Generation of a comprehensive load distribution algorithm in a gear pair and its effect on dynamic response

Abstract

Graphical/Tabular A coupled lumped parameter model is studied for a pair of spur gears to demonstrate tooth load distribution continuity with system deformation components. Shaft bending, the torsional deformation of the gear body, and the profile gap between mating surfaces are investigated to specify effects on load distribution. A nonlinear time -variant dynamic model of a pair of spur gears is established using the Lagrange method to see contact loss effects on dynamic transmission error. The nonlinear model considering torsional deformation and gear profile gap with the complete analytical approach is proposed as considering parabolic load distribution in contact that differs from existing literature. The workflow for obtaining load distribution and DTE is given in Figure A. Purpose: Gear pair mesh stiffness is affected by loading conditions due to some portion of the tooth surface not mating with the counter surface. How the contact loading state of the gear tooth surface effects the vibration behavior of the gear system is shown in this study. Theory and Methods: Gear pair stiffness is modeled in the frame of Weber Banaschek's theory. The shaft is modeled using the Timoshenko beam theory. With the proposed load distribution algorithm, the load distribution on the tooth, depending on the stiffness of the gear pair is found by separating the tooth into slices. Results: The response of the system is adversely affected by the decreasing gear mesh stiffness with partial contact loss. Conclusion: The ratio of lateral distances from the gear center to each bearing ends as much as it increases, and the amount of shaft deformation tends to increase gradually. Partial contact loss causes to increase in torsional deformation of the gear body. The reason is that distributed force accumulates at the less deformed side of the gear, increasing torque at the gear blank. Crowning provides to distribute the load larger section of the tooth surface when the load is distributed non -uniformly. It contributes to improving contact status depending on the condition.