THE EFFICIENCY OF GEARING UNDER FRICTION. 



Calvin M. Woodward. 



1. The energy lost through the friction of gears, is often 

 ignored, and none of the treatises on Applied Mathematics 

 give a satisfactory treatment of the subject. Moseley's ele- 

 gant discussion is a little involved; he deals too much with 

 conditions " behind the line of centers;" he fails to give exact 

 results in a finite form ; he furnishes no convenient formulae 

 for showing; at a glance the effect of the size of the rolling 

 circle in the case of epicycloidal teeth; and he gives no con- 

 venient material for comparing the efficiency of epicycloidal 

 teeth with the efficiency of involute teeth. 



The following discussion was in substance given to my class 

 nearly two years ago ; I have however recently reduced my 

 equations to such form that the efficiencies of the two kinds 

 of teeth can readily be compared without the trouble of 

 numerical examples. 



/ 



/ n, 

 \ / 



Figure 1, Showing two teeth in action during the "Approach." 



2. General Formulae for all Teeth. Let Fig. 1 represent 

 the geometrical conditions in a plane perpendicular to a pair 

 of parallel axes. C 1 and C 2 are the centers of two wheels, /, 

 their pitch point, i\ and r 2 their radii, and T the point of con- 

 tact of two teeth. JTis the common normal to the teeth in 



(95) 



