KEVOS® MAKEOS · Power Transmission
Tilting Pad (Kingsbury) Thrust Bearing Design (Operating Number, Film, Friction, Oil Flow, Temperature Rise)
For a tilting pad (Kingsbury or Michell) thrust bearing carrying an axial load, what pad layout, unit load and operating number result, and with the film factor and friction coefficient from the handbook charts, what minimum film, friction power, oil flow and temperature rise follow?
Tilting pad thrust bearing design by the handbook procedure: outside diameter D2 = √(4W ÷ (π Kg p) + D1²) (or the largest available), radial pad width a = (D2 − D1) ÷ 2, pitch-line circumference B = π(D1 + D2) ÷ 2, number of pads ≈ B Kg ÷ a, pad length ≈ B Kg ÷ i, pitch-line velocity U = B N ÷ 12, unit load p = W ÷ (i a b), operating number O = 1.45 × 10⁻⁷ Z2 U ÷ (5 p b) for reading the dimensionless film thickness α from the chart, minimum film hmin = α b, friction power Pf = f W U ÷ 33,000 with the friction coefficient f from the chart, oil flow Q = 0.0591 α i a b U and temperature rise Δt = 0.0217 f p ÷ (α c).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Axial load | N | Axial (thrust) load on the bearing. |
| Inside diameter D1 | mm | Inside diameter of the thrust face, set by the shaft and its clearance. |
| Outside diameter D2 | mm | Outside diameter of the pads, from the design unit load or the largest that fits. |
| Design unit load (for the diameter required) | kPa | Unit load used to find the outside diameter required; the handbook gives 200 psi normal and 500 psi (3447 kPa) maximum for tilting pad bearings. |
| Fraction of circumference occupied by pads Kg | Fraction of the circumference occupied by pads; 0.8 for tilting pad bearings. | |
| Number of pads chosen | pads | Number of pads, the even number nearest the estimate shown. |
| Pad length chosen b | mm | Pad length on the pitch line you choose, near the estimate B Kg ÷ i. |
| Speed N | rpm | Shaft speed. |
| Oil | ||
| Oil viscosity at outlet temperature | cP | Oil viscosity in centipoises at the outlet temperature (inlet plus the assumed rise). |
| Oil density | kg/m³ | Density of the oil. |
| Oil specific heat | kJ/(kg·K) | Specific heat of the oil. |
| Largest oil temperature rise you accept | °C | Largest temperature rise of the oil you accept; the handbook gives 50 °F (27.8 °C) as an acceptable maximum. |
| Read from the handbook charts | ||
| Film thickness factor α (Fig. 13, thousandths) | Dimensionless film thickness factor α read from the handbook’s Fig. 13 at the operating number shown, in thousandths (for example 0.30 for 0.30 × 10⁻³). | |
| Coefficient of friction f (Fig. 14, from α) | Coefficient of friction read from the handbook’s Fig. 14 at the film thickness factor. | |
| Least film thickness you accept | mm | Least minimum film thickness you accept; the handbook suggests about 0.001 in (0.025 mm) for small bearings and 0.002 in (0.051 mm) for larger and high-speed bearings. |
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: Axial load
- What it is
- Axial (thrust) load carried by the thrust 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 311376 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 diameter required.
- Get it right
- Include hydraulic, gear and impeller thrust at the worst running condition.
What this means: Inside diameter D1
- What it is
- Inside diameter of the thrust face.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 177.8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger bore needs a larger outside diameter for the same area.
- Get it right
- Set by the shaft diameter plus running clearance.
What this means: Outside diameter D2
- What it is
- Outside diameter of the thrust face or pads.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 381 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 pad width and pitch circumference.
- Get it right
- Round the diameter required to a convenient size, or use the largest that fits.
What this means: Design unit load (for the diameter required)
- What it is
- Unit load used to find the outside diameter required for the tilting pads.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0.000001 kPa to 20000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3447.4 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only changes the diameter required shown.
- Get it right
- About 1379 kPa (200 psi) normal and 3447 kPa (500 psi) maximum.
What this means: Fraction of circumference occupied by pads Kg
- What it is
- Fraction of the pitch circumference occupied by pads rather than grooves.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.8 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller fraction needs a larger outside diameter.
- Get it right
- Usually 0.8; 0.8 or 0.9 for tapered land bearings.
What this means: Number of pads chosen
- What it is
- Number of pads around the thrust face.
- Units and format
- Enter a number in pads: pads. The form accepts 2 pads to 100 pads. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 pads as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pad length and the unit load.
- Get it right
- Take the even number nearest the estimate shown.
