Effect of sliding friction on spur and helical gear dynamics and vibro-acoustics.

摘要

This study examines the salient effects of sliding friction on spur and helical gear dynamics and associated vibro-acoustic sources. First, new dynamic formulations are developed for spur and helical gear pairs based on a periodic description of the contact point and realistic mesh stiffness. Difficulty encountered in the existing discontinuous models is overcome by characterizing a smoother transition during the contact. Frictional forces and moments now appear as either excitations or periodically-varying parameters, since the frictional force changes direction at the pitch point/line. These result in a class of periodic ordinary differential equations with multiple and interacting coefficients, which characterize the effect of sliding friction in spur or helical gear dynamics. Predictions (based on multi-degree-of-freedom analytical models) match well with a benchmark finite element/contact mechanics code and/or experimental results.; Second, new analytical solutions are constructed which provide an efficient evaluation of the frictional effect as well as a more plausible explanation of dynamic interactions in multiple directions. Both single- and multi-term harmonic balance methods are utilized to predict dynamic mesh loads, friction forces and pinion/gear displacements. Such semi-analytical solutions explain the presence of higher harmonics in gear noise and vibration due to exponential modulations of the periodic stiffness, dynamic transmission error and sliding friction. This knowledge also analytically reveals the effect of the tooth profile modification in spur gears on the dynamic transmission error, under the influence of sliding friction. Further, the Floquet theory is applied to obtain closed-form solutions of the dynamic response for a helical gear pair, where the effect of sliding friction is quantified by an effective piecewise stiffness function. Analytical predictions, under both homogeneous and forced conditions, are validated using numerical simulations. The matrix-based methodology is found to be computationally efficient while leading to a better assessment of the dynamic stability.; Third, an improved source-path-receiver vibro-acoustic model is developed to quantify the effect of sliding friction on structure-borne noise. Interfacial bearing forces are predicted for the spur gear source sub-system given two gear whine excitations (static transmission error and sliding friction). Next, a computational model of the gearbox, with embedded bearing stiffness matrices, is developed to characterize the motilities of structural paths. Radiated sound pressure is then estimated by using two numerical techniques (the Rayleigh integral method and a substitute source technique). Predicted pressures match well with measured noise data over a range of operating torques. In particular, the proposed vibro-acoustic model quantifies the contribution of sliding friction, which could be significant when the transmission error is minimized through tooth modifications.