An investigation of the dynamic behavior of systems with noncircular gears

This study investigates the dynamic behavior of mechanical transmissions with noncircular gears. Three types of noncircular gears are studied, namely first-order and second-order elliptical gears as well as a noncircular gear that generates a saw-tooth-type velocity ratio. Their kinematic characteristics are first analyzed. The dynamic behavior of systems employing elliptical gears is investigated by considering the effect of the eccentricity ratio and the corresponding transmission function, the time-varying mesh stiffness, time-varying mesh inertia, mesh damping as well as the operating speed and external load. The influence of the system parameters on the different resonance and instability conditions is also investigated.; The simulation results of the noncircular gears are compared with those for the circular gears with the same center distance. The results show that the elliptical gears have better dynamic performance than the circular gears. Within the kinematic constraint for the angle of obliquity of the elliptical gears, it is shown that the larger the eccentricity is, the more advantage such gears can have. In addition, a study was conducted to investigate the dynamic behavior of noncircular gears with a saw-tooth-type velocity transmission ratio. Such noncircular gears can have better dynamic performance than the circular gears by reducing the magnitude of the tooth stiffness fluctuation.; It was found from the analysis of the dynamic magnification of tooth load that a zero magnification occurs for the circular gears when the percentage of input torque fluctuation equals the percentage fluctuation in mesh stiffness. A minimum magnification is also found for the three types of noncircular gears when the mesh stiffness fluctuation is tuned to the torque fluctuation.