Update on flexible-coupling considerations for OEM and plant designs

Couplings connect rotating shafts in equipment powered by electric motors and other drives. All transmit torque and angular velocity. Flexible variations compensate for misalignment. Many of the latter even address vibration and improve system dynamics.


These metal disc-spring couplings from Miki Pulley have ultra-high torsional stiffness to satisfy servomotor applications. Disc-spring designs also impart flexibility in axial, bending, and step-difference directions.

Design considerations include machine or installation construction and backlash, torsional stiffness, damping, inertia, torque ratings, maximum rpm, size, misalignments, ease of installation, robustness, and cost. For power transmission (as in motors for pumps and large material-handling setups) common choices are gear, disc, elastomeric tire, grid, jaw, and Oldham couplings because of their ruggedness and ability to transmit very large torques. Motion-control applications (as for axes employed in precise positioning of loads, for example) typically employ couplings capable of oft-more modest but far more precise torque transmission. These include curved-jaw, beam (slit), bellows, disc, and other zero-backlash couplings.

As we’ll explore, any misalignment that couplings accommodate should be what’s otherwise unavoidable even after proper machine-axis squaring and installation adjustments. That’s because misalignment — manifest as parallel, axial, and angular misalignment— degrades efficiency, induces bearing wear, and excites machine natural frequencies. To review, the maximum amount of angular misalignment for which a coupling can compensate is expressed in degrees; parallel misalignment between the shafts a coupling connects is expressed in inches or millimeters. Axial misalignment is also a length value; it’s the maximum permissible spread between coupled shafts — and in fact, a misalignment permutation often most affected by thermal effects. Flexible couplings for motion control are often less forgiving of misalignment than those for more straightforward power transmission, and resolve it with specialty design features.

A related phenomenon and a coupling consideration specific to motion-control installations is backlash. In applications for strict power transmission, backlash is far less of a concern than that of efficient torque transmission — and actually a characteristic that (in normal moderate quantities) helps make some couplings in these settings more efficient and forgiving of misalignment. In contrast, couplings on the outputs of steppers and servomotors are designed to prevent the lost motion that can degrade output-product quality or overall machine throughput.
Note there’s a difference between backlash (which is true mechanical clearance) and the torsional deflection or windup that all loaded rotary components exhibit. Most couplings for motion applications are inherently backlash free or preloaded to eliminate backlash — but they all have different torsional stiffnesses, which is sometimes a tradeoff for lateral flexibility.

Pitfalls to avoid during selection of couplings for motion

Design engineers often run into trouble when they neglect to account for environmental effects on couplings — particularly flexible couplings installed in gritty or caustic areas, vacuum environments, or places that are extremely hot or cold. Beyond that and the common design considerations already listed, designers must account for dynamic forces to which a coupling will be subject. Steer clear of using published an axis’ gearset or motor peak-torque values for setting its coupling’s nominal torque rating. That’s because this approach usually makes for an assembly with an oversized coupling and an unnecessary inertial increase.

Designers should also avoid the application of a coupling type simply because it’s a familiar technology. For example, beam couplings are extremely well known in industry, and they excel on axes transmitting moderate to light torque — as on leadscrew-driven motorized axes or where there’s a need for attachment of a precision encoder, for example. However, some particularly demanding designs may necessitate a flexible coupling type that maintains higher torsional stiffness.

On the other hand, it’s also unadvisable to simply pick a coupling based on high torsional stiffness. Many flexible couplings have an inherent stiffness that exceeds application requirements for servo tuning and motion accuracy. Even in motion designs requiring high stiffness for the shortest possible response time (as in equipment for electronics manufacturing, for example) couplings with good damping characteristics often offer more effective optimization than more torsional stiffness. (Refer to the section, “When motion designs need torsional stiffness — as well as damping” at the end of this section for information on this topic.) That’s because overly stiff couplings of many designs pose an unnecessary risk of fatigue.

02-bellows-coupling-stiffness-test-fixture-Courtesy-GAM-Entrprises 2

Here’s a common setup for quantifying the stiffness of bellows couplings. One end attaches to a fixed housing; the other coupling end attaches to a freely moving beam moment arm that’s loaded with various weights. Dial indicators on the fixed and free ends measure coupling torsional deflection. The fixture measures overall coupling stiffness, including the end hubs and bellows.

