## Are you sure about your arcs? Measuring arcs with stylus instruments

Many critical surfaces (ball bearings, bearing races, sockets and lenses, to name a few) are comprised of arcs or arc-like geometries.  As with other critical surfaces, controlling roughness and waviness on these curved surfaces can be extremely important. However, measuring arcs on these surfaces with many traditional stylus-based instruments poses fundamental challenges.

In this post we look at several considerations that may be affecting your ability to properly measure arcs and understand your curved surfaces using a stylus instrument.

## Errors due to surface “lay”

First off, we need to understand that when using a profile-based measurement we should measure across the surface lay–not along the lay. This can be a consideration when measuring over the arc of a shaft. In the case of a shaft produced by a manufacturing processes such as turning or grinding, the measurement should not be made in the circumferential direction. Circumferential profile measurements can be misleading. In some cases, where the stylus dwells on a ridge line or valley line, the roughness can be hidden. More commonly, the stylus may cross one or two ridge lines and distort the spacing between them. This can also result in reduced roughness as the feedrate features will appear as waviness.

### What can we do about the surface lay problem?

We should either measure axially (perpendicular to the lay) or use an areal/3D measurement.

## Errors due to resolution

In many cases, the measuring range of a typical stylus instrument needs to be increased in order to collect an adequate length of data on an arc.

Increasing the measuring range can, however, hurt the instrument’s resolution. A typical roughness instrument has a limited number of vertical resolution “steps” within the selected vertical range. If the vertical range is increased, the step sizes must also increase.

When the data is subsequently levelled and filtered, these “resolution steps” can show up as what appears to be “roughness:”

When using a large measuring range, some instruments not only measure with a lower resolution but they also perform their calculations at a lower resolution, which can result in a roughness profile with “digital steps.”

### What can we do about the resolution problem?

There are basically two answers: 1) use an instrument with a larger range-to-resolution, or 2) sample the surface with multiple, short traces measured at a smaller vertical range. (Note: the short traces may not be able to detect waviness.)

## Errors due to arcuate motion

The stylus of a profiling instrument does not move vertically. In fact, it moves along an arc. In other words, the stylus travel as based on “arcuate motion” whereby the tip moves along the horizontal (X) axis as a function of its vertical (Z) position.

Given this motion, a typical stylus instrument can distort a perfect radius. Let’s consider a convex shape. As the stylus moves from left to right over the convex surface the stylus shifts to the left as it climbs. (Consider the white stylus above, moving to the gray, then to the black as it climbs.) This has the tendency of lagging behind and taking longer to climb up the radius. Similarly, as the stylus falls down the right side of a convex shape, it moves from black to gray to white (above), again resulting in distortion in the measurement.

The arcuate motion results in a distorted measurement profile of this form:

A similar error occurs when measuring a concave surface:

The motion results in a distorted measurement profile of this form:

One way to determine if arcuate error is affecting your results is to make a measurement. Rotate the measured component 180° and re-measure. If the shape remains constant (for example, the right side is always steep), then the instrument is causing the error. If the shape moves with the component, then the shape is likely attributable to the component geometry.

### What can we do about arcuate errors?

The only way that arcuate error can be addressed is to use an instrument that calibrates and corrects for the arcuate motion of the stylus. Most common roughness instruments set a gain value with a roughness patch. These instruments cannot correct for arcuate motion. Instruments that can correct for arcuate motion are calibrated with precision spheres/hemispheres or precision angles/prisms.

## Errors due to filtering a curve

When measuring a curved profile it is important to remove the curvature before filtering for roughness and waviness. Some instruments do not have the ability to suppress advanced geometries such as arcs or polynomials, and this can result in a shift in the roughness profile when using a traditional Gaussian filter.

Some background… in order to assess “roughness” we need to first remove “waviness.” This is performed by a filter (see our post, “3 Steps to Understanding Surface Texture”). This filter is typically a Gaussian-weighted moving average. However, if we pass a moving average over a curved surface, the moving average will be biased “downward” for a convex surface and “upward” for a concave surface.

We can see this effect by taking an average of a region of points on an arc:

We determine waviness by moving the average over the length of the profile, which results in a waviness profile (red) that sits below the primary profile (blue) as shown here.

Here is a real-world example of this effect: the calculated waviness profile (red) clearly sits below the primary profile (blue).

Since the roughness profile is based on subtracting the waviness profile from the primary profile, we will end up with a roughness profile that sits above the zero line (for a convex surface). This upward shift can have significant impact on roughness parameters.

We can demonstrate this effect in our OmniSurf software on an actual, measured dataset. A convex profile was analyzed without first removing the arc, and a standard Gaussian filter was applied. This resulted in an “upwardly shifted” roughness profile and an average roughness (Ra) value of 0.254 micrometers.

