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Belt conveyor pull, torque and traction calculator

Engineering calculators (Beta)

Calculate drive pull from carry/return resistance and the whole moving belt mass. Optionally check flat-belt drum traction, maximum tension and load slip.

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

Nc=(m+mb/2)g cosθ; Nr=(mb/2)g cosθ; Rc=μbNc or ccNc; Rr=crNr; Fu=(m+mb)a+mg sinθ+Rc+Rr+F₀+Jf a/r²; Td=Fu r+Jd a/r; ωd=v/r; Tm=Td/(iη) if Td≥0, otherwise Td/i. Th=Tl+|Fu|; Tl,min=|Fu|/[exp(μdβ)−1]; Fproduct=m(a+g sinθ).

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

荷物側・戻り側の抵抗とベルト全周の移動質量から駆動力を求めます。任意で平ベルトのドラムすべり・最大張力・荷物のすべりを比較できます。

入力・結果・適用条件を確認する

主な入力

  • ベルトの荷物側の支持方法
  • 同時に載っている荷物の総質量 m
  • ベルト全周の総質量 mb（上側＋戻り側）
  • 駆動ドラムの有効直径 D
  • ベルト速度 v（正方向）
  • 進行方向の加速度 a（減速は負）
  • 搬送勾配 θ（下りは負）
  • ベルト下面と支持板の動摩擦係数 μb（例）
  • 荷物側の等価抵抗係数 cc（例）
  • 戻り側の等価抵抗係数 cr（例）
  • 上記に含めない追加走行抵抗 F₀（例）
  • 従動ドラム・支持ローラー等のドラム径換算慣性 Jf（例）
  • 駆動ドラム側の回転慣性 Jd（例）
  • 減速比 i=モーター回転数／駆動回転数
  • 正方向駆動の伝達効率 η
  • 現在の回転数・運転方向で使えるモーター軸トルク上限 Tlim（例）
  • 張力・ドラムと荷物のすべりも比較する
  • 運転中の低張力側張力 Tl（初期張力とは別、例）
  • ベルトとドラム間の静摩擦係数 μd（例）
  • 駆動ドラムへの巻付角 β
  • 実条件でのベルト・接合部の許容総張力 Tb（例）
  • 荷物とベルト上面間の静摩擦係数 μt（例）

得られる結果

  • 必要モーター軸トルク Tm（負は制動） (N·m)
  • ドラムがベルトへ伝える駆動力 Fu（符号付き） (N)
  • 駆動ドラム軸のトルク Td（慣性を含む） (N·m)
  • 駆動ドラム回転数 nd (rpm)
  • モーター回転数 nm (rpm)
  • 正方向の必要モーター入力動力 (W)
  • 損失を見込まない制動吸収動力 (W)
  • 荷物側＋戻り側＋追加の走行抵抗 (N)
  • 荷物側の走行抵抗 (N)
  • 戻り側の走行抵抗 (N)
  • 入力トルク上限／必要トルク絶対値 (—)
  • 必要な高張力側張力 Th (N)
  • すべらないための低張力側張力の理論下限 (N)
  • ドラムで伝達可能な力／必要駆動力絶対値 (—)
  • 入力許容総張力／必要高張力側張力 (—)
  • ベルトから荷物へ伝える接触力（符号付き） (N)
  • 荷物接触の摩擦上限／必要接触力絶対値 (—)

Nc=(m+mb/2)g cosθ; Nr=(mb/2)g cosθ; Rc=μbNc or ccNc; Rr=crNr; Fu=(m+mb)a+mg sinθ+Rc+Rr+F₀+Jf a/r²; Td=Fu r+Jd a/r; ωd=v/r; Tm=Td/(iη) if Td≥0, otherwise Td/i. Th=Tl+|Fu|; Tl,min=|Fu|/[exp(μdβ)−1]; Fproduct=m(a+g sinθ).

平ベルトで同一長さの荷物側・戻り側を持ち、ベルト質量を半分ずつに分ける基本モデルです。正方向走行、v≥0、|θ|≤60°。ベルト全周質量mbの加速を含みますが、一周で相殺するベルト自重の勾配成分は荷物の持上げ荷重へ足しません。荷物側のμbと荷物上面のμtは別の接触です。ローラーベッドのcc・戻り側crは指定基準荷重に対する等価値で、ローラー自重、軸受、曲げ、スカート等の別抵抗は必要に応じF₀へ入れ、二重計上を避けます。Jfは従動ドラム・支持ローラー等の自由回転体、Jdは駆動ドラム側の回転体を駆動ドラム径へ換算した慣性です。Jj(ωj/ωd)²を各群で合計します。ベルトの並進質量とモーターローターは含めません。Jfの加速分は張力差Fuに含み、Jdの加速分は駆動軸トルクだけに足します。平ベルトの巻付摩擦は張力差Fuに適用し、歯付きベルトの歯飛びやチェーンをこの式で判定しません。Tlは運転時の低張力側値を別に指定し、初期張力からの配分や必要テークアップ量は求めません。βはラジアン換算で計算します。Tbは幅全体・実接合・温度・速度に合う許容値です。荷物のすべりは搬送方向のみの合計比較で、転倒・蛇行・横滑りは別です。始動摩擦、蓄積搬送、カーブ、ベルトたるみ、過渡張力、軸荷重、構造強度、RMS・熱・寿命は対象外です。制動は逆損失を無視した換算で、装置の停止・回生能力は別途確認します。

