Extraction and use of frequency-domain relationships between time-varying gear meshing properties and diagnostic measurements

Abstract

In gears, the key diagnostic information is carried in the gearmesh stiffness and geometric profile errors. These two key gear meshing properties combine nonlinearly with rotations and displacements of the gear shafts to produce a time-varying gearmesh force. This in turn passes through the system dynamic response before finally resulting in actual diagnostic measurements (e.g., vibration or transmission error). The closed form analysis of such transfer paths is rendered impractical by the complexity of the time-varying gearmesh force, and has therefore so far mostly been studied through time-domain simulations. Inspired by a previous linearisation method, this paper develops a matrix-based procedure on a multiple-degree-of-freedom (MDOF) system to linearise the relationship between time-varying gear meshing properties (stiffness and geometric error) and measurements, thus producing frequency response functions (FRFs) between these key diagnostic inputs and the measurements. This FRFs are then used specifically to study the scarcely employed but highly promising diagnostic measurement of transmission error (TE), which is obtained by combining encoder measurements from the two gear shafts. The analysis of TE includes both an application of its experimental measurement for crack diagnostics under different operating conditions, and a discussion of the properties of the TE-FRF that make TE more robust to different operating conditions.