Types of springs and uses in vibration isolators and oscillators

A spring could be defined as any elastic body that can return to its original shape after “elastic” deformation, i.e. deformed before its breaking point. Usually springs are made of steels, but they can also be made from plastics.

A vibration isolator is a device that is designed to reduce incoming vibrations into a vibration-sensitive device. With correct design and careful specifications, springs can realise low natural frequencies e.g. below 10 Hz for example, ideal for applications requiring high vibration isolation performance.

In terms of damping, steels used in springs exhibit very low damping, with a damping coefficient of 0.005. This refers to how strongly they can resonate. Due to the low damping, coil springs are usually implemented with external dampers/damping mechanisms (e.g. viscous fluid, friction, air, or metal mesh), that will help deaden incoming shocks for example but also could affect the performance of the isolation.

Below table summarises some common types of springs, describing their load-deflection, stiffness, damping and frequency characteristics along with general comments about their loading ranges, deformation ranges, and applications. Typical springs such as helical coil types usually depend on torsion (or twisting) of individual coils to create compliance, while others could depend on slightly different mechanisms such as flexural or bending such as some flat wire spring types, sine springs, leaf springs, wave springs, and slotted springs.

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Helical Coil Springs

Typical Helical Coil Spring, with closed and grounded ends. © Saif Bunni

• Load-Deflection curve: Linear.
• Working Principle: Torsion.

One of the most common types for use in vibration isolators. Linear load-deflection curve means as load increases, deflection increases proportionally with a straight line, due to having a constant stiffness. Large allowable compression deformation could be up to 30–40% of initial height.

Variable Helical Coil Springs

A helical conical spring with closed and grounded ends. © Saif Bunni

• Load-Deflection curve: Non-Linear.
• Working Principle: Torsion.

This is a family of helical coil springs with variable parameters, for example having variable wire diameter along length or variable pitch (spacing between coils). These could include conical or corset shaped springs, and could vary either linearly or exponentially along their lengths.

Conical springs for example become more stiff with increased loads e.g. exhibit a hardening effect, making their load-deflection curve non-linear. This is due to smaller diameter coils being stiffer than wider diameter coils.

Depending on design, some advantages of non-linear or variable helical coil springs is that they could allow for larger deformations/deflections than straight types, and thus could support a wider range of loads.

A helical “flexure” coil spring, with rectangular cross-sectioned wire (or solid bar).

Helical Torsion Springs

Torsion spring.

• Load-Deflection curve: Non-Linear.
• Working Principle: Bending (flexural) and Torsion.

Helical Torsion springs differ from a typical helical coil by the addition of arms or legs to each end of the spring, which allows loading and activation of the coils of the spring using torque/rotational force, rather than a linear one. Therefore loading force could be varied by adjusting arm length. The load-deflection varies non-linearly by angle. A circular or rectangular bar could be used in the manufacture of the spring.

There seems to be differences in literature as to whether to apply torsion or beam theory to describe the working action of the spring. The primary mechanism is said to be bending stresses, which differs from torsion which is dependent on shear modulus. I personally believe small amount of torsion (shear stress) occurs as the coils bend closer together when winding up the spring.

Torsion springs are used in a huge variety of utility and everyday applications including precision instruments. They are very commonly used as oscillators in mechanical watches. On the other hand, they are also used in vibration isolation for rotational parts in automotive applications and even in suspension elements for military tanks.

Coned Disc Compression Springs (Belleville) Springs

Cross-sectional view showing a Belleville spring stack in series.

• Load-Deflection curve: Non-Linear.
• Working Principle: Bending (flexural).

Coned disc springs or otherwise known as Belleville washers exhibit both hardening and softening effects in its load-deflection curve, which depend on height of cone and thickness of disc, in addition to diameter. These are generally very stiff compared to coil structures so are used for high loading applications to provide compliance. They have applications ranging from use in joints of piping systems to vibration isolation for buildings. These springs can be stacked easily either in parallel or series configurations, which would alter the stiffness thus giving the designer flexibility and precision. When stacked, damping could be provided by linear friction between the stacked elements.

Leaf Springs

Double Eye Leaf Spring.

• Load-Deflection curve: Non-Linear.
• Working Principle: Bending (flexural).

Leaf springs consist of slender arc-shaped rectangular cross-sectioned beams, stacked together in various configurations to provide compliance, and fastened together by a central bolt. Leaf springs were very commonly used for cars, but nowadays more common in heavier vehicles like trucks and railway. Leaf springs work by bending stress, and due to the graduated lengths of the “leaves,” its deflection can be be approximated by a triangular plate. This also means the load-deflection is a non-linear curve.

Some other types of non-linear springs

Flat wire coil spring.

Flat Wire Spiral Springs: are formed from a metal strip (rectangular cross-section) precisely wound in the form of a spiral. This design allows for storage of a lot of energy in a compact form factor. Applications and sizes are wide ranging but they are known for use as oscillators in mechanical watches as balance springs. The behaviour of this spring can also be approximated by bending (flexural) stress.

Flat “Flexure” spiral spring.

Flat Flexure Springs: These are flat discs with usually a spiral pattern cutout in the metal to produce compliance. The underlying working mechanism also depend on bending stresses, so thicknesses and widths of the spiral arms could modify the overall stiffness of the spring. These could be very useful as they have a thin and flat form factor. Some applications include linear resonant haptic actuators (used in PS5 gaming controllers), pistons in an engine, and other novel applications.

A novel sine-shaped spring design, connected in series. Illustration based on Tobias 1959.

Sine Springs: a novel spring design which consists of a beam element buckled into an elliptical sine shape. Made from sheet metal shaped like a spring. It has a linear load-deflection region, with stiffening effect with increasing loads, making the load-deflection curve non-linear. One of the advantages of the design is that the sine elements can be stacked in parallel or series, and clamping angle can modify load-deflection behaviour.

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