Motion System Design Magazine
October 2003

What You Need to Know
About one-piece, helix-curved beams

Understanding how helical, curved beams operate... how their spiral cuts accommodate angular and parallel misalignment, axial motion, and system vibrations is the key to knowing how they will perform in a given application.

Helical-beam couplings
One-piece couplings that incorporate multiple machined spiral cuts are commonly called helical-beam or material flexing couplings.  In high-speed applications designers have two problems to worry about. Not only must designs satisfy torque, flexibility, and stiffness requirements, but they also must consider resonance. Because metallic couplings are torsionally stiff they provide little damping; this means they can impart high natural frequencies to systems and transmit motor excitation. Often the only way to reduce resonance is to change coupling mass -- usually indicating a corresponding change in size. However, reduced mass reduces torque-accommodating capabilities. Curved beam couplings help avoid this conflict. Their spiral-cut geometry is often altered to satisfy machine requirements while maintaining original dimensional specifications. When used within design limits, helical-beam couplings also display extraordinary long fatigue life.

Universal joint

Helica-beam components are sometimes used as single piece universal joints.  The oldest and most common universal joints are called Cardan or Hooke-type joints. They consist of hub yokes connected by a cross-shaped intermediate member. These popular connectors are still frequently used in automotive applications. But because the design consists of separate pieces, they usually require lubrication. As the joint wears, backlash between the joint parts grows. Even a well-lubricated universal joint requires periodic maintenance; cardan universal joints may also leak lubricant.

Performance-wise, Cardan universal joints can transmit relatively high torque with minimal radial loads. Still, these universal joints are incapable of compensating for parallel offset and axial misalignment. Cardan types also introduce rotational inconsistencies into drive systems, a phenomenon known as non-constant velocity rotation.

With their multiple spiral cuts, helical-beam universal joints are capable of accommodating up to 90° of angular misalignment. (Additionally, the design compensates for axial and parallel misalignment.) Flexure (coil) performance capabilities are determined by six major characteristics: outside and inside diameter, coil thickness, material, number of coils, and number of starts. By altering these characteristics, torque and misalignment capabilities (as well as torsional and lateral bending rates) can be modified. Additionally, one-piece universal joints do not exhibit backlash, do not have moving parts, and require no lubrication.

Coil Design
Altering coil geometry results in linear and more dramatically pronounced performance changes. As coil thickness increases, so does torsional stiffness and torque load rating. Coil thickness also influences a coupling's angularity (also called bending moment), parallel misalignment (radial load), torsional rate, and compression spring rate. Increasing the same coupling's inside diameter increases torsional flexibility while decreasing its torque load rating. Changing the inside diameter also affects torque capacity, bending moment, radial load, torsional rate, and compression spring rate. With varying coil length, torque capability remains constant while angularity, radial load, torsional rate, and compression spring rate are affected.

Changing the number of beams significantly changes all performance characteristics. A single-start spring, common to all wire-wound springs, is a single continuous coil element that starts at one end and terminates at the other. A double-start machined spring has two intertwined continuous coil elements. In effect, this puts two independent helixes in the same cylindrical plane. Multiple-start springs are preferred in precision applications because they not only provide redundant elastic elements should a failure occur, but failed coils are physically trapped within the coil by remaining coils.

The difference between a single beam and multi-beam flexure is analogous to the difference between a single and multi-lead screw. When compressed or stretched, single-start springs provide a reaction force plus a moment. (This moment is created because the line of action is through the longitudinal centerline of the spring, and the spring force is acting at the coil mean centerline. The distance between these centerlines provides the moment arm of the subject moment.) On multiple-start coils or flexures, all internal moments are resolved within the coil for uniform extension and compression.

Materials
Machined springs, couplings and u-joints can be manufactured from a variety of materials; high-strength and stainless steel, aluminum, titanium, and machinable plastics are not uncommon. Materials used depend on the environment in which the system will operate. Temperatures, corrosive atmospheres, magnetic (or non-magnetic) conditions, and high torques are considerations to be factored into coil design and material selected.

Aluminum couplings, u-joints and machined springs are especially popular because they are economical to make. These are most appropriate for applications that include encoders, resolvers, or leadscrews. This is because aluminum is light enough to deliver in high-speed motion control systems where fast response time is important.

Stainless steel, on the other hand, has a higher torque capacity and torsional stiffness. For these reasons, steel is appropriate for higher-duty applications on conveyors, pumps, and industrial equipment.

