546 hersey: laws of lubrication 



Equations (11) and (14) correspond to equations (5) and (6) 



respectively, and contain the two laws of lubrication in their 



most general form. 



If two bearings are geometrically similar as regards their 



c I 

 essential parts, the values of j:, j:, and the additional ratios r 



needed for fixing the shape (including the roughness) are the 

 same for both: if the bearings are similarly loaded as regards 

 direction and point of application of the force, the remaining 

 ratios r of equation (11) are the same for both. If, finally, the 

 bearings have the same relative oil supply or are similarly lubri- 

 cated the value of S is the same for both. Under these con- 

 ditions equation (11) reduces to 



/ = *(^) (Ua) 



Hence equation (11) states that in geometrically similar bearings 

 which are similarly loaded and lubricated, the coefficient of friction 



depends only on the single variable — . Equation (14) states 



that the carrying power of any hearing is directly proportional 

 to the product of viscosity by revolutions per unit time: the constant 

 •of proportionality 



en = e 



(14a) 







being the same for all geometrically similar bearings which are 

 similarly loaded and lubricated and which are similarly safe, i.e. 



( 



— I = constant. 



6. Dynamically similar bearings. Any two geometrically sim- 

 lar bearings B and B' which are similarly loaded and lubricated 

 {S = S') and which are running at the "corresponding" speeds, 

 pressures and viscosities defined by the equation 



M^ = ^LZL' (15) 



P v' 



must, by equations (11) and (12), have the same coefficient of 

 friction and the same relative film thickness. Such bearings may 



