Design Considerations

Consider a bearing of diameter D inside which a journal of diameter d and length l, which rotates at eccentricity e and speed N in rpm (N′ = N/60 in revolutions per second). The absolute viscosity of the lubricant is Z (Pa·s) and the coefficient of friction is µ. The minimum film thickness is h₀ (≈ 0.0001D).

Clearances

Diametral clearance: c_d = D − d
Radial clearance: c_r = c_d / 2

Eccentricity Ratio

ε = e / c_r

Film Thickness

At any angle φ: h = (c_d / 2) × (1 + ε cos φ)

Minimum film thickness relation: e = c / 2 − h₀

Average Pressure

For a radial load W on the journal: p = W / (d × l)

Coefficient of Friction

Defined as the ratio of tangential force to the radial load acting on the bearing.

Important Characteristics of Sliding Contact Bearings

1. Bearing Characteristic Number

Bearing characteristic number = ZN / p

At low speeds, the lubricant cannot separate the surfaces of the journal and bearing, resulting in metal-to-metal contact. With increase in speed N, more liquid is forced into the wedge-shaped clearance. This results in transition from thin film lubrication to thick film lubrication at a certain speed.

The coefficient of friction between the journal and bearing becomes minimum at an optimum speed and then increases with further speed.

2. Bearing Modulus

The value of bearing characteristic number corresponding to the minimum coefficient of friction is called bearing modulus (K).

To avoid seizure, the operating value of ZN/p should be at least 5 to 6 times K, and for fluctuating loads, at least 15K.

3. Sommerfeld Number

S = (ZN′ / p) × (r / c)²

This dimensionless number is used in hydrodynamic lubrication theory and correlates many dimensionless parameters.

4. Coefficient of Friction Equations

(a) Petroff’s Equation

µ = 2π² × (ZN / p) × (D / c_d)

Here, ZN/p is the bearing characteristic number and D/c_d is the clearance ratio (normally 500–1000).

(b) Mckee’s Equation

µ = 0.002 + 0.326 × (ZN / p) × (D / c_d)