Modeling and Detection of Localized Tooth Defects in Geared Systems

The early detection of failures in geared systems is an important industrial problem which has still to be addressed from both an experimental and theoretical viewpoint. The proposed paper combines some extensive numerical simulations of a single stage geared unit with localized tooth faults and the use of several detection techniques whose performances are compared and critically assessed. A model aimed at simulating the contributions of local tooth defects such as spalling to the gear dynamic behavior is set up. The pinion and the gear of a pair are assimilated to two rigid cylinders with all six degrees of freedom connected by a series of springs which represent gear body and gear tooth compliances on the base plane. Classical shaft finite elements including torsional, flexural and axial displacements can be superimposed to the gear element together with some lumped stiffnesses, masses, inertias, … which account for the load machines, bearings and couplings. Tooth defects are modeled by a distribution of normal deviations over a zone which can be located anywhere on the active tooth flanks. Among the numerous available signal processing techniques used in vibration monitoring, cepstrum analysis is sensitive, reliable and it can be adapted to complex geared system with several meshes. From an analytical analysis of the equations of motion, two complementary detection techniques based upon acceleration power cepstrum are proposed. The equations of motion and the contact problem between mating flanks are simultaneously solved by coupling an implicit time-step integration scheme and a unilateral normal contact algorithm. The results of the numerical simulations are used as a data base for the proposed detection techniques. The combined influence of the defect location, depth and extent is analyzed for two examples of spur and helical gears with various profile modifications and the effectiveness of the two complementary detection methods is discussed before some conclusions are drawn.