How to Calculate Plain Bearing Dimensions: A Step-by-Step Guide

To design a plain bearing (also known as a sleeve bearing or journal bearing), it's essential to determine the correct dimensions based on load, speed, material, and lubrication. The following guide explains the key parameters, formulas, and step-by-step calculations used in plain bearing design.

If you have specific details such as load, shaft speed, or bearing material, more precise calculations can be made.

🔹 Key Parameters in Plain Bearing Design

1. Bearing Diameter (D):
The inner diameter of the bearing, usually equal to the shaft diameter.

2. Bearing Length (L):
The axial length of the bearing, which determines load distribution.

3. Length-to-Diameter Ratio (L/D):
A critical ratio influencing performance and heat dissipation.
Typical ranges:

• 0.5 – 1.0: High-load, low-speed applications

• 1.0 – 1.5: General-purpose bearings

• 1.5 – 2.0: High-speed, light-load applications

4. Clearance (c):
Radial clearance between shaft and bearing, usually 0.001–0.002 × shaft diameter.

5. Load Capacity (W):
Determined by the allowable bearing pressure and projected area.

6. Lubrication Parameters:
Include viscosity, minimum film thickness, and pressure distribution.

🔹 Step-by-Step Bearing Dimension Calculation

Step 1: Determine Load and Speed

• Load (W): Radial or axial load the bearing must support (in N or lbs).

• Speed (N): Shaft rotational speed (in RPM or rad/s).

Step 2: Select the L/D Ratio

Choose the L/D ratio based on application conditions (load, speed, stability, and cooling).

Step 3: Calculate Bearing Diameter (D)

If shaft diameter is unknown, estimate using material strength:

D=4WπσD = sqrtD=πσ4W​​

Where σ is the allowable stress of the shaft material (e.g., 50–100 MPa for steel).

Step 4: Calculate Bearing Length (L)

$$L=(L/D)\times D$$

Example: For D = 50 mm and L/D = 1.2,

$$L=1.2\times 50=60mm$$

Step 5: Determine Radial Clearance (c)

$$c=0.001D\text{ to }0.002D$$

Example: For D = 50 mm,

$$c=0.05\text{–}0.1mm$$

Step 6: Check Load Capacity

p=WL×Dp = fracp=L×DW​

Typical allowable bearing pressures:

• Bronze: 1–7 MPa

• PTFE or Plastic: 0.1–1 MPa

Ensure p does not exceed the material's limit. If it does, increase L or D.

Step 7: Lubrication and Minimum Film Thickness

For hydrodynamic bearings:

hmin≈0.0002D to 0.0005Dh_ approx 0.0002D text 0.0005Dhmin​≈0.0002D to 0.0005D

Ensure the film thickness is greater than the surface roughness.
Use appropriate lubricant viscosity (e.g., ISO VG 32–68 for moderate speed and temperature).

Step 8: Frictional Torque and Power Loss

T=f×W×D2T = f times W times fracT=f×W×2D​ P=T×ωwhereω=2πN60P = T times omega quad text quad omega = fracP=T×ωwhereω=602πN​

Typical f values: 0.001–0.01 (for hydrodynamic lubrication).

Step 9: Heat Generation and Cooling

$$Q=P\text{ (in watts)}$$

Ensure proper cooling (oil circulation or external cooling) to keep bearing temperature below limits — typically ≤80°C for bronze.

🔹 Example Calculation

Given:

• Load, W = 5000 N

• Speed, N = 1000 RPM

• Material: Bronze (pₐₗₗ = 5 MPa)

• Desired L/D = 1.2

• Shaft material strength, σ = 80 MPa

1. Estimate Diameter:

D=4×5000π×80×106≈17.8mm⇒use D=20mmD = sqrt ≈ 17.8 mm Rightarrow text D = 20 mmD=π×80×1064×5000​​≈17.8mm⇒use D=20mm

2. Calculate Length:

$$L=1.2\times 20=24mm$$

3. Check Pressure:

p=500024×20=10.42MPa>5MPa (too high)p = frac = 10.42 MPa > 5 MPa textp=24×205000​=10.42MPa>5MPa (too high)

Increase dimensions: D = 30 mm, L = 36 mm

p=500030×36=4.63MPa (acceptable)p = frac = 4.63 MPa textp=30×365000​=4.63MPa (acceptable)

4. Clearance:

$$c=0.001\times 30\text{ to }0.002\times 30=0.03–0.06mm$$

5. Lubrication:
Select ISO VG 46 oil.

hmin≈0.0003×30=0.009mmh_ ≈ 0.0003×30 = 0.009 mmhmin​≈0.0003×30=0.009mm

🔹 Additional Notes

• Material Selection: Choose bearing material based on load, speed, and environmental factors (e.g., bronze for heavy-duty, PTFE for maintenance-free applications).

• Design Standards: Follow guidelines such as ISO 2795 or DIN 31652.

• Software Tools: Use design tools for precise hydrodynamic performance analysis.

• Manufacturing Tolerances: Ensure fits comply with ISO H7/g6 to maintain proper clearance.

✅ Conclusion

By following these steps, you can accurately calculate the dimensions of a plain bearing to ensure optimal performance, load capacity, and service life. Adjust parameters such as L/D ratio, clearance, and lubrication based on operating conditions for the best results.

Disclaimer: This information is provided without any liability or warranty. For technical details, please contact the engineer or manufacturer directly.