I have been working on fluid film lubrication and I am keen to learn the physical importance of Sommerfield Number used in fluid film lubrication/bearings. ( Since most of the cases the dynamic charecteristics of the bearings are compared w.r.t. Sommerfield Number)
First of all the Sommerfield Number is dimensionless, so it doesn't matter what units are used, provided they are consistent. If you solve Reynolds' equation for a lubricated contact, key variables are: fluid viscosity, load, speed, length, clearance etc. These can be combined into a dimensionless constant, which is used to calculate the ratio of the minimum oil film thickness to the clearance (another dimensionless constant). It is pretty obvious that if the load is high then the minimum oil film thickness will be low. This is also true if the speed is low. And if the viscosity is low. Therefore a dimensionless combination which has load on the numerator, and speed and viscosity on the denominator, with extra length/clearance terms being used to balance the dimensions, will give a good indication of the minimum oil film thickness in the contact. This is essentially the physical motivation behind the Sommerfeld number. Below is a link to a recent paper of mine on journal bearing lubrication. In the short bearing approximation (equation (1) in the paper) if you take all the variables over to the left hand side (just leaving a complicated function of eccentricity ratio on the right hand side), you effectively have eccentricity ratio as a function of Sommerfeld number.
Hope this helps
Ian Taylor
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