Challenges

The helical-beam's strength is its versatility; these devices have the inherent potential to simultaneously satisfy more than one criterion. The basic requirement of the helical beam as a coupling is to transmit torque loads without permanent distortion or damage and without imposing undue bending or radial loads on the driving motor or driven components. Another challenge is maintaining torsional stiffness.  Every helical beam coupling has some torsional flexibility.

Couplings can be configured -- with thicker coils, for example -- to meet application requirements. Good couplings compensate for misalignments and have high cycle life while exhibiting minimal effects on shafts and especially bearings. Bearing loads are primarily generated by a coupling's natural resistance to bending. They can be especially destructive to rotational components. For this reason, uniform transmission of radial and bending loads is paramount.

In a rotating system, constant velocity refers to the relative rotational speed of the input and output shafts. In a constant-velocity design, the driven end of a coupling turns at the same rate as the driver end. Backlash is one type of unwanted motion that degrades this constant velocity. Windup is another. As windup or backlash increases, so does a driven component’s angular displacement with respect to the driver. Depending on the coupling design, driven members can become 5° out of synch at full load, though some coupling designs go as low as 0.05° at full windup.

For servo couplings, the relationship between torque and windup must be linear in the operating range. To satisfy this requirement, the one-piece design of helical-beam couplings is especially good at reducing backlash. Having a constant spring rate at all coupling points of rotation helps alleviate angular misalignment. Otherwise, angular misalignment -- a setup problem occurring when shafts are aligned but nuts are not parallel -- can result in inconsistent velocity. Closely related, parallel misalignment occurs when shafts are parallel but not aligned. (Skew misalignment is when both angular and parallel misalignments are present.)

Lack of concentricity is yet another setup-related issue to be avoided if possible, since resulting sinusoidal variations are magnified by backlash. Finally, torsional variation is another problem that can induce differences in hub-to-hub velocities when couplings are subjected to dynamic loading. Again, the one-piece integrity of helical beam couplings better ensures stability.

Solid couplings can create high loads on shafts and bearings. This results in torque loss, as it requires more energy to compensate for the higher friction (which in turn increases system temperature). These side loads can markedly reduce the life of the system.

Coupling checklist

To enhance the ability of all components to work in unison, helical-beam couplings should be considered in the early design and made an integral part of the system. Requirements differ, so there is no such thing as one ideal coupling for all systems. Rather, there is an ideal coupling for every application. A helical beam coupling should:

• Accommodate misalignment

• Minimize adjacent bearing loads

• Absorb shock.  Is shock absorption needed? Is system accuracy a primary concern? What is the frequency of the entire system? A helical beam coupling must address all these requirements.

• Allow for axial motion.  Axial motion compensates for the expansion and extension of the motor shaft. Helical-beam couplings help relieve the stress caused by this movement.

• Provide the necessary torsional rate.  Revolutions per minute is an important design consideration, as centrifugal forces limit rotational speed. Some questions to ask about torque: What will the maximum (or startup) torque reach? What is the working (or continuous) torque? Is there a set direction of rotation or does the system reverse? If there are reversals, how quickly must they happen?

• Have a reasonable envelope, outside diameter and length.  Size constraints can be handled much more easily when designers consider the coupling in earlier design stages. Attachments can enhance the ability to incorporate two, three, or more separate pieces into a single piece of material.

• Incorporate reliable and quick attachments.  Beam couplings and universal joints can be designed to handle torque and misalignments with an infinite number of attachment requirements.

• Integrate as many additional functions as possible.  Other components not directly related to the coupling -- such as gears, shafts, spline bores, and threads -- can be integrated. In this way, one-piece couplings and universal joints can incorporate the correct torque and misalignment capacity, with reliable attachments. The net result is reduction in the number of parts and reduced system costs.

• Be cost effective.  In production it becomes time-consuming and too costly to align shafts perfectly; therefore, helical-beam couplings offer cost savings. Still, because couplings as integrated components work more reliably with all other components, determining the appropriate coupling should be part of the total design process and not a last-minute selection.

Thick and thin	See ID	Wrap reps	Multiple tracks
With material, diameter, and length equal, increasing coil thickness on a coupling increases its torsional stiffness and torque load rating.	As inside diameter increases on otherwise identical helical-beam couplings, torsional flexibility increases and torque load rating decreases.	Varying coil length has no effect on torque-carrying capabilities, but has a large effect on other performance properties.	Changing the number of beams significantly changes all performance characteristics

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For more information, contact Gary Boehm, senior research engineer.