bearing-preload

name	bearing-preload
description	Bearing preload — angular contact/tapered roller, axial preload types (rigid/spring), contact angle change, stiffness vs. preload, heat generation, DB/DF/DT arrangements, FAG/SKF preload tables.
metadata	{"priority":7,"promptSignals":{"phrases":["bearing preload","angular contact preload","axial preload bearing","bearing stiffness preload","duplex bearing","face-to-face back-to-back"],"minScore":3}}

Bearing Preload — Complete Skill

Purpose of Preload

Preload: internal axial force applied to bearing before external loading Benefits:

• Increases stiffness (critical for precision spindles)
• Eliminates clearance → no dead-band in response
• Improves running accuracy (reduces runout)
• Reduces vibration susceptibility

Drawbacks:

• Generates heat (friction loss)
• Reduces fatigue life if excessive
• Temperature sensitive (rigid preload)

Duplex Bearing Arrangements

DB (Back-to-Back / O arrangement): Contact angle lines diverge outward Better moment capacity (wide reaction span) Best for: combined radial + overturning moment loads Thermal expansion changes preload slightly

DF (Face-to-Face / X arrangement): Contact angle lines converge inward More sensitive to misalignment (shorter reaction span) Less rigid than DB; better for short overhanging shafts Thermal expansion partially relieves preload (more stable)

DT (Tandem arrangement): Both bearings carry load in same direction Higher axial capacity (both share thrust load) Cannot handle bidirectional thrust; use with opposing pair

Notation: DB/DF/DT for paired bearings; universal match (angular contact) grindable for any arrangement

Preload Quantification

Rigid preload (spacer-controlled): Inner and outer spacers of different length → creates exactly δ_preload of axial displacement F_preload = k_pair × δ_preload [N; k_pair = combined axial stiffness of pair [N/m]]

Spring preload (constant force): Spring stack gives constant F_preload regardless of temperature Better for temperature-cycling environments

Preload classes (angular contact 7xxx series):

Class	Symbol	Preload [N] (typical 30 mm bore)
Light	L or LP	10–50
Medium	M or MP	50–200
Heavy	H or HP	200–800

Exact values: from manufacturer tables for each designation (SKF, FAG, NSK preload tables)

Stiffness vs. Preload

Hertz contact (ball-raceway): δ = K_Hz × F^(2/3) [nonlinear spring; stiffness increases with load] k = dF/dδ = (3/2) × F^(1/3) / K_Hz [N/m; stiffness higher at higher load (preload)]

Axial stiffness of preloaded pair: At zero external load (only preload F_p): k_axial = (3/2) × F_p^(1/3) × K_stiffness [N/μm; K from bearing geometry]

Effect of preload on stiffness: Double the preload → stiffness increases by 2^(1/3) ≈ 1.26× (nonlinear)

Example (7206 bearing, F_p = 100 N): k_axial ≈ 35 N/μm (light preload) F_p = 400 N: k_axial ≈ 55 N/μm (heavy preload)

Contact Angle Change with Preload

Free contact angle α₀ (from catalog: typically 15°, 25°, or 40° for angular contact) Under axial preload F_a: cos α = cos α₀ × (1 + (F_a / K_const)^(2/3))^(-1/2) [contact angle increases with axial load]

Effect on load capacity: Higher contact angle → higher axial capacity; lower radial capacity Typical change: 15° → 20–25° under operating preload

Heat Generation from Preload

Bearing friction power (SKF model): P_friction = M_total × ω [W; ω in rad/s] M_total = M_rolling + M_sliding + M_seal + M_drag

Preload contribution to M_rolling: M_rolling ∝ F_p^(1/3) × ν_oil^(0.6) × n^(0.6) × d_mean [proportional to preload; increases with speed]

Temperature rise (equilibrium): ΔT = P_friction / (k_thermal × A_housing + Q_oil) [°C; k_thermal = housing conductance; A = surface area] Rigid preload: ΔT increases preload → more friction → higher ΔT → risk of thermal runaway (rare but possible)

Thermal runaway check: k_bearing × α_shaft × L × ΔT > F_preload_limit → unsafe Use spring preload or calculate maximum allowable ΔT for rigid preload

Selecting Preload Level

Machine tool spindle (high precision): Medium to heavy preload; k_axial target = 100–500 N/μm Heavy preload at low speed; light preload at high speed (some spindles use adjustable preload)

High-speed spindle (> 20,000 RPM): Speed parameter dn = n × d_bore [mm·RPM] For dn > 10⁶: use light or super-light preload to limit heat For dn = 0.5–1.0×10⁶: medium preload OK

General industrial: Light to medium preload; stiffness less critical than life

Testing and Verification

Measuring preload (after assembly): Running torque method: measure starting torque at low RPM; compare to torque vs. preload curve from manufacturer Vibration/noise test: run-up; check 1× runout and spindle frequency response

Runout specification (ISO 1132): Single bearing runout; axial + radial; affected by preload uniformity Machine tool spindle: axial + radial runout ≤ 1–5 μm (depending on class)

Standards and References

Standard	Scope
ISO 15241	Angular contact ball bearing dimensions
ISO 5593	Rolling bearing terminology
FAG / SKF Bearing Catalogues	Preload tables by designation
JIS B 1521	Ball bearing preload (Japanese)

Output

Provide: bearing arrangement (DB/DF/DT), preload class (L/M/H), preload force F_p [N], axial stiffness k_axial [N/μm] at preload, contact angle change α₀ → α [°], friction power P_friction [W], temperature rise estimate ΔT [°C] at operating speed, thermal runaway check, speed parameter dn [mm·RPM] vs. limit, spring vs. rigid preload recommendation, running torque verification value [N·mm], and applicable standard (ISO 15241, SKF/FAG preload tables).