spherical-roller-bearing

name	spherical-roller-bearing
description	Spherical roller bearing (SRB) design and selection — radial and axial load capacity, dynamic load rating C, static load rating C0, equivalent dynamic load P (combined radial Fr + axial Fa), ISO 281 L10 life calculation, modified rating life Lnm (ISO 281:2007), lubrication (grease vs. oil, speed parameter nDm), clearance groups (C3, C4), housing fits, shaft fits, preload vs. clearance, misalignment tolerance (2–3°), and SKF/FAG/Timken catalog selection.
metadata	{"priority":7,"promptSignals":{"phrases":["spherical roller bearing","SRB","roller bearing selection","bearing life calculation","L10 life","ISO 281"],"minScore":3}}

Spherical Roller Bearing — Complete Skill

Spherical Roller Bearing Design

Key Feature — Misalignment Tolerance

Defining characteristic: outer ring has spherical raceway (concave) → allows self-alignment up to ±2–3° shaft misalignment without loss of load capacity

Applications: paper mills, mining equipment, heavy machinery, conveyor drives, fans, marine propeller shafts — anywhere shaft deflection or housing misalignment is expected

Bearing geometry: Two rows of symmetrical barrel-shaped rollers; common spherical center on outer race Inner ring: two raceways at angle α (contact angle); outer ring: one common spherical surface Contact angle: α = 10–14° (typical); higher α → higher axial load capacity

Load Rating Basics

Dynamic and Static Load Ratings

Dynamic radial load rating C [kN]: C = b_m × f_c × (i × l_eff × cos α)^(7/9) × Z^(3/4) × D_w^(29/27) [ISO 281; complex formula; use catalog value] Physical meaning: load for 10⁶ revolutions at L10 = 1 million rev (later changed to 10⁶ rev per ISO 281)

Static radial load rating C₀ [kN]: C₀ = f₀ × Z × D_w × l_eff × cos α [ISO 76] Based on contact stress limit p₀ = 4,000 MPa for roller bearings (vs. 4,200 for ball bearings)

Typical SRB ratings (for reference; always use catalog): SKF 22316E (80×170×58 mm): C = 520 kN; C₀ = 670 kN SKF 22322E (110×240×80 mm): C = 940 kN; C₀ = 1,290 kN SKF 23226CC (130×230×64 mm): C = 900 kN; C₀ = 1,160 kN

Equivalent Dynamic Bearing Load

Combined Radial + Axial Loading (SRB)

General equivalent load formula (ISO 281): P = F_r + Y₁ × F_a [for F_a/F_r ≤ e; P = radial load dominates] P = 0.67 × F_r + Y₂ × F_a [for F_a/F_r > e; axial load significant] [e, Y₁, Y₂ = bearing-specific factors from catalog; depend on contact angle α]

Typical factors (α ≈ 12°, double-row SRB): e ≈ 0.25; Y₁ ≈ 2.5; Y₂ ≈ 3.5 (approximate; consult manufacturer catalog for exact)

Example: F_r = 100 kN; F_a = 30 kN; e = 0.25; F_a/F_r = 0.30 > 0.25 P = 0.67 × 100 + 3.5 × 30 = 67 + 105 = 172 kN (axial load dominates)

Axial load limits: Maximum axial load: F_a ≤ 0.25 × C₀ (typical guideline; check manufacturer) For large axial loads: consider paired single-row tapered roller bearings or thrust bearings

Bearing Life Calculation

ISO 281 Basic Rating Life

L10 life (basic rating life — 10% failure probability): L10 = (C / P)^p × 10⁶ rev [p = 10/3 for roller bearings; p = 3 for ball bearings] L10h = L10 / (60 × n) [hours; n = speed [rpm]]

Example: C = 520 kN; P = 172 kN; n = 1,200 rpm L10 = (520/172)^(10/3) × 10⁶ = (3.02)^(3.33) × 10⁶ = 34.6 × 10⁶ rev L10h = 34.6×10⁶ / (60×1200) = 481 hours (quite short — P is large relative to C)

ISO 281:2007 Modified Rating Life

Lnm — accounts for lubrication, contamination, and material quality: Lnm = a₁ × a_ISO × L10 [ISO 281:2007 Eq. 4]

a₁ — life factor for reliability: a₁ = 1.0 for 10% failure probability (standard L10) a₁ = 0.62 for 5% failure probability (L5) a₁ = 0.21 for 1% failure probability (L1)

a_ISO — life modification factor: a_ISO = f(κ × η_c, P/C) [from ISO 281 Annex A charts] κ = ν / ν₁ [viscosity ratio; ν = actual oil viscosity at operating T; ν₁ = required viscosity from speed-diameter]

Required kinematic viscosity ν₁ (at operating temperature): ν₁ = 45,000 / (n^0.83 × d_m^0.5) [mm²/s; n [rpm]; d_m = bearing pitch diameter = (D+d)/2 [mm]] [Valid for n > 1,000 rpm; for n < 1,000: ν₁ = 4,500/n^0.5 × d_m^(0.083)]

