Rotational Vibration of a Helical Gear Pair with Modified Tooth Surfaces : Rotational Motion of a Gear Pair and Its Dynamic Increment of Tooth Load

Abstract

The rotational motion of a gear pair with modified tooth surfaces under load is analyzed with their equivalent tooth profiles. The path of contact consists of two different curves connected discontinuously. On its continuous region, equations of motion are solved and the fluctuating tooth load is calculated. At the point where it is discontinuous, the impact load is calculated from the difference in angular momentum. The gear pair rotates steadily because the kinetic energy which is transferred from one member to the other in the mesh region is returned through the impact. The dynamic increment of tooth load during one period, i.e., the external force acting on the gear vibration system, is given by a periodical function composed of the fluctuating and the impact loads, which is expressed as a Fourier series. The newly developed method is applied to a gear pair with symmetrical convex tooth surfaces, by which most tooth surfaces modified for practical use can be approximated. An analytical equation for the amplitude of the dynamic increment of tooth load is derived and its characteristics are shown through a numerical example.