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Hertz contact stress: cylinders & spheres calculator

Engineering calculators (Beta)

Approximate cam/roller contact using local cylindrical or spherical curvature.

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

1/E*=(1−ν₁²)/E₁+(1−ν₂²)/E₂; line b=√(4FR*/(πLE*)), p₀=2F/(πbL); sphere a=(3FR*/(4E*))⅓, p₀=3F/(2πa²)

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

カム・ローラーなどを、局所曲率で円筒または球の接触として近似します。

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

  • 接触の形 (—)
  • 法線荷重 F (N / kN / mN)
  • 接触側の凸半径 R₁ (mm / cm / m)
  • 相手側の曲率半径 R₂ (mm / cm / m)
  • 相手面 (—)
  • 有効接触長 L (mm / cm / m)
  • 材料1のヤング率 (GPa / MPa / Pa)
  • 材料1のポアソン比 (—)
  • 材料2のヤング率 (GPa / MPa / Pa)
  • 材料2のポアソン比 (—)

得られる結果

  • 等価弾性率 E* (GPa)
  • 等価曲率半径 R* (mm)
  • 接触半幅b／接触円半径a (mm)
  • 最大接触圧 p₀ (MPa)
  • 球接触の弾性接近量（線接触は—） (mm)

計算式の概要

1/E*=(1−ν₁²)/E₁+(1−ν₂²)/E₂; line b=√(4FR*/(πLE*)), p₀=2F/(πbL); sphere a=(3FR*/(4E*))⅓, p₀=3F/(2πa²)

弾性・滑らかな非適合接触の基本式。カム全体の形状・圧力角・動荷重から法線力を求める機能ではありません。局所曲率と法線荷重を指定します。端部・潤滑・塑性・疲労寿命は含みません。

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

Approximate cam/roller contact using local cylindrical or spherical curvature.

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

  • Contact geometry (—)
  • Normal force F (N / kN / mN)
  • Convex radius R₁ (mm / cm / m)
  • Mating curvature radius R₂ (mm / cm / m)
  • Mating surface (—)
  • Effective contact length L (mm / cm / m)
  • Material 1 Young modulus (GPa / MPa / Pa)
  • Material 1 Poisson ratio (—)
  • Material 2 Young modulus (GPa / MPa / Pa)
  • Material 2 Poisson ratio (—)

Calculated results

  • Effective modulus E* (GPa)
  • Effective curvature radius R* (mm)
  • Contact half-width b / radius a (mm)
  • Maximum contact pressure p₀ (MPa)
  • Spherical elastic approach (line: —) (mm)

Formula overview

1/E*=(1−ν₁²)/E₁+(1−ν₂²)/E₂; line b=√(4FR*/(πLE*)), p₀=2F/(πbL); sphere a=(3FR*/(4E*))⅓, p₀=3F/(2πa²)

Elastic smooth nonconformal contact. This does not derive cam normal force from profile, pressure angle or dynamics; supply local curvature and normal load. Edge effects, lubrication, plasticity and fatigue life are excluded.

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

入力する単位を確認・換算する

Check and convert input units

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.