KEVOS® MAKEOS · Power Transmission
Journal Bearing Lubrication Analysis (Pressure Parameter, Friction, Oil Flow, Temperature Rise, Film Thickness)
For a pressure-fed plain journal bearing at a trial diametral clearance and an assumed oil temperature rise, what are the bearing pressure, pressure parameter, friction torque and power, the oil flow it needs and the flow it actually passes, the actual temperature rise and the minimum film thickness — and does the assumed rise hold or must I repeat with a new one?
One pass of the handbook’s journal bearing lubrication analysis: unit load pb = W ÷ (K l d) (K = 1 single oil hole, 2 central groove), clearance modulus m = cd ÷ d, bearing pressure parameter P = 6.9 (1000 m)² pb ÷ (Z N) and capacity number Cn = (l/d)² ÷ (60 P) for reading the eccentricity ratio and flow factor from the handbook figures, friction torque Tf = T r² Z N ÷ (6900 × 1000 m), friction horsepower Pf = K Tf N l ÷ 63,000, flow required QR = X Pf ÷ ta, hydrodynamic flow Q1 = N l cd q d ÷ 294, pressure flow Q2 = K′ ps cd³ d (1 + 1.5 ε²) ÷ (Z l), actual temperature rise t = X Pf ÷ (Q1 + Q2) and minimum film thickness ho = ½ cd (1 − ε), with the new assumed rise halfway between when the two differ by more than 5 °F.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load on the bearing | N | Radial load carried by the bearing. |
| Journal diameter d | mm | Diameter of the journal. |
| Bearing length l (half the length with a central groove) | mm | Bearing length as the handbook defines it: the whole length with a single oil hole, half the length with a central circumferential groove. |
| Oil feed | choice | How the oil is fed: a single hole or a central groove; it sets the constants K. |
| Speed N | rpm | Shaft speed. |
| Diametral clearance cd (operating) | mm | Diametral clearance at operating temperature, chosen on a trial basis (the handbook’s Fig. 6 suggests ranges by diameter and speed). |
| Oil supply pressure | kPa | Oil supply pressure at the bearing. |
| Assumed temperature rise of the oil | °C | Assumed rise of oil temperature through the bearing; the handbook starts with 20 °F (11.1 °C). |
| Read from the handbook figures | ||
| Oil viscosity at inlet temperature + assumed rise | cP | Absolute viscosity of the oil in centipoises at the inlet temperature plus the assumed rise, from the oil’s viscosity–temperature data. |
| Eccentricity ratio ε (Fig. 7, from P and l/d) | Eccentricity ratio read from the handbook’s Fig. 7 using the pressure parameter P and l/d shown in the results. | |
| Torque parameter T (Fig. 8 or 9) | Torque parameter read from the handbook’s Fig. 8 or 9 using 1/(1 − ε) and l/d. | |
| Flow factor q (Fig. 10, from Cn) | Flow factor read from the handbook’s Fig. 10 using the capacity number Cn shown in the results. | |
| Factor X (Table 5, or 0.1837 ÷ oil density × specific heat) | Factor X for mineral oil from the handbook’s Table 5 (about 12), or 0.1837 ÷ (density in lb/in³ × specific heat in Btu/lb °F). | |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load on the bearing
- What it is
- Radial load carried by the journal bearing.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 26689 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the unit load and the pressure parameter.
- Get it right
- Use the steady load; check peak loads separately.
What this means: Journal diameter d
- What it is
- Diameter of the journal running in the bearing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 58.42 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the unit load, friction torque and both oil flows.
- Get it right
- Usually set by shaft strength and deflection first.
What this means: Bearing length l (half the length with a centra…
- What it is
- Bearing length as the handbook defines it for the oil feed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 48.26 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer bearing lowers the unit load and passes more hydrodynamic flow.
- Get it right
- Whole length with a single oil hole; half the length with a central groove.
What this means: Oil feed
- What it is
- How oil is fed into the bearing: a single hole or a central circumferential groove.
- Units and format
- Choose one of 2 options from the list: Single oil hole (K = 1); Central groove (K = 2).
- Example
- The form opens with “Single oil hole (K = 1)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Sets the constants K used for load, friction and pressure flow.
- Get it right
- A central groove doubles the bearing constant and raises the pressure flow.
What this means: Speed N
- What it is
- Rotational speed of the shaft in the bearing.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4800 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises friction power and hydrodynamic flow.
- Get it right
- Use the running speed at the load being analysed.
What this means: Diametral clearance cd (operating)
- What it is
- Diametral clearance between journal and bearing at operating temperature.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0762 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More clearance passes more oil and cools the bearing but thins the film.
- Get it right
- Allow for thermal expansion of journal and bearing when converting to machining sizes.
