192.] 



FRICTION. 



191. Journal Friction. A journal, or trunnion, is the cylindrical end 

 of a horizontal shaft, by means of which the shaft is supported in its 

 bearing. The larger circle in Fig. 60 represents a cross-section of the 

 journal at right angles to the axis of the shaft. 



The shaft and journal may be regarded as rotating uniformly about 

 their common horizontal axis under the action of a driving force whose 

 moment with respect to a point O on the axis would have to be exactly 

 equal and opposite to that of the resistance, or load, if there were no 

 journal friction. For, in this case, the reaction of the bearing to the 

 weight WQ{ the shaft would act vertically 

 upwards through the axis of the shaft,- so 

 that its moment would be zero. 



The existence of friction at the place 

 of contact A between journal and bearing 

 requires an increase of the driving force, 

 which may be regarded as a small tan- 

 gential force P applied at any point B, 

 such that its moment P- OB equals the 

 moment about O of the frictional resist- 

 ance at A. 



192. Let C be the intersection of the 

 direction of this force /'with the vertical 



through O and A, which is the line of Pig 50. 



action of the weight W of the shaft. 



The resultant of P and W passes through C, and intersects the circum- 

 ference of the journal in a point D near A ; the total reaction of the 

 bearing is equal and opposite to this resultant. As the total reaction 

 must make an angle equal to the angle of friction < with the normal at 

 D which passes through the centre O, we have for the perpendicular 

 OE dropped from O on CD, 



OE = p = r sin <f>, 



where r is the radius of the journal. A circle described about O, with 

 p as radius, has the total reaction of the bearing as a tangent. This 

 circle is called the friction circle. As <J> is generally very small in the 

 case of journal friction, //, = tan< can be substituted for sin<, and we 

 have for the radius p of the friction circle 



As soon as any one point is known through which the total reaction 



