Bearing Characteristic Number And Summerfeld Number

Bearing characteristics number=ZN/P
where Z-absolute viscosity of lubricant(kg/m.s)
N-speed of the journal(rpm)
p-bearing pressure(N/mm^2)
It is a non dimensional number and is used in design of journal bearing.

Bearing characteristic number
Fig : 1. Coefficient of friction with ZN/p

Let , k = Bearing Modulus

μ = Coefficient of Friction 
μ = Φ[ ZN/P , d/c , l/d ]
where ,
              Φ = Functional relationship
              Z = Absolute viscosity of lubricants 
              N = Speed of journal 
              p = Bearing pressure 
             d  = Diameter of journal 
              l  = Length of bearing 
              c = Diametrical clearance

SpecimenUnstable Region Stable Region
LoadIncreases Increases
Power LossIncreases Increases
TemperatureIncreasesIncreases
Viscosity (Z)DecreasesDecreases
ZN/pDecreasesDecreases
Coefficient of FrictionIncreasesDecreases

ZN/p is termed as bearing characteristic number, the part of curve PQ represents the region of thick film lubrication between Q and R, viscosity (jet) or the speed are so low or the pressure “p” is so great. So the air combination will reduced the film thickness so that the partial metal to metal contact takes place.
In ‘RS’ region there are thin film, it is unstable region due to increase in load, temperature increases and overall value of ZN/p is decreases as a result increase in coefficient of friction.
In ‘PQ’ , It is stable region ,it has decrease in viscosity due to increase in load , overall value of ZN/p will reduced. Which result increase in coefficient of friction.
At the point ‘A’ minimum amount of friction occurs. At this point the value of ZN/p is known as bearing modulus.
The bearing should not operate at this value of ‘k’ because a slight increase in pressure will break the oil film and make journal to operate with metal to metal contact.This will results in high friction.

So, ‘k’ lies between 

              3k ≤ ZN/p ≤ 15k
Now ,
            μ = 33/10^8 ( ZN/p )( d/c ) + k
Where ,
                k = factor to correct end leakage 
                k = 0.002

 

Summerfeld Number :

Summerfeld number is a dimensionless parameter which is used extensively in design of journal bearing. It is denoted by “S’ .
                     
                                             S = ZN/p (d/c )²
    For the design purposes , it’s value is taken as 
                                           S = 14.3x 10^6

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