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Extension coil spring load and rate calculator

Engineering calculators (Beta)

Calculate extension load including initial tension, stiffness and coil-body shear stress; hook strength is separate.

Inputs

Choose units and enter numbers. Full-width digits and fractions such as 1/8 or 1 3/8 are accepted. Changing a unit converts the entered value.

Results

Reference calculation only. Results do not certify suitability for an actual design or its safety.

Diagram

Inputs: select a blue symbol to edit Results: red-orange values and lines

Formula and applicability

k=Gd⁴/(8D³nₐ); F=F₀+kx; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw·8FD/(πd³); E=F₀x+kx²/2.

Displayed values are rounded. Diagrams illustrate the calculation conditions. Initial material and fluid properties are examples; replace them with values for the actual material, temperature and conditions.

Reference
Using this information as a reference

Equations assume particular loads, supports and deformation ranges. Check inputs, units and the applicability of each equation. Diagrams explain conditions; they are not manufacturing drawings or proof of safety.

Material values are typical values or reference ranges, not certified product properties or ready-to-use design allowables. They vary with standards, product form, dimensions, temper and temperature. Check the specifications and inspection certificates for the actual product.

Displayed safety factors and checks apply only to the supplied inputs and calculation model. They do not automatically establish the safety of a complete design, including code compliance, service life, fatigue or joints. For actual design, manufacture and use, separately verify applicable regulations and standards, product specifications, and the necessary tests and engineering review.

この計算で求められること

初張力を含めた伸びと荷重、コイル胴部のせん断応力を確認します。フックの強度は別に扱います。

入力・結果・適用条件を確認する

主な入力

  • 線径 d
  • コイル平均径 D(外径ではない)
  • フックを除く有効巻数 nₐ
  • 横弾性係数 G(例)
  • 実測・指定した初張力 F₀
  • 密着状態からの伸び x
  • 胴部の比較用許容せん断応力 τa(例)

得られる結果

  • 指定伸びの引張力 F(x=0は開き始め) (N)
  • 胴部のばね定数 k (N/mm)
  • Wahl補正した胴部せん断応力 τ (MPa)
  • 指定伸びまでに外力がする仕事 (J)
  • ばね指数 C=D/d (—)
  • Wahl応力修正係数 Kw (—)
  • 入力許容せん断応力/胴部応力 (—)

k=Gd⁴/(8D³nₐ); F=F₀+kx; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw·8FD/(πd³); E=F₀x+kx²/2.

小さいピッチ角・一定平均径の円筒コイル胴部の線形弾性モデルです。D/d≥3、nₐ≥3の範囲に限定します。密着状態から伸ばし始める力がF₀で、初張力を材料名から推定しません。x=0の表示荷重はコイルが開き始める閾値であり、無外力でもF₀が外へ作用するという意味ではありません。フック・移行部の曲げ、応力集中、寿命、初張力の残留応力分布、過大な伸びによる径・ピッチ変化は別に確認します。許容値は材料・線径・加工・使用回数に合う値を指定します。入力例は製品定格ではありません。

関連する計算

What this calculator does

Calculate extension load including initial tension, stiffness and coil-body shear stress; hook strength is separate.

Inputs, outputs and applicability

Inputs

  • Wire diameter d
  • Mean coil diameter D, not outside diameter
  • Active body turns nₐ, excluding hooks
  • Shear modulus G (example)
  • Measured / specified initial tension F₀
  • Extension x from closed-coil state
  • Entered coil-body shear allowable τa (example)

Results

  • Pull force F at extension x (x=0: opening threshold) (N)
  • Coil-body spring rate k (N/mm)
  • Wahl-corrected coil-body shear stress τ (MPa)
  • External work to the entered extension (J)
  • Spring index C=D/d (—)
  • Wahl stress factor Kw (—)
  • Entered shear allowable / body stress (—)

k=Gd⁴/(8D³nₐ); F=F₀+kx; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw·8FD/(πd³); E=F₀x+kx²/2.

Linear elastic body model of a cylindrical close-coiled spring with small pitch angle and constant mean diameter, limited to D/d≥3 and nₐ≥3. F₀ is the measured/specified force that starts opening the coils; it is not inferred from the material name. At x=0, displayed F₀ is the opening threshold, not an external force produced without applied load. Hook/transition bending, stress concentrations, fatigue, residual initial-tension stress and large-extension diameter/pitch changes are separate checks. Establish the allowable for material, wire size, process and cycle duty. Examples are not product ratings.

Related tools

数値の感覚を、図と動きで確かめる

説明用の別モデルです。適用条件を確認してください。数値は自動転記しません。

See the idea in diagrams and motion

A separate explanatory model. Check its assumptions; values are not transferred.