| name | hydrodynamic-bearing |
| description | Hydrodynamic journal bearing design — Reynolds equation, Sommerfeld number, Ocvirk/Raimondi-Boyd charts, minimum film thickness, eccentricity, stability, bearing materials. |
| metadata | {"priority":7,"promptSignals":{"phrases":["hydrodynamic bearing","journal bearing","sleeve bearing","oil film bearing","Sommerfeld number","Reynolds equation"],"minScore":3}} |
Hydrodynamic Journal Bearing — Complete Skill
Operating Principle
Shaft rotates and drags viscous lubricant into converging wedge
Pressure builds in film to support load — no metal contact
Minimum film thickness h_min must be ≥ composite surface roughness
Geometry Parameters
D = journal diameter [mm]
L = bearing length [mm]
C = radial clearance = R_bearing - R_journal [mm]
e = eccentricity (journal center offset from bearing center) [mm]
ε = e/C = eccentricity ratio (0=centered, →1 = contact)
h_min = C(1-ε) = minimum film thickness [mm]
L/D = slenderness ratio (typically 0.5–1.5)
Sommerfeld Number (Bearing Number)
S = (r/C)² × μN/P
r = journal radius = D/2 [m or mm, consistent]
μ = dynamic viscosity [Pa·s or cP]
N = rotational speed [rev/s] (not rpm; divide by 60)
P = unit load = W/(LD) [Pa or N/mm²]
W = total load [N]
Design range: S = 0.05–5 (practical operating region)
Low S → high eccentricity (marginal; near contact)
High S → low eccentricity (heavily loaded with less load capacity)
Raimondi-Boyd Design Charts
Charts give (as function of S and L/D):
- ε (eccentricity ratio)
- h_min/C (minimum film thickness ratio)
- φ (attitude angle)
- f (coefficient of friction variable)
- Q (flow variable)
- T_max (temperature rise variable)
Key lookup: for given S and L/D, read h_min/C → check h_min ≥ 3×σ_rough
Minimum Film Thickness Criterion
h_min ≥ (Ra_journal + Ra_bearing) × 3 to 5 (safety factor)
Typical: h_min ≥ 5–25 μm for precision shafts
Hersey number: Ho = μN/P (dimensionless) — related to S × (C/r)²
Stribeck curve: below critical Ho → mixed lubrication → wear begins
Bearing Design Procedure
- Set W (load), N (speed), D (from shaft design)
- Select C/D ratio: C/D ≈ 0.001 to 0.002 (typical: C/D = 0.001)
- Set L/D = 0.5–1.0 (narrow for heat removal; wide for higher capacity)
- Choose lubricant (ISO VG 32, 46, 68, 100) and operating temperature → get μ
- Calculate P = W/(LD); compute S
- Enter Raimondi-Boyd charts for L/D: read ε, h_min/C, f
- Check h_min ≥ clearance minimum (surface roughness criterion)
- Calculate friction force F_f = f × W and power loss P_loss = F_f × V_surface
- Check temperature rise: ΔT = P_loss / (Q × ρ × c_p × oil flow rate)
- Verify adequate oil supply pressure (typically 0.2–0.5 MPa supply)
Bearing Stability (Whirl)
Half-frequency whirl: instability at twice running speed
Onset: ε < ~0.3 (lightly loaded) → susceptible to oil whirl
Stabilizing measures: lobed bearings, tilting-pad bearings, preload
Tilting-pad journal bearing (TPJB):
Most stable configuration; used in turbomachinery
Pads pivot to form film — eliminates cross-coupling stiffness → whirl-free
Bearing Coefficients (Dynamic)
Spring coefficients: k_xx, k_xy, k_yx, k_yy [N/m]
Damping coefficients: c_xx, c_xy, c_yx, c_yy [N·s/m]
From Lund perturbation or numerical Reynolds solution
Used in rotordynamic stability analysis
Materials
| Material | Max speed | Max load | Notes |
|---|
| Babbitt (tin-based) | High | Moderate | Self-lubricating on break-in; sacrificial |
| Babbitt (lead-based) | High | Moderate | Cheaper; lower fatigue |
| Copper-lead | High | High | Better fatigue; no tin |
| Aluminum alloy | Moderate | High | Good wear; rigid |
| Bronze (CuSn) | Low-mod | High | High load; poor conformability |
Output
Provide: D × L [mm], C [mm], L/D, S (Sommerfeld), ε, h_min [μm] vs. roughness criterion, friction coefficient f, power loss [W], temperature rise ΔT [°C], stability assessment (ε vs. whirl threshold).
