Source: https://guthlabs.ai/docs/instruments/gear-tooth-bending-stress-lewis-equation/implementation/

instrument implementation / implementation-contract

# Gear Tooth Bending Stress (Lewis Equation) implementation

A source-bound implementation contract for Gear Tooth Bending Stress (Lewis Equation); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t7-032

**Effect**: Computation or source lookup only

## Input and validation requirements

The zero-face-width input produces an undefined result and must be rejected. The specification also does not define the Lewis-factor table, interpolation behavior, or whether tangential force is signed or a positive magnitude, leaving lookup and convention hazards unresolved.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "Ft_N": 2000,
    "face_width_b_mm": 40,
    "module_m_mm": 2.5,
    "tooth_count": 20,
    "Lewis_factor_Y": 0.322
  },
  "expected_outputs": {
    "sigma_bending_MPa": 62.1118
  },
  "reference_data": {
    "Lewis_form_factor_20deg_full_depth_involute": {
      "tooth_count_20": 0.322
    },
    "source_convention": "Widely tabulated standard value; 20-degree full-depth involute Lewis factors, common Shigley machine-design textbook convention"
  },
  "working": "Denominator = b*m*Y = 40 mm * 2.5 mm * 0.322 = 32.2 mm^2. sigma = Ft/denominator = 2000 N / 32.2 mm^2 = 62.1118 N/mm^2 = 62.1118 MPa."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gear-tooth-bending-stress-lewis-equation/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/gear-tooth-bending-stress-lewis-equation/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gear-tooth-bending-stress-lewis-equation/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche7/tranche7-results.json`