関連する計算

What this calculator does

Calculate drive pull from carry/return resistance and the whole moving belt mass. Optionally check flat-belt drum traction, maximum tension and load slip.

Inputs, outputs and applicability

Inputs

  • Carrying-run support
  • Total product mass m on the carrying run
  • Whole-loop belt mass mb, carrying plus return runs
  • Effective drive drum diameter D
  • Belt speed v in the positive direction
  • Acceleration a (negative for deceleration)
  • Conveying slope θ (negative downhill)
  • Kinetic friction μb between belt underside and slider bed (example)
  • Equivalent carrying-run resistance coefficient cc (example)
  • Equivalent return-run resistance coefficient cr (example)
  • Additional running resistance F₀ excluded above (example)
  • Free drum/idler inertia Jf referred to the drive drum (example)
  • Driven-drum-side rotating inertia Jd (example)
  • Reduction i = motor speed / drive speed
  • Forward-drive efficiency η
  • Applicable motor-shaft torque limit Tlim at this speed/direction (example)
  • Check tension, drum traction and product slip
  • Operating low-side tension Tl, not initial pretension (example)
  • Static friction μd between belt and drum (example)
  • Drive-drum wrap angle β
  • Applicable allowable total belt/joint tension Tb (example)
  • Static friction μt between product and belt top (example)

Results

  • Required motor-shaft torque Tm (negative means braking) (N·m)
  • Drive pull Fu transmitted by the drum to the belt (signed) (N)
  • Drive-drum shaft torque Td including inertia (N·m)
  • Drive drum speed nd (rpm)
  • Motor speed nm (rpm)
  • Required forward-drive motor input power (W)
  • Lossless braking power to absorb (W)
  • Carry + return + additional running resistance (N)
  • Carrying-run resistance (N)
  • Return-run resistance (N)
  • Entered torque limit / absolute required torque (—)
  • Required high-side tension Th (N)
  • Theoretical minimum low-side tension for drum traction (N)
  • Available drum traction / absolute drive pull (—)
  • Entered total tension allowable / required high-side tension (—)
  • Contact force from belt to product (signed) (N)
  • Product traction limit / absolute required product contact force (—)

Nc=(m+mb/2)g cosθ; Nr=(mb/2)g cosθ; Rc=μbNc or ccNc; Rr=crNr; Fu=(m+mb)a+mg sinθ+Rc+Rr+F₀+Jf a/r²; Td=Fu r+Jd a/r; ωd=v/r; Tm=Td/(iη) if Td≥0, otherwise Td/i. Th=Tl+|Fu|; Tl,min=|Fu|/[exp(μdβ)−1]; Fproduct=m(a+g sinθ).

Basic flat-belt model with equal carrying/return lengths, splitting total belt mass equally. Positive travel, v≥0 and |θ|≤60°. Includes acceleration of the whole belt; its closed-loop gravity terms cancel, so only products contribute net gravity lift. Underside μb and product-top μt describe different contacts. Roller-bed cc and return cr are equivalent coefficients based on the stated normal loads; add excluded roller weight/bearing/flexure/skirt resistance in F₀ without double counting. Jf covers free drums/idlers, and Jd covers driven-drum-side rotating bodies, each referred by summing Jj(ωj/ωd)². Exclude translating belt mass and motor rotor inertia. Free-body acceleration enters Fu; driven-side inertia adds shaft torque only. Capstan traction applies to flat-belt tension difference, not toothed-belt tooth skip or chains. Enter operating low-side Tl separately; initial-pretension redistribution/take-up is not solved. β is converted to radians. Tb must apply to the full width, joint, temperature and speed. Product slip is an aggregate along-route check; tipping, tracking and lateral slip are separate. Excludes breakaway friction, accumulation, curves, belt sag, transient tension, shaft loads, structural checks, RMS/thermal duty and life. Braking uses lossless reverse conversion, not a stop/regeneration approval.

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