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#276 Spring Design -4: Load-Deflection Relationship for Helical Extension Springs

Category : Automation elements technology
February23, 2017

Unlike helical compression springs, non-linear characteristics cannot be added to helical extension springs. However, the initial tension can be put into the springs.

(1) Helical extension springs with initial tension

  • Initial tension, which is a force holding the coils against each other, can be put into helical extension springs even under a no-load condition.
  • The initial tension is created by twisting the wire in the direction of the coils in contact with one another during the spring winding process.
  • Cold-formed and solid-coiled springs are wound with some tension. In general, springs that are purposely designed to have initial tension are referred to as springs with initial tension.
  • The load and deflection characteristics of springs with and without the initial tension are shown in [Fig.1].
  • [Formula A] represents the relationship between loads and deflection of an extension spring shown in [Fig.1]. [Formula B] is a relational expression between loads and deflection of an extension spring with the initial tension.

    [Formula A]
    Load P (N) = Spring constant k (N/mm) × Deflection δ (mm)

    [Formula B]
    Load P (N) = Initial tension Pi (N) + Spring constant k (N/mm) × Deflection δ (mm)

  • Initial tension Pi will be calculated in the following formula: Formula

[Formula A]

(2) Advantages and disadvantages of springs with initial tension

This table summarizes advantages and disadvantages of springs with the initial tension added.

AdvantagesDisadvantages
  • Instability of springs under a no-load condition can be minimized.
  • Designing a smaller spring (larger load with smaller spring constant) is possible.
  • Load variation tends to be large at a specified length.
  • Even if it is necessary to perform low-temperature annealing to remove distortion occurred by coiling, the annealing result will not be sufficient.

(3) Various shapes of helical extension springs

Most of the helical extension springs are without non-linear characteristics on the spring plane and classified into the cylinder type and the spindle ends type. In addition to this classification by the outer shape, the springs can be also categorized by the hook shape on both ends.

Integrated double hooks

Semicircular hook, circular hook, reverse circular hook, side circular hook, square hook, U-hook, V-hook and more.

Separate hooks

Tapered end with circular hook, plug type, plate type

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