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 meshing, using the modified Timoshenko beam equation for a stubby cantilever beam of varying cross-sectional area, is presented. The kinematics and kinetic relationships of a shaft-driven spur gear are used to determine the force on the involute surface of the gear tooth. A convenient set of equations, used to locate this force, is presented. The co-ordinates of this force are given with respect to a gear fixed coordinate system, located at the base of the gear tooth. The governing equations of motion were then numerically solved, and dynamic simulations of the gear tooth response at different gear speeds were performed. This model was then compared with the empirical data from research performed at the NASA Lewis Research Center