thrust-bearing

name	thrust-bearing
description	Thrust bearing design — axial load capacity for tapered roller thrust, angular contact ball, spherical roller thrust, and hydrodynamic tilting-pad thrust bearings; ISO 281 dynamic load rating C_a and life L10; thrust bearing arrangement (paired angular contact, back-to-back vs. face-to-face); preload and axial stiffness; fluid film tilting-pad bearing (Kingsbury/Michell) load capacity and Sommerfeld number; and applications in turbomachinery, gearboxes, and marine propulsion.
metadata	{"priority":7,"promptSignals":{"phrases":["thrust bearing","axial bearing","angular contact bearing","tilting pad thrust bearing","thrust load capacity","Kingsbury bearing"],"minScore":3}}

Thrust Bearing Design — Complete Skill

Thrust Bearing Types and Selection

Classification by Load and Speed

Type	Axial Load	Speed	Stiffness	Application
Deep groove ball (Conrad)	Moderate	High	Moderate	General; light thrust
Angular contact ball (single)	High	High	High	Precision spindles; pumps
Angular contact ball (pair)	High	High	Very high	Machine tool spindles
Tapered roller thrust	Very high	Medium	High	Gearboxes; differentials
Spherical roller thrust	Very high	Medium	High	Vertical shaft machinery
Needle thrust	High	Medium	Compact	Gearbox thrust faces
Self-aligning ball thrust	Moderate	High	Self-aligning	Misalignment; propellers
Tilting-pad (fluid film)	Extreme	Very high	Moderate	Steam turbines; compressors
Hydrostatic thrust	Extreme	Low–high	Very high	Heavy mills; presses

Rolling Element Thrust Bearings (ISO 281)

Basic Dynamic Load Rating and Life

ISO 281 dynamic axial load rating C_a: L10 = (C_a / P_a)^p [millions of revolutions; p = 3 for ball; 10/3 for roller] L10h = L10 × 10⁶ / (60 × n) [hours; n = speed in RPM]

Equivalent axial load P_a: For pure thrust bearing: P_a = F_a [no radial load; axial only] For combined loading (angular contact): P_a = X × F_r + Y × F_a [X, Y from bearing table; depends on F_a/C_0 ratio]

Modified life (ISO 281:2007 Annex A): L_nm = a_1 × a_ISO × L10 [a_1 = reliability factor; a_ISO = life modification factor for lubrication and contamination] a_1 at 90% reliability = 1.0; 95%: 0.62; 99%: 0.21

Viscosity ratio for a_ISO: κ = ν / ν₁ [ν = operating kinematic viscosity; ν₁ = reference viscosity for adequate lubrication] ν₁ = 45,000 / (n^0.83 × d_m^0.5) [mm²/s; n = RPM; d_m = mean bearing diameter mm] κ > 2: a_ISO up to 4 (excellent lubrication); κ < 1: a_ISO < 1 (inadequate)

Angular Contact Ball Bearings

Contact angle α: 15°, 25°, 30°, 40° standard; higher α → greater axial capacity; lower radial capacity F_a_capacity ≈ C_a ≈ 0.5 × C × tan(α) [rough estimate; use catalog values]

Paired angular contact arrangements:

Back-to-back (DB): Load lines diverge away from bearing → wide effective span → high moment stiffness Suitable for: overhanging loads, cantilever shafts Rigid (positive) preload common

Face-to-face (DF): Load lines converge toward center → narrow span → lower moment stiffness but self-aligning Less sensitive to misalignment Suitable for: non-overhanging; shaft flexibility compensation

Tandem (DT): Both bearings carry axial load in same direction → double the axial capacity in one direction Cannot carry reverse thrust → pair with another DT or single bearing in opposite

Preload: Initial compression to eliminate internal clearance; increases stiffness; increases heat generation Light preload: C_a × 0.02; medium: × 0.05; heavy: × 0.10 Spring preload: constant force regardless of thermal expansion; rigid preload: position-controlled

Axial stiffness of angular contact pair: k_a = F_a / δ_a = C_a × f(preload) / (δ_a) [nonlinear; from Hertz contact] Approximate: k_a [N/μm] ≈ (C_a [kN])^(1/3) × constant × (cos α / sin α) At DB preload force F_pr: k_a = 2 × F_pr^(1/3) × K_Hertz × sin²α × (cos α / sin α)

Tapered Roller Thrust Bearings

High axial load capacity: conical rollers → line contact → high load capacity Configuration: pairs (indirect mounting) for bidirectional thrust

ABMA/ISO cone-cup assembly: D_contact = effective contact diameter; L = roller length C_a from catalog; typically C_a = 3–5× C for tapered thrust vs. standard tapered

Applications: automotive front-axle bearings (combined radial+thrust); heavy gearboxes; crane hooks

Spherical Roller Thrust Bearings

Self-aligning: spherical raceway compensates shaft misalignment up to ±1–2° High axial AND moderate radial capacity Typical: F_r ≤ 0.55 × F_a [radial load limited for thrust version] Speed limit: lower than angular contact due to roller sliding

Application: vertical shaft pumps; fan drives; cranes; mixing vessels; anything with shaft deflection

Fluid Film Tilting-Pad Thrust Bearings

Kingsbury/Michell Bearing

Principle: oil film pressure between shaft collar and pivoting pad; pad tilts to form converging wedge Converging wedge → hydrodynamic pressure → carries full axial load without metal contact

Geometric parameters: N_pads: 6–8 pads typical; r_i, r_o = inner and outer radius; sector angle θ_pad R_m = (r_o + r_i)/2 = mean radius; B_m = R_m × θ_pad = circumferential pad length (at mean radius) h₁, h₂ = film thickness (inlet, outlet); h₀ = minimum film thickness

