Study Of Contact Mechanics And Dynamic Performance Of Hypoid Gears

Hypoid gears are widly used in automobiles,aerospace,and construction machineries etc.Since long design period and poor operational reliability of hypoid gears,the innovation of their design technique is urgently required.The main problem of improvement of hypoid gears is the improvement of their dynamic analysis methods.Since previous dynamic analysis methods of hypoid gears are based on theoretical tooth surfaces,effects caused by deviations and misalignments of tooth surfaces can be not reflected.While dynamic analysis methods of hypoid gears improve rapidly with the development of the CAD/CAE technique and dynamics,the evaluation method of contact performance and the analysis method of error sensitivity still cannot satisfy requirements of the practical application.Therefore,a new analysis method of contact and dynamic performance for hypoid gears is proposed based on a digital composite tooth surface model in this study.The digital composite tooth surface model considers deviations and misalignments of tooth surfaces.Based on the digital composite tooth surface model,a new composite tooth contact analysis(CTCA)method and a new loaded composite tooth contact analysis(LCTCA)method for hypoid gears are developed.Furthermore,an evaluation method of error sensitivity and a dynamic analysis method for hypoid gears are proposed.This study focus on optimizing dynamic performance of hypoid gears and developing a new dynamic analysis system for other kind of gears.Based on obtained results,some meaningful conclusions can be drawn as follows:1.A new digital composite tooth surface model is developed based on deviations and misalignments of tooth surfaces via measurement on a coordinate measuring machine(CMM).There are two submodels in the digital composite tooth surface model,which are a theoretical tooth surface model and a real tooth surface model.The theoretical tooth surface model is obtained by enveloping of a generating cutter based on the theory of gearing.The real tooth surface model is built by overlaping deviations of tooth surfaces on the theoretical tooth surface model.The composite tooth surface model is built by overlaping misalignment components on the real tooth surface model.Hence,the digital composite tooth surface model can describe micro-geometry features and misalignments of hypoid gears.2.A new non-geometric-feature segmentation(NGFS)algorithm for the construction of the digital composite tooth surface model is developed based on the triangular Bézier surface model.The NGFS algorithm segments 3D measurement data of tooth surfaces into the form of Delaunay triangular meshes.A region-growing method is proposed to identify micro-geometry features of 3D measurement data obtained by CMM.A revised local interpolation algorithm is proposed to improve the accuracy of the NGFS algorithm.3.Formulas of second-order and third-order contact characters is proposed based on the proposed digital composite tooth surface model.Second-order and third-order contact characters that describe contact performance are obtained.A new composite tooth contact analysis(CTCA)method is proposed for calculation of contact patterns with a light load.4.A new continuous load distribution model of hypoid gears is proposed based on the digital composite tooth surface model and the minimum elastic potential energy theory.The time-varying meshing stiffness of hypoid gears with deviations and misalignments can be calculated.Based on the matrix of time-varying meshing stiffness,a new loaded composite tooth contact analysis(LCTCA)method is proposed for calculation of contact patterns with a heavy load.5.An error sensitivity evaluation method that reflects position variation tendency of the contact point and second-order contact characters of the composite tooth surface due to misalignments is developed.It can improve contact performance and increase stability of hypoid gear pairs to some extent.There are two submodels in this error sensitivity evaluation method,which are error sensitivity models of contact point position and second-order contact characters,respectively.The error sensitivity model of contact point position can describe deviation of the contact point of the composite tooth surface model,which is the center of a contact pattern.The error sensitivity model of second-order contact characters can describe effects of the contact path,shape of the contact pattern,and acceleration of hypoid gears.6.In order to simulate the interaction between the small-displacement gear vibration and the large-angular-displacement driveline torsional dynamics,a coupled multi-body dynamic and vibration model is proposed primarily for hypoid gears.This modeling technique possesses the capability of obtaining more realistic response and simulating a wide variety of operating conditions.Steady-state responses of the coupled multi-body dynamic and vibration model are calculated by a modified incremental harmonic balance method,which is efficient and accurate to obtain a periodic response of a multi-degree-of-freedom system.