Bearing Selection (`bearings`)

Check	IND	US	EU	ISO
Dynamic load rating utilization	implemented	—	—	—
Modified rating life Lnm (L_req/Lnm)	implemented	—	—	—
Static load rating C₀/P₀	implemented	—	—	—
Limiting speed margin	implemented	—	—	—

Purpose

Rolling-element bearing screening per ISO 281 (basic and modified rating life) and ISO 76 static load check. Multi-manufacturer catalog (SKF, FAG, NSK, Timken, NTN) with application profiles, series/sealing filters, and representative C, C₀, geometry, and limiting speed.

Physics & theory

Basic rating life L₁₀ is the life in revolutions (or hours at speed n) exceeded by 90% of bearings under constant equivalent load P = C:

L_{10 h} = \frac{a _{1} \cdot 1 0 ^{6}}{60 n} (\frac{C}{P})^{p}, p = 3 (ball), 10/3 (roller)

Modified rating life (ISO 281:2007 / SKF):

L_{nm} = a_{1} \cdot a_{SKF} \cdot (C / P)^{p} \cdot 1 0^{6} / (60 n), a_{SKF} \equiv a_{ISO}

where aSKF (ISO 281 aISO) is computed from viscosity ratio κ = ν/ν₁, contamination factor eC (ηc), and fatigue load limit Pu (catalog datasheet Pu when available; otherwise estimated as 0.025C for ball, 0.03C for roller).

Life model ceiling (screening, opt-in):

Method	Behavior
ISO 281 (default)	Lnm = a₁ · aISO · (C/P)^p; optional misalignment life derate a_mis
ISO 16281 screen	Adjusts P → P_adj = P · f_clearance · f_misalign · f_distrib (not full ISO 16281:2025 FEA)
Stress-life screen	Lnm uses a₁ · aISO · a_stress · … — transparent PhyCalcPro curve; not SKF GBLM / AFC
Hybrid / full ceramic	ISO 20056-inspired C / speed / life factors on rolling elements

Shaft FEM handoff can publish bearing slopes (rad) → misalignment (mrad) for the ceiling path.

Static safety (ISO 76):

s_{0} = C_{0} / P_{0} w h er e P_{0} i s t h ee q u i v a l e n t s t a t i c l o a d

Paired arrangements (O / X / T): treated as first-class engineering objects with:

Property	Screening model
Preload	Class as % of C (light/medium/heavy) or override force; folded into life Fa
Stiffness	Ka / Kr / Km with O ≫ X ≫ T moment multipliers
Axial displacement	δa = Fa / Ka (µm)
Thermal	Differential growth → preload shift; locating+floating float check
Rigidity comparison	Side-by-side O / X / T Ka, Km, δa, Km ratio vs O

Loads are split per bearing; system life is governed by the Weibull combination of station modified lives.

Variable load (ISO 281-1): optional two-step spectrum computes equivalent load and Palmgren-Miner combined life.

Inputs

Parameter	Description
Fr, Fa	Radial and axial loads
n	Operating speed (rpm)
L₁₀h target	Required rating life
Application profile	General radial, combined loads, heavy shock, high speed, space limited, thrust, locating/floating
Manufacturer	SKF, FAG, NSK, Timken, NTN
Bearing family / type	Deep groove, angular contact, NU/NJ/NUP cylindrical, tapered, spherical, needle, self-aligning, thrust
Series & sealing	Catalog series (62xx, 302xx, …) and open/shielded/sealed
Catalog designation	C, C₀, n_lim from catalog
Reliability a₁	90–99%
Lubricant	Oil or grease (ISO VG) + operating temperature
Contamination eC	ISO 281 cleanliness classes
Life method	ISO 281 / ISO 16281 screen / stress-life screen
Misalignment	Manual mrad and/or shaft FEM slopes
Rolling elements	Steel / hybrid ceramic / full ceramic
Internal clearance	C2 / CN / C3 / C4 (fit recommendation)
Mounting arrangement	Single, back-to-back (O), face-to-face (X), tandem (T)
Duplex preload class	None / light / medium / heavy (or override force)
Bearing span / float	Locating+floating thermal float; duplex thermal preload span
Variable load spectrum	Up to 12 ISO 281-1 steps (optional per-step speed)
Ring temperatures	Optional inner/outer temps for operating clearance
Ratings override	User C / C₀ / Pu when datasheet differs from catalog
Max bore	Shaft diameter constraint for auto-selection
Two-bearing wizard	Locating + floating system size/apply

