bearing-temperature

name	bearing-temperature
description	Bearing temperature analysis — friction heat generation, SKF friction model, thermal resistance, maximum operating temperature, oil/grease temperature limits, thermal runaway, ISO 15312.
metadata	{"priority":7,"promptSignals":{"phrases":["bearing temperature","bearing heat generation","bearing friction power","bearing thermal","bearing overheating","bearing thermal limit"],"minScore":3}}

Bearing Temperature Analysis — Complete Skill

Friction Heat Generation

SKF Friction Torque Model (Comprehensive)

Total friction torque: M_total = M_rr + M_sl + M_seal + M_drag [N·mm]

Rolling friction torque M_rr: M_rr = φ_ish × φ_rs × μ_rr × G_rr × (ν_oil × n)^0.6 [N·mm] μ_rr = 0.0004–0.0015 (rolling coefficient; material/geometry dependent) G_rr = f(bearing geometry, d_m) ν_oil = oil viscosity at operating T [cSt]; n = speed [RPM] φ_ish = inlet shear heating reduction factor; φ_rs = kinematic replenishment factor

Sliding friction torque M_sl: M_sl = G_sl × μ_sl [N·mm] μ_sl = 0.04–0.15 (sliding coefficient; lubrication dependent) G_sl = f(bearing load, geometry, contact area)

Seal friction torque M_seal: M_seal = K_S1 × d_S^β + K_S2 [N·mm; d_S = shaft diameter; K_S1, K_S2 from bearing type] Shielded bearing: negligible; Rubbing lip seal: significant

Drag/churning friction M_drag: M_drag = V_m × K_drag × (n × d_m)² × ρ_oil [N·mm; V_m = oil level factor; K_drag = geometry factor] Significant at high speeds or high oil level

Simplified Friction Power

For initial estimates: P_friction = M_total × ω = M_total × 2π n / 60 [W; M in N·mm; n in RPM] Divide by 1000: P_friction [W] = M_total [N·mm] × n [RPM] / 9549

Typical range: Lightly loaded bearing (P < 0.1C): P_friction ≈ 0.5–5 W Heavily loaded (P > 0.3C): P_friction ≈ 5–50 W High speed, large bearing: P_friction ≈ 100–1000 W

Thermal Resistance and Temperature Rise

Thermal network model: T_bearing = T_ambient + P_friction × R_thermal_total [°C]

Thermal resistance components: R_inner = resistance from inner ring to shaft → shaft temperature R_outer = resistance from outer ring to housing → housing temperature R_radiation+convection = outer housing to air

Approximate thermal resistance (per bearing):

Housing type	R_thermal [°C/W]
Isolated (no oil flow)	20–50
Good air circulation	10–20
Oil-circulating (forced)	1–5
Water-cooled housing	0.5–2

Equilibrium temperature: T_bearing = T_ambient + P_friction × R_outer For R_outer = 30°C/W, P_friction = 10 W: ΔT = 300°C → unacceptable → need cooling For P_friction = 1 W: ΔT = 30°C → acceptable (40°C ambient → 70°C bearing)

Maximum Bearing Temperature Limits

Standard bearing steel (52100): T_max = 120°C continuous (above this: ring softening → dimensional change → clearance change) Short-term T_max = 150°C (for special heat-stabilized bearings, marked S1/S2)

Dimensionally stabilized bearings: S1 (stabilized to 150°C): suffix S1; T_max continuous = 150°C S2 (200°C): T_max = 200°C; higher T_max steel or ceramics S4 (250°C): T_max = 250°C; used in baking ovens, sterilization

Ceramic balls (Si₃N₄): T_max > 500°C for ball itself; limited by steel ring: 120°C standard Hybrid bearing: Si₃N₄ balls + steel rings; advantage = lower inertia, not temperature

Grease temperature: Standard grease: T_max = 120°C (mineral oil base) Synthetic (PAO or ester): T_max = 150°C High-temperature grease (silicone or fluorocarbon): T_max = 200–260°C If T_bearing > T_grease_limit → relubrication interval must be shortened drastically

Oil temperature: ISO VG 46 mineral oil: T_max operating = 90°C; oxidizes above 90°C → shortened oil life Synthetic oil: T_max = 120–150°C

Relubrication Interval vs. Temperature

SKF relubrication interval tf: tf = t_f0 × [2^((T_ref - T_bearing) / 15)] [hr; t_f0 = base interval at 70°C; halves for each 15°C increase]

Example: t_f0 = 5000 hr at 70°C At T_bearing = 100°C: tf = 5000 × 2^((70-100)/15) = 5000 × 2^(-2) = 1250 hr At T_bearing = 120°C: tf = 5000 × 2^(-3.33) = 5000 × 0.1 = 500 hr

Thermal Runaway Detection and Prevention

Thermal runaway mechanism: Preload → friction → heat → thermal expansion → more preload → more friction (positive feedback loop) Most common in rigid-preloaded angular contact spindle bearings

Check: dF_preload/dT > k_thermal_dissipation → runaway possible Check: (k_bearing × α_shaft × L_shaft) > (k_thermal × A_housing) [conservative criterion]

Prevention: Use spring preload (constant force) for high-speed spindles Ensure adequate ventilation or active cooling Include thermal break in spindle housing design

Monitoring

RTD (Pt100) placement: Mount in housing near outer ring; distance < 5 mm from bearing (thermal lag reduces accuracy) Response time: sensor + housing thermal mass → typical lag 1–5 min

IR thermometry: Non-contact; useful for moving shafts; cannot read through oil film Thermocouple: faster response than RTD; useful for dynamic T monitoring

Alarm and trip settings (typical): Alarm: T_bearing > 80–90°C (above baseline by 20°C) Trip: T_bearing > 100–110°C

Standards

Standard	Scope
ISO 15312	Thermal speed limits for bearings
ISO 14839	Rotating machinery monitoring
ISO 13373	Condition monitoring procedures
SKF Bearing Technical Handbook	Friction model, thermal limits

Output

Provide: friction torque components M_rr + M_sl + M_seal + M_drag [N·mm], total friction power P_friction [W], bearing equilibrium temperature ΔT [°C] above ambient, check vs. bearing steel limit (120°C), grease temperature limit vs. operating temperature, relubrication interval tf [hours], thermal resistance R_thermal [°C/W] for housing configuration, thermal runaway risk (yes/no with criterion check), temperature monitoring type and alarm setpoints [°C], and applicable standard (ISO 15312, ISO 13373).