JUL A. 1898 



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- 

 crant 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. 



/a 



/ 



Figure 1, Sho-wing 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. Cj and C^^ are the centers of two wheels, /, 

 their pitch point, r^ and r^ their radii, and Tthe point of con- 

 tact of two teeth. T/is the common normal to the teeth in 



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