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Motor acceleration torque calculator

Engineering calculators (Beta)

Find motor shaft torque during constant acceleration, including inertia and gearing.

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

Jref = Jload/i²; α = ω/t; T = TL/(iη) + (Jm + Jref/η)α

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.

図で学んで、計算に戻る

計算の解説一覧 · 用途からツールを探す

Learn with diagrams, then calculate

All calculation guides · Find a tool by task

この計算で求められること

負荷慣性・減速比・加速時間から、加速中の軸トルクを求めます。

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

  • 出力軸側の負荷慣性 Jload (kg·m² / kg·cm² / kg·mm²)
  • モーター軸側の合計慣性 Jm (kg·m² / kg·cm² / kg·mm²)
  • 速度比 i = モーター速度 / 負荷速度 (—)
  • 減速機の正駆動効率 η (% / fraction / ‰)
  • 出力軸側の定常抵抗トルク TL (N·m / N·mm / mN·m)
  • 到達モーター速度 n (rpm / rad/s / °/s)
  • 停止からの加速時間 t (s / min / µs)

得られる結果

  • モーター側へ換算した負荷慣性 (kg·m²)
  • モーター角加速度 (rad/s²)
  • 定常抵抗分のトルク (N·m)
  • 慣性を加速するトルク (N·m)
  • 加速中の合計トルク (N·m)
  • 到達出力軸速度 (rpm)
  • 加速終了直前の軸動力 (kW)

計算式の概要

Jref = Jload/i²; α = ω/t; T = TL/(iη) + (Jm + Jref/η)α

停止から一定角加速度で正方向へ加速する理想モデルです。Jmにはローター・入力側回転部を含めてください。TLに加速トルクを重複加算しないでください。減速・逆駆動・RMS・熱容量・トルク速度特性・ブレーキ保持は扱いません。表示値だけでモーターを選定できません。

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 motor shaft torque during constant acceleration, including inertia and gearing.

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

  • Load inertia at output shaft Jload (kg·m² / kg·cm² / kg·mm²)
  • Total input-side inertia Jm (kg·m² / kg·cm² / kg·mm²)
  • Speed ratio i = motor speed / load speed (—)
  • Forward gearbox efficiency η (% / fraction / ‰)
  • Steady resisting torque at output TL (N·m / N·mm / mN·m)
  • Final motor speed n (rpm / rad/s / °/s)
  • Acceleration time from rest t (s / min / µs)

Calculated results

  • Load inertia reflected to input (kg·m²)
  • Motor angular acceleration (rad/s²)
  • Steady motor torque (N·m)
  • Acceleration torque (N·m)
  • Total torque during acceleration (N·m)
  • Final output speed (rpm)
  • Shaft power just before acceleration ends (kW)

Formula overview

Jref = Jload/i²; α = ω/t; T = TL/(iη) + (Jm + Jref/η)α

Constant forward acceleration from rest. Include rotor and other input-side rotating inertia in Jm. Do not include acceleration torque again in TL. Deceleration, back-driving, RMS torque, thermal duty, torque-speed limits and brake holding are excluded. This is not a complete motor selection.

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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入力する単位を確認・換算する

Check and convert input units

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.

数値の感覚を、図と動きで確かめる

説明用の別モデルです。適用条件を確認してください。数値は自動転記しません。

See the idea in diagrams and motion

A separate explanatory model. Check its assumptions; values are not transferred.