A new analytical model for evaluating the time-varying mesh stiffness of helical gears in healthy and spalling cases

Accurately evaluating the time-varying mesh stiffness (TVMS) of a mating gear pair is one of the most important aspects in gear vibration dynamic simulation. Existing work on estimating TVMS of helical gears with tooth spalls generally assumes the defects are in flat bottom shape which deviates from the spalling features as observed in curved bottom shape in practice. The cliff like spalling feature results in inaccurate calculation of TVMS of helical gears with such spalls. This paper proposes an advanced method to evaluate the TVMS of helical gears with tooth spalls with curved-bottom features. In the proposed method, the gear tooth is sliced along the center line of tooth spall in order to easily evaluate the equivalent cross-section area and area moments of inertia of the gear tooth which enables the proposed method adapts to tooth spall(s) with curvedbottom features in arbitrary position, angle and size. The proposed method corrects the foundation stiffness errors of existing methods and takes the influence of axial mesh forces into consideration. Its effectiveness on modelling tooth spalls with curved-bottom features for helical gears is validated by FEM (finite element method).