Understanding torsional rigidity: Bellows-coupling example

Torsional rigidity is an object’s resistance to torsion or twisting under applied torque. Torsional rigidity in couplings is torque per value of angular displacement, and it’s a value that affects overall machine design. Even slight variations degrade positioning accuracy and limit cycle speeds. Consider the case of bellows couplings and the specifics of how their moderately high torsional stiffness is verified and expressed:

Torsional stiffness Ct (in N·m/rad) = M/ѱ — where M = Torque, N·m and ѱ = Angular displacement, rad. Applied mass at an industry-set moment arm gives torque M = mgR, where m = mass, kg; R = Moment arm; g = Gravitational acceleration (9.81 m/sec2); and m = 0.38 m.

Angular displacement Δx from a test-setup dial indicator = Indicator reading (mm); τ = Indicator moment arm (mm); tan (ѱ) = Dx/ τ as noted in the illustration showing a typical fixture for measuring bellows-coupling torsional stiffness. Also — ѱ = arctan (Dx/ τ), degrees. So torsional stiffness in N·m/rad is Ct = M/ѱ (Nm/deg) = M·180/π · ѱ.

It’s usually unnecessary and impractical to test all components in design, which is why engineers use theoretical system-stiffness values. One caveat here related to couplings is that different manufacturers’ coupling-stiffness ratings vary with measurement methods. There can also be differences between published and measured values. Two tips from Mike Parzych of GAM Enterprises on this: Use caution when designing a motion machinery relying heavily on overall stiffness for good design performance. Also, look for evaluations that faithfully model performance characteristics to ensure stiffness and machine-assembly performance.

In fact, the most suitable coupling choice ultimately depends on application requirements and machine throughput. If improving axis positioning and cycle time is priority, focus on boosting powertrain stiffness. Selecting couplings with high torsional rigidity (among other things) can minimize lost motion from torsional windup. Shorter couplings or those with reinforced bellows can boost torsional rigidity values … But keep in mind that while a shorter coupling has higher rigidity (to 60 to 70%) misalignment compensation capabilities also decrease with length.

Alignment: Its importance cannot be overstated

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Misalignment can spur reaction forces and excitation of machine natural frequencies. One resonant frequency to avoid is that of the motor output assembly — defined by shaft diameter, overhang from the bearing, and material, as well as coupling type and weight.

No coupling — no matter how engineered — can correct for shafts that are excessively misaligned. The nature of flexible couplings occasionally misleads design engineers and assembly personnel (or more often, end users) into believing that they’re a fix-all for compromised or less exacting machine builds. But flexible couplings put into designs with excessive misalignment exhibit material stresses and fatigue and premature failure.

Though coupling failures do occasionally originate from couplings themselves, it’s far more common that coupling issues arise as a symptom of other design problems. If a motion design does exhibit coupling problems, avoid the temptation to simply upsize or upgrade that coupling. Such upgrades are often unnecessarily expensive and short-lived solutions that actually put system bearings as well as gearing and connected motors at risk of collateral damage.

Instead, make a holistic analysis of the design and consult the coupling manufacturer for assistance.
Note that when motion systems exhibit coupling issues long after a proper installation and run of service, it’s sometimes a result of some other change in the drive assembly. Even small changes to the motor, drive, or programming can be to blame — especially if a new motion sequence demands higher transmission of motor torque or the elimination of a previously held electronic limitation.

What are reaction forces?

All flexible couplings compensating for misalignment cause reaction forces, and their effect is significant if misalignment is excessive. These often-overlooked reaction forces transmit to connected shafts and support bearings, and can cause damage to motion axes — especially on precision designs with delicate bearings and slender shafts. Though couplings get their compliance from elastomeric deflection, sliding contact, and flexing coupling members, here we focus on the types most common for motion designs employing stepper or servomotors.

Ultimately, reaction-force magnitudes depend on the level of misalignment and the coupling type in use. Bellows couplings, so-called membrane couplings such as disc couplings, and beam couplings have thin sections of various designs capable of radial flexing. Resistance to misalignment — a spring-rate reaction defined as a force per unit of deflection — increases proportionally with shaft deflection. Because these couplings bend to accommodate misalignment, reaction force depends on the thickness of the flexible element.