Outputs

Equivalent loads P and P₀ (paired per-station when applicable)
Modified Lnm and basic L₁₀ with first-class factors: a₁, aSKF (≡ aISO), κ, eC (ηc), ν / ν₁, Pu/P
Arrangement analysis: preload, Ka/Kr/Km, axial displacement δa, thermal preload shift, O/X/T rigidity comparison
Defect frequencies BPFO / BPFI / BSF / FTF (screening geometry)
Grease life L₁₀h and/or relubrication interval tf
Adjusted reference speed n_θ and friction energy / CO₂ screening
Side-by-side OEM compare under the same duty
Intelligent recommendation with life / safety / cost and Explain Recommendation (Engineering Advisor narrative)
Persistent Design Summary right rail (bearing type, loads, Lnm, safety, ISO 281, catalog, status) — updates continuously as inputs change
PDF / Excel packages with named sections: Design Summary, Inputs, Catalog, ISO 281 factors, Arrangement, Recommendation, Checks, Formulas, Standards, Charts
Mounted kit BOM (housing SNL/UCP/FY/SAF-class + seal + grease)
Dynamic utilization P/C, static safety C₀/P₀, speed margin n_lim/n
Minimum load (skidding), SKF-inspired Mrr/Msl friction torque and power loss (screening)
Recommended shaft/housing fits and differential ring-ΔT operating clearance
Cross-OEM interchange candidates (same bore/type/C class)
Required C and C₀ for target life
Governing failure mode

Design codes & checks

ISO 281:2007 — Basic and modified rating life
ISO 76 — Static load rating screening
Catalog limiting speed (grease) and reference speed (oil) where listed
Defect frequencies — kinematic screening (verify Z, Bd against OEM for CM)

Assumptions & limitations

Constant load and speed unless variable spectrum is enabled
Pu from catalog with explicit datasheet vs C₀-ratio provenance; user override available
Representative catalog — not full vendor databases
Friction is screening Mrr/Msl — not full SKF four-component model
ISO 16281 and stress-life paths are screening only — not vendor GBLM, AFC, Bearinx, or full ISO 16281:2025
Housing SKUs are screening-class (SNL/UCP/…) — not full OEM mounted-product databases
CO₂ from friction power only — not a product LCA
Duplex paired C catalog multipliers use tandem axial convention (screening)
Temperature derating on C above 120 °C (screening factor)

Verification

CI: bearings-indicative-*.json (multiple rolling cases)
Gold harness: npm run test:bearings-gold / Vitest bearingsGold.test.ts (screening_reference; vendor cases pending paste)
Vitest: engine.test.ts, industryParity.test.ts, lifeModelCeiling.test.ts, auxMounted.test.ts
Engineer sign-off: validation-master-checklist.md (Machine → bearings) — pending ±5% vendor gold

Design workflow

Validate: ISO 281/76 forward check on selected designation.
Auto-design: Ranks catalog entries by manufacturer, application profile, life utilization, static SF, and speed margin within bore limit. Design mode passes the UI lubricant type, ISO VG, operating temperature, and contamination into ISO 281 screening (not fixed VG68 / normal_clean).
Handoff: Receives Fr₀/Fr₁, span, slopes from shafts (auto-apply); Fa may still need gear/user input (planar FEM warning).
System wizard: Size locating + floating pair and apply both designations.

References

ISO 281:2007 — Dynamic load ratings and rating life
ISO 76 — Static load ratings
Shigley, Ch. 11; SKF Rolling Bearings Catalogue

Bearing Selection

Assumptions

Limitations

Engineering checks