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The Engineer posted on October 23, 2006 | | 39502 views

Springs are fundamental mechanical components found in many mechanical systems. Developments in material, design procedures and manufacturing processes permit springs to be made with longer fatigue life, reduced complexity, and higher production rate. Most springs are linear which means the resisting force is linearly proportional to its displacement. Linear springs obey the Hooke's Law, F = k × Dx Where F is the resisting force, k is the spring constant, and Dx is the displacement. The most commonly used springs are of the three types below:

Compression Tension Torsion
Compression Tension Torsion

Design Guidelines

There are many different types of compression springs. The following figure illustrates the difference between them.

Plain, not ground Closed, not ground Closed, with ends ground
Plain, not ground Closed, not ground Closed, with ends ground

The spring constant, k, is a function of the spring's dimension and material property.
It is expressed as:

G: modulus of rigidity (shear modulus)
d: diameter of spring wires
D: diameter of spring coil
n: number of active coils (see below)
The spring displacement then becomes:

The number of active coil (n) depends on the spring's end geometry. The following table can be used as a guideline.

Plain, not ground
not ground
Closed with
ends ground
Number of Active Coils (n)
TC - 2
TC - 2

Where TC stands for total number of coils. The number of active coils is equal to the total number of coils minus the number of end coils that do not help carry the load.

Spring Material

Most springs are made with high-carbon spring steels, alloy spring steels, stainless spring steels, copper base spring alloys, and nickel base spring alloys.
  • High Carbon Spring Steel - These spring steels are the most commonly used of all spring materials because they are the least expense, are easily worked, and are readily available. They are not suitable for springs operating at high or low temperature or for shock or impact loading.

  • Alloy Spring Steel - These spring steels are used for conditions of high stress, and shock or impact loadings. They can withstand a wider temperature variation than high carbon spring steel and are available in either the annealed or pre-tempered conditions.

  • Stainless Spring Steel - The use of stainless spring steels has increased and there are compositions available that may be used for temperatures up to 288°C. They are all corrosion resistant but only the stainless 18-8 compositions should be used at sub-zero temperatures.

  • Copper Base Spring Alloys - Copper base alloys are more expensive than high carbon and alloy steels spring material. However they are frequently used in electrical components because of their good electrical properties and resistance to corrosion. They are suitable to use in sub-zero temperatures.

  • Nickel Base Spring Alloys - Nickel base alloys are corrosion resistant, and they can withstand a wide temperature fluctuation. The material is suitable to use in precise instruments because of their non-magnetic characteristic, but they also poses a high electrical resistance and therefore should not be used as an electrical conductor.

Spring Resonance

The dynamic behaviors of springs have to be analyzed when they are used in a moving mechanism. The nominal frequency of operation should be well under the spring's first resonant frequency; typically about 15-20 times lower for safety reason. The force the spring exerts as it approaches its resonant frequency will tend to decrease, which could have disastrous implications for the spring assembly.


The following is a list of spring materials and their references:
Spring Material
ASTM Reference
Music Wire ASTM A228 (0.80%-0.95% carbon)
Oil-Tempered MB Grade ASTM A229 (0.60%-0.70% carbon)
Oil-Tempered HB Grade SAE 1080 (0.75%-0.85% carbon)
Hard-Drawn MB Grade ASTM A227 (0.60%-0.70% carbon)
Cold-Rolled Spring Steel, Blue-Tempered or Annealed SAE 1074, 1064, 1070 (0.60%-0.80% carbon)
Cold-Rolled Spring Steel, Blue-Tempered Clock Steel SAE 1095 (0.90%-1.05% carbon)
Chromium Vanadium ASTM A231
Chromium Silicon ASTM A401