Hertzian Cylinder Contact Stress Calculator
Ideal Hertz line contact b=√(4W′R′/πE′), p0=2W′/(πb), independently verified effective radii/modulus convention. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
Hertz line contact models elastic pressure over a cylindrical contact region.
Hertz line contact models elastic pressure over a cylindrical contact region.1
Effective radius and modulus must match the chosen contact assumptions. Use Hertzian Cylinder Contact Stress Calculator to evaluate the supplied inputs under the specific model below.
When to use Hertzian Cylinder Contact Stress Calculator
Use Hertzian Cylinder Contact Stress Calculator to evaluate the supplied inputs under the specific model below. Establish the units, measurement scope and applicable model or recipe assumptions before entering values.
How to use Hertzian Cylinder Contact Stress Calculator and understand its results
- Establish the units, measurement scope and applicable model or recipe assumptions before entering values.
- Enter Normal force n, Contact length m, Effective radius m, Effective elastic modulus pa using the field table and validation rules below, then run the tool.
- Read Hertz line half width m, Hertz line peak pressure pa and interpret units, signs, ordering and placeholders as explained below.
- If the tool reports an input error, correct that field and rerun. A successful false result, empty match list or unknown-evidence placeholder has the specific meaning described here; check the limitations before applying the result.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| normalForceN | Normal force n | number | Required; constraints below |
| contactLengthM | Contact length m | number | Required; constraints below |
| effectiveRadiusM | Effective radius m | number | Required; constraints below |
| effectiveElasticModulusPa | Effective elastic modulus pa | number | Required; constraints below |
Enter nonnegative normal force F in N and positive contact length L in m, effective radius R in m and effective modulus E in Pa. Set line load q=F/L. Zero load returns zero half-width and pressure. Otherwise compute the elastic contact half-width and peak pressure shown below, without checking the independently chosen equivalent geometry or elastic regime.
q = F/L; b = sqrt(4qR/(πE)); peakPressurePa = 2q/(πb) Field order, units and branch conditions follow the implementation explanation above.
| Output field | Meaning | Value type |
|---|---|---|
| hertzLineHalfWidthM | Hertz line half width m | number |
| hertzLinePeakPressurePa | Hertz line peak pressure pa | number |
{
"input": {
"normalForceN": 10,
"contactLengthM": 2,
"effectiveRadiusM": 0.5,
"effectiveElasticModulusPa": 100
},
"output": {
"hertzLineHalfWidthM": 0.1784124116152771,
"hertzLinePeakPressurePa": 17.841241161527716
}
}Limitations and assumptions
Effective radius and modulus must match the chosen contact assumptions. Apply the exact scope and assumptions described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are stated above; extremely large inputs or outputs can also be rejected. These errors differ from successful results such as false, no matches or unknown evidence.
Alternative or Complementary methods
Use Brinell Hardness Indentation Calculator for a related task: Brinell hardness relates force to the curved indentation area under a ball.
Use Bracket Plate Yield Calculator for a related task: A rectangular plate's plastic moment can be converted into an ideal cantilever point load.
References
Similar or alternative tools
- Brinell Hardness Indentation Calculator
Brinell hardness relates force to the curved indentation area under a ball.
- Bracket Plate Yield Calculator
A rectangular plate's plastic moment can be converted into an ideal cantilever point load.