# Mechanical Engineering Design Notes

 Design Contents

 JOURNAL BEARING WITH HYDRODYNAMIC LUBRICATION - Effects of Variation of oil Viscosity with Temperature

1. Introduction
This page shows the results of running two Scilab programmes, one of which assumes the oil viscosity remains constant, results in column 2, and one which re-calculates the oil viscosity as the oil temperature rises, results in columns 3 to 6.
The computation assumes that the oil at the line of maximum oil film thickness is at the

A difficulty has been to develop an equation that is a reasonable fit to published data of how absolute viscosity varies with temperature - consequently the only data included in the first version of the program for viscosity as a function of temperature is for SAE grade 30 (engine) oil. The equation used is based on one published by A S Seireg and S Dandage (1):

Viscosity = Viscosityo exp[b/(T + 95)], b is a constant with units of oF and T is the temperature in oF. The viscosityo was in reyn. The programme uses SI units so the constants in the original data have been converted, however accuracy is probably little better than 8%.

I plan on providing more data for other grades soon.

Column 2 calculation results are for constant viscosity.
Where 2 entries are shown in the Inputs of a single column (e.g: viscosity, number of iterations), there will be 2 entries in all the Result cells affected.
The 'Average projected pressure' is based on the design specification load, above.
Columns 3 - 4 are from the programme which adjusts the viscosity according to the temperature as part of the iterative solution.
In Column 4, the eccentricity ratio has been increased from 0.59 (col. 3) to 0.62 which increases the resolved load carrying to that of the value shown for the constant viscosity programme (r.h. entry in col. 1).

 Inputs 2. Const. Viscosity 3. Var. Visc. 4. Journal dia, mm 40 Journal legth, mm 40 Radial clearance, mm 0.04 Load, N 2500 Shaft RPM 1800 Oil viscosity initially, Pa.s 0.0256 No. circumferential intervals 180 No. longitudinal intervals 16 SoR factor 0.9 Number of iterations to be used 2000, 5000 5000 5000 Initial oil temp. oC 60 Eccentricity ratio 0.59 0.59 0.62 Oil density, kg/m3 850 Specific heat of oil, J/kg.oC 1800 Oil supply pressure, Pa 100000 Oil supply hole dia. mm 4 Calculated results Sommerfeld no. 0.1229 0.1229 0.1229 Av. Proj. Pressure, MPa 1.56 1.56 1.56 Friction force, N 15.02 15.02 15.457 Friction power, w 56.6 56.6 58.27 Oil flow, l/s 0.003578 0.003578 0.00376 Oil temp. rise, oC 10.34 10.34 10.129 Load parallel to min oil film, N 1467, 1484 1322 1551 Load perpendicular to min. oil film, N 1870, 1903 1759 1930 Resolved load, N 2377.2, 2413.959 2201.1 2476.37 Angle of attitude, o 51.9, 52 53 51.2 Maximum pressure, MPa 3.581, 3.6287 3.253 3.76 Angle of max. pressure past downward vertical, o 19.9, 20.06 19.1 19.2

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

Listing of Scilab journal bearing programme - constant viscosity.

Listing of Scilab journal bearing programme - with viscosity varying as a function of temperature.

Comparison of Raimondi and Boyd chart result with Java applet (above) click here

I plan on updating the notes to give information about how the increase in temperature in reducing the oil viscosity effects the load carrying capability and the minimum oil film thickness.

Reference:
'Empirical Design Procedure for the Thermodynamic Behaviour of Journal Bearings', Lubrication Technology, vol. 104, April 1982, pp. 135-148.

David J Grieve, Revised: 9th February 2015