Study On The Defective Differential Bevel Gear Of An Electric Vehicle And Optimization Design Of Tooth Root

Due to the existence of brake energy recovery in electric vehicles compared to fuel vehicles,the working requirements of differential gears are higher.Therefore,this paper investigates the possible defects of the bevel gear in the differential gear of an electric vehicle.Based on this research,two methods are proposed to optimize the tooth root profile,which can reduce its maximum bending stress at the tooth root and thus improve the fatigue life of gears.Firstly,the geometric modeling of tooth surface pitting and tooth root cracking models of bevel gears was carried out by using UG to establish a three-dimensional model of the gear with defects.Then,the stresses of the two defects of tooth surface pitting and tooth root crack were analyzed by finite element analysis software in terms of size and location respectively,and the stress concentrations around the defects were found.Then the residual fatigue life of the bevel gear with defects was further obtained by the fatigue life analysis software on the basis of the stress analysis results,and it was found that the stress concentration of the root crack was more serious than that of the tooth surface pitting,and the residual fatigue of the gear with root crack was shorter.Secondly,this paper proposes a variable radius tooth root fillet design method for nonstandard planetary gears of differential gears.Based on the principle of spherical involute forming tooth surface,the geometric-mathematical model of the gear is established in the bevel tip coordinate system,and the general equation of the variable radius tooth root fillet is obtained.The root bending stress and fatigue life of variable radius root fillet bevel gears and fixed radius root fillet bevel gears are analyzed,and it is concluded that the variable radius root fillet can reduce the maximum root bending stress by 7.2% and the fatigue damage by 6.6%,thus extending the fatigue life of the differential gear.Finally,for standard spherical involute bevel gears,a tooth root transition surface design method composed of third-order Bessel curves is proposed.A mathematical model of gear geometry is established in the bevel top coordinate system,and the shape of the tooth root transition surface is controlled by four geometric parameters.Simulation of gear precision forging was carried out to verify the manufacturing feasibility of the proposed design method.Then,the response surface model between the four parameters and the maximum tooth root bending stress was established by the Box-Behnken test,and the mathematical relationship between them was obtained.Finally,the optimal combination of parameters was obtained by nonlinear programming,which resulted in a 23% reduction of the maximum tooth root bending stress.