Contamination factor η_c: Clean (filtered oil, ISO 14): η_c = 0.5–1.0 Slightly contaminated: η_c = 0.3–0.5 Contaminated: η_c = 0.1–0.3 Heavily contaminated: η_c < 0.1 → greatly reduced life

a_ISO lookup: κ ≥ 4 + η_c → a_ISO → 50 (upper limit) κ < 0.4 → a_ISO < 1 (poor lubrication → reduces life below L10) Typical well-lubricated: κ = 1–3; a_ISO = 3–10

Lubrication

Oil Lubrication

Viscosity selection: ISO VG 100–460 for industrial applications (speed-dependent) d_m × n < 5×10⁵: ISO VG 220–460 d_m × n = 5×10⁵ to 2×10⁶: ISO VG 100–220 d_m × n > 2×10⁶: ISO VG 46–100 (high speed; thin oil or oil-air)

Oil bath: fill to center of lowest roller; oil level sight glass Circulation (forced): filtered, cooled; for high-speed or high-temperature Oil-air lubrication: minimal oil quantity; efficient; for very high speed

Grease Lubrication

Grease compatibility: Lithium complex (Li-complex): -30 to +150°C; good shear stability; most common Polyurea: -20 to +160°C; good for high-speed; compatible with E2 seals Calcium sulfonate: -25 to +180°C; excellent water resistance; mining applications

Grease quantity: Initial fill: 30–50% of bearing cavity volume (overfilling causes churning heat) Re-greasing interval: t_grease [h] from SKF/FAG charts (depends on speed factor nDm, temperature, T_ambient) Rule of thumb: t_grease = 14,000 × (1/√(d_m × n) - 10^-5) [SKF simplified; d_m in mm; n in rpm]

SKF grease quantity per re-greasing: G_p = 0.005 × D × B [grams; D = bearing OD [mm]; B = bearing width [mm]]

Bearing Fits

Shaft and Housing Fits

Rotating inner ring (rotating shaft): interference fit on shaft → prevent creep Recommended shaft tolerances (ISO 286):

• Normal load: h6, j6, k6 (light to medium interference)
• Heavy load or impact: n6, m6 (greater interference) Interference = 6–15 μm for typical shaft diameters

Stationary outer ring (housing): clearance or transition fit → allow thermal expansion, adjustment Recommended housing bores: H7, G7 (clearance); J7, K7 (transition) For wandering ring (both inner and outer rotate): slight clearance → creep during life is acceptable with good sealing

Thermal expansion consideration: Temperature differential ΔT → ΔD = α_steel × d_shaft × ΔT α_steel = 11.7×10⁻⁶/°C; for d = 100 mm, ΔT = 50°C: ΔD = 0.059 mm Adjust interference to compensate (inner ring loosens with temperature rise for heated shaft)

Axial Retention

Locating vs. floating bearing: Locating (fixed) bearing: both rings constrained axially → takes axial load Floating (free) bearing: outer ring free in housing → accommodates thermal growth; no axial load SRBs commonly used as floating bearing (axial clearance in housing; outer ring slides)

Clearance group selection: Standard (CN): most applications; bearing has small operating clearance after fit-up and heating C3 (greater than CN): recommended when:

• Tight interference fits on shaft
• Operating temperature > 50°C above ambient
• Applications with heavy interference fits

C4 (greater than C3): heavy press fits + high temperature applications (e.g., hot strip mill work rolls) Selection: CN → C3 → C4 as interference fit increases and/or temperature increases

Seals and Shielding

SRB sealing options: Open (no seal): external sealing; grease must be contained by external labyrinth or seal Sealed (suffix S): factory-packed grease; no external relubrication required (life-greased) Shielded: light metal shield; reduces contamination; not sealed; regreasing possible

External seal types: V-ring (Nitrile): excellent for wet/contaminated environments; shaft speed up to 15 m/s Labyrinth seal: non-contact; low friction; oil or grease; for high-speed

Standards and References

Standard	Scope
ISO 281:2007	Rolling bearings — dynamic load ratings and rating life
ISO 76:2006	Rolling bearings — static load ratings
ISO 5593	Bearing vocabulary
ISO 15	Rolling bearings — radial internal clearance
SKF General Catalogue 6000	Comprehensive SRB selection and calculation
FAG Rolling Bearings Catalogue WL 41520	FAG equivalent

Output

Provide: application (speed n [rpm]; F_r [kN]; F_a [kN]; misalignment [°]; operating T [°C]; contamination level; life target L_required [hours]), bearing selection (series: 222xx/232xx/213xx/231xx; bore d [mm]; OD D [mm]; width B [mm]; C [kN]; C₀ [kN]; manufacturer reference), equivalent dynamic load P [kN] (Y₁/Y₂/e factors; F_a/F_r vs. e; calculation), basic L10 life [h] (C/P ratio; 10⁶ rev → hours at n rpm), modified Lnm life [h] (ν₁ [mm²/s] required; actual ν [mm²/s] at operating T; κ; η_c; a_ISO; Lnm = a₁×a_ISO×L10), lubrication (oil grade ISO VG or grease type; d_m×n speed factor; re-greasing interval [h] and quantity G_p [g]), shaft fit (ISO tolerance; interference Δ [μm]; check: interference vs. d/bore clearance group), housing fit (ISO tolerance; clearance group CN/C3/C4; basis), axial configuration (locating or floating; axial clearance in housing [mm]), and applicable standard (ISO 281:2007; ISO 15 clearance; catalog: SKF/FAG/Timken).