Machined springs provide precise linear deflection rates because virtually all residual stresses are eliminated.

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 joints

Helical-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 crossshaped 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 nonconstant 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

Select figure to enlarge.

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 doublestart 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.

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