Approximate expression for the single tooth pair slice mesh stiffness

Abstract

In many gear mesh stiffness models, the single tooth pair mesh stiffness is commonly approximated as having a parabolic-like symmetric shape along the path of contact with a fixed or contact ratio dependent amplitude. Even though this is a valid approximation under certain conditions, there is an asymmetry being disregarded and an amplitude being roughly approximated. In this work, a new straightforward analytical expression for the single tooth pair slice mesh stiffness is defined resorting to a parabolic approximation of the tooth pair structural stiffness that requires the definition of the asymmetry, relative amplitude and maximum value as a function of the gear parameters. In order to validate the developed work in terms of applicability and accuracy, a random sample of gears have their tooth pair structural stiffness approximation tested. The established asymmetry, relative amplitude and maximum value allow, in a fast and simple fashion, to obtain an accurate approximation. Different formulations of the single tooth pair slice mesh stiffness are compared, highlighting the importance of including the asymmetry and showing the improvements due to the new parameters.