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Wrap friction / capstan tension calculator

Engineering calculators (Beta)

Find the limiting tension ratio at impending slip from friction and wrap angle.

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

T1/T2=e^(μθ); torque=(T1−T2)r; θ in radians.

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

摩擦係数・巻付け角から、滑り出す境界での張力比を求めます。

入力・結果・適用条件を確認する

選択した形状・計算方法により、使う項目は変わります。実際の計算は上の図と入力欄で行えます。

主な入力

  • 静摩擦係数 μ(入力例) (—)
  • 実際の巻付け角 θ (° / rad)
  • 緩み側の張力 T2 (N / kN / mN)
  • 巻付け半径 r (mm / cm / m)

得られる結果

  • 滑り出す境界の張り側張力 T1 (N)
  • 張力比 T1/T2 (—)
  • 張力差によるトルクの大きさ (N·m)

計算式の概要

T1/T2=e^(μθ); torque=(T1−T2)r; θ in radians.

滑り出す直前の柔らかいロープ・平ベルトの理想摩擦モデルです。定常運転で常にこの張力になるわけではありません。V溝、曲げ剛性、遠心力、摩耗、ベルト強度、軸受荷重や駆動装置の選定は別の確認です。

現在選択中の方法には、操作欄の「計算式・適用条件」を使ってください。参考計算であり、設計全体の安全性を保証するものではありません。

関連する計算

What this calculator does

Find the limiting tension ratio at impending slip from friction and wrap angle.

Inputs, outputs and applicability

The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.

Inputs

  • Static friction coefficient μ (example) (—)
  • Actual wrap angle θ (° / rad)
  • Slack-side tension T2 (N / kN / mN)
  • Wrap radius r (mm / cm / m)

Calculated results

  • Tight-side tension at impending slip (N)
  • Tension ratio T1/T2 (—)
  • Torque from tension difference (N·m)

Formula overview

T1/T2=e^(μθ); torque=(T1−T2)r; θ in radians.

Ideal flexible rope / flat belt at impending slip. Operating tension is not necessarily this limit. V-groove wedging, bending stiffness, centrifugal force, wear, belt strength, bearing loads and drive selection are separate.

The displayed formula and conditions in the working panel apply to the currently selected model. Reference calculation only; it does not certify a complete design.

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