Hydrodynamic Plain Journal Bearing & Lubrication PRO Calculator
Design and verify hydrodynamic plain journal bearings evaluating Sommerfeld characteristic number (S), minimum oil film thickness (h₀), eccentricity ratio (ε), Raimondi-Boyd numerical coefficients, ASTM D341 Walther viscosity, friction power loss, side leakage flow, thermal equilibrium temperature rise (ΔT), and rotordynamic oil whirl stability screening per DIN 31652, ISO 7902-1/2/3, API 613 / API 617, and Shigley 11th Ed.
Engineering DisclaimerEngineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.
DIN 31652 / ISO 7902 Hydrodynamic Plain Bearing Executive Audit
Full Hydrodynamic (Λ = 34.63)
Rotordynamically Stable
Sommerfeld Number (S)
0.1865
L/D = 1.00 | ψ = 1.50 ‰
Min Film Thickness (h₀)
38.72 µm
ε = 0.484 (φ = 50.1°)
Friction Power Loss (H_f)
2.626 kW
f = 0.00669 (2,626 W)
Max Film Temp (T_max)
91.8 °C
ΔT = +36.8 °C (Limit: 115 °C)
Lubricant Supply Flow (Q)
4.649 L/min
Side Leakage Q_s: 2.667 L/min (57%)
Peak Hydro Pressure (P_max)
6.98 MPa
Mean P: 2.5 MPa (SF = 2.80)
Dynamic Viscosity (µ)
20.98 cP (mPa·s)
ν = 24.7 cSt @ 55°C
Journal Surface Speed (U)
15.71 m/s (50 rps)
Torque: 8.36 N·m
Engineering Standards Compliance (ISO 7902 / API 613 / API 617)
ISO 7902: PASS
API 613: COMPLIANT
•Complies with ISO 7902-1 steady-state hydrodynamic criteria (h₀ ≥ h_lim, P ≤ P_allow, T ≤ T_allow).
•Meets API 613 Special Purpose Gear Unit bearing limits (film thickness ≥ 12.5 µm, P ≤ 4.0 MPa).
Hydrodynamic Cross-Section & Pressure Wedge
MIN FILM (h₀)38.72 µm
ECCENTRICITY (ε)0.484 (0.036 mm)
PEAK PRESSURE (P_max)6.98 MPa
ATTITUDE ANGLE (φ)50.1°
Tribology & Thermal Hydrodynamics
ISO VG 46 (Industrial General Purpose & Turbomachinery) (ASTM D341 Walther Model)Operating: 55°C → 21.0 cP
Side Leakage Fraction
57.4% (2.667 L/min)
Oil Temp Rise (ΔT)
+36.8 °C (T_max = 91.8 °C)
Material Temp Margin
23.2 °C
Calculation Summary
Input Parameters
Bearing Dimensions (D × L)
100.0 × 100.0mm
Radial Clearance (c / ψ)
0.0750 mm (1.50 ‰)
Shaft Speed & Load
3000 RPM / 25.0 kN
Lubricant Grade
ISO VG 46 (Industrial General Purpose & Turbomachinery)
Dynamic Viscosity (µ @ T_op)
20.98 cP (55°C)
Bushing Material
Tin-Based Babbitt (White Metal, ASTM B23 Alloy 2)
Calculated Results
Sommerfeld Number (S)
0.1865
KEY
Min Fluid Film Thickness (h₀)
38.72µm
KEY
Eccentricity Ratio (ε)
0.484 (φ = 50.1°)
Lubrication Regime (Λ)
FULL-HYDRODYNAMIC (Λ = 34.63)
KEY
Friction Coefficient (f)
0.00669
Friction Power Loss (H_f)
2.626 kW
KEY
Maximum Film Temp (T_max)
91.8 °C
Total Supply Oil Flow (Q)
4.649 L/min
Peak Hydrodynamic Pressure (P_max)
6.98 MPa
Rotordynamic Stability
STABLE
KEY
Safety Notes
Calculated per DIN 31652 / ISO 7902 / Raimondi-Boyd. Full hydrodynamic fluid film verified (h₀ = 38.72 µm, S = 0.1865).
