Load and pv Calculations for Graphite Bearings: Sizing Self-Lubricated Bearings

1. Why pv Comes First

Metal bearings separate the pair with an oil film; graphite bearings run in boundary or dry friction, with heat generated directly at the contact. Two constraints follow:

1.Load: above material strength, graphite crushes locally — brittle materials have no yield stage

2.Heat: friction power (≈ μ·p·v) converts to heat in the contact zone, and graphite conductivity is limited (15–85 W/(m·K) by impregnation); excessive local temperature rise causes thermal cracking

Engineering merges both into two parameters:

• Specific load p (MPa) = force F / loaded area
• pv value (MPa·m/s) = p × surface velocity v

pv is essentially friction power per unit area — the common sizing language for self-lubricating materials (graphite, plastics, coated bearings). Selecting a graphite bearing = pushing actual pv below the allowable, with margin.

2. Sizing Flow

2.1 Step 1: Resolve Loads

Bearing loads are rarely purely radial. Resolve in order:

1.Radial force F_r: belt pull, gear mesh force, hydraulic unbalance of impeller/rotor, gravity component

2.Axial force F_a: single-suction impeller suction, gear helix axial component, installation preload

3.Resultant: F = √(F_r² + F_a²); if the axial share exceeds 30%, add a thrust structure (thrust disc/thrust bearing) rather than letting the radial carry it obliquely

2.2 Step 2: Specific Load

Radial bearing:

• p = F / (d × L), d = shaft diameter (mm), L = bearing length (mm), F in newtons
• p[MPa] = F[N] / (d[mm] × L[mm])

Thrust bearing (thrust disc):

• p = F_a / A, A = annular thrust area = π/4 × (D² - d²)
• Use effective contact area, not the nominal full OD area — thrust faces often have relieved regions

2.3 Step 3: pv Check

• Surface velocity v = π × d × n / 60000 (m/s; d in mm, n in rpm)
• pv = p × v
• Compare with allowable (table below), margin ≥ 2

2.4 Step 4: Match Clearance and Wear

Passing pv is not passing life. Size clearance by medium:

| Medium | Diametral clearance (% of d) | Notes |

|---|---|---|

| Dry friction | 0.10–0.20 | Must expel debris; too small seizes on wear particles |

| Water | 0.15–0.25 | Weak water film; too large builds no hydrodynamic pressure |

| Oil | 0.10–0.15 | Good film; take the tighter end |

| Abrasive media | 0.25–0.35 | Let sand pass through instead of embedding |

3. Allowable Reference Tables

3.1 By Lubrication Condition

| Lubrication | Allowable p | Allowable pv | Notes |

|---|---|---|---|

| Dry friction (intermittent) | 0.5–1.5 MPa | 0.5–1.5 MPa·m/s | Startup transients, low-speed barring |

| Dry friction (continuous) | ≤ 0.5 MPa | ≤ 1.0 MPa·m/s | Not recommended; derated service |

| Water-lubricated | 2–5 MPa | 3–8 MPa·m/s | Water pumps, marine pumps |

| Oil-lubricated | 2–5 MPa | 5–10 MPa·m/s | Lubrication systems, oil pumps |

| Gas-rich media | 1–2 MPa | 1–3 MPa·m/s | Compressors, steam |

These are order-of-magnitude references for impregnated carbon graphite; actual grades follow supplier data — base grain size, impregnant and density can shift allowables by 2×. The GB-series rating of ≤ 20 MPa is static strength (crush limit); operating allowables are far lower. The TD-series axial ≤ 10 MPa is the same story.

3.2 By Impregnant

| Impregnant | Character | pv correction |

|---|---|---|

| Resin | Low friction, dense | Baseline |

| Antimony | High strength, moderate conductivity | Pressure +20–40% |

| Copper | Best conductivity (~85 W/(m·K) class) | Best for dry/intermittent duty; pressure and speed +30–50% |

| Unimpregnated | Lower strength, good debris expulsion | Pressure −30–50%; suits low-speed light load |

3.3 By Environment

• Abrrasive media: knock allowable pv to 50–70%; wear rate is roughly linear with sand content
• High temperature (> 200°C): resin systems top out; switch to antimony/copper and use grade high-temperature data
• Low temperature (< -30°C): mind brittleness and contraction; open cold clearance 10–20%
• Corrosive media: screen media compatibility first (no copper in ammonia, no antimony in strong oxidizers), then discuss load

4. Worked Example

A submersible pump radial graphite bearing: shaft φ40 mm, length 60 mm, radial force 900 N, speed 2900 rpm, clean water.

1.Specific load: p = 900 / (40 × 60) = 0.375 MPa

2.Surface velocity: v = π × 40 × 2900 / 60000 = 6.07 m/s

3.pv: pv = 0.375 × 6.07 = 2.28 MPa·m/s

4.Check: water-lubricated allowable 3–8 → margin = 3 / 2.28 = 1.32 — below the 2× line, fails

5.Adjust: lengthen the bearing to 80 mm → p = 0.28 MPa → pv = 1.71 → margin 1.75, still low; switch to an antimony-impregnated grade (allowable +30%) → allowable 3.9–10.4 → margin 2.3, passes

6.Clearance: water 0.15%–0.25% × 40 = 0.06–0.10 mm

Two lessons: lengthening the bearing is cheaper than changing material, and the two can be combined; and at 2900 rpm surface velocity is not low — the "small pump, small load" intuition routinely underestimates pv.

5. Field Quick Reference

| Problem | Sizing angle |

|---|---|

| Crushed/cracked bearing | Specific load exceeded — compute p before blaming material |

| Local melting / thermal cracks | pv exceeded — friction power density too high |

| Fast uniform wear | Insufficient pv margin or sand; check medium first, margin second |

| Seizure (new installation) | Clearance too small; check cold/hot expansion delta |

| Bite marks on thrust face | Axial force exceeded or poor thrust-face lubrication |

Conclusion

Graphite bearing load sizing reduces to one sentence: specific load governs strength, pv governs temperature, clearance governs wear. The three-step calculation takes ten minutes and decides between 2,000 and 20,000 hours of life. When allowables are uncertain, lengthen the bearing and lower specific pressure — never rely on "graphite is hard." Brittle materials give no overload warning: the first exceedance is fracture.