Lubrication - Hydrodynamic Bearing Design |

Previous page: background theory

**1. Introduction**

A number of parameters may be under the control of the designer, but there are another group which are dependent on the first group and can be used to define operational limits for the bearing. Assumption 4, above, that the viscosity is constant throughout the film, is not very accurate as the oil temperature rises as it passes through the bearing and as the viscosity is strongly dependent upon the temperature, it means that bearing design normally involves some iteration, either using charts (those by A A Raimondi and J Boyd, 'A Solution for the Finite Journal Bearing and its Application to Analysis and Design: III', Trans. ASLE 1, 1958, 194-209, are widely used) or computer software.

Versions of the Raimondi and Boyd charts may be found here

Given or controlled by the designer:

- lubricant viscosity
- load per unit projected area
- speed, N
- dimensions: r, c, l and beta (the angle subtended by the load bearing portion of the bearing).

The following are dependent upon the first group:

- coefficient of friction
- temperature rise,
- oil flow rate, Q
- minimum film thickness, h
_{o}

Many charts use US units for viscosity, ie reyns (usually plotted as micro-reyns). To convert reyns to Pa.s, multiply by 6890.

In the absence of specific information, it may be assumed that mineral lubricating oil has a density of about 850 kg/m^{3} and a specific heat of about 1675 J/kg^{o}C.

For hydrodynamic bearings, a length / diameter ratio of about 1 (say 0.8 to 1.3) is believed to be a good compromise. l/d ratios of <1 may be used where a compact design is important, such as in a multicylinder automotive engine. Reducing the l/d ratio increases the flow out of the bearing ends, which aids cooling.

The minimum film thickness acceptable depends upon surface finish and should allow expected particles to pass through without causing damage. For some applications, eg in automotive engines, filtering is provided to remove particles whose size would be likely to exceed the minimum film thickness. The following h_{o} values have been suggested:

Maximum oil temperatures should not be allowed to be excessive as oxidation and degradation become rapid. For general purpose machinery, an oil operating temperature of 60^{o}C should give a good long life. Above 100^{o}C the rate of oxidation increases rapidly. Temperatures of 120^{o}C should be avoided in industrial equipment. In automotive engines lubricant temperatures can reach 180^{o}C, but automotive oils are specially formulated (and may even be fully 'synthetic') to withstand such conditions.

The list below gives typical values of bearing 'nominal' pressures (load/length x diameter).

Electric motors, steam turbines, gear reducers, centrifugal pumps about 1 MPa

Automotive engines - main bearings 4 - 5 MPa

Diesel engines - main bearing 6 - 12 MPa

**2. Design Procedure**

1 Select an l/d ratio, 1 is probably a good starting point.

2 Using the specified load and an appropriate 'nominal' pressure, select the bearing length and diameter.

3 Specify an appropriate radial clearance, c, probably based on either a close (H8/f7) or free (H9/d9) running fit.

4 Decide on an initial lubricant viscosity. Because viscosity varies considerably with temperature, it is normally necessary to carry out the calculations below at two values of viscosity, one slightly below and the other slightly above the anticipated final value.

5 Evaluate the 'bearing characteristic number' or Sommerfield number (S).

6 On a chart plotting the 'minimum film thickness variable' against the 'bearing characteristic number', read off the minimum film thickness number for the calculated bearing characteristic number and the selected l/d ratio.

7 The minimum film thickness can now be calculated - and checked to see if it is reasonable.

8 The eccentricity ratio can be calculated.

9 If required, the angular position of the minimum film thickness can be found from an appropriate chart.

10 On a chart plotting the 'coefficient of friction' variable against the 'bearing characteristic number', read off the coefficient of friction' variable for the calculated bearing characteristic number and the selected l/d ratio.

11 Calculate the coefficient of friction. Using this with the radius and load, calculate the torque needed to overcome the friction. Using the coefficient of friction and the shaft speed, calculate the power lost in friction.

12 On a chart plotting the 'flow variable' against the 'bearing characteistic number' read the flow variable for the calculated characteristic number and the selected l/d ratio. Calculate the total oil flow.

13 On a chart plotting the 'flow ratio' against the 'bearing characteristic number', read off the flow ratio for the calculated bearing characteristic number and the selected l/d ratio. Calculate the side leakage of lubricant.

14 Calculate the rise in temperature of the lubricant - it is common to assume all the heat is carried away by the flowing oil and the the temperature of the side leakage oil is the mean of the inlet and outlet temperatures.

15 On a viscosity - temperature chart, check the viscosity of the the oil after it's temperature has increased by the amount calculated above, and assuming an appropriate inlet temperature.

16 Repeat the above calculations as needed to check the results with a viscosity at the mean of the inlet and outlet lubricant temperatures.

**Notes about journal bearing computation ** is given here

**A worked example, using SI units** is given here.

**A Java Applet to assist with journal bearing design is given** here

David J Grieve, updated: 7th February 2015, 10th December 2009, 23rd June 2009, previously: 15th December 2005.