However, if we suppress an arc prior to filtering with the Gaussian, the filter does not shift the profile and we get a more realistic roughness value. In fact this roughness value is MUCH smaller than that which resulted from the shifted profile.

### What can we do about the meanline shift?

The best option is to remove the nominal geometry prior to filtering. If your measuring instrument does not have this option, then Digital Metrology’s OmniSurf can handle it for you. Another option is to use a 2nd order filter. These filters are being discussed in ISO standards and are not yet generally available in most measuring systems.

## Wrapping thing up…

As you can see, a seemingly simple measurement can sometimes be very misleading, and bad decisions can be made based on these error sources. In cases like this, Digital Metrology can step in and help you manage and understand your measurements. Better yet, Digital Metrology can help you understand your surfaces and what makes them work.

For more information on the measurement of arcs and many other surfaces and shapes, contact Digital Metrology today!

## Will your sealing surfaces leak?

A version of this article appeared in the November 2019 edition of Flow Control Magazine.

Surface shape and texture are critically important to a component’s functionality—particularly in sealing applications. Many instruments can measure surface texture, and today’s software allows us to analyze and quantify hundreds of aspects of the data. Yet, despite all the information that we can extract from surface texture measurements, most engineers continue to specify only basic height-based parameters such as average roughness or total flatness.

The challenge is that “sealing,” like so many surface functionalities, is not measurable purely in units of height. Local curvatures and the “connectedness” of surface features can provide much more valuable insight.

Morphological filters, which have been introduced in surface texture standards and literature in recent years,  provide a powerful way to simulate surfaces in contact. These filters are very well suited to predicting how a relatively soft surface (e.g., a gasket or seal) will interact with a relatively rigid surface.

## Can you spot a “good” sealing surface using Ra?

As we said earlier, the most common surface texture parameters that aree specified in sealing applications are based on heights measured along a profile. These include average roughness (Ra), average peak-to-valley height (Rz) and, in some cases, a waviness height (Wt). It’s not surprising that engineers specify these particular parameters, which are well known and readily measurable.

Unfortunately, these parameters don’t necessarily indicate how the surface will function. The image below shows two very different surfaces with virtually identical Ra, Rz and Wt values. If these parameters were specified on a print, the two surfaces would be indistinguishable, and they would pass similar quality control tests. Yet, none of these parameters would reveal that the repeating milling pattern in the second surface could create leak paths between mating surfaces.

In recent years new “functional parameters” have been developed to monitor particular functionalities. Engineers can use these parameters to compare design options during development, then specify the same parameters on prints.

One such functional analysis is based on morphological filters, which can simulate the shape of mating surfaces. In the image below we see morphological “closing” and “opening” filters applied to surfaces. The “filter” in both cases is the path of a virtual circle of a given radius that is moved along the surface data.

For the closing filter, the filter disk rides along the surface, acting as a “virtual gasket” that follows the peaks and leaves voids in the regions of the valleys. By analyzing the gaps created by the closing filter we can predict potential leakage under an actual gasket.

An “opening filter,” on the other hand, is like a disk pushed up from below the surface. An opening filter highlights sharp peaks in a surface (sharper than the disk’s radius) which may act as oil film penetration points, cosmetic defects, or stress concentrators which could lead to cracking.

For the remainder of this post we will focus on the closing filter and its use in predicting leaks.

A crucial aspect of morphological analysis is that the filters can be adjusted in real time, letting engineers explore how changes in materials, processes and tolerances might improve performance. One may, for example, shrink the radius of the closing filter; the smaller “disk” or “ball” can then enter more valleys, thereby modeling a more compliant gasket material. Or, by raising the cutoff wavelength for the waviness profile we can increase how much the virtual gasket will “crush” peak material.

The path of the closing filter (as shown in black in the figure above) may represent the amount of deformation to be expected by a seal or gasket. However, the difference between the measured surface and closing filter is much more important: it is a direct representation of the cross-sectional leakage area.

Morphological filtering is, in fact, the only surface texture analysis method that can model a sealing interface this directly, making it invaluable for understanding and controlling the root causes of leakage.

## How a closing filter can predict leakage

Earlier we showed two surfaces that were indistinguishable by common surface texture parameters. In the figure below, we revisit those surfaces. Their waviness profiles are shown below in red. This time we apply a closing filter, or “virtual gasket” with a radius of 5000mm, shown in black.

When the closing filter is applied to the first surface we see that it closely follows the waviness profile. Although the waviness is quite large in terms of total height, there are no abrupt changes that would indicate leak areas.

However, when the same closing filter is applied to the second surface, we can readily see large, periodic voids that cannot be sealed by the virtual gasket. These voids are cause for concern.

