Shaft critical speed API

Computes the first critical (whirling) speed by the Rayleigh static-deflection method ωc=√(g/δ), deriving δ from EI beam theory if not supplied, and the operating-speed resonance margin. Answers 'At what rpm does my shaft whirl?', 'Is my operating speed safely clear of resonance?'.

Price$0.06per request

MethodPOST

Route/v1/engineering/shaft-critical-speed

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

shaftcritical-speedwhirlingrayleighresonancerpmrotordynamicsmachine-design

API URLhttps://x402.hexl.dev/v1/engineering/shaft-critical-speed

Integration docs

Example request

{
  "staticDeflectionM": 0.0005,
  "operatingSpeedRpm": 900
}

Example response

{
  "staticDeflectionM": 0.0005,
  "criticalAngularSpeedRadS": 140.0475,
  "criticalSpeedRpm": 1337.355,
  "deflectionSource": "supplied static deflection",
  "formula": "ωc = √(g/δ), Nc = (30/π)·√(g/δ)",
  "interpretation": "Keep operating speed well clear (≳25%) of Nc to avoid resonant whirl.",
  "operatingSpeedRpm": 900,
  "speedRatioNoverNc": 0.673,
  "nearResonance": false
}

Input schema

{
  "type": "object",
  "required": [],
  "properties": {
    "staticDeflectionM": {
      "type": "number",
      "examples": [
        0.0005
      ]
    },
    "operatingSpeedRpm": {
      "type": "number",
      "examples": [
        900
      ]
    },
    "loadN": {
      "type": "number",
      "examples": [
        500
      ]
    },
    "spanM": {
      "type": "number",
      "examples": [
        1
      ]
    },
    "youngsModulusGpa": {
      "type": "number",
      "examples": [
        200
      ]
    },
    "momentOfInertiaM4": {
      "type": "number",
      "examples": [
        1e-7
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}