1*Step 1: Journal Geometry, Radial Clearance & Clearance Ratio**
Formula: \psi = \frac{c}{R} = \frac{2c}{D}, \quad A_p = L \cdot D
Substitution: D = 100.00 mm, L = 100.00 mm (L/D = 1.00), c = 0.0750 mm
Result: \psi = 1.500 \text{ ‰ (mils/in)}, \quad A_p = 10000.0 \text{ mm²}
Note: Radial clearance ratio defines the dimensional proportion between bearing bore and shaft journal diameter.
•*Step 2: Mean Projected Unit Pressure & Journal Kinematics**
Formula: P = \frac{W}{L \cdot D}, \quad n = \frac{N}{60}, \quad \omega = 2\pi n, \quad U = \omega R
Substitution: W = 25000.0 N, N = 3000 \text{ RPM}, R = 50.00 mm
Result: P = 2.500 MPa, \; n = 50.00 \text{ rev/s}, \; U = 15.71 \text{ m/s}
Note: Projected bearing pressure and journal surface speed determine the dynamic shearing velocity of the oil wedge.
•*Step 3: Lubricant Viscosity Calibration at Operating Temperature**
Formula: \log_{10}\log_{10}(\nu + 0.7) = A - B \cdot \log_{10}(T + 273.15), \quad \mu = \nu \cdot \rho \times 10^{-6}
Substitution: Lubricant Grade = ISO_VG_46, T_{\text{op}} = 55.0 °C
Result: \mu = 20.98 \text{ cP (mPa·s)}, \; \nu = 24.71 \text{ cSt}, \; \rho = 849.0 \text{ kg/m³}
Note: Standard ASTM D341 two-parameter temperature-viscosity relationship for industrial mineral and synthetic lubricants.
•*Step 4: Sommerfeld Characteristic Bearing Number (S)**
Formula: S = \left(\frac{R}{c}\right)^2 \frac{\mu \cdot n}{P}
Substitution: (R/c) = 666.7, \mu = 2.098e-2 \text{ Pa·s}, n = 50.00 \text{ rev/s}, P = 2.500e+6 \text{ Pa}
Result: S = 0.1865
Note: Fundamental dimensionless bearing parameter unifying geometry, speed, viscosity, and load.
•*Step 5: Raimondi-Boyd Numerical Equilibrium Solutions**
Formula: \varepsilon = f(S, L/D), \quad \phi = g(S, L/D), \quad \left(\frac{R}{c}\right)f = \Phi_f(S, L/D)
Substitution: Interpolated from Raimondi-Boyd / DIN 31652 solutions at S = 0.1865 and L/D = 1.00
Result: \varepsilon = 0.484, \; \phi = 50.1^\circ, \; \left(\frac{R}{c}\right)f = 4.46, \; \frac{Q}{R c n L} = 4.13, \; \frac{Q_s}{Q} = 0.574
Note: Dimensionless coefficients governing journal locus, friction torque, oil supply, and side leakage cooling.
•*Step 6: Minimum Fluid Film Thickness (h₀) & Specific Film Parameter (Λ)**
Formula: h_0 = c \cdot (1 - \varepsilon), \quad \Lambda = \frac{h_0}{\sqrt{R_{q1}^2 + R_{q2}^2}}
Substitution: c = 75.0 \text{ µm}, \varepsilon = 0.484, \sigma_s = 1.12 \text{ µm}
Result: h_0 = 38.72 \text{ µm (1.524 mils)}, \quad \Lambda = 34.63 \rightarrow \text{Full Hydrodynamic (Thick Film)}
Note: Film thickness parameter Λ ≥ 3.0 confirms full hydrodynamic fluid separation with zero metal-to-metal asperity wear.
•*Step 7: Frictional Power Dissipation & Thermal Equilibrium**
Formula: f = \left(\frac{c}{R}\right) \cdot \Phi_f, \quad H_f = 2\pi n f W R, \quad \Delta T = \frac{H_f}{\rho \cdot c_p \cdot Q_s}
Substitution: f = 0.00669, W = 25000 \text{ N}, Q_s = 2.667 \text{ L/min}
Result: f = 0.00669, \; H_f = 2.626 kW (2625.8 \text{ W}), \; \Delta T = 36.8^\circ\text{C} \rightarrow T_{\text{max}} = 91.8^\circ\text{C}
Note: Active side leakage flow carries away dissipated frictional shear heat, yielding the peak oil film temperature.
Engineering Disclaimer: Engineering calculations are provided for preliminary design and educational/reference purposes only. Users must verify all results according to applicable engineering standards, supplier data, manufacturing requirements, and professional engineering judgment.