What this means: Pad length chosen b
- What it is
- Length of each pad along the pitch line.
- 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 120.65 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, operating number and film.
- Get it right
- Near the estimate B Kg ÷ i shown; the example rounds 4.61 in up to 4.75 in.
What this means: Speed N
- What it is
- Rotational speed of the shaft.
- 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 3600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the pitch-line velocity, friction and film.
- Get it right
- Use the running speed at full thrust load.
Oil
What this means: Oil viscosity at outlet temperature
- What it is
- Viscosity of the oil in centipoises at the outlet temperature.
- 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 18 cP as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the operating number and the film.
- Get it right
- Inlet temperature plus the assumed rise, from the oil’s viscosity chart.
What this means: Oil density
- What it is
- Density of the lubricating oil.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 2000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 880 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- With the specific heat, sets the heat the oil carries per litre.
- Get it right
- About 850 to 900 kg/m³ for mineral oils.
What this means: Oil specific heat
- What it is
- Specific heat of the lubricating oil.
- Units and format
- Enter a number in kJ/(kg·K): kilojoules per kilogram per kelvin. The form accepts 0.000001 kJ/(kg·K) to 10 kJ/(kg·K). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.9953 kJ/(kg·K) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher specific heat lowers the temperature rise or the flow needed.
- Get it right
- About 1.9 to 2.0 kJ/(kg·K) for mineral oils.
What this means: Largest oil temperature rise you accept
- What it is
- Largest temperature rise of the oil through the bearing you accept.
- 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 27.778 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fails the design when the rise is higher.
- Get it right
- The handbook gives 27.8 °C (50 °F) as an acceptable maximum.
Read from the handbook charts
What this means: Film thickness factor α (Fig. 13, thousandths)
- What it is
- Dimensionless film thickness factor read from the handbook chart at the operating number.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Sets the film, the oil flow and the temperature rise.
- Get it right
- Enter it in thousandths, for example 0.30 for 0.30 × 10⁻³.
What this means: Coefficient of friction f (Fig. 14, from α)
- What it is
- Coefficient of friction of the tilting pads read from the handbook chart.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0036 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction power and temperature rise rise in proportion.
- Get it right
- Enter Fig. 14 with the film thickness factor α.
What this means: Least film thickness you accept
- What it is
- Least minimum film thickness you accept for this bearing.
- 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 0.0254 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Flags the design when the film is thinner.
- Get it right
- About 0.025 mm (0.001 in) for small and 0.051 mm (0.002 in) for large or high-speed bearings.
Method and formulas
- D2 = √(4W ÷ (π Kg p) + D1²); a = (D2 − D1) ÷ 2; B = π(D1 + D2) ÷ 2; i ≈ B Kg ÷ a; b ≈ B Kg ÷ i; U = B N ÷ 12; p = W ÷ (i a b).
- O = 1.45 × 10⁻⁷ Z2 U ÷ (5 p b); α from the chart; hmin = α b.
- Pf = f W U ÷ 33,000 hp; Q = 0.0591 α i a b U gpm; Δt = 0.0217 f p ÷ (α c) °F with c in Btu/gal °F.
- Inputs are converted to inches, pounds and °F for the handbook constants; results are shown in SI with the inch values.
- Example: 6 pads carry 4,233.6 kPa at an operating number of 1.8554 × 10⁻⁶; the film is 0.036195 mm and the oil rises 25.381 °C.
Limitations
- The film thickness factor α and the friction coefficient f come from the handbook’s charts for the optimum pivot location; read them at the operating number shown.
- For rotation in both directions the pivot must be at mid-pad, with little loss of performance.
- If the temperature rise is too high, add feed chamfers to raise the oil flow.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a tilting pad thrust bearing for a turbine, compressor or large pump
- Check the film and temperature rise of an existing pivoted pad bearing
- Estimate friction loss and oil flow for the lubrication system
Who it is for
- Machine designers
- Pump, compressor and turbine engineers
- Students
What you get
- Outside diameter required, pad width and pitch circumference
- Estimated number and length of pads
- Pitch-line velocity and unit load
- Operating number O
- Minimum film thickness
- Friction power, oil flow and temperature rise
Interpreting the result
- Tilting pads absorb misalignment and suit high loads and speeds, at higher cost.
- A larger operating number (higher speed or viscosity, lower load) thickens the film.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2339, 2352–2356. 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
Thrust bearings
In Plain Bearings by the Numbers
What it covers: Check a thrust face's area, unit load, sliding speed and PV, estimate its friction heat and oil flow with the KEVOS® thrust tools, and see why tapered lands and tilting pads carry load.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.