Gear-sets designed using standard tooth profiles are rarely optimum strength designs, where “optimum strength” is defined as the maximum tooth bending strength for minimum tooth numbers and tooth size. However, standard tooth profiles are widely used because of the difficulty of determining the amount of hob (or rack) “offset” necessary to cut optimum strength non-standard gears. Also, stresses are not easily calculated for non-standard tooth profiles since geometry factors (I and J) are not tabulated. This paper describes a computer-aided method for obtaining optimum strength designs of spur gears, through iterative strength calculations. Two common cases are considered in which a non-standard gear-set is to replace a standard gear-set with the same center distance. When the speed ratio must be rigidly maintained, the “long and short addendum method” can be used; when minor variations in speed ratio are permissible, the “non-standard center distance” method can be used and much larger increases in strength can be achieved. The methods are illustrated by a numerical example. Increases of strength in the range of 10 to 20 percent are typical when standard gears-sets are replaced by non-standard gears with the same center distance, assuming material properties remain constant. The procedure for estimating the hob offsets which yield optimum design is simple and novel, and has proved efficient in obtaining convergence in a few iterations of the optimization process.

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