Sommerfeld-type analysis: Dimensionless speed: N* = η × n × B_m² / (W × h₀²) [η = dynamic viscosity; n = shaft rev/s; W = load per pad] Load capacity: W = f_W × η × n × R_m × B_m × (B_m/h₀)² [f_W = bearing geometry factor from tables/charts]

Minimum film thickness criterion: h₀_min ≥ 3 × (σ_collar + σ_pad)_rms [surface roughness limit; no metal contact] h₀_min > 5 μm practical minimum; typically 15–50 μm at design condition

Pad pivot location: typically at 0.55–0.58 × B_m from leading edge (optimum for equal film inlet/outlet)

Temperature rise: ΔT_bearing = (P_loss × R_th_oil) = f × W × v / (ṁ_oil × cₚ_oil) [v = collar velocity = 2π × n × R_m; ṁ_oil = oil flow rate] Limit: T_oil < 100°C for mineral oil; T_babbitt < 130°C (melting of white metal)

Load Capacity Calculation

Tilting-pad thrust (approximate Raimondi-Boyd or Pinkus-Sternlicht charts): W/N_pads = p_avg × A_pad [p_avg = average pressure from chart given S number] Sommerfeld number: S = (η × n × N_pads) / (P × (R_m/c)²) [P = P_total/N_pads/A_pad; c = nominal clearance]

Practical capacity: Steel collar on babbitt pads: p_max = 3–5 MPa (30–50 bar) average pad pressure Example: 4-pad bearing; R_m = 200 mm; B_m = 150 mm; oil ISO VG 32 at 50°C (η = 22 cP = 0.022 Pa·s); n = 3,000 RPM A_pad ≈ R_m × θ_pad × (r_o − r_i) = 0.2 × 0.6 × 0.1 = 0.012 m² per pad (6-pad, 60° each) W_total = p_avg × A_pad × N_pads = 3×10⁶ × 0.012 × 6 = 216 kN total thrust capacity

Babbitt (White Metal) Properties

Babbitt (Sn-based): ASTM B23: Grade 1 (92 Sn): T_melt = 232°C; T_max operating = 130°C; hardness = 17 HB; excellent conformability Grade 2 (89 Sn): good corrosion resistance; standard turbine bearing Lead-based babbitt: cheaper; lower load capacity; being phased out (Pb regulations)

PTFE and composite pads: used in water-lubricated bearings (hydroelectric, marine) PEEK composite: higher load (< 7 MPa); higher T (< 250°C); no white metal melting risk

Axial Load Capacity Summary

Design check sequence:

1. Determine axial thrust F_a (from FBD, gear geometry, fluid pressure, etc.)
2. Select bearing type by speed, space, misalignment requirements
3. Calculate P_a (equivalent dynamic load including any radial component)
4. Calculate required C_a = P_a × (L10h × 60 × n / 10⁶)^(1/p) [p = 3 ball; 3.33 roller]
5. Select from catalog with C_a ≥ required C_a × safety factor (SF = 1.2–2.0)
6. Check static capacity: C_0a ≥ F_a × SF_static (SF = 2–4 for shock loads)
7. Check speed rating: n ≤ n_limit from catalog

Marine and Turbomachinery Applications

Marine propeller shaft thrust: Thrust F_T = T_propeller × η_shaft = (KT × ρ × n² × D⁴) × η Typical: 5–50 MN for large vessels → tilting-pad mandatory Michell bearing: 6–8 pads; babbitt; forced oil lubrication; dual-direction (ahead/astern)

Steam/gas turbine thrust: Axial unbalance due to steam/gas pressure differences; typically 200–2,000 kN Tilting-pad bearing; active clearance control; proximity probes to monitor axial position API 670: machinery protection standard; axial vibration and position monitoring

Compressor thrust: Centrifugal compressor: pressure imbalance → large axial thrust Balance piston or back-to-back impeller arrangement → reduced thrust → angular contact bearings feasible

Standards and References

Standard	Scope
ISO 281	Dynamic load ratings and life calculations
ISO 76	Static load ratings
API 670	Machinery protection (axial position monitoring)
ASTM B23	White metal (babbitt) alloys
SKF/NSK/Timken bearing catalogs	C_a, C_0a, speed limits, preload data

Output

Provide: shaft and load data (axial thrust F_a [kN]; radial load F_r [kN] if combined; speed n [RPM]; service life L_required [h]; reliability [%]; temperature T_op [°C]; environment: clean/contaminated/wet), bearing type selection (angular contact ball/tapered roller/spherical roller thrust/tilting-pad; rationale: load magnitude, speed, misalignment, space), equivalent load (P_a = X×F_r + Y×F_a [kN]; X, Y from bearing table; F_a/C_0 ratio used), required dynamic rating (C_a_required = P_a × (L10h×60×n/10⁶)^(1/p) [kN]), selected bearing (designation; C_a [kN]; C_0a [kN]; n_limit [RPM]; d [mm]; D [mm]; B [mm]; mass [kg]), modified life (L10h [h]; a_ISO from κ = ν/ν₁; L_nm = a₁ × a_ISO × L10h [h]; margin over L_required [%]), arrangement (DB/DF/DT; preload force [N] or preload class; axial stiffness k_a [N/μm] at preload), tilting-pad (if applicable: N_pads; R_m [mm]; B_m [mm]; p_avg [MPa]; h₀_min [μm]; ΔT_oil [°C]; babbitt grade), lubrication (oil grade ISO VG [xx]; viscosity at T_op [cSt]; feed pressure [bar]; flow rate [L/min]; cooling requirement), and applicable standard (ISO 281; API 670 for turbomachinery; ASTM B23 for babbitt).