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Belt tension and vibration frequency calculator

Engineering calculators (Beta)

Convert fundamental vibration frequency and tension using free-span length and mass per length.

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

T = 4 μ L² f²; f = √(T/μ)/(2L); c = √(T/μ).

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

自由スパンの長さと単位長さ質量から、基本振動の周波数と張力を相互に計算します。

入力・結果・適用条件を確認する

主な入力

  • 計算する方向
  • 接点間の自由スパン L
  • ベルト全幅の単位長さ質量 μ
  • 測定した基本振動数 f
  • 指定する張力 T
  • 製品指定の張力下限 Tmin(例)
  • 製品指定の張力上限 Tmax(例)

得られる結果

  • ベルト1本・1スパンの張力 T (N)
  • 基本振動周波数 f (Hz)
  • 横波の伝わる速さ c (m/s)
  • 張力下限に対応する周波数 fmin (Hz)
  • 張力上限に対応する周波数 fmax (Hz)

T = 4 μ L² f²; f = √(T/μ)/(2L); c = √(T/μ).

一様で曲げ剛性を無視できる張った弦の基本振動モデルです。Lはプーリー中心間でもベルト全周でもなく、接点間の自由部分。μはベルト全幅のkg/mです。測定周波数には高調波を使わないでください。短い・厚い・歯付きのベルトや端部拘束には製品固有の補正が必要な場合があります。下限・上限は実製品と使用状態の指定値に置き換えます。この計算だけで最適張力、伝達容量、軸受荷重を決定しません。

関連する計算

What this calculator does

Convert fundamental vibration frequency and tension using free-span length and mass per length.

Inputs, outputs and applicability

Inputs

  • Calculation direction
  • Free span L between tangent points
  • Mass per length μ of the whole belt width
  • Measured fundamental frequency f
  • Specified tension T
  • Product-specified lower tension Tmin (example)
  • Product-specified upper tension Tmax (example)

Results

  • Tension T in one belt span (N)
  • Fundamental frequency f (Hz)
  • Transverse wave speed c (m/s)
  • Frequency fmin at lower tension limit (Hz)
  • Frequency fmax at upper tension limit (Hz)

T = 4 μ L² f²; f = √(T/μ)/(2L); c = √(T/μ).

Fundamental transverse vibration of a uniform taut flexible string, neglecting bending stiffness. L is the free length between tangent points, not pulley-centre distance or total belt length. μ covers the entire belt width in kg/m. Do not substitute a harmonic frequency. Short, thick or toothed belts and end restraint may require product-specific correction. Replace example limits with the actual product/operating limits. This alone does not establish optimum tension, transmission capacity or bearing load.

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図で条件を整理してから計算し、最後に実際の部品仕様を確認します。

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Understand conditions with diagrams, calculate, then verify actual specifications.