MATHEMATICAL-MODEL OF A TIME AND POSITION VARIANT EXTERNAL LOAD ON A GEAR TOOTH USING THE MODIFIED TIMOSHENKO BEAM EQUATION

A piece wise continuous closed-form dynamic model of spur gear teeth m eshing, using the modified Timoshenko beam equation for a stubby canti lever beam of varying cross-sectional area, is presented. The kinemati cs and kinetic relationships of a shaft-driven spur gear are used to d etermine the force on the involute surface of the gear tooth. A conven ient set of equations, used to locate this force, is presented. The co -ordinates of this force are given with respect to a gear fixed coordi nate system, located at the base of the gear tooth. The governing equa tions of motion were then numerically solved, and dynamic simulations of the gear tooth response at different gear speeds were performed. Th is model was then compared with the empirical data from research perfo rmed at the NASA Lewis Research Center.(1)