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Springs are mechanical devices that can store potential energy because of their elasticity. The term elasticity refers to a property of materials that reflects their tendency to return to their original shape and size after having been subjected to a force that causes deformation after that force has been removed. The basic notion underlying the operation of springs is that they will always attempt to return to their initial size or position whenever a force is applied which changes their size, whether that be forces which are from compression, extension, or torsion.
Springs are often made of coiled, hardened steel, although non-ferrous metals such as bronze and titanium and even plastic are also used. For a more complete discussion on the different materials used in the manufacturing of springs, see our related guide on the types of spring materials.
How do Springs Work?
Springs operate based on a principle known as Hooke’s law, which is attributed to the British physicist Robert Hooke who published his ideas on springs in 1678. Hooke’s law states that the force exerted by a spring is proportional to the displacement from its initial or equilibrium position. This relationship can be expressed mathematically as:
where (F) represents the force generated by the spring, (Δx) represents the displacement or the amount of deformation from the spring’s relaxed or neutral position, and (k) is a parameter that is known as the spring constant.
The negative sign in the above expression reflects the directionality of the resulting force from the displacement of the spring. If you pull a spring apart (increase its length), the force that results will be in the opposite direction to the action you took (tending to return the spring back to its neutral position). Similarly, if you push on a string to reduce its length, the force that results will be in the opposite direction and will attempt to increase the spring’s length and return it to its neutral position.
The spring constant k is a function not only of the material used for manufacturing the spring but also is determined by several factors that relate to the geometry of the spring design. Those design factors include:
- The wire diameter of the spring material.
- The coil diameter, which is a measure of the tightness of the spring
- The free length of the spring, which represents its length when it is not attached to anything and is not undergoing displacement from equilibrium.
- The number of active coils contained in the spring, which means the number of coils that can expand and contract in normal use.
The unit of measure for the spring constant is a force unit divided by a length unit. In the metric system of measurement, this would be a Newton/meter, or Newton/centimeter, for example.
Springs that follow Hooke’s law behave linearly, meaning that the force generated by the spring is a linear function of the displacement or deformation from the neutral position. Materials have a so-called elastic limit – when the material is stretched beyond this point, it experiences permanent deformation and no longer has the capability to return to its original size and shape. Springs that are stretched too far and exceed the material’s elastic limit will no longer follow Hooke’s law.
Other types of springs, such as variable diameter springs (one that features conical, concave, or convex coils) are examples of springs that will also exhibit non-linear behavior with respect to their displacement from the neutral position, even if the deformation is within the elastic limit of the material.
Another example of a spring that will not obey Hooke’s law is variable pitch springs. The pitch of the spring is the number of coils that are used in each length or segment of the spring. Variable pitch springs often have a constant coil diameter, but the spring pitch changes over the length of the spring.
Key Spring Terminology and Definitions
Spring designers use several terms, parameters, and symbols when performing spring design. A summary of this key terminology appears below with examples of the symbology associated with many of these parameters.
- Active coils count (AC) – the number of coils that will deflect under load
- Buckling – refers to the bowing or lateral displacement of a compression spring.
- Slenderness ratio – is the ratio of the length of the spring to its mean diameter for helical springs. The propensity for buckling is related to the slenderness ratio L/D.
- Deflection – the motion of a spring as a result of the application or removal of a load to/from a spring.
- Compressed length (CL) – the value of the spring’s length when the spring is fully compressed.
- Coil Density – the number of coils per unit length of the spring.
- Elastic limit – the maximum value of stress that can be applied to the spring before permanent deformation occurs, meaning that the material no longer exhibits the ability to return to its pre-deformed size or shape when the stress is removed.
- Mean Coil Diameter (D) – the average diameter of the coils in the spring.
- Free angle – for helical torsion springs, represents the angular position of the two arms of the spring when not under load conditions.
- Spring wire diameter (d) – the diameter of the wire material used for the spring.
- Free length (FL) – the overall spring length measured without any loading applied to the spring.
- Hysteresis – represents the loss of mechanical energy during repetitive or cyclical loading or unloading of a spring. Losses are the result of frictional conditions in the spring support system as a result of the tendency for the ends of the spring to rotate during compression.
- Initial Tension (IT) – for extension springs, this is the value or magnitude of the force needed to be overcome before the coils of a close wound spring begin to open.
- Modulus in Shear or Torsion (G) – the coefficient of stiffness for compression and extension springs. Also called the Modulus of Rigidity.
- Modulus in Tension or Bending (E) – the coefficient of stiffness for torsion or flat springs. Also called Young’s Modulus.
- F = the deflection of the spring for N coils which are active (for linear displacement)
- Fo = the deflection of the spring for N coils which are active (for rotary displacement)
- Active length (L) – the length of the spring that is subject to deflection
- P = the load applied to the spring
- Pitch (ρ) – the center-to-center distance of the adjacent coils in an open wound spring.
- Rate – represents the chance in the load value per unit length change in the spring’s deflection. Units of measure are in force/distance such as lbs./in. or N/mm.
- Set permanent – is the change to the value of the length, height, or position of a spring as a result of the spring being stretched past the elastic limit.
- St = the torsion stress
- Sb = the bending stress
- Total coil count (TC) – the total number of coils in the spring, including active coils and inactive coils.
Types of Springs
There are various types of springs, the designs of which take advantage of different energy storage management. The common types of springs include the following:
- Compression springs
- Extension springs
- Torsion springs
- Constant force springs
- Belleville springs
- Drawbar springs
- Volute springs
- Garter springs
- Flat Springs
- Gas springs
- Air springs
More information on each of these types of springs may be found in our related article Types of Springs - A Thomas Buying Guide.
Spring Materials and Manufacturing
How are springs made? Springs are often made of hardened spring steel, which can either be pre-hardened before spring formation or hardened following formation. Helical springs include any type of spring that is made from bar stock or wire and which is formed into a helical shape. This category includes compression springs, extension springs, and torsion springs. Long stock wire is used and fed into an auto-coiler to produce those spring types. The wire stock can also be coiled on a lathe if a smaller run is being prepared, but there are many safety concerns to consider. Spring wire will uncoil dramatically if it is not tied down or if a machinist loses control of it. This uncoiling behavior can be extremely dangerous to those nearby, especially if it is a heavy gauge wire.
An auto-coiler is a machine that can force spring wire into a coiled shape. Although it has a similar name to an automotive autocoil transmission, it is a different device. They are typically adjustable machines that can alter the coil tension, length, and number. Auto-coilers use rollers to feed spring wire through headers and then quickly spin the wire around a cylinder. The quick spinning action forces the spring to adapt into a coiled helical shape. The auto-coiler then ejects the spring and coils the next piece of wire.
Leaf springs are formed differently from helical springs. First, a flat bar is sheared into shape and then a collection of bars is punched together. Several machines trim the resulting bars to remove extra metal and taper the ends. The spring is then heat-treated to harden the steel, while other treatments such as painting finishes are performed to match the spring to predetermined visual specifications.
This article presented a brief summary of springs including how they work, key terminology, the different types of springs, and how they are made. For information on other topics, consult our additional guides or visit the Thomas Supplier Discovery Platform where you can locate potential sources of supply for over 70,000 different product and service categories.
Other Springs Articles
- Types of Springs - A Thomas Buying Guide
- Types of Spring Materials
- Extension Spring End Types
- Torsion Spring Design Recommendations