Roymech engineering encyclopedia

General Notes on Springs


Springs are mechanical components that deform elastically under load and store mechanical energy. They are among the more highly stressed components used in machinery and are available in many forms to provide linear force, torque, energy storage, shock isolation and controlled movement.

This page summarises the general engineering principles common to spring design, including spring rate, load-deflection characteristics, energy storage, duty and operating states.

Need to choose a spring type?
See the Spring Selection and Design Guide for guidance on selecting between compression, extension, torsion, disc, leaf, spiral and other spring arrangements.

Contents

Spring Applications

Springs are used wherever controlled elastic deformation is required. Typical functions include:

  • Storing mechanical energy, as in clock and watch springs.
  • Absorbing energy in drives and reciprocating mechanisms.
  • Applying a controlled force, as in pressure-relief valves.
  • Maintaining the position of mechanical components, such as doors, levers and brake mechanisms.
  • Providing shock and vibration isolation.
  • Measuring or controlling force in scales and instruments.
  • Reducing manual effort in lifting, counterbalance and return mechanisms.
  • Maintaining contact or preload between mechanical components.

Spring Rate

An important parameter in spring design is the spring rate, or stiffness. It describes the change in load required to produce a corresponding change in spring deflection.

Linear Spring Rate

For a spring having a linear force-deflection characteristic, the spring rate is:

k = F δ

where:

  • k = linear spring rate (N/m or N/mm)
  • F = spring force (N)
  • δ = elastic deflection (m or mm)

For a non-linear spring, stiffness varies with deflection. The local or tangent spring rate may then be expressed as:

k = d F d δ

Rotational Spring Rate

For a spring operating through angular displacement, the corresponding rotational spring rate is torque divided by angular deflection:

k a = T θ

where:

  • ka = rotational spring rate (N m/rad)
  • T = torque (N m)
  • θ = angular displacement (rad)
Unit consistency: When spring dimensions are calculated in millimetres, spring rate is commonly expressed in N/mm and material modulus in N/mm2. SI metre-based units may equally be used, but the complete calculation must use a consistent set of units.

Spring Duty

The loading history of a spring is fundamental to its design. RoyMech's traditional classification divides spring applications broadly into three duty categories:

  1. High or cyclic duty – springs subjected to frequent or rapid load cycles, such as engine valve springs. Fatigue behaviour is normally a major design consideration.
  2. General duty – springs operating intermittently or for limited periods under varying loads.
  3. Static or sustained-load duty – springs used primarily to maintain a load or position for extended periods. Stress relaxation, creep where applicable, and permanent set may be important.

These descriptions are useful general classifications rather than universal standardised spring classes. Actual allowable stress and fatigue requirements depend on spring type, material, manufacturing process, environment and required service life.

Spring Load-Deflection Characteristics

Depending on geometry and construction, a spring may have a linear, progressive or degressive load-deflection characteristic.

  • Linear characteristic – spring force increases approximately in direct proportion to deflection and the spring rate remains approximately constant.
  • Progressive characteristic – spring rate increases as the spring is deflected.
  • Degressive characteristic – spring rate decreases as deflection increases over the relevant operating range.

Linear, progressive and degressive spring load-deflection characteristics

Non-linear characteristics can arise deliberately from spring geometry, variable pitch, changing numbers of active coils, contact between elements or combinations of different spring elements.

Spring Energy Storage

The mechanical energy stored by a spring during elastic loading is equal to the area under its load-deflection characteristic.

For a spring subjected to a force F acting through a displacement from x1 to x2, the deformation work is:

W x 1 → x 2 = ∫ x 1 x 2 F d x

For a linear spring, where force is proportional to displacement, the stored energy is the triangular area beneath the force-deflection curve:

W = 1 2 F δ = 1 2 k δ 2

Energy Stored by a Torsional Spring

For a spring subjected to torque T through an angular displacement from θ1 to θ2, the deformation work is:

W θ 1 → θ 2 = ∫ θ 1 θ 2 T d θ

For a linear torque-angle characteristic, where T = kaθ, the stored energy becomes:

W = 1 2 T θ = 1 2 k a θ 2

Energy is therefore represented geometrically by the area beneath the force-displacement or torque-angle curve. For a linear characteristic this area is triangular.

Spring Operating States

During manufacture, installation and operation a spring may be considered in several different loading states.

State Description
Free The spring is unloaded and at its free length, free angle or free position.
Preloaded An initial load or deflection is deliberately applied when the spring is installed or before its normal operating movement begins.
Loaded The spring is subjected to a load within its intended operating range.
Maximum operating load The highest load intended during normal design operation.
Limiting load A load associated with a specified material, stress, geometric or functional limit and not necessarily an acceptable continuous operating condition.

A strength-related limiting condition may be associated with yielding, permanent set or another specified material limit. A geometric limit can occur independently of material strength; for example, a compression spring may reach solid height when adjacent coils come into contact.

Limiting load is not necessarily a permissible working load. Normal operating loads should be established from the required deflection, stress, fatigue life, relaxation or set requirements and any geometric limitations applicable to the particular spring.

General Spring Design Considerations

Although the detailed equations depend on spring type, several considerations apply to most spring designs:

  • Material: Young's modulus or shear modulus determines elastic stiffness, while material strength, heat treatment and manufacturing condition influence allowable stress.
  • Stress: The highest local working stress must be considered rather than relying only on nominal applied force or torque.
  • Fatigue: Repeatedly loaded springs should be assessed using the stress range and required number of operating cycles.
  • Permanent set: Excessive stress can cause permanent deformation so that the spring does not return fully to its original free condition.
  • Relaxation: A spring maintained under load may gradually lose force, particularly at elevated temperature.
  • Stability: Long compression springs can buckle laterally and may require guidance or specific slenderness checks.
  • Dynamic behaviour: Rapidly cycled springs can experience surge, resonance and dynamic stresses that are not represented by static calculations.
  • Environment: Temperature, corrosion, wear and surface damage can substantially affect spring performance and fatigue life.
Engineering reference: The general relationships on this page provide a starting point for spring design. Detailed calculations should use the equations, material data and design criteria appropriate to the particular spring type and duty.
See Also