What this means: Oil supply pressure
- What it is
- Pressure at which oil is supplied to the bearing feed hole or groove.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206.84 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The pressure flow rises in proportion.
- Get it right
- Measure at the bearing, after any restrictor.
What this means: Assumed temperature rise of the oil
- What it is
- Assumed rise of oil temperature through the bearing for this pass.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 0.000001 °C to 100 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16.667 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the operating temperature at which the viscosity is read.
- Get it right
- Start with 11 °C (20 °F); then use the new value the tool gives.
Read from the handbook figures
What this means: Oil viscosity at inlet temperature + assumed ri…
- What it is
- Absolute viscosity of the oil in centipoises at the inlet temperature plus the assumed rise.
- Units and format
- Enter a number in cP: cP. The form accepts 0.000001 cP to 10000 cP. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.8 cP as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher viscosity raises friction and lowers the pressure parameter.
- Get it right
- Read it from the oil’s viscosity–temperature chart for its grade.
What this means: Eccentricity ratio ε (Fig. 7, from P and l/d)
- What it is
- Eccentricity ratio of the journal in the bearing, read from the handbook chart.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 0.999. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.86 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Higher eccentricity thins the minimum film and raises the pressure flow.
- Get it right
- Enter the chart at the pressure parameter P and l/d shown in the results.
What this means: Torque parameter T (Fig. 8 or 9)
- What it is
- Torque parameter read from the handbook chart at 1/(1 − ε) and l/d.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.53 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction torque and power rise in proportion.
- Get it right
- Use Fig. 8 for low and Fig. 9 for high eccentricity.
What this means: Flow factor q (Fig. 10, from Cn)
- What it is
- Flow factor read from the handbook chart at the bearing capacity number Cn.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.48 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The hydrodynamic flow rises in proportion.
- Get it right
- Cn is shown in the results for this pass.
What this means: Factor X (Table 5, or 0.1837 ÷ oil density × sp…
- What it is
- Heat factor of the oil linking friction power, flow and temperature rise.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 50. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.9 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The flow required and the temperature rise rise in proportion.
- Get it right
- About 12 for mineral oils (Table 5), or 0.1837 ÷ (density lb/in³ × specific heat Btu/lb °F).
Method and formulas
- pb = W ÷ (K l d) psi; m = cd ÷ d; P = 6.9 (1000 m)² pb ÷ (Z N); Cn = (l/d)² ÷ (60 P).
- Tf = T r² Z N ÷ (6900 × 1000 m) in·lb per inch; Pf = K Tf N l ÷ 63,000 hp.
- QR = X Pf ÷ ta; Q1 = N l cd q d ÷ 294 gpm; Q2 = K′ ps cd³ d (1 + 1.5 ε²) ÷ (Z l) gpm with K′ = 1.64 × 10⁵ (hole) or 2.35 × 10⁵ (groove).
- t = X Pf ÷ (Q1 + Q2); if t and ta differ by more than 5 °F, repeat with ta halfway between.
- ho = ½ cd (1 − ε); handbook minimum 200 µin below 1 in diameter, 500 µin for 1 to 4 in, 750 µin larger; temperature rise up to about 40 °F.
- Inputs are converted to inches, pounds, psi and °F for the handbook constants; results are shown in SI with the inch values.
- Example: the bearing passes 1.388 L/min and the oil rises 19.154 °C against 16.667 °C assumed; the minimum film is 0.005334 mm.
Limitations
- Eccentricity ratio, torque parameter and flow factor come from the handbook’s design charts; read them at the P and Cn shown and repeat until the temperature rise settles.
- Repeat the analysis for several clearances to choose a working clearance range, as the handbook describes.
- For full (360°) bearings in steady load; misalignment above about 0.0003 in per inch of length reduces the film.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pressure-fed sleeve bearing at a trial clearance
- Find the oil flow and temperature rise for a bearing design
- Plot film thickness, temperature rise, friction and flow against clearance
Who it is for
- Machine designers
- Rotating equipment engineers
- Lubrication engineers
What you get
- Unit load, clearance modulus and l/d
- Pressure parameter P and capacity number Cn (to read the figures)
- Friction torque and friction power
- Oil flow required and actual (hydrodynamic and pressure flow)
- Actual temperature rise and the next assumed rise
- Minimum film thickness against the handbook minimum
Interpreting the result
- When the actual rise exceeds the assumed rise, the oil runs thinner than assumed: repeat with the new assumed rise.
- A larger clearance passes more oil and runs cooler but thins the film.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2328–2338. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · KEVOS® original book
Supplying the oil
In Plain Bearings by the Numbers
What it covers: Calculate the side flow a journal bearing's film loses, compare it with an oil ring's or pump's supply, place grooves where film pressure is low, and keep the oil level and condition right.
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