Spiral Bevel Gears Nonlinear Dynamics: Chaotic Response Existence in Multi Degree of Freedom Systems

This study investigates the dynamic behavior of the spiral bevel gears (SBGs) by developing two degrees of freedom dynamic model (2 DOF) to four degrees of freedom (4 DOF), which involves the rotational shaft stiffness. The governing equations of motion are derived based on a nonlinear time-varying model. The nonlinearity and time dependency emanate from the backlash and contact ratio of the pinion and the gear, respectively. Depending on the working conditions, the system could experience a backside contact, which is an undesirable phenomenon in gear systems. A comparison between two systems, i.e., 2 DOF and 4 DOF, is done to understand what kind of phenomena are neglected by decreasing the DOF. The root mean square (RMS) diagrams and bifurcation diagrams are employed to analyze the vibration response of the system. The interesting point is that the simplification of the dynamic model could lead to a different dynamic response with respect to reality.