While the profile graphs clearly show the difference in sealing, we still need a numerical value to indicate the “amount of leakage” in order to specify and control these critical surfaces. The functional parameter “Wvoid” (void area per unit length) was developed as just such a measure of sealing quality. Wvoid is shown in OmniSurf in the figure above. The parameter is normalized per unit length, making it independent of the evaluation length and therefore more repeatable and stable.

We can extend this analysis into three dimensions as well. The image below shows how a closing filter is applied to a measured surface using the interactive filtering tools in OmniSurf3D.

In the above image the closing filter has been applied across the dataset (left) to create the “closing surface,” shown in transparent blue. On the right, the gap between the closing surface and measured surface is shown as a “void surface,” which represents the void areas where leakage may occur. As with the 2D analysis, changing the radius of the closing filter can simulate changes in conformability and sealing forces.

## Using Pit and Porosity Analysis to trace Leak Paths

Other advanced analyses in OmniSurf3D can help determine which voids in a surface may link up to form leak paths. Below we see the interactive “Pit and Porosity” analysis, which has been applied to a surface to analyze the pores (voids) which may lead to leakage.

The analysis shows a 3D map of surface heights on the left, the “material ratio curve” in the middle, and a plot of pores and leak paths on the right.

The porosity features shown in red are considered “closed pores,” meaning that they are completely enclosed by material at the given cutting plane. Blue features are “open pores,” meaning they open onto the edge of the data set. The green regions may be the most important. These are “edge-connected” regions, representing potential leak paths which are open along either the X or Y axis of the data set.

At any cross-sectional height level we can count the open and closed pores. Or, we can calculate the “pit density,” the number of pits per square centimeter. Pit density can give a better indication of the surface in general, irrespective of the size of the measurement area. Analysis tools like this make it easy to visualize what is happening as well as providing traceable numbers.

Morphological filters can indicate how well a surface will seal, as well as providing insight about other functionalities. These filters can be used to explore changes to materials and methods that may address the root causes of sealing issues, as well as providing parameters that can be specified on prints to guide production and track surface quality.

## Analyze Aspheric Lenses with OmniSurf or OmniSurf3D

Have you taken any good selfies lately? If you have, then you can thank an aspheric lens.  In fact, you can probably thank several of them.

An aspheric lens has a complex surface that departs from a basic spherical shape. A single asphere can replace a complex, multi-lens system, resulting in a smaller, lighter optical system.

Apart from cell phones, aspheres are also responsible for advances in eyeglasses, contact lenses, telescopes, cameras and optical instrumentation.  We even find them in grocery store price scanners and the backup camera on your car.

## But how do we analyze aspheric surfaces?

Because of their complexity, analyzing aspheres has long been the domain of expensive metrology software. But we are pleased to report that you can also analyze aspheric measurement data using OmniSurf or OmniSurf3D—in fact, it is a standard feature in both software pacakages!

The image below shows the setup screen for an aspheric surface in OmniSurf3D software:

Both OmniSurf and OmniSurf3D include this intuitive interface for configuring the aspheric reference geometry. We included a number of tools to make the process quick, including the ability to cut and paste the asphere’s coefficients and scale the live preview. Since it’s easy to make a typo when entering the coefficients, the Equation Test provides a handy way to validate the equation on-the-fly, at any radius position.

Once you have defined the reference shape you can then view the “residual” surface (the difference between the measured data and the reference).

The image below shows a measured aspheric surface in OmniSurf3D:

Here is the residual surface, with the reference subtracted:

In the residual data you can clearly see the fine machining marks left by the turning process. An engineer can use this information to fine-tune the manufacturing process.

## Automatically adjust the radius

For aspheres, a significant contributor to the residual form error can be due to an error in the base radius.  This can sometimes result from tooling wear. In these cases, the actual base radius is of interest.  To determine the actual base radius, the operator has to manually adjust the nominal radius and re-analyze the data until the residuals look acceptable.  This is a slow and difficult process.

Both OmniSurf and OmniSurf3D include a powerful, one-click “radius optimization” tool to automatically determine the aspheric radius based on the measured data. Here is a residual surface, calculated using the design radius:

Here is the same residual with the automatically optimized radius:

The flatter overall shape is indicative of a much better radius fit. This can be a major time-saver in a production or process development environment.

## Export and filtering

OmniSurf and OmniSurf3D also make it easy to filter the data to analyze the roughness and form. In OmniSurf3D, the Zernike polynomial terms can be exported for further analysis and modelling.

## Fast, affordable asphere analysis

Aspheric calculation is one of many advanced analyses that are included as part of our basic software. Check out all of the features and analyses on the OmniSurf or OmniSurf3D pages, or contact Digital Metrology to learn more.