tapered-roller-bearing

name	tapered-roller-bearing
description	Tapered roller bearing selection and design — equivalent load, induced thrust, mounting arrangements, L10 life (ISO 281), preload, TIMKEN/SKF methods.
metadata	{"priority":7,"promptSignals":{"phrases":["tapered roller bearing","tapered bearing","TIMKEN bearing","roller bearing life","cone and cup bearing"],"minScore":3}}

Tapered Roller Bearing — Complete Skill

Geometry and Key Feature

Single-row tapered roller bearing:

• Inner ring = cone; outer ring = cup
• Rollers inclined at contact angle α (typically 10°–29°)
• Can carry both radial and axial (one-direction) thrust
• Must be used in opposing pairs to handle bidirectional thrust

Self-induced thrust: radial load generates internal axial force F_a,induced = 0.47 F_r / K (where K = catalog factor ≈ C/(C_0) × 0.6) TIMKEN standard: F_i = 0.47 F_r / K or from catalog K-factor table

Equivalent Dynamic Load

P = 0.4 F_r + K × F_a (when F_a/F_r > e) P = F_r (when F_a/F_r ≤ e)

e = catalog constant (depends on contact angle; e ≈ 0.35–0.55) K = catalog constant (typically 1.5–2.5)

L10 Life (ISO 281)

L_10 = (C/P)^(10/3) [millions of revolutions] (roller exponent = 10/3) L_10h = L_10 × 10⁶ / (60n)

Opposing Pair (Back-to-Back vs. Face-to-Face)

Back-to-back (DB) arrangement:

• Wider effective span → better moment resistance
• Contact angle diverges outward
• Less susceptible to bearing preload from thermal expansion
• Preferred for overhanging loads

Face-to-face (DF) arrangement:

• Narrow effective span
• Contact angles converge → inferior moment stiffness
• Better for misalignment tolerance

Tandem (DT) arrangement:

• Both bearings carry load in same direction
• Used when single bearing insufficient for unidirectional thrust

Two-Bearing Analysis (TIMKEN Method)

For shaft with bearing A and bearing B (opposing pair):

1. Calculate external axial load F_ae and radial loads F_rA, F_rB
2. Compute induced thrust: F_iA = 0.47 F_rA/K_A; F_iB = 0.47 F_rB/K_B
3. Determine which bearing is "tight" (closing) and "loose" (opening)
4. Tight bearing: P_tight = 0.4 F_r + K(F_ae + F_i,loose)
5. Loose bearing: P_loose = F_r (if F_a/F_r ≤ e)
6. Calculate L_10 for both; life governed by lower

Mounting and Fits

Inner ring (cone) rotates: interference fit on shaft

• Light duty: k5; Medium: m5; Heavy: n5 Outer ring (cup) in housing: light press or push fit
• Adjustable arrangements: sliding fit for one bearing (H7)

Axial adjustment: TRBs must be adjusted for proper clearance or preload Adjustment by shimming or locknut to set play ≈ 0.05–0.15 mm end play (running clearance) Or preload: negative end play for higher stiffness

Cage and Lubrication

Cage materials: stamped steel, machined brass, polymer Grease: use bearing manufacturer's recommendation; 20–30% fill typical Operating temperature range: standard grease –30°C to +120°C; synthetic to +150°C

Heavy-Duty Applications

Wheel bearings (automotive): hub units with pre-adjusted preload, sealed Mining equipment: large bore (>150 mm), higher K factors Rolling mill: 4-row tapered roller; highest radial capacity Differential/axle: high axial + radial; typically DB or DT pairs

Stiffness

Tapered roller bearings have higher stiffness than ball bearings (line contact vs. point) Radial stiffness: k_r ≈ 3–8 × 10⁵ N/mm (size-dependent) Preloaded TRB pairs: k_axial ≈ 10⁵–10⁶ N/mm

Output

Provide: bearing designation (cone/cup number), C [kN], C_0 [kN], K, e, P_A and P_B [N], L_10h [hours] for both bearings, mounting arrangement (DB/DF/DT), end play or preload [mm], shaft and housing fit specifications.