Self-Lubricating Bearing Load Calculator and PV Factor Guide

Self-lubricating bearings, made from materials such as sintered bronze, PTFE composites, or graphite-filled bronze, operate without external lubrication. Solid lubricants embedded in these bearings transfer to the mating surface during operation, providing low friction and long service life.

The PV factor (Pressure × Velocity) is the key metric for assessing bearing load capacity and estimating wear life. Lower PV values generally correspond to longer operating life, while exceeding a material's PV limit can cause excessive heat, accelerated wear, or failure.

PV Factor Calculation

The PV factor is calculated using:

$$PV=P\times V$$

Where:

• P (Pressure): Load per unit projected area (MPa or psi).

• V (Velocity): Surface speed (m/s or ft/min).

Units:

• Metric: N/mm²·m/s

• Imperial: psi·ft/min (unitless after cancellation but typically reported as psi·ft/min)

Typical PV Limits for Self-Lubricating Materials (Dry Operation, Room Temperature)

Factors Affecting PV Limits:

• Temperature: Reduce PV by 20-50% above 80°C

• Lubrication: Intermittent lubrication can increase allowable PV by 20-50%

• Oscillation: Reciprocating motion reduces maximum V

• Surface Finish: Ra < 0.8 μm is ideal

Bearing Load Calculation Formula

1. Projected Area (A)

For cylindrical bushings:

$$A=d\times L$$

Where d = inner diameter, L = bushing length.

For flanged bushings, use only the cylindrical portion for radial loads. Axial thrust is handled by the flange:

Athrust=Flange OD2−d24A_text = fracAthrust​=4Flange OD2−d2​

2. Maximum Radial Load (W)

Wmax=Pmax×AW_text = P_text times AWmax​=Pmax​×A

3. Check Limits

Ensure:

P≤Pmax,V≤VmaxP le P_text, quad V le V_textP≤Pmax​,V≤Vmax​

4. Life Estimation

Approximate operating hours:

Lh≈kPVL_h approx fracLh​≈PVk​

Where k is a material constant (10⁴–10⁶ for polymers; test for accuracy).

For oscillating/reciprocating motion:

V=stroke length×cycles/min60 or 12 for unitsV = fracV=60 or 12 for unitsstroke length×cycles/min​

PV Factor Calculation Examples

Example 1: Standard Cylindrical Bushing (Sintered Bronze)

• Shaft: 25 mm

• Length: 30 mm

• Radial Load: 2,000 N

• Speed: 1,500 RPM

Step 1: Calculate P

$$A=25\times 30=750\text{ mm²},P=2,000/750=2.67\text{ MPa}$$

Step 2: Calculate V

V=π×25×1,50060,000≈1.96 m/sV = frac approx 1.96 textV=60,000π×25×1,500​≈1.96 m/s

Step 3: PV

$$PV=2.67\times 1.96\approx 5.23\text{ N/mm²cdotpm/s}$$

Assessment: Exceeds typical limit (3.5). Increasing L to 50 mm yields PV = 3.14 (acceptable). Estimated life: >5,000 hours at 80% duty cycle.

Example 2: Graphite-Filled Bronze, Imperial Units

• Shaft: 0.75 in

• Length: 1 in

• Load: 90 lbf

• Speed: 341 RPM

$$A=0.75\text{ in²},P=90/0.75=120\text{ psi}$$ $$V=0.262\times 0.75\times 341\approx 67\text{ ft/min}$$ $$PV=120\times 67=8,040\text{ psicdotpft/min}$$

Assessment: Within safe limit for continuous dry operation.

Example 3: Reciprocating Motion, PTFE Composite

• Shaft: 20 mm

• Length: 40 mm

• Load: 800 N

• Stroke: 50 mm

• Cycles: 120/min

$$A=20\times 40=800\text{ mm²},P=1\text{ MPa}$$ V=50×12060,000=0.1 m/sV = frac = 0.1 text V=60,00050×120​=0.1 m/s $$PV=1\times 0.1=0.1\text{ N/mm²cdotpm/s}$$

Assessment: Very low PV, ideal for low-speed oscillation. Estimated life: >20,000 hours.

Example 4: Flanged Self-Lubricating Bushing

• Cylindrical part: d = 16 mm, L = 20 mm

• Flange: OD = 24 mm, thickness = 2 mm

• Radial Load: 1,500 N

• Speed: 800 RPM

Radial PV Calculation

$$A=16\times 20=320\text{ mm²},P=1,500/320\approx 4.69\text{ MPa}$$ V=π×16×80060,000≈0.67 m/s,PV=3.14V = frac approx 0.67 text, quad PV = 3.14V=60,000π×16×800​≈0.67 m/s,PV=3.14

Assessment: At limit for continuous operation; short-term use acceptable.

Axial Thrust (Flange):

Aflange=π(212−152)≈679 mm²,Paxial=1,000/679≈1.47 MPaA_text = pi(21^2 – 15^2) approx 679 text, quad P_text = 1,000 / 679 approx 1.47 textAflange​=π(212−152)≈679 mm²,Paxial​=1,000/679≈1.47 MPa

Safe for axial loads <40 MPa.

Final Dimensions: ID = 16 mm, OD = 20 mm, L = 20 mm, flange OD = 24 mm, thickness = 2 mm.

Flanged Self-Lubricating Bushing Overview

Flanged bushings combine a radial sleeve with an integral flange for axial positioning. They simplify assembly and handle combined radial and thrust loads, ideal for pumps, hinges, or pivots requiring minimal end-play. The PV factor is calculated on the cylindrical (radial) portion.

Design Considerations:

• Sizing: Based on radial PV; flange thickness 1–3 mm, flange OD = 1.2–1.5 × ID, wall thickness 1–2 mm

• Load Handling: Radial via cylinder, axial via flange (max 2–5× radial)

• Installation: Press-fit into H7 bore, flange faces housing

• PV Adjustments: Reduce 10–20% for flanged edges; oscillation lowers max V

Sizing Example:

• Radial: 3,000 N, axial: 1,000 N, d = 30 mm, N = 500 RPM, graphite-filled bronze (PV_max = 2.5)

• Calculated cylindrical length: 30 mm

• Flange: OD = 42 mm, thickness = 3 mm

• Final: ID = 30 mm, OD = 36 mm, L = 30 mm, flange OD = 42 mm, thickness = 3 mm

Life and Optimization

Bearing life is roughly inversely proportional to PV². Testing prototypes under expected loads and duty cycles is recommended for accuracy. Online calculators or PV charts can provide quick checks, and adjustments should account for intermittent operation or oscillating motions.