Source: https://guthlabs.ai/docs/instruments/bearing-equivalent-dynamic-load-calculator/

instrument / verified-clean

# Bearing Equivalent Dynamic Load Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/bearing-equivalent-dynamic-load-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/bearing-equivalent-dynamic-load-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/bearing-equivalent-dynamic-load-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/bearing-equivalent-dynamic-load-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

**Tranche**: tranche-7

**Evidence ID**: t7-061

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The arithmetic formula is standard, but the instrument specification is underspecified for a reliable lookup-table implementation. It must identify the bearing manufacturer or table convention, bearing type and geometry, the e-ratio selection rule, valid input ranges, and pure-axial-load behavior. The honest label should state that the result is an equivalent dynamic load only, not bearing life or bearing-selection approval.

### Formula and scope findings

- P = XFr + YFa is the standard equivalent dynamic bearing-load equation only after the bearing type, contact angle, load ratio Fa/Fr, and applicable factor table have been selected.

- The specification does not define how X and Y are selected from bearing type/e-ratio tables. X and Y are not universal constants; they vary by bearing construction, contact angle, row arrangement, and manufacturer table.

- The specification omits the usual branch condition comparing Fa/Fr with e. For example, a commonly tabulated single-row deep-groove ball-bearing convention uses X=1, Y=0 when Fa/Fr <= e, and different factors when Fa/Fr > e.

- The specification does not state constraints that Fr and Fa must be nonnegative loads expressed in compatible units.

- The specification does not define handling for pure axial loading Fr=0, for which Fa/Fr is undefined and the applicable bearing calculation may require a separate manufacturer rule.

### Unit assumptions

- Fr and Fa must use the same force unit; P has that same force unit.

- The test vectors use newtons unless explicitly marked kN.

- X and Y are dimensionless.

- The e values and X/Y factors are dimensionless and apply only to the stated bearing-table convention.

- The table fragments use a widely tabulated ISO 281-based bearing-factor convention for single-row deep-groove ball bearings; the exact bearing manufacturer's catalog must take precedence for a production calculator.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The calculator cannot determine the formula branch without the missing bearing type/e-ratio factor tables, and an extreme but representable input combination overflows a typical floating-point implementation. Signed axial input also produces a physically invalid negative result unless the magnitude convention is enforced.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "bearing_type": "single-row deep-groove ball bearing, 15-degree contact-angle table",
    "Fr": 1000,
    "Fa": 0,
    "Fr_unit": "N",
    "Fa_unit": "N",
    "e": 0.22,
    "X": 1,
    "Y": 0
  },
  "expected_outputs": {
    "P": 1000,
    "P_unit": "N"
  },
  "reference_data": {
    "bearing_table": "single-row deep-groove ball bearing, 15-degree contact-angle factor table",
    "condition": "Fa/Fr <= e",
    "e": 0.22,
    "X": 1,
    "Y": 0,
    "source_convention": "widely tabulated standard value, ISO 281-based bearing-factor convention"
  },
  "working": "Fa/Fr = 0/1000 = 0. Since 0 <= e = 0.22, use X = 1 and Y = 0. P = XFr + YFa = (1)(1000 N) + (0)(0 N) = 1000 N."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

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

- `BOUNDARY_HAZARD_CATALOG.json`