BIZOMAT MAKEOS · Power Transmission
Hydrodynamic Journal Bearing Design (Load, Friction, Heat and Oil)
Is this plain journal bearing within its unit load, how much heat does oil friction make, and how much oil must flow to carry it away?
First design of a full-film hydrodynamic journal bearing: unit load on the projected area, length-to-diameter ratio, surface speed, Sommerfeld number, Petroff friction torque, friction coefficient and power loss (as the Petroff tool), and the oil flow to carry the heat at an allowed temperature rise, with checks of unit load, L/D and Sommerfeld number against your limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Radial load | N | Radial load on the bearing. |
| Journal diameter | mm | Diameter of the journal. |
| Bearing length | mm | Length of the bearing. |
| Radial clearance | mm | Radial clearance (half the diametral clearance). |
| Speed | rpm | Shaft speed. |
| Oil viscosity at the film temperature | mPa·s (cP) | Dynamic viscosity of the oil at its working film temperature. |
| Allowed oil temperature rise | K | Temperature rise of the oil through the bearing. |
| Oil specific heat | kJ/kg·K | Specific heat of the oil. |
| Oil density | kg/m³ | Density of the oil. |
| Largest unit load | MPa | Largest unit load for the bearing material and duty (your value). |
| Smallest L/D | Smallest length-to-diameter ratio you design to. | |
| Largest L/D | Largest length-to-diameter ratio you design to. | |
| Smallest Sommerfeld number | Smallest Sommerfeld number you accept, so the film stays thick enough (your value). |
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: Radial load
- What it is
- The radial force the shaft presses onto this bearing: its share of the shaft weight, belt pull, gear forces and other loads.
- 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 5000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Unit load rises in proportion and the Sommerfeld number falls; the Petroff friction loss does not depend on load.
- Get it right
- Use the reaction at this bearing, not the total load on the shaft if two bearings share it.
What this means: Journal diameter
- What it is
- The diameter of the part of the shaft that runs inside the bearing. It sets the unit load, the surface speed and the friction torque.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the journal itself, not the bearing bore; the difference between them is the clearance.
What this means: Bearing length
- What it is
- The axial length of the bearing surface that supports the journal. With the diameter it sets the projected area and the L/D ratio.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Unit load falls in inverse proportion to length, and the friction loss rises in proportion.
- Get it right
- Use the length that actually carries load; chamfers and circumferential oil grooves shorten it.
What this means: Radial clearance
- What it is
- The radial gap between journal and bearing when the journal is centred: half the difference between bore diameter and journal diameter.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.04 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Halving the clearance doubles the friction loss and quadruples the Sommerfeld number.
- Get it right
- Do not enter the diametral clearance; radial clearance is half of it.
What this means: Speed
- What it is
- The rotational speed of the journal in the bearing at the running condition being checked.
- 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 1500 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The Sommerfeld number rises in proportion to speed; friction power rises with its square.
What this means: Oil viscosity at the film temperature
- What it is
- The dynamic viscosity of the oil at the temperature of the film in the bearing, from the oil maker’s viscosity–temperature data.
- Units and format
- Enter a number in mPa·s (cP): mPa·s (cP). The form accepts 0.000001 mPa·s (cP) to 2000 mPa·s (cP). Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mPa·s (cP) as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Friction loss and the Sommerfeld number rise in proportion to viscosity.
- Get it right
- Oil grades quote kinematic viscosity (mm²/s) at a reference temperature; dynamic viscosity in mPa·s is kinematic viscosity times density in g/cm³, at the film temperature.
What this means: Allowed oil temperature rise
- What it is
- How much hotter the oil may leave the bearing than it enters, outlet minus inlet temperature. It sets how much oil must flow to carry the friction heat away.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0.000001 K to 60 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The oil flow needed is inversely proportional to the allowed rise.
- Get it right
- This is a temperature rise, not the oil temperature itself.
What this means: Oil specific heat
- What it is
- The heat one kilogram of the oil absorbs per degree of temperature rise, from the oil data sheet.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.000001 kJ/kg·K to 5 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.9 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
- The oil flow needed is inversely proportional to the specific heat.
- Get it right
- kJ/kg·K, not J/kg·K; a value a thousand times too large hides the oil flow needed.
What this means: Oil density
- What it is
- The mass per unit volume of the oil at its working temperature, used to turn the heat balance into a volume flow.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 1500 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 870 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The oil flow needed is inversely proportional to density.
What this means: Largest unit load
- What it is
- The highest unit load (radial load ÷ projected area L × d) you accept for this bearing material and duty, from the bearing material supplier or your design standard.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 50 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Smallest L/D
- What it is
- The shortest bearing you accept, as bearing length divided by journal diameter. Short bearings leak more oil from the sides.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a plain ratio (0.5 means the length is half the diameter).
What this means: Largest L/D
- What it is
- The longest bearing you accept, as bearing length divided by journal diameter. Long bearings are sensitive to shaft deflection and misalignment.
- Units and format
- Enter a plain number with no unit. The form accepts 0.2 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be larger than the smallest L/D, or the tool stops.
What this means: Smallest Sommerfeld number
- What it is
- The lowest Sommerfeld number you accept. The Sommerfeld number groups viscosity, speed, load and clearance; low values mean a thin oil film.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It only sets the pass or fail of the film check; take it from your design charts or practice.
Method and formulas
- Unit load p = W ÷ (L d); surface speed V = π d n ÷ 60 000.
- Sommerfeld S = (r ÷ c)² μ N ÷ p, with N in rev/s.
- Petroff torque T = 4π² r³ L μ N ÷ c; f = 2π² (μ N ÷ p)(r ÷ c); power loss = 2π N T (as the Petroff tool).
- Oil flow = power loss ÷ (ρ c_p ΔT).
- Example: 5000 N on a 50 × 50 mm bearing gives 2 MPa, S = 0.12207, and 75.699 W of friction needing 0.27477 L/min of oil.
Limitations
- Petroff assumes a concentric, lightly loaded journal; at heavy load use the design charts for film thickness.
- Oil flow here carries heat only; the bearing’s own side leakage must also be supplied.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a plain bearing for a pump, fan or turbine shaft
- Estimate bearing heat and oil supply
- Compare clearances and oil grades
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Unit load, L/D and surface speed
- Sommerfeld number and Petroff friction
- Power loss and oil flow
Interpreting the result
- A low Sommerfeld number means a thin film: raise viscosity or speed, or cut the clearance or unit load.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2326–2345. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
The Sommerfeld number and film thickness
In Plain Bearings by the Numbers
What it covers: Combine a journal bearing's variables into the Sommerfeld number, then find its eccentricity, thinnest film, attitude angle and peak pressure with the short-bearing solution and the BIZOMAT tool.
BIZOMAT 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.
Open the Hydrodynamic Journal Bearing Design (Load, Friction, Heat and Oil) calculator