Real-time Sommerfeld number, minimum film thickness and film thickness ratio Λ for journal bearings — with Stribeck curve and regime identification.
Bearing Parameters
Shaft Diameter D
mm
Bearing Length L
mm
Radial Clearance c
μm
Load W
N
Rotational Speed N
rpm
Dynamic Viscosity η
Pa·s
VG32≈0.03 · VG68≈0.06 · VG100≈0.09 Pa·s
Composite Roughness σ
μm
Ground: 0.2–0.5 · Turned: 0.5–2.0 μm
Results
—
Sommerfeld S
—
hmin [μm]
—
Λ = hmin/σ
—
Lube Regime
—
Friction μ
Stribeck Curve (μ vs ηN/P)
Film Thickness Ratio Λ vs Load W
CAE Integration
EHD (elastohydrodynamic) analysis in ANSYS Fluent or OpenFOAM couples fluid film with solid deformation for precise hmin predictions. The Stribeck curve is the starting point for tribological design of gearboxes, crankshaft bearings and turbine journal bearings.
Film thickness ratio: $\Lambda = h_{min}/\sigma_{comp}$, $\sigma_{comp}=\sqrt{\sigma_1^2+\sigma_2^2}$
Stribeck parameter: $\eta N/P$ ($N$ in rev/s, $P$ in Pa)
What is the Stribeck Curve & Lubrication Regime?
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What exactly is a "lubrication regime"? I see the simulator shows a graph with three zones, but what's physically happening in each one?
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Basically, it describes how two surfaces are kept apart by a lubricant. The Stribeck curve, which you see plotted here, maps friction against a combined parameter of speed, viscosity, and pressure. The three key regimes are: Boundary (surfaces touch), Mixed (partial contact), and Hydrodynamic (full separation by a fluid film). Try moving the Rotational Speed (N) slider up and down in the simulator—you'll see the red dot travel along the curve, jumping between these regimes in real-time.
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Wait, really? So the goal is to be in the "Hydrodynamic" regime? What determines if we get there? The simulator shows a "Sommerfeld Number" that gets bigger.
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Exactly! The Hydrodynamic regime gives the lowest friction and no wear. The key is the Sommerfeld number (S)—a dimensionless group that balances the lubricant's ability to generate pressure (from viscosity η and speed N) against the load squeezing the surfaces together (P). For instance, in a car engine's crankshaft bearing, high RPM (N) increases S and pushes it into the safe hydrodynamic zone. In the simulator, increase Load (W) and watch S decrease, potentially pulling the bearing back into the risky mixed regime.
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That makes sense. But the "Minimum Film Thickness" value seems tiny, like microns. How do we know if that's enough to prevent contact? The "Composite Roughness" parameter seems important.
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Great observation! The film thickness ($h_{min}$) must be larger than the combined roughness of the surfaces ($\sigma$) to ensure full separation. A common rule is the Lambda Ratio: $\Lambda = h_{min}/ \sigma$. If $\Lambda > 3$, you're safely hydrodynamic. If $\Lambda < 1$, you're in boundary contact. This is why the simulator includes Composite Roughness (σ)—it's the reality check. For a precision turbine bearing, you'd polish surfaces to a very low σ so even a thin film is sufficient.
Physical Model & Key Equations
The core of the model is the Sommerfeld Number (S), a dimensionless parameter that characterizes the bearing's operating condition. It compares the hydrodynamic pressure generation to the applied bearing pressure.
Where:
$\eta$ = Dynamic viscosity of lubricant [Pa·s]
$N$ = Rotational speed [rev/s]
$P = W/(DL)$ = Bearing pressure [Pa]
$D$ = Journal diameter [m], $L$ = Bearing length [m]
$c$ = Radial clearance [m] (gap when concentric) A higher S indicates a thicker, more stable fluid film.
The Minimum Film Thickness ($h_{min}$) is estimated from the eccentricity ratio ($\varepsilon$), which depends on the Sommerfeld number. It tells you the narrowest gap between the shaft and bearing.
Where:
$h_{min}$ = Minimum film thickness [m]
$\varepsilon$ = Eccentricity ratio (0 = concentric, 1 = contact) This is a key output for design. The Lambda Ratio $\Lambda = h_{min}/ \sigma$ (with composite roughness $\sigma$) determines the actual lubrication regime.
