Flexures Bring Motion Advantages

The technology amplifies piezoelectric travel by as much as an order of magnitude while remaining robust long-lived, and lubricant free.

Mention linear motion to many people, and they’ll most likely think of solutions like linear motors or rotary motors coupled with some sort of linear actuator. That’s all well and good in the macro world, but in the world of micro and nano positioning, the entire workspace may be on the order of a few hundred square micrometers or less. A ball-screw actuator is unlikely to get the job done. Piezoelectric actuators offer nanoscale resolution, but not necessarily over the length of travel required. Amplified by a flexure, however, the technology can provide a combination of resolution, travel, and reliability. In such a case, flexures just might be the best solution you never thought of.

A flexure is a solid, typically monolithic device that introduces displacement as a result of elastic deformation of the material. Unlike conventional bearings or actuators that produce motion courtesy of rolling or sliding surfaces, a flexure does not suffer from stiction or friction. Flexure designs can range from the very simple, such as a single ribbon of material like a leaf spring, to very complex multi-beam designs that can introduce linear displacement along multiple axes, or even rotation. They can be made of a wide range of materials, including nonmagnetic or even nonmetallic options.

Compared with conventional rigid-body mechanisms and bearings, flexure bearings offer multiple advantages. Because flexures have no moving parts, when properly specified they tend to be very robust, with minimal wear and essentially infinite lifetime. They deliver very high stiffness. They don’t require the level of precision machining needed for ball-bearing and crossed-roller-bearing stages, eliminating high-frequency parasitic motion introduced into ordinary bearings by surface defects. They don’t require lubrication. In the absence of a deforming force, they self center to a surprising degree. Flexures offer another important advantage – they perform well at linear velocities that would cause air bearings to skid.

The standard method for accomplishing multi-axis motion with conventional technologies is to stack several stages together, but this introduces displacement and adds both mass and cost. Flexure designs can actuate a single workpiece along multiple axes simultaneously.

Every technology has its downsides, of course. Probably the biggest drawback to flexures is their limited travel. That said, they can be built up of combined coarse and fine positioners that extend the length of travel while enhancing adjustability. State-of-the-art hybrid designs integrate the coarse and fine mechanism with a single encoder to create a mechanism that delivers nanoscale bidirectional repeatability and dynamic accuracy.

The cost trade-offs involved in flexures depends on the application. Simple flexures may be economical, but more complex versions must be fabricated using electric discharge machines (EDMs), which can be expensive. That said, conventional bearings wear quickly during rapid-scanning applications, degrading performance or causing performance or cause early failure.

Amplifying motion
Applications like microlithography or atomic force microscopy require precision positioning stages with high degrees of accuracy and repeatability. Designs incorporating ball bearings on rails deliver reasonably economical, low-friction solutions. The problem is that the real world enters the picture in the form of inescapable fabrication errors that add small variations to the motion. The result is a certain amount of differential slip that can degrade performance, causing wear and, eventually, brinelling that can lead to catastrophic failure. Crossed roller bearings, which substitute angled cylinders for ball bearings, provide better accuracy and stiffness. They do have limited resolution, however. They’re also vulnerable to contamination, which can cause early failure.

The alternative to these macro solutions is piezoelectric positioning. Piezoelectric positioners consist of stacks of very thin piezoelectric material that expands under an applied voltage (and generates a voltage when compressed). The thinner the laminations, the higher the resolution. Piezoelectric positioners provide quality performance but only over extremely short runs of travel. Adding a flexure into the system can expand the run of motion by an order of magnitude, however, allowing some stages to deliver nanoscale resolution over as much as 2 mm of travel.

A common construct a parallelogram flexure, which consists of a load supported by two flexures coupled to the piezoelectric stack (see figure 1). When the piezoelectric stack expands, it presses into the flexures, causing them to displace and move the load by distance proportional to the sine of the angle. End of the piezoelectric stack presses into the flexures, which are specified to be too stiff to merely bow, the load moves horizontally.

Figure 1: Adding flexures to a piezoelectric stack amplifies the motion
to increase run of travel. The drawback is that it can introduce runout.
(Courtesy of Physik Instrumente)

If we consider the distance  that the load travels for an expansion of the piezo electric stack, then

The downside of parallelogram flexure actuators is that they introduce second-order cross coupling between axes. This arctuate motion can lead to out-of-plane positioning error on the order of 0.1% of the distance traveled that goes as

where  is the out-of-plane error (lateral runout) and H is the flexure length. Although the error is nonzero, it’s repeatable enough to be compensated for. Alternatively, dual-beam flexures can provide sub-nanometer and sub-microradian performance (see figure 2).

 
Figure 2: A dual-flexure design amplifies motion
while controlling lateral run out. (Courtesy of Physik Instrumente)

Making an informed choice
As with virtually everything in motion control, there is no one correct solution, there’s only the best solution for the application at that moment. Another engineering truism holds that a solution is only as good as its specification. Although switching a design from a conventional positioning stage to a flexure/piezo design is relatively straightforward, engineering teams do need to think it through. What are the requirements? In general, even with flexures, a piezo stage can only supply a millimeter or two of travel. If that sufficient, however, and the application is space constrained or requires high resolution, a flexure might be the ideal approach, providing high dynamic range and long lifetime performance in an ultra-compact package. ”That means everything can be condensed in size and that saves cost all through the value chain,” says Scott Jordan, Physik Instrumente L.P.

Understanding the conditions of the application and using them to determine the best solution is the surest guarantee of success. “I’ve seen some motion manufacturers and OEM customers get into real trouble by specifying bearings where a flexure might be a better idea,” he says. He points to the example of a high-speed, high-frequency application. The design required a vertical bearing in the team chose a crossed-roller design. “They’re made of steel, they’re in a high humidity environment, and they’re scanning rapidly back and forth continuously, 24/7. It should be to no one’s surprise that those bearings loosen up and corrode and all sorts of things happen.” Although grease might protect the bearings from the humidity, it degrades the motion trajectory and attracts contamination. “It was a bad idea to use bearings in that application. A flexure would have been so much more sensible,” he adds.

Above all, Jordan stresses the need to look for a vendor that offers multiple types of technologies. As he engineering joke says, if the only tool you have is a hammer, every problem begins to look like a nail. For a broad spectrum of applications, conventional and crossed roller bearings may be a good solution. For a surprising number of applications these days, though, flexures might just be the best fit. “Have a conversation. Talk with suppliers that can give you perspective from a variety of direction,” he says. “If you just talk with a manufacturer who sells only flexures, then you’re going to be sold flexures. If you talk only with somebody who sells crossed-roller bearing stages, they’re going to be pushing crossed-roller bearing stages on you.

Flexures are no longer exotic solutions. They can be surprisingly cost-effective and their size advantages open up new degrees of freedom in the design process. “Engineers are sometimes unaware of all that can be done with flexure approaches,” Jordan says. “The multi-axis benefit, the ability to make parallel kinematic devices that guide the work piece from multiple directions simultaneously, and more. Flexures offer the opportunity to make mechanisms out of a variety of material and provide exquisite resolution. You just can’t get that with your garden-variety bearing.”