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Ball / lead screw theoretical thrust calculator

Engineering calculators (Beta)

Find drive torque from required thrust, or thrust from a known torque.

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

Next after thrust: screw-shaft buckling and critical speed

Formula and applicability

T = Fℓ/(2πη), F = 2πηT/ℓ, v = ωℓ/(2π), Pout = Fv, Pin = Tω

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

必要な推力からトルク、または既知のトルクから推力を求めます。

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

  • 必要な軸方向推力 F (N / kN / mN)
  • ねじに入力するトルク T (N·m / N·mm / mN·m)
  • リード ℓ(1回転の移動量) (mm / cm / m)
  • 正作動の効率 η (% / fraction / ‰)
  • ねじの回転数 n / 角速度 ω (rpm / rad/s / °/s)

得られる結果

  • 軸方向推力 F (N)
  • ねじ軸の駆動トルク T (N·m)
  • 直線移動速度 v (m/s)
  • 直線側の機械動力 (W)
  • ねじ軸への入力動力 (W)

計算式の概要

T = Fℓ/(2πη), F = 2πηT/ℓ, v = ωℓ/(2π), Pout = Fv, Pin = Tω

ねじ軸から直線側へ動力を伝える正作動モデルです。リードは1回転の移動量で、多条ねじではピッチと異なります。ηは指定条件でのねじ効率です。予圧・支持軸受・シールなどの追加トルク、回転慣性、危険速度、座屈、寿命、逆駆動・セルフロック・ブレーキ保持は含みません。締結ボルトの軸力とは別の計算です。

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 drive torque from required thrust, or thrust from a known torque.

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

  • Required axial thrust F (N / kN / mN)
  • Input torque at the screw T (N·m / N·mm / mN·m)
  • Lead ℓ (travel per revolution) (mm / cm / m)
  • Forward-drive efficiency η (% / fraction / ‰)
  • Screw speed n / angular velocity ω (rpm / rad/s / °/s)

Calculated results

  • Axial thrust F (N)
  • Drive torque at screw T (N·m)
  • Linear speed v (m/s)
  • Linear output mechanical power (W)
  • Screw-shaft input power (W)

Formula overview

T = Fℓ/(2πη), F = 2πηT/ℓ, v = ωℓ/(2π), Pout = Fv, Pin = Tω

Forward power transmission from screw shaft to linear load. Lead is travel per revolution and differs from pitch on multi-start screws. η is screw efficiency for the actual conditions. Preload, bearing and seal torque, rotational inertia, critical speed, buckling, life, backdriving, self-locking and brake holding are excluded. This differs from bolt tightening preload.

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.

Related tools

目的から順に確認する設計ガイド

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。

Purpose-based design guides

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

See the motion in an animation

Compare ball-screw size and speed in an animation →

Calculation inputs are not transferred automatically. Enter the required dimensions and speed in the animation.