Frequently Asked Questions
Generally, fluid lubrication is more likely to be established when S ≥ 0.1, and a stable fluid lubrication state is achieved when S is 1 or higher. However, the appropriate range varies depending on the bearing design and application. This tool visualizes the relationship between S and the oil film thickness ratio Λ on a Stribeck curve, allowing you to adjust design values in real time while confirming the lubrication regime.
Λ is the minimum oil film thickness divided by the composite surface roughness. Λ ≥ 3 indicates full fluid lubrication, 1 < Λ < 3 indicates mixed lubrication, and Λ ≤ 1 indicates boundary lubrication, where wear risk increases. This tool displays the Λ value in real time and plots the current operating point on the Stribeck curve, allowing you to modify parameters before entering the danger zone.
Reducing c increases S, which is beneficial for oil film formation, but it also raises the risk of seizure due to thermal expansion and machining errors. Additionally, wear from foreign particle contamination and stricter assembly precision requirements become concerns. This tool allows you to instantly check the changes in S and Λ when modifying c, helping in the design of appropriate clearance.
This tool handles dimensionless parameters (S, Λ) that are independent of material or oil type, making it applicable to various bearing materials such as white metal, copper alloys, and resins, as well as any lubricant including mineral oil, synthetic oil, and grease. However, to evaluate actual wear life and temperature rise, material properties and the viscosity-temperature characteristics of the oil must be considered separately.
Real-World Applications
Internal Combustion Engine Crankshaft Bearings: These operate across a huge speed range (idle to redline). Engineers use Stribeck analysis to ensure bearings stay hydrodynamic at cruise speed to minimize wear, while understanding that startup and shutdown cause brief boundary lubrication. The simulator parameters like Viscosity (η) are critical for choosing the correct engine oil grade.
Power Generation Turbine Journal Bearings: These high-speed, heavily loaded bearings are designed to run permanently in the hydrodynamic regime. The Radial Clearance (c) is machined with extreme precision to achieve the optimal film thickness for stability and load capacity, preventing catastrophic failure during decades of operation.
Automotive Gearbox and Differential Gears: While gears primarily experience elastohydrodynamic lubrication (EHL), the Stribeck curve principles still apply. Analysis of the film thickness helps in selecting lubricants with the right Dynamic Viscosity (η) and additives to protect surfaces during the mixed/boundary conditions experienced under high torque and low speed.
CAE-Driven Design (ANSYS, OpenFOAM): The simple model here is the starting point. In CAE, full EHD (Elastohydrodynamic) simulations couple fluid film equations with solid deformation of the bearing shell. This allows precise prediction of $h_{min}$ under real thermal and mechanical loads, directly optimizing the parameters you control in this simulator for next-generation machinery.
Common Misunderstandings and Points to Note
First, a common question with this simulator is, "Why doesn't the curve shape change even when I move parameters to extremes?" The Stribeck curve itself is a universal shape showing the "relationship" between the friction coefficient and the Sommerfeld number. What you are changing with the tool is where your current operating conditions lie on the curve (the red dot) and the specific oil film thickness and Λ value at that point. For example, even if you increase viscosity tenfold, the curve shape doesn't change, but you can observe the point moving significantly to the right into the hydrodynamic lubrication region, causing the Λ value to jump.
Next, avoid thinking simplistically that "Λ>3 is absolutely safe." Λ is a static evaluation. In real machinery, load fluctuations, shaft deflection, and repeated start-stop cycles can cause the oil film to momentarily thin. For instance, even if you calculate Λ=4 during design, practical wisdom involves setting a safety margin—like "ensure at least Λ>2.5"—considering fluctuating loads.
Finally, the units of input parameters and a sense of reality. The unit for dynamic viscosity η is Pa·s (Pascal-second), which differs from the commonly used cSt (centistokes). For example, a typical engine oil (SAE 30) has a dynamic viscosity of about 0.1 Pa·s (at 40°C). Inputting unrealistic values like 100 Pa·s might be interesting for a learning tool, but it's not useful for actual design. Get into the habit of first using the order of magnitude of the tool's default values (0.01–0.1 Pa·s) as a baseline.