But bellows and beam couplings have multiple coils or convolutions, so work as flexible shafts that sweep through complementary bows as the mode of misalignment compensation. Torque transmission is through members in shear, so the convolutions can be thin and keep radial forces low while maximizing torsional stiffness. In contrast, membrane-coupling variations transmit torque via bending members, so need thick members to get high torsional stiffness. Such couplings’ bending (through complementary directions) also compensates for shaft misalignment. The catch is that these torsionally stiff couplings can induce significant radial-reaction forces if excessive misalignment is present.

Because radial-force magnitude depends on bend severity, minimizing bending angles reduces the detrimental forces on support bearings (though can reduce misalignment capacity, too). Some membrane couplings address more misalignment with a central member between the flexible members; the added distance imparts an ability to turn while making shallower bends (and lower radial forces) for a radial shaft offset. In fact, aforementioned beam and bellows couplings with divided flex-element arrays also sometimes leverage more distance between flexure points to get shallower bends for a given radial shaft offset. Short models sometimes connect via an intermediate shaft.

In contrast, elastomeric couplings have myriad torsional-damping properties and transmit torque in shear, bending, and compression. Coupling class is key with this design: Some versions exhibit zero backlash while others rated for use in power-transmission applications can exhibit minute inter-hub rotation. Most variations transmit torque (and address misalignment) through compressible elastomeric-insert spiders trapped between jawed halves … and induce reaction forces when connecting shafts with excessive radial shaft deflection. Jaw designs can accommodate more misalignment (and minimize detrimental forces on the shafts’ support bearings) with softer elastomer spiders, though that sometimes reduces torsional stiffness.

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Bellows couplings have a low moment of inertia and suitable for dynamic applications — as those on precision motion axes. Shown here is an example from R+W America. It has balancing bores on the clamping hubs to ensure balanced installation; friction-based clamping and high-grade stainless-steel bellows ensure zero backlash. Some versions of these bellows couplings work on axes running to 10,000 rpm; some finely-balanced variations can run even faster.

Remember that if excessive misalignment is a concern, consult with coupling manufacturers on the design. Their engineers may suggest design improvements; offer coupling types to resolve the misalignment without inducing unacceptable reaction forces; and supply charts of reaction forces that a given coupling is projected to induce under a given set of conditions.

When motion designs need torsional stiffness — as well as damping

New technological improvements in servomotors have spurred dramatic improvements in response frequencies. The catch is that vibration (and hunting) tend to arise when designers apply high gain settings to servo systems and use advanced couplings with high torsional stiffness — such as disc or bellows-type couplings, for example.

One way to resolve hunting in setups with high gain settings is to use couplings with vibration-damping capabilities. Here, couplings with hydrogenated nitrile butyl rubber (HNBR) center elements are one option to make servo systems for precision automation tasks (as those in semiconductor manufacturing) more responsive. Sometimes called high-gain rubber couplings, these have an integrated structure that includes aluminum hubs on both ends molded with vibration-reducing HNBR to prevent backlash but stay flexible. The rubber-lined claw structure optimizes torsional rigidity as well as damping.

Bode plots show how high-gain rubber couplings increase servomotor gain beyond the capacity of comparable couplings with high torsional stiffness.

Gain width between 0 dB and the point at which there’s a phase delay in the Bode plot is -180° — and this is called the gain margin. General guidelines for servo systems recommend gain margins between 10 and 20 dB. As servomotor gain rises, gain margin decreases. When the gain margin falls below 10 dB, hunting tends to occur.

Consider the limit gain (the servo gain at which hunting occurs) of assemblies using high-gain rubber-type couplings. The value of 17.40 dB surpasses that of other coupling types. Plus because the gain margin is above 10 dB, the servomotor gain of the rubber-insert couplings effectively shortens stabilization time and increasing throughput. More specifically, a system with a 12-msec limit gain might see improvement to a 3-msec limit gain simply by switching to a rubber-type coupling. This suppresses hunting and minimizes time for stabilization.

This information on high-gain rubber couplings is provided by Paulo Castelo, technical solutions supervisor at NBK America. Stay tuned to Design World’s own couplingtips.com in the coming weeks for a detailed feature on servomotor couplings and related stiffness, hunting, damping, and stabilization considerations.

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