tend to think of it as something like 2½D. In the simple example of creating something by a turning process on a lathe, we create a 2-D shape on the surface, but then extend that shape into 3-D by rotating the part around its axis. But by controlling that one 2-D shape, you basically control the third dimension as well.

But this is not the case with everything, and certainly as we make more and more complex products and they have more complex functionalities and surfaces, most people realize we have to get better at understanding these things three-dimensionally, specifying them three-dimensionally, measuring them three-dimensionally, and controlling the manufacturing processes three-dimensionally.

In summary, these new standards don’t take away anything you had before. They simply add capability. If you can think of why measuring the peaks separately from the valleys or using something like root mean square averages is meaningful for the functional characteristics of your components, you can now specify those and there are tools available to measure them. You’ve still got the option to specify the total form error, and the definition of the total hasn’t changed from before: just the terminology. What is really being provided is just a bit of additional capability now, with the potential to provide a whole lot more in the future.