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ENGINEERING CALCULATORS

Torsion coil spring torque and body stress calculator

Engineering calculators (Beta)

Estimate body torsional rate and torque for winding-in angular deflection, excluding flexible-arm deflection.

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

kφ=Ed⁴/(64Dnₐ); M=kφφ (φ in rad); σ=32M/(πd³); U=kφφ²/2.

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.

Calculations do not submit input values to a server. Results are not an automatic code-compliance or safety determination.

この計算で求められること

巻き込む向きの変位角から、腕部のたわみを除いたコイル胴部の回転ばね定数とトルクを求めます。

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
  • 有効巻数 nₐ
  • 縦弾性係数 E（例）
  • 自由状態から巻き込む変位角 φ
  • 胴部の比較用許容曲げ応力 σa（例）

得られる結果

  • 巻込みトルク M (N·m)
  • 胴部の回転ばね定数 kφ (N·m/rad)
  • 胴部の公称曲げ応力 σ (MPa)
  • 胴部の弾性エネルギー U (J)
  • ばね指数 C=D/d (—)
  • 入力許容曲げ応力／胴部公称応力 (—)

kφ=Ed⁴/(64Dnₐ); M=kφφ (φ in rad); σ=32M/(πd³); U=kφφ²/2.

円筒コイルを巻き込む方向・線形弾性・一定平均径の胴部だけの基本モデルです。D/d≥3、nₐ≥3、0≤φ≤180°に限定します。計算には縦弾性係数Eを使い、圧縮・引張コイルの横弾性係数Gとは異なります。腕部が柔らかい場合は全体のばね定数がこの値より小さくなり、同じ角度に対するトルクも変わります。表示応力は公称値で、腕部の荷重導入や曲率による最大局所応力、巻戻し方向、摩擦、案内棒への抱き付き、巻数・径の変化、疲労は含みません。許容応力は同じ公称応力の評価基準に合う値を指定してください。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

Estimate body torsional rate and torque for winding-in angular deflection, excluding flexible-arm deflection.

Inputs, outputs and applicability

Inputs

  • Wire diameter d
  • Mean coil diameter D
  • Active body turns nₐ
  • Young modulus E (example)
  • Winding-in deflection φ from free state
  • Entered nominal body bending allowable σa (example)

Results

  • Winding-in torque M (N·m)
  • Body rotational stiffness kφ (N·m/rad)
  • Nominal coil-body bending stress σ (MPa)
  • Elastic energy U of the body (J)
  • Spring index C=D/d (—)
  • Entered bending allowable / nominal body stress (—)

kφ=Ed⁴/(64Dnₐ); M=kφφ (φ in rad); σ=32M/(πd³); U=kφφ²/2.

Basic constant-diameter, linear-elastic cylindrical coil-body model for winding-in motion only, with D/d≥3, nₐ≥3 and 0≤φ≤180°. Uses Young modulus E, unlike the shear modulus G used for compression/extension coils. Flexible arms reduce assembly stiffness and change torque for a given total angular deflection. Displayed stress is nominal; arm load introduction, curvature-related local peaks, winding-out, friction, mandrel gripping, changing coil geometry and fatigue are excluded. Use an allowable consistent with this nominal-stress basis. Examples are not product ratings.

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