Based on the mathematical model of involute gear at any rotary angle

the calculation mathematical model of any point on the root is put forward by fold section analytics

and the calculating formula’s accuracy of curvature radius in this mathematical model is validated. By this mathematical model

it is realized the numerical analysis of maximum stress and stress distribution on the root with different parameter of tool profile and different teeth number. The result will offer reference data for design of involute gear and optimization of parameter choice

and offer new mathematical model for numerical analysis of root stress.