by Jeff Walker

In a perfect world, every CMM would be built entirely of “unobtanium,” a well-known fictional aerospace material that possesses exactly the combination of properties needed to achieve some otherwise unachievable goal. The variety used in the perfect CMM has a zero coefficient of thermal expansion, infinite stiffness and no mass. Housed in an absolute vacuum at zero K and operated by tractor beams, which induce neither heat nor stress into the structure, it would be the ideal CMM. Unfortunately, we don’t live in a perfect world.

Our CMMs are subject to myriad error-inducing factors, including dynamic thermal and mechanical stresses, inconsistent and nonlinear material responses, inappropriate human inputs, and--perhaps the greatest error-inducer of all--economics. CMM builders counter these error-inducers with a toolbox that includes good design, carefully selected materials and sophisticated software-based compensation systems--but it’s an ongoing, uphill battle.

The software solution

Because we live in the computer age, CMM designs in the past few years have emphasized software compensation tools. Great strides have been made and continue to be made in this arena. But as these tools get better and better, the limits of their ability to improve CMM performance also become clearer.

It’s now possible, for example, to compensate for thermal errors in the entire structure of a CMM, all the way from the baseplate to the very tip of the probe. Moreover, today’s best software can place the virtual origin point for thermal expansion calculations anywhere on the machine--not just at the mechanical datum point--to minimize distance-related translation errors. Compensation for mechanical errors is equally sophisticated.

Compensation algorithms are very good and getting better, but they’re ultimately discrete digital systems applied to a dynamic analog reality. The fit is not, cannot, and never will be perfect.

To make matters even more difficult, random influences like thermistor tolerances and thermal response variations within individual samples of the same material are also present in the real world. In practice, these factors produce an inescapable residual error that can be as high as 10 percent.

Considering that the coefficient of thermal expansion for aluminum is nominally 23 ppm per degree Celsius, a 1° C change in temperature can produce an uncontrolled and uncontrollable potential compensation error of 2.3 µm in just a 1 m length. More costly components and more frequent, time-consuming calibration routines can reduce the residual error, but it can never be totally eliminated because it’s inherent in the compensation process itself.

Today, we’re beginning to recognize the ultimate limits of software compensation, and tomorrow we’ll be bumping hard against them. In the future, the gains from this technology will be progressively smaller while the cost of each increment in terms of hardware expense and machine utilization will be significantly higher.

Where we go from here

If software compensation appears to be reaching its practical limits, what else can be done to improve the performance of today’s and tomorrow’s CMMs? The answer is most likely a return to the basics of engineering a stiffer, more stable and smoother operating platform that will minimize the amount of compensation required in the first place.

That process will include the use of new materials, better bearings and more sophisticated designs for all of the components and subsystems of a CMM. This will be complicated by the need to achieve higher performance at a lower relative cost while providing more usable uptime and greater application flexibility to the CMM consumer. It’s a tall order.

More stable machines

When it appeared that software compensation would be the ultimate solution to the problem of thermal growth in CMM components, aluminum became a favorite engineering material with many machine builders. Relatively stiff, light, easily machined and inexpensive, aluminum’s only major flaw is its high thermal response rate. This is a negative that everyone believed software compensation would easily overcome.

Today we know better. Most high-end CMMs, and a growing number of mid-range and even low-end machines, now use some form of ceramic or composite for the critical bridge beam structure. The reason is that ceramics are extremely stiff, relatively light and thermally stable. One of the better ceramic materials, polycrystalline aluminum oxide, is a full 330 percent stiffer than aluminum, yet it’s only 32 percent heavier and has less than a quarter of aluminum’s coefficient of thermal expansion.

Assuming the same 10 percent residual error in the software compensation system discussed earlier, a ceramic beam would have a compensation error of only 0.6 µm in the same 1 m length, whereas aluminum has an error of 2.3 µm. It’s still not perfect but much smaller and therefore much less detrimental to the overall accuracy of the measurement being taken.

But thermal growth isn’t the only stability issue in CMM design. Dimensional changes related to both static and dynamic mechanical stresses must also be considered and compensated for. Unless they’re somehow relieved, every material has some level of stress locked into its crystalline and/or mechanical structure during its creation or fabrication.

In machined or fabricated metallic components, these stresses can be significant, even after artificial stress-relief processing. In the case of natural materials like granite, such stresses are negligible because of millions of years of natural stress relief. That is one of the reasons granite is the universally preferred material for CMM bases. Modern polycrystalline ceramics fall somewhere in between but are much closer to granite in natural stability than they are to fabricated metallic components.

Stability is greatly influenced by good mechanical design, particularly of the interfaces between components. So-called “kinematic” design strategies strive to minimize--and ultimately eliminate--the introduction of any stress into a structure at its various mechanical interfaces. Although the subject of kinematic design is too broad and detailed for this discussion, it’s widely used in fixture design where the classic 3-2-1 location system provides an excellent example of its application.

Achieving optimum stability in a structure such as a CMM requires a detailed analysis of every component in the structure. Even the shape of a beam can make a significant difference in its thermal and dimensional performance.

