Gear-tooth Lewis bending API

Computes spur-gear tooth-root bending stress σ=Wt/(F·m·Y) via the Lewis equation, with the Barth dynamic factor and the safe tangential load for an allowable stress. Answers 'What is the root bending stress on my gear tooth?', 'What tangential load can it carry?'.

Price$0.06per request

MethodPOST

Route/v1/engineering/gear-lewis-bending

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

gearlewistooth-bendingspur-gearroot-stressbarth-factormodulemachine-design

API URLhttps://x402.hexl.dev/v1/engineering/gear-lewis-bending

Integration docs

Example request

{
  "tangentialLoadN": 3000,
  "moduleMm": 4,
  "faceWidthMm": 40,
  "lewisFormFactorY": 0.32,
  "pitchLineVelocityMs": 12.2,
  "allowableStressMpa": 200
}

Example response

{
  "rootBendingStressMpa": 58.5938,
  "formula": "σ = Wt/(F·m·Y), Kv = (6.1+V)/6.1 (Barth)",
  "interpretation": "Lewis treats the tooth as a cantilever; small module or face width spikes root stress.",
  "velocityFactorKv": 3,
  "dynamicBendingStressMpa": 175.7812,
  "safeTangentialLoadN": 10240,
  "factorOfSafety": 3.4133
}

Input schema

{
  "type": "object",
  "required": [
    "tangentialLoadN",
    "moduleMm",
    "faceWidthMm",
    "lewisFormFactorY"
  ],
  "properties": {
    "tangentialLoadN": {
      "type": "number",
      "examples": [
        3000
      ]
    },
    "moduleMm": {
      "type": "number",
      "examples": [
        4
      ]
    },
    "faceWidthMm": {
      "type": "number",
      "examples": [
        40
      ]
    },
    "lewisFormFactorY": {
      "type": "number",
      "examples": [
        0.32
      ]
    },
    "pitchLineVelocityMs": {
      "type": "number",
      "examples": [
        12.2
      ]
    },
    "allowableStressMpa": {
      "type": "number",
      "examples": [
        200
      ]
    }
  }
}

Output schema

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