For example, corners tend to be thermal stress points because they heat and cool more quickly than flat surfaces. As a result, rectangular structures tend to be more stable than triangular structures because the corner-induced stresses are symmetrical.

However, triangular structures are both lighter and less expensive than rectangular structures of the same capacity because they contain less material. They’re also easier to fit with preloaded air bearings, as illustrated on page 41.

A cost-driven design will choose triangular beams, whereas performance-driven design will choose the more costly rectangular beams. Over the long run, however, the more expensive design will prove to be the more cost-effective because it’s substantially more stable, and that means it requires fewer recalibrations and delivers more usable uptime. In the end, stability translates directly into reduced measurement costs for the end-user.

Stiffer machines

Stiffness is the second major goal in CMM design, and stiffness without mass is the essential characteristic of CMM-style unobtanium. Materials with high stiffness-to-weight ratios tend to minimize many of the mechanical errors inherent in CMM design. Stiff, light real-world materials reduce the mass of moving elements, permitting smaller drives, less heat, shorter measuring cycles and lower costs.

The greater stiffness of ceramic beams shows up in analyses of bridge behavior under acceleration. When accelerated, the bridge beam is subjected to a directional deformation force directly proportional to the acceleration. For an aluminum beam, the resulting directional deformation is nearly twice that of an equivalent ceramic beam, despite the fact that the ceramic component is 32 percent heavier.

In practical terms, this means the ceramic beam can be accelerated nearly twice as fast as the aluminum beam while maintaining deformation within a comparable range. Greater acceleration translates directly into shorter traverse time and reduced cycle time for any given movement and ultimately into a lower total cost for any given inspection task.

Another material with greater stiffness than aluminum--200 percent, to be exact--is steel, which is used increasingly in structural components such as support legs on advanced CMMs. Because of its high strength, steel--like ceramic materials--offers an opportunity to design structures with enhanced performance and only a small weight penalty compared to aluminum. And, like ceramics, steel’s greater stiffness permits higher acceleration and reduced cycle times and inspection costs.

Stiffer bearings

Most CMMs today use air bearings to support moving components, but all air bearings do not deliver the same level of performance. The key influence on air bearing stiffness is the gap required to support a given load--the smaller the gap, the stiffer the bearing, all else being equal.

Conventional air bearings, the type used on most CMMs, generally have several orifices placed in a pattern across the otherwise smooth face of the bearing “pad.” These orifices distribute pressurized air to lift the pad away from the surface to create the bearing gap and support the load.

There is another design, however. It has been found that creating an annular groove on the pad face and connecting it to one or more orifices using straight grooves produces a more efficient bearing. The performance difference is dramatic.

For a given load, surface area and air volume, the plain bearing will have 3.5 times the gap of the grooved design. Viewed from the stiffness perspective, with all else being equal, the grooved bearing delivers 140,000 N/mm compared to the plain-pad design’s 40,000 N/mm.

In the context of a CMM, this greater stiffness translates directly into enhanced accuracy but also means the moving elements can accommodate greater accelerations. As is the case with stiffer materials, greater acceleration made possible by stiffer bearings also means shorter cycles and reduced measurement costs.

Smoother operation

Although software-based compensation systems are rapidly nearing the point of diminishing returns, the same cannot be said for software-based motion control efforts. Today, most CMMs use a simple acceleration/deceleration algorithm that produces a trapezoidal plot. The strategy is to accelerate to maximum velocity as quickly as possible, maintain that velocity as long as possible, and then decelerate to zero as quickly as possible, as illustrated below.

At first glance, this strategy might appear to deliver optimum cycle times. After all, going as fast as possible should be the key to getting from point A to point B in the minimum amount of time; in a large, robust structure, it may well be.

But CMMs are not large, beefy structures. For a CMM, this strategy produces a substantial wait at the end of the motion while the machine “settles down” and dissipates the stresses and vibration generated by the acceleration/deceleration process.

A better strategy is to control the motion to produce a pair of gentle “S curves” during acceleration and deceleration. In practice, this approach may add a fraction of a second to the traverse time from point A to point B, but this will be more than compensated for by the reduction of waiting time once point B is reached.

In an intermittently used laboratory machine, the difference may be negligible. But, in a production-monitoring application, which fully utilizes the CMM’s capabilities, the difference in cost-per-measurement can be substantial enough to pay for the more sophisticated capabilities in a short time.

Scanning the future

No discussion of modern CMM design is complete without some mention of scanning--unquestionably the technology of the future. Because scanning is done “on the fly,” taking measurements with all elements of the machine in motion, it will quickly surpass the capability of software-based compensation systems--unless the machine is designed from the ground up to minimize the need for such compensation systems. It’s already happening.

It’s time for the industry to get back to basics and engineer CMMs that are optimally stable, stiff and smooth, independent of the compensation system. The materials exist, and none of them are “unobtanium.” The technology exists. It’s time to shift the industry’s primary focus away from compensation and back to sound design.

About the author

Jeff Walker is manager of marketing and new products at LK Metrology Systems Inc. in Brighton, Michigan.